SPARSE GENERALIZED FUNCTIONAL LINEAR MODEL FOR PREDICTING REMISSION STATUS OF DEPRESSION PATIENTS
Liu, Yashu; Nie, Zhi; Zhou, Jiayu; Farnum, Michael; Narayan, Vaibhav A; Wittenberg, Gayle; Ye, Jieping
2014-01-01
Complex diseases such as major depression affect people over time in complicated patterns. Longitudinal data analysis is thus crucial for understanding and prognosis of such diseases and has received considerable attention in the biomedical research community. Traditional classification and regression methods have been commonly applied in a simple (controlled) clinical setting with a small number of time points. However, these methods cannot be easily extended to the more general setting for longitudinal analysis, as they are not inherently built for time-dependent data. Functional regression, in contrast, is capable of identifying the relationship between features and outcomes along with time information by assuming features and/or outcomes as random functions over time rather than independent random variables. In this paper, we propose a novel sparse generalized functional linear model for the prediction of treatment remission status of the depression participants with longitudinal features. Compared to traditional functional regression models, our model enables high-dimensional learning, smoothness of functional coefficients, longitudinal feature selection and interpretable estimation of functional coefficients. Extensive experiments have been conducted on the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) data set and the results show that the proposed sparse functional regression method achieves significantly higher prediction power than existing approaches. PMID:24297562
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.
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.
Enhanced multi-level block ILU preconditioning strategies for general sparse linear systems
NASA Astrophysics Data System (ADS)
Saad, Yousef; Zhang, Jun
2001-05-01
This paper introduces several strategies to deal with pivot blocks in multi-level block incomplete LU factorization (BILUM) preconditioning techniques. These techniques are aimed at increasing the robustness and controlling the amount of fill-ins of BILUM for solving large sparse linear systems when large-size blocks are used to form block-independent set. Techniques proposed in this paper include double-dropping strategies, approximate singular-value decomposition, variable size blocks and use of an arrowhead block submatrix. We point out the advantages and disadvantages of these strategies and discuss their efficient implementations. Numerical experiments are conducted to show the usefulness of the new techniques in dealing with hard-to-solve problems arising from computational fluid dynamics. In addition, we discuss the relation between multi-level ILU preconditioning methods and algebraic multi-level methods.
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.
PSPIKE: A Parallel Hybrid Sparse Linear System Solver
NASA Astrophysics Data System (ADS)
Manguoglu, Murat; Sameh, Ahmed H.; Schenk, Olaf
The availability of large-scale computing platforms comprised of tens of thousands of multicore processors motivates the need for the next generation of highly scalable sparse linear system solvers. These solvers must optimize parallel performance, processor (serial) performance, as well as memory requirements, while being robust across broad classes of applications and systems. In this paper, we present a new parallel solver that combines the desirable characteristics of direct methods (robustness) and effective iterative solvers (low computational cost), while alleviating their drawbacks (memory requirements, lack of robustness). Our proposed hybrid solver is based on the general sparse solver PARDISO, and the “Spike” family of hybrid solvers. The resulting algorithm, called PSPIKE, is as robust as direct solvers, more reliable than classical preconditioned Krylov subspace methods, and much more scalable than direct sparse solvers. We support our performance and parallel scalability claims using detailed experimental studies and comparison with direct solvers, as well as classical preconditioned Krylov methods.
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.
Anisotropic interpolation of sparse generalized image samples.
Bourquard, Aurélien; Unser, Michael
2013-02-01
Practical image-acquisition systems are often modeled as a continuous-domain prefilter followed by an ideal sampler, where generalized samples are obtained after convolution with the impulse response of the device. In this paper, our goal is to interpolate images from a given subset of such samples. We express our solution in the continuous domain, considering consistent resampling as a data-fidelity constraint. To make the problem well posed and ensure edge-preserving solutions, we develop an efficient anisotropic regularization approach that is based on an improved version of the edge-enhancing anisotropic diffusion equation. Following variational principles, our reconstruction algorithm minimizes successive quadratic cost functionals. To ensure fast convergence, we solve the corresponding sequence of linear problems by using multigrid iterations that are specifically tailored to their sparse structure. We conduct illustrative experiments and discuss the potential of our approach both in terms of algorithmic design and reconstruction quality. In particular, we present results that use as little as 2% of the image samples. PMID:22968212
The efficient parallel iterative solution of large sparse linear systems
Jones, M.T.; Plassmann, P.E.
1992-06-01
The development of efficient, general-purpose software for the iterative solution of sparse linear systems on a parallel MIMD computer requires an interesting combination of expertise. Parallel graph heuristics, convergence analysis, and basic linear algebra implementation issues must all be considered. In this paper, we discuss how we have incorporated recent results in these areas into a general-purpose iterative solver. First, we consider two recently developed parallel graph coloring heuristics. We show how the method proposed by Luby, based on determining maximal independent sets, can be modified to run in an asynchronous manner and give aa expected running time bound for this modified heuristic. In addition, a number of graph reduction heuristics are described that are used in our implementation to improve the individual processor performance. The effect of these various graph reductions on the solution of sparse triangular systems is categorized. Finally, we discuss the performance of this solver from the perspective of two large-scale applications: a piezoelectric crystal finite-element modeling problem, and a nonlinear optimization problem to determine the minimum energy configuration of a three-dimensional, layered superconductor model.
A model of asynchronous iterative algorithms for solving large, sparse, linear systems
NASA Technical Reports Server (NTRS)
Reed, D. A.; Patrick, M. L.
1984-01-01
Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension.
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.
Parallel, iterative solution of sparse linear systems: Models and architectures
NASA Technical Reports Server (NTRS)
Reed, D. A.; Patrick, M. L.
1984-01-01
A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed.
Recent History Functional Linear Models for Sparse Longitudinal Data
Kim, Kion; Şentürk, Damla; Li, Runze
2011-01-01
We consider the recent history functional linear models, relating a longitudinal response to a longitudinal predictor where the predictor process only in a sliding window into the recent past has an effect on the response value at the current time. We propose an estimation procedure for recent history functional linear models that is geared towards sparse longitudinal data, where the observation times across subjects are irregular and total number of measurements per subject is small. The proposed estimation procedure builds upon recent developments in literature for estimation of functional linear models with sparse data and utilizes connections between the recent history functional linear models and varying coefficient models. We establish uniform consistency of the proposed estimators, propose prediction of the response trajectories and derive their asymptotic distribution leading to asymptotic point-wise confidence bands. We include a real data application and simulation studies to demonstrate the efficacy of the proposed methodology. PMID:21691421
Iterative algorithms for large sparse linear systems on parallel computers
NASA Technical Reports Server (NTRS)
Adams, L. M.
1982-01-01
Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.
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.
Scalable Library for the Parallel Solution of Sparse Linear Systems
Energy Science and Technology Software Center (ESTSC)
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
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.
On A Nonlinear Generalization of Sparse Coding and Dictionary Learning
Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba
2013-01-01
Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝd, and the dictionary is learned from the training data using the vector space structure of ℝd and its Euclidean L2-metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis. PMID:24129583
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.
lp-lq penalty for sparse linear and sparse multiple kernel multitask learning.
Rakotomamonjy, Alain; Flamary, Rémi; Gasso, Gilles; Canu, Stéphane
2011-08-01
Recently, there has been much interest around multitask learning (MTL) problem with the constraints that tasks should share a common sparsity profile. Such a problem can be addressed through a regularization framework where the regularizer induces a joint-sparsity pattern between task decision functions. We follow this principled framework and focus on l(p)-l(q) (with 0 ≤ p ≤ 1 and 1 ≤ q ≤ 2) mixed norms as sparsity-inducing penalties. Our motivation for addressing such a larger class of penalty is to adapt the penalty to a problem at hand leading thus to better performances and better sparsity pattern. For solving the problem in the general multiple kernel case, we first derive a variational formulation of the l(1)-l(q) penalty which helps us in proposing an alternate optimization algorithm. Although very simple, the latter algorithm provably converges to the global minimum of the l(1)-l(q) penalized problem. For the linear case, we extend existing works considering accelerated proximal gradient to this penalty. Our contribution in this context is to provide an efficient scheme for computing the l(1)-l(q) proximal operator. Then, for the more general case, when , we solve the resulting nonconvex problem through a majorization-minimization approach. The resulting algorithm is an iterative scheme which, at each iteration, solves a weighted l(1)-l(q) sparse MTL problem. Empirical evidences from toy dataset and real-word datasets dealing with brain-computer interface single-trial electroencephalogram classification and protein subcellular localization show the benefit of the proposed approaches and algorithms. PMID:21813358
Visual Tracking via Sparse and Local Linear Coding.
Wang, Guofeng; Qin, Xueying; Zhong, Fan; Liu, Yue; Li, Hongbo; Peng, Qunsheng; Yang, Ming-Hsuan
2015-11-01
The state search is an important component of any object tracking algorithm. Numerous algorithms have been proposed, but stochastic sampling methods (e.g., particle filters) are arguably one of the most effective approaches. However, the discretization of the state space complicates the search for the precise object location. In this paper, we propose a novel tracking algorithm that extends the state space of particle observations from discrete to continuous. The solution is determined accurately via iterative linear coding between two convex hulls. The algorithm is modeled by an optimal function, which can be efficiently solved by either convex sparse coding or locality constrained linear coding. The algorithm is also very flexible and can be combined with many generic object representations. Thus, we first use sparse representation to achieve an efficient searching mechanism of the algorithm and demonstrate its accuracy. Next, two other object representation models, i.e., least soft-threshold squares and adaptive structural local sparse appearance, are implemented with improved accuracy to demonstrate the flexibility of our algorithm. Qualitative and quantitative experimental results demonstrate that the proposed tracking algorithm performs favorably against the state-of-the-art methods in dynamic scenes. PMID:26353352
Sparse Substring Pattern Set Discovery Using Linear Programming Boosting
NASA Astrophysics Data System (ADS)
Kashihara, Kazuaki; Hatano, Kohei; Bannai, Hideo; Takeda, Masayuki
In this paper, we consider finding a small set of substring patterns which classifies the given documents well. We formulate the problem as 1 norm soft margin optimization problem where each dimension corresponds to a substring pattern. Then we solve this problem by using LPBoost and an optimal substring discovery algorithm. Since the problem is a linear program, the resulting solution is likely to be sparse, which is useful for feature selection. We evaluate the proposed method for real data such as movie reviews.
On time delay estimation from a sparse linear prediction perspective.
He, Hongsen; Yang, Tao; Chen, Jingdong
2015-02-01
This paper proposes a sparse linear prediction based algorithm to estimate time difference of arrival. This algorithm unifies the cross correlation method without prewhitening and that with prewhitening via an ℓ2/ℓ1 optimization process, which is solved by an augmented Lagrangian alternating direction method. It also forms a set of time delay estimators that make a tradeoff between prewhitening and non-prewhitening through adjusting a regularization parameter. The effectiveness of the proposed algorithm is demonstrated in noisy and reverberant environments. PMID:25698037
Kernelized Elastic Net Regularization: Generalization Bounds, and Sparse Recovery.
Feng, Yunlong; Lv, Shao-Gao; Hang, Hanyuan; Suykens, Johan A K
2016-03-01
Kernelized elastic net regularization (KENReg) is a kernelization of the well-known elastic net regularization (Zou & Hastie, 2005 ). The kernel in KENReg is not required to be a Mercer kernel since it learns from a kernelized dictionary in the coefficient space. Feng, Yang, Zhao, Lv, and Suykens ( 2014 ) showed that KENReg has some nice properties including stability, sparseness, and generalization. In this letter, we continue our study on KENReg by conducting a refined learning theory analysis. This letter makes the following three main contributions. First, we present refined error analysis on the generalization performance of KENReg. The main difficulty of analyzing the generalization error of KENReg lies in characterizing the population version of its empirical target function. We overcome this by introducing a weighted Banach space associated with the elastic net regularization. We are then able to conduct elaborated learning theory analysis and obtain fast convergence rates under proper complexity and regularity assumptions. Second, we study the sparse recovery problem in KENReg with fixed design and show that the kernelization may improve the sparse recovery ability compared to the classical elastic net regularization. Finally, we discuss the interplay among different properties of KENReg that include sparseness, stability, and generalization. We show that the stability of KENReg leads to generalization, and its sparseness confidence can be derived from generalization. Moreover, KENReg is stable and can be simultaneously sparse, which makes it attractive theoretically and practically. PMID:26735744
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.
