MGMRES: A generalization of GMRES for solving large sparse nonsymmetric linear systems
Young, D.M.; Chen, Jen Yuan
1996-11-01
This paper is concerned with the solution of the linear system Au = b, where A is a real square nonsingular matrix which is large, sparse and nonsymmetric. We consider the use of Krylov subspace methods. We first choose an initial approximation u{sup (0)} to the solution {bar u} = A{sup -1}b. The GMRES (Generalized Minimum Residual Algorithm for Solving Non Symmetric Linear Systems) method was developed by Saad and Schultz (1986) and used extensively for many years, for sparse systems. This paper considers a generalization of GMRES; it is similar to GMRES except that we let Z = A{sup T}Y, where Y is a nonsingular matrix which is symmetric but not necessarily SPD.
A general parallel sparse-blocked matrix multiply for linear scaling SCF theory
NASA Astrophysics Data System (ADS)
Challacombe, Matt
2000-06-01
A general approach to the parallel sparse-blocked matrix-matrix multiply is developed in the context of linear scaling self-consistent-field (SCF) theory. The data-parallel message passing method uses non-blocking communication to overlap computation and communication. The space filling curve heuristic is used to achieve data locality for sparse matrix elements that decay with “separation”. Load balance is achieved by solving the bin packing problem for blocks with variable size.With this new method as the kernel, parallel performance of the simplified density matrix minimization (SDMM) for solution of the SCF equations is investigated for RHF/6-31G ∗∗ water clusters and RHF/3-21G estane globules. Sustained rates above 5.7 GFLOPS for the SDMM have been achieved for (H 2 O) 200 with 95 Origin 2000 processors. Scalability is found to be limited by load imbalance, which increases with decreasing granularity, due primarily to the inhomogeneous distribution of variable block sizes.
MGMRES: A generalization of GMRES for solving large sparse nonsymmetric linear systems
Young, D.M.; Chen, J.Y.
1994-12-31
The authors are concerned with the solution of the linear system (1): Au = b, where A is a real square nonsingular matrix which is large, sparse and non-symmetric. They consider the use of Krylov subspace methods. They first choose an initial approximation u{sup (0)} to the solution {bar u} = A{sup {minus}1}B of (1). They also choose an auxiliary matrix Z which is nonsingular. For n = 1,2,{hor_ellipsis} they determine u{sup (n)} such that u{sup (n)} {minus} u{sup (0)}{epsilon}K{sub n}(r{sup (0)},A) where K{sub n}(r{sup (0)},A) is the (Krylov) subspace spanned by the Krylov vectors r{sup (0)}, Ar{sup (0)}, {hor_ellipsis}, A{sup n{minus}1}r{sup 0} and where r{sup (0)} = b{minus}Au{sup (0)}. If ZA is SPD they also require that (u{sup (n)}{minus}{bar u}, ZA(u{sup (n)}{minus}{bar u})) be minimized. If, on the other hand, ZA is not SPD, then they require that the Galerkin condition, (Zr{sup n}, v) = 0, be satisfied for all v{epsilon}K{sub n}(r{sup (0)}, A) where r{sup n} = b{minus}Au{sup (n)}. In this paper the authors consider a generalization of GMRES. This generalized method, which they refer to as `MGMRES`, is very similar to GMRES except that they let Z = A{sup T}Y where Y is a nonsingular matrix which is symmetric by not necessarily SPD.
General polynomial factorization-based design of sparse periodic linear arrays.
Mitra, Sanjit K; Mondal, Kalyan; Tchobanou, Mikhail K; Dolecek, Gordana Jovanovic
2010-09-01
We have developed several methods of designing sparse periodic arrays based upon the polynomial factorization method. In these methods, transmit and receive aperture polynomials are selected such that their product results in a polynomial representing the desired combined transmit/receive (T/R) effective aperture function. A desired combined T/R effective aperture is simply an aperture with an appropriate width exhibiting a spectrum that corresponds to the desired two-way radiation pattern. At least one of the two aperture functions that constitute the combined T/R effective aperture function will be a sparse polynomial. A measure of sparsity of the designed array is defined in terms of the element reduction factor. We show that elements of a linear array can be reduced with varying degrees of beam mainlobe width to sidelobe reduction properties.
Iterative solution of general sparse linear systems on clusters of workstations
Lo, Gen-Ching; Saad, Y.
1996-12-31
Solving sparse irregularly structured linear systems on parallel platforms poses several challenges. First, sparsity makes it difficult to exploit data locality, whether in a distributed or shared memory environment. A second, perhaps more serious challenge, is to find efficient ways to precondition the system. Preconditioning techniques which have a large degree of parallelism, such as multicolor SSOR, often have a slower rate of convergence than their sequential counterparts. Finally, a number of other computational kernels such as inner products could ruin any gains gained from parallel speed-ups, and this is especially true on workstation clusters where start-up times may be high. In this paper we discuss these issues and report on our experience with PSPARSLIB, an on-going project for building a library of parallel iterative sparse matrix solvers.
Sparse linear programming subprogram
Hanson, R.J.; Hiebert, K.L.
1981-12-01
This report describes a subprogram, SPLP(), for solving linear programming problems. The package of subprogram units comprising SPLP() is written in Fortran 77. The subprogram SPLP() is intended for problems involving at most a few thousand constraints and variables. The subprograms are written to take advantage of sparsity in the constraint matrix. A very general problem statement is accepted by SPLP(). It allows upper, lower, or no bounds on the variables. Both the primal and dual solutions are returned as output parameters. The package has many optional features. Among them is the ability to save partial results and then use them to continue the computation at a later time.
Approximate inverse preconditioners for general sparse matrices
Chow, E.; Saad, Y.
1994-12-31
Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection.
Inpainting with sparse linear combinations of exemplars
Wohlberg, Brendt
2008-01-01
We introduce a new exemplar-based inpainting algorithm based on representing the region to be inpainted as a sparse linear combination of blocks extracted from similar parts of the image being inpainted. This method is conceptually simple, being computed by functional minimization, and avoids the complexity of correctly ordering the filling in of missing regions of other exemplar-based methods. Initial performance comparisons on small inpainting regions indicate that this method provides similar or better performance than other recent methods.
Sparse brain network using penalized linear regression
NASA Astrophysics Data System (ADS)
Lee, Hyekyoung; Lee, Dong Soo; Kang, Hyejin; Kim, Boong-Nyun; Chung, Moo K.
2011-03-01
Sparse partial correlation is a useful connectivity measure for brain networks when it is difficult to compute the exact partial correlation in the small-n large-p setting. In this paper, we formulate the problem of estimating partial correlation as a sparse linear regression with a l1-norm penalty. The method is applied to brain network consisting of parcellated regions of interest (ROIs), which are obtained from FDG-PET images of the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. To validate the results, we check their reproducibilities of the obtained brain networks by the leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.
Parallel iterative methods for sparse linear and nonlinear equations
NASA Technical Reports Server (NTRS)
Saad, Youcef
1989-01-01
As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.
Out-of-Core Solutions of Complex Sparse Linear Equations
NASA Technical Reports Server (NTRS)
Yip, E. L.
1982-01-01
ETCLIB is library of subroutines for obtaining out-of-core solutions of complex sparse linear equations. Routines apply to dense and sparse matrices too large to be stored in core. Useful for solving any set of linear equations, but particularly useful in cases where coefficient matrix has no special properties that guarantee convergence with any of interative processes. The only assumption made is that coefficient matrix is not singular.
Reconstruction Techniques for Sparse Multistatic Linear Array Microwave Imaging
Sheen, David M.; Hall, Thomas E.
2014-06-09
Sequentially-switched linear arrays are an enabling technology for a number of near-field microwave imaging applications. Electronically sequencing along the array axis followed by mechanical scanning along an orthogonal axis allows dense sampling of a two-dimensional aperture in near real-time. In this paper, a sparse multi-static array technique will be described along with associated Fourier-Transform-based and back-projection-based image reconstruction algorithms. Simulated and measured imaging results are presented that show the effectiveness of the sparse array technique along with the merits and weaknesses of each image reconstruction approach.
NASA Astrophysics Data System (ADS)
Pilipchuk, L. A.; Pilipchuk, A. S.
2015-11-01
In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure.
Pilipchuk, L. A.; Pilipchuk, A. S.
2015-11-30
In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure.
Accelerating sparse linear algebra using graphics processing units
NASA Astrophysics Data System (ADS)
Spagnoli, Kyle E.; Humphrey, John R.; Price, Daniel K.; Kelmelis, Eric J.
2011-06-01
The modern graphics processing unit (GPU) found in many standard personal computers is a highly parallel math processor capable of over 1 TFLOPS of peak computational throughput at a cost similar to a high-end CPU with excellent FLOPS-to-watt ratio. High-level sparse linear algebra operations are computationally intense, often requiring large amounts of parallel operations and would seem a natural fit for the processing power of the GPU. Our work is on a GPU accelerated implementation of sparse linear algebra routines. We present results from both direct and iterative sparse system solvers. The GPU execution model featured by NVIDIA GPUs based on CUDA demands very strong parallelism, requiring between hundreds and thousands of simultaneous operations to achieve high performance. Some constructs from linear algebra map extremely well to the GPU and others map poorly. CPUs, on the other hand, do well at smaller order parallelism and perform acceptably during low-parallelism code segments. Our work addresses this via hybrid a processing model, in which the CPU and GPU work simultaneously to produce results. In many cases, this is accomplished by allowing each platform to do the work it performs most naturally. For example, the CPU is responsible for graph theory portion of the direct solvers while the GPU simultaneously performs the low level linear algebra routines.
Scalable Library for the Parallel Solution of Sparse Linear Systems
1993-07-14
BlockSolve is a scalable parallel software library for the solution of large sparse, symmetric systems of linear equations. It runs on a variety of parallel architectures and can easily be ported to others. BlockSovle is primarily intended for the solution of sparse linear systems that arise from physical problems having multiple degrees of freedom at each node point. For example, when the finite element method is used to solve practical problems in structural engineering, eachmore » node will typically have anywhere from 3-6 degrees of freedom associated with it. BlockSolve is written to take advantage of problems of this nature; however, it is still reasonably efficient for problems that have only one degree of freedom associated with each node, such as the three-dimensional Poisson problem. It does not require that the matrices have any particular structure other than being sparse and symmetric. BlockSolve is intended to be used within real application codes. It is designed to work best in the context of our experience which indicated that most application codes solve the same linear systems with several different right-hand sides and/or linear systems with the same structure, but different matrix values multiple times.« less
A multi-level method for sparse linear systems
Shapira, Y.
1997-09-01
A multi-level method for the solution of sparse linear systems is introduced. The definition of the method is based on data from the coefficient matrix alone. An upper bound for the condition number is available for certain symmetric positive definite (SPD) problems. Numerical experiments confirm the analysis and illustrate the efficiency of the method for diffusion problems with discontinuous coefficients with discontinuities which are not aligned with the coarse meshes.
Reconstruction techniques for sparse multistatic linear array microwave imaging
NASA Astrophysics Data System (ADS)
Sheen, David M.; Hall, Thomas E.
2014-06-01
Sequentially-switched linear arrays are an enabling technology for a number of near-field microwave imaging applications. Electronically sequencing along the array axis followed by mechanical scanning along an orthogonal axis allows dense sampling of a two-dimensional aperture in near real-time. The Pacific Northwest National Laboratory (PNNL) has developed this technology for several applications including concealed weapon detection, groundpenetrating radar, and non-destructive inspection and evaluation. These techniques form three-dimensional images by scanning a diverging beam swept frequency transceiver over a two-dimensional aperture and mathematically focusing or reconstructing the data into three-dimensional images. Recently, a sparse multi-static array technology has been developed that reduces the number of antennas required to densely sample the linear array axis of the spatial aperture. This allows a significant reduction in cost and complexity of the linear-array-based imaging system. The sparse array has been specifically designed to be compatible with Fourier-Transform-based image reconstruction techniques; however, there are limitations to the use of these techniques, especially for extreme near-field operation. In the extreme near-field of the array, back-projection techniques have been developed that account for the exact location of each transmitter and receiver in the linear array and the 3-D image location. In this paper, the sparse array technique will be described along with associated Fourier-Transform-based and back-projection-based image reconstruction algorithms. Simulated imaging results are presented that show the effectiveness of the sparse array technique along with the merits and weaknesses of each image reconstruction approach.
Polygenic Modeling with Bayesian Sparse Linear Mixed Models
Zhou, Xiang; Carbonetto, Peter; Stephens, Matthew
2013-01-01
Both linear mixed models (LMMs) and sparse regression models are widely used in genetics applications, including, recently, polygenic modeling in genome-wide association studies. These two approaches make very different assumptions, so are expected to perform well in different situations. However, in practice, for a given dataset one typically does not know which assumptions will be more accurate. Motivated by this, we consider a hybrid of the two, which we refer to as a “Bayesian sparse linear mixed model” (BSLMM) that includes both these models as special cases. We address several key computational and statistical issues that arise when applying BSLMM, including appropriate prior specification for the hyper-parameters and a novel Markov chain Monte Carlo algorithm for posterior inference. We apply BSLMM and compare it with other methods for two polygenic modeling applications: estimating the proportion of variance in phenotypes explained (PVE) by available genotypes, and phenotype (or breeding value) prediction. For PVE estimation, we demonstrate that BSLMM combines the advantages of both standard LMMs and sparse regression modeling. For phenotype prediction it considerably outperforms either of the other two methods, as well as several other large-scale regression methods previously suggested for this problem. Software implementing our method is freely available from http://stephenslab.uchicago.edu/software.html. PMID:23408905
Learning a Nonnegative Sparse Graph for Linear Regression.
Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung
2015-09-01
Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.
General linear chirplet transform
NASA Astrophysics Data System (ADS)
Yu, Gang; Zhou, Yiqi
2016-03-01
Time-frequency (TF) analysis (TFA) method is an effective tool to characterize the time-varying feature of a signal, which has drawn many attentions in a fairly long period. With the development of TFA, many advanced methods are proposed, which can provide more precise TF results. However, some restrictions are introduced inevitably. In this paper, we introduce a novel TFA method, termed as general linear chirplet transform (GLCT), which can overcome some limitations existed in current TFA methods. In numerical and experimental validations, by comparing with current TFA methods, some advantages of GLCT are demonstrated, which consist of well-characterizing the signal of multi-component with distinct non-linear features, being independent to the mathematical model and initial TFA method, allowing for the reconstruction of the interested component, and being non-sensitivity to noise.
Solving sparse triangular linear systems on parallel computers
NASA Technical Reports Server (NTRS)
Anderson, Edward; Saad, Youcef
1989-01-01
This paper describes and compares three parallel algorithms for solving sparse triangular systems of equations. These methods involve some preprocessing overhead and are primarily of interest in solving many systems with the same coefficient matrix. The first approach is to use a fixed blocksize and form the inverse of the diagonal blocks. The second approach is to use a variable blocksize and reorder the unknowns so that the diagonal blocks are diagonal matrices. The latter technique is called level scheduling because of how it is represented in the adjacency graph, and both row-wise and jagged diagonal storage for the off-diagonal blocks are considered. These techniques are analyzed for general parallel computers and experiments are presented for the eight-processor Alliant FX/8.
Generalized Linear Covariance Analysis
NASA Astrophysics Data System (ADS)
Markley, F. Landis; Carpenter, J. Russell
2009-01-01
This paper presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into "solve-for" and "consider" parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and a priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and a priori solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the "variance sandpile" and the "sensitivity mosaic," and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.
Generalized Linear Covariance Analysis
NASA Technical Reports Server (NTRS)
Carpenter, James R.; Markley, F. Landis
2014-01-01
This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.
Generalized Linear Covariance Analysis
NASA Technical Reports Server (NTRS)
Carpenter, J. Russell; Markley, F. Landis
2008-01-01
We review and extend in two directions the results of prior work on generalized covariance analysis methods. This prior work allowed for partitioning of the state space into "solve-for" and "consider" parameters, allowed for differences between the formal values and the true values of the measurement noise, process noise, and a priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and a priori solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator s anchor time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the "variance sandpile" and the "sensitivity mosaic," and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.
A linear geospatial streamflow modeling system for data sparse environments
Asante, Kwabena O.; Arlan, Guleid A.; Pervez, Md Shahriar; Rowland, James
2008-01-01
In many river basins around the world, inaccessibility of flow data is a major obstacle to water resource studies and operational monitoring. This paper describes a geospatial streamflow modeling system which is parameterized with global terrain, soils and land cover data and run operationally with satellite‐derived precipitation and evapotranspiration datasets. Simple linear methods transfer water through the subsurface, overland and river flow phases, and the resulting flows are expressed in terms of standard deviations from mean annual flow. In sample applications, the modeling system was used to simulate flow variations in the Congo, Niger, Nile, Zambezi, Orange and Lake Chad basins between 1998 and 2005, and the resulting flows were compared with mean monthly values from the open‐access Global River Discharge Database. While the uncalibrated model cannot predict the absolute magnitude of flow, it can quantify flow anomalies in terms of relative departures from mean flow. Most of the severe flood events identified in the flow anomalies were independently verified by the Dartmouth Flood Observatory (DFO) and the Emergency Disaster Database (EM‐DAT). Despite its limitations, the modeling system is valuable for rapid characterization of the relative magnitude of flood hazards and seasonal flow changes in data sparse settings.
Quantization of general linear electrodynamics
Rivera, Sergio; Schuller, Frederic P.
2011-03-15
General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength 2-form and induction 2-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory predictive and physically interpretable. Taking into account the higher-order polynomial dispersion relation and associated causal structure of general linear electrodynamics, we carefully develop its Hamiltonian formulation from first principles. Canonical quantization of the resulting constrained system then results in a quantum vacuum which is sensitive to the constitutive tensor of the classical theory. As an application we calculate the Casimir effect in a birefringent linear optical medium.
Mahrous, Hesham; Ward, Rabab
2016-01-01
This paper proposes a compressive sensing (CS) method for multi-channel electroencephalogram (EEG) signals in Wireless Body Area Network (WBAN) applications, where the battery life of sensors is limited. For the single EEG channel case, known as the single measurement vector (SMV) problem, the Block Sparse Bayesian Learning-BO (BSBL-BO) method has been shown to yield good results. This method exploits the block sparsity and the intra-correlation (i.e., the linear dependency) within the measurement vector of a single channel. For the multichannel case, known as the multi-measurement vector (MMV) problem, the Spatio-Temporal Sparse Bayesian Learning (STSBL-EM) method has been proposed. This method learns the joint correlation structure in the multichannel signals by whitening the model in the temporal and the spatial domains. Our proposed method represents the multi-channels signal data as a vector that is constructed in a specific way, so that it has a better block sparsity structure than the conventional representation obtained by stacking the measurement vectors of the different channels. To reconstruct the multichannel EEG signals, we modify the parameters of the BSBL-BO algorithm, so that it can exploit not only the linear but also the non-linear dependency structures in a vector. The modified BSBL-BO is then applied on the vector with the better sparsity structure. The proposed method is shown to significantly outperform existing SMV and also MMV methods. It also shows significant lower compression errors even at high compression ratios such as 10:1 on three different datasets. PMID:26861335
Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems
Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; Thornquist, Heidi
2012-01-01
Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less
Iterative solutions of sparse linear systems on systolic arrays. Technical report
Melhem, R.
1987-03-01
The idea of grouping the non-zero elements of a sparse matrix into few strips that are almost parallel is applied to the design of a systolic accelerator for sparse matrix operations. This accelerator is, then, integrated into a complete systolic system for the solution of large sparse linear systems of equations. The design demonstrates that the application of systolic arrays is not limited to regular computations, and that computationally irregular problems may be solved on systolic networks if local storage is provided in each systolic cell for buffering the irregularity in the data movement and for absorbing the irregularity in the computation.
Gene Golub; Kwok Ko
2009-03-30
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.
NASA Technical Reports Server (NTRS)
Reed, D. A.; Patrick, M. L.
1985-01-01
The applicability of static data flow architectures to the iterative solution of sparse linear systems of equations is investigated. An analytic performance model of a static data flow computation is developed. This model includes both spatial parallelism, concurrent execution in multiple PE's, and pipelining, the streaming of data from array memories through the PE's. The performance model is used to analyze a row partitioned iterative algorithm for solving sparse linear systems of algebraic equations. Based on this analysis, design parameters for the static data flow architecture as a function of matrix sparsity and dimension are proposed.
Leng, Chengcai; Yu, Dongdong; Zhang, Shuang; An, Yu; Hu, Yifang
2015-01-01
Optical molecular imaging is a promising technique and has been widely used in physiology, and pathology at cellular and molecular levels, which includes different modalities such as bioluminescence tomography, fluorescence molecular tomography and Cerenkov luminescence tomography. The inverse problem is ill-posed for the above modalities, which cause a nonunique solution. In this paper, we propose an effective reconstruction method based on the linearized Bregman iterative algorithm with sparse regularization (LBSR) for reconstruction. Considering the sparsity characteristics of the reconstructed sources, the sparsity can be regarded as a kind of a priori information and sparse regularization is incorporated, which can accurately locate the position of the source. The linearized Bregman iteration method is exploited to minimize the sparse regularization problem so as to further achieve fast and accurate reconstruction results. Experimental results in a numerical simulation and in vivo mouse demonstrate the effectiveness and potential of the proposed method. PMID:26421055
SuperLU{_}DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
Li, Xiaoye S.; Demmel, James W.
2002-03-27
In this paper, we present the main algorithmic features in the software package SuperLU{_}DIST, a distributed-memory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with focus on scalability issues, and demonstrate the parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication pattern for sparse Gaussian elimination, which makes it more scalable on distributed memory machines. Based on this a priori knowledge, we designed highly parallel and scalable algorithms for both LU decomposition and triangular solve and we show that they are suitable for large-scale distributed memory machines.
The impact of improved sparse linear solvers on industrial engineering applications
Heroux, M.; Baddourah, M.; Poole, E.L.; Yang, Chao Wu
1996-12-31
There are usually many factors that ultimately determine the quality of computer simulation for engineering applications. Some of the most important are the quality of the analytical model and approximation scheme, the accuracy of the input data and the capability of the computing resources. However, in many engineering applications the characteristics of the sparse linear solver are the key factors in determining how complex a problem a given application code can solve. Therefore, the advent of a dramatically improved solver often brings with it dramatic improvements in our ability to do accurate and cost effective computer simulations. In this presentation we discuss the current status of sparse iterative and direct solvers in several key industrial CFD and structures codes, and show the impact that recent advances in linear solvers have made on both our ability to perform challenging simulations and the cost of those simulations. We also present some of the current challenges we have and the constraints we face in trying to improve these solvers. Finally, we discuss future requirements for sparse linear solvers on high performance architectures and try to indicate the opportunities that exist if we can develop even more improvements in linear solver capabilities.
BIRD: A general interface for sparse distributed memory simulators
NASA Technical Reports Server (NTRS)
Rogers, David
1990-01-01
Kanerva's sparse distributed memory (SDM) has now been implemented for at least six different computers, including SUN3 workstations, the Apple Macintosh, and the Connection Machine. A common interface for input of commands would both aid testing of programs on a broad range of computer architectures and assist users in transferring results from research environments to applications. A common interface also allows secondary programs to generate command sequences for a sparse distributed memory, which may then be executed on the appropriate hardware. The BIRD program is an attempt to create such an interface. Simplifying access to different simulators should assist developers in finding appropriate uses for SDM.
Improving the energy efficiency of sparse linear system solvers on multicore and manycore systems.
Anzt, H; Quintana-Ortí, E S
2014-06-28
While most recent breakthroughs in scientific research rely on complex simulations carried out in large-scale supercomputers, the power draft and energy spent for this purpose is increasingly becoming a limiting factor to this trend. In this paper, we provide an overview of the current status in energy-efficient scientific computing by reviewing different technologies used to monitor power draft as well as power- and energy-saving mechanisms available in commodity hardware. For the particular domain of sparse linear algebra, we analyse the energy efficiency of a broad collection of hardware architectures and investigate how algorithmic and implementation modifications can improve the energy performance of sparse linear system solvers, without negatively impacting their performance. PMID:24842036
Sparse linear regression with elastic net regularization for brain-computer interfaces.
Kelly, John W; Degenhart, Alan D; Siewiorek, Daniel P; Smailagic, Asim; Wang, Wei
2012-01-01
This paper demonstrates the feasibility of decoding neuronal population signals using a sparse linear regression model with an elastic net penalty. In offline analysis of real electrocorticographic (ECoG) neural data the elastic net achieved a timepoint decoding accuracy of 95% for classifying hand grasps vs. rest, and 82% for moving a cursor in 1-D space towards a target. These results were superior to those obtained using ℓ(2)-penalized and unpenalized linear regression, and marginally better than ℓ(1)-penalized regression. Elastic net and the ℓ(1)-penalty also produced sparse feature sets, but the elastic net did not eliminate correlated features, which could result in a more stable decoder for brain-computer interfaces.
Improving the energy efficiency of sparse linear system solvers on multicore and manycore systems.
Anzt, H; Quintana-Ortí, E S
2014-06-28
While most recent breakthroughs in scientific research rely on complex simulations carried out in large-scale supercomputers, the power draft and energy spent for this purpose is increasingly becoming a limiting factor to this trend. In this paper, we provide an overview of the current status in energy-efficient scientific computing by reviewing different technologies used to monitor power draft as well as power- and energy-saving mechanisms available in commodity hardware. For the particular domain of sparse linear algebra, we analyse the energy efficiency of a broad collection of hardware architectures and investigate how algorithmic and implementation modifications can improve the energy performance of sparse linear system solvers, without negatively impacting their performance.
ZELINSKI, ADAM C.; GOYAL, VIVEK K.; ADALSTEINSSON, ELFAR
2010-01-01
A problem that arises in slice-selective magnetic resonance imaging (MRI) radio-frequency (RF) excitation pulse design is abstracted as a novel linear inverse problem with a simultaneous sparsity constraint. Multiple unknown signal vectors are to be determined, where each passes through a different system matrix and the results are added to yield a single observation vector. Given the matrices and lone observation, the objective is to find a simultaneously sparse set of unknown vectors that approximately solves the system. We refer to this as the multiple-system single-output (MSSO) simultaneous sparse approximation problem. This manuscript contrasts the MSSO problem with other simultaneous sparsity problems and conducts an initial exploration of algorithms with which to solve it. Greedy algorithms and techniques based on convex relaxation are derived and compared empirically. Experiments involve sparsity pattern recovery in noiseless and noisy settings and MRI RF pulse design. PMID:20445814
Algorithms for solving large sparse systems of simultaneous linear equations on vector processors
NASA Technical Reports Server (NTRS)
David, R. E.
1984-01-01
Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.
Linear program relaxation of sparse nonnegative recovery in compressive sensing microarrays.
Qin, Linxia; Xiu, Naihua; Kong, Lingchen; Li, Yu
2012-01-01
Compressive sensing microarrays (CSM) are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR) which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss the l₁ relaxation of the SNR. By defining nonnegative restricted isometry/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and the l₁ relaxation share the common unique solution. Besides, we show that any solution to the SNR must be one of the extreme points of the underlying feasible set. PMID:23251229
Linear equality constraints in the general linear mixed model.
Edwards, L J; Stewart, P W; Muller, K E; Helms, R W
2001-12-01
Scientists may wish to analyze correlated outcome data with constraints among the responses. For example, piecewise linear regression in a longitudinal data analysis can require use of a general linear mixed model combined with linear parameter constraints. Although well developed for standard univariate models, there are no general results that allow a data analyst to specify a mixed model equation in conjunction with a set of constraints on the parameters. We resolve the difficulty by precisely describing conditions that allow specifying linear parameter constraints that insure the validity of estimates and tests in a general linear mixed model. The recommended approach requires only straightforward and noniterative calculations to implement. We illustrate the convenience and advantages of the methods with a comparison of cognitive developmental patterns in a study of individuals from infancy to early adulthood for children from low-income families.
NASA Astrophysics Data System (ADS)
Deglint, Jason; Kazemzadeh, Farnoud; Wong, Alexander; Clausi, David A.
2015-09-01
One method to acquire multispectral images is to sequentially capture a series of images where each image contains information from a different bandwidth of light. Another method is to use a series of beamsplitters and dichroic filters to guide different bandwidths of light onto different cameras. However, these methods are very time consuming and expensive and perform poorly in dynamic scenes or when observing transient phenomena. An alternative strategy to capturing multispectral data is to infer this data using sparse spectral reflectance measurements captured using an imaging device with overlapping bandpass filters, such as a consumer digital camera using a Bayer filter pattern. Currently the only method of inferring dense reflectance spectra is the Wiener adaptive filter, which makes Gaussian assumptions about the data. However, these assumptions may not always hold true for all data. We propose a new technique to infer dense reflectance spectra from sparse spectral measurements through the use of a non-linear regression model. The non-linear regression model used in this technique is the random forest model, which is an ensemble of decision trees and trained via the spectral characterization of the optical imaging system and spectral data pair generation. This model is then evaluated by spectrally characterizing different patches on the Macbeth color chart, as well as by reconstructing inferred multispectral images. Results show that the proposed technique can produce inferred dense reflectance spectra that correlate well with the true dense reflectance spectra, which illustrates the merits of the technique.
Many-core graph analytics using accelerated sparse linear algebra routines
NASA Astrophysics Data System (ADS)
Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric
2016-05-01
Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.
LANZ: Software solving the large sparse symmetric generalized eigenproblem
NASA Technical Reports Server (NTRS)
Jones, Mark T.; Patrick, Merrell L.
1990-01-01
A package, LANZ, for solving the large symmetric generalized eigenproblem is described. The package was tested on four different architectures: Convex 200, CRAY Y-MP, Sun-3, and Sun-4. The package uses a Lanczos' method and is based on recent research into solving the generalized eigenproblem.
Statistical method for sparse coding of speech including a linear predictive model
NASA Astrophysics Data System (ADS)
Rufiner, Hugo L.; Goddard, John; Rocha, Luis F.; Torres, María E.
2006-07-01
Recently, different methods for obtaining sparse representations of a signal using dictionaries of waveforms have been studied. They are often motivated by the way the brain seems to process certain sensory signals. Algorithms have been developed using a specific criterion to choose the waveforms occurring in the representation. The waveforms are choosen from a fixed dictionary and some algorithms also construct them as a part of the method. In the case of speech signals, most approaches do not take into consideration the important temporal correlations that are exhibited. It is known that these correlations are well approximated by linear models. Incorporating this a priori knowledge of the signal can facilitate the search for a suitable representation solution and also can help with its interpretation. Lewicki proposed a method to solve the noisy and overcomplete independent component analysis problem. In the present paper we propose a modification of this statistical technique for obtaining a sparse representation using a generative parametric model. The representations obtained with the method proposed here and other techniques are applied to artificial data and real speech signals, and compared using different coding costs and sparsity measures. The results show that the proposed method achieves more efficient representations of these signals compared to the others. A qualitative analysis of these results is also presented, which suggests that the restriction imposed by the parametric model is helpful in discovering meaningful characteristics of the signals.
Solving very large, sparse linear systems on mesh-connected parallel computers
NASA Technical Reports Server (NTRS)
Opsahl, Torstein; Reif, John
1987-01-01
The implementation of Pan and Reif's Parallel Nested Dissection (PND) algorithm on mesh connected parallel computers is described. This is the first known algorithm that allows very large, sparse linear systems of equations to be solved efficiently in polylog time using a small number of processors. How the processor bound of PND can be matched to the number of processors available on a given parallel computer by slowing down the algorithm by constant factors is described. Also, for the important class of problems where G(A) is a grid graph, a unique memory mapping that reduces the inter-processor communication requirements of PND to those that can be executed on mesh connected parallel machines is detailed. A description of an implementation on the Goodyear Massively Parallel Processor (MPP), located at Goddard is given. Also, a detailed discussion of data mappings and performance issues is given.
RASL: robust alignment by sparse and low-rank decomposition for linearly correlated images.
Peng, Yigang; Ganesh, Arvind; Wright, John; Xu, Wenli; Ma, Yi
2012-11-01
This paper studies the problem of simultaneously aligning a batch of linearly correlated images despite gross corruption (such as occlusion). Our method seeks an optimal set of image domain transformations such that the matrix of transformed images can be decomposed as the sum of a sparse matrix of errors and a low-rank matrix of recovered aligned images. We reduce this extremely challenging optimization problem to a sequence of convex programs that minimize the sum of l1-norm and nuclear norm of the two component matrices, which can be efficiently solved by scalable convex optimization techniques. We verify the efficacy of the proposed robust alignment algorithm with extensive experiments on both controlled and uncontrolled real data, demonstrating higher accuracy and efficiency than existing methods over a wide range of realistic misalignments and corruptions.
Sparse Regression as a Sparse Eigenvalue Problem
NASA Technical Reports Server (NTRS)
Moghaddam, Baback; Gruber, Amit; Weiss, Yair; Avidan, Shai
2008-01-01
We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization
Comparison of l₁-Norm SVR and Sparse Coding Algorithms for Linear Regression.
Zhang, Qingtian; Hu, Xiaolin; Zhang, Bo
2015-08-01
Support vector regression (SVR) is a popular function estimation technique based on Vapnik's concept of support vector machine. Among many variants, the l1-norm SVR is known to be good at selecting useful features when the features are redundant. Sparse coding (SC) is a technique widely used in many areas and a number of efficient algorithms are available. Both l1-norm SVR and SC can be used for linear regression. In this brief, the close connection between the l1-norm SVR and SC is revealed and some typical algorithms are compared for linear regression. The results show that the SC algorithms outperform the Newton linear programming algorithm, an efficient l1-norm SVR algorithm, in efficiency. The algorithms are then used to design the radial basis function (RBF) neural networks. Experiments on some benchmark data sets demonstrate the high efficiency of the SC algorithms. In particular, one of the SC algorithms, the orthogonal matching pursuit is two orders of magnitude faster than a well-known RBF network designing algorithm, the orthogonal least squares algorithm.
Generalized Linear Models in Family Studies
ERIC Educational Resources Information Center
Wu, Zheng
2005-01-01
Generalized linear models (GLMs), as defined by J. A. Nelder and R. W. M. Wedderburn (1972), unify a class of regression models for categorical, discrete, and continuous response variables. As an extension of classical linear models, GLMs provide a common body of theory and methodology for some seemingly unrelated models and procedures, such as…
Fahmy, Ahmed S.; Gabr, Refaat E.; Heberlein, Keith; Hu, Xiaoping P.
2006-01-01
Image reconstruction from nonuniformly sampled spatial frequency domain data is an important problem that arises in computed imaging. Current reconstruction techniques suffer from limitations in their model and implementation. In this paper, we present a new reconstruction method that is based on solving a system of linear equations using an efficient iterative approach. Image pixel intensities are related to the measured frequency domain data through a set of linear equations. Although the system matrix is too dense and large to solve by direct inversion in practice, a simple orthogonal transformation to the rows of this matrix is applied to convert the matrix into a sparse one up to a certain chosen level of energy preservation. The transformed system is subsequently solved using the conjugate gradient method. This method is applied to reconstruct images of a numerical phantom as well as magnetic resonance images from experimental spiral imaging data. The results support the theory and demonstrate that the computational load of this method is similar to that of standard gridding, illustrating its practical utility. PMID:23165034
NASA Technical Reports Server (NTRS)
Kincaid, D. R.; Young, D. M.
1984-01-01
Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.
Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.
2015-12-01
We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less
Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.
2015-12-01
We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-ups that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.
NASA Astrophysics Data System (ADS)
Joshi, Deepti; St-Hilaire, André; Daigle, Anik; Ouarda, Taha B. M. J.
2013-04-01
SummaryThis study attempts to compare the performance of two statistical downscaling frameworks in downscaling hydrological indices (descriptive statistics) characterizing the low flow regimes of three rivers in Eastern Canada - Moisie, Romaine and Ouelle. The statistical models selected are Relevance Vector Machine (RVM), an implementation of Sparse Bayesian Learning, and the Automated Statistical Downscaling tool (ASD), an implementation of Multiple Linear Regression. Inputs to both frameworks involve climate variables significantly (α = 0.05) correlated with the indices. These variables were processed using Canonical Correlation Analysis and the resulting canonical variates scores were used as input to RVM to estimate the selected low flow indices. In ASD, the significantly correlated climate variables were subjected to backward stepwise predictor selection and the selected predictors were subsequently used to estimate the selected low flow indices using Multiple Linear Regression. With respect to the correlation between climate variables and the selected low flow indices, it was observed that all indices are influenced, primarily, by wind components (Vertical, Zonal and Meridonal) and humidity variables (Specific and Relative Humidity). The downscaling performance of the framework involving RVM was found to be better than ASD in terms of Relative Root Mean Square Error, Relative Mean Absolute Bias and Coefficient of Determination. In all cases, the former resulted in less variability of the performance indices between calibration and validation sets, implying better generalization ability than for the latter.
Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems
NASA Astrophysics Data System (ADS)
Puzyrev, Vladimir; Koric, Seid; Wilkin, Scott
2016-04-01
High performance computing is absolutely necessary for large-scale geophysical simulations. In order to obtain a realistic image of a geologically complex area, industrial surveys collect vast amounts of data making the computational cost extremely high for the subsequent simulations. A major computational bottleneck of modeling and inversion algorithms is solving the large sparse systems of linear ill-conditioned equations in complex domains with multiple right hand sides. Recently, parallel direct solvers have been successfully applied to multi-source seismic and electromagnetic problems. These methods are robust and exhibit good performance, but often require large amounts of memory and have limited scalability. In this paper, we evaluate modern direct solvers on large-scale modeling examples that previously were considered unachievable with these methods. Performance and scalability tests utilizing up to 65,536 cores on the Blue Waters supercomputer clearly illustrate the robustness, efficiency and competitiveness of direct solvers compared to iterative techniques. Wide use of direct methods utilizing modern parallel architectures will allow modeling tools to accurately support multi-source surveys and 3D data acquisition geometries, thus promoting a more efficient use of the electromagnetic methods in geophysics.
Extended Generalized Linear Latent and Mixed Model
ERIC Educational Resources Information Center
Segawa, Eisuke; Emery, Sherry; Curry, Susan J.
2008-01-01
The generalized linear latent and mixed modeling (GLLAMM framework) includes many models such as hierarchical and structural equation models. However, GLLAMM cannot currently accommodate some models because it does not allow some parameters to be random. GLLAMM is extended to overcome the limitation by adding a submodel that specifies a…
Joubert, W.D.; Carey, G.F.; Kohli, H.; Lorber, A.; McLay, R.T.; Shen, Y.; Berner, N.A. |; Kalhan, A. |
1995-01-01
PCG (Preconditioned Conjugate Gradient package) is a system for solving linear equations of the form Au = b, for A a given matrix and b and u vectors. PCG, employing various gradient-type iterative methods coupled with preconditioners, is designed for general linear systems, with emphasis on sparse systems such as these arising from discretization of partial differential equations arising from physical applications. It can be used to solve linear equations efficiently on parallel computer architectures. Much of the code is reusable across architectures and the package is portable across different systems; the machines that are currently supported is listed. This manual is intended to be the general-purpose reference describing all features of the package accessible to the user; suggestions are also given regarding which methods to use for a given problem.
Generalized Sparse Classifiers for Decoding Cognitive States in fMRI
NASA Astrophysics Data System (ADS)
Ng, Bernard; Vahdat, Arash; Hamarneh, Ghassan; Abugharbieh, Rafeef
The high dimensionality of functional magnetic resonance imaging (fMRI) data presents major challenges to fMRI pattern classification. Directly applying standard classifiers often results in overfitting, which limits the generalizability of the results. In this paper, we propose a new group of classifiers, "Generalized Sparse Classifiers" (GSC), to alleviate this overfitting problem. GSC draws upon the recognition that numerous standard classifiers can be reformulated under a regression framework, which enables state-of-the-art regularization techniques, e.g. elastic net, to be directly employed. Building on this regularized regression framework, we exploit an extension of elastic net that permits general properties, such as spatial smoothness, to be integrated. GSC thus facilitates simultaneous sparse feature selection and classification, while providing greater flexibility in the choice of penalties. We validate on real fMRI data and demonstrate how explicitly modeling spatial correlations inherent in brain activity using GSC can provide superior predictive performance and interpretability over standard classifiers.
Pinski, Peter; Riplinger, Christoph; Neese, Frank E-mail: frank.neese@cec.mpg.de; Valeev, Edward F. E-mail: frank.neese@cec.mpg.de
2015-07-21
In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in
Interpretable exemplar-based shape classification using constrained sparse linear models
NASA Astrophysics Data System (ADS)
Sigurdsson, Gunnar A.; Yang, Zhen; Tran, Trac D.; Prince, Jerry L.
2015-03-01
Many types of diseases manifest themselves as observable changes in the shape of the affected organs. Using shape classification, we can look for signs of disease and discover relationships between diseases. We formulate the problem of shape classification in a holistic framework that utilizes a lossless scalar field representation and a non-parametric classification based on sparse recovery. This framework generalizes over certain classes of unseen shapes while using the full information of the shape, bypassing feature extraction. The output of the method is the class whose combination of exemplars most closely approximates the shape, and furthermore, the algorithm returns the most similar exemplars along with their similarity to the shape, which makes the result simple to interpret. Our results show that the method offers accurate classification between three cerebellar diseases and controls in a database of cerebellar ataxia patients. For reproducible comparison, promising results are presented on publicly available 2D datasets, including the ETH-80 dataset where the method achieves 88.4% classification accuracy.
Fisher, Charles K.; Mehta, Pankaj
2014-01-01
Human associated microbial communities exert tremendous influence over human health and disease. With modern metagenomic sequencing methods it is now possible to follow the relative abundance of microbes in a community over time. These microbial communities exhibit rich ecological dynamics and an important goal of microbial ecology is to infer the ecological interactions between species directly from sequence data. Any algorithm for inferring ecological interactions must overcome three major obstacles: 1) a correlation between the abundances of two species does not imply that those species are interacting, 2) the sum constraint on the relative abundances obtained from metagenomic studies makes it difficult to infer the parameters in timeseries models, and 3) errors due to experimental uncertainty, or mis-assignment of sequencing reads into operational taxonomic units, bias inferences of species interactions due to a statistical problem called “errors-in-variables”. Here we introduce an approach, Learning Interactions from MIcrobial Time Series (LIMITS), that overcomes these obstacles. LIMITS uses sparse linear regression with boostrap aggregation to infer a discrete-time Lotka-Volterra model for microbial dynamics. We tested LIMITS on synthetic data and showed that it could reliably infer the topology of the inter-species ecological interactions. We then used LIMITS to characterize the species interactions in the gut microbiomes of two individuals and found that the interaction networks varied significantly between individuals. Furthermore, we found that the interaction networks of the two individuals are dominated by distinct “keystone species”, Bacteroides fragilis and Bacteroided stercosis, that have a disproportionate influence on the structure of the gut microbiome even though they are only found in moderate abundance. Based on our results, we hypothesize that the abundances of certain keystone species may be responsible for individuality in the human
Fisher, Charles K; Mehta, Pankaj
2014-01-01
Human associated microbial communities exert tremendous influence over human health and disease. With modern metagenomic sequencing methods it is now possible to follow the relative abundance of microbes in a community over time. These microbial communities exhibit rich ecological dynamics and an important goal of microbial ecology is to infer the ecological interactions between species directly from sequence data. Any algorithm for inferring ecological interactions must overcome three major obstacles: 1) a correlation between the abundances of two species does not imply that those species are interacting, 2) the sum constraint on the relative abundances obtained from metagenomic studies makes it difficult to infer the parameters in timeseries models, and 3) errors due to experimental uncertainty, or mis-assignment of sequencing reads into operational taxonomic units, bias inferences of species interactions due to a statistical problem called "errors-in-variables". Here we introduce an approach, Learning Interactions from MIcrobial Time Series (LIMITS), that overcomes these obstacles. LIMITS uses sparse linear regression with boostrap aggregation to infer a discrete-time Lotka-Volterra model for microbial dynamics. We tested LIMITS on synthetic data and showed that it could reliably infer the topology of the inter-species ecological interactions. We then used LIMITS to characterize the species interactions in the gut microbiomes of two individuals and found that the interaction networks varied significantly between individuals. Furthermore, we found that the interaction networks of the two individuals are dominated by distinct "keystone species", Bacteroides fragilis and Bacteroided stercosis, that have a disproportionate influence on the structure of the gut microbiome even though they are only found in moderate abundance. Based on our results, we hypothesize that the abundances of certain keystone species may be responsible for individuality in the human gut
Identification of general linear mechanical systems
NASA Technical Reports Server (NTRS)
Sirlin, S. W.; Longman, R. W.; Juang, J. N.
1983-01-01
Previous work in identification theory has been concerned with the general first order time derivative form. Linear mechanical systems, a large and important class, naturally have a second order form. This paper utilizes this additional structural information for the purpose of identification. A realization is obtained from input-output data, and then knowledge of the system input, output, and inertia matrices is used to determine a set of linear equations whereby we identify the remaining unknown system matrices. Necessary and sufficient conditions on the number, type and placement of sensors and actuators are given which guarantee identificability, and less stringent conditions are given which guarantee generic identifiability. Both a priori identifiability and a posteriori identifiability are considered, i.e., identifiability being insured prior to obtaining data, and identifiability being assured with a given data set.
NASA Astrophysics Data System (ADS)
Bao, Qian; Han, Kuoye; Lin, Yun; Zhang, Bingchen; Liu, Jianguo; Hong, Wen
2016-01-01
We propose an imaging algorithm for downward-looking sparse linear array three-dimensional synthetic aperture radar (DLSLA 3-D SAR) in the circumstance of cross-track sparse and nonuniform array configuration. Considering the off-grid effect and the resolution improvement, the algorithm combines pseudo-polar formatting algorithm, reweighed atomic norm minimization (RANM), and a parametric relaxation-based cyclic approach (RELAX) to improve the imaging performance with a reduced number of array antennas. RANM is employed in the cross-track imaging after pseudo-polar formatting the DLSLA 3-D SAR echo signal, then the reconstructed results are refined by RELAX. By taking advantage of the reweighted scheme, RANM can improve the resolution of the atomic norm minimization, and outperforms discretized compressive sensing schemes that suffer from off-grid effect. The simulated and real data experiments of DLSLA 3-D SAR verify the performance of the proposed algorithm.
A research of 3D gravity inversion based on the recovery of sparse underdetermined linear equations
NASA Astrophysics Data System (ADS)
Zhaohai, M.
2014-12-01
Because of the properties of gravity data, it is made difficult to solve the problem of multiple solutions. There are two main types of 3D gravity inversion methods：One of two methods is based on the improvement of the instability of the sensitive matrix, solving the problem of multiple solutions and instability in 3D gravity inversion. Another is to join weight function into the 3D gravity inversion iteration. Through constant iteration, it can renewal density values and weight function to achieve the purpose to solve the multiple solutions and instability of the 3D gravity data inversion. Thanks to the sparse nature of the solutions of 3D gravity data inversions, we can transform it into a sparse equation. Then, through solving the sparse equations, we can get perfect 3D gravity inversion results. The main principle is based on zero norm of sparse matrix solution of the equation. Zero norm is mainly to solve the nonzero solution of the sparse matrix. However, the method of this article adopted is same as the principle of zero norm. But the method is the opposite of zero norm to obtain zero value solution. Through the form of a Gaussian fitting solution of the zero norm, we can find the solution by using regularization principle. Moreover, this method has been proved that it had a certain resistance to random noise in the mathematics, and it was more suitable than zero norm for the solution of the geophysical data. 3D gravity which is adopted in this article can well identify abnormal body density distribution characteristics, and it can also recognize the space position of abnormal distribution very well. We can take advantage of the density of the upper and lower limit penalty function to make each rectangular residual density within a reasonable range. Finally, this 3D gravity inversion is applied to a variety of combination model test, such as a single straight three-dimensional model, the adjacent straight three-dimensional model and Y three
Sparse-view x-ray CT reconstruction via total generalized variation regularization
NASA Astrophysics Data System (ADS)
Niu, Shanzhou; Gao, Yang; Bian, Zhaoying; Huang, Jing; Chen, Wufan; Yu, Gaohang; Liang, Zhengrong; Ma, Jianhua
2014-06-01
Sparse-view CT reconstruction algorithms via total variation (TV) optimize the data iteratively on the basis of a noise- and artifact-reducing model, resulting in significant radiation dose reduction while maintaining image quality. However, the piecewise constant assumption of TV minimization often leads to the appearance of noticeable patchy artifacts in reconstructed images. To obviate this drawback, we present a penalized weighted least-squares (PWLS) scheme to retain the image quality by incorporating the new concept of total generalized variation (TGV) regularization. We refer to the proposed scheme as ‘PWLS-TGV’ for simplicity. Specifically, TGV regularization utilizes higher order derivatives of the objective image, and the weighted least-squares term considers data-dependent variance estimation, which fully contribute to improving the image quality with sparse-view projection measurement. Subsequently, an alternating optimization algorithm was adopted to minimize the associative objective function. To evaluate the PWLS-TGV method, both qualitative and quantitative studies were conducted by using digital and physical phantoms. Experimental results show that the present PWLS-TGV method can achieve images with several noticeable gains over the original TV-based method in terms of accuracy and resolution properties.
NASA Astrophysics Data System (ADS)
Hashemi, Nezhad Z.; Karami, A.