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.
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
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
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.
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.
The search for high level parallelism for the iterative solution of large sparse linear systems
Young, D.M.
1988-07-01
In this paper the author is concerned with the numerical solution, based on iterative methods, of large sparse systems of linear algebraic equations of the type which arise in the numerical solution of elliptic and parabolic partial differential equations by finite difference or finite element methods. He considers linear systems of the form Au = b where A is a given N x N matrix which is large and sparse and where b is a given N x 1 column vector. He will assumes that A is symmetric and positive definite (SPD). He considers iterative algorithms which consist of a basic iterative method, such as the Richardson, Jacobi, SSOR or incomplete Cholesky method, combined with an acceleration procedure such as Chebyshev acceleration or conjugate gradient acceleration. The object of this paper is, however, to examine some high-level methods for achieving parallelism. Such techniques involve only matrix/vector operations and do not involve working with blocks of the matrix, subdividing the region, or using different meshes. It is expected that if effective high-level methods could be developed, they could be combined with block and domain decomposition methods, and related methods, to obtain even greater speedups. It is also expected that by working at a higher level it will eventually be possible to develop general purpose software for parallel machines similar to the ITPACK software packages which have already been developed for sequential and vector machines. The discussion here is primarily devoted to describing various techniques which the author and others have considered for obtaining high-level parallelism. The author plans to continue research on these techniques and eventually to develop algorithms and programs for multiprocessors based on them.
LU-decomposition with iterative refinement for solving sparse linear systems
NASA Astrophysics Data System (ADS)
Al-Kurdi, Ahmad; Kincaid, David R.
2006-01-01
In the solution of a system of linear algebraic equations Ax=b with a large sparse coefficient matrix A, the LU-decomposition with iterative refinement (LUIR) is compared with the LU-decomposition with direct solution (LUDS), which is without iterative refinement. We verify by numerical experiments that the use of sparse matrix techniques with LUIR may result in a reduction of both the computing time and the storage requirements. The powers of a Boolean matrix strategy (PBS) is used in an effort to achieve such a reduction and in an attempt to control the sparsity. We conclude that iterative refinement procedures may be efficiently used as an option in software for the solution of sparse linear systems of equations.
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
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.
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.
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.
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
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.
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.
A scalable 2-D parallel sparse solver
Kothari, S.C.; Mitra, S.
1995-12-01
Scalability beyond a small number of processors, typically 32 or less, is known to be a problem for existing parallel general sparse (PGS) direct solvers. This paper presents a parallel general sparse PGS direct solver for general sparse linear systems on distributed memory machines. The algorithm is based on the well-known sequential sparse algorithm Y12M. To achieve efficient parallelization, a 2-D scattered decomposition of the sparse matrix is used. The proposed algorithm is more scalable than existing parallel sparse direct solvers. Its scalability is evaluated on a 256 processor nCUBE2s machine using Boeing/Harwell benchmark matrices.
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.
Zhang, Yu; Zhou, Guoxu; Jin, Jing; Zhao, Qibin; Wang, Xingyu; Cichocki, Andrzej
2014-02-01
Two main issues for event-related potential (ERP) classification in brain-computer interface (BCI) application are curse-of-dimensionality and bias-variance tradeoff, which may deteriorate classification performance, especially with insufficient training samples resulted from limited calibration time. This study introduces an aggregation of sparse linear discriminant analyses (ASLDA) to overcome these problems. In the ASLDA, multiple sparse discriminant vectors are learned from differently l1-regularized least-squares regressions by exploiting the equivalence between LDA and least-squares regression, and are subsequently aggregated to form an ensemble classifier, which could not only implement automatic feature selection for dimensionality reduction to alleviate curse-of-dimensionality, but also decrease the variance to improve generalization capacity for new test samples. Extensive investigation and comparison are carried out among the ASLDA, the ordinary LDA and other competing ERP classification algorithms, based on different three ERP datasets. Experimental results indicate that the ASLDA yields better overall performance for single-trial ERP classification when insufficient training samples are available. This suggests the proposed ASLDA is promising for ERP classification in small sample size scenario to improve the practicability of BCI. PMID:24344691
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
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.
LANZ - SOFTWARE FOR SOLVING THE LARGE SPARSE SYMMETRIC GENERALIZED EIGENPROBLEM
NASA Technical Reports Server (NTRS)
Jones, M. T.
1994-01-01
LANZ is a sophisticated algorithm based on the simple Lanczos method for solving the generalized eigenvalue problem. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the basic Lanczos algorithm. The program has been successfully used to solve problems such as: 1) finding the vibration frequencies and mode shape vectors of a structure, and 2) finding the smallest load at which a structure will buckle. Several methods exist for solving the large symmetric generalized eigenvalue problem. LANZ offers an alternative to the popular sub-space iteration approach. The program includes a new algorithm for solving the tri-diagonal matrices that arise when using the Lanczos method. Procedurally, LANZ starts with the user's initial shift, then executes the Lanczos algorithm until: 1) the desired number of eigenvalues is found; 2) no storage space is left; or 3) LANZ determines that a new shift is needed. When a new shift is needed, the program selects it based on accumulated information. At each iteration, LANZ examines the converged and unconverged eigenvalues along with the inertia counts to ensure that no eigenvalues have been missed. LANZ is written in FORTRAN 77 and C language. It was originally designed to run on computers that support vector processing such as the CRAY Y-MP and is therefore optimized for vector machines. Makefiles are included for the Sun3, Sun4, Cray Y-MP, and CONVEX 220. When implemented on a Sun4 computer, LANZ required 670K of main memory. The standard distribution medium for this program is a .25 inch streaming magnetic cartridge tape in Unix tar format. It is also available on a 3.5 inch diskette in UNIX tar format. LANZ was developed in 1989. Sun3 and Sun4 are trademarks of Sun Microsystems, Inc. Cray Y-MP is a trademark of Cray Research, Inc. CONVEX 220 is a trademark of Convex Computer Corporation.
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…
Two-Dimensional Pattern-Coupled Sparse Bayesian Learning via Generalized Approximate Message Passing
NASA Astrophysics Data System (ADS)
Fang, Jun; Zhang, Lizao; Li, Hongbin
2016-06-01
We consider the problem of recovering two-dimensional (2-D) block-sparse signals with \\emph{unknown} cluster patterns. Two-dimensional block-sparse patterns arise naturally in many practical applications such as foreground detection and inverse synthetic aperture radar imaging. To exploit the block-sparse structure, we introduce a 2-D pattern-coupled hierarchical Gaussian prior model to characterize the statistical pattern dependencies among neighboring coefficients. Unlike the conventional hierarchical Gaussian prior model where each coefficient is associated independently with a unique hyperparameter, the pattern-coupled prior for each coefficient not only involves its own hyperparameter, but also its immediate neighboring hyperparameters. Thus the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage 2-D structured-sparse solutions. An expectation-maximization (EM) strategy is employed to obtain the maximum a posterior (MAP) estimate of the hyperparameters, along with the posterior distribution of the sparse signal. In addition, the generalized approximate message passing (GAMP) algorithm is embedded into the EM framework to efficiently compute an approximation of the posterior distribution of hidden variables, which results in a significant reduction in computational complexity. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.
Lemme, Andre; Reinhart, René Felix; Steil, Jochen Jakob
2012-09-01
We present an efficient online learning scheme for non-negative sparse coding in autoencoder neural networks. It comprises a novel synaptic decay rule that ensures non-negative weights in combination with an intrinsic self-adaptation rule that optimizes sparseness of the non-negative encoding. We show that non-negativity constrains the space of solutions such that overfitting is prevented and very similar encodings are found irrespective of the network initialization and size. We benchmark the novel method on real-world datasets of handwritten digits and faces. The autoencoder yields higher sparseness and lower reconstruction errors than related offline algorithms based on matrix factorization. It generalizes to new inputs both accurately and without costly computations, which is fundamentally different from the classical matrix factorization approaches. PMID:22706093
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.
BlockSolve v1.1: Scalable library software for the parallel solution of sparse linear systems
Jones, M.T.; Plassmann, P.E.
1993-03-01
BlockSolve is a software library for solving large, sparse systems of linear equations on massively parallel computers. The matrices must be symmetric, but may have an arbitrary sparsity structure. BlockSolve is a portable package that is compatible with several different message-passing pardigms. This report gives detailed instructions on the use of BlockSolve in applications programs.
BlockSolve v1. 1: Scalable library software for the parallel solution of sparse linear systems
Jones, M.T.; Plassmann, P.E.
1993-03-01
BlockSolve is a software library for solving large, sparse systems of linear equations on massively parallel computers. The matrices must be symmetric, but may have an arbitrary sparsity structure. BlockSolve is a portable package that is compatible with several different message-passing pardigms. This report gives detailed instructions on the use of BlockSolve in applications programs.
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.
NASA Astrophysics Data System (ADS)
Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.
2016-02-01
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. Overall, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.
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.
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.
Pinski, Peter; Riplinger, Christoph; Valeev, Edward F; Neese, Frank
2015-07-21
In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in
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 gut
Multiconlitron: a general piecewise linear classifier.
Yujian, Li; Bo, Liu; Xinwu, Yang; Yaozong, Fu; Houjun, Li
2011-02-01
Based on the "convexly separable" concept, we present a solid geometric theory and a new general framework to design piecewise linear classifiers for two arbitrarily complicated nonintersecting classes by using a "multiconlitron," which is a union of multiple conlitrons that comprise a set of hyperplanes or linear functions surrounding a convex region for separating two convexly separable datasets. We propose a new iterative algorithm called the cross distance minimization algorithm (CDMA) to compute hard margin non-kernel support vector machines (SVMs) via the nearest point pair between two convex polytopes. Using CDMA, we derive two new algorithms, i.e., the support conlitron algorithm (SCA) and the support multiconlitron algorithm (SMA) to construct support conlitrons and support multiconlitrons, respectively, which are unique and can separate two classes by a maximum margin as in an SVM. Comparative experiments show that SMA can outperform linear SVM on many of the selected databases and provide similar results to radial basis function SVM on some of them, while SCA performs better than linear SVM on three out of four applicable databases. Other experiments show that SMA and SCA may be further improved to draw more potential in the new research direction of piecewise linear learning. PMID:21138800
Yu, D.C.; Wang, H. )
1990-05-01
This paper presents a new parallel computational method to solve the forward and backward substitutions (F/B) of sparse linear equations. The architectural model is a multiprocessor hypercube, based on the Taged Token Dataflow Architecture (TTDA). Communication overhead is considered. The differences of the operating time-units among the subtraction, multiplication, and division are modelled. A processor scheduling algorithm is also introduced. In the algorithm, a highly sparse operational sequence matrix C is developed. From the C matrix, the minimal completion time, the critical path, and the scheduling of the processors for the proposed parallel F/B can be determined. Detailed explanation of the implementation of the TTDA architecture in the proposed method is provided. A number of power systems have been examined and a number of scenarios have been simulated to test the performance of the proposed method. The results are presented and discussed in this paper.
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.
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.
SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression *
Sun, Qiang; Zhu, Hongtu; Liu, Yufeng; Ibrahim, Joseph G.
2014-01-01
The aim of this paper is to develop a sparse projection regression modeling (SPReM) framework to perform multivariate regression modeling with a large number of responses and a multivariate covariate of interest. We propose two novel heritability ratios to simultaneously perform dimension reduction, response selection, estimation, and testing, while explicitly accounting for correlations among multivariate responses. Our SPReM is devised to specifically address the low statistical power issue of many standard statistical approaches, such as the Hotelling’s T2 test statistic or a mass univariate analysis, for high-dimensional data. We formulate the estimation problem of SPREM as a novel sparse unit rank projection (SURP) problem and propose a fast optimization algorithm for SURP. Furthermore, we extend SURP to the sparse multi-rank projection (SMURP) by adopting a sequential SURP approximation. Theoretically, we have systematically investigated the convergence properties of SURP and the convergence rate of SURP estimates. Our simulation results and real data analysis have shown that SPReM out-performs other state-of-the-art methods. PMID:26527844
Preconditioned conjugate gradient algorithms and software for solving large sparse linear systems
Young, D.M.; Jea, K.C.; Mai, Tsun-Zee
1987-03-01
The classical form of the conjugate gradient method (CG method), developed by Hestenes and Stiefel, for solving the linear system Au = b is applicable when the coefficient matrix A is symmetric and positive definite (SPD). In this paper we consider various alternative forms of the CG method as well as generalizations to cases where A is not necessarily SPD. This analysis includes the ''preconditioned conjugate gradient method'' which is equivalent to conjugate gradient acceleration of a basic iterative method corresponding to a preconditioned system. Both the symmetrizable case and the nonsymmetrizable case are considered. For the nonsymmetrizable case there are very few useful theoretical results available. A package of programs, known as ITPACK, has been developed as a tool for carrying out experimental studies on various algorithms. Preliminary conclusions based on experimental results are given. 42 refs.
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
NASA Astrophysics Data System (ADS)
Singh, Vimal; Tewfik, Ahmed H.
2011-03-01
Cardiac minimal invasive surgeries such as catheter based radio frequency ablation of atrial fibrillation requires high-precision tracking of inner cardiac surfaces in order to ascertain constant electrode-surface contact. Majority of cardiac motion tracking systems are either limited to outer surface or track limited slices/sectors of inner surface in echocardiography data which are unrealizable in MIS due to the varying resolution of ultrasound with depth and speckle effect. In this paper, a system for high accuracy real-time 3D tracking of both cardiac surfaces using sparse samples of outer-surface only is presented. This paper presents a novel approach to model cardiac inner surface deformations as simple functions of outer surface deformations in the spherical harmonic domain using multiple maximal-likelihood linear regressors. Tracking system uses subspace clustering to identify potential deformation spaces for outer surfaces and trains ML linear regressors using pre-operative MRI/CT scan based training set. During tracking, sparse-samples from outer surfaces are used to identify the active outer surface deformation space and reconstruct outer surfaces in real-time under least squares formulation. Inner surface is reconstructed using tracked outer surface with trained ML linear regressors. High-precision tracking and robustness of the proposed system are demonstrated through results obtained on a real patient dataset with tracking root mean square error <= (0.23 +/- 0.04)mm and <= (0.30 +/- 0.07)mm for outer & inner surfaces respectively.
Sparse-view X-ray CT Reconstruction via Total Generalized Variation Regularization
Niu, Shanzhou; Gao, Yang; Bian, Zhaoying; Huang, Jing; Chen, Wufan; Yu, Gaohang; Liang, Zhengrong; Ma, Jianhua
2014-01-01
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. PMID:24842150
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.
Sparse-view x-ray CT reconstruction via total generalized variation regularization.
Niu, Shanzhou; Gao, Yang; Bian, Zhaoying; Huang, Jing; Chen, Wufan; Yu, Gaohang; Liang, Zhengrong; Ma, Jianhua
2014-06-21
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. PMID:24842150
On the order of general linear methods.
Constantinescu, E. M.; Mathematics and Computer Science
2009-09-01
General linear (GL) methods are numerical algorithms used to solve ODEs. The standard order conditions analysis involves the GL matrix itself and a starting procedure; however, a finishing method (F) is required to extract the actual ODE solution. The standard order analysis and stability are sufficient for the convergence of any GL method. Nonetheless, using a simple GL scheme, we show that the order definition may be too restrictive. Specifically, the order for GL methods with low order intermediate components may be underestimated. In this note we explore the order conditions for GL schemes and propose a new definition for characterizing the order of GL methods, which is focused on the final result--the outcome of F--and can provide more effective algebraic order conditions.
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.
Approximate Orthogonal Sparse Embedding for Dimensionality Reduction.
Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Yang, Jian; Zhang, David
2016-04-01
Locally linear embedding (LLE) is one of the most well-known manifold learning methods. As the representative linear extension of LLE, orthogonal neighborhood preserving projection (ONPP) has attracted widespread attention in the field of dimensionality reduction. In this paper, a unified sparse learning framework is proposed by introducing the sparsity or L1-norm learning, which further extends the LLE-based methods to sparse cases. Theoretical connections between the ONPP and the proposed sparse linear embedding are discovered. The optimal sparse embeddings derived from the proposed framework can be computed by iterating the modified elastic net and singular value decomposition. We also show that the proposed model can be viewed as a general model for sparse linear and nonlinear (kernel) subspace learning. Based on this general model, sparse kernel embedding is also proposed for nonlinear sparse feature extraction. Extensive experiments on five databases demonstrate that the proposed sparse learning framework performs better than the existing subspace learning algorithm, particularly in the cases of small sample sizes. PMID:25955995
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.
Chae, S.H.
1988-01-01
This dissertation describes an intelligent rule-based iterative parallel algorithm for solving randomly distributed large sparse linear systems of equations, and also the efficient parallel processing computer architecture for the implementation of the algorithm. Implemented with the Jacobi iterative method, the intelligent rule-based algorithm reduces the parallel execution time by reducing the individual inner product operation time. A static dataflow architecture is proposed for implementing the intelligent rule-based iterative parallel algorithm. The dataflow computer architecture has the capability to support parallelism exploited in the algorithm, and the execute the algorithm asynchronously. The proposed computer architecture consists of a main processor, several control processors, scalar slave processors, and pipelined slave processors. Several control processors share with the main processor the heavy burden of allocation of operation packets and of sychronization for parallel processing.
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
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
NASA Astrophysics Data System (ADS)
Ma, Sangback
In this paper we compare various parallel preconditioners such as Point-SSOR (Symmetric Successive OverRelaxation), ILU(0) (Incomplete LU) in the Wavefront ordering, ILU(0) in the Multi-color ordering, Multi-Color Block SOR (Successive OverRelaxation), SPAI (SParse Approximate Inverse) and pARMS (Parallel Algebraic Recursive Multilevel Solver) for solving large sparse linear systems arising from two-dimensional PDE (Partial Differential Equation)s on structured grids. Point-SSOR is well-known, and ILU(0) is one of the most popular preconditioner, but it is inherently serial. ILU(0) in the Wavefront ordering maximizes the parallelism in the natural order, but the lengths of the wave-fronts are often nonuniform. ILU(0) in the Multi-color ordering is a simple way of achieving a parallelism of the order N, where N is the order of the matrix, but its convergence rate often deteriorates as compared to that of natural ordering. We have chosen the Multi-Color Block SOR preconditioner combined with direct sparse matrix solver, since for the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with the Multi-Color ordering. By using block version we expect to minimize the interprocessor communications. SPAI computes the sparse approximate inverse directly by least squares method. Finally, ARMS is a preconditioner recursively exploiting the concept of independent sets and pARMS is the parallel version of ARMS. Experiments were conducted for the Finite Difference and Finite Element discretizations of five two-dimensional PDEs with large meshsizes up to a million on an IBM p595 machine with distributed memory. Our matrices are real positive, i. e., their real parts of the eigenvalues are positive. We have used GMRES(m) as our outer iterative method, so that the convergence of GMRES(m) for our test matrices are mathematically guaranteed. Interprocessor communications were done using MPI (Message Passing Interface) primitives. The
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.
Complexity transitions in global algorithms for sparse linear systems over finite fields
NASA Astrophysics Data System (ADS)
Braunstein, A.; Leone, M.; Ricci-Tersenghi, F.; Zecchina, R.
2002-09-01
We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois field modulo q. Using tools from statistical mechanics we are able to identify phase transitions in the structure of the solution space and to connect them to the changes in the performance of a global algorithm, namely Gaussian elimination. Crossing phase boundaries produces a dramatic increase in memory and CPU requirements necessary for the algorithms. In turn, this causes the saturation of the upper bounds for the running time. We illustrate the results on the specific problem of integer factorization, which is of central interest for deciphering messages encrypted with the RSA cryptosystem.
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.
On generalized hamming weighs for Galois ring linear codes
Ashikhmin, A.
1997-08-01
The definition of generalized Hamming weights (GHW) for linear codes over Galois rings is discussed. The properties of GHW for Galois ring linear codes are stated. Upper and existence bounds for GHW of Z{sub 4}-linear codes and a lower bound for GHW of the Kerdock code over Z{sub 4} are derived. GHW of some Z{sub 4}-linear codes are determined.
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. PMID:20866130
Generalized Multicarrier CDMA: Unification and Linear Equalization
NASA Astrophysics Data System (ADS)
Giannakis, Georgios B.; Anghel, Paul A.; Wang, Zhengdao
2005-12-01
Relying on block-symbol spreading and judicious design of user codes, this paper builds on the generalized multicarrier (GMC) quasisynchronous CDMA system that is capable of multiuser interference (MUI) elimination and intersymbol interference (ISI) suppression with guaranteed symbol recovery, regardless of the wireless frequency-selective channels. GMC-CDMA affords an all-digital unifying framework, which encompasses single-carrier and several multicarrier (MC) CDMA systems. Besides the unifying framework, it is shown that GMC-CDMA offers flexibility both in full load (maximum number of users allowed by the available bandwidth) and in reduced load settings. A novel blind channel estimation algorithm is also derived. Analytical evaluation and simulations illustrate the superior error performance and flexibility of uncoded GMC-CDMA over competing MC-CDMA alternatives especially in the presence of uplink multipath channels.
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…
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.
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)
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.
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.
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…
A General Linear Model Approach to Adjusting the Cumulative GPA.
ERIC Educational Resources Information Center
Young, John W.
A general linear model (GLM), using least-squares techniques, was used to develop a criterion measure to replace freshman year grade point average (GPA) in college admission predictive validity studies. Problems with the use of GPA include those associated with the combination of grades from different courses and disciplines into a single measure,…
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.
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
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
Capsule deformation and orientation in general linear flows
NASA Astrophysics Data System (ADS)
Szatmary, Alex; Eggleton, Charles
2010-11-01
We considered the response of spherical and non-spherical capsules to general flows. (A capsule is an elastic membrane enclosing a fluid, immersed in fluid.) First, we established that nonspherical capsules align with the imposed irrotational linear flow; this means that initial orientation does not affect steady-state capsule deformation, so this steady-state deformation can be determined entirely by the capillary number and the type of flow. The type of flow is characterized by r: r=0 for axisymmetric flows, and r=1 for planar flows; intermediate values of r are combinations of planar and axisymmetric flow. By varying the capillary number and r, all irrotational linear Stokes flows can be generated. For the same capillary number, planar flows lead to more deformation than uniaxial or biaxial extensional flows. Deformation varies monotonically with r, so one can determine bounds on capsule deformation in general flow by only looking at uniaxial, biaxial, and planar flow. These results are applicable to spheres in all linear flows and to ellipsoids in irrotational linear flow.
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.
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.
Clutter locus equation for more general linear array orientation
NASA Astrophysics Data System (ADS)
Bickel, Douglas L.
2011-06-01
The clutter locus is an important concept in space-time adaptive processing (STAP) for ground moving target indicator (GMTI) radar systems. The clutter locus defines the expected ground clutter location in the angle-Doppler domain. Typically in literature, the clutter locus is presented as a line, or even a set of ellipsoids, under certain assumptions about the geometry of the array. Most often, the array is assumed to be in the horizontal plane containing the velocity vector. This paper will give a more general 3-dimensional interpretation of the clutter locus for a general linear array orientation.