2015-10-01
Hyperspectral images (HSI) have high spectral and low spatial resolutions. However, multispectral images (MSI) usually have low spectral and high spatial resolutions. In various applications HSI with high spectral and spatial resolutions are required. In this paper, a new method for spatial resolution enhancement of HSI using high resolution MSI based on sparse coding and linear spectral unmixing (SCLSU) is introduced. In the proposed method (SCLSU), high spectral resolution features of HSI and high spatial resolution features of MSI are fused. In this case, the sparse representation of some high resolution MSI and linear spectral unmixing (LSU) model of HSI and MSI is simultaneously used in order to construct high resolution HSI (HRHSI). The fusion process of HSI and MSI is formulated as an ill-posed inverse problem. It is solved by the Split Augmented Lagrangian Shrinkage Algorithm (SALSA) and an orthogonal matching pursuit (OMP) algorithm. Finally, the proposed algorithm is applied to the Hyperion and ALI datasets. Compared with the other state-of-the-art algorithms such as Coupled Nonnegative Matrix Factorization (CNMF) and local spectral unmixing, the SCLSU has significantly increased the spatial resolution and in addition the spectral content of HSI is well maintained.
NASA Astrophysics Data System (ADS)
Wu, Bo; Zhu, Yong; Huang, Xin; Li, Jiayi
2016-10-01
Sparse representation classification (SRC) is becoming a promising tool for hyperspectral image (HSI) classification, where the Euclidean spectral distance (ESD) is widely used to reflect the fidelity between the original and reconstructed signals. In this paper, a generalized model is proposed to extend SRC by characterizing the spectral fidelity with flexible similarity measures. To validate the flexibility, several typical similarity measures-the spectral angle similarity (SAS), spectral information divergence (SID), the structural similarity index measure (SSIM), and the ESD-are included in the generalized model. Furthermore, a general solution based on a gradient descent technique is used to solve the nonlinear optimization problem formulated by the flexible similarity measures. To test the generalized model, two actual HSIs were used, and the experimental results confirm the ability of the proposed model to accommodate the various spectral similarity measures. Performance comparisons with the ESD, SAS, SID, and SSIM criteria were also conducted, and the results consistently show the advantages of the generalized model for HSI classification in terms of overall accuracy and kappa coefficient.
Song, Dong; Robinson, Brian S; Hampson, Robert E; Marmarelis, Vasilis Z; Deadwyler, Sam A; Berger, Theodore W
2015-01-01
In order to build hippocampal prostheses for restoring memory functions, we build multi-input, multi-output (MIMO) nonlinear dynamical models of the human hippocampus. Spike trains are recorded from the hippocampal CA3 and CA1 regions of epileptic patients performing a memory-dependent delayed match-to-sample task. Using CA3 and CA1 spike trains as inputs and outputs respectively, second-order sparse generalized Laguerre-Volterra models are estimated with group lasso and local coordinate descent methods to capture the nonlinear dynamics underlying the spike train transformations. These models can accurately predict the CA1 spike trains based on the ongoing CA3 spike trains and thus will serve as the computational basis of the hippocampal memory prosthesis.
Permutation inference for the general linear model
Winkler, Anderson M.; Ridgway, Gerard R.; Webster, Matthew A.; Smith, Stephen M.; Nichols, Thomas E.
2014-01-01
Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (glms) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on glm parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm – the “randomise” algorithm – for permutation inference with the glm. PMID:24530839
Jones, M.T.; Plassmann, P.E.
1995-12-01
BlockSolve95 is a software library for solving large, sparse systems of linear equations on massively parallel computers or networks of workstations. The matrices must be symmetric in structure; however, the matrix nonzero values may be either symmetric or nonsymmetric. The nonzeros must be real valued. BlockSolve95 uses a message-passing paradigm and achieves portability through the use of the MPI message-passing standard. Emphasis has been placed on achieving both good professor performance through the use of higher-level BLAS and scalability through the use of advanced algorithms. This report gives detailed instructions on the use of BlockSolve95 and descriptions of a number of program examples that can be used as templates for application programs.
NASA Astrophysics Data System (ADS)
Mohammadi-Ghazi, Reza; Büyüköztürk, Oral
2016-04-01
Singularity expansion method (SEM) is a system identification approach with applications in solving inverse scattering problems, electromagnetic interaction problems, remote sensing, and radars. In this approach, the response of a system is represented in terms of its complex poles; therefore, this method not only extracts the fundamental frequencies of the system from the signal, but also provides sufficient information about system's damping if its transient response is analyzed. There are various techniques in SEM among which the generalized pencil-of-function (GPOF) is the computationally most stable and the least sensitive one to noise. However, SEM methods, including GPOF, suffer from imposition of spurious poles on the expansion of signals due to the lack of apriori information about the number of true poles. In this study we address this problem by proposing sparse generalized pencil-of-function (SGPOF). The proposed method excludes the spurious poles through sparsity-based regularization with ℓ1-norm. This study is backed by numerical examples as well as an application example which employs the proposed technique for structural health monitoring (SHM) and compares the results with other signal processing methods.
Ma, S.; Chronopoulos, A.T. )
1990-01-01
This paper reports on the restructure of three outstanding iterative methods for large space nonsymmetric linear systems. These methods are CGS (conjugate gradient squared), CRS (conjugate residual squared), and Orthomin(k). The restructured methods are more suitable for vector and parallel processing. The authors implemented these methods on a parallel vector system. The linear systems for the numerical tests are obtained from discretizing four two- dimensional elliptic partial differential equations by finite difference and finite element methods. A vectorizable and parallelizable version of incomplete LU preconditioning is used. The authors restructured the subroutines to enhance the data locality in vector machines with storage hierarchy. Speedup was measured for multitasking by four processors.
Liang, Yujie; Ying, Rendong; Lu, Zhenqi; Liu, Peilin
2014-01-01
In the design phase of sensor arrays during array signal processing, the estimation performance and system cost are largely determined by array aperture size. In this article, we address the problem of joint direction-of-arrival (DOA) estimation with distributed sparse linear arrays (SLAs) and propose an off-grid synchronous approach based on distributed compressed sensing to obtain larger array aperture. We focus on the complex source distribution in the practical applications and classify the sources into common and innovation parts according to whether a signal of source can impinge on all the SLAs or a specific one. For each SLA, we construct a corresponding virtual uniform linear array (ULA) to create the relationship of random linear map between the signals respectively observed by these two arrays. The signal ensembles including the common/innovation sources for different SLAs are abstracted as a joint spatial sparsity model. And we use the minimization of concatenated atomic norm via semidefinite programming to solve the problem of joint DOA estimation. Joint calculation of the signals observed by all the SLAs exploits their redundancy caused by the common sources and decreases the requirement of array size. The numerical results illustrate the advantages of the proposed approach. PMID:25420150
Irreducible Characters of General Linear Superalgebra and Super Duality
NASA Astrophysics Data System (ADS)
Cheng, Shun-Jen; Lam, Ngau
2010-09-01
We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical Kazhdan-Lusztig theory. Furthermore, we prove that certain parabolic BGG categories over the general linear algebra and over the general linear superalgebra are equivalent. We also verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category of the general linear superalgebra.
An automatic multigrid method for the solution of sparse linear systems
NASA Technical Reports Server (NTRS)
Shapira, Yair; Israeli, Moshe; Sidi, Avram
1993-01-01
An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.
Collective synchronization as a method of learning and generalization from sparse data
NASA Astrophysics Data System (ADS)
Miyano, Takaya; Tsutsui, Takako
2008-02-01
We propose a method for extracting general features from multivariate data using a network of phase oscillators subject to an analogue of the Kuramoto model for collective synchronization. In this method, the natural frequencies of the oscillators are extended to vector quantities to which multivariate data are assigned. The common frequency vectors of the groups of partially synchronized oscillators are interpreted to be the template vectors representing the general features of the data set. We show that the proposed method becomes equivalent to the self-organizing map algorithm devised by Kohonen when the governing equations are linearized about their solutions of partial synchronization. As a case study to test the utility of our method, we applied it to care-needs-certification data in the Japanese public long-term care insurance program, and found major general patterns in the health status of the elderly needing nursing care.
ERIC Educational Resources Information Center
Cheong, Yuk Fai; Kamata, Akihito
2013-01-01
In this article, we discuss and illustrate two centering and anchoring options available in differential item functioning (DIF) detection studies based on the hierarchical generalized linear and generalized linear mixed modeling frameworks. We compared and contrasted the assumptions of the two options, and examined the properties of their DIF…
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.
Analysis, tuning and comparison of two general sparse solvers for distributed memory computers
Amestoy, P.R.; Duff, I.S.; L'Excellent, J.-Y.; Li, X.S.
2000-06-30
We describe the work performed in the context of a Franco-Berkeley funded project between NERSC-LBNL located in Berkeley (USA) and CERFACS-ENSEEIHT located in Toulouse (France). We discuss both the tuning and performance analysis of two distributed memory sparse solvers (superlu from Berkeley and mumps from Toulouse) on the 512 processor Cray T3E from NERSC (Lawrence Berkeley National Laboratory). This project gave us the opportunity to improve the algorithms and add new features to the codes. We then quite extensively analyze and compare the two approaches on a set of large problems from real applications. We further explain the main differences in the behavior of the approaches on artificial regular grid problems. As a conclusion to this activity report, we mention a set of parallel sparse solvers on which this type of study should be extended.
Linear stability of general magnetically insulated electron flow
NASA Astrophysics Data System (ADS)
Swegle, J. A.; Mendel, C. W., Jr.; Seidel, D. B.; Quintenz, J. P.
1984-03-01
A linear stability theory for magnetically insulated systems was formulated by linearizing the general 3-D, time dependent theory of Mendel, Seidel, and Slut. It is found that, case of electron trajectories which are nearly laminar, with only small transverse motion, several suggestive simplifications occur in the eigenvalue equations.
Linear stability of general magnetically insulated electron flow
Swegle, J.A.; Mendel, C.W. Jr.; Seidel, D.B.; Quintenz, J.P.
1984-01-01
We have formulated a linear stability theory for magnetically insulated systems by linearizing the general 3-D, time-dependent theory of Mendel, Seidel, and Slutz. In the physically interesting case of electron trajectories which are nearly laminar, with only small transverse motion, we have found that several suggestive simplifications occur in the eigenvalue equations.
The General Linear Model and Direct Standardization: A Comparison.
ERIC Educational Resources Information Center
Little, Roderick J. A.; Pullum, Thomas W.
1979-01-01
Two methods of analyzing nonorthogonal (uneven cell sizes) cross-classified data sets are compared. The methods are direct standardization and the general linear model. The authors illustrate when direct standardization may be a desirable method of analysis. (JKS)
From linear to generalized linear mixed models: A case study in repeated measures
Technology Transfer Automated Retrieval System (TEKTRAN)
Compared to traditional linear mixed models, generalized linear mixed models (GLMMs) can offer better correspondence between response variables and explanatory models, yielding more efficient estimates and tests in the analysis of data from designed experiments. Using proportion data from a designed...
A Bayesian approach for inducing sparsity in generalized linear models with multi-category response
2015-01-01
Background The dimension and complexity of high-throughput gene expression data create many challenges for downstream analysis. Several approaches exist to reduce the number of variables with respect to small sample sizes. In this study, we utilized the Generalized Double Pareto (GDP) prior to induce sparsity in a Bayesian Generalized Linear Model (GLM) setting. The approach was evaluated using a publicly available microarray dataset containing 99 samples corresponding to four different prostate cancer subtypes. Results A hierarchical Sparse Bayesian GLM using GDP prior (SBGG) was developed to take into account the progressive nature of the response variable. We obtained an average overall classification accuracy between 82.5% and 94%, which was higher than Support Vector Machine, Random Forest or a Sparse Bayesian GLM using double exponential priors. Additionally, SBGG outperforms the other 3 methods in correctly identifying pre-metastatic stages of cancer progression, which can prove extremely valuable for therapeutic and diagnostic purposes. Importantly, using Geneset Cohesion Analysis Tool, we found that the top 100 genes produced by SBGG had an average functional cohesion p-value of 2.0E-4 compared to 0.007 to 0.131 produced by the other methods. Conclusions Using GDP in a Bayesian GLM model applied to cancer progression data results in better subclass prediction. In particular, the method identifies pre-metastatic stages of prostate cancer with substantially better accuracy and produces more functionally relevant gene sets. PMID:26423345
Linear equations in general purpose codes for stiff ODEs
Shampine, L. F.
1980-02-01
It is noted that it is possible to improve significantly the handling of linear problems in a general-purpose code with very little trouble to the user or change to the code. In such situations analytical evaluation of the Jacobian is a lot cheaper than numerical differencing. A slight change in the point at which the Jacobian is evaluated results in a more accurate Jacobian in linear problems. (RWR)
Optimal explicit strong-stability-preserving general linear methods.
Constantinescu, E.; Sandu, A.
2010-07-01
This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both Runge-Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A global optimization strategy is used to find the most efficient schemes that have low storage requirements. Numerical results illustrate the theoretical findings.
A review of some extensions to generalized linear models.
Lindsey, J K
Although generalized linear models are reasonably well known, they are not as widely used in medical statistics as might be appropriate, with the exception of logistic, log-linear, and some survival models. At the same time, the generalized linear modelling methodology is decidedly outdated in that more powerful methods, involving wider classes of distributions, non-linear regression, censoring and dependence among responses, are required. Limitations of the generalized linear modelling approach include the need for the iterated weighted least squares (IWLS) procedure for estimation and deviances for inferences; these restrict the class of models that can be used and do not allow direct comparisons among models from different distributions. Powerful non-linear optimization routines are now available and comparisons can more fruitfully be made using the complete likelihood function. The link function is an artefact, necessary for IWLS to function with linear models, but that disappears once the class is extended to truly non-linear models. Restricting comparisons of responses under different treatments to differences in means can be extremely misleading if the shape of the distribution is changing. This may involve changes in dispersion, or of other shape-related parameters such as the skewness in a stable distribution, with the treatments or covariates. Any exact likelihood function, defined as the probability of the observed data, takes into account the fact that all observable data are interval censored, thus directly encompassing the various types of censoring possible with duration-type data. In most situations this can now be as easily used as the traditional approximate likelihood based on densities. Finally, methods are required for incorporating dependencies among responses in models including conditioning on previous history and on random effects. One important procedure for constructing such likelihoods is based on Kalman filtering. PMID:10474135
Beam envelope calculations in general linear coupled lattices
Chung, Moses; Qin, Hong; Groening, Lars; Xiao, Chen; Davidson, Ronald C.
2015-01-15
The envelope equations and Twiss parameters (β and α) provide important bases for uncoupled linear beam dynamics. For sophisticated beam manipulations, however, coupling elements between two transverse planes are intentionally introduced. The recently developed generalized Courant-Snyder theory offers an effective way of describing the linear beam dynamics in such coupled systems with a remarkably similar mathematical structure to the original Courant-Snyder theory. In this work, we present numerical solutions to the symmetrized matrix envelope equation for β which removes the gauge freedom in the matrix envelope equation for w. Furthermore, we construct the transfer and beam matrices in terms of the generalized Twiss parameters, which enables calculation of the beam envelopes in arbitrary linear coupled systems.
Beam envelope calculations in general linear coupled lattices
NASA Astrophysics Data System (ADS)
Chung, Moses; Qin, Hong; Groening, Lars; Davidson, Ronald C.; Xiao, Chen
2015-01-01
The envelope equations and Twiss parameters (β and α) provide important bases for uncoupled linear beam dynamics. For sophisticated beam manipulations, however, coupling elements between two transverse planes are intentionally introduced. The recently developed generalized Courant-Snyder theory offers an effective way of describing the linear beam dynamics in such coupled systems with a remarkably similar mathematical structure to the original Courant-Snyder theory. In this work, we present numerical solutions to the symmetrized matrix envelope equation for β which removes the gauge freedom in the matrix envelope equation for w. Furthermore, we construct the transfer and beam matrices in terms of the generalized Twiss parameters, which enables calculation of the beam envelopes in arbitrary linear coupled systems.
Confidence Intervals for Assessing Heterogeneity in Generalized Linear Mixed Models
ERIC Educational Resources Information Center
Wagler, Amy E.
2014-01-01
Generalized linear mixed models are frequently applied to data with clustered categorical outcomes. The effect of clustering on the response is often difficult to practically assess partly because it is reported on a scale on which comparisons with regression parameters are difficult to make. This article proposes confidence intervals for…
Canonical Correlation Analysis as the General Linear Model.
ERIC Educational Resources Information Center
Vidal, Sherry
The concept of the general linear model (GLM) is illustrated and how canonical correlation analysis is the GLM is explained, using a heuristic data set to demonstrate how canonical correlation analysis subsumes various multivariate and univariate methods. The paper shows how each of these analyses produces a synthetic variable, like the Yhat…
NASA Astrophysics Data System (ADS)
Prabhakar, Sunil Kumar; Rajaguru, Harikumar
2015-12-01
The most common and frequently occurring neurological disorder is epilepsy and the main method useful for the diagnosis of epilepsy is electroencephalogram (EEG) signal analysis. Due to the length of EEG recordings, EEG signal analysis method is quite time-consuming when it is processed manually by an expert. This paper proposes the application of Linear Graph Embedding (LGE) concept as a dimensionality reduction technique for processing the epileptic encephalographic signals and then it is classified using Sparse Representation Classifiers (SRC). SRC is used to analyze the classification of epilepsy risk levels from EEG signals and the parameters such as Sensitivity, Specificity, Time Delay, Quality Value, Performance Index and Accuracy are analyzed.
The generalized sidelobe canceller based on quaternion widely linear processing.
Tao, Jian-wu; Chang, Wen-xiu
2014-01-01
We investigate the problem of quaternion beamforming based on widely linear processing. First, a quaternion model of linear symmetric array with two-component electromagnetic (EM) vector sensors is presented. Based on array's quaternion model, we propose the general expression of a quaternion semiwidely linear (QSWL) beamformer. Unlike the complex widely linear beamformer, the QSWL beamformer is based on the simultaneous operation on the quaternion vector, which is composed of two jointly proper complex vectors, and its involution counterpart. Second, we propose a useful implementation of QSWL beamformer, that is, QSWL generalized sidelobe canceller (GSC), and derive the simple expressions of the weight vectors. The QSWL GSC consists of two-stage beamformers. By designing the weight vectors of two-stage beamformers, the interference is completely canceled in the output of QSWL GSC and the desired signal is not distorted. We derive the array's gain expression and analyze the performance of the QSWL GSC in the presence of one type of interference. The advantage of QSWL GSC is that the main beam can always point to the desired signal's direction and the robustness to DOA mismatch is improved. Finally, simulations are used to verify the performance of the proposed QSWL GSC. PMID:24955425
The Generalized Sidelobe Canceller Based on Quaternion Widely Linear Processing
Tao, Jian-wu; Chang, Wen-xiu
2014-01-01
We investigate the problem of quaternion beamforming based on widely linear processing. First, a quaternion model of linear symmetric array with two-component electromagnetic (EM) vector sensors is presented. Based on array's quaternion model, we propose the general expression of a quaternion semiwidely linear (QSWL) beamformer. Unlike the complex widely linear beamformer, the QSWL beamformer is based on the simultaneous operation on the quaternion vector, which is composed of two jointly proper complex vectors, and its involution counterpart. Second, we propose a useful implementation of QSWL beamformer, that is, QSWL generalized sidelobe canceller (GSC), and derive the simple expressions of the weight vectors. The QSWL GSC consists of two-stage beamformers. By designing the weight vectors of two-stage beamformers, the interference is completely canceled in the output of QSWL GSC and the desired signal is not distorted. We derive the array's gain expression and analyze the performance of the QSWL GSC in the presence of one type of interference. The advantage of QSWL GSC is that the main beam can always point to the desired signal's direction and the robustness to DOA mismatch is improved. Finally, simulations are used to verify the performance of the proposed QSWL GSC. PMID:24955425
Estimating classification images with generalized linear and additive models.
Knoblauch, Kenneth; Maloney, Laurence T
2008-12-22
Conventional approaches to modeling classification image data can be described in terms of a standard linear model (LM). We show how the problem can be characterized as a Generalized Linear Model (GLM) with a Bernoulli distribution. We demonstrate via simulation that this approach is more accurate in estimating the underlying template in the absence of internal noise. With increasing internal noise, however, the advantage of the GLM over the LM decreases and GLM is no more accurate than LM. We then introduce the Generalized Additive Model (GAM), an extension of GLM that can be used to estimate smooth classification images adaptively. We show that this approach is more robust to the presence of internal noise, and finally, we demonstrate that GAM is readily adapted to estimation of higher order (nonlinear) classification images and to testing their significance.
NASA Astrophysics Data System (ADS)
Riplinger, Christoph; Pinski, Peter; Becker, Ute; Valeev, Edward F.; Neese, Frank
2016-01-01
Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous
Riplinger, Christoph; Pinski, Peter; Becker, Ute; Valeev, Edward F; Neese, Frank
2016-01-14
Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate
Riplinger, Christoph; Pinski, Peter; Becker, Ute; Valeev, Edward F; Neese, Frank
2016-01-14
Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate
Credibility analysis of risk classes by generalized linear model
NASA Astrophysics Data System (ADS)
Erdemir, Ovgucan Karadag; Sucu, Meral
2016-06-01
In this paper generalized linear model (GLM) and credibility theory which are frequently used in nonlife insurance pricing are combined for reliability analysis. Using full credibility standard, GLM is associated with limited fluctuation credibility approach. Comparison criteria such as asymptotic variance and credibility probability are used to analyze the credibility of risk classes. An application is performed by using one-year claim frequency data of a Turkish insurance company and results of credible risk classes are interpreted.
Generalization of continuous-variable quantum cloning with linear optics
NASA Astrophysics Data System (ADS)
Zhai, Zehui; Guo, Juan; Gao, Jiangrui
2006-05-01
We propose an asymmetric quantum cloning scheme. Based on the proposal and experiment by Andersen [Phys. Rev. Lett. 94, 240503 (2005)], we generalize it to two asymmetric cases: quantum cloning with asymmetry between output clones and between quadrature variables. These optical implementations also employ linear elements and homodyne detection only. Finally, we also compare the utility of symmetric and asymmetric cloning in an analysis of a squeezed-state quantum key distribution protocol and find that the asymmetric one is more advantageous.
Linear spin-2 fields in most general backgrounds
NASA Astrophysics Data System (ADS)
Bernard, Laura; Deffayet, Cédric; Schmidt-May, Angnis; von Strauss, Mikael
2016-04-01
We derive the full perturbative equations of motion for the most general background solutions in ghost-free bimetric theory in its metric formulation. Clever field redefinitions at the level of fluctuations enable us to circumvent the problem of varying a square-root matrix appearing in the theory. This greatly simplifies the expressions for the linear variation of the bimetric interaction terms. We show that these field redefinitions exist and are uniquely invertible if and only if the variation of the square-root matrix itself has a unique solution, which is a requirement for the linearized theory to be well defined. As an application of our results we examine the constraint structure of ghost-free bimetric theory at the level of linear equations of motion for the first time. We identify a scalar combination of equations which is responsible for the absence of the Boulware-Deser ghost mode in the theory. The bimetric scalar constraint is in general not manifestly covariant in its nature. However, in the massive gravity limit the constraint assumes a covariant form when one of the interaction parameters is set to zero. For that case our analysis provides an alternative and almost trivial proof of the absence of the Boulware-Deser ghost. Our findings generalize previous results in the metric formulation of massive gravity and also agree with studies of its vielbein version.
NASA Astrophysics Data System (ADS)
Nordtvedt, K.
2015-11-01
A local system of bodies in General Relativity whose exterior metric field asymptotically approaches the Minkowski metric effaces any effects of the matter distribution exterior to its Minkowski boundary condition. To enforce to all orders this property of gravity which appears to hold in nature, a method using linear algebraic scaling equations is developed which generates by an iterative process an N-body Lagrangian expansion for gravity's motion-independent potentials which fulfills exterior effacement along with needed metric potential expansions. Then additional properties of gravity - interior effacement and Lorentz time dilation and spatial contraction - produce additional iterative, linear algebraic equations for obtaining the full non-linear and motion-dependent N-body gravity Lagrangian potentials as well.
Comparative Study of Algorithms for Automated Generalization of Linear Objects
NASA Astrophysics Data System (ADS)
Azimjon, S.; Gupta, P. K.; Sukhmani, R. S. G. S.
2014-11-01
Automated generalization, rooted from conventional cartography, has become an increasing concern in both geographic information system (GIS) and mapping fields. All geographic phenomenon and the processes are bound to the scale, as it is impossible for human being to observe the Earth and the processes in it without decreasing its scale. To get optimal results, cartographers and map-making agencies develop set of rules and constraints, however these rules are under consideration and topic for many researches up until recent days. Reducing map generating time and giving objectivity is possible by developing automated map generalization algorithms (McMaster and Shea, 1988). Modification of the scale traditionally is a manual process, which requires knowledge of the expert cartographer, and it depends on the experience of the user, which makes the process very subjective as every user may generate different map with same requirements. However, automating generalization based on the cartographic rules and constrains can give consistent result. Also, developing automated system for map generation is the demand of this rapid changing world. The research that we have conveyed considers only generalization of the roads, as it is one of the indispensable parts of a map. Dehradun city, Uttarakhand state of India was selected as a study area. The study carried out comparative study of the generalization software sets, operations and algorithms available currently, also considers advantages and drawbacks of the existing software used worldwide. Research concludes with the development of road network generalization tool and with the final generalized road map of the study area, which explores the use of open source python programming language and attempts to compare different road network generalization algorithms. Thus, the paper discusses the alternative solutions for automated generalization of linear objects using GIS-technologies. Research made on automated of road network
Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D. Kühn, Oliver
2015-06-28
Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into a few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation, which can be rigorously derived by means of a linear projection technique. Within this framework, a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here, we discuss that this task is more naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic overestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom.
Elastic capsule deformation in general irrotational linear flows
Szatmary, Alex C.; Eggleton, Charles D.
2012-01-01
Knowledge of the response of elastic capsules to imposed fluid flow is necessary for predicting deformation and motion of biological cells and synthetic capsules in microfluidic devices and in the microcirculation. Capsules have been studied in shear, planar extensional, and axisymmetric extensional flows. Here, the flow gradient matrix of a general irrotational linear flow is characterized by two parameters, its strain rate, defined as the maximum of the principal strain rates, and by a new term, q, the difference in the two lesser principal strain rates, scaled by the maximum principal strain rate; this characterization is valid for ellipsoids in irrotational linear flow, and it gives good results for spheres in general linear flows at low capillary numbers. We demonstrate that deformable non-spherical particles align with the principal axes of an imposed irrotational flow. Thus, it is most practical to model deformation of non-spherical particles already aligned with the flow, rather than considering each arbitrary orientation. Capsule deformation was modeled for a sphere, a prolate spheroid, and an oblate spheroid, subjected to combinations of uniaxial, biaxial, and planar extensional flows; modeling was performed using the immersed boundary method. The time response of each capsule to each flow was found, as were the steady-state deformation factor, mean strain energy, and surface area. For a given capillary number, planar flows led to more deformation than uniaxial or biaxial extensional flows. Capsule behavior in all cases was bounded by the response of capsules to uniaxial, biaxial, and planar extensional flow. PMID:23426110
Generalization of continuous-variable quantum cloning with linear optics
Zhai Zehui; Guo Juan; Gao Jiangrui
2006-05-15
We propose an asymmetric quantum cloning scheme. Based on the proposal and experiment by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)], we generalize it to two asymmetric cases: quantum cloning with asymmetry between output clones and between quadrature variables. These optical implementations also employ linear elements and homodyne detection only. Finally, we also compare the utility of symmetric and asymmetric cloning in an analysis of a squeezed-state quantum key distribution protocol and find that the asymmetric one is more advantageous.
General linear mode conversion coefficient in one dimension
NASA Astrophysics Data System (ADS)
Littlejohn, Robert G.; Flynn, William G.
1993-03-01
A general formula is presented for the mode conversion coefficient for linear mode conversion in one dimension, in terms of an arbitrary 2 x 2 reduced dispersion matrix describing the coupling of the modes. The mode conversion coefficient has three invariance properties which are discussed, namely, invariance under scaling transformations, canonical transformations, and a certain kind of Lorentz transformation. Formulas for the S matrix of mode conversion are also presented. The example of the conversion of electromagnetic waves to electrostatic waves in the ionosphere is used to illustrate the formulas.
General linear mode conversion coefficient in one dimension
NASA Astrophysics Data System (ADS)
Littlejohn, Robert G.; Flynn, William G.
1993-03-01
A general formula is presented for the mode conversion coefficient for linear mode conversion in one dimension, in terms of an arbitrary 2×2 reduced dispersion matrix describing the coupling of the modes. The mode conversion coefficient has three invariance properties which are discussed, namely, invariance under scaling transformations, canonical transformations, and a certain kind of Lorentz transformation. Formulas for the S matrix of mode conversion are also presented. The example of the conversion of electromagnetic waves to electrostatic waves in the ionosphere is used to illustrate the formulas.
Generalized space and linear momentum operators in quantum mechanics
Costa, Bruno G. da
2014-06-15
We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator p{sup ^}{sub q}, and its canonically conjugate deformed position operator x{sup ^}{sub q}. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
Generalized space and linear momentum operators in quantum mechanics
NASA Astrophysics Data System (ADS)
da Costa, Bruno G.; Borges, Ernesto P.
2014-06-01
We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator hat{p}_q, and its canonically conjugate deformed position operator hat{x}_q. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
General mirror pairs for gauged linear sigma models
NASA Astrophysics Data System (ADS)
Aspinwall, Paul S.; Plesser, M. Ronen
2015-11-01
We carefully analyze the conditions for an abelian gauged linear σ-model to exhibit nontrivial IR behavior described by a nonsingular superconformal field theory determining a superstring vacuum. This is done without reference to a geometric phase, by associating singular behavior to a noncompact space of (semi-)classical vacua. We find that models determined by reflexive combinatorial data are nonsingular for generic values of their parameters. This condition has the pleasant feature that the mirror of a nonsingular gauged linear σ-model is another such model, but it is clearly too strong and we provide an example of a non-reflexive mirror pair. We discuss a weaker condition inspired by considering extremal transitions, which is also mirror symmetric and which we conjecture to be sufficient. We apply these ideas to extremal transitions and to understanding the way in which both Berglund-Hübsch mirror symmetry and the Vafa-Witten mirror orbifold with discrete torsion can be seen as special cases of the general combinatorial duality of gauged linear σ-models. In the former case we encounter an example showing that our weaker condition is still not necessary.
Finding Nonoverlapping Substructures of a Sparse Matrix
Pinar, Ali; Vassilevska, Virginia
2005-08-11
Many applications of scientific computing rely on computations on sparse matrices. The design of efficient implementations of sparse matrix kernels is crucial for the overall efficiency of these applications. Due to the high compute-to-memory ratio and irregular memory access patterns, the performance of sparse matrix kernels is often far away from the peak performance on a modern processor. Alternative data structures have been proposed, which split the original matrix A into A{sub d} and A{sub s}, so that A{sub d} contains all dense blocks of a specified size in the matrix, and A{sub s} contains the remaining entries. This enables the use of dense matrix kernels on the entries of A{sub d} producing better memory performance. In this work, we study the problem of finding a maximum number of nonoverlapping dense blocks in a sparse matrix, which is previously not studied in the sparse matrix community. We show that the maximum nonoverlapping dense blocks problem is NP-complete by using a reduction from the maximum independent set problem on cubic planar graphs. We also propose a 2/3-approximation algorithm that runs in linear time in the number of nonzeros in the matrix. This extended abstract focuses on our results for 2x2 dense blocks. However we show that our results can be generalized to arbitrary sized dense blocks, and many other oriented substructures, which can be exploited to improve the memory performance of sparse matrix operations.
Robust face recognition via sparse representation.
Wright, John; Yang, Allen Y; Ganesh, Arvind; Sastry, S Shankar; Ma, Yi
2009-02-01
We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by l{1}-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as Eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.
GENERALIZED PARTIALLY LINEAR MIXED-EFFECTS MODELS INCORPORATING MISMEASURED COVARIATES
Liang, Hua
2009-01-01
In this article we consider a semiparametric generalized mixed-effects model, and propose combining local linear regression, and penalized quasilikelihood and local quasilikelihood techniques to estimate both population and individual parameters and nonparametric curves. The proposed estimators take into account the local correlation structure of the longitudinal data. We establish normality for the estimators of the parameter and asymptotic expansion for the estimators of the nonparametric part. For practical implementation, we propose an appropriate algorithm. We also consider the measurement error problem in covariates in our model, and suggest a strategy for adjusting the effects of measurement errors. We apply the proposed models and methods to study the relation between virologic and immunologic responses in AIDS clinical trials, in which virologic response is classified into binary variables. A dataset from an AIDS clinical study is analyzed. PMID:20160899
Diagnostic Measures for Generalized Linear Models with Missing Covariates
ZHU, HONGTU; IBRAHIM, JOSEPH G.; SHI, XIAOYAN
2009-01-01
In this paper, we carry out an in-depth investigation of diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for generalized linear models. Our diagnostic measures include case-deletion measures and conditional residuals. We use the conditional residuals to construct goodness-of-fit statistics for testing possible misspecifications in model assumptions, including the sampling distribution. We develop specific strategies for incorporating missing data into goodness-of-fit statistics in order to increase the power of detecting model misspecification. A resampling method is proposed to approximate the p-value of the goodness-of-fit statistics. Simulation studies are conducted to evaluate our methods and a real data set is analysed to illustrate the use of our various diagnostic measures. PMID:20037674
Optimization in generalized linear models: A case study
NASA Astrophysics Data System (ADS)
Silva, Eliana Costa e.; Correia, Aldina; Lopes, Isabel Cristina
2016-06-01
The maximum likelihood method is usually chosen to estimate the regression parameters of Generalized Linear Models (GLM) and also for hypothesis testing and goodness of fit tests. The classical method for estimating GLM parameters is the Fisher scores. In this work we propose to compute the estimates of the parameters with two alternative methods: a derivative-based optimization method, namely the BFGS method which is one of the most popular of the quasi-Newton algorithms, and the PSwarm derivative-free optimization method that combines features of a pattern search optimization method with a global Particle Swarm scheme. As a case study we use a dataset of biological parameters (phytoplankton) and chemical and environmental parameters of the water column of a Portuguese reservoir. The results show that, for this dataset, BFGS and PSwarm methods provided a better fit, than Fisher scores method, and can be good alternatives for finding the estimates for the parameters of a GLM.
Using parallel banded linear system solvers in generalized eigenvalue problems
NASA Technical Reports Server (NTRS)
Zhang, Hong; Moss, William F.
1994-01-01
Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speedup is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.
Using parallel banded linear system solvers in generalized eigenvalue problems
NASA Technical Reports Server (NTRS)
Zhang, Hong; Moss, William F.
1993-01-01
Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.
Cervigram image segmentation based on reconstructive sparse representations
NASA Astrophysics Data System (ADS)
Zhang, Shaoting; Huang, Junzhou; Wang, Wei; Huang, Xiaolei; Metaxas, Dimitris
2010-03-01
We proposed an approach based on reconstructive sparse representations to segment tissues in optical images of the uterine cervix. Because of large variations in image appearance caused by the changing of the illumination and specular reflection, the color and texture features in optical images often overlap with each other and are not linearly separable. By leveraging sparse representations the data can be transformed to higher dimensions with sparse constraints and become more separated. K-SVD algorithm is employed to find sparse representations and corresponding dictionaries. The data can be reconstructed from its sparse representations and positive and/or negative dictionaries. Classification can be achieved based on comparing the reconstructive errors. In the experiments we applied our method to automatically segment the biomarker AcetoWhite (AW) regions in an archive of 60,000 images of the uterine cervix. Compared with other general methods, our approach showed lower space and time complexity and higher sensitivity.
Structured Multifrontal Sparse Solver
2014-05-01
StruMF is an algebraic structured preconditioner for the interative solution of large sparse linear systems. The preconditioner corresponds to a multifrontal variant of sparse LU factorization in which some dense blocks of the factors are approximated with low-rank matrices. It is algebraic in that it only requires the linear system itself, and the approximation threshold that determines the accuracy of individual low-rank approximations. Favourable rank properties are obtained using a block partitioning which is amore » refinement of the partitioning induced by nested dissection ordering.« less
Haley, Benjamin M.; Paunesku, Tatjana; Grdina, David J.; Woloschak, Gayle E.
2015-01-01
Introduction The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREFLSS). It was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limited number of animal studies. Methods and Results We argue that the linear-quadratic model does not provide appropriate support to estimate the risk of contemporary exposures. In this work, we re-estimated DDREFLSS using 15 animal studies that were not included in BEIR VII’s original analysis. Acute exposure data led to a DDREFLSS estimate from 0.9 to 3.0. By contrast, data that included both acute and protracted exposures led to a DDREFLSS estimate from 4.8 to infinity. These two estimates are significantly different, violating the assumptions of the linear-quadratic model, which predicts that DDREFLSS values calculated in either way should be the same. Conclusions Therefore, we propose that future estimates of the risk of protracted exposures should be based on direct comparisons of data from acute and protracted exposures, rather than from extrapolations from a linear-quadratic model. The risk of low dose exposures may be extrapolated from these protracted estimates, though we encourage ongoing debate as to whether this is the most valid approach. We also encourage efforts to enlarge the datasets used to estimate the risk of protracted exposures by including both human and animal data, carcinogenesis outcomes, a wider range of exposures, and by making more radiobiology data publicly accessible. We believe that these steps will
Adaptive Error Estimation in Linearized Ocean General Circulation Models
NASA Technical Reports Server (NTRS)
Chechelnitsky, Michael Y.
1999-01-01
Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large
Haley, Benjamin M.; Paunesku, Tatjana; Grdina, David J.; Woloschak, Gayle E.; Aravindan, Natarajan
2015-12-09
The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREF_{LSS}). As a result, it was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limited number of animal studies.
Haley, Benjamin M.; Paunesku, Tatjana; Grdina, David J.; Woloschak, Gayle E.; Aravindan, Natarajan
2015-12-09
The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREFLSS). As a result, it was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limitedmore » number of animal studies.« less
Models for cultural inheritance: a general linear model.
Feldman, M W; Cavalli-Sforza, L L
1975-07-01
A theory of cultural evolution is proposed based on a general linear mode of cultural transmission. The trait of an individual is assumed to depend on the values of the same trait in other individuals of the same, the previous or earlier generation. The transmission matrix W has as its elements the proportional contributions of each individual (i) of one generation to each individual (j) of another. In addition, there is random variation (copy error or innovation) for each individual. Means and variances of a group of N individuals change with time and will stabilize asymptotically if the matrix W is irreducible and aperiodic. The rate of convergence is geometric and is governed by the largest non-unit eigenvalue of W. Groups fragment and evolve independently if W is reducible. The means of independent groups vary at random at a predicted rate, a phenomenon termed "random cultural drift". Variances within a group tend to be small, assuming cultural homogeneity. Transmission matrices of the teacher/leader type, and of parental type have been specifically considered, as well as social hierarchies. Various limitations, extensions, and some chances of application are discussed.
Bayesian Inference for Generalized Linear Models for Spiking Neurons
Gerwinn, Sebastian; Macke, Jakob H.; Bethge, Matthias
2010-01-01
Generalized Linear Models (GLMs) are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate. PMID:20577627
A general protocol to afford enantioenriched linear homoprenylic amines.
Bosque, Irene; Foubelo, Francisco; Gonzalez-Gomez, Jose C
2013-11-21
The reaction of a readily obtained chiral branched homoprenylamonium salt with a range of aldehydes, including aliphatic substrates, affords the corresponding linear isomers in good yields and enantioselectivities.
GENERAL: Linear Optical Scheme for Implementing Optimal Real State Cloning
NASA Astrophysics Data System (ADS)
Wan, Hong-Bo; Ye, Liu
2010-06-01
We propose an experimental scheme for implementing the optimal 1 → 3 real state cloning via linear optical elements. This method relies on one polarized qubit and two location qubits and is feasible with current experimental technology.
User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.
NASA Technical Reports Server (NTRS)
Reddy, C. J.
2000-01-01
PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.
Generalizing a Categorization of Students' Interpretations of Linear Kinematics Graphs
ERIC Educational Resources Information Center
Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul
2016-01-01
We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque…
PYESSENCE: Generalized Coupled Quintessence Linear Perturbation Python Code
NASA Astrophysics Data System (ADS)
Leithes, Alexander
2016-09-01
PYESSENCE evolves linearly perturbed coupled quintessence models with multiple (cold dark matter) CDM fluid species and multiple DE (dark energy) scalar fields, and can be used to generate quantities such as the growth factor of large scale structure for any coupled quintessence model with an arbitrary number of fields and fluids and arbitrary couplings.
A General Linear Method for Equating with Small Samples
ERIC Educational Resources Information Center
Albano, Anthony D.
2015-01-01
Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…
Guisan, A.; Edwards, T.C.; Hastie, T.
2002-01-01
An important statistical development of the last 30 years has been the advance in regression analysis provided by generalized linear models (GLMs) and generalized additive models (GAMs). Here we introduce a series of papers prepared within the framework of an international workshop entitled: Advances in GLMs/GAMs modeling: from species distribution to environmental management, held in Riederalp, Switzerland, 6-11 August 2001. We first discuss some general uses of statistical models in ecology, as well as provide a short review of several key examples of the use of GLMs and GAMs in ecological modeling efforts. We next present an overview of GLMs and GAMs, and discuss some of their related statistics used for predictor selection, model diagnostics, and evaluation. Included is a discussion of several new approaches applicable to GLMs and GAMs, such as ridge regression, an alternative to stepwise selection of predictors, and methods for the identification of interactions by a combined use of regression trees and several other approaches. We close with an overview of the papers and how we feel they advance our understanding of their application to ecological modeling. ?? 2002 Elsevier Science B.V. All rights reserved.
Generalizing a categorization of students' interpretations of linear kinematics graphs
NASA Astrophysics Data System (ADS)
Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul
2016-06-01
We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.
Sparse matrix test collections
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.
The general RF tuning for IH-DTL linear accelerators
NASA Astrophysics Data System (ADS)
Lu, Y. R.; Ratzinger, U.; Schlitt, B.; Tiede, R.
2007-11-01
The RF tuning is the most important research for achieving the resonant frequency and the flatness of electric field distributions along the axis of RF accelerating structures. The six different tuning concepts and that impacts on the longitudinal field distributions have been discussed in detail combining the RF tuning process of a 1:2 modeled 20.85 MV compact IH-DTL cavity, which was designed to accelerate proton, helium, oxygen or C 4+ from 400 keV/ u to 7 MeV/u and used as the linear injector of 430 MeV/ u synchrotron [Y.R. Lu, S. Minaev, U. Ratzinger, B. Schlitt, R.Tiede, The Compact 20MV IH-DTL for the Heidelberg Therapy Facility, in: Proceedings of the LINAC Conference, Luebeck, Germany, 2004 [1]; Y.R. Lu, Frankfurt University Dissertation, 2005. [2
Threaded Operations on Sparse Matrices
Sneed, Brett
2015-09-01
We investigate the use of sparse matrices and OpenMP multi-threading on linear algebra operations involving them. Several sparse matrix data structures are presented. Implementation of the multi- threading primarily occurs in the level one and two BLAS functions used within the four algorithms investigated{the Power Method, Conjugate Gradient, Biconjugate Gradient, and Jacobi's Method. The bene ts of launching threads once per high level algorithm are explored.
Item Purification in Differential Item Functioning Using Generalized Linear Mixed Models
ERIC Educational Resources Information Center
Liu, Qian
2011-01-01
For this dissertation, four item purification procedures were implemented onto the generalized linear mixed model for differential item functioning (DIF) analysis, and the performance of these item purification procedures was investigated through a series of simulations. Among the four procedures, forward and generalized linear mixed model (GLMM)…
NASA Astrophysics Data System (ADS)
Rudy, Ashley C. A.; Lamoureux, Scott F.; Treitz, Paul; van Ewijk, Karin Y.
2016-07-01
To effectively assess and mitigate risk of permafrost disturbance, disturbance-prone areas can be predicted through the application of susceptibility models. In this study we developed regional susceptibility models for permafrost disturbances using a field disturbance inventory to test the transferability of the model to a broader region in the Canadian High Arctic. Resulting maps of susceptibility were then used to explore the effect of terrain variables on the occurrence of disturbances within this region. To account for a large range of landscape characteristics, the model was calibrated using two locations: Sabine Peninsula, Melville Island, NU, and Fosheim Peninsula, Ellesmere Island, NU. Spatial patterns of disturbance were predicted with a generalized linear model (GLM) and generalized additive model (GAM), each calibrated using disturbed and randomized undisturbed locations from both locations and GIS-derived terrain predictor variables including slope, potential incoming solar radiation, wetness index, topographic position index, elevation, and distance to water. Each model was validated for the Sabine and Fosheim Peninsulas using independent data sets while the transferability of the model to an independent site was assessed at Cape Bounty, Melville Island, NU. The regional GLM and GAM validated well for both calibration sites (Sabine and Fosheim) with the area under the receiver operating curves (AUROC) > 0.79. Both models were applied directly to Cape Bounty without calibration and validated equally with AUROC's of 0.76; however, each model predicted disturbed and undisturbed samples differently. Additionally, the sensitivity of the transferred model was assessed using data sets with different sample sizes. Results indicated that models based on larger sample sizes transferred more consistently and captured the variability within the terrain attributes in the respective study areas. Terrain attributes associated with the initiation of disturbances were
Computer analysis of general linear networks using digraphs.
NASA Technical Reports Server (NTRS)
Mcclenahan, J. O.; Chan, S.-P.
1972-01-01
Investigation of the application of digraphs in analyzing general electronic networks, and development of a computer program based on a particular digraph method developed by Chen. The Chen digraph method is a topological method for solution of networks and serves as a shortcut when hand calculations are required. The advantage offered by this method of analysis is that the results are in symbolic form. It is limited, however, by the size of network that may be handled. Usually hand calculations become too tedious for networks larger than about five nodes, depending on how many elements the network contains. Direct determinant expansion for a five-node network is a very tedious process also.
The Generalized Logit-Linear Item Response Model for Binary-Designed Items
ERIC Educational Resources Information Center
Revuelta, Javier
2008-01-01
This paper introduces the generalized logit-linear item response model (GLLIRM), which represents the item-solving process as a series of dichotomous operations or steps. The GLLIRM assumes that the probability function of the item response is a logistic function of a linear composite of basic parameters which describe the operations, and the…
P-SPARSLIB: A parallel sparse iterative solution package
Saad, Y.
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.
van Meurs, Brian; Wiggert, Nicole; Wicker, Isaac; Lissek, Shmuel
2014-06-01
Fear-conditioning experiments in the anxiety disorders focus almost exclusively on passive-emotional, Pavlovian conditioning, rather than active-behavioral, instrumental conditioning. Paradigms eliciting both types of conditioning are needed to study maladaptive, instrumental behaviors resulting from Pavlovian abnormalities found in clinical anxiety. One such Pavlovian abnormality is generalization of fear from a conditioned danger-cue (CS+) to resembling stimuli. Though lab-based findings repeatedly link overgeneralized Pavlovian-fear to clinical anxiety, no study assesses the degree to which Pavlovian overgeneralization corresponds with maladaptive, overgeneralized instrumental-avoidance. The current effort fills this gap by validating a novel fear-potentiated startle paradigm including Pavlovian and instrumental components. The paradigm is embedded in a computer game during which shapes appear on the screen. One shape paired with electric-shock serves as CS+, and other resembling shapes, presented in the absence of shock, serve as generalization stimuli (GSs). During the game, participants choose whether to behaviorally avoid shock at the cost of poorer performance. Avoidance during CS+ is considered adaptive because shock is a real possibility. By contrast, avoidance during GSs is considered maladaptive because shock is not a realistic prospect and thus unnecessarily compromises performance. Results indicate significant Pavlovian-instrumental relations, with greater generalization of Pavlovian fear associated with overgeneralization of maladaptive instrumental-avoidance.
van Meurs, Brian; Wiggert, Nicole; Wicker, Isaac; Lissek, Shmuel
2016-01-01
Fear-conditioning experiments in the anxiety disorders focus almost exclusively on passive-emotional, Pavlovian conditioning, rather than active-behavioral, instrumental conditioning. Paradigms eliciting both types of conditioning are needed to study maladaptive, instrumental behaviors resulting from Pavlovian abnormalities found in clinical anxiety. One such Pavlovian abnormality is generalization of fear from a conditioned danger-cue (CS+) to resembling stimuli. Though lab-based findings repeatedly link overgeneralized Pavlovian-fear to clinical anxiety, no study assesses the degree to which Pavlovian overgeneralization corresponds with maladaptive, overgeneralized instrumental-avoidance. The current effort fills this gap by validating a novel fear-potentiated startle paradigm including Pavlovian and instrumental components. The paradigm is embedded in a computer game during which shapes appear on the screen. One shape paired with electric-shock serves as CS+, and other resembling shapes, presented in the absence of shock, serve as generalization stimuli (GSs). During the game, participants choose whether to behaviorally avoid shock at the cost of poorer performance. Avoidance during CS+ is considered adaptive because shock is a real possibility. By contrast, avoidance during GSs is considered maladaptive because shock is not a realistic prospect and thus unnecessarily compromises performance. Results indicate significant Pavlovian-instrumental relations, with greater generalization of Pavlovian fear associated with overgeneralization of maladaptive instrumental-avoidance. PMID:24768950
Sparse Multinomial Logistic Regression via Approximate Message Passing
NASA Astrophysics Data System (ADS)
Byrne, Evan; Schniter, Philip
2016-11-01
For the problem of multi-class linear classification and feature selection, we propose approximate message passing approaches to sparse multinomial logistic regression (MLR). First, we propose two algorithms based on the Hybrid Generalized Approximate Message Passing (HyGAMP) framework: one finds the maximum a posteriori (MAP) linear classifier and the other finds an approximation of the test-error-rate minimizing linear classifier. Then we design computationally simplified variants of these two algorithms. Next, we detail methods to tune the hyperparameters of their assumed statistical models using Stein's unbiased risk estimate (SURE) and expectation-maximization (EM), respectively. Finally, using both synthetic and real-world datasets, we demonstrate improved error-rate and runtime performance relative to existing state-of-the-art approaches to sparse MLR.
Zhao, Yingfeng; Liu, Sanyang
2016-01-01
We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient. PMID:27547676
Zhao, Yingfeng; Liu, Sanyang
2016-01-01
We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.
NASA Technical Reports Server (NTRS)
Rankin, C. C.
1988-01-01
A consistent linearization is provided for the element-dependent corotational formulation, providing the proper first and second variation of the strain energy. As a result, the warping problem that has plagued flat elements has been overcome, with beneficial effects carried over to linear solutions. True Newton quadratic convergence has been restored to the Structural Analysis of General Shells (STAGS) code for conservative loading using the full corotational implementation. Some implications for general finite element analysis are discussed, including what effect the automatic frame invariance provided by this work might have on the development of new, improved elements.
Optimal explicit strong-stability-preserving general linear methods : complete results.
Constantinescu, E. M.; Sandu, A.; Mathematics and Computer Science; Virginia Polytechnic Inst. and State Univ.
2009-03-03
This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both Runge-Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A global optimization strategy is used to find the most efficient schemes that have low storage requirements. Numerical results illustrate the theoretical findings.
Carrasco, Josep L
2010-09-01
The classical concordance correlation coefficient (CCC) to measure agreement among a set of observers assumes data to be distributed as normal and a linear relationship between the mean and the subject and observer effects. Here, the CCC is generalized to afford any distribution from the exponential family by means of the generalized linear mixed models (GLMMs) theory and applied to the case of overdispersed count data. An example of CD34+ cell count data is provided to show the applicability of the procedure. In the latter case, different CCCs are defined and applied to the data by changing the GLMM that fits the data. A simulation study is carried out to explore the behavior of the procedure with a small and moderate sample size.
Facial expression recognition with facial parts based sparse representation classifier
NASA Astrophysics Data System (ADS)
Zhi, Ruicong; Ruan, Qiuqi
2009-10-01
Facial expressions play important role in human communication. The understanding of facial expression is a basic requirement in the development of next generation human computer interaction systems. Researches show that the intrinsic facial features always hide in low dimensional facial subspaces. This paper presents facial parts based facial expression recognition system with sparse representation classifier. Sparse representation classifier exploits sparse representation to select face features and classify facial expressions. The sparse solution is obtained by solving l1 -norm minimization problem with constraint of linear combination equation. Experimental results show that sparse representation is efficient for facial expression recognition and sparse representation classifier obtain much higher recognition accuracies than other compared methods.
Sparse principal component analysis in medical shape modeling
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Volk, Wolfram; Suh, Joungsik
2013-12-01
The prediction of formability is one of the most important tasks in sheet metal process simulation. The common criterion in industrial applications is the Forming Limit Curve (FLC). The big advantage of FLCs is the easy interpretation of simulation or measurement data in combination with an ISO standard for the experimental determination. However, the conventional FLCs are limited to almost linear and unbroken strain paths, i.e. deformation histories with non-linear strain increments often lead to big differences in comparison to the prediction of the FLC. In this paper a phenomenological approach, the so-called Generalized Forming Limit Concept (GFLC), is introduced to predict the localized necking on arbitrary deformation history with unlimited number of non-linear strain increments. The GFLC consists of the conventional FLC and an acceptable number of experiments with bi-linear deformation history. With the idea of the new defined "Principle of Equivalent Pre-Forming" every deformation state built up of two linear strain increments can be transformed to a pure linear strain path with the same used formability of the material. In advance this procedure can be repeated as often as necessary. Therefore, it allows a robust and cost effective analysis of beginning instability in Finite Element Analysis (FEA) for arbitrary deformation histories. In addition, the GFLC is fully downwards compatible to the established FLC for pure linear strain paths.
A BGG-Type Resolution for Tensor Modules over General Linear Superalgebra
NASA Astrophysics Data System (ADS)
Cheng, Shun-Jen; Kwon, Jae-Hoon; Lam, Ngau
2008-04-01
We construct a Bernstein Gelfand Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra. As a consequence it follows that the unique maximal submodule of a corresponding reducible Kac module is generated by its proper singular vector.
Time series models based on generalized linear models: some further results.
Li, W K
1994-06-01
This paper considers the problem of extending the classical moving average models to time series with conditional distributions given by generalized linear models. These models have the advantage of easy construction and estimation. Statistical modelling techniques are also proposed. Some simulation results and an illustrative example are reported to illustrate the methodology. The models will have potential applications in longitudinal data analysis. PMID:8068850
ERIC Educational Resources Information Center
Battauz, Michela; Bellio, Ruggero
2011-01-01
This paper proposes a structural analysis for generalized linear models when some explanatory variables are measured with error and the measurement error variance is a function of the true variables. The focus is on latent variables investigated on the basis of questionnaires and estimated using item response theory models. Latent variable…
Estimation of Complex Generalized Linear Mixed Models for Measurement and Growth
ERIC Educational Resources Information Center
Jeon, Minjeong
2012-01-01
Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…
Regression Is a Univariate General Linear Model Subsuming Other Parametric Methods as Special Cases.
ERIC Educational Resources Information Center
Vidal, Sherry
Although the concept of the general linear model (GLM) has existed since the 1960s, other univariate analyses such as the t-test and the analysis of variance models have remained popular. The GLM produces an equation that minimizes the mean differences of independent variables as they are related to a dependent variable. From a computer printout…
Generalized model of double random phase encoding based on linear algebra
NASA Astrophysics Data System (ADS)
Nakano, Kazuya; Takeda, Masafumi; Suzuki, Hiroyuki; Yamaguchi, Masahiro
2013-01-01
We propose a generalized model for double random phase encoding (DRPE) based on linear algebra. We defined the DRPE procedure in six steps. The first three steps form an encryption procedure, while the later three steps make up a decryption procedure. We noted that the first (mapping) and second (transform) steps can be generalized. As an example of this generalization, we used 3D mapping and a transform matrix, which is a combination of a discrete cosine transform and two permutation matrices. Finally, we investigated the sensitivity of the proposed model to errors in the decryption key.
Implementing general quantum measurements on linear optical and solid-state qubits
NASA Astrophysics Data System (ADS)
Ota, Yukihiro; Ashhab, Sahel; Nori, Franco
2013-03-01
We show a systematic construction for implementing general measurements on a single qubit, including both strong (or projection) and weak measurements. We mainly focus on linear optical qubits. The present approach is composed of simple and feasible elements, i.e., beam splitters, wave plates, and polarizing beam splitters. We show how the parameters characterizing the measurement operators are controlled by the linear optical elements. We also propose a method for the implementation of general measurements in solid-state qubits. Furthermore, we show an interesting application of the general measurements, i.e., entanglement amplification. YO is partially supported by the SPDR Program, RIKEN. SA and FN acknowledge ARO, NSF grant No. 0726909, JSPS-RFBR contract No. 12-02-92100, Grant-in-Aid for Scientific Research (S), MEXT Kakenhi on Quantum Cybernetics, and the JSPS via its FIRST program.
Shen, Mouquan; Park, Ju H
2016-07-01
This paper addresses the H∞ filtering of continuous Markov jump linear systems with general transition probabilities and output quantization. S-procedure is employed to handle the adverse influence of the quantization and a new approach is developed to conquer the nonlinearity induced by uncertain and unknown transition probabilities. Then, sufficient conditions are presented to ensure the filtering error system to be stochastically stable with the prescribed performance requirement. Without specified structure imposed on introduced slack variables, a flexible filter design method is established in terms of linear matrix inequalities. The effectiveness of the proposed method is validated by a numerical example. PMID:27129765
NASA Technical Reports Server (NTRS)
Szyld, D. B.
1984-01-01
A brief description of the Model of the World Economy implemented at the Institute for Economic Analysis is presented, together with our experience in converting the software to vector code. For each time period, the model is reduced to a linear system of over 2000 variables. The matrix of coefficients has a bordered block diagonal structure, and we show how some of the matrix operations can be carried out on all diagonal blocks at once.
Tussupbayev, Samat; Govind, Niranjan; Lopata, Kenneth A.; Cramer, Christopher J.
2015-03-10
We assess the performance of real-time time-dependent density functional theory (RT-TDDFT) for the calculation of absorption spectra of 12 organic dye molecules relevant to photovoltaics and dye sensitized solar cells with 8 exchange-correlation functionals (3 traditional, 3 global hybrids, and 2 range-separated hybrids). We compare the calculations with traditional linear-response (LR) TDDFT. In addition, we demonstrate the efficacy of the RT-TDDFT approach to calculate wide absorption spectra of two large chromophores relevant to photovoltaics and molecular switches.
Local influence to detect influential data structures for generalized linear mixed models.
Ouwens, M J; Tan, F E; Berger, M P
2001-12-01
This article discusses the generalization of the local influence measures for normally distributed responses to local influence measures for generalized linear models with random effects. For these models, it is shown that the subject-oriented influence measure is a special case of the proposed observation-oriented influence measure. A two-step diagnostic procedure is proposed. The first step is to search for influential subjects. A search for influential observations is proposed as the second step. An illustration of a two-treatment, multiple-period crossover trial demonstrates the practical importance of the detection of influential observations in addition to the detection of influential subjects.
Enhancing Scalability of Sparse Direct Methods
Li, Xiaoye S.; Demmel, James; Grigori, Laura; Gu, Ming; Xia,Jianlin; Jardin, Steve; Sovinec, Carl; Lee, Lie-Quan
2007-07-23
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.
HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL SPARSE BINARY REGRESSION
Mukherjee, Rajarshi; Pillai, Natesh S.; Lin, Xihong
2015-01-01
In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a function of two components: a design matrix sparsity index and signal strength, each of which is a function of the sparsity of the alternative. For any alternative, if the design matrix sparsity index is too high, any test is asymptotically powerless irrespective of the magnitude of signal strength. For binary design matrices with the sparsity index that is not too high, our results are parallel to those in the Gaussian case. In this context, we derive detection boundaries for both dense and sparse regimes. For the dense regime, we show that the generalized likelihood ratio is rate optimal; for the sparse regime, we propose an extended Higher Criticism Test and show it is rate optimal and sharp. We illustrate the finite sample properties of the theoretical results using simulation studies. PMID:26246645
Fitting host-parasitoid models with CV2 > 1 using hierarchical generalized linear models.
Perry, J N; Noh, M S; Lee, Y; Alston, R D; Norowi, H M; Powell, W; Rennolls, K
2000-01-01
The powerful general Pacala-Hassell host-parasitoid model for a patchy environment, which allows host density-dependent heterogeneity (HDD) to be distinguished from between-patch, host density-independent heterogeneity (HDI), is reformulated within the class of the generalized linear model (GLM) family. This improves accessibility through the provision of general software within well-known statistical systems, and allows a rich variety of models to be formulated. Covariates such as age class, host density and abiotic factors may be included easily. For the case where there is no HDI, the formulation is a simple GLM. When there is HDI in addition to HDD, the formulation is a hierarchical generalized linear model. Two forms of HDI model are considered, both with between-patch variability: one has binomial variation within patches and one has extra-binomial, overdispersed variation within patches. Examples are given demonstrating parameter estimation with standard errors, and hypothesis testing. For one example given, the extra-binomial component of the HDI heterogeneity in parasitism is itself shown to be strongly density dependent. PMID:11416907
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
NASA Astrophysics Data System (ADS)
Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.; Noller, Johannes
2016-08-01
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ``Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.
Normality of raw data in general linear models: The most widespread myth in statistics
Kery, Marc; Hatfield, Jeff S.
2003-01-01
In years of statistical consulting for ecologists and wildlife biologists, by far the most common misconception we have come across has been the one about normality in general linear models. These comprise a very large part of the statistical models used in ecology and include t tests, simple and multiple linear regression, polynomial regression, and analysis of variance (ANOVA) and covariance (ANCOVA). There is a widely held belief that the normality assumption pertains to the raw data rather than to the model residuals. We suspect that this error may also occur in countless published studies, whenever the normality assumption is tested prior to analysis. This may lead to the use of nonparametric alternatives (if there are any), when parametric tests would indeed be appropriate, or to use of transformations of raw data, which may introduce hidden assumptions such as multiplicative effects on the natural scale in the case of log-transformed data. Our aim here is to dispel this myth. We very briefly describe relevant theory for two cases of general linear models to show that the residuals need to be normally distributed if tests requiring normality are to be used, such as t and F tests. We then give two examples demonstrating that the distribution of the response variable may be nonnormal, and yet the residuals are well behaved. We do not go into the issue of how to test normality; instead we display the distributions of response variables and residuals graphically.
Random generalized linear model: a highly accurate and interpretable ensemble predictor
2013-01-01
Background Ensemble predictors such as the random forest are known to have superior accuracy but their black-box predictions are difficult to interpret. In contrast, a generalized linear model (GLM) is very interpretable especially when forward feature selection is used to construct the model. However, forward feature selection tends to overfit the data and leads to low predictive accuracy. Therefore, it remains an important research goal to combine the advantages of ensemble predictors (high accuracy) with the advantages of forward regression modeling (interpretability). To address this goal several articles have explored GLM based ensemble predictors. Since limited evaluations suggested that these ensemble predictors were less accurate than alternative predictors, they have found little attention in the literature. Results Comprehensive evaluations involving hundreds of genomic data sets, the UCI machine learning benchmark data, and simulations are used to give GLM based ensemble predictors a new and careful look. A novel bootstrap aggregated (bagged) GLM predictor that incorporates several elements of randomness and instability (random subspace method, optional interaction terms, forward variable selection) often outperforms a host of alternative prediction methods including random forests and penalized regression models (ridge regression, elastic net, lasso). This random generalized linear model (RGLM) predictor provides variable importance measures that can be used to define a “thinned” ensemble predictor (involving few features) that retains excellent predictive accuracy. Conclusion RGLM is a state of the art predictor that shares the advantages of a random forest (excellent predictive accuracy, feature importance measures, out-of-bag estimates of accuracy) with those of a forward selected generalized linear model (interpretability). These methods are implemented in the freely available R software package randomGLM. PMID:23323760
Capelli bitableaux and Z-forms of general linear Lie superalgebras.
Brini, A; Teolis, A G
1990-01-01
The combinatorics of the enveloping algebra UQ(pl(L)) of the general linear Lie superalgebra of a finite dimensional Z2-graded Q-vector space is studied. Three non-equivalent Z-forms of UQ(pl(L)) are introduced: one of these Z-forms is a version of the Kostant Z-form and the others are Lie algebra analogs of Rota and Stein's straightening formulae for the supersymmetric algebra Super[L P] and for its dual Super[L* P*]. The method is based on an extension of Capelli's technique of variabili ausiliarie to algebras containing positively and negatively signed elements. PMID:11607048
LESS: a model-based classifier for sparse subspaces.
Veenman, Cor J; Tax, David M J
2005-09-01
In this paper, we specifically focus on high-dimensional data sets for which the number of dimensions is an order of magnitude higher than the number of objects. From a classifier design standpoint, such small sample size problems have some interesting challenges. The first challenge is to find, from all hyperplanes that separate the classes, a separating hyperplane which generalizes well for future data. A second important task is to determine which features are required to distinguish the classes. To attack these problems, we propose the LESS (Lowest Error in a Sparse Subspace) classifier that efficiently finds linear discriminants in a sparse subspace. In contrast with most classifiers for high-dimensional data sets, the LESS classifier incorporates a (simple) data model. Further, by means of a regularization parameter, the classifier establishes a suitable trade-off between subspace sparseness and classification accuracy. In the experiments, we show how LESS performs on several high-dimensional data sets and compare its performance to related state-of-the-art classifiers like, among others, linear ridge regression with the LASSO and the Support Vector Machine. It turns out that LESS performs competitively while using fewer dimensions.
Lo, Steson; Andrews, Sally
2015-01-01
Linear mixed-effect models (LMMs) are being increasingly widely used in psychology to analyse multi-level research designs. This feature allows LMMs to address some of the problems identified by Speelman and McGann (2013) about the use of mean data, because they do not average across individual responses. However, recent guidelines for using LMM to analyse skewed reaction time (RT) data collected in many cognitive psychological studies recommend the application of non-linear transformations to satisfy assumptions of normality. Uncritical adoption of this recommendation has important theoretical implications which can yield misleading conclusions. For example, Balota et al. (2013) showed that analyses of raw RT produced additive effects of word frequency and stimulus quality on word identification, which conflicted with the interactive effects observed in analyses of transformed RT. Generalized linear mixed-effect models (GLMM) provide a solution to this problem by satisfying normality assumptions without the need for transformation. This allows differences between individuals to be properly assessed, using the metric most appropriate to the researcher's theoretical context. We outline the major theoretical decisions involved in specifying a GLMM, and illustrate them by reanalysing Balota et al.'s datasets. We then consider the broader benefits of using GLMM to investigate individual differences. PMID:26300841
Digit Span is (mostly) related linearly to general intelligence: Every extra bit of span counts.
Gignac, Gilles E; Weiss, Lawrence G
2015-12-01
Historically, Digit Span has been regarded as a relatively poor indicator of general intellectual functioning (g). In fact, Wechsler (1958) contended that beyond an average level of Digit Span performance, there was little benefit to possessing a greater memory span. Although Wechsler's position does not appear to have ever been tested empirically, it does appear to have become clinical lore. Consequently, the purpose of this investigation was to test Wechsler's contention on the Wechsler Adult Intelligence Scale-Fourth Edition normative sample (N = 1,800; ages: 16 - 69). Based on linear and nonlinear contrast analyses of means, as well as linear and nonlinear bifactor model analyses, all 3 Digit Span indicators (LDSF, LDSB, and LDSS) were found to exhibit primarily linear associations with FSIQ/g. Thus, the commonly held position that Digit Span performance beyond an average level is not indicative of greater intellectual functioning was not supported. The results are discussed in light of the increasing evidence across multiple domains that memory span plays an important role in intellectual functioning.
Sparse pseudospectral approximation method
NASA Astrophysics Data System (ADS)
Constantine, Paul G.; Eldred, Michael S.; Phipps, Eric T.
2012-07-01
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two or three dimensions, a sparse grid numerical integration rule offers accuracy with a smaller node set compared to tensor product approximation. However, when using a sparse rule to approximately integrate these coefficients, one often finds unacceptable errors in the coefficients associated with higher degree polynomials. By reexamining Smolyak's algorithm and exploiting the connections between interpolation and projection in tensor product spaces, we construct a sparse pseudospectral approximation method that accurately reproduces the coefficients of basis functions that naturally correspond to the sparse grid integration rule. The compelling numerical results show that this is the proper way to use sparse grid integration rules for pseudospectral approximation.
Fomichev, S. V.; Becker, W.
2010-06-15
Both linear and nonlinear scattering and absorption of a laser pulse by spherical nanoclusters with free electrons and with a diffuse surface are considered in the collisionless hydrodynamics approximation. The developed model of forced collective motion of electrons confined to a cluster permits one consistently to introduce into the theory all the sources of nonlinearity, as well as the inhomogeneity of the cluster near its boundary. Two different perturbation theories corresponding to different laser intensity ranges are developed in this context, and both cold metal clusters and hot laser-heated or -ionized clusters are considered within the same approach. In the present article, after developing the full nonlinear model, the linear response to the laser field of the free-electron cluster with diffuse surface is investigated in detail, especially the properties of the linear Mie resonance (width and position). Under certain conditions, depending on the various cluster parameters secondary resonances are found. The properties of resonance-enhanced third-order harmonic generation and nonlinear laser absorption and their dependence on the shape of the diffuse surface will be presented separately.
The heritability of general cognitive ability increases linearly from childhood to young adulthood.
Haworth, C M A; Wright, M J; Luciano, M; Martin, N G; de Geus, E J C; van Beijsterveldt, C E M; Bartels, M; Posthuma, D; Boomsma, D I; Davis, O S P; Kovas, Y; Corley, R P; Defries, J C; Hewitt, J K; Olson, R K; Rhea, S-A; Wadsworth, S J; Iacono, W G; McGue, M; Thompson, L A; Hart, S A; Petrill, S A; Lubinski, D; Plomin, R
2010-11-01
Although common sense suggests that environmental influences increasingly account for individual differences in behavior as experiences accumulate during the course of life, this hypothesis has not previously been tested, in part because of the large sample sizes needed for an adequately powered analysis. Here we show for general cognitive ability that, to the contrary, genetic influence increases with age. The heritability of general cognitive ability increases significantly and linearly from 41% in childhood (9 years) to 55% in adolescence (12 years) and to 66% in young adulthood (17 years) in a sample of 11 000 pairs of twins from four countries, a larger sample than all previous studies combined. In addition to its far-reaching implications for neuroscience and molecular genetics, this finding suggests new ways of thinking about the interface between nature and nurture during the school years. Why, despite life's 'slings and arrows of outrageous fortune', do genetically driven differences increasingly account for differences in general cognitive ability? We suggest that the answer lies with genotype-environment correlation: as children grow up, they increasingly select, modify and even create their own experiences in part based on their genetic propensities. PMID:19488046
Linear stability of a generalized multi-anticipative car following model with time delays
NASA Astrophysics Data System (ADS)
Ngoduy, D.
2015-05-01
In traffic flow, the multi-anticipative driving behavior describes the reaction of a vehicle to the driving behavior of many vehicles in front where as the time delay is defined as a physiological parameter reflecting the period of time between perceiving a stimulus of leading vehicles and performing a relevant action such as acceleration or deceleration. A lot of effort has been undertaken to understand the effects of either multi-anticipative driving behavior or time delays on traffic flow dynamics. This paper is a first attempt to analytically investigate the dynamics of a generalized class of car-following models with multi-anticipative driving behavior and different time delays associated with such multi-anticipations. To this end, this paper puts forwards to deriving the (long-wavelength) linear stability condition of such a car-following model and study how the combination of different choices of multi-anticipations and time delays affects the instabilities of traffic flow with respect to a small perturbation. It is found that the effect of delays and multi-anticipations are model-dependent, that is, the destabilization effect of delays is suppressed by the stabilization effect of multi-anticipations. Moreover, the weight factor reflecting the distribution of the driver's sensing to the relative gaps of leading vehicles is less sensitive to the linear stability condition of traffic flow than the weight factor for the relative speed of those leading vehicles.
Fan, Yurui; Huang, Guohe; Veawab, Amornvadee
2012-01-01
In this study, a generalized fuzzy linear programming (GFLP) method was developed to deal with uncertainties expressed as fuzzy sets that exist in the constraints and objective function. A stepwise interactive algorithm (SIA) was advanced to solve GFLP model and generate solutions expressed as fuzzy sets. To demonstrate its application, the developed GFLP method was applied to a regional sulfur dioxide (SO2) control planning model to identify effective SO2 mitigation polices with a minimized system performance cost under uncertainty. The results were obtained to represent the amount of SO2 allocated to different control measures from different sources. Compared with the conventional interval-parameter linear programming (ILP) approach, the solutions obtained through GFLP were expressed as fuzzy sets, which can provide intervals for the decision variables and objective function, as well as related possibilities. Therefore, the decision makers can make a tradeoff between model stability and the plausibility based on solutions obtained through GFLP and then identify desired policies for SO2-emission control under uncertainty.
NASA Astrophysics Data System (ADS)
Silbey, R.; Munn, R. W.
1980-02-01
An improved general theory of electronic transport in molecular crystals with local linear electron-phonon coupling is presented. It is valid for arbitrary electronic and phonon bandwidths and for arbitrary electron-phonon coupling strength, yielding small-polaron theory for narrow electronic bands and strong coupling, and semiconductor theory for wide electronic bands and weak coupling. Detailed results are derived for electronic excitations fully clothed with phonons and having a bandwidth no larger than the phonon frequency; the electronic and phonon densities of states are taken as Gaussian for simplicity. The dependence of the diffusion coefficient on temperature and on the other parameters is analyzed thoroughly. The calculated behavior provides a rational interpretation of observed trends in the magnitude and temperature dependence of charge-carrier drift mobilities in molecular crystals.
Generalized Linear Models for Identifying Predictors of the Evolutionary Diffusion of Viruses
Beard, Rachel; Magee, Daniel; Suchard, Marc A.; Lemey, Philippe; Scotch, Matthew
2014-01-01
Bioinformatics and phylogeography models use viral sequence data to analyze spread of epidemics and pandemics. However, few of these models have included analytical methods for testing whether certain predictors such as population density, rates of disease migration, and climate are drivers of spatial spread. Understanding the specific factors that drive spatial diffusion of viruses is critical for targeting public health interventions and curbing spread. In this paper we describe the application and evaluation of a model that integrates demographic and environmental predictors with molecular sequence data. The approach parameterizes evolutionary spread of RNA viruses as a generalized linear model (GLM) within a Bayesian inference framework using Markov chain Monte Carlo (MCMC). We evaluate this approach by reconstructing the spread of H5N1 in Egypt while assessing the impact of individual predictors on evolutionary diffusion of the virus. PMID:25717395
Solving the Linear Balance Equation on the Globe as a Generalized Inverse Problem
NASA Technical Reports Server (NTRS)
Lu, Huei-Iin; Robertson, Franklin R.
1999-01-01
A generalized (pseudo) inverse technique was developed to facilitate a better understanding of the numerical effects of tropical singularities inherent in the spectral linear balance equation (LBE). Depending upon the truncation, various levels of determinancy are manifest. The traditional fully-determined (FD) systems give rise to a strong response, while the under-determined (UD) systems yield a weak response to the tropical singularities. The over-determined (OD) systems result in a modest response and a large residual in the tropics. The FD and OD systems can be alternatively solved by the iterative method. Differences in the solutions of an UD system exist between the inverse technique and the iterative method owing to the non- uniqueness of the problem. A realistic balanced wind was obtained by solving the principal components of the spectral LBE in terms of vorticity in an intermediate resolution. Improved solutions were achieved by including the singular-component solutions which best fit the observed wind data.
NASA Astrophysics Data System (ADS)
Zhang, Ya; Tian, Yu-Ping
2010-11-01
This article studies the consensus problem for a group of sampled-data general linear dynamical agents over random communication networks. Dynamic output feedback protocols are applied to solve the consensus problem. When the sampling period is sufficiently small, it is shown that as long as the mean topology has globally reachable nodes, the mean square consensus can be achieved by selecting protocol parameters so that n - 1 specified subsystems are simultaneously stabilised. However, when the sampling period is comparatively large, it is revealed that differing from low-order integrator multi-agent systems the consensus problem may be unsolvable. By using the hybrid dynamical system theory, an allowable upper bound of sampling period is further proposed. Two approaches to designing protocols are also provided. Simulations are given to illustrate the validity of the proposed approaches.
Dose-shaping using targeted sparse optimization
Sayre, George A.; Ruan, Dan
2013-07-15
Purpose: Dose volume histograms (DVHs) are common tools in radiation therapy treatment planning to characterize plan quality. As statistical metrics, DVHs provide a compact summary of the underlying plan at the cost of losing spatial information: the same or similar dose-volume histograms can arise from substantially different spatial dose maps. This is exactly the reason why physicians and physicists scrutinize dose maps even after they satisfy all DVH endpoints numerically. However, up to this point, little has been done to control spatial phenomena, such as the spatial distribution of hot spots, which has significant clinical implications. To this end, the authors propose a novel objective function that enables a more direct tradeoff between target coverage, organ-sparing, and planning target volume (PTV) homogeneity, and presents our findings from four prostate cases, a pancreas case, and a head-and-neck case to illustrate the advantages and general applicability of our method.Methods: In designing the energy minimization objective (E{sub tot}{sup sparse}), the authors utilized the following robust cost functions: (1) an asymmetric linear well function to allow differential penalties for underdose, relaxation of prescription dose, and overdose in the PTV; (2) a two-piece linear function to heavily penalize high dose and mildly penalize low and intermediate dose in organs-at risk (OARs); and (3) a total variation energy, i.e., the L{sub 1} norm applied to the first-order approximation of the dose gradient in the PTV. By minimizing a weighted sum of these robust costs, general conformity to dose prescription and dose-gradient prescription is achieved while encouraging prescription violations to follow a Laplace distribution. In contrast, conventional quadratic objectives are associated with a Gaussian distribution of violations, which is less forgiving to large violations of prescription than the Laplace distribution. As a result, the proposed objective E{sub tot
Lou, Xinyuan; Wu, Ping; Zhang, Anping; Zhang, Ruoqing; Tang, Yawen
2015-09-16
Herein, we rationally design and construct a novel type of sparsely studded noble-metal nanocrystals inside graphene hollow sphere network (abbreviated as noble-metal@G HSN) through an electrostatic-attraction-directed self-assembly approach. The formation of Pt@G and Pd@G hollow sphere networks have been illustrated as examples using SiO2 spheres as templates. Moreover, the electrocatalytic performance of the Pt@G HSN for methanol oxidation reaction has been examined as a proof-of-concept demonstration of the compositional and structural superiorities of noble-metal@G HSN toward electrocatalyst utilization. The as-prepared Pt@G HSN manifests higher catalytic activity and markedly enhanced long-term durability in comparison with commercial Pt/C catalyst. PMID:26305582
Unification of the general non-linear sigma model and the Virasoro master equation
Boer, J. de; Halpern, M.B. |
1997-06-01
The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affinie Lie algebra) of the WZW model, while the einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal field theories, together with a presumable large class of new conformal field theories. The basic idea is to consider spin-two operators of the form L{sub ij}{partial_derivative}x{sup i}{partial_derivative}x{sup j} in the background of a general sigma model. The requirement that these operators satisfy the Virasoro algebra leads to a set of equations called the unified Einstein-Virasoro master equation, in which the spin-two spacetime field L{sub ij} cuples to the usual spacetime fields of the sigma model. The one-loop form of this unified system is presented, and some of its algebraic and geometric properties are discussed.
On a general theory for compressing process and aeroacoustics: linear analysis
NASA Astrophysics Data System (ADS)
Mao, F.; Shi, Y. P.; Wu, J. Z.
2010-06-01
Of the three mutually coupled fundamental processes (shearing, compressing, and thermal) in a general fluid motion, only the general formulation for the compressing process and a subprocess of it, the subject of aeroacoustics, as well as their physical coupling with shearing and thermal processes, have so far not reached a consensus. This situation has caused difficulties for various in-depth complex multiprocess flow diagnosis, optimal configuration design, and flow/noise control. As the first step toward the desired formulation in fully nonlinear regime, this paper employs the operator factorization method to revisit the analytic linear theories of the fundamental processes and their decomposition, especially the further splitting of compressing process into acoustic and entropy modes, developed in 1940s-1980s. The flow treated here is small disturbances of a compressible, viscous, and heat-conducting polytropic gas in an unbounded domain with arbitrary source of mass, external body force, and heat addition. Previous results are thereby revised and extended to a complete and unified theory. The theory provides a necessary basis and valuable guidance for developing corresponding nonlinear theory by clarifying certain basic issues, such as the proper choice of characteristic variables of compressing process and the feature of their governing equations.
Generalized linear transport theory in dilute neutral gases and dispersion relation of sound waves.
Bendib, A; Bendib-Kalache, K; Gombert, M M; Imadouchene, N
2006-10-01
The transport processes in dilute neutral gases are studied by using the kinetic equation with a collision relaxation model that meets all conservation requirements. The kinetic equation is solved keeping the whole anisotropic part of the distribution function with the use of the continued fractions. The conservative laws of the collision operator are taken into account with the projection operator techniques. The generalized heat flux and stress tensor are calculated in the linear approximation, as functions of the lower moments, i.e., the density, the flow velocity and the temperature. The results obtained are valid for arbitrary collision frequency nu with the respect to kv(t) and the characteristic frequency omega, where k(-1) is the characteristic length scale of the system and v(t) is the thermal velocity. The transport coefficients constitute accurate closure relations for the generalized hydrodynamic equations. An application to the dispersion and the attenuation of sound waves in the whole collisionality regime is presented. The results obtained are in very good agreement with the experimental data. PMID:17155048
Canary, Jana D; Blizzard, Leigh; Barry, Ronald P; Hosmer, David W; Quinn, Stephen J
2016-05-01
Generalized linear models (GLM) with a canonical logit link function are the primary modeling technique used to relate a binary outcome to predictor variables. However, noncanonical links can offer more flexibility, producing convenient analytical quantities (e.g., probit GLMs in toxicology) and desired measures of effect (e.g., relative risk from log GLMs). Many summary goodness-of-fit (GOF) statistics exist for logistic GLM. Their properties make the development of GOF statistics relatively straightforward, but it can be more difficult under noncanonical links. Although GOF tests for logistic GLM with continuous covariates (GLMCC) have been applied to GLMCCs with log links, we know of no GOF tests in the literature specifically developed for GLMCCs that can be applied regardless of link function chosen. We generalize the Tsiatis GOF statistic originally developed for logistic GLMCCs, (TG), so that it can be applied under any link function. Further, we show that the algebraically related Hosmer-Lemeshow (HL) and Pigeon-Heyse (J(2) ) statistics can be applied directly. In a simulation study, TG, HL, and J(2) were used to evaluate the fit of probit, log-log, complementary log-log, and log models, all calculated with a common grouping method. The TG statistic consistently maintained Type I error rates, while those of HL and J(2) were often lower than expected if terms with little influence were included. Generally, the statistics had similar power to detect an incorrect model. An exception occurred when a log GLMCC was incorrectly fit to data generated from a logistic GLMCC. In this case, TG had more power than HL or J(2) . PMID:26584470
Canary, Jana D; Blizzard, Leigh; Barry, Ronald P; Hosmer, David W; Quinn, Stephen J
2016-05-01
Generalized linear models (GLM) with a canonical logit link function are the primary modeling technique used to relate a binary outcome to predictor variables. However, noncanonical links can offer more flexibility, producing convenient analytical quantities (e.g., probit GLMs in toxicology) and desired measures of effect (e.g., relative risk from log GLMs). Many summary goodness-of-fit (GOF) statistics exist for logistic GLM. Their properties make the development of GOF statistics relatively straightforward, but it can be more difficult under noncanonical links. Although GOF tests for logistic GLM with continuous covariates (GLMCC) have been applied to GLMCCs with log links, we know of no GOF tests in the literature specifically developed for GLMCCs that can be applied regardless of link function chosen. We generalize the Tsiatis GOF statistic originally developed for logistic GLMCCs, (TG), so that it can be applied under any link function. Further, we show that the algebraically related Hosmer-Lemeshow (HL) and Pigeon-Heyse (J(2) ) statistics can be applied directly. In a simulation study, TG, HL, and J(2) were used to evaluate the fit of probit, log-log, complementary log-log, and log models, all calculated with a common grouping method. The TG statistic consistently maintained Type I error rates, while those of HL and J(2) were often lower than expected if terms with little influence were included. Generally, the statistics had similar power to detect an incorrect model. An exception occurred when a log GLMCC was incorrectly fit to data generated from a logistic GLMCC. In this case, TG had more power than HL or J(2) .
Sparse extreme learning machine for classification.
Bai, Zuo; Huang, Guang-Bin; Wang, Danwei; Wang, Han; Westover, M Brandon
2014-10-01
Extreme learning machine (ELM) was initially proposed for single-hidden-layer feedforward neural networks (SLFNs). In the hidden layer (feature mapping), nodes are randomly generated independently of training data. Furthermore, a unified ELM was proposed, providing a single framework to simplify and unify different learning methods, such as SLFNs, least square support vector machines, proximal support vector machines, and so on. However, the solution of unified ELM is dense, and thus, usually plenty of storage space and testing time are required for large-scale applications. In this paper, a sparse ELM is proposed as an alternative solution for classification, reducing storage space and testing time. In addition, unified ELM obtains the solution by matrix inversion, whose computational complexity is between quadratic and cubic with respect to the training size. It still requires plenty of training time for large-scale problems, even though it is much faster than many other traditional methods. In this paper, an efficient training algorithm is specifically developed for sparse ELM. The quadratic programming problem involved in sparse ELM is divided into a series of smallest possible sub-problems, each of which are solved analytically. Compared with SVM, sparse ELM obtains better generalization performance with much faster training speed. Compared with unified ELM, sparse ELM achieves similar generalization performance for binary classification applications, and when dealing with large-scale binary classification problems, sparse ELM realizes even faster training speed than unified ELM. PMID:25222727
Validity of tests under covariate-adaptive biased coin randomization and generalized linear models.
Shao, Jun; Yu, Xinxin
2013-12-01
Some covariate-adaptive randomization methods have been used in clinical trials for a long time, but little theoretical work has been done about testing hypotheses under covariate-adaptive randomization until Shao et al. (2010) who provided a theory with detailed discussion for responses under linear models. In this article, we establish some asymptotic results for covariate-adaptive biased coin randomization under generalized linear models with possibly unknown link functions. We show that the simple t-test without using any covariate is conservative under covariate-adaptive biased coin randomization in terms of its Type I error rate, and that a valid test using the bootstrap can be constructed. This bootstrap test, utilizing covariates in the randomization scheme, is shown to be asymptotically as efficient as Wald's test correctly using covariates in the analysis. Thus, the efficiency loss due to not using covariates in the analysis can be recovered by utilizing covariates in covariate-adaptive biased coin randomization. Our theory is illustrated with two most popular types of discrete outcomes, binary responses and event counts under the Poisson model, and exponentially distributed continuous responses. We also show that an alternative simple test without using any covariate under the Poisson model has an inflated Type I error rate under simple randomization, but is valid under covariate-adaptive biased coin randomization. Effects on the validity of tests due to model misspecification is also discussed. Simulation studies about the Type I errors and powers of several tests are presented for both discrete and continuous responses. PMID:23848580
Power Calculations for General Linear Multivariate Models Including Repeated Measures Applications.
Muller, Keith E; Lavange, Lisa M; Ramey, Sharon Landesman; Ramey, Craig T
1992-12-01
Recently developed methods for power analysis expand the options available for study design. We demonstrate how easily the methods can be applied by (1) reviewing their formulation and (2) describing their application in the preparation of a particular grant proposal. The focus is a complex but ubiquitous setting: repeated measures in a longitudinal study. Describing the development of the research proposal allows demonstrating the steps needed to conduct an effective power analysis. Discussion of the example also highlights issues that typically must be considered in designing a study. First, we discuss the motivation for using detailed power calculations, focusing on multivariate methods in particular. Second, we survey available methods for the general linear multivariate model (GLMM) with Gaussian errors and recommend those based on F approximations. The treatment includes coverage of the multivariate and univariate approaches to repeated measures, MANOVA, ANOVA, multivariate regression, and univariate regression. Third, we describe the design of the power analysis for the example, a longitudinal study of a child's intellectual performance as a function of mother's estimated verbal intelligence. Fourth, we present the results of the power calculations. Fifth, we evaluate the tradeoffs in using reduced designs and tests to simplify power calculations. Finally, we discuss the benefits and costs of power analysis in the practice of statistics. We make three recommendations: Align the design and hypothesis of the power analysis with the planned data analysis, as best as practical.Embed any power analysis in a defensible sensitivity analysis.Have the extent of the power analysis reflect the ethical, scientific, and monetary costs. We conclude that power analysis catalyzes the interaction of statisticians and subject matter specialists. Using the recent advances for power analysis in linear models can further invigorate the interaction. PMID:24790282
Sparse matrix-vector multiplication on a reconfigurable supercomputer
Dubois, David H; Dubois, Andrew J; Boorman, Thomas M; Connor, Carolyn M; Poole, Steve
2008-01-01
Double precision floating point Sparse Matrix-Vector Multiplication (SMVM) is a critical computational kernel used in iterative solvers for systems of sparse linear equations. The poor data locality exhibited by sparse matrices along with the high memory bandwidth requirements of SMVM result in poor performance on general purpose processors. Field Programmable Gate Arrays (FPGAs) offer a possible alternative with their customizable and application-targeted memory sub-system and processing elements. In this work we investigate two separate implementations of the SMVM on an SRC-6 MAPStation workstation. The first implementation investigates the peak performance capability, while the second implementation balances the amount of instantiated logic with the available sustained bandwidth of the FPGA subsystem. Both implementations yield the same sustained performance with the second producing a much more efficient solution. The metrics of processor and application balance are introduced to help provide some insight into the efficiencies of the FPGA and CPU based solutions explicitly showing the tight coupling of the available bandwidth to peak floating point performance. Due to the FPGA's ability to balance the amount of implemented logic to the available memory bandwidth it can provide a much more efficient solution. Finally, making use of the lessons learned implementing the SMVM, we present an fully implemented nonpreconditioned Conjugate Gradient Algorithm utilizing the second SMVM design.
Development and validation of a general purpose linearization program for rigid aircraft models
NASA Technical Reports Server (NTRS)
Duke, E. L.; Antoniewicz, R. F.
1985-01-01
A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.
Development and validation of a general purpose linearization program for rigid aircraft models
NASA Technical Reports Server (NTRS)
Duke, E. L.; Antoniewicz, R. F.
1985-01-01
This paper discusses a FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high-performance aircraft.
NASA Astrophysics Data System (ADS)
Elliott, J.; de Souza, R. S.; Krone-Martins, A.; Cameron, E.; Ishida, E. E. O.; Hilbe, J.
2015-04-01
Machine learning techniques offer a precious tool box for use within astronomy to solve problems involving so-called big data. They provide a means to make accurate predictions about a particular system without prior knowledge of the underlying physical processes of the data. In this article, and the companion papers of this series, we present the set of Generalized Linear Models (GLMs) as a fast alternative method for tackling general astronomical problems, including the ones related to the machine learning paradigm. To demonstrate the applicability of GLMs to inherently positive and continuous physical observables, we explore their use in estimating the photometric redshifts of galaxies from their multi-wavelength photometry. Using the gamma family with a log link function we predict redshifts from the PHoto-z Accuracy Testing simulated catalogue and a subset of the Sloan Digital Sky Survey from Data Release 10. We obtain fits that result in catastrophic outlier rates as low as ∼1% for simulated and ∼2% for real data. Moreover, we can easily obtain such levels of precision within a matter of seconds on a normal desktop computer and with training sets that contain merely thousands of galaxies. Our software is made publicly available as a user-friendly package developed in Python, R and via an interactive web application. This software allows users to apply a set of GLMs to their own photometric catalogues and generates publication quality plots with minimum effort. By facilitating their ease of use to the astronomical community, this paper series aims to make GLMs widely known and to encourage their implementation in future large-scale projects, such as the Large Synoptic Survey Telescope.
Geedipally, Srinivas Reddy; Lord, Dominique; Dhavala, Soma Sekhar
2012-03-01
There has been a considerable amount of work devoted by transportation safety analysts to the development and application of new and innovative models for analyzing crash data. One important characteristic about crash data that has been documented in the literature is related to datasets that contained a large amount of zeros and a long or heavy tail (which creates highly dispersed data). For such datasets, the number of sites where no crash is observed is so large that traditional distributions and regression models, such as the Poisson and Poisson-gamma or negative binomial (NB) models cannot be used efficiently. To overcome this problem, the NB-Lindley (NB-L) distribution has recently been introduced for analyzing count data that are characterized by excess zeros. The objective of this paper is to document the application of a NB generalized linear model with Lindley mixed effects (NB-L GLM) for analyzing traffic crash data. The study objective was accomplished using simulated and observed datasets. The simulated dataset was used to show the general performance of the model. The model was then applied to two datasets based on observed data. One of the dataset was characterized by a large amount of zeros. The NB-L GLM was compared with the NB and zero-inflated models. Overall, the research study shows that the NB-L GLM not only offers superior performance over the NB and zero-inflated models when datasets are characterized by a large number of zeros and a long tail, but also when the crash dataset is highly dispersed. PMID:22269508
Generalized Jeans' Escape of Pick-Up Ions in Quasi-Linear Relaxation
NASA Technical Reports Server (NTRS)
Moore, T. E.; Khazanov, G. V.
2011-01-01
Jeans escape is a well-validated formulation of upper atmospheric escape that we have generalized to estimate plasma escape from ionospheres. It involves the computation of the parts of particle velocity space that are unbound by the gravitational potential at the exobase, followed by a calculation of the flux carried by such unbound particles as they escape from the potential well. To generalize this approach for ions, we superposed an electrostatic ambipolar potential and a centrifugal potential, for motions across and along a divergent magnetic field. We then considered how the presence of superthermal electrons, produced by precipitating auroral primary electrons, controls the ambipolar potential. We also showed that the centrifugal potential plays a small role in controlling the mass escape flux from the terrestrial ionosphere. We then applied the transverse ion velocity distribution produced when ions, picked up by supersonic (i.e., auroral) ionospheric convection, relax via quasi-linear diffusion, as estimated for cometary comas [1]. The results provide a theoretical basis for observed ion escape response to electromagnetic and kinetic energy sources. They also suggest that super-sonic but sub-Alfvenic flow, with ion pick-up, is a unique and important regime of ion-neutral coupling, in which plasma wave-particle interactions are driven by ion-neutral collisions at densities for which the collision frequency falls near or below the gyro-frequency. As another possible illustration of this process, the heliopause ribbon discovered by the IBEX mission involves interactions between the solar wind ions and the interstellar neutral gas, in a regime that may be analogous [2].
Sparse distributed memory overview
NASA Technical Reports Server (NTRS)
Raugh, Mike
1990-01-01
The Sparse Distributed Memory (SDM) project is investigating the theory and applications of massively parallel computing architecture, called sparse distributed memory, that will support the storage and retrieval of sensory and motor patterns characteristic of autonomous systems. The immediate objectives of the project are centered in studies of the memory itself and in the use of the memory to solve problems in speech, vision, and robotics. Investigation of methods for encoding sensory data is an important part of the research. Examples of NASA missions that may benefit from this work are Space Station, planetary rovers, and solar exploration. Sparse distributed memory offers promising technology for systems that must learn through experience and be capable of adapting to new circumstances, and for operating any large complex system requiring automatic monitoring and control. Sparse distributed memory is a massively parallel architecture motivated by efforts to understand how the human brain works. Sparse distributed memory is an associative memory, able to retrieve information from cues that only partially match patterns stored in the memory. It is able to store long temporal sequences derived from the behavior of a complex system, such as progressive records of the system's sensory data and correlated records of the system's motor controls.
Fast inference in generalized linear models via expected log-likelihoods.
Ramirez, Alexandro D; Paninski, Liam
2014-04-01
Generalized linear models play an essential role in a wide variety of statistical applications. This paper discusses an approximation of the likelihood in these models that can greatly facilitate computation. The basic idea is to replace a sum that appears in the exact log-likelihood by an expectation over the model covariates; the resulting "expected log-likelihood" can in many cases be computed significantly faster than the exact log-likelihood. In many neuroscience experiments the distribution over model covariates is controlled by the experimenter and the expected log-likelihood approximation becomes particularly useful; for example, estimators based on maximizing this expected log-likelihood (or a penalized version thereof) can often be obtained with orders of magnitude computational savings compared to the exact maximum likelihood estimators. A risk analysis establishes that these maximum EL estimators often come with little cost in accuracy (and in some cases even improved accuracy) compared to standard maximum likelihood estimates. Finally, we find that these methods can significantly decrease the computation time of marginal likelihood calculations for model selection and of Markov chain Monte Carlo methods for sampling from the posterior parameter distribution. We illustrate our results by applying these methods to a computationally-challenging dataset of neural spike trains obtained via large-scale multi-electrode recordings in the primate retina.
Garcia, J M; Teodoro, F; Cerdeira, R; Coelho, L M R; Kumar, Prashant; Carvalho, M G
2016-09-01
A methodology to predict PM10 concentrations in urban outdoor environments is developed based on the generalized linear models (GLMs). The methodology is based on the relationship developed between atmospheric concentrations of air pollutants (i.e. CO, NO2, NOx, VOCs, SO2) and meteorological variables (i.e. ambient temperature, relative humidity (RH) and wind speed) for a city (Barreiro) of Portugal. The model uses air pollution and meteorological data from the Portuguese monitoring air quality station networks. The developed GLM considers PM10 concentrations as a dependent variable, and both the gaseous pollutants and meteorological variables as explanatory independent variables. A logarithmic link function was considered with a Poisson probability distribution. Particular attention was given to cases with air temperatures both below and above 25°C. The best performance for modelled results against the measured data was achieved for the model with values of air temperature above 25°C compared with the model considering all ranges of air temperatures and with the model considering only temperature below 25°C. The model was also tested with similar data from another Portuguese city, Oporto, and results found to behave similarly. It is concluded that this model and the methodology could be adopted for other cities to predict PM10 concentrations when these data are not available by measurements from air quality monitoring stations or other acquisition means. PMID:26839052
Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
Bellini, Emilio; Sawicki, Ignacy E-mail: ignacy.sawicki@outlook.com
2014-07-01
We present a turnkey solution, ready for implementation in numerical codes, for the study of linear structure formation in general scalar-tensor models involving a single universally coupled scalar field. We show that the totality of cosmological information on the gravitational sector can be compressed — without any redundancy — into five independent and arbitrary functions of time only and one constant. These describe physical properties of the universe: the observable background expansion history, fractional matter density today, and four functions of time describing the properties of the dark energy. We show that two of those dark-energy property functions control the existence of anisotropic stress, the other two — dark-energy clustering, both of which are can be scale-dependent. All these properties can in principle be measured, but no information on the underlying theory of acceleration beyond this can be obtained. We present a translation between popular models of late-time acceleration (e.g. perfect fluids, f(R), kinetic gravity braiding, galileons), as well as the effective field theory framework, and our formulation. In this way, implementing this formulation numerically would give a single tool which could consistently test the majority of models of late-time acceleration heretofore proposed.