Genetic parameters for racing records in trotters using linear and generalized linear models.
Suontama, M; van der Werf, J H J; Juga, J; Ojala, M
2012-09-01
Heritability and repeatability and genetic and phenotypic correlations were estimated for trotting race records with linear and generalized linear models using 510,519 records on 17,792 Finnhorses and 513,161 records on 25,536 Standardbred trotters. Heritability and repeatability were estimated for single racing time and earnings traits with linear models, and logarithmic scale was used for racing time and fourth-root scale for earnings to correct for nonnormality. Generalized linear models with a gamma distribution were applied for single racing time and with a multinomial distribution for single earnings traits. In addition, genetic parameters for annual earnings were estimated with linear models on the observed and fourth-root scales. Racing success traits of single placings, winnings, breaking stride, and disqualifications were analyzed using generalized linear models with a binomial distribution. Estimates of heritability were greatest for racing time, which ranged from 0.32 to 0.34. Estimates of heritability were low for single earnings with all distributions, ranging from 0.01 to 0.09. Annual earnings were closer to normal distribution than single earnings. Heritability estimates were moderate for annual earnings on the fourth-root scale, 0.19 for Finnhorses and 0.27 for Standardbred trotters. Heritability estimates for binomial racing success variables ranged from 0.04 to 0.12, being greatest for winnings and least for breaking stride. Genetic correlations among racing traits were high, whereas phenotypic correlations were mainly low to moderate, except correlations between racing time and earnings were high. On the basis of a moderate heritability and moderate to high repeatability for racing time and annual earnings, selection of horses for these traits is effective when based on a few repeated records. Because of high genetic correlations, direct selection for racing time and annual earnings would also result in good genetic response in racing success
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.
A general linear model for MEG beamformer imaging.
Brookes, Matthew J; Gibson, Andrew M; Hall, Stephen D; Furlong, Paul L; Barnes, Gareth R; Hillebrand, Arjan; Singh, Krish D; Holliday, Ian E; Francis, Sue T; Morris, Peter G
2004-11-01
A new general linear model (GLM) beamformer method is described for processing magnetoencephalography (MEG) data. A standard nonlinear beamformer is used to determine the time course of neuronal activation for each point in a predefined source space. A Hilbert transform gives the envelope of oscillatory activity at each location in any chosen frequency band (not necessary in the case of sustained (DC) fields), enabling the general linear model to be applied and a volumetric T statistic image to be determined. The new method is illustrated by a two-source simulation (sustained field and 20 Hz) and is shown to provide accurate localization. The method is also shown to locate accurately the increasing and decreasing gamma activities to the temporal and frontal lobes, respectively, in the case of a scintillating scotoma. The new method brings the advantages of the general linear model to the analysis of MEG data and should prove useful for the localization of changing patterns of activity across all frequency ranges including DC (sustained fields). PMID:15528094
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.
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.
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.
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.
Marginally specified generalized linear mixed models: a robust approach.
Mills, J E; Field, C A; Dupuis, D J
2002-12-01
Longitudinal data modeling is complicated by the necessity to deal appropriately with the correlation between observations made on the same individual. Building on an earlier nonrobust version proposed by Heagerty (1999, Biometrics 55, 688-698), our robust marginally specified generalized linear mixed model (ROBMS-GLMM) provides an effective method for dealing with such data. This model is one of the first to allow both population-averaged and individual-specific inference. As well, it adopts the flexibility and interpretability of generalized linear mixed models for introducing dependence but builds a regression structure for the marginal mean, allowing valid application with time-dependent (exogenous) and time-independent covariates. These new estimators are obtained as solutions of a robustified likelihood equation involving Huber's least favorable distribution and a collection of weights. Huber's least favorable distribution produces estimates that are resistant to certain deviations from the random effects distributional assumptions. Innovative weighting strategies enable the ROBMS-GLMM to perform well when faced with outlying observations both in the response and covariates. We illustrate the methodology with an analysis of a prospective longitudinal study of laryngoscopic endotracheal intubation, a skill that numerous health-care professionals are expected to acquire. The principal goal of our research is to achieve robust inference in longitudinal analyses. PMID:12495126
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
Energy Science and Technology Software Center (ESTSC)
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
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.
The left invariant metric in the general linear group
NASA Astrophysics Data System (ADS)
Andruchow, E.; Larotonda, G.; Recht, L.; Varela, A.
2014-12-01
Left invariant metrics induced by the p-norms of the trace in the matrix algebra are studied on the general linear group. By means of the Euler-Lagrange equations, existence and uniqueness of extremal paths for the length functional are established, and regularity properties of these extremal paths are obtained. Minimizing paths in the group are shown to have a velocity with constant singular values and multiplicity. In several special cases, these geodesic paths are computed explicitly. In particular the Riemannian geodesics, corresponding to the case p = 2, are characterized as the product of two one-parameter groups. It is also shown that geodesics are one-parameter groups if and only if the initial velocity is a normal matrix. These results are further extended to the context of compact operators with p-summable spectrum, where a differential equation for the spectral projections of the velocity vector of an extremal path is obtained.
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.
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
General Linear Rf-Current Drive Calculation in Toroidal Plasma
NASA Astrophysics Data System (ADS)
Smirnov, A. P.; Harvey, R. W.; Prater, R.
2009-04-01
A new general linear calculation of RF current drive has been implemented in the GENRAY all-frequencies RF ray tracing code. This is referred to as the ADJ-QL package, and is based on the Karney, et al. [1] relativistic Green function calculator, ADJ, generalized to non-circular plasmas in toroidal geometry, and coupled with full, bounce-averaged momentum-space RF quasilinear flux [2] expressions calculated at each point along the RF ray trajectories. This approach includes momentum conservation, polarization effects and the influence of trapped electrons. It is assumed that the electron distribution function remains close to a relativistic Maxwellian function. Within the bounds of these assumptions, small banana width, toroidal geometry and low collisionality, the calculation is applicable for all-frequencies RF electron current drive including electron cyclotron, lower hybrid, fast waves and electron Bernstein waves. GENRAY ADJ-QL calculations of the relativistic momentum-conserving current drive have been applied in several cases: benchmarking of electron cyclotron current drive in ITER against other code results; and electron Bernstein and high harmonic fast wave current drive in NSTX. The impacts of momentum conservation on the current drive are also shown for these cases.
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
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.
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
Sparse representation with kernels.
Gao, Shenghua; Tsang, Ivor Wai-Hung; Chia, Liang-Tien
2013-02-01
Recent research has shown the initial success of sparse coding (Sc) in solving many computer vision tasks. Motivated by the fact that kernel trick can capture the nonlinear similarity of features, which helps in finding a sparse representation of nonlinear features, we propose kernel sparse representation (KSR). Essentially, KSR is a sparse coding technique in a high dimensional feature space mapped by an implicit mapping function. We apply KSR to feature coding in image classification, face recognition, and kernel matrix approximation. More specifically, by incorporating KSR into spatial pyramid matching (SPM), we develop KSRSPM, which achieves a good performance for image classification. Moreover, KSR-based feature coding can be shown as a generalization of efficient match kernel and an extension of Sc-based SPM. We further show that our proposed KSR using a histogram intersection kernel (HIK) can be considered a soft assignment extension of HIK-based feature quantization in the feature coding process. Besides feature coding, comparing with sparse coding, KSR can learn more discriminative sparse codes and achieve higher accuracy for face recognition. Moreover, KSR can also be applied to kernel matrix approximation in large scale learning tasks, and it demonstrates its robustness to kernel matrix approximation, especially when a small fraction of the data is used. Extensive experimental results demonstrate promising results of KSR in image classification, face recognition, and kernel matrix approximation. All these applications prove the effectiveness of KSR in computer vision and machine learning tasks. PMID:23014744
Linear and generalized linear models for the detection of QTL effects on within-subject variability
Wittenburg, Dörte; Guiard, Volker; Liese, Friedrich; Reinsch, Norbert
2007-01-01
Summary Quantitative trait loci (QTLs) may affect not only the mean of a trait but also its variability. A special aspect is the variability between multiple measured traits of genotyped animals, such as the within-litter variance of piglet birth weights. The sample variance of repeated measurements is assigned as an observation for every genotyped individual. It is shown that the conditional distribution of the non-normally distributed trait can be approximated by a gamma distribution. To detect QTL effects in the daughter design, a generalized linear model with the identity link function is applied. Suitable test statistics are constructed to test the null hypothesis H0: No QTL with effect on the within-litter variance is segregating versus HA: There is a QTL with effect on the variability of birth weight within litter. Furthermore, estimates of the QTL effect and the QTL position are introduced and discussed. The efficiency of the presented tests is compared with a test based on weighted regression. The error probability of the first type as well as the power of QTL detection are discussed and compared for the different tests. PMID:18208630
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.
An assessment of estimation methods for generalized linear mixed models with binary outcomes
Capanu, Marinela; Gönen, Mithat; Begg, Colin B.
2013-01-01
Two main classes of methodology have been developed for addressing the analytical intractability of generalized linear mixed models (GLMMs): likelihood-based methods and Bayesian methods. Likelihood-based methods such as the penalized quasi-likelihood approach have been shown to produce biased estimates especially for binary clustered data with small clusters sizes. More recent methods using adaptive Gaussian quadrature perform well but can be overwhelmed by problems with large numbers of random effects, and efficient algorithms to better handle these situations have not yet been integrated in standard statistical packages. Bayesian methods, though they have good frequentist properties when the model is correct, are known to be computationally intensive and also require specialized code, limiting their use in practice. In this article we introduce a modification of the hybrid approach of Capanu and Begg [1] as a bridge between the likelihood-based and Bayesian approaches by employing Bayesian estimation for the variance components followed by Laplacian estimation for the regression coefficients. We investigate its performance as well as that of several likelihood-based methods in the setting of GLMMs with binary outcomes. We apply the methods to three datasets and conduct simulations to illustrate their properties. Simulation results indicate that for moderate to large numbers of observations per random effect, adaptive Gaussian quadrature and the Laplacian approximation are very accurate, with adaptive Gaussian quadrature preferable as the number of observations per random effect increases. The hybrid approach is overall similar to the Laplace method, and it can be superior for data with very sparse random effects. PMID:23839712
Connections between Generalizing and Justifying: Students' Reasoning with Linear Relationships
ERIC Educational Resources Information Center
Ellis, Amy B.
2007-01-01
Research investigating algebra students' abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students' errors, less is known about what students do understand to be general and convincing. This study examines the ways in which…
NASA Astrophysics Data System (ADS)
Pavošević, Fabijan; Pinski, Peter; Riplinger, Christoph; Neese, Frank; Valeev, Edward F.
2016-04-01
We present a formulation of the explicitly correlated second-order Møller-Plesset (MP2-F12) energy in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the domain based local pair-natural orbital-MP2 (DLPNO-MP2) method by us recently [Pinski et al., J. Chem. Phys. 143, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes), the O (" separators="N ) DLPNO-MP2-F12 method becomes less expensive than the conventional O (" separators="N5 ) MP2-F12 for n between 10 and 15, for double- and triple-zeta basis sets; for the largest alkane, C200H402, in def2-TZVP basis, the observed computational complexity is N˜1.6, largely due to the cubic cost of computing the mean-field operators. The method reproduces the canonical MP2-F12 energy with high precision: 99.9% of the canonical correlation energy is recovered with the default truncation parameters. Although its cost is significantly higher than that of DLPNO-MP2 method, the cost increase is compensated by the great reduction of the basis set error due to explicit correlation.
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…
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…
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.
Guisan, A.; Edwards, T.C., Jr.; 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.
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.
Amestoy, Patrick R.; Duff, Iain S.; L'Excellent, Jean-Yves; Li, Xiaoye S.
2001-10-10
We examine the mechanics of the send and receive mechanism of MPI and in particular how we can implement message passing in a robust way so that our performance is not significantly affected by changes to the MPI system. This leads us to using the Isend/Irecv protocol which will entail sometimes significant algorithmic changes. We discuss this within the context of two different algorithms for sparse Gaussian elimination that we have parallelized. One is a multifrontal solver called MUMPS, the other is a supernodal solver called SuperLU. Both algorithms are difficult to parallelize on distributed memory machines. Our initial strategies were based on simple MPI point-to-point communication primitives. With such approaches, the parallel performance of both codes are very sensitive to the MPI implementation, the way MPI internal buffers are used in particular. We then modified our codes to use more sophisticated nonblocking versions of MPI communication. This significantly improved the performance robustness (independent of the MPI buffering mechanism) and scalability, but at the cost of increased code complexity.
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
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 Technical Reports Server (NTRS)
Stevens, P. K.
1981-01-01
This paper presents a generalization of the Nyquist stability criterion to include general multivariable linear stationary systems subject to linear static and dynamic feedback. At the same time, a unifying proof is given for all known versions of the Nyquist criterion for finite dimensional systems.
A note on rank reduction in sparse multivariate regression
Chen, Kun; Chan, Kung-Sik
2016-01-01
A reduced-rank regression with sparse singular value decomposition (RSSVD) approach was proposed by Chen et al. for conducting variable selection in a reduced-rank model. To jointly model the multivariate response, the method efficiently constructs a prespecified number of latent variables as some sparse linear combinations of the predictors. Here, we generalize the method to also perform rank reduction, and enable its usage in reduced-rank vector autoregressive (VAR) modeling to perform automatic rank determination and order selection. We show that in the context of stationary time-series data, the generalized approach correctly identifies both the model rank and the sparse dependence structure between the multivariate response and the predictors, with probability one asymptotically. We demonstrate the efficacy of the proposed method by simulations and analyzing a macro-economical multivariate time series using a reduced-rank VAR model. PMID:26997938
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.
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
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
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.
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
Voxel selection in FMRI data analysis based on sparse representation.
Li, Yuanqing; Namburi, Praneeth; Yu, Zhuliang; Guan, Cuntai; Feng, Jianfeng; Gu, Zhenghui
2009-10-01
Multivariate pattern analysis approaches toward detection of brain regions from fMRI data have been gaining attention recently. In this study, we introduce an iterative sparse-representation-based algorithm for detection of voxels in functional MRI (fMRI) data with task relevant information. In each iteration of the algorithm, a linear programming problem is solved and a sparse weight vector is subsequently obtained. The final weight vector is the mean of those obtained in all iterations. The characteristics of our algorithm are as follows: 1) the weight vector (output) is sparse; 2) the magnitude of each entry of the weight vector represents the significance of its corresponding variable or feature in a classification or regression problem; and 3) due to the convergence of this algorithm, a stable weight vector is obtained. To demonstrate the validity of our algorithm and illustrate its application, we apply the algorithm to the Pittsburgh Brain Activity Interpretation Competition 2007 functional fMRI dataset for selecting the voxels, which are the most relevant to the tasks of the subjects. Based on this dataset, the aforementioned characteristics of our algorithm are analyzed, and a comparison between our method with the univariate general-linear-model-based statistical parametric mapping is performed. Using our method, a combination of voxels are selected based on the principle of effective/sparse representation of a task. Data analysis results in this paper show that this combination of voxels is suitable for decoding tasks and demonstrate the effectiveness of our method. PMID:19567340
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.
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…
ERIC Educational Resources Information Center
Henson, Robin K.
In General Linear Model (GLM) analyses, it is important to interpret structure coefficients, along with standardized weights, when evaluating variable contribution to observed effects. Although often used in canonical correlation analysis, structure coefficients are less frequently used in multiple regression and several other multivariate…
Learning Sparse Representations of Depth
NASA Astrophysics Data System (ADS)
Tosic, Ivana; Olshausen, Bruno A.; Culpepper, Benjamin J.
2011-09-01
This paper introduces a new method for learning and inferring sparse representations of depth (disparity) maps. The proposed algorithm relaxes the usual assumption of the stationary noise model in sparse coding. This enables learning from data corrupted with spatially varying noise or uncertainty, typically obtained by laser range scanners or structured light depth cameras. Sparse representations are learned from the Middlebury database disparity maps and then exploited in a two-layer graphical model for inferring depth from stereo, by including a sparsity prior on the learned features. Since they capture higher-order dependencies in the depth structure, these priors can complement smoothness priors commonly used in depth inference based on Markov Random Field (MRF) models. Inference on the proposed graph is achieved using an alternating iterative optimization technique, where the first layer is solved using an existing MRF-based stereo matching algorithm, then held fixed as the second layer is solved using the proposed non-stationary sparse coding algorithm. This leads to a general method for improving solutions of state of the art MRF-based depth estimation algorithms. Our experimental results first show that depth inference using learned representations leads to state of the art denoising of depth maps obtained from laser range scanners and a time of flight camera. Furthermore, we show that adding sparse priors improves the results of two depth estimation methods: the classical graph cut algorithm by Boykov et al. and the more recent algorithm of Woodford et al.
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.
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.
Zhou, Shaohua Kevin; Aggarwal, Gaurav; Chellappa, Rama; Jacobs, David W
2007-02-01
Traditional photometric stereo algorithms employ a Lambertian reflectance model with a varying albedo field and involve the appearance of only one object. In this paper, we generalize photometric stereo algorithms to handle all appearances of all objects in a class, in particular the human face class, by making use of the linear Lambertian property. A linear Lambertian object is one which is linearly spanned by a set of basis objects and has a Lambertian surface. The linear property leads to a rank constraint and, consequently, a factorization of an observation matrix that consists of exemplar images of different objects (e.g., faces of different subjects) under different, unknown illuminations. Integrability and symmetry constraints are used to fully recover the subspace bases using a novel linearized algorithm that takes the varying albedo field into account. The effectiveness of the linear Lambertian property is further investigated by using it for the problem of illumination-invariant face recognition using just one image. Attached shadows are incorporated in the model by a careful treatment of the inherent nonlinearity in Lambert's law. This enables us to extend our algorithm to perform face recognition in the presence of multiple illumination sources. Experimental results using standard data sets are presented. PMID:17170477
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
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.
Non-linear regime of the Generalized Minimal Massive Gravity in critical points
NASA Astrophysics Data System (ADS)
Setare, M. R.; Adami, H.
2016-03-01
The Generalized Minimal Massive Gravity (GMMG) theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. In the present paper we obtain exact solutions to the GMMG field equations in the non-linear regime of the model. GMMG model about AdS_3 space is conjectured to be dual to a 2-dimensional CFT. We study the theory in critical points corresponding to the central charges c_-=0 or c_+=0, in the non-linear regime. We show that AdS_3 wave solutions are present, and have logarithmic form in critical points. Then we study the AdS_3 non-linear deformation solution. Furthermore we obtain logarithmic deformation of extremal BTZ black hole. After that using Abbott-Deser-Tekin method we calculate the energy and angular momentum of these types of black hole solutions.
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.
Linear and nonlinear associations between general intelligence and personality in Project TALENT.
Major, Jason T; Johnson, Wendy; Deary, Ian J
2014-04-01
Research on the relations of personality traits to intelligence has primarily been concerned with linear associations. Yet, there are no a priori reasons why linear relations should be expected over nonlinear ones, which represent a much larger set of all possible associations. Using 2 techniques, quadratic and generalized additive models, we tested for linear and nonlinear associations of general intelligence (g) with 10 personality scales from Project TALENT (PT), a nationally representative sample of approximately 400,000 American high school students from 1960, divided into 4 grade samples (Flanagan et al., 1962). We departed from previous studies, including one with PT (Reeve, Meyer, & Bonaccio, 2006), by modeling latent quadratic effects directly, controlling the influence of the common factor in the personality scales, and assuming a direction of effect from g to personality. On the basis of the literature, we made 17 directional hypotheses for the linear and quadratic associations. Of these, 53% were supported in all 4 male grades and 58% in all 4 female grades. Quadratic associations explained substantive variance above and beyond linear effects (mean R² between 1.8% and 3.6%) for Sociability, Maturity, Vigor, and Leadership in males and Sociability, Maturity, and Tidiness in females; linear associations were predominant for other traits. We discuss how suited current theories of the personality-intelligence interface are to explain these associations, and how research on intellectually gifted samples may provide a unique way of understanding them. We conclude that nonlinear models can provide incremental detail regarding personality and intelligence associations. PMID:24660993
Block sparse Cholesky algorithms on advanced uniprocessor computers
Ng, E.G.; Peyton, B.W.
1991-12-01
As with many other linear algebra algorithms, devising a portable implementation of sparse Cholesky factorization that performs well on the broad range of computer architectures currently available is a formidable challenge. Even after limiting our attention to machines with only one processor, as we have done in this report, there are still several interesting issues to consider. For dense matrices, it is well known that block factorization algorithms are the best means of achieving this goal. We take this approach for sparse factorization as well. This paper has two primary goals. First, we examine two sparse Cholesky factorization algorithms, the multifrontal method and a blocked left-looking sparse Cholesky method, in a systematic and consistent fashion, both to illustrate the strengths of the blocking techniques in general and to obtain a fair evaluation of the two approaches. Second, we assess the impact of various implementation techniques on time and storage efficiency, paying particularly close attention to the work-storage requirement of the two methods and their variants.
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
Semiparametric Analysis of Heterogeneous Data Using Varying-Scale Generalized Linear Models
Xie, Minge; Simpson, Douglas G.; Carroll, Raymond J.
2009-01-01
This article describes a class of heteroscedastic generalized linear regression models in which a subset of the regression parameters are rescaled nonparametrically, and develops efficient semiparametric inferences for the parametric components of the models. Such models provide a means to adapt for heterogeneity in the data due to varying exposures, varying levels of aggregation, and so on. The class of models considered includes generalized partially linear models and nonparametrically scaled link function models as special cases. We present an algorithm to estimate the scale function nonparametrically, and obtain asymptotic distribution theory for regression parameter estimates. In particular, we establish that the asymptotic covariance of the semiparametric estimator for the parametric part of the model achieves the semiparametric lower bound. We also describe bootstrap-based goodness-of-scale test. We illustrate the methodology with simulations, published data, and data from collaborative research on ultrasound safety. PMID:19444331
Linear relations in microbial reaction systems: a general overview of their origin, form, and use.
Noorman, H J; Heijnen, J J; Ch A M Luyben, K
1991-09-01
In microbial reaction systems, there are a number of linear relations among net conversion rates. These can be very useful in the analysis of experimental data. This article provides a general approach for the formation and application of the linear relations. Two type of system descriptions, one considering the biomass as a black box and the other based on metabolic pathways, are encountered. These are defined in a linear vector and matrix algebra framework. A correct a priori description can be obtained by three useful tests: the independency, consistency, and observability tests. The independency are different. The black box approach provides only conservations relations. They are derived from element, electrical charge, energy, and Gibbs energy balances. The metabolic approach provides, in addition to the conservation relations, metabolic and reaction relations. These result from component, energy, and Gibbs energy balances. Thus it is more attractive to use the metabolic description than the black box approach. A number of different types of linear relations given in the literature are reviewed. They are classified according to the different categories that result from the black box or the metabolic system description. Validation of hypotheses related to metabolic pathways can be supported by experimental validation of the linear metabolic relations. However, definite proof from biochemical evidence remains indispensable. PMID:18604879
Application of the Hyper-Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes.
Khazraee, S Hadi; Sáez-Castillo, Antonio Jose; Geedipally, Srinivas Reddy; Lord, Dominique
2015-05-01
The hyper-Poisson distribution can handle both over- and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation-specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper-Poisson distribution in analyzing motor vehicle crash count data. The hyper-Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway-highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness-of-fit measures indicated that the hyper-Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper-Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway-Maxwell-Poisson model previously developed for the same data set. The advantages of the hyper-Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper-Poisson model can handle both over- and underdispersed crash data. Although not a major issue for the Conway-Maxwell-Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model. PMID:25385093
Unified Einstein-Virasoro Master Equation in the General Non-Linear Sigma Model
Boer, J. de; Halpern, M.B.