Use of the generalized linear models in data related to dental caries index.
Javali, S B; Pandit, Parameshwar V
2007-01-01
The aim of this study is to encourage and initiate the application of generalized linear models (GLMs) in the analysis of the covariates of decayed, missing, and filled teeth (DMFT) index data, which is not necessarily normally distributed. GLMs can be performed assuming underlying many distributions; in fact Poisson distribution with log built-in link function and binomial distribution with Logit and Probit built-in link functions are considered. The Poisson model is used for modeling the DMFT index data and the Logit and Probit models are employed to model the dichotomous outcome of DMFT = 0 and DMFT not equal to 0 (caries free/caries present). The data comprised 7188 subjects aged 18-30 years from the study on the oral health status of Karnataka state conducted by SDM College of Dental Sciences and Hospital, Dharwad, Karnataka, India. The Poisson model and binomial models (Logit and Probit) displayed dissimilarity in the outcome of results at 5% level of significance ( P <0.05). The binomial models were a poor fit, whereas the Poisson model showed a good fit for the DMFT index data. Therefore, a suitable modeling approach for DMFT index data is to use a Poisson model for the DMFT response and a binomial model for the caries free and caries present (DMFT = 0 and DMFT not equal to 0). These GLMs allow separate estimation of those covariates which influence the magnitude of caries. PMID:17938491
Garcia, J M; Teodoro, F; Cerdeira, R; Coelho, L M R; Kumar, Prashant; Carvalho, M G
2016-09-01
A methodology to predict PM10 concentrations in urban outdoor environments is developed based on the generalized linear models (GLMs). The methodology is based on the relationship developed between atmospheric concentrations of air pollutants (i.e. CO, NO2, NOx, VOCs, SO2) and meteorological variables (i.e. ambient temperature, relative humidity (RH) and wind speed) for a city (Barreiro) of Portugal. The model uses air pollution and meteorological data from the Portuguese monitoring air quality station networks. The developed GLM considers PM10 concentrations as a dependent variable, and both the gaseous pollutants and meteorological variables as explanatory independent variables. A logarithmic link function was considered with a Poisson probability distribution. Particular attention was given to cases with air temperatures both below and above 25°C. The best performance for modelled results against the measured data was achieved for the model with values of air temperature above 25°C compared with the model considering all ranges of air temperatures and with the model considering only temperature below 25°C. The model was also tested with similar data from another Portuguese city, Oporto, and results found to behave similarly. It is concluded that this model and the methodology could be adopted for other cities to predict PM10 concentrations when these data are not available by measurements from air quality monitoring stations or other acquisition means.
NASA Astrophysics Data System (ADS)
García-Díaz, J. Carlos
2009-11-01
Fault detection and diagnosis is an important problem in process engineering. Process equipments are subject to malfunctions during operation. Galvanized steel is a value added product, furnishing effective performance by combining the corrosion resistance of zinc with the strength and formability of steel. Fault detection and diagnosis is an important problem in continuous hot dip galvanizing and the increasingly stringent quality requirements in automotive industry has also demanded ongoing efforts in process control to make the process more robust. When faults occur, they change the relationship among these observed variables. This work compares different statistical regression models proposed in the literature for estimating the quality of galvanized steel coils on the basis of short time histories. Data for 26 batches were available. Five variables were selected for monitoring the process: the steel strip velocity, four bath temperatures and bath level. The entire data consisting of 48 galvanized steel coils was divided into sets. The first training data set was 25 conforming coils and the second data set was 23 nonconforming coils. Logistic regression is a modeling tool in which the dependent variable is categorical. In most applications, the dependent variable is binary. The results show that the logistic generalized linear models do provide good estimates of quality coils and can be useful for quality control in manufacturing process.
Master equation solutions in the linear regime of characteristic formulation of general relativity
NASA Astrophysics Data System (ADS)
Cedeño M., C. E.; de Araujo, J. C. N.
2015-12-01
From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and Mädler, for a Minkowski's background, were able to show that it is possible to derive a fourth order ordinary differential equation, called master equation, for the J metric variable of the Bondi-Sachs metric. Once β , another Bondi-Sachs potential, is obtained from the field equations, and J is obtained from the master equation, the other metric variables are solved integrating directly the rest of the field equations. In the past, the master equation was solved for the first multipolar terms, for both the Minkowski's and Schwarzschild's backgrounds. Also, Mädler recently reported a generalisation of the exact solutions to the linearised field equations when a Minkowski's background is considered, expressing the master equation family of solutions for the vacuum in terms of Bessel's functions of the first and the second kind. Here, we report new solutions to the master equation for any multipolar moment l , with and without matter sources in terms only of the first kind Bessel's functions for the Minkowski, and in terms of the Confluent Heun's functions (Generalised Hypergeometric) for radiative (nonradiative) case in the Schwarzschild's background. We particularize our families of solutions for the known cases for l =2 reported previously in the literature and find complete agreement, showing the robustness of our results.
Fast inference in generalized linear models via expected log-likelihoods
Ramirez, Alexandro D.; Paninski, Liam
2015-01-01
Generalized linear models play an essential role in a wide variety of statistical applications. This paper discusses an approximation of the likelihood in these models that can greatly facilitate computation. The basic idea is to replace a sum that appears in the exact log-likelihood by an expectation over the model covariates; the resulting “expected log-likelihood” can in many cases be computed significantly faster than the exact log-likelihood. In many neuroscience experiments the distribution over model covariates is controlled by the experimenter and the expected log-likelihood approximation becomes particularly useful; for example, estimators based on maximizing this expected log-likelihood (or a penalized version thereof) can often be obtained with orders of magnitude computational savings compared to the exact maximum likelihood estimators. A risk analysis establishes that these maximum EL estimators often come with little cost in accuracy (and in some cases even improved accuracy) compared to standard maximum likelihood estimates. Finally, we find that these methods can significantly decrease the computation time of marginal likelihood calculations for model selection and of Markov chain Monte Carlo methods for sampling from the posterior parameter distribution. We illustrate our results by applying these methods to a computationally-challenging dataset of neural spike trains obtained via large-scale multi-electrode recordings in the primate retina. PMID:23832289
Assessment of cross-frequency coupling with confidence using generalized linear models
Kramer, M. A.; Eden, U. T.
2013-01-01
Background Brain voltage activity displays distinct neuronal rhythms spanning a wide frequency range. How rhythms of different frequency interact – and the function of these interactions – remains an active area of research. Many methods have been proposed to assess the interactions between different frequency rhythms, in particular measures that characterize the relationship between the phase of a low frequency rhythm and the amplitude envelope of a high frequency rhythm. However, an optimal analysis method to assess this cross-frequency coupling (CFC) does not yet exist. New Method Here we describe a new procedure to assess CFC that utilizes the generalized linear modeling (GLM) framework. Results We illustrate the utility of this procedure in three synthetic examples. The proposed GLM-CFC procedure allows a rapid and principled assessment of CFC with confidence bounds, scales with the intensity of the CFC, and accurately detects biphasic coupling. Comparison with Existing Methods Compared to existing methods, the proposed GLM-CFC procedure is easily interpretable, possesses confidence intervals that are easy and efficient to compute, and accurately detects biphasic coupling. Conclusions The GLM-CFC statistic provides a method for accurate and statistically rigorous assessment of CFC. PMID:24012829
Yock, Adam D. Kudchadker, Rajat J.; Rao, Arvind; Dong, Lei; Beadle, Beth M.; Garden, Adam S.; Court, Laurence E.
2014-05-15
Purpose: The purpose of this work was to develop and evaluate the accuracy of several predictive models of variation in tumor volume throughout the course of radiation therapy. Methods: Nineteen patients with oropharyngeal cancers were imaged daily with CT-on-rails for image-guided alignment per an institutional protocol. The daily volumes of 35 tumors in these 19 patients were determined and used to generate (1) a linear model in which tumor volume changed at a constant rate, (2) a general linear model that utilized the power fit relationship between the daily and initial tumor volumes, and (3) a functional general linear model that identified and exploited the primary modes of variation between time series describing the changing tumor volumes. Primary and nodal tumor volumes were examined separately. The accuracy of these models in predicting daily tumor volumes were compared with those of static and linear reference models using leave-one-out cross-validation. Results: In predicting the daily volume of primary tumors, the general linear model and the functional general linear model were more accurate than the static reference model by 9.9% (range: −11.6%–23.8%) and 14.6% (range: −7.3%–27.5%), respectively, and were more accurate than the linear reference model by 14.2% (range: −6.8%–40.3%) and 13.1% (range: −1.5%–52.5%), respectively. In predicting the daily volume of nodal tumors, only the 14.4% (range: −11.1%–20.5%) improvement in accuracy of the functional general linear model compared to the static reference model was statistically significant. Conclusions: A general linear model and a functional general linear model trained on data from a small population of patients can predict the primary tumor volume throughout the course of radiation therapy with greater accuracy than standard reference models. These more accurate models may increase the prognostic value of information about the tumor garnered from pretreatment computed tomography
Robust Sparse Blind Source Separation
NASA Astrophysics Data System (ADS)
Chenot, Cecile; Bobin, Jerome; Rapin, Jeremy
2015-11-01
Blind Source Separation is a widely used technique to analyze multichannel data. In many real-world applications, its results can be significantly hampered by the presence of unknown outliers. In this paper, a novel algorithm coined rGMCA (robust Generalized Morphological Component Analysis) is introduced to retrieve sparse sources in the presence of outliers. It explicitly estimates the sources, the mixing matrix, and the outliers. It also takes advantage of the estimation of the outliers to further implement a weighting scheme, which provides a highly robust separation procedure. Numerical experiments demonstrate the efficiency of rGMCA to estimate the mixing matrix in comparison with standard BSS techniques.
LOFAR sparse image reconstruction
NASA Astrophysics Data System (ADS)
Garsden, H.; Girard, J. N.; Starck, J. L.; Corbel, S.; Tasse, C.; Woiselle, A.; McKean, J. P.; van Amesfoort, A. S.; Anderson, J.; Avruch, I. M.; Beck, R.; Bentum, M. J.; Best, P.; Breitling, F.; Broderick, J.; Brüggen, M.; Butcher, H. R.; Ciardi, B.; de Gasperin, F.; de Geus, E.; de Vos, M.; Duscha, S.; Eislöffel, J.; Engels, D.; Falcke, H.; Fallows, R. A.; Fender, R.; Ferrari, C.; Frieswijk, W.; Garrett, M. A.; Grießmeier, J.; Gunst, A. W.; Hassall, T. E.; Heald, G.; Hoeft, M.; Hörandel, J.; van der Horst, A.; Juette, E.; Karastergiou, A.; Kondratiev, V. I.; Kramer, M.; Kuniyoshi, M.; Kuper, G.; Mann, G.; Markoff, S.; McFadden, R.; McKay-Bukowski, D.; Mulcahy, D. D.; Munk, H.; Norden, M. J.; Orru, E.; Paas, H.; Pandey-Pommier, M.; Pandey, V. N.; Pietka, G.; Pizzo, R.; Polatidis, A. G.; Renting, A.; Röttgering, H.; Rowlinson, A.; Schwarz, D.; Sluman, J.; Smirnov, O.; Stappers, B. W.; Steinmetz, M.; Stewart, A.; Swinbank, J.; Tagger, M.; Tang, Y.; Tasse, C.; Thoudam, S.; Toribio, C.; Vermeulen, R.; Vocks, C.; van Weeren, R. J.; Wijnholds, S. J.; Wise, M. W.; Wucknitz, O.; Yatawatta, S.; Zarka, P.; Zensus, A.
2015-03-01
Context. The LOw Frequency ARray (LOFAR) radio telescope is a giant digital phased array interferometer with multiple antennas distributed in Europe. It provides discrete sets of Fourier components of the sky brightness. Recovering the original brightness distribution with aperture synthesis forms an inverse problem that can be solved by various deconvolution and minimization methods. Aims: Recent papers have established a clear link between the discrete nature of radio interferometry measurement and the "compressed sensing" (CS) theory, which supports sparse reconstruction methods to form an image from the measured visibilities. Empowered by proximal theory, CS offers a sound framework for efficient global minimization and sparse data representation using fast algorithms. Combined with instrumental direction-dependent effects (DDE) in the scope of a real instrument, we developed and validated a new method based on this framework. Methods: We implemented a sparse reconstruction method in the standard LOFAR imaging tool and compared the photometric and resolution performance of this new imager with that of CLEAN-based methods (CLEAN and MS-CLEAN) with simulated and real LOFAR data. Results: We show that i) sparse reconstruction performs as well as CLEAN in recovering the flux of point sources; ii) performs much better on extended objects (the root mean square error is reduced by a factor of up to 10); and iii) provides a solution with an effective angular resolution 2-3 times better than the CLEAN images. Conclusions: Sparse recovery gives a correct photometry on high dynamic and wide-field images and improved realistic structures of extended sources (of simulated and real LOFAR datasets). This sparse reconstruction method is compatible with modern interferometric imagers that handle DDE corrections (A- and W-projections) required for current and future instruments such as LOFAR and SKA.
Approximation and compression with sparse orthonormal transforms.
Sezer, Osman Gokhan; Guleryuz, Onur G; Altunbasak, Yucel
2015-08-01
We propose a new transform design method that targets the generation of compression-optimized transforms for next-generation multimedia applications. The fundamental idea behind transform compression is to exploit regularity within signals such that redundancy is minimized subject to a fidelity cost. Multimedia signals, in particular images and video, are well known to contain a diverse set of localized structures, leading to many different types of regularity and to nonstationary signal statistics. The proposed method designs sparse orthonormal transforms (SOTs) that automatically exploit regularity over different signal structures and provides an adaptation method that determines the best representation over localized regions. Unlike earlier work that is motivated by linear approximation constructs and model-based designs that are limited to specific types of signal regularity, our work uses general nonlinear approximation ideas and a data-driven setup to significantly broaden its reach. We show that our SOT designs provide a safe and principled extension of the Karhunen-Loeve transform (KLT) by reducing to the KLT on Gaussian processes and by automatically exploiting non-Gaussian statistics to significantly improve over the KLT on more general processes. We provide an algebraic optimization framework that generates optimized designs for any desired transform structure (multiresolution, block, lapped, and so on) with significantly better n -term approximation performance. For each structure, we propose a new prototype codec and test over a database of images. Simulation results show consistent increase in compression and approximation performance compared with conventional methods. PMID:25823033
Fast Solution in Sparse LDA for Binary Classification
NASA Technical Reports Server (NTRS)
Moghaddam, Baback
2010-01-01
An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic
NASA Astrophysics Data System (ADS)
Yu, Chih-Jen; Chou, Chien
2011-03-01
An equivalence theory based on a unitary optical system of a generalized elliptical phase retarder was derived. Whereas the elliptical phase retarder can be treated as the combination of a linear phase retarder and a polarization rotator equivalently. Three fundamental parameters, including the elliptical phase retardation, the azimuth angle and the ellipticity angle of the fast elliptical eigen-polarization state were derived. All parameters of a generalized elliptical phase retarder can be determined from the analytical solution of the characteristic parameters of the optical components: linear phase retardation and fast axis angle of the equivalently linear phase retarder respectively, and polarization rotation angle of an equivalent polarization rotator. In this study, the experimental verification was demonstrated by testing a twisted nematic liquid crystal device (TNLCD) treated as a generalized elliptical phase retarder. A dual-frequency heterodyne ellipsometer was setup and the experimental result demonstrates the capability of the equivalent theory on elliptical birefringence measurement at high sensitivity by using heterodyne technique.
Generalized Functional Linear Models for Gene-based Case-Control Association Studies
Mills, James L.; Carter, Tonia C.; Lobach, Iryna; Wilson, Alexander F.; Bailey-Wilson, Joan E.; Weeks, Daniel E.; Xiong, Momiao
2014-01-01
By using functional data analysis techniques, we developed generalized functional linear models for testing association between a dichotomous trait and multiple genetic variants in a genetic region while adjusting for covariates. Both fixed and mixed effect models are developed and compared. Extensive simulations show that Rao's efficient score tests of the fixed effect models are very conservative since they generate lower type I errors than nominal levels, and global tests of the mixed effect models generate accurate type I errors. Furthermore, we found that the Rao's efficient score test statistics of the fixed effect models have higher power than the sequence kernel association test (SKAT) and its optimal unified version (SKAT-O) in most cases when the causal variants are both rare and common. When the causal variants are all rare (i.e., minor allele frequencies less than 0.03), the Rao's efficient score test statistics and the global tests have similar or slightly lower power than SKAT and SKAT-O. In practice, it is not known whether rare variants or common variants in a gene are disease-related. All we can assume is that a combination of rare and common variants influences disease susceptibility. Thus, the improved performance of our models when the causal variants are both rare and common shows that the proposed models can be very useful in dissecting complex traits. We compare the performance of our methods with SKAT and SKAT-O on real neural tube defects and Hirschsprung's disease data sets. The Rao's efficient score test statistics and the global tests are more sensitive than SKAT and SKAT-O in the real data analysis. Our methods can be used in either gene-disease genome-wide/exome-wide association studies or candidate gene analyses. PMID:25203683
Protein structure validation by generalized linear model root-mean-square deviation prediction.
Bagaria, Anurag; Jaravine, Victor; Huang, Yuanpeng J; Montelione, Gaetano T; Güntert, Peter
2012-02-01
Large-scale initiatives for obtaining spatial protein structures by experimental or computational means have accentuated the need for the critical assessment of protein structure determination and prediction methods. These include blind test projects such as the critical assessment of protein structure prediction (CASP) and the critical assessment of protein structure determination by nuclear magnetic resonance (CASD-NMR). An important aim is to establish structure validation criteria that can reliably assess the accuracy of a new protein structure. Various quality measures derived from the coordinates have been proposed. A universal structural quality assessment method should combine multiple individual scores in a meaningful way, which is challenging because of their different measurement units. Here, we present a method based on a generalized linear model (GLM) that combines diverse protein structure quality scores into a single quantity with intuitive meaning, namely the predicted coordinate root-mean-square deviation (RMSD) value between the present structure and the (unavailable) "true" structure (GLM-RMSD). For two sets of structural models from the CASD-NMR and CASP projects, this GLM-RMSD value was compared with the actual accuracy given by the RMSD value to the corresponding, experimentally determined reference structure from the Protein Data Bank (PDB). The correlation coefficients between actual (model vs. reference from PDB) and predicted (model vs. "true") heavy-atom RMSDs were 0.69 and 0.76, for the two datasets from CASD-NMR and CASP, respectively, which is considerably higher than those for the individual scores (-0.24 to 0.68). The GLM-RMSD can thus predict the accuracy of protein structures more reliably than individual coordinate-based quality scores.
Use of generalized linear models and digital data in a forest inventory of Northern Utah
Moisen, G.G.; Edwards, T.C.
1999-01-01
Forest inventories, like those conducted by the Forest Service's Forest Inventory and Analysis Program (FIA) in the Rocky Mountain Region, are under increased pressure to produce better information at reduced costs. Here we describe our efforts in Utah to merge satellite-based information with forest inventory data for the purposes of reducing the costs of estimates of forest population totals and providing spatial depiction of forest resources. We illustrate how generalized linear models can be used to construct approximately unbiased and efficient estimates of population totals while providing a mechanism for prediction in space for mapping of forest structure. We model forest type and timber volume of five tree species groups as functions of a variety of predictor variables in the northern Utah mountains. Predictor variables include elevation, aspect, slope, geographic coordinates, as well as vegetation cover types based on satellite data from both the Advanced Very High Resolution Radiometer (AVHRR) and Thematic Mapper (TM) platforms. We examine the relative precision of estimates of area by forest type and mean cubic-foot volumes under six different models, including the traditional double sampling for stratification strategy. Only very small gains in precision were realized through the use of expensive photointerpreted or TM-based data for stratification, while models based on topography and spatial coordinates alone were competitive. We also compare the predictive capability of the models through various map accuracy measures. The models including the TM-based vegetation performed best overall, while topography and spatial coordinates alone provided substantial information at very low cost.
Power analysis for generalized linear mixed models in ecology and evolution
Johnson, Paul C D; Barry, Sarah J E; Ferguson, Heather M; Müller, Pie
2015-01-01
‘Will my study answer my research question?’ is the most fundamental question a researcher can ask when designing a study, yet when phrased in statistical terms – ‘What is the power of my study?’ or ‘How precise will my parameter estimate be?’ – few researchers in ecology and evolution (EE) try to answer it, despite the detrimental consequences of performing under- or over-powered research. We suggest that this reluctance is due in large part to the unsuitability of simple methods of power analysis (broadly defined as any attempt to quantify prospectively the ‘informativeness’ of a study) for the complex models commonly used in EE research. With the aim of encouraging the use of power analysis, we present simulation from generalized linear mixed models (GLMMs) as a flexible and accessible approach to power analysis that can account for random effects, overdispersion and diverse response distributions.We illustrate the benefits of simulation-based power analysis in two research scenarios: estimating the precision of a survey to estimate tick burdens on grouse chicks and estimating the power of a trial to compare the efficacy of insecticide-treated nets in malaria mosquito control. We provide a freely available R function, sim.glmm, for simulating from GLMMs.Analysis of simulated data revealed that the effects of accounting for realistic levels of random effects and overdispersion on power and precision estimates were substantial, with correspondingly severe implications for study design in the form of up to fivefold increases in sampling effort. We also show the utility of simulations for identifying scenarios where GLMM-fitting methods can perform poorly.These results illustrate the inadequacy of standard analytical power analysis methods and the flexibility of simulation-based power analysis for GLMMs. The wider use of these methods should contribute to improving the quality of study design in EE. PMID:25893088
The linear co-variance between joint muscle torques is not a generalized principle.
Sande de Souza, Luciane Aparecida Pascucci; Dionísio, Valdeci Carlos; Lerena, Mario Adrian Misailidis; Marconi, Nadia Fernanda; Almeida, Gil Lúcio
2009-06-01
In 1996, Gottlieb et al. [Gottlieb GL, Song Q, Hong D, Almeida GL, Corcos DM. Coordinating movement at two joints: A principle of linear covariance. J Neurophysiol 1996;75(4):1760-4] identified a linear co-variance between the joint muscle torques generated at two connected joints. The joint muscle torques changed directions and magnitudes in a synchronized and linear fashion and called it the principle of linear co-variance. Here we showed that this principle cannot hold for some class of movements. Neurologically normal subjects performed multijoint movements involving elbow and shoulder with reversal towards three targets in the sagittal plane without any constraints. The movement kinematics was calculated using the X and Y coordinates of the markers positioned over the joints. Inverse dynamics was used to calculate the joint muscle, interaction and net torques. We found that for the class of voluntary movements analyzed, the joint muscle torques of the elbow and the shoulder were not linearly correlated. The same was observed for the interaction torques. But, the net torques at both joints, i.e., the sum of the interaction and the joint muscle torques were linearly correlated. We showed that by decoupling the joint muscle torques, but keeping the net torques linearly correlated, the CNS was able to generate fast and accurate movements with straight fingertip paths. The movement paths were typical of the ones in which the joint muscle torques were linearly correlated.
Finding nonoverlapping substructures of a sparse matrix
Pinar, Ali; Vassilevska, Virginia
2004-08-09
Many applications of scientific computing rely on computations on sparse matrices, thus the design of efficient implementations of sparse matrix kernels is crucial for the overall efficiency of these applications. Due to the high compute-to-memory ratio and irregular memory access patterns, the performance of sparse matrix kernels is often far away from the peak performance on a modern processor. Alternative data structures have been proposed, which split the original matrix A into A{sub d} and A{sub s}, so that A{sub d} contains all dense blocks of a specified size in the matrix, and A{sub s} contains the remaining entries. This enables the use of dense matrix kernels on the entries of A{sub d} producing better memory performance. In this work, we study the problem of finding a maximum number of non overlapping rectangular dense blocks in a sparse matrix, which has not been studied in the sparse matrix community. We show that the maximum non overlapping dense blocks problem is NP-complete by using a reduction from the maximum independent set problem on cubic planar graphs. We also propose a 2/3-approximation algorithm for 2 times 2 blocks that runs in linear time in the number of nonzeros in the matrix. We discuss alternatives to rectangular blocks such as diagonal blocks and cross blocks and present complexity analysis and approximation algorithms.
NASA Technical Reports Server (NTRS)
Holdaway, Daniel; Kent, James
2015-01-01
The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.
Sparse dictionary learning for fMRI analysis using autocorrelation maximization.
Khalid, Muhammad Usman; Shah, Adnan; Seghouane, Abd-Krim
2015-08-01
In this paper, the effect of temporal autocorrelations in functional magnetic resonance imaging (fMRI) data on sparse dictionary learning (SDL) is addressed. For sparse general linear model (sGLM), the fMRI time-series is modeled as a linear mixture of several signals such as neural dynamics, structured noise, random noise and unexplained signal variations on the basis of spatial sparseness. These signals are considered as underlying sources and SDL is used to estimate them. However, the sparse GLM model does not take into account the autocorrelations in fMRI data. To address this shortcoming, a new model is proposed to incorporate the prior knowledge about lag-1 autocorrelation into dictionary update stage. This helps improve the sensitivity and specificity of the fMRI data during statistical analysis. Using a simulation study, the effect of the proposed dictionary update on sGLM is compared to conventional sGLM by utilizing various detrending techniques. Furthermore, the proposed update is validated in an sGLM framework for real fMRI datasets, which shows its better capability to estimate neural dynamics in presence of spatiotemporal dependencies.
General methods for determining the linear stability of coronal magnetic fields
NASA Technical Reports Server (NTRS)
Craig, I. J. D.; Sneyd, A. D.; Mcclymont, A. N.
1988-01-01
A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak.
Generalizations of the theorem of minimum entropy production to linear systems involving inertia
NASA Astrophysics Data System (ADS)
Rebhan, E.
1985-07-01
The temporal behavior of the excess entropy production Pex is investigated in linear electrical networks and in systems which can be described either by the linearized equations of viscous hydrodynamics or of resistive magnetohydrodynamics. As a result of inertial effects Pex is an oscillatory quantity. A kinetic potential is constructed which contains Pex additively. It is an upper bound of Pex and decreases monotonically in time, enforcing Pex-->0 as t-->∞.
NASA Astrophysics Data System (ADS)
Begley, Matthew R.; Creton, Costantino; McMeeking, Robert M.
2015-11-01
A general asymptotic plane strain crack tip stress field is constructed for linear versions of neo-Hookean materials, which spans a wide variety of special cases including incompressible Mooney elastomers, the compressible Blatz-Ko elastomer, several cases of the Ogden constitutive law and a new result for a compressible linear neo-Hookean material. The nominal stress field has dominant terms that have a square root singularity with respect to the distance of material points from the crack tip in the undeformed reference configuration. At second order, there is a uniform tension parallel to the crack. The associated displacement field in plane strain at leading order has dependence proportional to the square root of the same coordinate. The relationship between the amplitude of the crack tip singularity (a stress intensity factor) and the plane strain energy release rate is outlined for the general linear material, with simplified relationships presented for notable special cases.
Meta-analysis of Complex Diseases at Gene Level with Generalized Functional Linear Models.
Fan, Ruzong; Wang, Yifan; Chiu, Chi-Yang; Chen, Wei; Ren, Haobo; Li, Yun; Boehnke, Michael; Amos, Christopher I; Moore, Jason H; Xiong, Momiao
2016-02-01
We developed generalized functional linear models (GFLMs) to perform a meta-analysis of multiple case-control studies to evaluate the relationship of genetic data to dichotomous traits adjusting for covariates. Unlike the previously developed meta-analysis for sequence kernel association tests (MetaSKATs), which are based on mixed-effect models to make the contributions of major gene loci random, GFLMs are fixed models; i.e., genetic effects of multiple genetic variants are fixed. Based on GFLMs, we developed chi-squared-distributed Rao's efficient score test and likelihood-ratio test (LRT) statistics to test for an association between a complex dichotomous trait and multiple genetic variants. We then performed extensive simulations to evaluate the empirical type I error rates and power performance of the proposed tests. The Rao's efficient score test statistics of GFLMs are very conservative and have higher power than MetaSKATs when some causal variants are rare and some are common. When the causal variants are all rare [i.e., minor allele frequencies (MAF) < 0.03], the Rao's efficient score test statistics have similar or slightly lower power than MetaSKATs. The LRT statistics generate accurate type I error rates for homogeneous genetic-effect models and may inflate type I error rates for heterogeneous genetic-effect models owing to the large numbers of degrees of freedom and have similar or slightly higher power than the Rao's efficient score test statistics. GFLMs were applied to analyze genetic data of 22 gene regions of type 2 diabetes data from a meta-analysis of eight European studies and detected significant association for 18 genes (P < 3.10 × 10(-6)), tentative association for 2 genes (HHEX and HMGA2; P ≈ 10(-5)), and no association for 2 genes, while MetaSKATs detected none. In addition, the traditional additive-effect model detects association at gene HHEX. GFLMs and related tests can analyze rare or common variants or a combination of the two and
NASA Astrophysics Data System (ADS)
Irmak, Suat; Mutiibwa, Denis
2010-08-01
The 1-D and single layer combination-based energy balance Penman-Monteith (PM) model has limitations in practical application due to the lack of canopy resistance (rc) data for different vegetation surfaces. rc could be estimated by inversion of the PM model if the actual evapotranspiration (ETa) rate is known, but this approach has its own set of issues. Instead, an empirical method of estimating rc is suggested in this study. We investigated the relationships between primary micrometeorological parameters and rc and developed seven models to estimate rc for a nonstressed maize canopy on an hourly time step using a generalized-linear modeling approach. The most complex rc model uses net radiation (Rn), air temperature (Ta), vapor pressure deficit (VPD), relative humidity (RH), wind speed at 3 m (u3), aerodynamic resistance (ra), leaf area index (LAI), and solar zenith angle (Θ). The simplest model requires Rn, Ta, and RH. We present the practical implementation of all models via experimental validation using scaled up rc data obtained from the dynamic diffusion porometer-measured leaf stomatal resistance through an extensive field campaign in 2006. For further validation, we estimated ETa by solving the PM model using the modeled rc from all seven models and compared the PM ETa estimates with the Bowen ratio energy balance system (BREBS)-measured ETa for an independent data set in 2005. The relationships between hourly rc versus Ta, RH, VPD, Rn, incoming shortwave radiation (Rs), u3, wind direction, LAI, Θ, and ra were presented and discussed. We demonstrated the negative impact of exclusion of LAI when modeling rc, whereas exclusion of ra and Θ did not impact the performance of the rc models. Compared to the calibration results, the validation root mean square difference between observed and modeled rc increased by 5 s m-1 for all rc models developed, ranging from 9.9 s m-1 for the most complex model to 22.8 s m-1 for the simplest model, as compared with the
Chen, Gang; Adleman, Nancy E; Saad, Ziad S; Leibenluft, Ellen; Cox, Robert W
2014-10-01
All neuroimaging packages can handle group analysis with t-tests or general linear modeling (GLM). However, they are quite hamstrung when there are multiple within-subject factors or when quantitative covariates are involved in the presence of a within-subject factor. In addition, sphericity is typically assumed for the variance-covariance structure when there are more than two levels in a within-subject factor. To overcome such limitations in the traditional AN(C)OVA and GLM, we adopt a multivariate modeling (MVM) approach to analyzing neuroimaging data at the group level with the following advantages: a) there is no limit on the number of factors as long as sample sizes are deemed appropriate; b) quantitative covariates can be analyzed together with within-subject factors; c) when a within-subject factor is involved, three testing methodologies are provided: traditional univariate testing (UVT) with sphericity assumption (UVT-UC) and with correction when the assumption is violated (UVT-SC), and within-subject multivariate testing (MVT-WS); d) to correct for sphericity violation at the voxel level, we propose a hybrid testing (HT) approach that achieves equal or higher power via combining traditional sphericity correction methods (Greenhouse-Geisser and Huynh-Feldt) with MVT-WS. To validate the MVM methodology, we performed simulations to assess the controllability for false positives and power achievement. A real FMRI dataset was analyzed to demonstrate the capability of the MVM approach. The methodology has been implemented into an open source program 3dMVM in AFNI, and all the statistical tests can be performed through symbolic coding with variable names instead of the tedious process of dummy coding. Our data indicates that the severity of sphericity violation varies substantially across brain regions. The differences among various modeling methodologies were addressed through direct comparisons between the MVM approach and some of the GLM implementations in
Sparse inpainting and isotropy
Feeney, Stephen M.; McEwen, Jason D.; Peiris, Hiranya V.; Marinucci, Domenico; Cammarota, Valentina; Wandelt, Benjamin D. E-mail: marinucc@axp.mat.uniroma2.it E-mail: h.peiris@ucl.ac.uk E-mail: cammarot@axp.mat.uniroma2.it
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.
Efficient quantum circuits for arbitrary sparse unitaries
Jordan, Stephen P.; Wocjan, Pawel
2009-12-15
Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row or column, and these entries are efficiently computable. One can formulate a model of computation based on the composition of sparse unitaries which includes the quantum Turing machine model, the quantum circuit model, anyonic models, permutational quantum computation, and discrete time quantum walks as special cases. Thus, we obtain a simple unified proof that these models are all contained in BQP. Furthermore, our general method for implementing sparse unitaries simplifies several existing quantum algorithms.
Shirokov, M. E.
2013-11-15
The method of complementary channel for analysis of reversibility (sufficiency) of a quantum channel with respect to families of input states (pure states for the most part) are considered and applied to Bosonic linear (quasi-free) channels, in particular, to Bosonic Gaussian channels. The obtained reversibility conditions for Bosonic linear channels have clear physical interpretation and their sufficiency is also shown by explicit construction of reversing channels. The method of complementary channel gives possibility to prove necessity of these conditions and to describe all reversed families of pure states in the Schrodinger representation. Some applications in quantum information theory are considered. Conditions for existence of discrete classical-quantum subchannels and of completely depolarizing subchannels of a Bosonic linear channel are presented.
NASA Technical Reports Server (NTRS)
Kanerva, Pentti
1988-01-01
Theoretical models of the human brain and proposed neural-network computers are developed analytically. Chapters are devoted to the mathematical foundations, background material from computer science, the theory of idealized neurons, neurons as address decoders, and the search of memory for the best match. Consideration is given to sparse memory, distributed storage, the storage and retrieval of sequences, the construction of distributed memory, and the organization of an autonomous learning system.
Kanerva, P.
1988-01-01
Theoretical models of the human brain and proposed neural-network computers are developed analytically. Chapters are devoted to the mathematical foundations, background material from computer science, the theory of idealized neurons, neurons as address decoders, and the search of memory for the best match. Consideration is given to sparse memory, distributed storage, the storage and retrieval of sequences, the construction of distributed memory, and the organization of an autonomous learning system. 63 refs.
Huppert, Theodore J
2016-01-01
Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of light to measure changes in cerebral blood oxygenation levels. In the majority of NIRS functional brain studies, analysis of this data is based on a statistical comparison of hemodynamic levels between a baseline and task or between multiple task conditions by means of a linear regression model: the so-called general linear model. Although these methods are similar to their implementation in other fields, particularly for functional magnetic resonance imaging, the specific application of these methods in fNIRS research differs in several key ways related to the sources of noise and artifacts unique to fNIRS. In this brief communication, we discuss the application of linear regression models in fNIRS and the modifications needed to generalize these models in order to deal with structured (colored) noise due to systemic physiology and noise heteroscedasticity due to motion artifacts. The objective of this work is to present an overview of these noise properties in the context of the linear model as it applies to fNIRS data. This work is aimed at explaining these mathematical issues to the general fNIRS experimental researcher but is not intended to be a complete mathematical treatment of these concepts. PMID:26989756
Fast wavelet based sparse approximate inverse preconditioner
Wan, W.L.
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.
Recent advances toward a general purpose linear-scaling quantum force field.
Giese, Timothy J; Huang, Ming; Chen, Haoyuan; York, Darrin M
2014-09-16
Conspectus There is need in the molecular simulation community to develop new quantum mechanical (QM) methods that can be routinely applied to the simulation of large molecular systems in complex, heterogeneous condensed phase environments. Although conventional methods, such as the hybrid quantum mechanical/molecular mechanical (QM/MM) method, are adequate for many problems, there remain other applications that demand a fully quantum mechanical approach. QM methods are generally required in applications that involve changes in electronic structure, such as when chemical bond formation or cleavage occurs, when molecules respond to one another through polarization or charge transfer, or when matter interacts with electromagnetic fields. A full QM treatment, rather than QM/MM, is necessary when these features present themselves over a wide spatial range that, in some cases, may span the entire system. Specific examples include the study of catalytic events that involve delocalized changes in chemical bonds, charge transfer, or extensive polarization of the macromolecular environment; drug discovery applications, where the wide range of nonstandard residues and protonation states are challenging to model with purely empirical MM force fields; and the interpretation of spectroscopic observables. Unfortunately, the enormous computational cost of conventional QM methods limit their practical application to small systems. Linear-scaling electronic structure methods (LSQMs) make possible the calculation of large systems but are still too computationally intensive to be applied with the degree of configurational sampling often required to make meaningful comparison with experiment. In this work, we present advances in the development of a quantum mechanical force field (QMFF) suitable for application to biological macromolecules and condensed phase simulations. QMFFs leverage the benefits provided by the LSQM and QM/MM approaches to produce a fully QM method that is able to
ERIC Educational Resources Information Center
Yan, Jun; Aseltine, Robert H., Jr.; Harel, Ofer
2013-01-01
Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…
Linear and Nonlinear Optical Properties in Spherical Quantum Dots: Generalized Hulthén Potential
NASA Astrophysics Data System (ADS)
Onyeaju, M. C.; Idiodi, J. O. A.; Ikot, A. N.; Solaimani, M.; Hassanabadi, H.
2016-09-01
In this work, we studied the optical properties of spherical quantum dots confined in Hulthén potential with the appropriate centrifugal term included. The approximate solution of the bound state and wave functions were obtained from the Schrödinger wave equation by applying the factorization method. Also, we have used the density matrix formalism to investigate the linear and third-order nonlinear absorption coefficient and refractive index changes.
General-linear-models approach for comparing the response of several species in acute-toxicity tests
Daniels, K.L.; Goyert, J.C.; Farrell, M.P.; Strand, R.H.
1982-01-01
Acute toxicity tests (bioassays) estimate the concentration of a chemical required to produce a response (usually death) in fifty percent of a population (the LC50). Simple comparisons of LC5C values among several species are often inadequate because species can have identical LC50 values while their overall response to a chemical may differ in either the threshold concentration (intercept) or the rate of response (slope). A sequential approach using a general linear model is presented for testing differences among species in their overall response to a chemical. This method tests for equality of slopes followed by a test for equality of regression lines. This procedure employs the Statistical Analysis System's General Linear Models procedure for conducting a weighted least squares analysis with a convariable.
SPARSKIT: A basic tool kit for sparse matrix computations
NASA Technical Reports Server (NTRS)
Saad, Youcef
1990-01-01
Presented here are the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations. The starting point is the Harwell/Boeing collection of matrices for which the authors provide a number of tools. Among other things, the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, and performing linear algebra operations with sparse matrices.
NASA Astrophysics Data System (ADS)
Rukolaine, Sergey A.
2016-05-01
In classical kinetic models a particle free path distribution is exponential, but this is more likely to be an exception than a rule. In this paper we derive a generalized linear Boltzmann equation (GLBE) for a general free path distribution in the framework of Alt's model. In the case that the free path distribution has at least first and second finite moments we construct an asymptotic solution to the initial value problem for the GLBE for small mean free paths. In the special case of the one-speed transport problem the asymptotic solution results in a diffusion approximation to the GLBE.
and Drayton Munster, Miroslav Stoyanov
2013-09-20
Sparse Grids are the family of methods of choice for multidimensional integration and interpolation in low to moderate number of dimensions. The method is to select extend a one dimensional set of abscissas, weights and basis functions by taking a subset of all possible tensor products. The module provides the ability to create global and local approximations based on polynomials and wavelets. The software has three components, a library, a wrapper for the library that provides a command line interface via text files ad a MATLAB interface via the command line tool.
2007-04-12
The Sparse Image Format (SIF) is a file format for storing spare raster images. It works by breaking an image down into tiles. Space is savid by only storing non-uniform tiles, i.e. tiles with at least two different pixel values. If a tile is completely uniform, its common pixel value is stored instead of the complete tile raster. The software is a library in the C language used for manipulating files in SIF format. Itmore » supports large files (> 2GB) and is designed to build in Windows and Linux environments.« less
2013-09-20
Sparse Grids are the family of methods of choice for multidimensional integration and interpolation in low to moderate number of dimensions. The method is to select extend a one dimensional set of abscissas, weights and basis functions by taking a subset of all possible tensor products. The module provides the ability to create global and local approximations based on polynomials and wavelets. The software has three components, a library, a wrapper for the library thatmore » provides a command line interface via text files ad a MATLAB interface via the command line tool.« less
Eads, Damian Ryan
2007-04-12
The Sparse Image Format (SIF) is a file format for storing spare raster images. It works by breaking an image down into tiles. Space is savid by only storing non-uniform tiles, i.e. tiles with at least two different pixel values. If a tile is completely uniform, its common pixel value is stored instead of the complete tile raster. The software is a library in the C language used for manipulating files in SIF format. It supports large files (> 2GB) and is designed to build in Windows and Linux environments.
Hochi, Y; Kido, T; Nogawa, K; Kito, H; Shaikh, Z A
1995-01-01
To determine the maximum allowable intake limits for chronic dietary exposure to cadmium (Cd), the dose-response relationship between total Cd intake and prevalence of renal dysfunction was examined using general linear models considering the effect of age as a confounder. The target population comprised 1850 Cd-exposed and 294 non-exposed inhabitants of Ishikawa, Japan. They were divided into 96 subgroups by sex, age (four categories) cadmium concentrations in rice (three categories) and length of residence (four categories). As indicators of the cadmium-induced renal dysfunction, glucose, total protein, amino nitrogen, beta 2-microglobulin and metallothionein in urine were employed. General linear models were fitted statistically to the relationship among prevalence of renal dysfunction, sex, age and total Cd intake. Prevalence of abnormal urinary findings other than glucosuria had significant associations with total Cd intake. When total Cd intake corresponding to the mean prevalence of each abnormal urinary finding in the non-exposed subjects was calculated using general linear models, total Cd intakes corresponding to glucosuria, proteinuria, aminoaciduria (men only) and proteinuria with glucosuria were determined to be ca. 2.2-3.8 g and those corresponding to prevalence of metallothioneinuria were calculated as ca. 1.5-2.6 g. The low-molecular-weight protein in urine was confirmed to be a more sensitive indicator of renal dysfunction, and these total Cd intake values were close to those calculated previously by simple regression analysis, suggesting them to be reasonable values as the maximum allowable intake of Cd.
Beynon, R J
1985-01-01
Software for non-linear curve fitting has been written in BASIC to execute on the British Broadcasting Corporation Microcomputer. The program uses the direct search algorithm Pattern-search, a robust algorithm that has the additional advantage of needing specification of the function without inclusion of the partial derivatives. Although less efficient than gradient methods, the program can be readily configured to solve low-dimensional optimization problems that are normally encountered in life sciences. In writing the software, emphasis has been placed upon the 'user interface' and making the most efficient use of the facilities provided by the minimal configuration of this system.
Sparse regularization for force identification using dictionaries
NASA Astrophysics Data System (ADS)
Qiao, Baijie; Zhang, Xingwu; Wang, Chenxi; Zhang, Hang; Chen, Xuefeng
2016-04-01
The classical function expansion method based on minimizing l2-norm of the response residual employs various basis functions to represent the unknown force. Its difficulty lies in determining the optimum number of basis functions. Considering the sparsity of force in the time domain or in other basis space, we develop a general sparse regularization method based on minimizing l1-norm of the coefficient vector of basis functions. The number of basis functions is adaptively determined by minimizing the number of nonzero components in the coefficient vector during the sparse regularization process. First, according to the profile of the unknown force, the dictionary composed of basis functions is determined. Second, a sparsity convex optimization model for force identification is constructed. Third, given the transfer function and the operational response, Sparse reconstruction by separable approximation (SpaRSA) is developed to solve the sparse regularization problem of force identification. Finally, experiments including identification of impact and harmonic forces are conducted on a cantilever thin plate structure to illustrate the effectiveness and applicability of SpaRSA. Besides the Dirac dictionary, other three sparse dictionaries including Db6 wavelets, Sym4 wavelets and cubic B-spline functions can also accurately identify both the single and double impact forces from highly noisy responses in a sparse representation frame. The discrete cosine functions can also successfully reconstruct the harmonic forces including the sinusoidal, square and triangular forces. Conversely, the traditional Tikhonov regularization method with the L-curve criterion fails to identify both the impact and harmonic forces in these cases.
A General Method for Solving Systems of Non-Linear Equations
NASA Technical Reports Server (NTRS)
Nachtsheim, Philip R.; Deiss, Ron (Technical Monitor)
1995-01-01
The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.
Sparse Bayesian Learning for DOA Estimation with Mutual Coupling
Dai, Jisheng; Hu, Nan; Xu, Weichao; Chang, Chunqi
2015-01-01
Sparse Bayesian learning (SBL) has given renewed interest to the problem of direction-of-arrival (DOA) estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs). Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM) algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD) to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise. PMID:26501284
Sparse Bayesian learning for DOA estimation with mutual coupling.
Dai, Jisheng; Hu, Nan; Xu, Weichao; Chang, Chunqi
2015-01-01
Sparse Bayesian learning (SBL) has given renewed interest to the problem of direction-of-arrival (DOA) estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs). Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM) algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD) to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise. PMID:26501284
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
A substructure coupling procedure applicable to general linear time-invariant dynamic systems
NASA Technical Reports Server (NTRS)
Howsman, T. G.; Craig, R. R., Jr.
1984-01-01
A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the non-self-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order model for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.
Marín-Sanguino, Alberto; Torres, Néstor V
2003-08-01
A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously presented indirect optimization method (IOM) developed within biochemical systems theory. It is called GMA-IOM because it makes use of the generalized mass action (GMA) as the model system representation form. The GMA representation avoids flux aggregation and thus prevents possible stoichiometric errors. The optimization of a system is used to illustrate and compare the features, advantages and shortcomings of both versions of the IOM method as a general strategy for designing improved microbial strains of biotechnological interest. Special attention has been paid to practical problems for the actual implementation of the new proposed strategy, such as the total protein content of the engineered strain or the deviation from the original steady state and its influence on cell viability.
A substructure coupling procedure applicable to general linear time-invariant dynamic systems
NASA Technical Reports Server (NTRS)
Howsman, T. G.; Craig, R. R., Jr.
1984-01-01
A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the nonself-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order mode for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.
ERIC Educational Resources Information Center
Thompson, Bruce
The relationship between analysis of variance (ANOVA) methods and their analogs (analysis of covariance and multiple analyses of variance and covariance--collectively referred to as OVA methods) and the more general analytic case is explored. A small heuristic data set is used, with a hypothetical sample of 20 subjects, randomly assigned to five…
Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region
NASA Technical Reports Server (NTRS)
Shin, Jong-Yeob
2007-01-01
For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.
Microcontroller-based intelligent low-cost-linear-sensor-camera for general edge detection
NASA Astrophysics Data System (ADS)
Hussmann, Stephan; Justen, Detlef
1997-09-01
With this paper we would like to present an intelligent low- cost-camera. Intelligent means that a microcontroller does all the controlling and provides several in- and outputs. The camera is a stand-alone system. The basic element of the camera is a linear sensor that consists of a photodiode array (PDA). In comparison with standard CCD-chips this type of sensor is a low cost component and its operation is very simple. Furthermore this paper shows the mechanical, electrical and electro-optical differences between CCD- and PDA-sensors. So the reader will be able to choose the right sensor for a particular task. Two cases of industrial applications are listed at the end of this paper.
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2005-01-01
A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.
Fingerprint Compression Based on Sparse Representation.
Shao, Guangqi; Wu, Yanping; A, Yong; Liu, Xiao; Guo, Tiande
2014-02-01
A new fingerprint compression algorithm based on sparse representation is introduced. Obtaining an overcomplete dictionary from a set of fingerprint patches allows us to represent them as a sparse linear combination of dictionary atoms. In the algorithm, we first construct a dictionary for predefined fingerprint image patches. For a new given fingerprint images, represent its patches according to the dictionary by computing l(0)-minimization and then quantize and encode the representation. In this paper, we consider the effect of various factors on compression results. Three groups of fingerprint images are tested. The experiments demonstrate that our algorithm is efficient compared with several competing compression techniques (JPEG, JPEG 2000, and WSQ), especially at high compression ratios. The experiments also illustrate that the proposed algorithm is robust to extract minutiae.