1996-06-05
The Virasoro master equation (VME) describes the general affine-Virasoro construction $T=L^abJ_aJ_b+iD^a \\dif J_a$ in the operator algebra of the WZW model, where $L^ab$ is the inverse inertia tensor and $D^a $ is the improvement vector. In this paper, we generalize this construction to find the general (one-loop) Virasoro construction in the operator algebra of the general non-linear sigma model. The result is a unified Einstein-Virasoro master equation which couples the spacetime spin-two field $L^ab$ to the background fields of the sigma model. For a particular solution $L_G^ab$, the unified system reduces to the canonical stress tensors and conventional Einstein equations of the sigma model, and the system reduces to the general affine-Virasoro construction and the VME when the sigma model is taken to be the WZW action. More generally, the unified system describes a space of conformal field theories which is presumably much larger than the sum of the general affine-Virasoro construction and the sigma model with its canonical stress tensors. We also discuss a number of algebraic and geometrical properties of the system, including its relation to an unsolved problem in the theory of $G$-structures on manifolds with torsion.
Numerical study of fourth-order linearized compact schemes for generalized NLS equations
NASA Astrophysics Data System (ADS)
Liao, Hong-lin; Shi, Han-sheng; Zhao, Ying
2014-08-01
The fourth-order compact approximation for the spatial second-derivative and several linearized approaches, including the time-lagging method of Zhang et al. (1995), the local-extrapolation technique of Chang et al. (1999) and the recent scheme of Dahlby et al. (2009), are considered in constructing fourth-order linearized compact difference (FLCD) schemes for generalized NLS equations. By applying a new time-lagging linearized approach, we propose a symmetric fourth-order linearized compact difference (SFLCD) scheme, which is shown to be more robust in long-time simulations of plane wave, breather, periodic traveling-wave and solitary wave solutions. Numerical experiments suggest that the SFLCD scheme is a little more accurate than some other FLCD schemes and the split-step compact difference scheme of Dehghan and Taleei (2010). Compared with the time-splitting pseudospectral method of Bao et al. (2003), our SFLCD method is more suitable for oscillating solutions or the problems with a rapidly varying potential.
Normality of raw data in general linear models: The most widespread myth in statistics
Kery, M.; Hatfield, J.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.
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.
Sparse matrix techniques applied to modal analysis of multi-section duct liners
NASA Technical Reports Server (NTRS)
Arnold, W. R.
1975-01-01
A simplified procedure is presented for analysis of ducts with discretely nonuniform properties. The analysis uses basis functions as the generalized coordinates. The duct eigenfunctions are approximated by finite series of these functions. The emphasis is on solution of the resulting large sparse set of linear equations. Characteristics of sparse matrix algorithms are outlined and some criteria for application are established. Analogies with structural methods are used to illustrate variations which can increase efficiency in generating values for design optimization routines. The effects of basis function selection, number of eigenfunctions and identification and ordering of equations on the sparsity and solution stability are included.
Generalized stochastic resonance in a linear fractional system with a random delay
NASA Astrophysics Data System (ADS)
Gao, Shi-Long
2012-12-01
The generalized stochastic resonance (GSR) phenomena in a linear fractional random-delayed system driven by a weak periodic signal and an additive noise are considered in this paper. A random delay is considered for a linear fractional Langevin equation to describe the intercellular signal transmission and material exchange processes in ion channels. By virtue of the small delay approximation and Laplace transformation, the analytical expression for the amplitude of the first-order steady state moment is obtained. The simulation results show that the amplitude curves as functions of different system parameters behave non-monotonically and exhibit typical characteristics of GSR phenomena. Furthermore, a physical explanation for all the GSR phenomena is given and the cooperative effects of random delay and the fractional memory are also discussed.
The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation
NASA Astrophysics Data System (ADS)
Sifalakis, A. G.; Fokas, A. S.; Fulton, S. R.; Saridakis, Y. G.
2008-09-01
A new approach for analyzing boundary value problems for linear and for integrable nonlinear PDEs was introduced in Fokas [A unified transform method for solving linear and certain nonlinear PDEs, Proc. Roy. Soc. London Ser. A 53 (1997) 1411-1443]. For linear elliptic PDEs, an important aspect of this approach is the characterization of a generalized Dirichlet to Neumann map: given the derivative of the solution along a direction of an arbitrary angle to the boundary, the derivative of the solution perpendicularly to this direction is computed without solving on the interior of the domain. This is based on the analysis of the so-called global relation, an equation which couples known and unknown components of the derivative on the boundary and which is valid for all values of a complex parameter k. A collocation-type numerical method for solving the global relation for the Laplace equation in an arbitrary bounded convex polygon was introduced in Fulton et al. [An analytical method for linear elliptic PDEs and its numerical implementation, J. Comput. Appl. Math. 167 (2004) 465-483]. Here, by choosing a different set of the "collocation points" (values for k), we present a significant improvement of the results in Fulton et al. [An analytical method for linear elliptic PDEs and its numerical implementation, J. Comput. Appl. Math. 167 (2004) 465-483]. The new collocation points lead to well-conditioned collocation methods. Their combination with sine basis functions leads to a collocation matrix whose diagonal blocks are point diagonal matrices yielding efficient implementation of iterative methods; numerical experimentation suggests quadratic convergence. The choice of Chebyshev basis functions leads to higher order convergence, which for regular polygons appear to be exponential.
Prediction of siRNA potency using sparse logistic regression.
Hu, Wei; Hu, John
2014-06-01
RNA interference (RNAi) can modulate gene expression at post-transcriptional as well as transcriptional levels. Short interfering RNA (siRNA) serves as a trigger for the RNAi gene inhibition mechanism, and therefore is a crucial intermediate step in RNAi. There have been extensive studies to identify the sequence characteristics of potent siRNAs. One such study built a linear model using LASSO (Least Absolute Shrinkage and Selection Operator) to measure the contribution of each siRNA sequence feature. This model is simple and interpretable, but it requires a large number of nonzero weights. We have introduced a novel technique, sparse logistic regression, to build a linear model using single-position specific nucleotide compositions which has the same prediction accuracy of the linear model based on LASSO. The weights in our new model share the same general trend as those in the previous model, but have only 25 nonzero weights out of a total 84 weights, a 54% reduction compared to the previous model. Contrary to the linear model based on LASSO, our model suggests that only a few positions are influential on the efficacy of the siRNA, which are the 5' and 3' ends and the seed region of siRNA sequences. We also employed sparse logistic regression to build a linear model using dual-position specific nucleotide compositions, a task LASSO is not able to accomplish well due to its high dimensional nature. Our results demonstrate the superiority of sparse logistic regression as a technique for both feature selection and regression over LASSO in the context of siRNA design. PMID:21091052
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
Standard errors for EM estimates in generalized linear models with random effects.
Friedl, H; Kauermann, G
2000-09-01
A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulas are used to approximate the integrals in the EM algorithm, where two different approaches are pursued, i.e., Gauss-Hermite quadrature in the case of Gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations. PMID:10985213
Robust root clustering for linear uncertain systems using generalized Lyapunov theory
NASA Technical Reports Server (NTRS)
Yedavalli, R. K.
1993-01-01
Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.
Flexible analysis of digital PCR experiments using generalized linear mixed models.
Vynck, Matthijs; Vandesompele, Jo; Nijs, Nele; Menten, Björn; De Ganck, Ariane; Thas, Olivier
2016-09-01
The use of digital PCR for quantification of nucleic acids is rapidly growing. A major drawback remains the lack of flexible data analysis tools. Published analysis approaches are either tailored to specific problem settings or fail to take into account sources of variability. We propose the generalized linear mixed models framework as a flexible tool for analyzing a wide range of experiments. We also introduce a method for estimating reference gene stability to improve accuracy and precision of copy number and relative expression estimates. We demonstrate the usefulness of the methodology on a complex experimental setup. PMID:27551671
Location-scale cumulative odds models for ordinal data: a generalized non-linear model approach.
Cox, C
1995-06-15
Proportional odds regression models for multinomial probabilities based on ordered categories have been generalized in two somewhat different directions. Models having scale as well as location parameters for adjustment of boundaries (on an unobservable, underlying continuum) between categories have been employed in the context of ROC analysis. Partial proportional odds models, having different regression adjustments for different multinomial categories, have also been proposed. This paper considers a synthesis and further generalization of these two families. With use of a number of examples, I discuss and illustrate properties of this extended family of models. Emphasis is on the computation of maximum likelihood estimates of parameters, asymptotic standard deviations, and goodness-of-fit statistics with use of non-linear regression programs in standard statistical software such as SAS. PMID:7667560
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. PMID:25774642
Spatial temporal disaggregation of daily rainfall from a generalized linear model
NASA Astrophysics Data System (ADS)
Segond, M.-L.; Onof, C.; Wheater, H. S.
2006-12-01
SummaryThis paper describes a methodology for continuous simulation of spatially-distributed hourly rainfall, based on observed data from a daily raingauge network. Generalized linear models (GLMs), which can represent the spatial and temporal non-stationarities of multi-site daily rainfall (Chandler, R.E., Wheater, H.S., 2002. Analysis of rainfall variability using generalised linear models: a case study from the west of Ireland. Water Resources Research, 38 (10), 1192. doi:10.1029/2001WR000906), are combined with a single-site disaggregation model based on Poisson cluster processes (Koutsoyiannis, D., Onof, C., 2001. Rainfall disaggregation using adjusting procedures on a Poisson cluster model. Journal of Hydrology 246, 109-122). The resulting sub-daily temporal profile is then applied linearly to all sites over the catchment to reproduce the spatially-varying daily totals. The method is tested for the River Lee catchment, UK, a tributary of the Thames covering an area of 1400 km 2. Twenty simulations of 12 years of hourly rainfall are generated at 20 sites and compared with the historical series. The proposed model preserves most standard statistics but has some limitations in the representation of extreme rainfall and the correlation structure. The method can be extended to sites within the modelled region not used in the model calibration.
Thermodynamic bounds and general properties of optimal efficiency and power in linear responses.