Generalized linear stability of non-inertial rimming flow in a rotating horizontal cylinder.
Aggarwal, Himanshu; Tiwari, Naveen
2015-10-01
The stability of a thin film of viscous liquid inside a horizontally rotating cylinder is studied using modal and non-modal analysis. The equation governing the film thickness is derived within lubrication approximation and up to first order in aspect ratio (average film thickness to radius of the cylinder). Effect of gravity, viscous stress and capillary pressure are considered in the model. Steady base profiles are computed in the parameter space of interest that are uniform in the axial direction. A linear stability analysis is performed on these base profiles to study their stability to axial perturbations. The destabilizing behavior of aspect ratio and surface tension is demonstrated which is attributed to capillary instability. The transient growth that gives maximum amplification of any initial disturbance and the pseudospectra of the stability operator are computed. These computations reveal weak effect of non-normality of the operator and the results of eigenvalue analysis are recovered after a brief transient period. Results from nonlinear simulations are also presented which also confirm the validity of the modal analysis for the flow considered in this study. PMID:26496740
NASA Technical Reports Server (NTRS)
Denning, Peter J.
1989-01-01
Sparse distributed memory was proposed be Pentti Kanerva as a realizable architecture that could store large patterns and retrieve them based on partial matches with patterns representing current sensory inputs. This memory exhibits behaviors, both in theory and in experiment, that resemble those previously unapproached by machines - e.g., rapid recognition of faces or odors, discovery of new connections between seemingly unrelated ideas, continuation of a sequence of events when given a cue from the middle, knowing that one doesn't know, or getting stuck with an answer on the tip of one's tongue. These behaviors are now within reach of machines that can be incorporated into the computing systems of robots capable of seeing, talking, and manipulating. Kanerva's theory is a break with the Western rationalistic tradition, allowing a new interpretation of learning and cognition that respects biology and the mysteries of individual human beings.
Zhang, Lihe; Lu, Huchuan; Du, Dandan; Liu, Luning
2016-02-01
In this paper, we propose a novel tracking framework based on a sparse and discriminative hashing method. Different from the previous work, we treat object tracking as an approximate nearest neighbor searching process in a binary space. Using the hash functions, the target templates and the candidates can be projected into the Hamming space, facilitating the distance calculation and tracking efficiency. First, we integrate both the inter-class and intra-class information to train multiple hash functions for better classification, while most classifiers in previous tracking methods usually neglect the inter-class correlation, which may cause the inaccuracy. Then, we introduce sparsity into the hash coefficient vectors for dynamic feature selection, which is crucial to select the discriminative and stable features to adapt to visual variations during the tracking process. Extensive experiments on various challenging sequences show that the proposed algorithm performs favorably against the state-of-the-art methods.
Learning Stable Multilevel Dictionaries for Sparse Representations.
Thiagarajan, Jayaraman J; Ramamurthy, Karthikeyan Natesan; Spanias, Andreas
2015-09-01
Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The increasing need for learning sparse models in large-scale applications motivates the development of efficient, robust, and provably good dictionary learning algorithms. Algorithmic stability and generalizability are desirable characteristics for dictionary learning algorithms that aim to build global dictionaries, which can efficiently model any test data similar to the training samples. In this paper, we propose an algorithm to learn dictionaries for sparse representations from large scale data, and prove that the proposed learning algorithm is stable and generalizable asymptotically. The algorithm employs a 1-D subspace clustering procedure, the K-hyperline clustering, to learn a hierarchical dictionary with multiple levels. We also propose an information-theoretic scheme to estimate the number of atoms needed in each level of learning and develop an ensemble approach to learn robust dictionaries. Using the proposed dictionaries, the sparse code for novel test data can be computed using a low-complexity pursuit procedure. We demonstrate the stability and generalization characteristics of the proposed algorithm using simulations. We also evaluate the utility of the multilevel dictionaries in compressed recovery and subspace learning applications.
Algorithms for sparse nonnegative Tucker decompositions.
Mørup, Morten; Hansen, Lars Kai; Arnfred, Sidse M
2008-08-01
There is a increasing interest in analysis of large-scale multiway data. The concept of multiway data refers to arrays of data with more than two dimensions, that is, taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions for tensors are the Tucker model and the more restricted PARAFAC model. Both models can be viewed as generalizations of the regular factor analysis to data of more than two modalities. Nonnegative matrix factorization (NMF), in conjunction with sparse coding, has recently been given much attention due to its part-based and easy interpretable representation. While NMF has been extended to the PARAFAC model, no such attempt has been done to extend NMF to the Tucker model. However, if the tensor data analyzed are nonnegative, it may well be relevant to consider purely additive (i.e., nonnegative) Tucker decompositions). To reduce ambiguities of this type of decomposition, we develop updates that can impose sparseness in any combination of modalities, hence, proposed algorithms for sparse nonnegative Tucker decompositions (SN-TUCKER). We demonstrate how the proposed algorithms are superior to existing algorithms for Tucker decompositions when the data and interactions can be considered nonnegative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is more appropriate for the data as well as to select the number of components by turning off excess components. The algorithms for SN-TUCKER can be downloaded from Mørup (2007).
General, database-driven fast-feedback system for the Stanford Linear Collider
Rouse, F.; Allison, S.; Castillo, S.; Gromme, T.; Hall, B.; Hendrickson, L.; Himel, T.; Krauter, K.; Sass, B.' Shoaee, H.
1991-05-01
A new feedback system has been developed for stabilizing the SLC beams at many locations. The feedback loops are designed to sample and correct at the 60 Hz repetition rate of the accelerator. Each loop can be distributed across several of the standard 80386 microprocessors which control the SLC hardware. A new communications system, KISNet, has been implemented to pass signals between the microprocessors at this rate. The software is written in a general fashion using the state space formalism of digital control theory. This allows a new loop to be implemented by just setting up the online database and perhaps installing a communications link. 3 refs., 4 figs.
Reconstruction of sparse connectivity in neural networks from spike train covariances
NASA Astrophysics Data System (ADS)
Pernice, Volker; Rotter, Stefan
2013-03-01
The inference of causation from correlation is in general highly problematic. Correspondingly, it is difficult to infer the existence of physical synaptic connections between neurons from correlations in their activity. Covariances in neural spike trains and their relation to network structure have been the subject of intense research, both experimentally and theoretically. The influence of recurrent connections on covariances can be characterized directly in linear models, where connectivity in the network is described by a matrix of linear coupling kernels. However, as indirect connections also give rise to covariances, the inverse problem of inferring network structure from covariances can generally not be solved unambiguously. Here we study to what degree this ambiguity can be resolved if the sparseness of neural networks is taken into account. To reconstruct a sparse network, we determine the minimal set of linear couplings consistent with the measured covariances by minimizing the L1 norm of the coupling matrix under appropriate constraints. Contrary to intuition, after stochastic optimization of the coupling matrix, the resulting estimate of the underlying network is directed, despite the fact that a symmetric matrix of count covariances is used for inference. The performance of the new method is best if connections are neither exceedingly sparse, nor too dense, and it is easily applicable for networks of a few hundred nodes. Full coupling kernels can be obtained from the matrix of full covariance functions. We apply our method to networks of leaky integrate-and-fire neurons in an asynchronous-irregular state, where spike train covariances are well described by a linear model.
General dispersion formulae for atomic third-order non-linear optical properties
NASA Astrophysics Data System (ADS)
Bishop, David M.
1988-12-01
Dispersion formulae for the parallel and perpendicular optical hyperpolarizabilities γ ∥ω=γ xxxx(—ω σ;ω 1,ω 2ω 3) and γ ·ω =γ xzzx(—ω σ;ω 1,ω 2,ω 3), where ω σ=ω 1+ω 2+ω 3, are (for atoms): γ ∥ω/γ ∥0=1+ Aω L2+ O(ω 4),γ ·ω/γ ·0=1+ Bω L2+ O(ω 4), 1/3γ ∥ω/γ ·ω=1+ Cω L2+ O(ω 4), where A is independent of the process, B is proportional to 1+ az where z is independent of the process and a=(ω σω 3—ω 1ω 2)/ω L2, C is proportional to 1-6 a, and ω L2=ω σ2+ω 12+ω 22+ω 32. The coefficients A, B and C are related by C= A— B. These results are more general than those previously reported and asymptotically exact for low frequencies.
Biohybrid Control of General Linear Systems Using the Adaptive Filter Model of Cerebellum
Wilson, Emma D.; Assaf, Tareq; Pearson, Martin J.; Rossiter, Jonathan M.; Dean, Paul; Anderson, Sean R.; Porrill, John
2015-01-01
The adaptive filter model of the cerebellar microcircuit has been successfully applied to biological motor control problems, such as the vestibulo-ocular reflex (VOR), and to sensory processing problems, such as the adaptive cancelation of reafferent noise. It has also been successfully applied to problems in robotics, such as adaptive camera stabilization and sensor noise cancelation. In previous applications to inverse control problems, the algorithm was applied to the velocity control of a plant dominated by viscous and elastic elements. Naive application of the adaptive filter model to the displacement (as opposed to velocity) control of this plant results in unstable learning and control. To be more generally useful in engineering problems, it is essential to remove this restriction to enable the stable control of plants of any order. We address this problem here by developing a biohybrid model reference adaptive control (MRAC) scheme, which stabilizes the control algorithm for strictly proper plants. We evaluate the performance of this novel cerebellar-inspired algorithm with MRAC scheme in the experimental control of a dielectric electroactive polymer, a class of artificial muscle. The results show that the augmented cerebellar algorithm is able to accurately control the displacement response of the artificial muscle. The proposed solution not only greatly extends the practical applicability of the cerebellar-inspired algorithm, but may also shed light on cerebellar involvement in a wider range of biological control tasks. PMID:26257638
Jiang, Fei; Ma, Yanyuan; Wang, Yuanjia
2015-01-01
We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient functions of time, and use B-splines to estimate the unspecified function of the single index component. The covariance structure is taken into account via a working model, which provides valid estimation and inference procedure whether or not it captures the true covariance. The estimation method is applicable to both continuous and discrete outcomes. We derive large sample properties of the estimation procedure and show different convergence rate of each component of the model. The asymptotic properties when the kernel and regression spline methods are combined in a nested fashion has not been studied prior to this work even in the independent data case. PMID:26283801
NASA Astrophysics Data System (ADS)
Cedeño M, C. E.; de Araujo, J. C. N.
2016-05-01
A study of binary systems composed of two point particles with different masses in the linear regime of the characteristic formulation of general relativity with a Minkowski background is provided. The present paper generalizes a previous study by Bishop et al. The boundary conditions at the world tubes generated by the particles's orbits are explored, where the metric variables are decomposed in spin-weighted spherical harmonics. The power lost by the emission of gravitational waves is computed using the Bondi News function. The power found is the well-known result obtained by Peters and Mathews using a different approach. This agreement validates the approach considered here. Several multipole term contributions to the gravitational radiation field are also shown.
Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging
Fowler, Michael James
2014-04-25
In industrial and engineering applications, X-ray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy X-rays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in X-ray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edge-localizing prior for deconvolution; a smoothing prior with non-negativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy
The generalized cross-validation method applied to geophysical linear traveltime tomography
NASA Astrophysics Data System (ADS)
Bassrei, A.; Oliveira, N. P.
2009-12-01
The oil industry is the major user of Applied Geophysics methods for the subsurface imaging. Among different methods, the so-called seismic (or exploration seismology) methods are the most important. Tomography was originally developed for medical imaging and was introduced in exploration seismology in the 1980's. There are two main classes of geophysical tomography: those that use only the traveltimes between sources and receivers, which is a cinematic approach and those that use the wave amplitude itself, being a dynamic approach. Tomography is a kind of inverse problem, and since inverse problems are usually ill-posed, it is necessary to use some method to reduce their deficiencies. These difficulties of the inverse procedure are associated with the fact that the involved matrix is ill-conditioned. To compensate this shortcoming, it is appropriate to use some technique of regularization. In this work we make use of regularization with derivative matrices, also called smoothing. There is a crucial problem in regularization, which is the selection of the regularization parameter lambda. We use generalized cross validation (GCV) as a tool for the selection of lambda. GCV chooses the regularization parameter associated with the best average prediction for all possible omissions of one datum, corresponding to the minimizer of GCV function. GCV is used for an application in traveltime tomography, where the objective is to obtain the 2-D velocity distribution from the measured values of the traveltimes between sources and receivers. We present results with synthetic data, using a geological model that simulates different features, like a fault and a reservoir. The results using GCV are very good, including those contaminated with noise, and also using different regularization orders, attesting the feasibility of this technique.
Iwasaki, Yuichi; Brinkman, Stephen F
2015-04-01
Increased concerns about the toxicity of chemical mixtures have led to greater emphasis on analyzing the interactions among the mixture components based on observed effects. The authors applied a generalized linear mixed model (GLMM) to analyze survival of brown trout (Salmo trutta) acutely exposed to metal mixtures that contained copper and zinc. Compared with dominant conventional approaches based on an assumption of concentration addition and the concentration of a chemical that causes x% effect (ECx), the GLMM approach has 2 major advantages. First, binary response variables such as survival can be modeled without any transformations, and thus sample size can be taken into consideration. Second, the importance of the chemical interaction can be tested in a simple statistical manner. Through this application, the authors investigated whether the estimated concentration of the 2 metals binding to humic acid, which is assumed to be a proxy of nonspecific biotic ligand sites, provided a better prediction of survival effects than dissolved and free-ion concentrations of metals. The results suggest that the estimated concentration of metals binding to humic acid is a better predictor of survival effects, and thus the metal competition at the ligands could be an important mechanism responsible for effects of metal mixtures. Application of the GLMM (and the generalized linear model) presents an alternative or complementary approach to analyzing mixture toxicity. PMID:25524054
Aerial Scene Recognition using Efficient Sparse Representation
Cheriyadat, Anil M
2012-01-01
Advanced scene recognition systems for processing large volumes of high-resolution aerial image data are in great demand today. However, automated scene recognition remains a challenging problem. Efficient encoding and representation of spatial and structural patterns in the imagery are key in developing automated scene recognition algorithms. We describe an image representation approach that uses simple and computationally efficient sparse code computation to generate accurate features capable of producing excellent classification performance using linear SVM kernels. Our method exploits unlabeled low-level image feature measurements to learn a set of basis vectors. We project the low-level features onto the basis vectors and use simple soft threshold activation function to derive the sparse features. The proposed technique generates sparse features at a significantly lower computational cost than other methods~\\cite{Yang10, newsam11}, yet it produces comparable or better classification accuracy. We apply our technique to high-resolution aerial image datasets to quantify the aerial scene classification performance. We demonstrate that the dense feature extraction and representation methods are highly effective for automatic large-facility detection on wide area high-resolution aerial imagery.
Estimating sparse precision matrices
NASA Astrophysics Data System (ADS)
Padmanabhan, Nikhil; White, Martin; Zhou, Harrison H.; O'Connell, Ross
2016-08-01
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological precision matrices are often approximately sparse, the method allows one to exploit this sparsity of the precision matrix to more quickly converge to an asymptotic 1/sqrt{N_sim} rate while simultaneously providing an error model for all of the terms. Such an estimate can be used as the starting point for further regularization efforts which can improve upon the 1/sqrt{N_sim} limit above, and incorporating such additional steps is straightforward within this framework. We demonstrate the technique with toy models and with an example motivated by large-scale structure two-point analysis, showing significant improvements in the rate of convergence. For the large-scale structure example, we find errors on the precision matrix which are factors of 5 smaller than for the sample precision matrix for thousands of simulations or, alternatively, convergence to the same error level with more than an order of magnitude fewer simulations.
Parallel preconditioning techniques for sparse CG solvers
Basermann, A.; Reichel, B.; Schelthoff, C.
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.
NASA Astrophysics Data System (ADS)
Xiong, Y. P.; Xing, J. T.; Price, W. G.
2003-10-01
Generalized integrated structure-control dynamical systems consisting of any number of active/passive controllers and three-dimensional rigid/flexible substructures are investigated. The developed mathematical model assessing the behaviour of these complex systems includes description of general boundary conditions, the interaction mechanisms between structures, power flows and control characteristics. Three active control strategies are examined. That is, multiple channel absolute/relative velocity feedback controllers, their hybrid combination and an existing passive control system to which the former control systems are attached in order to improve overall control efficiency. From the viewpoint of continuum mechanics, an analytical solution of this generalized structure-control system has been developed allowing predictions of the dynamic responses at any point on or in substructures of the coupled system. Absolute or relative dynamic response or receptance, transmissibility, mobility, transfer functions have been derived to evaluate complex dynamic interaction mechanisms through various transmission paths. The instantaneous and time-averaged power flow of energy input, transmission and dissipation or absorption within and between the source substructure, control subsystems and controlled substructure are presented. The general theory developed provides an integrated framework to solve various vibration isolation and control problems and provides a basis to develop a general algorithm that may allow the user to build arbitrarily complex linear control models using simple commands and inputs. The proposed approach is applied to a practical example to illustrate and validate the mathematical model as well as to assess control effectiveness and to provide important guidelines to assist vibration control designers.
Sparse image reconstruction for molecular imaging.
Ting, Michael; Raich, Raviv; Hero, Alfred O
2009-06-01
The application that motivates this paper is molecular imaging at the atomic level. When discretized at subatomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution of the image with the system point spread function (psf). Such is the case with magnetic resonance force microscopy (MRFM), an emerging technology where imaging of an individual tobacco mosaic virus was recently demonstrated with nanometer resolution. We also consider additive white Gaussian noise (AWGN) in the measurements. Many prior works of sparse estimators have focused on the case when H has low coherence; however, the system matrix H in our application is the convolution matrix for the system psf. A typical convolution matrix has high coherence. This paper, therefore, does not assume a low coherence H. A discrete-continuous form of the Laplacian and atom at zero (LAZE) p.d.f. used by Johnstone and Silverman is formulated, and two sparse estimators derived by maximizing the joint p.d.f. of the observation and image conditioned on the hyperparameters. A thresholding rule that generalizes the hard and soft thresholding rule appears in the course of the derivation. This so-called hybrid thresholding rule, when used in the iterative thresholding framework, gives rise to the hybrid estimator, a generalization of the lasso. Estimates of the hyperparameters for the lasso and hybrid estimator are obtained via Stein's unbiased risk estimate (SURE). A numerical study with a Gaussian psf and two sparse images shows that the hybrid estimator outperforms the lasso.
NASA Astrophysics Data System (ADS)
Hernandez, Svea
2012-10-01
CTE measurements are made using the "internal sparse field test", along the parallelaxis. The "POS=" optional parameter, introduced during cycle 11, is used to provideoff-center MSM positioning of some slits. All exposures are internals.
NASA Astrophysics Data System (ADS)
Wolfe, Michael
2011-10-01
CTE measurements are made using the "internal sparse field test", along the parallelaxis. The "POS=" optional parameter, introduced during cycle 11, is used to provideoff-center MSM positionings of some slits. All exposures are internals.
NASA Astrophysics Data System (ADS)
Wolfe, Michael
2010-09-01
CTE measurements are made using the "internal sparse field test", along the parallelaxis. The "POS=" optional parameter, introduced during cycle 11, is used to provideoff-center MSM positionings of some slits. All exposures are internals.
NASA Astrophysics Data System (ADS)
Hernandez, Svea
2013-10-01
CTE measurements are made using the "internal sparse field test", along the parallelaxis. The "POS=" optional parameter, introduced during cycle 11, is used to provideoff-center MSM positioning of some slits. All exposures are internals.
NASA Astrophysics Data System (ADS)
Wolfe, Michael
2009-07-01
CTE measurements are made using the "internal sparse field test", along the parallelaxis. The "POS=" optional parameter, introduced during cycle 11, is used to provideoff-center MSM positionings of some slits. All exposures are internals.
NASA Astrophysics Data System (ADS)
Edwards, C. L.; Edwards, M. L.
2009-05-01
MEMS micro-mirror technology offers the opportunity to replace larger optical actuators with smaller, faster ones for lidar, network switching, and other beam steering applications. Recent developments in modeling and simulation of MEMS two-axis (tip-tilt) mirrors have resulted in closed-form solutions that are expressed in terms of physical, electrical and environmental parameters related to the MEMS device. The closed-form analytical expressions enable dynamic time-domain simulations without excessive computational overhead and are referred to as the Micro-mirror Pointing Model (MPM). Additionally, these first-principle models have been experimentally validated with in-situ static, dynamic, and stochastic measurements illustrating their reliability. These models have assumed that the mirror has a rectangular shape. Because the corners can limit the dynamic operation of a rectangular mirror, it is desirable to shape the mirror, e.g., mitering the corners. Presented in this paper is the formulation of a generalized electrostatic micromirror (GEM) model with an arbitrary convex piecewise linear shape that is readily implemented in MATLAB and SIMULINK for steady-state and dynamic simulations. Additionally, such a model permits an arbitrary shaped mirror to be approximated as a series of linearly tapered segments. Previously, "effective area" arguments were used to model a non-rectangular shaped mirror with an equivalent rectangular one. The GEM model shows the limitations of this approach and provides a pre-fabrication tool for designing mirror shapes.
Chen, Vivian Yi-Ju; Yang, Tse-Chuan
2012-08-01
An increasing interest in exploring spatial non-stationarity has generated several specialized analytic software programs; however, few of these programs can be integrated natively into a well-developed statistical environment such as SAS. We not only developed a set of SAS macro programs to fill this gap, but also expanded the geographically weighted generalized linear modeling (GWGLM) by integrating the strengths of SAS into the GWGLM framework. Three features distinguish our work. First, the macro programs of this study provide more kernel weighting functions than the existing programs. Second, with our codes the users are able to better specify the bandwidth selection process compared to the capabilities of existing programs. Third, the development of the macro programs is fully embedded in the SAS environment, providing great potential for future exploration of complicated spatially varying coefficient models in other disciplines. We provided three empirical examples to illustrate the use of the SAS macro programs and demonstrated the advantages explained above.
Tsai, Miao-Yu
2015-03-01
The problem of variable selection in the generalized linear-mixed models (GLMMs) is pervasive in statistical practice. For the purpose of variable selection, many methodologies for determining the best subset of explanatory variables currently exist according to the model complexity and differences between applications. In this paper, we develop a "higher posterior probability model with bootstrap" (HPMB) approach to select explanatory variables without fitting all possible GLMMs involving a small or moderate number of explanatory variables. Furthermore, to save computational load, we propose an efficient approximation approach with Laplace's method and Taylor's expansion to approximate intractable integrals in GLMMs. Simulation studies and an application of HapMap data provide evidence that this selection approach is computationally feasible and reliable for exploring true candidate genes and gene-gene associations, after adjusting for complex structures among clusters.
Wang, Tao; He, Peng; Ahn, Kwang Woo; Wang, Xujing; Ghosh, Soumitra; Laud, Purushottam
2015-01-01
The generalized linear mixed model (GLMM) is a useful tool for modeling genetic correlation among family data in genetic association studies. However, when dealing with families of varied sizes and diverse genetic relatedness, the GLMM has a special correlation structure which often makes it difficult to be specified using standard statistical software. In this study, we propose a Cholesky decomposition based re-formulation of the GLMM so that the re-formulated GLMM can be specified conveniently via “proc nlmixed” and “proc glimmix” in SAS, or OpenBUGS via R package BRugs. Performances of these procedures in fitting the re-formulated GLMM are examined through simulation studies. We also apply this re-formulated GLMM to analyze a real data set from Type 1 Diabetes Genetics Consortium (T1DGC). PMID:25873936
ERIC Educational Resources Information Center
Xu, Xueli; von Davier, Matthias
2008-01-01
The general diagnostic model (GDM) utilizes located latent classes for modeling a multidimensional proficiency variable. In this paper, the GDM is extended by employing a log-linear model for multiple populations that assumes constraints on parameters across multiple groups. This constrained model is compared to log-linear models that assume…
Sparse Methods for Biomedical Data
Ye, Jieping; Liu, Jun
2013-01-01
Following recent technological revolutions, the investigation of massive biomedical data with growing scale, diversity, and complexity has taken a center stage in modern data analysis. Although complex, the underlying representations of many biomedical data are often sparse. For example, for a certain disease such as leukemia, even though humans have tens of thousands of genes, only a few genes are relevant to the disease; a gene network is sparse since a regulatory pathway involves only a small number of genes; many biomedical signals are sparse or compressible in the sense that they have concise representations when expressed in a proper basis. Therefore, finding sparse representations is fundamentally important for scientific discovery. Sparse methods based on the ℓ1 norm have attracted a great amount of research efforts in the past decade due to its sparsity-inducing property, convenient convexity, and strong theoretical guarantees. They have achieved great success in various applications such as biomarker selection, biological network construction, and magnetic resonance imaging. In this paper, we review state-of-the-art sparse methods and their applications to biomedical data. PMID:24076585
A Bayesian semiparametric model for bivariate sparse longitudinal data.
Das, Kiranmoy; Li, Runze; Sengupta, Subhajit; Wu, Rongling
2013-09-30
Mixed-effects models have recently become popular for analyzing sparse longitudinal data that arise naturally in biological, agricultural and biomedical studies. Traditional approaches assume independent residuals over time and explain the longitudinal dependence by random effects. However, when bivariate or multivariate traits are measured longitudinally, this fundamental assumption is likely to be violated because of intertrait dependence over time. We provide a more general framework where the dependence of the observations from the same subject over time is not assumed to be explained completely by the random effects of the model. We propose a novel, mixed model-based approach and estimate the error-covariance structure nonparametrically under a generalized linear model framework. We use penalized splines to model the general effect of time, and we consider a Dirichlet process mixture of normal prior for the random-effects distribution. We analyze blood pressure data from the Framingham Heart Study where body mass index, gender and time are treated as covariates. We compare our method with traditional methods including parametric modeling of the random effects and independent residual errors over time. We conduct extensive simulation studies to investigate the practical usefulness of the proposed method. The current approach is very helpful in analyzing bivariate irregular longitudinal traits. PMID:23553747
Vector sparse representation of color image using quaternion matrix analysis.
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. PMID:25643407
NASA Astrophysics Data System (ADS)
Rio, Daniel; Rawlings, Robert; Woltz, Lawrence; Gilman, Jodi; Hommer, Daniel
2009-02-01
The general linear model (GLM) has been extensively applied to fMRI data in the time domain. However, traditionally time series data can be analyzed in the Fourier domain where the assumptions made as to the noise in the signal can be less restrictive and statistical tests are mathematically more rigorous. A complex form of the GLM in the Fourier domain has been applied to the analysis of fMRI (BOLD) data. This methodology has a number of advantages over temporal methods: 1. Noise in the fMRI data is modeled more generally and closer to that actually seen in the data. 2. Any input function is allowed regardless of the timing. 3. Non-parametric estimation of the transfer functions at each voxel are possible. 4. Rigorous statistical inference of single subjects is possible. This is demonstrated in the analysis of an experimental design with random exponentially distributed stimulus inputs (a two way ANOVA design with input stimuli images of alcohol, non-alcohol beverage and positive or negative images) sampled at 400 milliseconds. This methodology applied to a pair of subjects showed precise and interesting results (e.g. alcoholic beverage images attenuate the response of negative images in an alcoholic as compared to a control subject).
NASA Astrophysics Data System (ADS)
Choi, Hon-Chit; Wen, Lingfeng; Eberl, Stefan; Feng, Dagan
2006-03-01
Dynamic Single Photon Emission Computed Tomography (SPECT) has the potential to quantitatively estimate physiological parameters by fitting compartment models to the tracer kinetics. The generalized linear least square method (GLLS) is an efficient method to estimate unbiased kinetic parameters and parametric images. However, due to the low sensitivity of SPECT, noisy data can cause voxel-wise parameter estimation by GLLS to fail. Fuzzy C-Mean (FCM) clustering and modified FCM, which also utilizes information from the immediate neighboring voxels, are proposed to improve the voxel-wise parameter estimation of GLLS. Monte Carlo simulations were performed to generate dynamic SPECT data with different noise levels and processed by general and modified FCM clustering. Parametric images were estimated by Logan and Yokoi graphical analysis and GLLS. The influx rate (K I), volume of distribution (V d) were estimated for the cerebellum, thalamus and frontal cortex. Our results show that (1) FCM reduces the bias and improves the reliability of parameter estimates for noisy data, (2) GLLS provides estimates of micro parameters (K I-k 4) as well as macro parameters, such as volume of distribution (Vd) and binding potential (BP I & BP II) and (3) FCM clustering incorporating neighboring voxel information does not improve the parameter estimates, but improves noise in the parametric images. These findings indicated that it is desirable for pre-segmentation with traditional FCM clustering to generate voxel-wise parametric images with GLLS from dynamic SPECT data.
Wang, Chi; Dominici, Francesca; Parmigiani, Giovanni; Zigler, Corwin Matthew
2015-09-01
Confounder selection and adjustment are essential elements of assessing the causal effect of an exposure or treatment in observational studies. Building upon work by Wang et al. (2012, Biometrics 68, 661-671) and Lefebvre et al. (2014, Statistics in Medicine 33, 2797-2813), we propose and evaluate a Bayesian method to estimate average causal effects in studies with a large number of potential confounders, relatively few observations, likely interactions between confounders and the exposure of interest, and uncertainty on which confounders and interaction terms should be included. Our method is applicable across all exposures and outcomes that can be handled through generalized linear models. In this general setting, estimation of the average causal effect is different from estimation of the exposure coefficient in the outcome model due to noncollapsibility. We implement a Bayesian bootstrap procedure to integrate over the distribution of potential confounders and to estimate the causal effect. Our method permits estimation of both the overall population causal effect and effects in specified subpopulations, providing clear characterization of heterogeneous exposure effects that may vary considerably across different covariate profiles. Simulation studies demonstrate that the proposed method performs well in small sample size situations with 100-150 observations and 50 covariates. The method is applied to data on 15,060 US Medicare beneficiaries diagnosed with a malignant brain tumor between 2000 and 2009 to evaluate whether surgery reduces hospital readmissions within 30 days of diagnosis.
NASA Astrophysics Data System (ADS)
Lebovka, Nikolai I.; Tarasevich, Yuri Yu.; Dubinin, Dmitri O.; Laptev, Valeri V.; Vygornitskii, Nikolai V.
2015-12-01
The jamming and percolation for two generalized models of random sequential adsorption (RSA) of linear k -mers (particles occupying k adjacent sites) on a square lattice are studied by means of Monte Carlo simulation. The classical RSA model assumes the absence of overlapping of the new incoming particle with the previously deposited ones. The first model is a generalized variant of the RSA model for both k -mers and a lattice with defects. Some of the occupying k adjacent sites are considered as insulating and some of the lattice sites are occupied by defects (impurities). For this model even a small concentration of defects can inhibit percolation for relatively long k -mers. The second model is the cooperative sequential adsorption one where, for each new k -mer, only a restricted number of lateral contacts z with previously deposited k -mers is allowed. Deposition occurs in the case when z ≤(1 -d ) zm where zm=2 (k +1 ) is the maximum numbers of the contacts of k -mer, and d is the fraction of forbidden contacts. Percolation is observed only at some interval kmin≤k ≤kmax where the values kmin and kmax depend upon the fraction of forbidden contacts d . The value kmax decreases as d increases. A logarithmic dependence of the type log10(kmax) =a +b d , where a =4.04 ±0.22 ,b =-4.93 ±0.57 , is obtained.
Wang, Chi; Dominici, Francesca; Parmigiani, Giovanni; Zigler, Corwin Matthew
2015-01-01
Summary Confounder selection and adjustment are essential elements of assessing the causal effect of an exposure or treatment in observational studies. Building upon work by Wang et al. (2012) and Lefebvre et al. (2014), we propose and evaluate a Bayesian method to estimate average causal effects in studies with a large number of potential confounders, relatively few observations, likely interactions between confounders and the exposure of interest, and uncertainty on which confounders and interaction terms should be included. Our method is applicable across all exposures and outcomes that can be handled through generalized linear models. In this general setting, estimation of the average causal effect is different from estimation of the exposure coefficient in the outcome model due to non-collapsibility. We implement a Bayesian bootstrap procedure to integrate over the distribution of potential confounders and to estimate the causal effect. Our method permits estimation of both the overall population causal effect and effects in specified subpopulations, providing clear characterization of heterogeneous exposure effects that may vary considerably across different covariate profiles. Simulation studies demonstrate that the proposed method performs well in small sample size situations with 100 to 150 observations and 50 covariates. The method is applied to data on 15060 US Medicare beneficiaries diagnosed with a malignant brain tumor between 2000 and 2009 to evaluate whether surgery reduces hospital readmissions within thirty days of diagnosis. PMID:25899155
MAP Support Detection for Greedy Sparse Signal Recovery Algorithms in Compressive Sensing
NASA Astrophysics Data System (ADS)
Lee, Namyoon
2016-10-01
A reliable support detection is essential for a greedy algorithm to reconstruct a sparse signal accurately from compressed and noisy measurements. This paper proposes a novel support detection method for greedy algorithms, which is referred to as "\\textit{maximum a posteriori (MAP) support detection}". Unlike existing support detection methods that identify support indices with the largest correlation value in magnitude per iteration, the proposed method selects them with the largest likelihood ratios computed under the true and null support hypotheses by simultaneously exploiting the distributions of sensing matrix, sparse signal, and noise. Leveraging this technique, MAP-Matching Pursuit (MAP-MP) is first presented to show the advantages of exploiting the proposed support detection method, and a sufficient condition for perfect signal recovery is derived for the case when the sparse signal is binary. Subsequently, a set of iterative greedy algorithms, called MAP-generalized Orthogonal Matching Pursuit (MAP-gOMP), MAP-Compressive Sampling Matching Pursuit (MAP-CoSaMP), and MAP-Subspace Pursuit (MAP-SP) are presented to demonstrate the applicability of the proposed support detection method to existing greedy algorithms. From empirical results, it is shown that the proposed greedy algorithms with highly reliable support detection can be better, faster, and easier to implement than basis pursuit via linear programming.
Wavelet Sparse Approximate Inverse Preconditioners
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Tang, W.-P.; Wan, W. L.
1996-01-01
There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
Content addressable systolic array for sparse matrix computation
Wing, O.
1983-01-01
A systolic array is proposed which is specifically designed to solve a system of sparse linear equations. The array consists of a number of processing elements connected in a ring. Each processing element has its own content addressable memory where the nonzero elements of the sparse matrix are stored. Matrix elements to which elementary operations are applied are extracted from the memory by content addressing. The system of equations is solved in a systolic fashion and the solution is obtained in nz+5n-2 steps where nz is the number of nonzero elements along and below the diagonal and n is the number of equations. 13 references.
Towards an Accurate Performance Modeling of Parallel SparseFactorization
Grigori, Laura; Li, Xiaoye S.
2006-05-26
We present a performance model to analyze a parallel sparseLU factorization algorithm on modern cached-based, high-end parallelarchitectures. Our model characterizes the algorithmic behavior bytakingaccount the underlying processor speed, memory system performance, aswell as the interconnect speed. The model is validated using theSuperLU_DIST linear system solver, the sparse matrices from realapplications, and an IBM POWER3 parallel machine. Our modelingmethodology can be easily adapted to study performance of other types ofsparse factorizations, such as Cholesky or QR.
Robust head pose estimation using locality-constrained sparse coding
NASA Astrophysics Data System (ADS)
Kim, Hyunduk; Lee, Sang-Heon; Sohn, Myoung-Kyu
2015-12-01
Sparse coding (SC) method has been shown to deliver successful result in a variety of computer vision applications. However, it does not consider the underlying structure of the data in the feature space. On the other hand, locality constrained linear coding (LLC) utilizes locality constraint to project each input data into its local-coordinate system. Based on the recent success of LLC, we propose a novel locality-constrained sparse coding (LSC) method to overcome the limitation of the SC. In experiments, the proposed algorithms were applied to head pose estimation applications. Experimental results demonstrated that the LSC method is better than state-of-the-art methods.
NASA Astrophysics Data System (ADS)
Cariolle, D.; Teyssèdre, H.
2007-01-01
This article describes the validation of a linear parameterization of the ozone photochemistry for use in upper tropospheric and stratospheric studies. The present work extends a previously developed scheme by improving the 2D model used to derive the coefficients of the parameterization. The chemical reaction rates are updated from a compilation that includes recent laboratory works. Furthermore, the polar ozone destruction due to heterogeneous reactions at the surface of the polar stratospheric clouds is taken into account as a function of the stratospheric temperature and the total chlorine content. Two versions of the parameterization are tested. The first one only requires the resolution of a continuity equation for the time evolution of the ozone mixing ratio, the second one uses one additional equation for a cold tracer. The parameterization has been introduced into the chemical transport model MOCAGE. The model is integrated with wind and temperature fields from the ECMWF operational analyses over the period 2000-2004. Overall, the results show a very good agreement between the modelled ozone distribution and the Total Ozone Mapping Spectrometer (TOMS) satellite data and the "in-situ" vertical soundings. During the course of the integration the model does not show any drift and the biases are generally small. The model also reproduces fairly well the polar ozone variability, with notably the formation of "ozone holes" in the southern hemisphere with amplitudes and seasonal evolutions that follow the dynamics and time evolution of the polar vortex. The introduction of the cold tracer further improves the model simulation by allowing additional ozone destruction inside air masses exported from the high to the mid-latitudes, and by maintaining low ozone contents inside the polar vortex of the southern hemisphere over longer periods in spring time. It is concluded that for the study of climatic scenarios or the assimilation of ozone data, the present
Lebovka, Nikolai I; Tarasevich, Yuri Yu; Dubinin, Dmitri O; Laptev, Valeri V; Vygornitskii, Nikolai V
2015-12-01
The jamming and percolation for two generalized models of random sequential adsorption (RSA) of linear k-mers (particles occupying k adjacent sites) on a square lattice are studied by means of Monte Carlo simulation. The classical RSA model assumes the absence of overlapping of the new incoming particle with the previously deposited ones. The first model is a generalized variant of the RSA model for both k-mers and a lattice with defects. Some of the occupying k adjacent sites are considered as insulating and some of the lattice sites are occupied by defects (impurities). For this model even a small concentration of defects can inhibit percolation for relatively long k-mers. The second model is the cooperative sequential adsorption one where, for each new k-mer, only a restricted number of lateral contacts z with previously deposited k-mers is allowed. Deposition occurs in the case when z≤(1-d)z(m) where z(m)=2(k+1) is the maximum numbers of the contacts of k-mer, and d is the fraction of forbidden contacts. Percolation is observed only at some interval k(min)≤k≤k(max) where the values k(min) and k(max) depend upon the fraction of forbidden contacts d. The value k(max) decreases as d increases. A logarithmic dependence of the type log(10)(k(max))=a+bd, where a=4.04±0.22,b=-4.93±0.57, is obtained. PMID:26764641
Vock, David M; Davidian, Marie; Tsiatis, Anastasios A
2014-01-01
Generalized linear and nonlinear mixed models (GMMMs and NLMMs) are commonly used to represent non-Gaussian or nonlinear longitudinal or clustered data. A common assumption is that the random effects are Gaussian. However, this assumption may be unrealistic in some applications, and misspecification of the random effects density may lead to maximum likelihood parameter estimators that are inconsistent, biased, and inefficient. Because testing if the random effects are Gaussian is difficult, previous research has recommended using a flexible random effects density. However, computational limitations have precluded widespread use of flexible random effects densities for GLMMs and NLMMs. We develop a SAS macro, SNP_NLMM, that overcomes the computational challenges to fit GLMMs and NLMMs where the random effects are assumed to follow a smooth density that can be represented by the seminonparametric formulation proposed by Gallant and Nychka (1987). The macro is flexible enough to allow for any density of the response conditional on the random effects and any nonlinear mean trajectory. We demonstrate the SNP_NLMM macro on a GLMM of the disease progression of toenail infection and on a NLMM of intravenous drug concentration over time.
NASA Astrophysics Data System (ADS)
Asong, Zilefac E.; Khaliq, M. N.; Wheater, H. S.
2016-02-01
Based on the Generalized Linear Model (GLM) framework, a multisite stochastic modelling approach is developed using daily observations of precipitation and minimum and maximum temperatures from 120 sites located across the Canadian Prairie Provinces: Alberta, Saskatchewan and Manitoba. Temperature is modeled using a two-stage normal-heteroscedastic model by fitting mean and variance components separately. Likewise, precipitation occurrence and conditional precipitation intensity processes are modeled separately. The relationship between precipitation and temperature is accounted for by using transformations of precipitation as covariates to predict temperature fields. Large scale atmospheric covariates from the National Center for Environmental Prediction Reanalysis-I, teleconnection indices, geographical site attributes, and observed precipitation and temperature records are used to calibrate these models for the 1971-2000 period. Validation of the developed models is performed on both pre- and post-calibration period data. Results of the study indicate that the developed models are able to capture spatiotemporal characteristics of observed precipitation and temperature fields, such as inter-site and inter-variable correlation structure, and systematic regional variations present in observed sequences. A number of simulated weather statistics ranging from seasonal means to characteristics of temperature and precipitation extremes and some of the commonly used climate indices are also found to be in close agreement with those derived from observed data. This GLM-based modelling approach will be developed further for multisite statistical downscaling of Global Climate Model outputs to explore climate variability and change in this region of Canada.
Vock, David M; Davidian, Marie; Tsiatis, Anastasios A
2014-01-01
Generalized linear and nonlinear mixed models (GMMMs and NLMMs) are commonly used to represent non-Gaussian or nonlinear longitudinal or clustered data. A common assumption is that the random effects are Gaussian. However, this assumption may be unrealistic in some applications, and misspecification of the random effects density may lead to maximum likelihood parameter estimators that are inconsistent, biased, and inefficient. Because testing if the random effects are Gaussian is difficult, previous research has recommended using a flexible random effects density. However, computational limitations have precluded widespread use of flexible random effects densities for GLMMs and NLMMs. We develop a SAS macro, SNP_NLMM, that overcomes the computational challenges to fit GLMMs and NLMMs where the random effects are assumed to follow a smooth density that can be represented by the seminonparametric formulation proposed by Gallant and Nychka (1987). The macro is flexible enough to allow for any density of the response conditional on the random effects and any nonlinear mean trajectory. We demonstrate the SNP_NLMM macro on a GLMM of the disease progression of toenail infection and on a NLMM of intravenous drug concentration over time. PMID:24688453
Vock, David M.; Davidian, Marie; Tsiatis, Anastasios A.
2014-01-01
Generalized linear and nonlinear mixed models (GMMMs and NLMMs) are commonly used to represent non-Gaussian or nonlinear longitudinal or clustered data. A common assumption is that the random effects are Gaussian. However, this assumption may be unrealistic in some applications, and misspecification of the random effects density may lead to maximum likelihood parameter estimators that are inconsistent, biased, and inefficient. Because testing if the random effects are Gaussian is difficult, previous research has recommended using a flexible random effects density. However, computational limitations have precluded widespread use of flexible random effects densities for GLMMs and NLMMs. We develop a SAS macro, SNP_NLMM, that overcomes the computational challenges to fit GLMMs and NLMMs where the random effects are assumed to follow a smooth density that can be represented by the seminonparametric formulation proposed by Gallant and Nychka (1987). The macro is flexible enough to allow for any density of the response conditional on the random effects and any nonlinear mean trajectory. We demonstrate the SNP_NLMM macro on a GLMM of the disease progression of toenail infection and on a NLMM of intravenous drug concentration over time. PMID:24688453
Monda, D.P.; Galat, D.L.; Finger, S.E.; Kaiser, M.S.
1995-01-01
Toxicity of un-ionized ammonia (NH3-N) to the midge, Chironomus riparius was compared, using laboratory culture (well) water and sewage effluent (≈0.4 mg/L NH3-N) in two 96-h, static-renewal toxicity experiments. A generalized linear model was used for data analysis. For the first and second experiments, respectively, LC50 values were 9.4 mg/L (Test 1A) and 6.6 mg/L (Test 2A) for ammonia in well water, and 7.8 mg/L (Test 1B) and 4.1 mg/L (Test 2B) for ammonia in sewage effluent. Slopes of dose-response curves for Tests 1A and 2A were equal, but mortality occurred at lower NH3-N concentrations in Test 2A (unequal intercepts). Response ofC. riparius to NH3 in effluent was not consistent; dose-response curves for tests 1B and 2B differed in slope and intercept. Nevertheless, C. riparius was more sensitive to ammonia in effluent than in well water in both experiments, indicating a synergistic effect of ammonia in sewage effluent. These results demonstrate the advantages of analyzing the organisms entire range of response, as opposed to generating LC50 values, which represent only one point on the dose-response curve.
Tian, Fenghua; Liu, Hanli
2013-01-01
One of the main challenges in functional diffuse optical tomography (DOT) is to accurately recover the depth of brain activation, which is even more essential when differentiating true brain signals from task-evoked artifacts in the scalp. Recently, we developed a depth-compensated algorithm (DCA) to minimize the depth localization error in DOT. However, the semi-infinite model that was used in DCA deviated significantly from the realistic human head anatomy. In the present work, we incorporated depth-compensated DOT (DC-DOT) with a standard anatomical atlas of human head. Computer simulations and human measurements of sensorimotor activation were conducted to examine and prove the depth specificity and quantification accuracy of brain atlas-based DC-DOT. In addition, node-wise statistical analysis based on the general linear model (GLM) was also implemented and performed in this study, showing the robustness of DC-DOT that can accurately identify brain activation at the correct depth for functional brain imaging, even when co-existing with superficial artifacts. PMID:23859922
Huang, A.B.; Yortsos, Y.C.
1984-09-01
This paper reports on the continuation of previous work in the linear stability of immiscible, two-phase flow displacement processes in porous media that includes continuously changing mobility and capillary effects. In Part I simple basic-flow profiles that allow exact solutions to be obtained were investigated. First, the stability of non-capillary flows corresponding to a straight line fractional flow is examined. Next, the stability of capillary flows for general basic flow profiles is examined. For values of the viscosity ratio above the critical, the numerical results show that the displacement is unstable to small disturbances of wavelength larger than a critical value, and stable otherwise. This effect is attributed to the stabilizing action of capillarity. Values of wavelength corresponding to the highest rate of growth are numerically determined. It is found that stability is enhanced at lower values of the capillary number and the injection rate. Finally, a limited sensitivity study of the effect on stability of the functional forms of relative permeability and capillary pressure is carried out.
Mendes, T M; Guimarães-Okamoto, P T C; Machado-de-Avila, R A; Oliveira, D; Melo, M M; Lobato, Z I; Kalapothakis, E; Chávez-Olórtegui, C
2015-06-01
This communication describes the general characteristics of the venom from the Brazilian scorpion Tityus fasciolatus, which is an endemic species found in the central Brazil (States of Goiás and Minas Gerais), being responsible for sting accidents in this area. The soluble venom obtained from this scorpion is toxic to mice being the LD50 is 2.984 mg/kg (subcutaneally). SDS-PAGE of the soluble venom resulted in 10 fractions ranged in size from 6 to 10-80 kDa. Sheep were employed for anti-T. fasciolatus venom serum production. Western blotting analysis showed that most of these venom proteins are immunogenic. T. fasciolatus anti-venom revealed consistent cross-reactivity with venom antigens from Tityus serrulatus. Using known primers for T. serrulatus toxins, we have identified three toxins sequences from T. fasciolatus venom. Linear epitopes of these toxins were localized and fifty-five overlapping pentadecapeptides covering complete amino acid sequence of the three toxins were synthesized in cellulose membrane (spot-synthesis technique). The epitopes were located on the 3D structures and some important residues for structure/function were identified.
Xiao, Xun; Geyer, Veikko F; Bowne-Anderson, Hugo; Howard, Jonathon; Sbalzarini, Ivo F
2016-08-01
Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy.
Pernet, Cyril R.
2014-01-01
This tutorial presents several misconceptions related to the use the General Linear Model (GLM) in functional Magnetic Resonance Imaging (fMRI). The goal is not to present mathematical proofs but to educate using examples and computer code (in Matlab). In particular, I address issues related to (1) model parameterization (modeling baseline or null events) and scaling of the design matrix; (2) hemodynamic modeling using basis functions, and (3) computing percentage signal change. Using a simple controlled block design and an alternating block design, I first show why “baseline” should not be modeled (model over-parameterization), and how this affects effect sizes. I also show that, depending on what is tested; over-parameterization does not necessarily impact upon statistical results. Next, using a simple periodic vs. random event related design, I show how the hemodynamic model (hemodynamic function only or using derivatives) can affects parameter estimates, as well as detail the role of orthogonalization. I then relate the above results to the computation of percentage signal change. Finally, I discuss how these issues affect group analyses and give some recommendations. PMID:24478622
Uga, Minako; Dan, Ippeita; Sano, Toshifumi; Dan, Haruka; Watanabe, Eiju
2014-01-01
Abstract. An increasing number of functional near-infrared spectroscopy (fNIRS) studies utilize a general linear model (GLM) approach, which serves as a standard statistical method for functional magnetic resonance imaging (fMRI) data analysis. While fMRI solely measures the blood oxygen level dependent (BOLD) signal, fNIRS measures the changes of oxy-hemoglobin (oxy-Hb) and deoxy-hemoglobin (deoxy-Hb) signals at a temporal resolution severalfold higher. This suggests the necessity of adjusting the temporal parameters of a GLM for fNIRS signals. Thus, we devised a GLM-based method utilizing an adaptive hemodynamic response function (HRF). We sought the optimum temporal parameters to best explain the observed time series data during verbal fluency and naming tasks. The peak delay of the HRF was systematically changed to achieve the best-fit model for the observed oxy- and deoxy-Hb time series data. The optimized peak delay showed different values for each Hb signal and task. When the optimized peak delays were adopted, the deoxy-Hb data yielded comparable activations with similar statistical power and spatial patterns to oxy-Hb data. The adaptive HRF method could suitably explain the behaviors of both Hb parameters during tasks with the different cognitive loads during a time course, and thus would serve as an objective method to fully utilize the temporal structures of all fNIRS data. PMID:26157973
NASA Astrophysics Data System (ADS)
de Souza, R. S.; Hilbe, J. M.; Buelens, B.; Riggs, J. D.; Cameron, E.; Ishida, E. E. O.; Chies-Santos, A. L.; Killedar, M.
2015-10-01
In this paper, the third in a series illustrating the power of generalized linear models (GLMs) for the astronomical community, we elucidate the potential of the class of GLMs which handles count data. The size of a galaxy's globular cluster (GC) population (NGC) is a prolonged puzzle in the astronomical literature. It falls in the category of count data analysis, yet it is usually modelled as if it were a continuous response variable. We have developed a Bayesian negative binomial regression model to study the connection between NGC and the following galaxy properties: central black hole mass, dynamical bulge mass, bulge velocity dispersion and absolute visual magnitude. The methodology introduced herein naturally accounts for heteroscedasticity, intrinsic scatter, errors in measurements in both axes (either discrete or continuous) and allows modelling the population of GCs on their natural scale as a non-negative integer variable. Prediction intervals of 99 per cent around the trend for expected NGC comfortably envelope the data, notably including the Milky Way, which has hitherto been considered a problematic outlier. Finally, we demonstrate how random intercept models can incorporate information of each particular galaxy morphological type. Bayesian variable selection methodology allows for automatically identifying galaxy types with different productions of GCs, suggesting that on average S0 galaxies have a GC population 35 per cent smaller than other types with similar brightness.
Xiao, Xun; Geyer, Veikko F; Bowne-Anderson, Hugo; Howard, Jonathon; Sbalzarini, Ivo F
2016-08-01
Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy. PMID:27104582
NASA Astrophysics Data System (ADS)
Asong, Z. E.; Khaliq, M. N.; Wheater, H. S.
2016-08-01
In this study, a multisite multivariate statistical downscaling approach based on the Generalized Linear Model (GLM) framework is developed to downscale daily observations of precipitation and minimum and maximum temperatures from 120 sites located across the Canadian Prairie Provinces: Alberta, Saskatchewan and Manitoba. First, large scale atmospheric covariates from the National Center for Environmental Prediction (NCEP) Reanalysis-I, teleconnection indices, geographical site attributes, and observed precipitation and temperature records are used to calibrate GLMs for the 1971-2000 period. Then the calibrated models are used to generate daily sequences of precipitation and temperature for the 1962-2005 historical (conditioned on NCEP predictors), and future period (2006-2100) using outputs from five CMIP5 (Coupled Model Intercomparison Project Phase-5) Earth System Models corresponding to Representative Concentration Pathway (RCP): RCP2.6, RCP4.5, and RCP8.5 scenarios. The results indicate that the fitted GLMs are able to capture spatiotemporal characteristics of observed precipitation and temperature fields. According to the downscaled future climate, mean precipitation is projected to increase in summer and decrease in winter while minimum temperature is expected to warm faster than the maximum temperature. Climate extremes are projected to intensify with increased radiative forcing.
Mendes, T M; Guimarães-Okamoto, P T C; Machado-de-Avila, R A; Oliveira, D; Melo, M M; Lobato, Z I; Kalapothakis, E; Chávez-Olórtegui, C
2015-06-01
This communication describes the general characteristics of the venom from the Brazilian scorpion Tityus fasciolatus, which is an endemic species found in the central Brazil (States of Goiás and Minas Gerais), being responsible for sting accidents in this area. The soluble venom obtained from this scorpion is toxic to mice being the LD50 is 2.984 mg/kg (subcutaneally). SDS-PAGE of the soluble venom resulted in 10 fractions ranged in size from 6 to 10-80 kDa. Sheep were employed for anti-T. fasciolatus venom serum production. Western blotting analysis showed that most of these venom proteins are immunogenic. T. fasciolatus anti-venom revealed consistent cross-reactivity with venom antigens from Tityus serrulatus. Using known primers for T. serrulatus toxins, we have identified three toxins sequences from T. fasciolatus venom. Linear epitopes of these toxins were localized and fifty-five overlapping pentadecapeptides covering complete amino acid sequence of the three toxins were synthesized in cellulose membrane (spot-synthesis technique). The epitopes were located on the 3D structures and some important residues for structure/function were identified. PMID:25817000
NASA Astrophysics Data System (ADS)
Guo, Yang; Sivalingam, Kantharuban; Valeev, Edward F.; Neese, Frank
2016-03-01
Multi-reference (MR) electronic structure methods, such as MR configuration interaction or MR perturbation theory, can provide reliable energies and properties for many molecular phenomena like bond breaking, excited states, transition states or magnetic properties of transition metal complexes and clusters. However, owing to their inherent complexity, most MR methods are still too computationally expensive for large systems. Therefore the development of more computationally attractive MR approaches is necessary to enable routine application for large-scale chemical systems. Among the state-of-the-art MR methods, second-order N-electron valence state perturbation theory (NEVPT2) is an efficient, size-consistent, and intruder-state-free method. However, there are still two important bottlenecks in practical applications of NEVPT2 to large systems: (a) the high computational cost of NEVPT2 for large molecules, even with moderate active spaces and (b) the prohibitive cost for treating large active spaces. In this work, we address problem (a) by developing a linear scaling "partially contracted" NEVPT2 method. This development uses the idea of domain-based local pair natural orbitals (DLPNOs) to form a highly efficient algorithm. As shown previously in the framework of single-reference methods, the DLPNO concept leads to an enormous reduction in computational effort while at the same time providing high accuracy (approaching 99.9% of the correlation energy), robustness, and black-box character. In the DLPNO approach, the virtual space is spanned by pair natural orbitals that are expanded in terms of projected atomic orbitals in large orbital domains, while the inactive space is spanned by localized orbitals. The active orbitals are left untouched. Our implementation features a highly efficient "electron pair prescreening" that skips the negligible inactive pairs. The surviving pairs are treated using the partially contracted NEVPT2 formalism. A detailed comparison
Guo, Yang; Sivalingam, Kantharuban; Valeev, Edward F; Neese, Frank
2016-03-01
Multi-reference (MR) electronic structure methods, such as MR configuration interaction or MR perturbation theory, can provide reliable energies and properties for many molecular phenomena like bond breaking, excited states, transition states or magnetic properties of transition metal complexes and clusters. However, owing to their inherent complexity, most MR methods are still too computationally expensive for large systems. Therefore the development of more computationally attractive MR approaches is necessary to enable routine application for large-scale chemical systems. Among the state-of-the-art MR methods, second-order N-electron valence state perturbation theory (NEVPT2) is an efficient, size-consistent, and intruder-state-free method. However, there are still two important bottlenecks in practical applications of NEVPT2 to large systems: (a) the high computational cost of NEVPT2 for large molecules, even with moderate active spaces and (b) the prohibitive cost for treating large active spaces. In this work, we address problem (a) by developing a linear scaling "partially contracted" NEVPT2 method. This development uses the idea of domain-based local pair natural orbitals (DLPNOs) to form a highly efficient algorithm. As shown previously in the framework of single-reference methods, the DLPNO concept leads to an enormous reduction in computational effort while at the same time providing high accuracy (approaching 99.9% of the correlation energy), robustness, and black-box character. In the DLPNO approach, the virtual space is spanned by pair natural orbitals that are expanded in terms of projected atomic orbitals in large orbital domains, while the inactive space is spanned by localized orbitals. The active orbitals are left untouched. Our implementation features a highly efficient "electron pair prescreening" that skips the negligible inactive pairs. The surviving pairs are treated using the partially contracted NEVPT2 formalism. A detailed comparison
Guo, Yang; Sivalingam, Kantharuban; Valeev, Edward F; Neese, Frank
2016-03-01
Multi-reference (MR) electronic structure methods, such as MR configuration interaction or MR perturbation theory, can provide reliable energies and properties for many molecular phenomena like bond breaking, excited states, transition states or magnetic properties of transition metal complexes and clusters. However, owing to their inherent complexity, most MR methods are still too computationally expensive for large systems. Therefore the development of more computationally attractive MR approaches is necessary to enable routine application for large-scale chemical systems. Among the state-of-the-art MR methods, second-order N-electron valence state perturbation theory (NEVPT2) is an efficient, size-consistent, and intruder-state-free method. However, there are still two important bottlenecks in practical applications of NEVPT2 to large systems: (a) the high computational cost of NEVPT2 for large molecules, even with moderate active spaces and (b) the prohibitive cost for treating large active spaces. In this work, we address problem (a) by developing a linear scaling "partially contracted" NEVPT2 method. This development uses the idea of domain-based local pair natural orbitals (DLPNOs) to form a highly efficient algorithm. As shown previously in the framework of single-reference methods, the DLPNO concept leads to an enormous reduction in computational effort while at the same time providing high accuracy (approaching 99.9% of the correlation energy), robustness, and black-box character. In the DLPNO approach, the virtual space is spanned by pair natural orbitals that are expanded in terms of projected atomic orbitals in large orbital domains, while the inactive space is spanned by localized orbitals. The active orbitals are left untouched. Our implementation features a highly efficient "electron pair prescreening" that skips the negligible inactive pairs. The surviving pairs are treated using the partially contracted NEVPT2 formalism. A detailed comparison
Joint sparse representation for robust multimodal biometrics recognition.
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.
Joint sparse representation for robust multimodal biometrics recognition.
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. PMID:24231870
FPGA implementation of sparse matrix algorithm for information retrieval
NASA Astrophysics Data System (ADS)
Bojanic, Slobodan; Jevtic, Ruzica; Nieto-Taladriz, Octavio
2005-06-01
Information text data retrieval requires a tremendous amount of processing time because of the size of the data and the complexity of information retrieval algorithms. In this paper the solution to this problem is proposed via hardware supported information retrieval algorithms. Reconfigurable computing may adopt frequent hardware modifications through its tailorable hardware and exploits parallelism for a given application through reconfigurable and flexible hardware units. The degree of the parallelism can be tuned for data. In this work we implemented standard BLAS (basic linear algebra subprogram) sparse matrix algorithm named Compressed Sparse Row (CSR) that is showed to be more efficient in terms of storage space requirement and query-processing timing over the other sparse matrix algorithms for information retrieval application. Although inverted index algorithm is treated as the de facto standard for information retrieval for years, an alternative approach to store the index of text collection in a sparse matrix structure gains more attention. This approach performs query processing using sparse matrix-vector multiplication and due to parallelization achieves a substantial efficiency over the sequential inverted index. The parallel implementations of information retrieval kernel are presented in this work targeting the Virtex II Field Programmable Gate Arrays (FPGAs) board from Xilinx. A recent development in scientific applications is the use of FPGA to achieve high performance results. Computational results are compared to implementations on other platforms. The design achieves a high level of parallelism for the overall function while retaining highly optimised hardware within processing unit.
NASA Astrophysics Data System (ADS)
Goudfrooij, Paul
1997-07-01
CTE measurements are made using the "sparse field test", along both the serial and parallel axes. This program needs special commanding to provide {a} off-center MSM positionings of some slits, and {b} the ability to read out with any amplifier {A, B, C, or D}. All exposures are internals.
2010-01-01
Background Near-infrared spectroscopy (NIRS) is a non-invasive neuroimaging technique that recently has been developed to measure the changes of cerebral blood oxygenation associated with brain activities. To date, for functional brain mapping applications, there is no standard on-line method for analysing NIRS data. Methods In this paper, a novel on-line NIRS data analysis framework taking advantages of both the general linear model (GLM) and the Kalman estimator is devised. The Kalman estimator is used to update the GLM coefficients recursively, and one critical coefficient regarding brain activities is then passed to a t-statistical test. The t-statistical test result is used to update a topographic brain activation map. Meanwhile, a set of high-pass filters is plugged into the GLM to prevent very low-frequency noises, and an autoregressive (AR) model is used to prevent the temporal correlation caused by physiological noises in NIRS time series. A set of data recorded in finger tapping experiments is studied using the proposed framework. Results The obtained results suggest that the method can effectively track the task related brain activation areas, and prevent the noise distortion in the estimation while the experiment is running. Thereby, the potential of the proposed method for real-time NIRS-based brain imaging was demonstrated. Conclusions This paper presents a novel on-line approach for analysing NIRS data for functional brain mapping applications. This approach demonstrates the potential of a real-time-updating topographic brain activation map. PMID:21138595
NASA Astrophysics Data System (ADS)
Widyaningsih, Yekti; Saefuddin, Asep; Notodiputro, Khairil A.; Wigena, Aji H.
2012-05-01
The objective of this research is to build a nested generalized linear mixed model using an ordinal response variable with some covariates. There are three main jobs in this paper, i.e. parameters estimation procedure, simulation, and implementation of the model for the real data. At the part of parameters estimation procedure, concepts of threshold, nested random effect, and computational algorithm are described. The simulations data are built for 3 conditions to know the effect of different parameter values of random effect distributions. The last job is the implementation of the model for the data about poverty in 9 districts of Java Island. The districts are Kuningan, Karawang, and Majalengka chose randomly in West Java; Temanggung, Boyolali, and Cilacap from Central Java; and Blitar, Ngawi, and Jember from East Java. The covariates in this model are province, number of bad nutrition cases, number of farmer families, and number of health personnel. In this modeling, all covariates are grouped as ordinal scale. Unit observation in this research is sub-district (kecamatan) nested in district, and districts (kabupaten) are nested in province. For the result of simulation, ARB (Absolute Relative Bias) and RRMSE (Relative Root of mean square errors) scale is used. They show that prov parameters have the highest bias, but more stable RRMSE in all conditions. The simulation design needs to be improved by adding other condition, such as higher correlation between covariates. Furthermore, as the result of the model implementation for the data, only number of farmer family and number of medical personnel have significant contributions to the level of poverty in Central Java and East Java province, and only district 2 (Karawang) of province 1 (West Java) has different random effect from the others. The source of the data is PODES (Potensi Desa) 2008 from BPS (Badan Pusat Statistik).
NASA Astrophysics Data System (ADS)
Cariolle, D.; Teyssèdre, H.
2007-05-01
This article describes the validation of a linear parameterization of the ozone photochemistry for use in upper tropospheric and stratospheric studies. The present work extends a previously developed scheme by improving the 2-D model used to derive the coefficients of the parameterization. The chemical reaction rates are updated from a compilation that includes recent laboratory work. Furthermore, the polar ozone destruction due to heterogeneous reactions at the surface of the polar stratospheric clouds is taken into account as a function of the stratospheric temperature and the total chlorine content. Two versions of the parameterization are tested. The first one only requires the solution of a continuity equation for the time evolution of the ozone mixing ratio, the second one uses one additional equation for a cold tracer. The parameterization has been introduced into the chemical transport model MOCAGE. The model is integrated with wind and temperature fields from the ECMWF operational analyses over the period 2000-2004. Overall, the results from the two versions show a very good agreement between the modelled ozone distribution and the Total Ozone Mapping Spectrometer (TOMS) satellite data and the "in-situ" vertical soundings. During the course of the integration the model does not show any drift and the biases are generally small, of the order of 10%. The model also reproduces fairly well the polar ozone variability, notably the formation of "ozone holes" in the Southern Hemisphere with amplitudes and a seasonal evolution that follow the dynamics and time evolution of the polar vortex. The introduction of the cold tracer further improves the model simulation by allowing additional ozone destruction inside air masses exported from the high to the mid-latitudes, and by maintaining low ozone content inside the polar vortex of the Southern Hemisphere over longer periods in spring time. It is concluded that for the study of climate scenarios or the assimilation of
Blind source separation by sparse decomposition
NASA Astrophysics Data System (ADS)
Zibulevsky, Michael; Pearlmutter, Barak A.
2000-04-01
The blind source separation problem is to extract the underlying source signals from a set of their linear mixtures, where the mixing matrix is unknown. This situation is common, eg in acoustics, radio, and medical signal processing. We exploit the property of the sources to have a sparse representation in a corresponding signal dictionary. Such a dictionary may consist of wavelets, wavelet packets, etc., or be obtained by learning from a given family of signals. Starting from the maximum a posteriori framework, which is applicable to the case of more sources than mixtures, we derive a few other categories of objective functions, which provide faster and more robust computations, when there are an equal number of sources and mixtures. Our experiments with artificial signals and with musical sounds demonstrate significantly better separation than other known techniques.
Amesos2 Templated Direct Sparse Solver Package
2011-05-24
Amesos2 is a templated direct sparse solver package. Amesos2 provides interfaces to direct sparse solvers, rather than providing native solver capabilities. Amesos2 is a derivative work of the Trilinos package Amesos.
Galaxy redshift surveys with sparse sampling
Chiang, Chi-Ting; Wullstein, Philipp; Komatsu, Eiichiro; Jee, Inh; Jeong, Donghui; Blanc, Guillermo A.; Ciardullo, Robin; Gronwall, Caryl; Hagen, Alex; Schneider, Donald P.; Drory, Niv; Fabricius, Maximilian; Landriau, Martin; Finkelstein, Steven; Jogee, Shardha; Cooper, Erin Mentuch; Tuttle, Sarah; Gebhardt, Karl; Hill, Gary J.
2013-12-01
Survey observations of the three-dimensional locations of galaxies are a powerful approach to measure the distribution of matter in the universe, which can be used to learn about the nature of dark energy, physics of inflation, neutrino masses, etc. A competitive survey, however, requires a large volume (e.g., V{sub survey} ∼ 10Gpc{sup 3}) to be covered, and thus tends to be expensive. A ''sparse sampling'' method offers a more affordable solution to this problem: within a survey footprint covering a given survey volume, V{sub survey}, we observe only a fraction of the volume. The distribution of observed regions should be chosen such that their separation is smaller than the length scale corresponding to the wavenumber of interest. Then one can recover the power spectrum of galaxies with precision expected for a survey covering a volume of V{sub survey} (rather than the volume of the sum of observed regions) with the number density of galaxies given by the total number of observed galaxies divided by V{sub survey} (rather than the number density of galaxies within an observed region). We find that regularly-spaced sampling yields an unbiased power spectrum with no window function effect, and deviations from regularly-spaced sampling, which are unavoidable in realistic surveys, introduce calculable window function effects and increase the uncertainties of the recovered power spectrum. On the other hand, we show that the two-point correlation function (pair counting) is not affected by sparse sampling. While we discuss the sparse sampling method within the context of the forthcoming Hobby-Eberly Telescope Dark Energy Experiment, the method is general and can be applied to other galaxy surveys.
Sparse, Decorrelated Odor Coding in the Mushroom Body Enhances Learned Odor Discrimination
Lin, Andrew C.; Bygrave, Alexei; de Calignon, Alix; Lee, Tzumin; Miesenböck, Gero
2014-01-01
Summary Sparse coding may be a general strategy of neural systems to augment memory capacity. In Drosophila, sparse odor coding by the Kenyon cells of the mushroom body is thought to generate a large number of precisely addressable locations for the storage of odor-specific memories. However, it remains untested how sparse coding relates to behavioral performance. Here we demonstrate that sparseness is controlled by a negative feedback circuit between Kenyon cells and the GABAergic anterior paired lateral (APL) neuron. Systematic activation and blockade of each leg of this feedback circuit show that Kenyon cells activate APL and APL inhibits Kenyon cells. Disrupting the Kenyon cell-APL feedback loop decreases the sparseness of Kenyon cell odor responses, increases inter-odor correlations, and prevents flies from learning to discriminate similar, but not dissimilar, odors. These results suggest that feedback inhibition suppresses Kenyon cell activity to maintain sparse, decorrelated odor coding and thus the odor-specificity of memories. PMID:24561998
Linearithmic time sparse and convex maximum margin clustering.
Zhang, Xiao-Lei; Wu, Ji
2012-12-01
Recently, a new clustering method called maximum margin clustering (MMC) was proposed and has shown promising performances. It was originally formulated as a difficult nonconvex integer problem. To make the MMC problem practical, the researchers either relaxed the original MMC problem to inefficient convex optimization problems or reformulated it to nonconvex optimization problems, which sacrifice the convexity for efficiency. However, no approaches can both hold the convexity and be efficient. In this paper, a new linearithmic time sparse and convex MMC algorithm, called support-vector-regression-based MMC (SVR-MMC), is proposed. Generally, it first uses the SVR as the core of the MMC. Then, it is relaxed as a convex optimization problem, which is iteratively solved by the cutting-plane algorithm. Each cutting-plane subproblem is further decomposed to a serial supervised SVR problem by a new global extended-level method (GELM). Finally, each supervised SVR problem is solved in a linear time complexity by a new sparse-kernel SVR (SKSVR) algorithm. We further extend the SVR-MMC algorithm to the multiple-kernel clustering (MKC) problem and the multiclass MMC (M3C) problem, which are denoted as SVR-MKC and SVR-M3C, respectively. One key point of the algorithms is the utilization of the SVR. It can prevent the MMC and its extensions meeting an integer matrix programming problem. Another key point is the new SKSVR. It provides a linear time interface to the nonlinear kernel scenarios, so that the SVR-MMC and its extensions can keep a linearthmic time complexity in nonlinear kernel scenarios. Our experimental results on various real-world data sets demonstrate the effectiveness and the efficiency of the SVR-MMC and its two extensions. Moreover, the unsupervised application of the SVR-MKC to the voice activity detection (VAD) shows that the SVR-MKC can achieve good performances that are close to its supervised counterpart, meet the real-time demand of the VAD, and need no
Heydari, Shahram; Miranda-Moreno, Luis F; Liping, Fu
2014-12-01
In fall 2009, a new speed limit of 40 km/h was introduced on local streets in Montreal (previous speed limit: 50 km/h). This paper proposes a methodology to efficiently estimate the effect of such reduction on speeding behaviors. We employ a full Bayes before-after approach, which overcomes the limitations of the empirical Bayes method. The proposed methodology allows for the analysis of speed data using hourly observations. Therefore, the entire daily profile of speed is considered. Furthermore, it accounts for the entire distribution of speed in contrast to the traditional approach of considering only a point estimate such as 85th percentile speed. Different reference speeds were used to examine variations in the treatment effectiveness in terms of speeding rate and frequency. In addition to comparing rates of vehicles exceeding reference speeds of 40 km/h and 50 km/h (speeding), we verified how the implemented treatment affected "excessive speeding" behaviors (exceeding 80 km/h). To model operating speeds, two Bayesian generalized mixed linear models were utilized. These models have the advantage of addressing the heterogeneity problem in observations and efficiently capturing potential intra-site correlations. A variety of site characteristics, temporal variables, and environmental factors were considered. The analyses indicated that variables such as lane width and night hour had an increasing effect on speeding. Conversely, roadside parking had a decreasing effect on speeding. One-way and lane width had an increasing effect on excessive speeding, whereas evening hour had a decreasing effect. This study concluded that although the treatment was effective with respect to speed references of 40 km/h and 50 km/h, its effectiveness was not significant with respect to excessive speeding-which carries a great risk to pedestrians and cyclists in urban areas. Therefore, caution must be taken in drawing conclusions about the effectiveness of speed limit reduction. This
ERIC Educational Resources Information Center
Chen, Haiwen
2012-01-01
In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…
ERIC Educational Resources Information Center
Dimitrov, Dimiter M.; Raykov, Tenko; AL-Qataee, Abdullah Ali
2015-01-01
This article is concerned with developing a measure of general academic ability (GAA) for high school graduates who apply to colleges, as well as with the identification of optimal weights of the GAA indicators in a linear combination that yields a composite score with maximal reliability and maximal predictive validity, employing the framework of…
ERIC Educational Resources Information Center
Bashaw, W. L., Ed.; Findley, Warren G., Ed.
This volume contains the five major addresses and subsequent discussion from the Symposium on the General Linear Models Approach to the Analysis of Experimental Data in Educational Research, which was held in 1967 in Athens, Georgia. The symposium was designed to produce systematic information, including new methodology, for dissemination to the…
Guided wavefield reconstruction from sparse measurements
NASA Astrophysics Data System (ADS)
Mesnil, Olivier; Ruzzene, Massimo
2016-02-01
Guided wave measurements are at the basis of several Non-Destructive Evaluation (NDE) techniques. Although sparse measurements of guided wave obtained using piezoelectric sensors can efficiently detect and locate defects, extensive informa-tion on the shape and subsurface location of defects can be extracted from full-field measurements acquired by Laser Doppler Vibrometers (LDV). Wavefield acquisition from LDVs is generally a slow operation due to the fact that the wave propagation to record must be repeated for each point measurement and the initial conditions must be reached between each measurement. In this research, a Sparse Wavefield Reconstruction (SWR) process using Compressed Sensing is developed. The goal of this technique is to reduce the number of point measurements needed to apply NDE techniques by at least one order of magnitude by extrapolating the knowledge of a few randomly chosen measured pixels over an over-sampled grid. To achieve this, the Lamb wave propagation equation is used to formulate a basis of shape functions in which the wavefield has a sparse representation, in order to comply with the Compressed Sensing requirements and use l1-minimization solvers. The main assumption of this reconstruction process is that every material point of the studied area is a potential source. The Compressed Sensing matrix is defined as being the contribution that would have been received at a measurement location from each possible source, using the dispersion relations of the specimen computed using a Semi-Analytical Finite Element technique. The measurements are then processed through an l1-minimizer to find a minimum corresponding to the set of active sources and their corresponding excitation functions. This minimum represents the best combination of the parameters of the model matching the sparse measurements. Wavefields are then reconstructed using the propagation equation. The set of active sources found by minimization contains all the wave
Color Sparse Representations for Image Processing: Review, Models, and Prospects.
Barthélemy, Quentin; Larue, Anthony; Mars, Jérôme I
2015-11-01
Sparse representations have been extended to deal with color images composed of three channels. A review of dictionary-learning-based sparse representations for color images is made here, detailing the differences between the models, and comparing their results on the real and simulated data. These models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering/transformation of the color channels. Moreover, this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix-based color filtering, which highlights the filtering implicitly applied through this model. Based on this reformulation, the new color filtering model is introduced, using unconstrained filters. In this model, spatial morphologies of color images are encoded by atoms, and colors are encoded by color filters. Color variability is no longer captured in increasing the dictionary size, but with color filters, this gives an efficient color representation.
Finding communities in sparse networks
NASA Astrophysics Data System (ADS)
Singh, Abhinav; Humphries, Mark D.
2015-03-01
Spectral algorithms based on matrix representations of networks are often used to detect communities, but classic spectral methods based on the adjacency matrix and its variants fail in sparse networks. New spectral methods based on non-backtracking random walks have recently been introduced that successfully detect communities in many sparse networks. However, the spectrum of non-backtracking random walks ignores hanging trees in networks that can contain information about their community structure. We introduce the reluctant backtracking operators that explicitly account for hanging trees as they admit a small probability of returning to the immediately previous node, unlike the non-backtracking operators that forbid an immediate return. We show that the reluctant backtracking operators can detect communities in certain sparse networks where the non-backtracking operators cannot, while performing comparably on benchmark stochastic block model networks and real world networks. We also show that the spectrum of the reluctant backtracking operator approximately optimises the standard modularity function. Interestingly, for this family of non- and reluctant-backtracking operators the main determinant of performance on real-world networks is whether or not they are normalised to conserve probability at each node.
Highly parallel sparse Cholesky factorization
NASA Technical Reports Server (NTRS)
Gilbert, John R.; Schreiber, Robert
1990-01-01
Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms.
Neonatal Atlas Construction Using Sparse Representation
Shi, Feng; Wang, Li; Wu, Guorong; Li, Gang; Gilmore, John H.; Lin, Weili; Shen, Dinggang
2014-01-01
Atlas construction generally includes first an image registration step to normalize all images into a common space and then an atlas building step to fuse the information from all the aligned images. Although numerous atlas construction studies have been performed to improve the accuracy of the image registration step, unweighted or simply weighted average is often used in the atlas building step. In this article, we propose a novel patch-based sparse representation method for atlas construction after all images have been registered into the common space. By taking advantage of local sparse representation, more anatomical details can be recovered in the built atlas. To make the anatomical structures spatially smooth in the atlas, the anatomical feature constraints on group structure of representations and also the overlapping of neighboring patches are imposed to ensure the anatomical consistency between neighboring patches. The proposed method has been applied to 73 neonatal MR images with poor spatial resolution and low tissue contrast, for constructing a neonatal brain atlas with sharp anatomical details. Experimental results demonstrate that the proposed method can significantly enhance the quality of the constructed atlas by discovering more anatomical details especially in the highly convoluted cortical regions. The resulting atlas demonstrates superior performance of our atlas when applied to spatially normalizing three different neonatal datasets, compared with other start-of-the-art neonatal brain atlases. PMID:24638883
Image fusion via nonlocal sparse K-SVD dictionary learning.
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.
Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing
Yoshida, Ryo; West, Mike
2010-01-01
We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate “artificial” posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data. PMID:20890391
Sparse Matrices in MATLAB: Design and Implementation
NASA Technical Reports Server (NTRS)
Gilbert, John R.; Moler, Cleve; Schreiber, Robert
1992-01-01
The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations. The only change to the outward appearance of the MATLAB language is a pair of commands to create full or sparse matrices. Nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.
A General Family of Limited Information Goodness-of-Fit Statistics for Multinomial Data
ERIC Educational Resources Information Center
Joe, Harry; Maydeu-Olivares, Alberto
2010-01-01
Maydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009-1020, "2005"; Psychometrika 71:713-732, "2006") introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are…
Lewis, Robert Michael (College of William and Mary, Williamsburg, VA); Torczon, Virginia Joanne (College of William and Mary, Williamsburg, VA); Kolda, Tamara Gibson
2006-08-01
We consider the solution of nonlinear programs in the case where derivatives of the objective function and nonlinear constraints are unavailable. To solve such problems, we propose an adaptation of a method due to Conn, Gould, Sartenaer, and Toint that proceeds by approximately minimizing a succession of linearly constrained augmented Lagrangians. Our modification is to use a derivative-free generating set direct search algorithm to solve the linearly constrained subproblems. The stopping criterion proposed by Conn, Gould, Sartenaer and Toint for the approximate solution of the subproblems requires explicit knowledge of derivatives. Such information is presumed absent in the generating set search method we employ. Instead, we show that stationarity results for linearly constrained generating set search methods provide a derivative-free stopping criterion, based on a step-length control parameter, that is sufficient to preserve the convergence properties of the original augmented Lagrangian algorithm.
Optimized sparse-particle aerosol representations for modeling cloud-aerosol interactions
NASA Astrophysics Data System (ADS)
Fierce, Laura; McGraw, Robert
2016-04-01
Sparse representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Here we introduce a new framework for representing aerosol distributions, based on the method of moments. Given a set of moment constraints, we show how linear programming can be used to identify collections of sparse particles that approximately maximize distributional entropy. The collections of sparse particles derived from this approach reproduce CCN activity of the exact model aerosol distributions with high accuracy. Additionally, the linear programming techniques described in this study can be used to bound key aerosol properties, such as the number concentration of CCN. Unlike the commonly used sparse representations, such as modal and sectional schemes, the maximum-entropy moment-based approach is not constrained to pre-determined size bins or assumed distribution shapes. This study is a first step toward a new aerosol simulation scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.
Image Super-Resolution via Adaptive Regularization and Sparse Representation.
Cao, Feilong; Cai, Miaomiao; Tan, Yuanpeng; Zhao, Jianwei
2016-07-01
Previous studies have shown that image patches can be well represented as a sparse linear combination of elements from an appropriately selected over-complete dictionary. Recently, single-image super-resolution (SISR) via sparse representation using blurred and downsampled low-resolution images has attracted increasing interest, where the aim is to obtain the coefficients for sparse representation by solving an l0 or l1 norm optimization problem. The l0 optimization is a nonconvex and NP-hard problem, while the l1 optimization usually requires many more measurements and presents new challenges even when the image is the usual size, so we propose a new approach for SISR recovery based on regularization nonconvex optimization. The proposed approach is potentially a powerful method for recovering SISR via sparse representations, and it can yield a sparser solution than the l1 regularization method. We also consider the best choice for lp regularization with all p in (0, 1), where we propose a scheme that adaptively selects the norm value for each image patch. In addition, we provide a method for estimating the best value of the regularization parameter λ adaptively, and we discuss an alternate iteration method for selecting p and λ . We perform experiments, which demonstrates that the proposed regularization nonconvex optimization method can outperform the convex optimization method and generate higher quality images.
Beam hardening correction for sparse-view CT reconstruction
NASA Astrophysics Data System (ADS)
Liu, Wenlei; Rong, Junyan; Gao, Peng; Liao, Qimei; Lu, HongBing
2015-03-01
Beam hardening, which is caused by spectrum polychromatism of the X-ray beam, may result in various artifacts in the reconstructed image and degrade image quality. The artifacts would be further aggravated for the sparse-view reconstruction due to insufficient sampling data. Considering the advantages of the total-variation (TV) minimization in CT reconstruction with sparse-view data, in this paper, we propose a beam hardening correction method for sparse-view CT reconstruction based on Brabant's modeling. In this correction model for beam hardening, the attenuation coefficient of each voxel at the effective energy is modeled and estimated linearly, and can be applied in an iterative framework, such as simultaneous algebraic reconstruction technique (SART). By integrating the correction model into the forward projector of the algebraic reconstruction technique (ART), the TV minimization can recover images when only a limited number of projections are available. The proposed method does not need prior information about the beam spectrum. Preliminary validation using Monte Carlo simulations indicates that the proposed method can provide better reconstructed images from sparse-view projection data, with effective suppression of artifacts caused by beam hardening. With appropriate modeling of other degrading effects such as photon scattering, the proposed framework may provide a new way for low-dose CT imaging.
Inverse lithography using sparse mask representations
NASA Astrophysics Data System (ADS)
Ionescu, Radu C.; Hurley, Paul; Apostol, Stefan
2015-03-01
We present a novel optimisation algorithm for inverse lithography, based on optimization of the mask derivative, a domain inherently sparse, and for rectilinear polygons, invertible. The method is first developed assuming a point light source, and then extended to general incoherent sources. What results is a fast algorithm, producing manufacturable masks (the search space is constrained to rectilinear polygons), and flexible (specific constraints such as minimal line widths can be imposed). One inherent trick is to treat polygons as continuous entities, thus making aerial image calculation extremely fast and accurate. Requirements for mask manufacturability can be integrated in the optimization without too much added complexity. We also explain how to extend the scheme for phase-changing mask optimization.
NASA Technical Reports Server (NTRS)
Utku, S.
1969-01-01
A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.
Improved bidirectional retrieval of sparse patterns stored by Hebbian learning.
Sommer, Friedrich T.; Palm, Gunther
1999-03-01
The Willshaw model is asymptotically the most efficient neural associative memory (NAM), but its finite version is hampered by high retrieval errors. Iterative retrieval has been proposed in a large number of different models to improve performance in auto-association tasks. In this paper, bidirectional retrieval for the hetero-associative memory task is considered: we define information efficiency as a general performance measure for bidirectional associative memory (BAM) and determine its asymptotic bound for the bidirectional Willshaw model. For the finite Willshaw model, an efficient new bidirectional retrieval strategy is proposed, the appropriate combinatorial model analysis is derived, and implications of the proposed sparse BAM for applications and brain theory are discussed. The distribution of the dendritic sum in the finite Willshaw model given by Buckingham and Willshaw [Buckingham, J., & Willshaw, D. (1992). Performance characteristics of associative nets. Network, 3, 407-414] allows no fast numerical evaluation. We derive a combinatorial formula with a highly reduced evaluation time that is used in the improved error analysis of the basic model and for estimation of the retrieval error in the naive model extension, where bidirectional retrieval is employed in the hetero-associative Willshaw model. The analysis rules out the naive BAM extension as a promising improvement. A new bidirectional retrieval algorithm - called crosswise bidirectional (CB) retrieval - is presented. The cross talk error is significantly reduced without employing more complex learning procedures or dummy augmentation in the pattern coding, as proposed in other refined BAM models [Wang, Y. F., Cruz, J. B., & Mulligan, J. H. (1990). Two coding strategies for bidirectional associative memory. IEEE Trans. Neural Networks, 1(1), 81-92; Leung, C.-S., Chan, L.-W., & Lai, E. (1995). Stability, capacity and statistical dynamics of second-order bidirectional associative memory. IEEE Trans
Multi-source adaptation joint kernel sparse representation for visual classification.
Tao, JianWen; Hu, Wenjun; Wen, Shiting
2016-04-01
Most of the existing domain adaptation learning (DAL) methods relies on a single source domain to learn a classifier with well-generalized performance for the target domain of interest, which may lead to the so-called negative transfer problem. To this end, many multi-source adaptation methods have been proposed. While the advantages of using multi-source domains of information for establishing an adaptation model have been widely recognized, how to boost the robustness of the computational model for multi-source adaptation learning has only recently received attention. To address this issue for achieving enhanced performance, we propose in this paper a novel algorithm called multi-source Adaptation Regularization Joint Kernel Sparse Representation (ARJKSR) for robust visual classification problems. Specifically, ARJKSR jointly represents target dataset by a sparse linear combination of training data of each source domain in some optimal Reproduced Kernel Hilbert Space (RKHS), recovered by simultaneously minimizing the inter-domain distribution discrepancy and maximizing the local consistency, whilst constraining the observations from both target and source domains to share their sparse representations. The optimization problem of ARJKSR can be solved using an efficient alternative direction method. Under the framework ARJKSR, we further learn a robust label prediction matrix for the unlabeled instances of target domain based on the classical graph-based semi-supervised learning (GSSL) diagram, into which multiple Laplacian graphs constructed with the ARJKSR are incorporated. The validity of our method is examined by several visual classification problems. Results demonstrate the superiority of our method in comparison to several state-of-the-arts. PMID:26894961
Yang, Jiachen; Ding, Zhiyong; Guo, Fei; Wang, Huogen; Hughes, Nick
2015-11-01
In this paper, we investigate the problem of optimization of multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction function, the problem studied in this paper is how to learn effective hyper-predictor for a tuple of data points, so that a complex loss function corresponding to a multivariate performance measure can be minimized. We propose to present the tuple of data points to a tuple of sparse codes via a dictionary, and then apply a linear function to compare a sparse code against a given candidate class label. To learn the dictionary, sparse codes, and parameter of the linear function, we propose a joint optimization problem. In this problem, the both the reconstruction error and sparsity of sparse code, and the upper bound of the complex loss function are minimized. Moreover, the upper bound of the loss function is approximated by the sparse codes and the linear function parameter. To optimize this problem, we develop an iterative algorithm based on descent gradient methods to learn the sparse codes and hyper-predictor parameter alternately. Experiment results on some benchmark data sets show the advantage of the proposed methods over other state-of-the-art algorithms.
NASA Astrophysics Data System (ADS)
Sharma, S.; Narayan, A.
2001-06-01
The non-linear oscillation of inter-connected satellites system about its equilibrium position in the neighabourhood of main resonance ??=3D 1, under the combined effects of the solar radiation pressure and the dissipative forces of general nature has been discussed. It is found that the oscillation of the system gets disturbed when the frequency of the natural oscillation approaches the resonance frequency.
Compressive sensing of sparse tensors.
Friedland, Shmuel; Li, Qun; Schonfeld, Dan
2014-10-01
Compressive sensing (CS) has triggered an enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact reconstruction through relatively few nonadaptive linear measurements. While conventional CS theory relies on data representation in the form of vectors, many data types in various applications, such as color imaging, video sequences, and multisensor networks, are intrinsically represented by higher order tensors. Application of CS to higher order data representation is typically performed by conversion of the data to very long vectors that must be measured using very large sampling matrices, thus imposing a huge computational and memory burden. In this paper, we propose generalized tensor compressive sensing (GTCS)-a unified framework for CS of higher order tensors, which preserves the intrinsic structure of tensor data with reduced computational complexity at reconstruction. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we propound two reconstruction procedures, a serial method and a parallelizable method. We then compare the performance of the proposed method with Kronecker compressive sensing (KCS) and multiway compressive sensing (MWCS). We demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both reconstruction accuracy (within a range of compression ratios) and processing speed. The major disadvantage of our methods (and of MWCS as well) is that the compression ratios may be worse than that offered by KCS.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems.
Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan
2016-04-12
Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. PMID:27035946
Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models.
Fan, Jianqing; Feng, Yang; Song, Rui
2011-06-01
A variable screening procedure via correlation learning was proposed in Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonparametric learning. Our nonparametric independence screening is called NIS, a specific member of the sure independence screening. Several closely related variable screening procedures are proposed. Under general nonparametric models, it is shown that under some mild technical conditions, the proposed independence screening methods enjoy a sure screening property. The extent to which the dimensionality can be reduced by independence screening is also explicitly quantified. As a methodological extension, a data-driven thresholding and an iterative nonparametric independence screening (INIS) are also proposed to enhance the finite sample performance for fitting sparse additive models. The simulation results and a real data analysis demonstrate that the proposed procedure works well with moderate sample size and large dimension and performs better than competing methods.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan
2016-01-01
Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. PMID:27035946
Huang, Lei; Jin, Yan; Gao, Yaozong; Thung, Kim-Han; Shen, Dinggang
2016-10-01
Alzheimer's disease (AD) is an irreversible neurodegenerative disease and affects a large population in the world. Cognitive scores at multiple time points can be reliably used to evaluate the progression of the disease clinically. In recent studies, machine learning techniques have shown promising results on the prediction of AD clinical scores. However, there are multiple limitations in the current models such as linearity assumption and missing data exclusion. Here, we present a nonlinear supervised sparse regression-based random forest (RF) framework to predict a variety of longitudinal AD clinical scores. Furthermore, we propose a soft-split technique to assign probabilistic paths to a test sample in RF for more accurate predictions. In order to benefit from the longitudinal scores in the study, unlike the previous studies that often removed the subjects with missing scores, we first estimate those missing scores with our proposed soft-split sparse regression-based RF and then utilize those estimated longitudinal scores at all the previous time points to predict the scores at the next time point. The experiment results demonstrate that our proposed method is superior to the traditional RF and outperforms other state-of-art regression models. Our method can also be extended to be a general regression framework to predict other disease scores. PMID:27500865
Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems
NASA Technical Reports Server (NTRS)
Oliker, Leonid; Li, Xiaoye; Heber, Gerd; Biswas, Rupak
2000-01-01
The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.
Compressive Sensing Based Design of Sparse Tripole Arrays.
Hawes, Matthew; Liu, Wei; Mihaylova, Lyudmila
2015-12-10
This paper considers the problem of designing sparse linear tripole arrays. In such arrays at each antenna location there are three orthogonal dipoles, allowing full measurement of both the horizontal and vertical components of the received waveform. We formulate this problem from the viewpoint of Compressive Sensing (CS). However, unlike for isotropic array elements (single antenna), we now have three complex valued weight coefficients associated with each potential location (due to the three dipoles), which have to be simultaneously minimised. If this is not done, we may only set the weight coefficients of individual dipoles to be zero valued, rather than complete tripoles, meaning some dipoles may remain at each location. Therefore, the contributions of this paper are to formulate the design of sparse tripole arrays as an optimisation problem, and then we obtain a solution based on the minimisation of a modified l1 norm or a series of iteratively solved reweighted minimisations, which ensure a truly sparse solution. Design examples are provided to verify the effectiveness of the proposed methods and show that a good approximation of a reference pattern can be achieved using fewer tripoles than a Uniform Linear Array (ULA) of equivalent length.
Compressive Sensing Based Design of Sparse Tripole Arrays
Hawes, Matthew; Liu, Wei; Mihaylova, Lyudmila
2015-01-01
This paper considers the problem of designing sparse linear tripole arrays. In such arrays at each antenna location there are three orthogonal dipoles, allowing full measurement of both the horizontal and vertical components of the received waveform. We formulate this problem from the viewpoint of Compressive Sensing (CS). However, unlike for isotropic array elements (single antenna), we now have three complex valued weight coefficients associated with each potential location (due to the three dipoles), which have to be simultaneously minimised. If this is not done, we may only set the weight coefficients of individual dipoles to be zero valued, rather than complete tripoles, meaning some dipoles may remain at each location. Therefore, the contributions of this paper are to formulate the design of sparse tripole arrays as an optimisation problem, and then we obtain a solution based on the minimisation of a modified l1 norm or a series of iteratively solved reweighted minimisations, which ensure a truly sparse solution. Design examples are provided to verify the effectiveness of the proposed methods and show that a good approximation of a reference pattern can be achieved using fewer tripoles than a Uniform Linear Array (ULA) of equivalent length. PMID:26690436
Towards robust and effective shape modeling: sparse shape composition.
Zhang, Shaoting; Zhan, Yiqiang; Dewan, Maneesh; Huang, Junzhou; Metaxas, Dimitris N; Zhou, Xiang Sean
2012-01-01
Organ shape plays an important role in various clinical practices, e.g., diagnosis, surgical planning and treatment evaluation. It is usually derived from low level appearance cues in medical images. However, due to diseases and imaging artifacts, low level appearance cues might be weak or misleading. In this situation, shape priors become critical to infer and refine the shape derived by image appearances. Effective modeling of shape priors is challenging because: (1) shape variation is complex and cannot always be modeled by a parametric probability distribution; (2) a shape instance derived from image appearance cues (input shape) may have gross errors; and (3) local details of the input shape are difficult to preserve if they are not statistically significant in the training data. In this paper we propose a novel Sparse Shape Composition model (SSC) to deal with these three challenges in a unified framework. In our method, a sparse set of shapes in the shape repository is selected and composed together to infer/refine an input shape. The a priori information is thus implicitly incorporated on-the-fly. Our model leverages two sparsity observations of the input shape instance: (1) the input shape can be approximately represented by a sparse linear combination of shapes in the shape repository; (2) parts of the input shape may contain gross errors but such errors are sparse. Our model is formulated as a sparse learning problem. Using L1 norm relaxation, it can be solved by an efficient expectation-maximization (EM) type of framework. Our method is extensively validated on two medical applications, 2D lung localization in X-ray images and 3D liver segmentation in low-dose CT scans. Compared to state-of-the-art methods, our model exhibits better performance in both studies. PMID:21963296
Image fusion using sparse overcomplete feature dictionaries
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.
Kuhls-Gilcrist, Andrew T.; Gupta, Sandesh K.; Bednarek, Daniel R.; Rudin, Stephen
2010-01-01
The MTF, NNPS, and DQE are standard linear system metrics used to characterize intrinsic detector performance. To evaluate total system performance for actual clinical conditions, generalized linear system metrics (GMTF, GNNPS and GDQE) that include the effect of the focal spot distribution, scattered radiation, and geometric unsharpness are more meaningful and appropriate. In this study, a two-dimensional (2D) generalized linear system analysis was carried out for a standard flat panel detector (FPD) (194-micron pixel pitch and 600-micron thick CsI) and a newly-developed, high-resolution, micro-angiographic fluoroscope (MAF) (35-micron pixel pitch and 300-micron thick CsI). Realistic clinical parameters and x-ray spectra were used. The 2D detector MTFs were calculated using the new Noise Response method and slanted edge method and 2D focal spot distribution measurements were done using a pin-hole assembly. The scatter fraction, generated for a uniform head equivalent phantom, was measured and the scatter MTF was simulated with a theoretical model. Different magnifications and scatter fractions were used to estimate the 2D GMTF, GNNPS and GDQE for both detectors. Results show spatial non-isotropy for the 2D generalized metrics which provide a quantitative description of the performance of the complete imaging system for both detectors. This generalized analysis demonstrated that the MAF and FPD have similar capabilities at lower spatial frequencies, but that the MAF has superior performance over the FPD at higher frequencies even when considering focal spot blurring and scatter. This 2D generalized performance analysis is a valuable tool to evaluate total system capabilities and to enable optimized design for specific imaging tasks. PMID:21243038
Accelerated Gibbs Sampling for Infinite Sparse Factor Analysis
Andrzejewski, D M
2011-09-12
The Indian Buffet Process (IBP) gives a probabilistic model of sparse binary matrices with an unbounded number of columns. This construct can be used, for example, to model a fixed numer of observed data points (rows) associated with an unknown number of latent features (columns). Markov Chain Monte Carlo (MCMC) methods are often used for IBP inference, and in this technical note, we provide a detailed review of the derivations of collapsed and accelerated Gibbs samplers for the linear-Gaussian infinite latent feature model. We also discuss and explain update equations for hyperparameter resampling in a 'full Bayesian' treatment and present a novel slice sampler capable of extending the accelerated Gibbs sampler to the case of infinite sparse factor analysis by allowing the use of real-valued latent features.
Universal regularizers for robust sparse coding and modeling.
Ramírez, Ignacio; Sapiro, Guillermo
2012-09-01
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 theory, we propose a framework for designing sparsity regularization terms which have theoretical and practical advantages when compared with the more standard l(0) or l(1) ones. The presentation of the framework and theoretical foundations is complemented with examples that show its practical advantages in image denoising, zooming and classification.