Jiang, Jian-Hua
2014-10-01
We study the optimal exergy efficiency and power for thermodynamic systems with an Onsager-type "current-force" relationship describing the linear response to external influences. We derive, in analytic forms, the maximum efficiency and optimal efficiency for maximum power for a thermodynamic machine described by a N×N symmetric Onsager matrix with arbitrary integer N. The figure of merit is expressed in terms of the largest eigenvalue of the "coupling matrix" which is solely determined by the Onsager matrix. Some simple but general relationships between the power and efficiency at the conditions for (i) maximum efficiency and (ii) optimal efficiency for maximum power are obtained. We show how the second law of thermodynamics bounds the optimal efficiency and the Onsager matrix and relate those bounds together. The maximum power theorem (Jacobi's Law) is generalized to all thermodynamic machines with a symmetric Onsager matrix in the linear-response regime. We also discuss systems with an asymmetric Onsager matrix (such as systems under magnetic field) for a particular situation and we show that the reversible limit of efficiency can be reached at finite output power. Cooperative effects are found to improve the figure of merit significantly in systems with multiply cross-correlated responses. Application to example systems demonstrates that the theory is helpful in guiding the search for high performance materials and structures in energy researches. PMID:25375457
James, Gareth M.; Sabatti, Chiara; Zhou, Nengfeng; Zhu, Ji
2011-01-01
In many organisms the expression levels of each gene are controlled by the activation levels of known “Transcription Factors” (TF). A problem of considerable interest is that of estimating the “Transcription Regulation Networks” (TRN) relating the TFs and genes. While the expression levels of genes can be observed, the activation levels of the corresponding TFs are usually unknown, greatly increasing the difficulty of the problem. Based on previous experimental work, it is often the case that partial information about the TRN is available. For example, certain TFs may be known to regulate a given gene or in other cases a connection may be predicted with a certain probability. In general, the biology of the problem indicates there will be very few connections between TFs and genes. Several methods have been proposed for estimating TRNs. However, they all suffer from problems such as unrealistic assumptions about prior knowledge of the network structure or computational limitations. We propose a new approach that can directly utilize prior information about the network structure in conjunction with observed gene expression data to estimate the TRN. Our approach uses L1 penalties on the network to ensure a sparse structure. This has the advantage of being computationally efficient as well as making many fewer assumptions about the network structure. We use our methodology to construct the TRN for E. coli and show that the estimate is biologically sensible and compares favorably with previous estimates. PMID:21625366
Gao, Xieping; Li, Bodong; Xiao, Fen
2013-12-01
Multidimensional linear phase perfect reconstruction filter bank (MDLPPRFB) can be designed and implemented via lattice structure. The lattice structure for the MDLPPRFB with filter support N(MΞ) has been published by Muramatsu , where M is the decimation matrix, Ξ is a positive integer diagonal matrix, and N(N) denotes the set of integer vectors in the fundamental parallelepiped of the matrix N. Obviously, if Ξ is chosen to be other positive diagonal matrices instead of only positive integer ones, the corresponding lattice structure would provide more choices of filter banks, offering better trade-off between filter support and filter performance. We call such resulted filter bank as generalized-support MDLPPRFB (GSMDLPPRFB). The lattice structure for GSMDLPPRFB, however, cannot be designed by simply generalizing the process that Muramatsu employed. Furthermore, the related theories to assist the design also become different from those used by Muramatsu . Such issues will be addressed in this paper. To guide the design of GSMDLPPRFB, the necessary and sufficient conditions are established for a generalized-support multidimensional filter bank to be linear-phase. To determine the cases we can find a GSMDLPPRFB, the necessary conditions about the existence of it are proposed to be related with filter support and symmetry polarity (i.e., the number of symmetric filters ns and antisymmetric filters na). Based on a process (different from the one Muramatsu used) that combines several polyphase matrices to construct the starting block, one of the core building blocks of lattice structure, the lattice structure for GSMDLPPRFB is developed and shown to be minimal. Additionally, the result in this paper includes Muramatsu's as a special case. PMID:23974625
NASA Astrophysics Data System (ADS)
Kim, Tae-Jeong; Kim, Ki-Young; Shin, Dong-Hoon; Kwon, Hyun-Han
2015-04-01
It has been widely acknowledged that the appropriate simulation of natural streamflow at ungauged sites is one of the fundamental challenges to hydrology community. In particular, the key to reliable runoff simulation in ungauged basins is a reliable rainfall-runoff model and a parameter estimation. In general, parameter estimation in rainfall-runoff models is a complex issue due to an insufficient hydrologic data. This study aims to regionalize the parameters of the continuous rainfall-runoff model in conjunction with Bayesian statistical techniques to facilitate uncertainty analysis. First, this study uses the Bayesian Markov Chain Monte Carlo scheme for the Sacramento rainfall-runoff model that has been widely used around the world. The Sacramento model is calibrated against daily runoff observation, and thirteen parameters of the model are optimized as well as posterior distributor distributions for each parameter are derived. Second, we applied Bayesian generalized linear regression model to set of the parameters with basin characteristics (e.g. area and slope), to obtain a functional relationship between pairs of variables. The proposed model was validated in two gauged watersheds in accordance with the efficiency criteria such as the Nash-Sutcliffe efficiency, coefficient of efficiency, index of agreement and coefficient of correlation. The future study will be further focused on uncertainty analysis to fully incorporate propagation of the uncertainty into the regionalization framework. KEYWORDS: Ungauge, Parameter, Sacramento, Generalized linear model, Regionalization Acknowledgement This research was supported by a Grant (13SCIPA01) from Smart Civil Infrastructure Research Program funded by the Ministry of Land, Infrastructure and Transport (MOLIT) of Korea government and the Korea Agency for Infrastructure Technology Advancement (KAIA).
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
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
Model Averaging Methods for Weight Trimming in Generalized Linear Regression Models
Elliott, Michael R.
2012-01-01
In sample surveys where units have unequal probabilities of inclusion, associations between the inclusion probability and the statistic of interest can induce bias in unweighted estimates. This is true even in regression models, where the estimates of the population slope may be biased if the underlying mean model is misspecified or the sampling is nonignorable. Weights equal to the inverse of the probability of inclusion are often used to counteract this bias. Highly disproportional sample designs have highly variable weights; weight trimming reduces large weights to a maximum value, reducing variability but introducing bias. Most standard approaches are ad hoc in that they do not use the data to optimize bias-variance trade-offs. This article uses Bayesian model averaging to create “data driven” weight trimming estimators. We extend previous results for linear regression models (Elliott 2008) to generalized linear regression models, developing robust models that approximate fully-weighted estimators when bias correction is of greatest importance, and approximate unweighted estimators when variance reduction is critical. PMID:23275683
A General Linear Relaxometry Model of R1 Using Imaging Data
Callaghan, Martina F; Helms, Gunther; Lutti, Antoine; Mohammadi, Siawoosh; Weiskopf, Nikolaus
2015-01-01
Purpose The longitudinal relaxation rate (R1) measured in vivo depends on the local microstructural properties of the tissue, such as macromolecular, iron, and water content. Here, we use whole brain multiparametric in vivo data and a general linear relaxometry model to describe the dependence of R1 on these components. We explore a) the validity of having a single fixed set of model coefficients for the whole brain and b) the stability of the model coefficients in a large cohort. Methods Maps of magnetization transfer (MT) and effective transverse relaxation rate (R2*) were used as surrogates for macromolecular and iron content, respectively. Spatial variations in these parameters reflected variations in underlying tissue microstructure. A linear model was applied to the whole brain, including gray/white matter and deep brain structures, to determine the global model coefficients. Synthetic R1 values were then calculated using these coefficients and compared with the measured R1 maps. Results The model's validity was demonstrated by correspondence between the synthetic and measured R1 values and by high stability of the model coefficients across a large cohort. Conclusion A single set of global coefficients can be used to relate R1, MT, and R2* across the whole brain. Our population study demonstrates the robustness and stability of the model. Magn Reson Med, 2014. © 2014 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. Magn Reson Med 73:1309–1314, 2015. © 2014 Wiley Periodicals, Inc. PMID:24700606
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.
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.
Generalized linear joint PP-PS inversion based on two constraints
NASA Astrophysics Data System (ADS)
Fang, Yuan; Zhang, Feng-Qi; Wang, Yan-Chun
2016-03-01
Conventional joint PP—PS inversion is based on approximations of the Zoeppritz equations and assumes constant VP/VS; therefore, the inversion precision and stability cannot satisfy current exploration requirements. We propose a joint PP—PS inversion method based on the exact Zoeppritz equations that combines Bayesian statistics and generalized linear inversion. A forward model based on the exact Zoeppritz equations is built to minimize the error of the approximations in the large-angle data, the prior distribution of the model parameters is added as a regularization item to decrease the ill-posed nature of the inversion, low-frequency constraints are introduced to stabilize the low-frequency data and improve robustness, and a fast algorithm is used to solve the objective function while minimizing the computational load. The proposed method has superior antinoising properties and well reproduces real data.
Computing Confidence Bounds for Power and Sample Size of the General Linear Univariate Model
Taylor, Douglas J.; Muller, Keith E.
2013-01-01
The power of a test, the probability of rejecting the null hypothesis in favor of an alternative, may be computed using estimates of one or more distributional parameters. Statisticians frequently fix mean values and calculate power or sample size using a variance estimate from an existing study. Hence computed power becomes a random variable for a fixed sample size. Likewise, the sample size necessary to achieve a fixed power varies randomly. Standard statistical practice requires reporting uncertainty associated with such point estimates. Previous authors studied an asymptotically unbiased method of obtaining confidence intervals for noncentrality and power of the general linear univariate model in this setting. We provide exact confidence intervals for noncentrality, power, and sample size. Such confidence intervals, particularly one-sided intervals, help in planning a future study and in evaluating existing studies. PMID:24039272
Sparse representation for vehicle recognition
NASA Astrophysics Data System (ADS)
Monnig, Nathan D.; Sakla, Wesam
2014-06-01
The Sparse Representation for Classification (SRC) algorithm has been demonstrated to be a state-of-the-art algorithm for facial recognition applications. Wright et al. demonstrate that under certain conditions, the SRC algorithm classification performance is agnostic to choice of linear feature space and highly resilient to image corruption. In this work, we examined the SRC algorithm performance on the vehicle recognition application, using images from the semi-synthetic vehicle database generated by the Air Force Research Laboratory. To represent modern operating conditions, vehicle images were corrupted with noise, blurring, and occlusion, with representation of varying pose and lighting conditions. Experiments suggest that linear feature space selection is important, particularly in the cases involving corrupted images. Overall, the SRC algorithm consistently outperforms a standard k nearest neighbor classifier on the vehicle recognition task.
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.
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
Extracting H I cosmological signal with generalized needlet internal linear combination
NASA Astrophysics Data System (ADS)
Olivari, L. C.; Remazeilles, M.; Dickinson, C.
2016-03-01
H I intensity mapping is a new observational technique to map fluctuations in the large-scale structure of matter using the 21 cm emission line of atomic hydrogen (H I). Sensitive H I intensity mapping experiments have the potential to detect Baryon Acoustic Oscillations at low redshifts (z ≲ 1) in order to constrain the properties of dark energy. Observations of the H I signal will be contaminated by instrumental noise and, more significantly, by astrophysical foregrounds, such as Galactic synchrotron emission, which is at least four orders of magnitude brighter than the H I signal. Foreground cleaning is recognized as one of the key challenges for future radio astronomy surveys. We study the ability of the Generalized Needlet Internal Linear Combination (GNILC) method to subtract radio foregrounds and to recover the cosmological H I signal for a general H I intensity mapping experiment. The GNILC method is a new technique that uses both frequency and spatial information to separate the components of the observed data. Our results show that the method is robust to the complexity of the foregrounds. For simulated radio observations including H I emission, Galactic synchrotron, Galactic free-free, radio sources, and 0.05 mK thermal noise, we find that the GNILC method can reconstruct the H I power spectrum for multipoles 30 < ℓ < 150 with 6 per cent accuracy on 50 per cent of the sky for a redshift z ˜ 0.25.
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.
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.
Grassmannian sparse representations
NASA Astrophysics Data System (ADS)
Azary, Sherif; Savakis, Andreas
2015-05-01
We present Grassmannian sparse representations (GSR), a sparse representation Grassmann learning framework for efficient classification. Sparse representation classification offers a powerful approach for recognition in a variety of contexts. However, a major drawback of sparse representation methods is their computational performance and memory utilization for high-dimensional data. A Grassmann manifold is a space that promotes smooth surfaces where points represent subspaces and the relationship between points is defined by the mapping of an orthogonal matrix. Grassmann manifolds are well suited for computer vision problems because they promote high between-class discrimination and within-class clustering, while offering computational advantages by mapping each subspace onto a single point. The GSR framework combines Grassmannian kernels and sparse representations, including regularized least squares and least angle regression, to improve high accuracy recognition while overcoming the drawbacks of performance and dependencies on high dimensional data distributions. The effectiveness of GSR is demonstrated on computationally intensive multiview action sequences, three-dimensional action sequences, and face recognition datasets.
Native ultrametricity of sparse random ensembles
NASA Astrophysics Data System (ADS)
Avetisov, V.; Krapivsky, P. L.; Nechaev, S.
2016-01-01
We investigate the eigenvalue density in ensembles of large sparse Bernoulli random matrices. Analyzing in detail the spectral density of ensembles of linear subgraphs, we discuss its ultrametric nature and show that near the spectrum boundary, the tails of the spectral density exhibit a Lifshitz singularity typical for Anderson localization. We pay attention to an intriguing connection of the spectral density to the Dedekind η-function. We conjecture that ultrametricity emerges in rare-event statistics and is inherit to generic complex sparse systems.