Pothen, A.
1999-02-01
Gary Kumfert and Alex Pothen have improved the quality and run time of two ordering algorithms for minimizing the wavefront and envelope size of sparse matrices and graphs. These algorithms compute orderings for irregular data structures (e.g., unstructured meshes) that reduce the number of cache misses on modern workstation architectures. They have completed the implementation of a parallel solver for sparse, symmetric indefinite systems for distributed memory computers such as the IBM SP-2. The indefiniteness requires one to incorporate block pivoting (2 by 2 blocks) in the algorithm, thus demanding dynamic, parallel data structures. This is the first reported parallel solver for the indefinite problem. Direct methods for solving systems of linear equations employ sophisticated combinatorial and algebraic algorithms that contribute to software complexity, and hence it is natural to consider object-oriented design (OOD) in this context. The authors have continued to create software for solving sparse systems of linear equations by direct methods employing OOD. Fast computation of robust preconditioners is a priority for solving large systems of equations on unstructured grids and in other applications. They have developed new algorithms and software that can compute incomplete factorization preconditioners for high level fill in time proportional to the number of floating point operations and memory accesses.
Half-quadratic-based iterative minimization for robust sparse representation.
He, Ran; Zheng, Wei-Shi; Tan, Tieniu; Sun, Zhenan
2014-02-01
Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explores their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to performing both error correction and error detection. More specifically, by using the additive form of HQ, we propose an ℓ1-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative form of HQ, we propose an ℓ1-regularized error detection method by learning from uncorrupted data iteratively. We also show that the ℓ1-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the performance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings.
NASA Astrophysics Data System (ADS)
Tsuboi, Zengo
2013-05-01
In [1] (Z. Tsuboi, Nucl. Phys. B 826 (2010) 399, arxiv:arXiv:0906.2039), we proposed Wronskian-like solutions of the T-system for [ M , N ]-hook of the general linear superalgebra gl (M | N). We have generalized these Wronskian-like solutions to the ones for the general T-hook, which is a union of [M1 ,N1 ]-hook and [M2 ,N2 ]-hook (M =M1 +M2, N =N1 +N2). These solutions are related to Weyl-type supercharacter formulas of infinite dimensional unitarizable modules of gl (M | N). Our solutions also include a Wronskian-like solution discussed in [2] (N. Gromov, V. Kazakov, S. Leurent, Z. Tsuboi, JHEP 1101 (2011) 155, arxiv:arXiv:1010.2720) in relation to the AdS5 /CFT4 spectral problem.
Index statistical properties of sparse random graphs
NASA Astrophysics Data System (ADS)
Metz, F. L.; Stariolo, Daniel A.
2015-10-01
Using the replica method, we develop an analytical approach to compute the characteristic function for the probability PN(K ,λ ) that a large N ×N adjacency matrix of sparse random graphs has K eigenvalues below a threshold λ . The method allows to determine, in principle, all moments of PN(K ,λ ) , from which the typical sample-to-sample fluctuations can be fully characterized. For random graph models with localized eigenvectors, we show that the index variance scales linearly with N ≫1 for |λ |>0 , with a model-dependent prefactor that can be exactly calculated. Explicit results are discussed for Erdös-Rényi and regular random graphs, both exhibiting a prefactor with a nonmonotonic behavior as a function of λ . These results contrast with rotationally invariant random matrices, where the index variance scales only as lnN , with an universal prefactor that is independent of λ . Numerical diagonalization results confirm the exactness of our approach and, in addition, strongly support the Gaussian nature of the index fluctuations.
Sparse representation for the ISAR image reconstruction
NASA Astrophysics Data System (ADS)
Hu, Mengqi; Montalbo, John; Li, Shuxia; Sun, Ligang; Qiao, Zhijun G.
2016-05-01
In this paper, a sparse representation of the data for an inverse synthetic aperture radar (ISAR) system is provided in two dimensions. The proposed sparse representation motivates the use a of a Convex Optimization that recovers the image with far less samples, which is required by Nyquist-Shannon sampling theorem to increases the efficiency and decrease the cost of calculation in radar imaging.
Sparse Modeling for Astronomical Data Analysis
NASA Astrophysics Data System (ADS)
Ikeda, Shiro; Odaka, Hirokazu; Uemura, Makoto
2016-03-01
For astronomical data analysis, there have been proposed multiple methods based on sparse modeling. We have proposed a method for Compton camera imaging. The proposed approach is a sparse modeling method, but the derived algorithm is different from LASSO. We explain the problem and how we derived the method.
Dictionary construction in sparse methods for image restoration
Wohlberg, Brendt
2010-01-01
Sparsity-based methods have achieved very good performance in a wide variety of image restoration problems, including denoising, inpainting, super-resolution, and source separation. These methods are based on the assumption that the image to be reconstructed may be represented as a superposition of a few known components, and the appropriate linear combination of components is estimated by solving an optimization such as Basis Pursuit De-Noising (BPDN). Considering that the K-SVD constructs a dictionary which has been optimised for mean performance over a training set, it is not too surprising that better performance can be achieved by selecting a custom dictionary for each individual block to be reconstructed. The nearest neighbor dictionary construction can be understood geometrically as a method for estimating the local projection into the manifold of image blocks, whereas the K-SVD dictionary makes more sense within a source-coding framework (it is presented as a generalization of the k-means algorithm for constructing a VQ codebook), is therefore, it could be argued, less appropriate in principle, for reconstruction problems. One can, of course, motivate the use of the K-SVD in reconstruction application on practical grounds, avoiding the computational expense of constructing a different dictionary for each block to be denoised. Since the performance of the nearest neighbor dictionary decreases when the dictionary becomes sufficiently large, this method is also superior to the approach of utilizing the entire training set as a dictionary (and this can also be understood within the image block manifold model). In practical terms, the tradeoff is between the computational cost of a nearest neighbor search (which can be achieved very efficiently), or of increased cost at the sparse optimization.
NASA Technical Reports Server (NTRS)
Ustino, Eugene A.
2006-01-01
This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches
NASA Technical Reports Server (NTRS)
Tal-Ezer, Hillel
1987-01-01
During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.
NASA Technical Reports Server (NTRS)
Gupta, K. K.; Akyuz, F. A.; Heer, E.
1972-01-01
This program, an extension of the linear equilibrium problem solver ELAS, is an updated and extended version of its earlier form (written in FORTRAN 2 for the IBM 7094 computer). A synchronized material property concept utilizing incremental time steps and the finite element matrix displacement approach has been adopted for the current analysis. A special option enables employment of constant time steps in the logarithmic scale, thereby reducing computational efforts resulting from accumulative material memory effects. A wide variety of structures with elastic or viscoelastic material properties can be analyzed by VISCEL. The program is written in FORTRAN 5 language for the Univac 1108 computer operating under the EXEC 8 system. Dynamic storage allocation is automatically effected by the program, and the user may request up to 195K core memory in a 260K Univac 1108/EXEC 8 machine. The physical program VISCEL, consisting of about 7200 instructions, has four distinct links (segments), and the compiled program occupies a maximum of about 11700 words decimal of core storage.
Blind deconvolution of images using optimal sparse representations.
Bronstein, Michael M; Bronstein, Alexander M; Zibulevsky, Michael; Zeevi, Yehoshua Y
2005-06-01
The relative Newton algorithm, previously proposed for quasi-maximum likelihood blind source separation and blind deconvolution of one-dimensional signals is generalized for blind deconvolution of images. Smooth approximation of the absolute value is used as the nonlinear term for sparse sources. In addition, we propose a method of sparsification, which allows blind deconvolution of arbitrary sources, and show how to find optimal sparsifying transformations by supervised learning.
Maximum constrained sparse coding for image representation
NASA Astrophysics Data System (ADS)
Zhang, Jie; Zhao, Danpei; Jiang, Zhiguo
2015-12-01
Sparse coding exhibits good performance in many computer vision applications by finding bases which capture highlevel semantics of the data and learning sparse coefficients in terms of the bases. However, due to the fact that bases are non-orthogonal, sparse coding can hardly preserve the samples' similarity, which is important for discrimination. In this paper, a new image representing method called maximum constrained sparse coding (MCSC) is proposed. Sparse representation with more active coefficients means more similarity information, and the infinite norm is added to the solution for this purpose. We solve the optimizer by constraining the codes' maximum and releasing the residual to other dictionary atoms. Experimental results on image clustering show that our method can preserve the similarity of adjacent samples and maintain the sparsity of code simultaneously.
Large-scale sparse singular value computations
NASA Technical Reports Server (NTRS)
Berry, Michael W.
1992-01-01
Four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture are presented. Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography are emphasized. The target architectures for implementations are the CRAY-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications which require approximate pseudo-inverses of large sparse Jacobian matrices.
Sparse distributed memory: Principles and operation
NASA Technical Reports Server (NTRS)
Flynn, M. J.; Kanerva, P.; Bhadkamkar, N.
1989-01-01
Sparse distributed memory is a generalized random access memory (RAM) for long (1000 bit) binary words. Such words can be written into and read from the memory, and they can also be used to address the memory. The main attribute of the memory is sensitivity to similarity, meaning that a word can be read back not only by giving the original write address but also by giving one close to it as measured by the Hamming distance between addresses. Large memories of this kind are expected to have wide use in speech recognition and scene analysis, in signal detection and verification, and in adaptive control of automated equipment, in general, in dealing with real world information in real time. The memory can be realized as a simple, massively parallel computer. Digital technology has reached a point where building large memories is becoming practical. Major design issues were resolved which were faced in building the memories. The design is described of a prototype memory with 256 bit addresses and from 8 to 128 K locations for 256 bit words. A key aspect of the design is extensive use of dynamic RAM and other standard components.
Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices
NASA Technical Reports Server (NTRS)
Freund, Roland
1989-01-01
We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.
Lipparini, Filippo; Scalmani, Giovanni; Lagardère, Louis; Stamm, Benjamin; Cancès, Eric; Maday, Yvon; Piquemal, Jean-Philip; Frisch, Michael J; Mennucci, Benedetta
2014-11-14
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute. PMID:25399133
Lipparini, Filippo; Scalmani, Giovanni; Frisch, Michael J.; Lagardère, Louis; Stamm, Benjamin; Cancès, Eric; Maday, Yvon; Piquemal, Jean-Philip; Mennucci, Benedetta
2014-11-14
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.
NASA Astrophysics Data System (ADS)
Lipparini, Filippo; Scalmani, Giovanni; Lagardère, Louis; Stamm, Benjamin; Cancès, Eric; Maday, Yvon; Piquemal, Jean-Philip; Frisch, Michael J.; Mennucci, Benedetta
2014-11-01
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.
Inversion of magnetotelluric data in a sparse model domain
NASA Astrophysics Data System (ADS)
Nittinger, Christian G.; Becken, Michael
2016-06-01
The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-posed problem. Smoothing constraints are widely employed to estimate a regularized solution. Here, we present an alternative inversion scheme that estimates a sparse representation of the model in a wavelet basis. The objective of the inversion is to determine the few non-zero wavelet coefficients which are required to fit the data. This approach falls into the class of sparsity constrained inversion schemes and minimizes the combination of the data misfit in a least squares ℓ2 sense and of a model coefficient norm in a ℓ1 sense (ℓ2-ℓ1 minimization). The ℓ1 coefficient norm renders the solution sparse in a suitable representation such as the multi-resolution wavelet basis, but does not impose explicit structural penalties on the model as it is the case for ℓ2 regularization. The presented numerical algorithm solves the mixed ℓ2-ℓ1 norm minimization problem for the non-linear magnetotelluric inverse problem. We demonstrate the feasibility of our algorithm on synthetic 2-D MT data as well as on a real data example. We found that sparse models can be estimated by inversion and that the spatial distribution of non-vanishing coefficients indicates regions in the model which are resolved.
Very sparse LSSVM reductions for large-scale data.
Mall, Raghvendra; Suykens, Johan A K
2015-05-01
Least squares support vector machines (LSSVMs) have been widely applied for classification and regression with comparable performance with SVMs. The LSSVM model lacks sparsity and is unable to handle large-scale data due to computational and memory constraints. A primal fixed-size LSSVM (PFS-LSSVM) introduce sparsity using Nyström approximation with a set of prototype vectors (PVs). The PFS-LSSVM model solves an overdetermined system of linear equations in the primal. However, this solution is not the sparsest. We investigate the sparsity-error tradeoff by introducing a second level of sparsity. This is done by means of L0 -norm-based reductions by iteratively sparsifying LSSVM and PFS-LSSVM models. The exact choice of the cardinality for the initial PV set is not important then as the final model is highly sparse. The proposed method overcomes the problem of memory constraints and high computational costs resulting in highly sparse reductions to LSSVM models. The approximations of the two models allow to scale the models to large-scale datasets. Experiments on real-world classification and regression data sets from the UCI repository illustrate that these approaches achieve sparse models without a significant tradeoff in errors.
Efficient nearest neighbors via robust sparse hashing.
Cherian, Anoop; Sra, Suvrit; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2014-08-01
This paper presents a new nearest neighbor (NN) retrieval framework: robust sparse hashing (RSH). Our approach is inspired by the success of dictionary learning for sparse coding. Our key idea is to sparse code the data using a learned dictionary, and then to generate hash codes out of these sparse codes for accurate and fast NN retrieval. But, direct application of sparse coding to NN retrieval poses a technical difficulty: when data are noisy or uncertain (which is the case with most real-world data sets), for a query point, an exact match of the hash code generated from the sparse code seldom happens, thereby breaking the NN retrieval. Borrowing ideas from robust optimization theory, we circumvent this difficulty via our novel robust dictionary learning and sparse coding framework called RSH, by learning dictionaries on the robustified counterparts of the perturbed data points. The algorithm is applied to NN retrieval on both simulated and real-world data. Our results demonstrate that RSH holds significant promise for efficient NN retrieval against the state of the art.
NASA Astrophysics Data System (ADS)
Malekan, Mohammad; Barros, Felicio Bruzzi
2016-07-01
Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global-local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global-local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global-local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global-local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global-local enrichments lead to ill-conditioned system matrices and bad convergence rate.
NASA Astrophysics Data System (ADS)
Malekan, Mohammad; Barros, Felicio Bruzzi
2016-11-01
Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global-local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global-local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global-local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global-local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global-local enrichments lead to ill-conditioned system matrices and bad convergence rate.
A balanced decomposition algorithm for parallel solutions of very large sparse systems
Zecevic, A.I.; Siljak, D.D.
1995-12-01
In this paper we present an algorithm for balanced bordered block diagonal (BBD) decompositions of very large symmetric positive definite or diagonally dominant sparse matrices. The algorithm represents a generalization of the method described, and is primarily aimed at parallel solutions of very large sparse systems (> 20,000 equations). A variety of experimental results are provided to illustrate the performance of the algorithm and demonstrate its potential for computing on massively parallel architectures.
Sparse High Dimensional Models in Economics.
Fan, Jianqing; Lv, Jinchi; Qi, Lei
2011-09-01
This paper reviews the literature on sparse high dimensional models and discusses some applications in economics and finance. Recent developments of theory, methods, and implementations in penalized least squares and penalized likelihood methods are highlighted. These variable selection methods are proved to be effective in high dimensional sparse modeling. The limits of dimensionality that regularization methods can handle, the role of penalty functions, and their statistical properties are detailed. Some recent advances in ultra-high dimensional sparse modeling are also briefly discussed. PMID:22022635
Sparse High Dimensional Models in Economics
Fan, Jianqing; Lv, Jinchi; Qi, Lei
2010-01-01
This paper reviews the literature on sparse high dimensional models and discusses some applications in economics and finance. Recent developments of theory, methods, and implementations in penalized least squares and penalized likelihood methods are highlighted. These variable selection methods are proved to be effective in high dimensional sparse modeling. The limits of dimensionality that regularization methods can handle, the role of penalty functions, and their statistical properties are detailed. Some recent advances in ultra-high dimensional sparse modeling are also briefly discussed. PMID:22022635
Mathematical strategies for filtering complex systems: Regularly spaced sparse observations
Harlim, J. Majda, A.J.
2008-05-01
Real time filtering of noisy turbulent signals through sparse observations on a regularly spaced mesh is a notoriously difficult and important prototype filtering problem. Simpler off-line test criteria are proposed here as guidelines for filter performance for these stiff multi-scale filtering problems in the context of linear stochastic partial differential equations with turbulent solutions. Filtering turbulent solutions of the stochastically forced dissipative advection equation through sparse observations is developed as a stringent test bed for filter performance with sparse regular observations. The standard ensemble transform Kalman filter (ETKF) has poor skill on the test bed and even suffers from filter divergence, surprisingly, at observable times with resonant mean forcing and a decaying energy spectrum in the partially observed signal. Systematic alternative filtering strategies are developed here including the Fourier Domain Kalman Filter (FDKF) and various reduced filters called Strongly Damped Approximate Filter (SDAF), Variance Strongly Damped Approximate Filter (VSDAF), and Reduced Fourier Domain Kalman Filter (RFDKF) which operate only on the primary Fourier modes associated with the sparse observation mesh while nevertheless, incorporating into the approximate filter various features of the interaction with the remaining modes. It is shown below that these much cheaper alternative filters have significant skill on the test bed of turbulent solutions which exceeds ETKF and in various regimes often exceeds FDKF, provided that the approximate filters are guided by the off-line test criteria. The skill of the various approximate filters depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a precise fashion elucidated here.
NASA Astrophysics Data System (ADS)
Harko, T.; Mak, M. K.
2016-09-01
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n=1, and for the indexes n=1/2 and n=1/5, respectively. The case of n=3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.
Estimation of sparse directed acyclic graphs for multivariate counts data.
Han, Sung Won; Zhong, Hua
2016-09-01
The next-generation sequencing data, called high-throughput sequencing data, are recorded as count data, which are generally far from normal distribution. Under the assumption that the count data follow the Poisson log-normal distribution, this article provides an L1-penalized likelihood framework and an efficient search algorithm to estimate the structure of sparse directed acyclic graphs (DAGs) for multivariate counts data. In searching for the solution, we use iterative optimization procedures to estimate the adjacency matrix and the variance matrix of the latent variables. The simulation result shows that our proposed method outperforms the approach which assumes multivariate normal distributions, and the log-transformation approach. It also shows that the proposed method outperforms the rank-based PC method under sparse network or hub network structures. As a real data example, we demonstrate the efficiency of the proposed method in estimating the gene regulatory networks of the ovarian cancer study. PMID:26849781
GENERALIZED DOUBLE PARETO SHRINKAGE.
Armagan, Artin; Dunson, David B; Lee, Jaeyong
2013-01-01
We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and Normal-Jeffreys' priors. While it has a spike at zero like the Laplace density, it also has a Student's t-like tail behavior. Bayesian computation is straightforward via a simple Gibbs sampling algorithm. We investigate the properties of the maximum a posteriori estimator, as sparse estimation plays an important role in many problems, reveal connections with some well-established regularization procedures, and show some asymptotic results. The performance of the prior is tested through simulations and an application.
Sparse alignment for robust tensor learning.
Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming
2014-10-01
Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods. PMID:25291733
Partitioning sparse matrices with eigenvectors of graphs
NASA Technical Reports Server (NTRS)
Pothen, Alex; Simon, Horst D.; Liou, Kang-Pu
1990-01-01
The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph. The Laplacian eigenvectors of grid graphs can be computed from Kronecker products involving the eigenvectors of path graphs, and these eigenvectors can be used to compute good separators in grid graphs. A heuristic algorithm is designed to compute a vertex separator in a general graph by first computing an edge separator in the graph from an eigenvector of the Laplacian matrix, and then using a maximum matching in a subgraph to compute the vertex separator. Results on the quality of the separators computed by the spectral algorithm are presented, and these are compared with separators obtained from other algorithms for computing separators. Finally, the time required to compute the Laplacian eigenvector is reported, and the accuracy with which the eigenvector must be computed to obtain good separators is considered. The spectral algorithm has the advantage that it can be implemented on a medium-size multiprocessor in a straightforward manner.
Sparse distributed memory prototype: Principles of operation
NASA Technical Reports Server (NTRS)
Flynn, Michael J.; Kanerva, Pentti; Ahanin, Bahram; Bhadkamkar, Neal; Flaherty, Paul; Hickey, Philip
1988-01-01
Sparse distributed memory is a generalized random access memory (RAM) for long binary words. Such words can be written into and read from the memory, and they can be used to address the memory. The main attribute of the memory is sensitivity to similarity, meaning that a word can be read back not only by giving the original right address but also by giving one close to it as measured by the Hamming distance between addresses. Large memories of this kind are expected to have wide use in speech and scene analysis, in signal detection and verification, and in adaptive control of automated equipment. The memory can be realized as a simple, massively parallel computer. Digital technology has reached a point where building large memories is becoming practical. The research is aimed at resolving major design issues that have to be faced in building the memories. The design of a prototype memory with 256-bit addresses and from 8K to 128K locations for 256-bit words is described. A key aspect of the design is extensive use of dynamic RAM and other standard components.
On finding supernodes for sparse matrix computations
Liu, J.W.H. . Dept. of Computer Science); Ng, E.; Peyton, B.W. )
1990-06-01
A simple characterization of fundamental supernodes is given in terms of the row subtrees of sparse Cholesky factors in the elimination tree. Using this characterization, we present an efficient algorithm that determines the set of such supernodes in time proportional to the number of nonzeros and equations in the original matrix. Experimental results are included to demonstrate the use of this algorithm in the context of sparse supernodal symbolic factorization. 18 refs., 3 figs., 3 tabs.
Visual tracking via robust multitask sparse prototypes
NASA Astrophysics Data System (ADS)
Zhang, Huanlong; Hu, Shiqiang; Yu, Junyang
2015-03-01
Sparse representation has been applied to an online subspace learning-based tracking problem. To handle partial occlusion effectively, some researchers introduce l1 regularization to principal component analysis (PCA) reconstruction. However, in these traditional tracking methods, the representation of each object observation is often viewed as an individual task so the inter-relationship between PCA basis vectors is ignored. We propose a new online visual tracking algorithm with multitask sparse prototypes, which combines multitask sparse learning with PCA-based subspace representation. We first extend a visual tracking algorithm with sparse prototypes in multitask learning framework to mine inter-relations between subtasks. Then, to avoid the problem that enforcing all subtasks to share the same structure may result in degraded tracking results, we impose group sparse constraints on the coefficients of PCA basis vectors and element-wise sparse constraints on the error coefficients, respectively. Finally, we show that the proposed optimization problem can be effectively solved using the accelerated proximal gradient method with the fast convergence. Experimental results compared with the state-of-the-art tracking methods demonstrate that the proposed algorithm achieves favorable performance when the object undergoes partial occlusion, motion blur, and illumination changes.
Learning discriminative dictionary for group sparse representation.
Sun, Yubao; Liu, Qingshan; Tang, Jinhui; Tao, Dacheng
2014-09-01
In recent years, sparse representation has been widely used in object recognition applications. How to learn the dictionary is a key issue to sparse representation. A popular method is to use l1 norm as the sparsity measurement of representation coefficients for dictionary learning. However, the l1 norm treats each atom in the dictionary independently, so the learned dictionary cannot well capture the multisubspaces structural information of the data. In addition, the learned subdictionary for each class usually shares some common atoms, which weakens the discriminative ability of the reconstruction error of each subdictionary. This paper presents a new dictionary learning model to improve sparse representation for image classification, which targets at learning a class-specific subdictionary for each class and a common subdictionary shared by all classes. The model is composed of a discriminative fidelity, a weighted group sparse constraint, and a subdictionary incoherence term. The discriminative fidelity encourages each class-specific subdictionary to sparsely represent the samples in the corresponding class. The weighted group sparse constraint term aims at capturing the structural information of the data. The subdictionary incoherence term is to make all subdictionaries independent as much as possible. Because the common subdictionary represents features shared by all classes, we only use the reconstruction error of each class-specific subdictionary for classification. Extensive experiments are conducted on several public image databases, and the experimental results demonstrate the power of the proposed method, compared with the state-of-the-arts.
The MUSIC algorithm for sparse objects: a compressed sensing analysis
NASA Astrophysics Data System (ADS)
Fannjiang, Albert C.
2011-03-01
The multiple signal classification (MUSIC) algorithm, and its extension for imaging sparse extended objects, with noisy data is analyzed by compressed sensing (CS) techniques. A thresholding rule is developed to augment the standard MUSIC algorithm. The notion of restricted isometry property (RIP) and an upper bound on the restricted isometry constant (RIC) are employed to establish sufficient conditions for the exact localization by MUSIC with or without noise. In the noiseless case, the sufficient condition gives an upper bound on the numbers of random sampling and incident directions necessary for exact localization. In the noisy case, the sufficient condition assumes additionally an upper bound for the noise-to-object ratio in terms of the RIC and the dynamic range of objects. This bound points to the super-resolution capability of the MUSIC algorithm. Rigorous comparison of performance between MUSIC and the CS minimization principle, basis pursuit denoising (BPDN), is given. In general, the MUSIC algorithm guarantees to recover, with high probability, s scatterers with n= {O}(s^2) random sampling and incident directions and sufficiently high frequency. For the favorable imaging geometry where the scatterers are distributed on a transverse plane MUSIC guarantees to recover, with high probability, s scatterers with a median frequency and n= {O}(s) random sampling/incident directions. Moreover, for the problems of spectral estimation and source localizations both BPDN and MUSIC guarantee, with high probability, to identify exactly the frequencies of random signals with the number n= {O}(s) of sampling times. However, in the absence of abundant realizations of signals, BPDN is the preferred method for spectral estimation. Indeed, BPDN can identify the frequencies approximately with just one realization of signals with the recovery error at worst linearly proportional to the noise level. Numerical results confirm that BPDN outperforms MUSIC in the well
NASA Astrophysics Data System (ADS)
Ramos, Tomás; Rubilar, Guillermo F.; Obukhov, Yuri N.
2015-02-01
We study the problem of the definition of the energy-momentum tensor of light in general moving non-dispersive media with linear constitutive law. Using the basic principles of classical field theory, we show that for the correct understanding of the problem, one needs to carefully distinguish situations when the material medium is modeled either as a background on which light propagates or as a dynamical part of the total system. In the former case, we prove that the (generalized) Belinfante-Rosenfeld (BR) tensor for the electromagnetic field coincides with the Minkowski tensor. We derive a complete set of balance equations for this open system and show that the symmetries of the background medium are directly related to the conservation of the Minkowski quantities. In particular, for isotropic media, the angular momentum of light is conserved despite of the fact that the Minkowski tensor is non-symmetric. For the closed system of light interacting with matter, we model the material medium as a relativistic non-dissipative fluid and we prove that it is always possible to express the total BR tensor of the closed system either in the Abraham or in the Minkowski separation. However, in the case of dynamical media, the balance equations have a particularly convenient form in terms of the Abraham tensor. Our results generalize previous attempts and provide a first principles basis for a unified understanding of the long-standing Abraham-Minkowski controversy without ad hoc arguments.
Threshold partitioning of sparse matrices and applications to Markov chains
Choi, Hwajeong; Szyld, D.B.
1996-12-31
It is well known that the order of the variables and equations of a large, sparse linear system influences the performance of classical iterative methods. In particular if, after a symmetric permutation, the blocks in the diagonal have more nonzeros, classical block methods have a faster asymptotic rate of convergence. In this paper, different ordering and partitioning algorithms for sparse matrices are presented. They are modifications of PABLO. In the new algorithms, in addition to the location of the nonzeros, the values of the entries are taken into account. The matrix resulting after the symmetric permutation has dense blocks along the diagonal, and small entries in the off-diagonal blocks. Parameters can be easily adjusted to obtain, for example, denser blocks, or blocks with elements of larger magnitude. In particular, when the matrices represent Markov chains, the permuted matrices are well suited for block iterative methods that find the corresponding probability distribution. Applications to three types of methods are explored: (1) Classical block methods, such as Block Gauss Seidel. (2) Preconditioned GMRES, where a block diagonal preconditioner is used. (3) Iterative aggregation method (also called aggregation/disaggregation) where the partition obtained from the ordering algorithm with certain parameters is used as an aggregation scheme. In all three cases, experiments are presented which illustrate the performance of the methods with the new orderings. The complexity of the new algorithms is linear in the number of nonzeros and the order of the matrix, and thus adding little computational effort to the overall solution.
Brief announcement: Hypergraph parititioning for parallel sparse matrix-matrix multiplication
Ballard, Grey; Druinsky, Alex; Knight, Nicholas; Schwartz, Oded
2015-01-01
The performance of parallel algorithms for sparse matrix-matrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Furthermore, our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computationmore » to improve application-specific algorithms for multiplying sparse matrices.« less
Sparse recovery of the multimodal and dispersive characteristics of Lamb waves.
Harley, Joel B; Moura, José M F
2013-05-01
Guided waves in plates, known as Lamb waves, are characterized by complex, multimodal, and frequency dispersive wave propagation, which distort signals and make their analysis difficult. Estimating these multimodal and dispersive characteristics from experimental data becomes a difficult, underdetermined inverse problem. To accurately and robustly recover these multimodal and dispersive properties, this paper presents a methodology referred to as sparse wavenumber analysis based on sparse recovery methods. By utilizing a general model for Lamb waves, waves propagating in a plate structure, and robust l1 optimization strategies, sparse wavenumber analysis accurately recovers the Lamb wave's frequency-wavenumber representation with a limited number of surface mounted transducers. This is demonstrated with both simulated and experimental data in the presence of multipath reflections. With accurate frequency-wavenumber representations, sparse wavenumber synthesis is then used to accurately remove multipath interference in each measurement and predict the responses between arbitrary points on a plate.
Brief announcement: Hypergraph parititioning for parallel sparse matrix-matrix multiplication
Ballard, Grey; Druinsky, Alex; Knight, Nicholas; Schwartz, Oded
2015-01-01
The performance of parallel algorithms for sparse matrix-matrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Furthermore, our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computation to improve application-specific algorithms for multiplying sparse matrices.
Ling, Jun; Zhao, Kexin; Li, Jian; Nordenvaad, Magnus Lundberg
2011-07-01
This paper addresses multi-input multi-output (MIMO) communications over sparse acoustic channels suffering from frequency modulations. An extension of the recently introduced SLIM algorithm, which stands for sparse learning via iterative minimization, is presented to estimate the sparse and frequency modulated acoustic channels. The extended algorithm is referred to as generalization of SLIM (GoSLIM). The sparseness is exploited through a hierarchical Bayesian model, and because GoSLIM is user parameter free, it is easy to use in practical applications. Moreover this paper considers channel equalization and symbol detection for various MIMO transmission schemes, including both space-time block coding and spatial multiplexing, under the challenging channel conditions. The effectiveness of the proposed approaches is demonstrated using in-water experimental measurements recently acquired during WHOI09 and ACOMM10 experiments.
NASA Astrophysics Data System (ADS)
Grimault, S.; Lucas, T.; Quellec, S.; Mariette, F.
2004-09-01
MRI thermometry methods are usually based on the temperature dependence of the proton resonance frequency. Unfortunately, these methods are very sensitive to the phase drift induced by the instability of the scanner which prevents any temperature mapping over long periods of time. A general method based on 3D spatial modelling of the phase drift as a function of time is presented. The MRI temperature measurements were validated on gel samples with uniform and constant temperature and with a linear temperature gradient. In the case of uniform temperature conditions, correction of the phase drift proved to be essential when long periods of acquisition were required, as bias could reach values of up to 200 °C in its absence. The temperature uncertainty measured by MRI was 1.2 °C in average over 290 min. This accuracy is coherent with the requirements for food applications especially when thermocouples are useless.
Crack growth sparse pursuit for wind turbine blade
NASA Astrophysics Data System (ADS)
Li, Xiang; Yang, Zhibo; Zhang, Han; Du, Zhaohui; Chen, Xuefeng
2015-01-01
One critical challenge to achieving reliable wind turbine blade structural health monitoring (SHM) is mainly caused by composite laminates with an anisotropy nature and a hard-to-access property. The typical pitch-catch PZTs approach generally detects structural damage with both measured and baseline signals. However, the accuracy of imaging or tomography by delay-and-sum approaches based on these signals requires improvement in practice. Via the model of Lamb wave propagation and the establishment of a dictionary that corresponds to scatters, a robust sparse reconstruction approach for structural health monitoring comes into view for its promising performance. This paper proposes a neighbor dictionary that identifies the first crack location through sparse reconstruction and then presents a growth sparse pursuit algorithm that can precisely pursue the extension of the crack. An experiment with the goal of diagnosing a composite wind turbine blade with an artificial crack is performed, and it validates the proposed approach. The results give competitively accurate crack detection with the correct locations and extension length.
Robust Reconstruction of Complex Networks from Sparse Data
NASA Astrophysics Data System (ADS)
Han, Xiao; Shen, Zhesi; Wang, Wen-Xu; Di, Zengru
2015-01-01
Reconstructing complex networks from measurable data is a fundamental problem for understanding and controlling collective dynamics of complex networked systems. However, a significant challenge arises when we attempt to decode structural information hidden in limited amounts of data accompanied by noise and in the presence of inaccessible nodes. Here, we develop a general framework for robust reconstruction of complex networks from sparse and noisy data. Specifically, we decompose the task of reconstructing the whole network into recovering local structures centered at each node. Thus, the natural sparsity of complex networks ensures a conversion from the local structure reconstruction into a sparse signal reconstruction problem that can be addressed by using the lasso, a convex optimization method. We apply our method to evolutionary games, transportation, and communication processes taking place in a variety of model and real complex networks, finding that universal high reconstruction accuracy can be achieved from sparse data in spite of noise in time series and missing data of partial nodes. Our approach opens new routes to the network reconstruction problem and has potential applications in a wide range of fields.
An Efficient Scheme for Updating Sparse Cholesky Factors
NASA Technical Reports Server (NTRS)
Raghavan, Padma
2002-01-01
Raghavan had earlier developed the software package DCSPACK which can be used for solving sparse linear systems where the coefficient matrix is symmetric and positive definite (this project was not funded by NASA but by agencies such as NSF). DSCPACK-S is the serial code and DSCPACK-P is a parallel implementation suitable for multiprocessors or networks-of-workstations with message passing using MCI. The main algorithm used is the Cholesky factorization of a sparse symmetric positive positive definite matrix A = LL(T). The code can also compute the factorization A = LDL(T). The complexity of the software arises from several factors relating to the sparsity of the matrix A. A sparse N x N matrix A has typically less that cN nonzeroes where c is a small constant. If the matrix were dense, it would have O(N2) nonzeroes. The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L. An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill. DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others. Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b. The first two steps are symbolic and are performed using the graph of the matrix. The numeric factorization step is of dominant cost and there are several schemes for improving performance by exploiting the nested and dense structure of groups of columns in the factor. The latter are aimed at better utilization of the cache-memory hierarchy on modem processors to prevent cache-misses and provide execution
Inverse sparse tracker with a locally weighted distance metric.
Wang, Dong; Lu, Huchuan; Xiao, Ziyang; Yang, Ming-Hsuan
2015-09-01
Sparse representation has been recently extensively studied for visual tracking and generally facilitates more accurate tracking results than classic methods. In this paper, we propose a sparsity-based tracking algorithm that is featured with two components: 1) an inverse sparse representation formulation and 2) a locally weighted distance metric. In the inverse sparse representation formulation, the target template is reconstructed with particles, which enables the tracker to compute the weights of all particles by solving only one l1 optimization problem and thereby provides a quite efficient model. This is in direct contrast to most previous sparse trackers that entail solving one optimization problem for each particle. However, we notice that this formulation with normal Euclidean distance metric is sensitive to partial noise like occlusion and illumination changes. To this end, we design a locally weighted distance metric to replace the Euclidean one. Similar ideas of using local features appear in other works, but only being supported by popular assumptions like local models could handle partial noise better than holistic models, without any solid theoretical analysis. In this paper, we attempt to explicitly explain it from a mathematical view. On that basis, we further propose a method to assign local weights by exploiting the temporal and spatial continuity. In the proposed method, appearance changes caused by partial occlusion and shape deformation are carefully considered, thereby facilitating accurate similarity measurement and model update. The experimental validation is conducted from two aspects: 1) self validation on key components and 2) comparison with other state-of-the-art algorithms. Results over 15 challenging sequences show that the proposed tracking algorithm performs favorably against the existing sparsity-based trackers and the other state-of-the-art methods. PMID:25935033
Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods
Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev
2013-01-01
Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72–88, 2013. PMID:23847452
Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods.
Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev
2013-05-01
Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72-88, 2013.
NASA Astrophysics Data System (ADS)
Vossos, Spyridon; Vossos, Elias
2016-08-01
closed LSTT is reduced, if one RIO has small velocity wrt another RIO. Thus, we have infinite number of closed LSTTs, each one with the corresponding SR theory. In case that we relate accelerated observers with variable metric of spacetime, we have the case of General Relativity (GR). For being that clear, we produce a generalized Schwarzschild metric, which is in accordance with any SR based on this closed complex LSTT and Einstein equations. The application of this kind of transformations to the SR and GR is obvious. But, the results may be applied to any linear space of dimension four endowed with steady or variable metric, whose elements (four- vectors) have spatial part (vector) with Euclidean metric.
Piccardo, Matteo; Bloino, Julien; Barone, Vincenzo
2015-01-01
Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods. © 2015 Wiley Periodicals, Inc. PMID:26345131
An empirical investigation of sparse distributed memory using discrete speech recognition
NASA Technical Reports Server (NTRS)
Danforth, Douglas G.
1990-01-01
Presented here is a step by step analysis of how the basic Sparse Distributed Memory (SDM) model can be modified to enhance its generalization capabilities for classification tasks. Data is taken from speech generated by a single talker. Experiments are used to investigate the theory of associative memories and the question of generalization from specific instances.
Removing sparse noise from hyperspectral images with sparse and low-rank penalties
NASA Astrophysics Data System (ADS)
Tariyal, Snigdha; Aggarwal, Hemant Kumar; Majumdar, Angshul
2016-03-01
In diffraction grating, at times, there are defective pixels on the focal plane array; this results in horizontal lines of corrupted pixels in some channels. Since only a few such pixels exist, the corruption/noise is sparse. Studies on sparse noise removal from hyperspectral noise are parsimonious. To remove such sparse noise, a prior work exploited the interband spectral correlation along with intraband spatial redundancy to yield a sparse representation in transform domains. We improve upon the prior technique. The intraband spatial redundancy is modeled as a sparse set of transform coefficients and the interband spectral correlation is modeled as a rank deficient matrix. The resulting optimization problem is solved using the split Bregman technique. Comparative experimental results show that our proposed approach is better than the previous one.
Shevenell, L.A.; Beauchamp, J.J.
1994-11-01
Several waste disposal sites are located on or adjacent to the karstic Maynardville Limestone (Cmn) and the Copper Ridge Dolomite (Ccr) at the Oak Ridge Y-12 Plant. These formations receive contaminants in groundwaters from nearby disposal sites, which can be transported quite rapidly due to the karst flow system. In order to evaluate transport processes through the karst aquifer, the solutional aspects of the formations must be characterized. As one component of this characterization effort, statistical analyses were conducted on the data related to cavities in order to determine if a suitable model could be identified that is capable of predicting the probability of cavity size or distribution in locations for which drilling data are not available. Existing data on the locations (East, North coordinates), depths (and elevations), and sizes of known conduits and other water zones were used in the analyses. Two different models were constructed in the attempt to predict the distribution of cavities in the vicinity of the Y-12 Plant: General Linear Models (GLM), and Logistic Regression Models (LOG). Each of the models attempted was very sensitive to the data set used. Models based on subsets of the full data set were found to do an inadequate job of predicting the behavior of the full data set. The fact that the Ccr and Cmn data sets differ significantly is not surprising considering the hydrogeology of the two formations differs. Flow in the Cmn is generally at elevations between 600 and 950 ft and is dominantly strike parallel through submerged, partially mud-filled cavities with sizes up to 40 ft, but more typically less than 5 ft. Recognized flow in the Ccr is generally above 950 ft elevation, with flow both parallel and perpendicular to geologic strike through conduits, which tend to be large than those on the Cnm, and are often not fully saturated at the shallower depths.
JiTTree: A Just-in-Time Compiled Sparse GPU Volume Data Structure.
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.
Image Super-Resolution Based on Structure-Modulated Sparse Representation.
Zhang, Yongqin; Liu, Jiaying; Yang, Wenhan; Guo, Zongming
2015-09-01
Sparse representation has recently attracted enormous interests in the field of image restoration. The conventional sparsity-based methods enforce sparse coding on small image patches with certain constraints. However, they neglected the characteristics of image structures both within the same scale and across the different scales for the image sparse representation. This drawback limits the modeling capability of sparsity-based super-resolution methods, especially for the recovery of the observed low-resolution images. In this paper, we propose a joint super-resolution framework of structure-modulated sparse representations to improve the performance of sparsity-based image super-resolution. The proposed algorithm formulates the constrained optimization problem for high-resolution image recovery. The multistep magnification scheme with the ridge regression is first used to exploit the multiscale redundancy for the initial estimation of the high-resolution image. Then, the gradient histogram preservation is incorporated as a regularization term in sparse modeling of the image super-resolution problem. Finally, the numerical solution is provided to solve the super-resolution problem of model parameter estimation and sparse representation. Extensive experiments on image super-resolution are carried out to validate the generality, effectiveness, and robustness of the proposed algorithm. Experimental results demonstrate that our proposed algorithm, which can recover more fine structures and details from an input low-resolution image, outperforms the state-of-the-art methods both subjectively and objectively in most cases.
Sparse Representation-Based Image Quality Index With Adaptive Sub-Dictionaries.
Li, Leida; Cai, Hao; Zhang, Yabin; Lin, Weisi; Kot, Alex C; Sun, Xingming
2016-08-01
Distortions cause structural changes in digital images, leading to degraded visual quality. Dictionary-based sparse representation has been widely studied recently due to its ability to extract inherent image structures. Meantime, it can extract image features with slightly higher level semantics. Intuitively, sparse representation can be used for image quality assessment, because visible distortions can cause significant changes to the sparse features. In this paper, a new sparse representation-based image quality assessment model is proposed based on the construction of adaptive sub-dictionaries. An overcomplete dictionary trained from natural images is employed to capture the structure changes between the reference and distorted images by sparse feature extraction via adaptive sub-dictionary selection. Based on the observation that image sparse features are invariant to weak degradations and the perceived image quality is generally influenced by diverse issues, three auxiliary quality features are added, including gradient, color, and luminance information. The proposed method is not sensitive to training images, so a universal dictionary can be adopted for quality evaluation. Extensive experiments on five public image quality databases demonstrate that the proposed method produces the state-of-the-art results, and it delivers consistently well performances when tested in different image quality databases.
JiTTree: A Just-in-Time Compiled Sparse GPU Volume Data Structure.
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. PMID:26529746
Parallel sparse and dense information coding streams in the electrosensory midbrain.
Sproule, Michael K J; Metzen, Michael G; Chacron, Maurice J
2015-10-21
Efficient processing of incoming sensory information is critical for an organism's survival. It has been widely observed across systems and species that the representation of sensory information changes across successive brain areas. Indeed, peripheral sensory neurons tend to respond densely to a broad range of sensory stimuli while more central neurons tend to instead respond sparsely to a narrow range of stimuli. Such a transition might be advantageous as sparse neural codes are thought to be metabolically efficient and optimize coding efficiency. Here we investigated whether the neural code transitions from dense to sparse within the midbrain Torus semicircularis (TS) of weakly electric fish. Confirming previous results, we found both dense and sparse coding neurons. However, subsequent histological classification revealed that most dense neurons projected to higher brain areas. Our results thus provide strong evidence against the hypothesis that the neural code transitions from dense to sparse in the electrosensory system. Rather, they support the alternative hypothesis that higher brain areas receive parallel streams of dense and sparse coded information from the electrosensory midbrain. We discuss the implications and possible advantages of such a coding strategy and argue that it is a general feature of sensory processing.
Jin, Haoran; Yang, Keji; Wu, Shiwei; Wu, Haiteng; Chen, Jian
2016-04-01
Sparse deconvolution is widely used in the field of non-destructive testing (NDT) for improving the temporal resolution. Generally, the reference signals involved in sparse deconvolution are measured from the reflection echoes of standard plane block, which cannot accurately describe the acoustic properties at different spatial positions. Therefore, the performance of sparse deconvolution will deteriorate, due to the deviations in reference signals. Meanwhile, it is inconvenient for automatic ultrasonic NDT using manual measurement of reference signals. To overcome these disadvantages, a modified sparse deconvolution based on automatic estimation of reference signals is proposed in this paper. By estimating the reference signals, the deviations would be alleviated and the accuracy of sparse deconvolution is therefore improved. Based on the automatic estimation of reference signals, regional sparse deconvolution is achievable by decomposing the whole B-scan image into small regions of interest (ROI), and the image dimensionality is significantly reduced. Since the computation time of proposed method has a power dependence on the signal length, the computation efficiency is therefore improved significantly with this strategy. The performance of proposed method is demonstrated using immersion measurement of scattering targets and steel block with side-drilled holes. The results verify that the proposed method is able to maintain the vertical resolution enhancement and noise-suppression capabilities in different scenarios. PMID:26773787
Deploying temporary networks for upscaling of sparse network stations
NASA Astrophysics Data System (ADS)
Coopersmith, Evan J.; Cosh, Michael H.; Bell, Jesse E.; Kelly, Victoria; Hall, Mark; Palecki, Michael A.; Temimi, Marouane
2016-10-01
Soil observations networks at the national scale play an integral role in hydrologic modeling, drought assessment, agricultural decision support, and our ability to understand climate change. Understanding soil moisture variability is necessary to apply these measurements to model calibration, business and consumer applications, or even human health issues. The installation of soil moisture sensors as sparse, national networks is necessitated by limited financial resources. However, this results in the incomplete sampling of the local heterogeneity of soil type, vegetation cover, topography, and the fine spatial distribution of precipitation events. To this end, temporary networks can be installed in the areas surrounding a permanent installation within a sparse network. The temporary networks deployed in this study provide a more representative average at the 3 km and 9 km scales, localized about the permanent gauge. The value of such temporary networks is demonstrated at test sites in Millbrook, New York and Crossville, Tennessee. The capacity of a single U.S. Climate Reference Network (USCRN) sensor set to approximate the average of a temporary network at the 3 km and 9 km scales using a simple linear scaling function is tested. The capacity of a temporary network to provide reliable estimates with diminishing numbers of sensors, the temporal stability of those networks, and ultimately, the relationship of the variability of those networks to soil moisture conditions at the permanent sensor are investigated. In this manner, this work demonstrates the single-season installation of a temporary network as a mechanism to characterize the soil moisture variability at a permanent gauge within a sparse network.
Tensor methods for large, sparse unconstrained optimization
Bouaricha, A.
1996-11-01
Tensor methods for unconstrained optimization were first introduced by Schnabel and Chow [SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate size problems. This paper extends these methods to large, sparse unconstrained optimization problems. This requires an entirely new way of solving the tensor model that makes the methods suitable for solving large, sparse optimization problems efficiently. We present test results for sets of problems where the Hessian at the minimizer is nonsingular and where it is singular. These results show that tensor methods are significantly more efficient and more reliable than standard methods based on Newton`s method.
Analog system for computing sparse codes
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.
Multisnapshot Sparse Bayesian Learning for DOA
NASA Astrophysics Data System (ADS)
Gerstoft, Peter; Mecklenbrauker, Christoph F.; Xenaki, Angeliki; Nannuru, Santosh
2016-10-01
The directions of arrival (DOA) of plane waves are estimated from multi-snapshot sensor array data using Sparse Bayesian Learning (SBL). The prior source amplitudes is assumed independent zero-mean complex Gaussian distributed with hyperparameters the unknown variances (i.e. the source powers). For a complex Gaussian likelihood with hyperparameter the unknown noise variance, the corresponding Gaussian posterior distribution is derived. For a given number of DOAs, the hyperparameters are automatically selected by maximizing the evidence and promote sparse DOA estimates. The SBL scheme for DOA estimation is discussed and evaluated competitively against LASSO ($\\ell_1$-regularization), conventional beamforming, and MUSIC
Sparse Density Estimation on the Multinomial Manifold.
Hong, Xia; Gao, Junbin; Chen, Sheng; Zia, Tanveer
2015-11-01
A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators. PMID:25647665
Independence test for sparse data
NASA Astrophysics Data System (ADS)
García, J. E.; González-López, V. A.
2016-06-01
In this paper a new non-parametric independence test is presented. García and González-López (2014) [1] introduced the LIS test for the hypothesis of independence between two continuous random variables, the test proposed in this work is a generalization of the LIS test. The new test does not require the assumption of continuity for the random variables, it test is applied to two datasets and also compared with the Pearson's Chi-squared test.
Bennewitz, J; Bögelein, S; Stratz, P; Rodehutscord, M; Piepho, H P; Kjaer, J B; Bessei, W
2014-04-01
Feather pecking and aggressive pecking is a well-known problem in egg production. In the present study, genetic parameters for 4 feather-pecking-related traits were estimated using generalized linear mixed models. The traits were bouts of feather pecking delivered (FPD), bouts of feather pecking received (FPR), bouts of aggressive pecking delivered (APD), and bouts of aggressive pecking received (APR). An F2-design was established from 2 divergent selected founder lines. The lines were selected for low or high feather pecking for 10 generations. The number of F2 hens was 910. They were housed in pens with around 40 birds. Each pen was observed in 21 sessions of 20 min, distributed over 3 consecutive days. An animal model was applied that treated the bouts observed within 20 min as repeated observations. An over-dispersed Poisson distribution was assumed for observed counts and the link function was a log link. The model included a random animal effect, a random permanent environment effect, and a random day-by-hen effect. Residual variance was approximated on the link scale by the delta method. The results showed a heritability around 0.10 on the link scale for FPD and APD and of 0.04 for APR. The heritability of FPR was zero. For all behavior traits, substantial permanent environmental effects were observed. The approximate genetic correlation between FPD and APD (FPD and APR) was 0.81 (0.54). Egg production and feather eating records were collected on the same hens as well and were analyzed with a generalized linear mixed model, assuming a binomial distribution and using a probit link function. The heritability on the link scale for egg production was 0.40 and for feather eating 0.57. The approximate genetic correlation between FPD and egg production was 0.50 and between FPD and feather eating 0.73. Selection might help to reduce feather pecking, but this might result in an unfavorable correlated selection response reducing egg production. Feather eating and
Thin-film sparse boundary array design for passive acoustic mapping during ultrasound therapy.
Coviello, Christian M; Kozick, Richard J; Hurrell, Andrew; Smith, Penny Probert; Coussios, Constantin-C
2012-10-01
A new 2-D hydrophone array for ultrasound therapy monitoring is presented, along with a novel algorithm for passive acoustic mapping using a sparse weighted aperture. The array is constructed using existing polyvinylidene fluoride (PVDF) ultrasound sensor technology, and is utilized for its broadband characteristics and its high receive sensitivity. For most 2-D arrays, high-resolution imagery is desired, which requires a large aperture at the cost of a large number of elements. The proposed array's geometry is sparse, with elements only on the boundary of the rectangular aperture. The missing information from the interior is filled in using linear imaging techniques. After receiving acoustic emissions during ultrasound therapy, this algorithm applies an apodization to the sparse aperture to limit side lobes and then reconstructs acoustic activity with high spatiotemporal resolution. Experiments show verification of the theoretical point spread function, and cavitation maps in agar phantoms correspond closely to predicted areas, showing the validity of the array and methodology. PMID:23143581
Sparse Algorithms Are Not Stable: A No-Free-Lunch Theorem.
Huan Xu; Caramanis, C; Mannor, S
2012-01-01
We consider two desired properties of learning algorithms: sparsity and algorithmic stability. Both properties are believed to lead to good generalization ability. We show that these two properties are fundamentally at odds with each other: A sparse algorithm cannot be stable and vice versa. Thus, one has to trade off sparsity and stability in designing a learning algorithm. In particular, our general result implies that ℓ(1)-regularized regression (Lasso) cannot be stable, while ℓ(2)-regularized regression is known to have strong stability properties and is therefore not sparse.
Sparse Multi-Static Arrays for Near-Field Millimeter-Wave Imaging
Sheen, David M.
2013-12-31
This paper describes a novel design technique for sparse multi-static linear arrays. The methods described allow the development of densely sampled linear arrays suitable for high-resolution near-field imaging that require dramatically fewer antenna and switch elements than the previous state of the art. The techniques used are related to sparse array techniques used in radio astronomy applications, but differ significantly in design due to the transmit-receive nature of the arrays, and the application to linear arrays that achieve dense uniform sampling suitable for high-resolution near-field imaging. As many as 3 to 5 or more samples per antenna can be obtained, compared to 1 sample per antenna for the current state of the art. This could dramatically reduce cost and improve performance over current active millimeter-wave imaging systems.
Infrared image recognition based on structure sparse and atomic sparse parallel
NASA Astrophysics Data System (ADS)
Wu, Yalu; Li, Ruilong; Xu, Yi; Wang, Liping
2015-12-01
Use the redundancy of the super complete dictionary can capture the structural features of the image effectively, can achieving the effective representation of the image. However, the commonly used atomic sparse representation without regard the structure of the dictionary and the unrelated non-zero-term in the process of the computation, though structure sparse consider the structure feature of dictionary, the majority coefficients of the blocks maybe are non-zero, it may affect the identification efficiency. For the disadvantages of these two sparse expressions, a weighted parallel atomic sparse and sparse structure is proposed, and the recognition efficiency is improved by the adaptive computation of the optimal weights. The atomic sparse expression and structure sparse expression are respectively, and the optimal weights are calculated by the adaptive method. Methods are as follows: training by using the less part of the identification sample, the recognition rate is calculated by the increase of the certain step size and t the constraint between weight. The recognition rate as the Z axis, two weight values respectively as X, Y axis, the resulting points can be connected in a straight line in the 3 dimensional coordinate system, by solving the highest recognition rate, the optimal weights can be obtained. Through simulation experiments can be known, the optimal weights based on adaptive method are better in the recognition rate, weights obtained by adaptive computation of a few samples, suitable for parallel recognition calculation, can effectively improve the recognition rate of infrared images.
Bacheler, N.M.; Hightower, J.E.; Burdick, S.M.; Paramore, L.M.; Buckel, J.A.; Pollock, K.H.
2010-01-01
Estimating the selectivity patterns of various fishing gears is a critical component of fisheries stock assessment due to the difficulty in obtaining representative samples from most gears. We used short-term recoveries (n = 3587) of tagged red drum Sciaenops ocellatus to directly estimate age- and length-based selectivity patterns using generalized linear models. The most parsimonious models were selected using AIC, and standard deviations were estimated using simulations. Selectivity of red drum was dependent upon the regulation period in which the fish was caught, the gear used to catch the fish (i.e., hook-and-line, gill nets, pound nets), and the fate of the fish upon recovery (i.e., harvested or released); models including all first-order interactions between main effects outperformed models without interactions. Selectivity of harvested fish was generally dome-shaped and shifted toward larger, older fish in response to regulation changes. Selectivity of caught-and-released red drum was highest on the youngest and smallest fish in the early and middle regulation periods, but increased on larger, legal-sized fish in the late regulation period. These results suggest that catch-and-release mortality has consistently been high for small, young red drum, but has recently become more common in larger, older fish. This method of estimating selectivity from short-term tag recoveries is valuable because it is simpler than full tag-return models, and may be more robust because yearly fishing and natural mortality rates do not need to be modeled and estimated. ?? 2009 Elsevier B.V.
Burdick, Summer M.; Hightower, Joseph E.; Bacheler, Nathan M.; Paramore, Lee M.; Buckel, Jeffrey A.; Pollock, Kenneth H.
2010-01-01
Estimating the selectivity patterns of various fishing gears is a critical component of fisheries stock assessment due to the difficulty in obtaining representative samples from most gears. We used short-term recoveries (n = 3587) of tagged red drum Sciaenops ocellatus to directly estimate age- and length-based selectivity patterns using generalized linear models. The most parsimonious models were selected using AIC, and standard deviations were estimated using simulations. Selectivity of red drum was dependent upon the regulation period in which the fish was caught, the gear used to catch the fish (i.e., hook-and-line, gill nets, pound nets), and the fate of the fish upon recovery (i.e., harvested or released); models including all first-order interactions between main effects outperformed models without interactions. Selectivity of harvested fish was generally dome-shaped and shifted toward larger, older fish in response to regulation changes. Selectivity of caught-and-released red drum was highest on the youngest and smallest fish in the early and middle regulation periods, but increased on larger, legal-sized fish in the late regulation period. These results suggest that catch-and-release mortality has consistently been high for small, young red drum, but has recently become more common in larger, older fish. This method of estimating selectivity from short-term tag recoveries is valuable because it is simpler than full tag-return models, and may be more robust because yearly fishing and natural mortality rates do not need to be modeled and estimated.
Sparse Downscaling and Adaptive Fusion of Multi-sensor Precipitation
NASA Astrophysics Data System (ADS)
Ebtehaj, M.; Foufoula, E.
2011-12-01
The past decades have witnessed a remarkable emergence of new sources of multiscale multi-sensor precipitation data including data from global spaceborne active and passive sensors, regional ground based weather surveillance radars and local rain-gauges. Resolution enhancement of remotely sensed rainfall and optimal integration of multi-sensor data promise a posteriori estimates of precipitation fluxes with increased accuracy and resolution to be used in hydro-meteorological applications. In this context, new frameworks are proposed for resolution enhancement and multiscale multi-sensor precipitation data fusion, which capitalize on two main observations: (1) sparseness of remotely sensed precipitation fields in appropriately chosen transformed domains, (e.g., in wavelet space) which promotes the use of the newly emerged theory of sparse representation and compressive sensing for resolution enhancement; (2) a conditionally Gaussian Scale Mixture (GSM) parameterization in the wavelet domain which allows exploiting the efficient linear estimation methodologies, while capturing the non-Gaussian data structure of rainfall. The proposed methodologies are demonstrated using a data set of coincidental observations of precipitation reflectivity images by the spaceborne precipitation radar (PR) aboard the Tropical Rainfall Measurement Mission (TRMM) satellite and ground-based NEXRAD weather surveillance Doppler radars. Uniqueness and stability of the solution, capturing non-Gaussian singular structure of rainfall, reduced uncertainty of estimation and efficiency of computation are the main advantages of the proposed methodologies over the commonly used standard Gaussian techniques.
Configurable hardware integrate and fire neurons for sparse approximation.
Shapero, Samuel; Rozell, Christopher; Hasler, Paul
2013-09-01
Sparse approximation is an important optimization problem in signal and image processing applications. A Hopfield-Network-like system of integrate and fire (IF) neurons is proposed as a solution, using the Locally Competitive Algorithm (LCA) to solve an overcomplete L1 sparse approximation problem. A scalable system architecture is described, including IF neurons with a nonlinear firing function, and current-based synapses to provide linear computation. A network of 18 neurons with 12 inputs is implemented on the RASP 2.9v chip, a Field Programmable Analog Array (FPAA) with directly programmable floating gate elements. Said system uses over 1400 floating gates, the largest system programmed on a FPAA to date. The circuit successfully reproduced the outputs of a digital optimization program, converging to within 4.8% RMS, and an objective cost only 1.7% higher on average. The active circuit consumed 559 μA of current at 2.4 V and converges on solutions in 25 μs, with measurement of the converged spike rate taking an additional 1 ms. Extrapolating the scaling trends to a N=1000 node system, the spiking LCA compares favorably with state-of-the-art digital solutions, and analog solutions using a non-spiking approach.
One-step Sparse Estimates in Nonconcave Penalized Likelihood Models.
Zou, Hui; Li, Runze
2008-08-01
Fan & Li (2001) propose a family of variable selection methods via penalized likelihood using concave penalty functions. The nonconcave penalized likelihood estimators enjoy the oracle properties, but maximizing the penalized likelihood function is computationally challenging, because the objective function is nondifferentiable and nonconcave. In this article we propose a new unified algorithm based on the local linear approximation (LLA) for maximizing the penalized likelihood for a broad class of concave penalty functions. Convergence and other theoretical properties of the LLA algorithm are established. A distinguished feature of the LLA algorithm is that at each LLA step, the LLA estimator can naturally adopt a sparse representation. Thus we suggest using the one-step LLA estimator from the LLA algorithm as the final estimates. Statistically, we show that if the regularization parameter is appropriately chosen, the one-step LLA estimates enjoy the oracle properties with good initial estimators. Computationally, the one-step LLA estimation methods dramatically reduce the computational cost in maximizing the nonconcave penalized likelihood. We conduct some Monte Carlo simulation to assess the finite sample performance of the one-step sparse estimation methods. The results are very encouraging.
Semi-implicit Integration Factor Methods on Sparse Grids for High-Dimensional Systems
Wang, Dongyong; Chen, Weitao; Nie, Qing
2015-01-01
Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method. PMID:25897178
Second SIAM conference on sparse matrices: Abstracts. Final technical report
1996-12-31
This report contains abstracts on the following topics: invited and long presentations (IP1 & LP1); sparse matrix reordering & graph theory I; sparse matrix tools & environments I; eigenvalue computations I; iterative methods & acceleration techniques I; applications I; parallel algorithms I; sparse matrix reordering & graphy theory II; sparse matrix tool & environments II; least squares & optimization I; iterative methods & acceleration techniques II; applications II; eigenvalue computations II; least squares & optimization II; parallel algorithms II; sparse direct methods; iterative methods & acceleration techniques III; eigenvalue computations III; and sparse matrix reordering & graph theory III.
NASA Astrophysics Data System (ADS)
Stoykov, S.; Atanassov, E.; Margenov, S.
2016-10-01
Many of the scientific applications involve sparse or dense matrix operations, such as solving linear systems, matrix-matrix products, eigensolvers, etc. In what concerns structural nonlinear dynamics, the computations of periodic responses and the determination of stability of the solution are of primary interest. Shooting method iswidely used for obtaining periodic responses of nonlinear systems. The method involves simultaneously operations with sparse and dense matrices. One of the computationally expensive operations in the method is multiplication of sparse by dense matrices. In the current work, a new algorithm for sparse matrix by dense matrix products is presented. The algorithm takes into account the structure of the sparse matrix, which is obtained by space discretization of the nonlinear Mindlin's plate equation of motion by the finite element method. The algorithm is developed to use the vector engine of Intel Xeon Phi coprocessors. It is compared with the standard sparse matrix by dense matrix algorithm and the one developed by Intel MKL and it is shown that by considering the properties of the sparse matrix better algorithms can be developed.
Rio, Daniel E; Rawlings, Robert R; Woltz, Lawrence A; Gilman, Jodi; Hommer, Daniel W
2013-01-01
A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI) blood-oxygen level-dependent (BOLD) multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measures experimental design, the model has been extended to handle multivariate time series data and demonstrated on control and alcoholic subjects taken from data previously analyzed in the temporal domain. Analysis of BOLD data is typically carried out in the time domain where the data has a high temporal correlation. These analyses generally employ parametric models of the hemodynamic response function (HRF) where prewhitening of the data is attempted using autoregressive (AR) models for the noise. However, this data can be analyzed in the Fourier domain. Here, assumptions made on the noise structure are less restrictive, and hypothesis tests can be constructed based on voxel-specific nonparametric estimates of the hemodynamic transfer function (HRF in the Fourier domain). This is especially important for experimental designs involving multiple states (either stimulus or drug induced) that may alter the form of the response function.
NASA Astrophysics Data System (ADS)
Fujii, Y.; Nakano, T.; Usui, N.; Matsumoto, S.; Tsujino, H.; Kamachi, M.
2014-12-01
This study develops a strategy for tracing a target water mass, and applies it to analyzing the pathway of the North Pacific Intermediate Water (NPIW) from the subarctic gyre to the northwestern part of the subtropical gyre south of Japan in a simulation of an ocean general circulation model. This strategy estimates the pathway of the water mass that travels from an origin to a destination area during a specific period using a conservation property concerning tangent linear and adjoint models. In our analysis, a large fraction of the low salinity origin water mass of NPIW initially comes from the Okhotsk or Bering Sea, flows through the southeastern side of the Kuril Islands, and is advected to the Mixed Water Region (MWR) by the Oyashio current. It then enters the Kuroshio Extension (KE) at the first KE ridge, and is advected eastward by the KE current. However, it deviates southward from the KE axis around 158°E over the Shatsky Rise, or around 170ºE on the western side of the Emperor Seamount Chain, and enters the subtropical gyre. It is finally transported westward by the recirculation flow. This pathway corresponds well to the shortcut route of NPIW from MWR to the region south of Japan inferred from analysis of the long-term freshening trend of NPIW observation.
Matas, Marina; Picornell, Antònia; Cifuentes, Carmen; Payeras, Antoni; Bassa, Antoni; Homar, Francesc; González-Candelas, Fernando; López-Labrador, F Xavier; Moya, Andrés; Ramon, Maria M; Castro, José A
2013-01-01
Chronic hepatitis C virus (HCV) infection is the main cause of advanced and end-stage liver disease world-wide, and an important factor of morbidity and mortality in Human Immunodeficiency virus-1 (HIV-1) co-infected individuals. Whereas the genetic variability of HCV has been studied extensively in monoinfected patients, comprehensive analyses of both patient and virus characteristics are still scarce in HCV/HIV co-infection. In order to find correlates for liver damage, we sought to analyze demographic, epidemiological and clinical features of HCV/HIV co-infected patients along with the genetic makeup of HCV (viral subtypes and lineage studied by nucleotide sequencing and phylogenetic analysis of the NS5B region). We used the Generalized Linear Model (GLM) methodology in order to integrate data from the virus and the infected host to find predictors for liver damage. The degree of liver disease was evaluated indirectly by means of two indexes (APRI and FIB-4) and accounting for the time since infection, to estimate fibrosis progression rates. Our analyses identified a reduced number of variables (both from the virus and the host) implicated in liver damage, which included the stage of HIV infection, levels of gamma-glutamil transferase and cholesterol, and some distinct HCV phylogenetic clades. PMID:23174528
Kobayashi, Etsuko; Suwazono, Yasushi; Honda, Ryumon; Dochi, Mire; Nishijo, Muneko; Kido, Teruhiko; Nakagawa, Hideaki
2009-01-01
A 10-year follow-up study was conducted to investigate the effects of renal handling of calcium (Ca) and phosphorus (P) after the removal of cadmium-polluted soil in rice paddies and replacing it with nonpolluted soil. Using a general linear mixed model, serial changes of Ca and P concentrations in urine and serum (Ca-U/S, P-U/S), fractional excretion of Ca (FECa), and percent tubular reabsorption of P (%TRP) were determined in 37 persons requiring observation in the Cd-polluted Kakehashi River Basin, Japan. Ca-U and Ca-S remained within the normal range in both sexes. FECa in men returned to the normal level within 3.3 years from the completion of soil replacement. Overall, it is suggested that the renal handling of Ca showed no or only a slight change throughout the observation period in both sexes. P-U decreased gradually. P-S showed lower than normal values in the men and values at the lower end of the normal range in women, although the values recovered gradually to normal. %TRP values remained low throughout the observation period and the values did not recover in either sex. However, the results of P-U and P-S suggested that the renal handling of P may recover after the completion of soil replacement.
Multilevel sparse functional principal component analysis.
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. PMID:24872597
Multilevel sparse functional principal component analysis
Di, Chongzhi; Crainiceanu, Ciprian M.; Jank, Wolfgang S.
2014-01-01
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. PMID:24872597
Self-Control in Sparsely Coded Networks
NASA Astrophysics Data System (ADS)
Dominguez, D. R. C.; Bollé, D.
1998-03-01
A complete self-control mechanism is proposed in the dynamics of neural networks through the introduction of a time-dependent threshold, determined in function of both the noise and the pattern activity in the network. Especially for sparsely coded models this mechanism is shown to considerably improve the storage capacity, the basins of attraction, and the mutual information content.
Sparse matrix orderings for factorized inverse preconditioners
Benzi, M.; Tuama, M.
1998-09-01
The effect of reorderings on the performance of factorized sparse approximate inverse preconditioners is considered. It is shown that certain reorderings can be very beneficial both in the preconditioner construction phase and in terms of the rate of convergence of the preconditioned iteration.
STIS Sparse Field CTE test {Cycle 9}
NASA Astrophysics Data System (ADS)
Goudfrooij, Paul
2000-07-01
CTE measurements are made using the "sparse field test", along both the serial and parallel axes. This program needs special commanding to provide {a} off-center MSM positionings of some slits, and {b} the ability to read out with any amplifier {A, B, C, or D}. All exposures are internals.
STIS Sparse Field CTE test {Cycle 8}
NASA Astrophysics Data System (ADS)
Goudfrooij, Paul
1999-07-01
CTE measurements are made using the "sparse field test", along both the serial and parallel axes. This program needs special commanding to provide {a} off-center MSM positionings of some slits, and {b} the ability to read out with any amplifier {A, B, C, or D}. All exposures are internals.
SAR Image Despeckling Via Structural Sparse Representation
NASA Astrophysics Data System (ADS)
Lu, Ting; Li, Shutao; Fang, Leyuan; Benediktsson, Jón Atli
2016-12-01
A novel synthetic aperture radar (SAR) image despeckling method based on structural sparse representation is introduced. The proposed method utilizes the fact that different regions in SAR images correspond to varying terrain reflectivity. Therefore, SAR images can be split into a heterogeneous class (with a varied terrain reflectivity) and a homogeneous class (with a constant terrain reflectivity). In the proposed method, different sparse representation based despeckling schemes are designed by combining the different region characteristics in SAR images. For heterogeneous regions with rich structure and texture information, structural dictionaries are learned to appropriately represent varied structural characteristics. Specifically, each patch in these regions is sparsely coded with the best fitted structural dictionary, thus good structure preservation can be obtained. For homogenous regions without rich structure and texture information, the highly redundant photometric self-similarity is exploited to suppress speckle noise without introducing artifacts. That is achieved by firstly learning the sub-dictionary, then simultaneously sparsely coding for each group of photometrically similar image patches. Visual and objective experimental results demonstrate the superiority of the proposed method over the-state-of-the-art methods.
A Comparative Study of Sparse Associative Memories
NASA Astrophysics Data System (ADS)
Gripon, Vincent; Heusel, Judith; Löwe, Matthias; Vermet, Franck
2016-07-01
We study various models of associative memories with sparse information, i.e. a pattern to be stored is a random string of 0s and 1s with about log N 1s, only. We compare different synaptic weights, architectures and retrieval mechanisms to shed light on the influence of the various parameters on the storage capacity.
Sparse matrix transform for fast projection to reduced dimension
Theiler, James P; Cao, Guangzhi; Bouman, Charles A
2010-01-01
We investigate three algorithms that use the sparse matrix transform (SMT) to produce variance-maximizing linear projections to a lower-dimensional space. The SMT expresses the projection as a sequence of Givens rotations and this enables computationally efficient implementation of the projection operator. The baseline algorithm uses the SMT to directly approximate the optimal solution that is given by principal components analysis (PCA). A variant of the baseline begins with a standard SMT solution, but prunes the sequence of Givens rotations to only include those that contribute to the variance maximization. Finally, a simpler and faster third algorithm is introduced; this also estimates the projection operator with a sequence of Givens rotations, but in this case, the rotations are chosen to optimize a criterion that more directly expresses the dimension reduction criterion.
Nonlinear Spike-And-Slab Sparse Coding for Interpretable Image Encoding
Shelton, Jacquelyn A.; Sheikh, Abdul-Saboor; Bornschein, Jörg; Sterne, Philip; Lücke, Jörg
2015-01-01
Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) and modelling varying pixel intensities. Traditionally, images are modelled as a sparse linear superposition of dictionary elements, where the probabilistic view of this problem is that the coefficients follow a Laplace or Cauchy prior distribution. We propose a novel model that instead uses a spike-and-slab prior and nonlinear combination of components. With the prior, our model can easily represent exact zeros for e.g. the absence of an image component, such as an edge, and a distribution over non-zero pixel intensities. With the nonlinearity (the nonlinear max combination rule), the idea is to target occlusions; dictionary elements correspond to image components that can occlude each other. There are major consequences of the model assumptions made by both (non)linear approaches, thus the main goal of this paper is to isolate and highlight differences between them. Parameter optimization is analytically and computationally intractable in our model, thus as a main contribution we design an exact Gibbs sampler for efficient inference which we can apply to higher dimensional data using latent variable preselection. Results on natural and artificial occlusion-rich data with controlled forms of sparse structure show that our model can extract a sparse set of edge-like components that closely match the generating process, which we refer to as interpretable components. Furthermore, the sparseness of the solution closely follows the ground-truth number of components/edges in the images. The linear model did not learn such edge-like components with any level of sparsity. This suggests that our model can adaptively well-approximate and characterize the meaningful generation process. PMID:25954947
Vilar, Lara; Gómez, Israel; Martínez-Vega, Javier; Echavarría, Pilar; Riaño, David; Martín, M Pilar
2016-01-01
The socio-economic factors are of key importance during all phases of wildfire management that include prevention, suppression and restoration. However, modeling these factors, at the proper spatial and temporal scale to understand fire regimes is still challenging. This study analyses socio-economic drivers of wildfire occurrence in central Spain. This site represents a good example of how human activities play a key role over wildfires in the European Mediterranean basin. Generalized Linear Models (GLM) and machine learning Maximum Entropy models (Maxent) predicted wildfire occurrence in the 1980s and also in the 2000s to identify changes between each period in the socio-economic drivers affecting wildfire occurrence. GLM base their estimation on wildfire presence-absence observations whereas Maxent on wildfire presence-only. According to indicators like sensitivity or commission error Maxent outperformed GLM in both periods. It achieved a sensitivity of 38.9% and a commission error of 43.9% for the 1980s, and 67.3% and 17.9% for the 2000s. Instead, GLM obtained 23.33, 64.97, 9.41 and 18.34%, respectively. However GLM performed steadier than Maxent in terms of the overall fit. Both models explained wildfires from predictors such as population density and Wildland Urban Interface (WUI), but differed in their relative contribution. As a result of the urban sprawl and an abandonment of rural areas, predictors like WUI and distance to roads increased their contribution to both models in the 2000s, whereas Forest-Grassland Interface (FGI) influence decreased. This study demonstrates that human component can be modelled with a spatio-temporal dimension to integrate it into wildfire risk assessment. PMID:27557113
Vilar, Lara; Gómez, Israel; Martínez-Vega, Javier; Echavarría, Pilar; Riaño, David; Martín, M. Pilar
2016-01-01
The socio-economic factors are of key importance during all phases of wildfire management that include prevention, suppression and restoration. However, modeling these factors, at the proper spatial and temporal scale to understand fire regimes is still challenging. This study analyses socio-economic drivers of wildfire occurrence in central Spain. This site represents a good example of how human activities play a key role over wildfires in the European Mediterranean basin. Generalized Linear Models (GLM) and machine learning Maximum Entropy models (Maxent) predicted wildfire occurrence in the 1980s and also in the 2000s to identify changes between each period in the socio-economic drivers affecting wildfire occurrence. GLM base their estimation on wildfire presence-absence observations whereas Maxent on wildfire presence-only. According to indicators like sensitivity or commission error Maxent outperformed GLM in both periods. It achieved a sensitivity of 38.9% and a commission error of 43.9% for the 1980s, and 67.3% and 17.9% for the 2000s. Instead, GLM obtained 23.33, 64.97, 9.41 and 18.34%, respectively. However GLM performed steadier than Maxent in terms of the overall fit. Both models explained wildfires from predictors such as population density and Wildland Urban Interface (WUI), but differed in their relative contribution. As a result of the urban sprawl and an abandonment of rural areas, predictors like WUI and distance to roads increased their contribution to both models in the 2000s, whereas Forest-Grassland Interface (FGI) influence decreased. This study demonstrates that human component can be modelled with a spatio-temporal dimension to integrate it into wildfire risk assessment. PMID:27557113
Vilar, Lara; Gómez, Israel; Martínez-Vega, Javier; Echavarría, Pilar; Riaño, David; Martín, M Pilar
2016-01-01
The socio-economic factors are of key importance during all phases of wildfire management that include prevention, suppression and restoration. However, modeling these factors, at the proper spatial and temporal scale to understand fire regimes is still challenging. This study analyses socio-economic drivers of wildfire occurrence in central Spain. This site represents a good example of how human activities play a key role over wildfires in the European Mediterranean basin. Generalized Linear Models (GLM) and machine learning Maximum Entropy models (Maxent) predicted wildfire occurrence in the 1980s and also in the 2000s to identify changes between each period in the socio-economic drivers affecting wildfire occurrence. GLM base their estimation on wildfire presence-absence observations whereas Maxent on wildfire presence-only. According to indicators like sensitivity or commission error Maxent outperformed GLM in both periods. It achieved a sensitivity of 38.9% and a commission error of 43.9% for the 1980s, and 67.3% and 17.9% for the 2000s. Instead, GLM obtained 23.33, 64.97, 9.41 and 18.34%, respectively. However GLM performed steadier than Maxent in terms of the overall fit. Both models explained wildfires from predictors such as population density and Wildland Urban Interface (WUI), but differed in their relative contribution. As a result of the urban sprawl and an abandonment of rural areas, predictors like WUI and distance to roads increased their contribution to both models in the 2000s, whereas Forest-Grassland Interface (FGI) influence decreased. This study demonstrates that human component can be modelled with a spatio-temporal dimension to integrate it into wildfire risk assessment.
Shirazi, Mohammadali; Lord, Dominique; Dhavala, Soma Sekhar; Geedipally, Srinivas Reddy
2016-06-01
Crash data can often be characterized by over-dispersion, heavy (long) tail and many observations with the value zero. Over the last few years, a small number of researchers have started developing and applying novel and innovative multi-parameter models to analyze such data. These multi-parameter models have been proposed for overcoming the limitations of the traditional negative binomial (NB) model, which cannot handle this kind of data efficiently. The research documented in this paper continues the work related to multi-parameter models. The objective of this paper is to document the development and application of a flexible NB generalized linear model with randomly distributed mixed effects characterized by the Dirichlet process (NB-DP) to model crash data. The objective of the study was accomplished using two datasets. The new model was compared to the NB and the recently introduced model based on the mixture of the NB and Lindley (NB-L) distributions. Overall, the research study shows that the NB-DP model offers a better performance than the NB model once data are over-dispersed and have a heavy tail. The NB-DP performed better than the NB-L when the dataset has a heavy tail, but a smaller percentage of zeros. However, both models performed similarly when the dataset contained a large amount of zeros. In addition to a greater flexibility, the NB-DP provides a clustering by-product that allows the safety analyst to better understand the characteristics of the data, such as the identification of outliers and sources of dispersion. PMID:26945472
Inferring propagation paths for sparsely observed perturbations on complex networks
Massucci, Francesco Alessandro; Wheeler, Jonathan; Beltrán-Debón, Raúl; Joven, Jorge; Sales-Pardo, Marta; Guimerà, Roger
2016-01-01
In a complex system, perturbations propagate by following paths on the network of interactions among the system’s units. In contrast to what happens with the spreading of epidemics, observations of general perturbations are often very sparse in time (there is a single observation of the perturbed system) and in “space” (only a few perturbed and unperturbed units are observed). A major challenge in many areas, from biology to the social sciences, is to infer the propagation paths from observations of the effects of perturbation under these sparsity conditions. We address this problem and show that it is possible to go beyond the usual approach of using the shortest paths connecting the known perturbed nodes. Specifically, we show that a simple and general probabilistic model, which we solved using belief propagation, provides fast and accurate estimates of the probabilities of nodes being perturbed.
Super-sparsely view-sampled cone-beam CT by incorporating prior data.
Abbas, Sajid; Min, Jonghwan; Cho, Seungryong
2013-01-01
Computed tomography (CT) is widely used in medicine for diagnostics or for image-guided therapies, and is also popular in industrial applications for nondestructive testing. CT conventionally requires a large number of projections to produce volumetric images of a scanned object, because the conventional image reconstruction algorithm is based on filtered-backprojection. This requirement may result in relatively high radiation dose to the patients in medical CT unless the radiation dose at each view angle is reduced, and can cause expensive scanning time and efforts in industrial CT applications. Sparse- view CT may provide a viable option to address both issues including high radiation dose and expensive scanning efforts. However, image reconstruction from sparsely sampled data in CT is in general very challenging, and much efforts have been made to develop algorithms for such an image reconstruction problem. Image total-variation minimization algorithm inspired by compressive sensing theory has recently been developed, which exploits the sparseness of the image derivative magnitude and can reconstruct images from sparse-view data to a similar quality of the images conventionally reconstructed from many views. In successive CT scans, prior CT image of an object and its projection data may be readily available, and the current CT image may have not much difference from the prior image. Considering the sparseness of such a difference image between the successive scans, image reconstruction of the difference image may be achieved from very sparsely sampled data. In this work, we showed that one can further reduce the number of projections, resulting in a super-sparse scan, for a good quality image reconstruction with the aid of a prior data. Both numerical and experimental results are provided.
A sparse grid based method for generative dimensionality reduction of high-dimensional data
NASA Astrophysics Data System (ADS)
Bohn, Bastian; Garcke, Jochen; Griebel, Michael
2016-03-01
Generative dimensionality reduction methods play an important role in machine learning applications because they construct an explicit mapping from a low-dimensional space to the high-dimensional data space. We discuss a general framework to describe generative dimensionality reduction methods, where the main focus lies on a regularized principal manifold learning variant. Since most generative dimensionality reduction algorithms exploit the representer theorem for reproducing kernel Hilbert spaces, their computational costs grow at least quadratically in the number n of data. Instead, we introduce a grid-based discretization approach which automatically scales just linearly in n. To circumvent the curse of dimensionality of full tensor product grids, we use the concept of sparse grids. Furthermore, in real-world applications, some embedding directions are usually more important than others and it is reasonable to refine the underlying discretization space only in these directions. To this end, we employ a dimension-adaptive algorithm which is based on the ANOVA (analysis of variance) decomposition of a function. In particular, the reconstruction error is used to measure the quality of an embedding. As an application, the study of large simulation data from an engineering application in the automotive industry (car crash simulation) is performed.
NASA Technical Reports Server (NTRS)
Pflaum, Christoph
1996-01-01
A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.
Causal Network Inference Via Group Sparse Regularization.
Bolstad, Andrew; Van Veen, Barry D; Nowak, Robert
2011-06-11
This paper addresses the problem of inferring sparse causal networks modeled by multivariate autoregressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a "false connection score" ψ. In particular, we show that consistent recovery is possible even when the number of observations of the network is far less than the number of parameters describing the network, provided that ψ < 1. The false connection score is also demonstrated to be a useful metric of recovery in nonasymptotic regimes. The conditions suggest a modified gLasso procedure which tends to improve the false connection score and reduce the chances of reversing the direction of causal influence. Computational experiments and a real network based electrocorticogram (ECoG) simulation study demonstrate the effectiveness of the approach.
Statistical prediction with Kanerva's sparse distributed memory
NASA Technical Reports Server (NTRS)
Rogers, David
1989-01-01
A new viewpoint of the processing performed by Kanerva's sparse distributed memory (SDM) is presented. In conditions of near- or over-capacity, where the associative-memory behavior of the model breaks down, the processing performed by the model can be interpreted as that of a statistical predictor. Mathematical results are presented which serve as the framework for a new statistical viewpoint of sparse distributed memory and for which the standard formulation of SDM is a special case. This viewpoint suggests possible enhancements to the SDM model, including a procedure for improving the predictiveness of the system based on Holland's work with genetic algorithms, and a method for improving the capacity of SDM even when used as an associative memory.
Solving large sparse eigenvalue problems on supercomputers
NASA Technical Reports Server (NTRS)
Philippe, Bernard; Saad, Youcef
1988-01-01
An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed.
Sparse representation for color image restoration.
Mairal, Julien; Elad, Michael; Sapiro, Guillermo
2008-01-01
Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted dictionaries for images has been a major challenge. The K-SVD has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks. In this paper, we address the problem of learning dictionaries for color images and extend the K-SVD-based grayscale image denoising algorithm that appears in. This work puts forward ways for handling nonhomogeneous noise and missing information, paving the way to state-of-the-art results in applications such as color image denoising, demosaicing, and inpainting, as demonstrated in this paper. PMID:18229804
Causal Network Inference Via Group Sparse Regularization
Bolstad, Andrew; Van Veen, Barry D.; Nowak, Robert
2011-01-01
This paper addresses the problem of inferring sparse causal networks modeled by multivariate autoregressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a “false connection score” ψ. In particular, we show that consistent recovery is possible even when the number of observations of the network is far less than the number of parameters describing the network, provided that ψ < 1. The false connection score is also demonstrated to be a useful metric of recovery in nonasymptotic regimes. The conditions suggest a modified gLasso procedure which tends to improve the false connection score and reduce the chances of reversing the direction of causal influence. Computational experiments and a real network based electrocorticogram (ECoG) simulation study demonstrate the effectiveness of the approach. PMID:21918591
Neural process reconstruction from sparse user scribbles.
Roberts, Mike; Jeong, Won-Ki; Vázquez-Reina, Amelio; Unger, Markus; Bischof, Horst; Lichtman, Jeff; Pfister, Hanspeter
2011-01-01
We present a novel semi-automatic method for segmenting neural processes in large, highly anisotropic EM (electron microscopy) image stacks. Our method takes advantage of sparse scribble annotations provided by the user to guide a 3D variational segmentation model, thereby allowing our method to globally optimally enforce 3D geometric constraints on the segmentation. Moreover, we leverage a novel algorithm for propagating segmentation constraints through the image stack via optimal volumetric pathways, thereby allowing our method to compute highly accurate 3D segmentations from very sparse user input. We evaluate our method by reconstructing 16 neural processes in a 1024 x 1024 x 50 nanometer-scale EM image stack of a mouse hippocampus. We demonstrate that, on average, our method is 68% more accurate than previous state-of-the-art semi-automatic methods. PMID:22003670
KLU2 Direct Linear Solver Package
2012-01-04
KLU2 is a direct sparse solver for solving unsymmetric linear systems. It is related to the existing KLU solver, (in Amesos package and also as a stand-alone package from University of Florida) but provides template support for scalar and ordinal types. It uses a left looking LU factorization method.
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
Branicki, M.; Majda, A.J.
2013-05-15
Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
NASA Astrophysics Data System (ADS)
Branicki, M.; Majda, A. J.
2013-05-01
Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically 'superresolved' velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum of
Notes on implementation of sparsely distributed memory
NASA Technical Reports Server (NTRS)
Keeler, J. D.; Denning, P. J.
1986-01-01
The Sparsely Distributed Memory (SDM) developed by Kanerva is an unconventional memory design with very interesting and desirable properties. The memory works in a manner that is closely related to modern theories of human memory. The SDM model is discussed in terms of its implementation in hardware. Two appendices discuss the unconventional approaches of the SDM: Appendix A treats a resistive circuit for fast, parallel address decoding; and Appendix B treats a systolic array for high throughput read and write operations.
Modified sparse regularization for electrical impedance tomography.
Fan, Wenru; Wang, Huaxiang; Xue, Qian; Cui, Ziqiang; Sun, Benyuan; Wang, Qi
2016-03-01
Electrical impedance tomography (EIT) aims to estimate the electrical properties at the interior of an object from current-voltage measurements on its boundary. It has been widely investigated due to its advantages of low cost, non-radiation, non-invasiveness, and high speed. Image reconstruction of EIT is a nonlinear and ill-posed inverse problem. Therefore, regularization techniques like Tikhonov regularization are used to solve the inverse problem. A sparse regularization based on L1 norm exhibits superiority in preserving boundary information at sharp changes or discontinuous areas in the image. However, the limitation of sparse regularization lies in the time consumption for solving the problem. In order to further improve the calculation speed of sparse regularization, a modified method based on separable approximation algorithm is proposed by using adaptive step-size and preconditioning technique. Both simulation and experimental results show the effectiveness of the proposed method in improving the image quality and real-time performance in the presence of different noise intensities and conductivity contrasts. PMID:27036798
Modified sparse regularization for electrical impedance tomography.
Fan, Wenru; Wang, Huaxiang; Xue, Qian; Cui, Ziqiang; Sun, Benyuan; Wang, Qi
2016-03-01
Electrical impedance tomography (EIT) aims to estimate the electrical properties at the interior of an object from current-voltage measurements on its boundary. It has been widely investigated due to its advantages of low cost, non-radiation, non-invasiveness, and high speed. Image reconstruction of EIT is a nonlinear and ill-posed inverse problem. Therefore, regularization techniques like Tikhonov regularization are used to solve the inverse problem. A sparse regularization based on L1 norm exhibits superiority in preserving boundary information at sharp changes or discontinuous areas in the image. However, the limitation of sparse regularization lies in the time consumption for solving the problem. In order to further improve the calculation speed of sparse regularization, a modified method based on separable approximation algorithm is proposed by using adaptive step-size and preconditioning technique. Both simulation and experimental results show the effectiveness of the proposed method in improving the image quality and real-time performance in the presence of different noise intensities and conductivity contrasts.
Mean-field sparse optimal control
Fornasier, Massimo; Piccoli, Benedetto; Rossi, Francesco
2014-01-01
We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modelling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dynamics of the probability distribution of the followers. In the classical mean-field theory, one studies the behaviour of a large number of small individuals freely interacting with each other, by simplifying the effect of all the other individuals on any given individual by a single averaged effect. In this paper, we address instead the situation where the leaders are actually influenced also by an external policy maker, and we propagate its effect for the number N of followers going to infinity. The technical derivation of the sparse mean-field optimal control is realized by the simultaneous development of the mean-field limit of the equations governing the followers dynamics together with the Γ-limit of the finite dimensional sparse optimal control problems. PMID:25288818
SAR Image despeckling via sparse representation
NASA Astrophysics Data System (ADS)
Wang, Zhongmei; Yang, Xiaomei; Zheng, Liang
2014-11-01
SAR image despeckling is an active research area in image processing due to its importance in improving the quality of image for object detection and classification.In this paper, a new approach is proposed for multiplicative noise in SAR image removal based on nonlocal sparse representation by dictionary learning and collaborative filtering. First, a image is divided into many patches, and then a cluster is formed by clustering log-similar image patches using Fuzzy C-means (FCM). For each cluster, an over-complete dictionary is computed using the K-SVD method that iteratively updates the dictionary and the sparse coefficients. The patches belonging to the same cluster are then reconstructed by a sparse combination of the corresponding dictionary atoms. The reconstructed patches are finally collaboratively aggregated to build the denoised image. The experimental results show that the proposed method achieves much better results than many state-of-the-art algorithms in terms of both objective evaluation index (PSNR and ENL) and subjective visual perception.
Framelet-Based Sparse Unmixing of Hyperspectral Images.
Zhang, Guixu; Xu, Yingying; Fang, Faming
2016-04-01
Spectral unmixing aims at estimating the proportions (abundances) of pure spectrums (endmembers) in each mixed pixel of hyperspectral data. Recently, a semi-supervised approach, which takes the spectral library as prior knowledge, has been attracting much attention in unmixing. In this paper, we propose a new semi-supervised unmixing model, termed framelet-based sparse unmixing (FSU), which promotes the abundance sparsity in framelet domain and discriminates the approximation and detail components of hyperspectral data after framelet decomposition. Due to the advantages of the framelet representations, e.g., images have good sparse approximations in framelet domain, and most of the additive noises are included in the detail coefficients, the FSU model has a better antinoise capability, and accordingly leads to more desirable unmixing performance. The existence and uniqueness of the minimizer of the FSU model are then discussed, and the split Bregman algorithm and its convergence property are presented to obtain the minimal solution. Experimental results on both simulated data and real data demonstrate that the FSU model generally performs better than the compared methods. PMID:26849863
Sparse MEG source imaging in Landau-Kleffner syndrome.
Zhu, Min; Zhang, Wenbo; Dickens, Deanna; Ding, Lei
2011-01-01
Epilepsy patients with Landau-Kleffner syndrome (LKS) usually have a normal brain structure, which makes it a challenge to identify the epileptogenic zone only based on magnetic resonance imaging (MRI) data. A sparse source imaging technique called variation based sparse cortical current density (VB-SCCD) imaging was adopted here to reconstruct cortical sources of magnetoencephalography (MEG) interictal spikes from an LKS patient. Realistic boundary element (BE) head and cortex models were built by segmenting structural MRI. 148-channel MEG was recorded for 10 minutes between seizures. Total 29 epileptiform spikes were selected for analysis. The primary cortical sources were observed locating at the left intra- and perisylvian cortex. Multiple extrasylvian sources were identified as the secondary sources. The spatio-temporal patterns of cortical sources provide more insights about the neuronal synchrony and propagation of epileptic discharges. Our observations were consistent with presurgical diagnosis for this patient and observation of aphasia in LKS. The present results suggest that the promising of VB-SCCD technique in assisting with presurgical planning and studying the neural network for LKS in determining the lateralization of epileptic origins. It can further be applied to non-invasively localize and/or lateralize eloquent cortex for language for epilepsy patients in general in the future.
Generalized subspace correction methods
Kolm, P.; Arbenz, P.; Gander, W.
1996-12-31
A fundamental problem in scientific computing is the solution of large sparse systems of linear equations. Often these systems arise from the discretization of differential equations by finite difference, finite volume or finite element methods. Iterative methods exploiting these sparse structures have proven to be very effective on conventional computers for a wide area of applications. Due to the rapid development and increasing demand for the large computing powers of parallel computers, it has become important to design iterative methods specialized for these new architectures.
A survey of packages for large linear systems
Wu, Kesheng; Milne, Brent
2000-02-11
This paper evaluates portable software packages for the iterative solution of very large sparse linear systems on parallel architectures. While we cannot hope to tell individual users which package will best suit their needs, we do hope that our systematic evaluation provides essential unbiased information about the packages and the evaluation process may serve as an example on how to evaluate these packages. The information contained here include feature comparisons, usability evaluations and performance characterizations. This review is primarily focused on self-contained packages that can be easily integrated into an existing program and are capable of computing solutions to very large sparse linear systems of equations. More specifically, it concentrates on portable parallel linear system solution packages that provide iterative solution schemes and related preconditioning schemes because iterative methods are more frequently used than competing schemes such as direct methods. The eight packages evaluated are: Aztec, BlockSolve,ISIS++, LINSOL, P-SPARSLIB, PARASOL, PETSc, and PINEAPL. Among the eight portable parallel iterative linear system solvers reviewed, we recommend PETSc and Aztec for most application programmers because they have well designed user interface, extensive documentation and very responsive user support. Both PETSc and Aztec are written in the C language and are callable from Fortran. For those users interested in using Fortran 90, PARASOL is a good alternative. ISIS++is a good alternative for those who prefer the C++ language. Both PARASOL and ISIS++ are relatively new and are continuously evolving. Thus their user interface may change. In general, those packages written in Fortran 77 are more cumbersome to use because the user may need to directly deal with a number of arrays of varying sizes. Languages like C++ and Fortran 90 offer more convenient data encapsulation mechanisms which make it easier to implement a clean and intuitive user
A joint sparse representation-based method for double-trial evoked potentials estimation.
Yu, Nannan; Liu, Haikuan; Wang, Xiaoyan; Lu, Hanbing
2013-12-01
In this paper, we present a novel approach to solving an evoked potentials estimating problem. Generally, the evoked potentials in two consecutive trials obtained by repeated identical stimuli of the nerves are extremely similar. In order to trace evoked potentials, we propose a joint sparse representation-based double-trial evoked potentials estimation method, taking full advantage of this similarity. The estimation process is performed in three stages: first, according to the similarity of evoked potentials and the randomness of a spontaneous electroencephalogram, the two consecutive observations of evoked potentials are considered as superpositions of the common component and the unique components; second, making use of their characteristics, the two sparse dictionaries are constructed; and finally, we apply the joint sparse representation method in order to extract the common component of double-trial observations, instead of the evoked potential in each trial. A series of experiments carried out on simulated and human test responses confirmed the superior performance of our method.
Normalization for Sparse Encoding of Odors by a Wide-Field Interneuron
Papadopoulou, Maria; Cassenaer, Stijn; Nowotny, Thomas; Laurent, Gilles
2011-01-01
Summary 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. PMID:21551062
Efficient visual tracking via low-complexity sparse representation
NASA Astrophysics Data System (ADS)
Lu, Weizhi; Zhang, Jinglin; Kpalma, Kidiyo; Ronsin, Joseph
2015-12-01
Thanks to its good performance on object recognition, sparse representation has recently been widely studied in the area of visual object tracking. Up to now, little attention has been paid to the complexity of sparse representation, while most works are focused on the performance improvement. By reducing the computation load related to sparse representation hundreds of times, this paper proposes by far the most computationally efficient tracking approach based on sparse representation. The proposal simply consists of two stages of sparse representation, one is for object detection and the other for object validation. Experimentally, it achieves better performance than some state-of-the-art methods in both accuracy and speed.
Object-oriented algorithmic laboratory for ordering sparse matrices
Kumfert, G K
2000-05-01
We focus on two known NP-hard problems that have applications in sparse matrix computations: the envelope/wavefront reduction problem and the fill reduction problem. Envelope/wavefront reducing orderings have a wide range of applications including profile and frontal solvers, incomplete factorization preconditioning, graph reordering for cache performance, gene sequencing, and spatial databases. Fill reducing orderings are generally limited to--but an inextricable part of--sparse matrix factorization. Our major contribution to this field is the design of new and improved heuristics for these NP-hard problems and their efficient implementation in a robust, cross-platform, object-oriented software package. In this body of research, we (1) examine current ordering algorithms, analyze their asymptotic complexity, and characterize their behavior in model problems, (2) introduce new and improved algorithms that address deficiencies found in previous heuristics, (3) implement an object-oriented library of these algorithms in a robust, modular fashion without significant loss of efficiency, and (4) extend our algorithms and software to address both generalized and constrained problems. We stress that the major contribution is the algorithms and the implementation; the whole being greater than the sum of its parts. The initial motivation for implementing our algorithms in object-oriented software was to manage the inherent complexity. During our research came the realization that the object-oriented implementation enabled new possibilities augmented algorithms that would not have been as natural to generalize from a procedural implementation. Some extensions are constructed from a family of related algorithmic components, thereby creating a poly-algorithm that can adapt its strategy to the properties of the specific problem instance dynamically. Other algorithms are tailored for special constraints by aggregating algorithmic components and having them collaboratively
Brown, Kristen A.; Harlim, John
2013-02-15
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.