Dictionary learning method for joint sparse representation-based image fusion
NASA Astrophysics Data System (ADS)
Zhang, Qiheng; Fu, Yuli; Li, Haifeng; Zou, Jian
2013-05-01
Recently, sparse representation (SR) and joint sparse representation (JSR) have attracted a lot of interest in image fusion. The SR models signals by sparse linear combinations of prototype signal atoms that make a dictionary. The JSR indicates that different signals from the various sensors of the same scene form an ensemble. These signals have a common sparse component and each individual signal owns an innovation sparse component. The JSR offers lower computational complexity compared with SR. First, for JSR-based image fusion, we give a new fusion rule. Then, motivated by the method of optimal directions (MOD), for JSR, we propose a novel dictionary learning method (MODJSR) whose dictionary updating procedure is derived by employing the JSR structure one time with singular value decomposition (SVD). MODJSR has lower complexity than the K-SVD algorithm which is often used in previous JSR-based fusion algorithms. To capture the image details more efficiently, we proposed the generalized JSR in which the signals ensemble depends on two dictionaries. MODJSR is extended to MODGJSR in this case. MODJSR/MODGJSR can simultaneously carry out dictionary learning, denoising, and fusion of noisy source images. Some experiments are given to demonstrate the validity of the MODJSR/MODGJSR for image fusion.
NASA Astrophysics Data System (ADS)
Jellison, Gerald E., Jr.; Griffiths, C. Owen; Holcomb, David E.; Rouleau, Christopher M.
2002-09-01
The two-modulator generalized ellipsometer (2-MGE) is a spectroscopic polarization-sensitive optical instrument that is sensitive to both standard ellipsometric parameters from isotropic samples as well as cross polarization terms arising from anisotropic samples. In reflection mode, teh 2-MGE has been used to measure the complex dielectric functions of several uniaxial crystals, including TiO2, ZnO, and BiI3. The 2-MGE can also be used in the transmission mode, in which the complete Mueller matrix of a sample can be determined (using 4 zone measurements). If the sample is a linear diattenuator and retarder, then only a single zone is required to determine the sample retardation, diattenuation, the principal axis direction, and the depolarization. These measurements have been performed in two different modes: 1) Spectroscopic, where the current wavelength limits are 260 to 850 nm, and 2) Spatially resolved (Current resolution ~30-50 microns) at a single wavelength. The latter mode results in retardation, linear diattenuation, and principal axis direction "maps" of the sample. Two examples are examined in this paper. First, a simple Polaroid film polarizer is measured, where it is seen that the device behaves nearly ideally in its design wavelength range (visible), but acts more as a retarder in the infrared. Second, congruently grown LiNbO3 is examined under bias. These results show that there are significant variations in the electric field-Pockels coefficient product within the material. Spectroscopic measurements are used to determine the dispersion of the r22 Pockels coefficient.
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
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.
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
Shin, Yongyun; Raudenbush, Stephen W
2013-01-01
This article extends single-level missing data methods to efficient estimation of a Q-level nested hierarchical general linear model given ignorable missing data with a general missing pattern at any of the Q levels. The key idea is to reexpress a desired hierarchical model as the joint distribution of all variables including the outcome that are subject to missingness, conditional on all of the covariates that are completely observed and to estimate the joint model under normal theory. The unconstrained joint model, however, identifies extraneous parameters that are not of interest in subsequent analysis of the hierarchical model and that rapidly multiply as the number of levels, the number of variables subject to missingness, and the number of random coefficients grow. Therefore, the joint model may be extremely high dimensional and difficult to estimate well unless constraints are imposed to avoid the proliferation of extraneous covariance components at each level. Furthermore, the over-identified hierarchical model may produce considerably biased inferences. The challenge is to represent the constraints within the framework of the Q-level model in a way that is uniform without regard to Q; in a way that facilitates efficient computation for any number of Q levels; and also in a way that produces unbiased and efficient analysis of the hierarchical model. Our approach yields Q-step recursive estimation and imputation procedures whose qth-step computation involves only level-q data given higher-level computation components. We illustrate the approach with a study of the growth in body mass index analyzing a national sample of elementary school children. PMID:24077621
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].
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.
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
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.
The overlooked potential of Generalized Linear Models in astronomy, I: Binomial regression
NASA Astrophysics Data System (ADS)
de Souza, R. S.; Cameron, E.; Killedar, M.; Hilbe, J.; Vilalta, R.; Maio, U.; Biffi, V.; Ciardi, B.; Riggs, J. D.
2015-09-01
Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific enquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper-the first in a series aimed at illustrating the power of these methods in astronomical applications-we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes from cosmological hydro-simulations including detailed chemistry, gas physics, and stellar feedback. We predict that for a dark mini-halo with metallicity ≈ 1.3 × 10-4Z⨀, an increase of 1.2 × 10-2 in the gas molecular fraction, increases the probability of star formation occurrence by a factor of 75%. Finally, we highlight the use of receiver operating characteristic curves as a diagnostic for binary classifiers, and ultimately we use these to demonstrate the competitive predictive performance of GLMs against the popular technique of artificial neural networks.
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.
Sensitivity Analysis of Linear Elastic Cracked Structures Using Generalized Finite Element Method
NASA Astrophysics Data System (ADS)
Pal, Mahendra Kumar; Rajagopal, Amirtham
2014-09-01
In this work, a sensitivity analysis of linear elastic cracked structures using two-scale Generalized Finite Element Method (GFEM) is presented. The method is based on computation of material derivatives, mutual potential energies, and direct differentiation. In a computational setting, the discrete form of the mutual potential energy release rate is simple and easy to calculate, as it only requires the multiplication of the displacement vectors and stiffness sensitivity matrices. By judiciously choosing the velocity field, the method only requires displacement response in a sub-domain close to the crack tip, thus making the method computationally efficient. The method thus requires an exact computation of displacement response in a sub-domain close to the crack tip. To this end, in this study we have used a two-scale GFEM for sensitivity analysis. GFEM is based on the enrichment of the classical finite element approximation. These enrichment functions incorporate the discontinuity response in the domain. Three numerical examples which comprise mode-I and mixed mode deformations are presented to evaluate the accuracy of the fracture parameters calculated by the proposed method.
Chen, Gang; Adleman, Nancy E.; Saad, Ziad S.; Leibenluft, Ellen; Cox, RobertW.
2014-01-01
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. PMID:24954281
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.
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.
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
Sparse and redundant representations for inverse problems and recognition
NASA Astrophysics Data System (ADS)
Patel, Vishal M.
Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed
Use of generalized linear models and digital data in a forest inventory of Northern Utah
Moisen, G.G.; Edwards, T.C., Jr.
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.
Generalized functional linear models for gene-based case-control association studies.
Fan, Ruzong; Wang, Yifan; Mills, James L; Carter, Tonia C; Lobach, Iryna; Wilson, Alexander F; Bailey-Wilson, Joan E; Weeks, Daniel E; Xiong, Momiao
2014-11-01
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 region 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 datasets. 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
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.
Resistant multiple sparse canonical correlation.
Coleman, Jacob; Replogle, Joseph; Chandler, Gabriel; Hardin, Johanna
2016-04-01
Canonical correlation analysis (CCA) is a multivariate technique that takes two datasets and forms the most highly correlated possible pairs of linear combinations between them. Each subsequent pair of linear combinations is orthogonal to the preceding pair, meaning that new information is gleaned from each pair. By looking at the magnitude of coefficient values, we can find out which variables can be grouped together, thus better understanding multiple interactions that are otherwise difficult to compute or grasp intuitively. CCA appears to have quite powerful applications to high-throughput data, as we can use it to discover, for example, relationships between gene expression and gene copy number variation. One of the biggest problems of CCA is that the number of variables (often upwards of 10,000) makes biological interpretation of linear combinations nearly impossible. To limit variable output, we have employed a method known as sparse canonical correlation analysis (SCCA), while adding estimation which is resistant to extreme observations or other types of deviant data. In this paper, we have demonstrated the success of resistant estimation in variable selection using SCCA. Additionally, we have used SCCA to find multiple canonical pairs for extended knowledge about the datasets at hand. Again, using resistant estimators provided more accurate estimates than standard estimators in the multiple canonical correlation setting. R code is available and documented at https://github.com/hardin47/rmscca. PMID:26963062
Sparse subspace clustering: algorithm, theory, and applications.
Elhamifar, Ehsan; Vidal, René
2013-11-01
Many real-world problems deal with collections of high-dimensional data, such as images, videos, text, and web documents, DNA microarray data, and more. Often, such high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories to which the data belong. In this paper, we propose and study an algorithm, called sparse subspace clustering, to cluster data points that lie in a union of low-dimensional subspaces. The key idea is that, among the infinitely many possible representations of a data point in terms of other points, a sparse representation corresponds to selecting a few points from the same subspace. This motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces. Since solving the sparse optimization program is in general NP-hard, we consider a convex relaxation and show that, under appropriate conditions on the arrangement of the subspaces and the distribution of the data, the proposed minimization program succeeds in recovering the desired sparse representations. The proposed algorithm is efficient and can handle data points near the intersections of subspaces. Another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances, such as noise, sparse outlying entries, and missing entries, by incorporating the model of the data into the sparse optimization program. We demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real-world problems of motion segmentation and face clustering. PMID:24051734
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.
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.
A unified approach to sparse signal processing
NASA Astrophysics Data System (ADS)
Marvasti, Farokh; Amini, Arash; Haddadi, Farzan; Soltanolkotabi, Mahdi; Khalaj, Babak Hossein; Aldroubi, Akram; Sanei, Saeid; Chambers, Janathon
2012-12-01
A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing, and rate of innovation. The redundancy introduced by channel coding in finite and real Galois fields is then related to over-sampling with similar reconstruction algorithms. The error locator polynomial (ELP) and iterative methods are shown to work quite effectively for both sampling and coding applications. The methods of Prony, Pisarenko, and MUltiple SIgnal Classification (MUSIC) are next shown to be targeted at analyzing signals with sparse frequency domain representations. Specifically, the relations of the approach of Prony to an annihilating filter in rate of innovation and ELP in coding are emphasized; the Pisarenko and MUSIC methods are further improvements of the Prony method under noisy environments. The iterative methods developed for sampling and coding applications are shown to be powerful tools in spectral estimation. Such narrowband spectral estimation is then related to multi-source location and direction of arrival estimation in array processing. Sparsity in unobservable source signals is also shown to facilitate source separation in sparse component analysis; the algorithms developed in this area such as linear programming and matching pursuit are also widely used in compressed sensing. Finally
Optical sparse aperture imaging.
Miller, Nicholas J; Dierking, Matthew P; Duncan, Bradley D
2007-08-10
The resolution of a conventional diffraction-limited imaging system is proportional to its pupil diameter. A primary goal of sparse aperture imaging is to enhance resolution while minimizing the total light collection area; the latter being desirable, in part, because of the cost of large, monolithic apertures. Performance metrics are defined and used to evaluate several sparse aperture arrays constructed from multiple, identical, circular subapertures. Subaperture piston and/or tilt effects on image quality are also considered. We selected arrays with compact nonredundant autocorrelations first described by Golay. We vary both the number of subapertures and their relative spacings to arrive at an optimized array. We report the results of an experiment in which we synthesized an image from multiple subaperture pupil fields by masking a large lens with a Golay array. For this experiment we imaged a slant edge feature of an ISO12233 resolution target in order to measure the modulation transfer function. We note the contrast reduction inherent in images formed through sparse aperture arrays and demonstrate the use of a Wiener-Helstrom filter to restore contrast in our experimental images. Finally, we describe a method to synthesize images from multiple subaperture focal plane intensity images using a phase retrieval algorithm to obtain estimates of subaperture pupil fields. Experimental results from synthesizing an image of a point object from multiple subaperture images are presented, and weaknesses of the phase retrieval method for this application are discussed. PMID:17694146
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.
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.
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