Cucheb: A GPU implementation of the filtered Lanczos procedure

NASA Astrophysics Data System (ADS)

Aurentz, Jared L.; Kalantzis, Vassilis; Saad, Yousef

2017-11-01

This paper describes the software package Cucheb, a GPU implementation of the filtered Lanczos procedure for the solution of large sparse symmetric eigenvalue problems. The filtered Lanczos procedure uses a carefully chosen polynomial spectral transformation to accelerate convergence of the Lanczos method when computing eigenvalues within a desired interval. This method has proven particularly effective for eigenvalue problems that arise in electronic structure calculations and density functional theory. We compare our implementation against an equivalent CPU implementation and show that using the GPU can reduce the computation time by more than a factor of 10. Program Summary Program title: Cucheb Program Files doi:http://dx.doi.org/10.17632/rjr9tzchmh.1 Licensing provisions: MIT Programming language: CUDA C/C++ Nature of problem: Electronic structure calculations require the computation of all eigenvalue-eigenvector pairs of a symmetric matrix that lie inside a user-defined real interval. Solution method: To compute all the eigenvalues within a given interval a polynomial spectral transformation is constructed that maps the desired eigenvalues of the original matrix to the exterior of the spectrum of the transformed matrix. The Lanczos method is then used to compute the desired eigenvectors of the transformed matrix, which are then used to recover the desired eigenvalues of the original matrix. The bulk of the operations are executed in parallel using a graphics processing unit (GPU). Runtime: Variable, depending on the number of eigenvalues sought and the size and sparsity of the matrix. Additional comments: Cucheb is compatible with CUDA Toolkit v7.0 or greater.

Spectral simulation of unsteady compressible flow past a circular cylinder

NASA Technical Reports Server (NTRS)

Don, Wai-Sun; Gottlieb, David

1990-01-01

An unsteady compressible viscous wake flow past a circular cylinder was successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for periodic problems is introduced. It was further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It was been shown that the solution of a model problem has exponential growth in time if improper boundary conditions are used. A characteristic boundary condition, which is based on the characteristics of the Euler equations of gas dynamics, was derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.

Multidimensional spectral load balancing

DOEpatents

Hendrickson, Bruce A.; Leland, Robert W.

1996-12-24

A method of and apparatus for graph partitioning involving the use of a plurality of eigenvectors of the Laplacian matrix of the graph of the problem for which load balancing is desired. The invention is particularly useful for optimizing parallel computer processing of a problem and for minimizing total pathway lengths of integrated circuits in the design stage.

Matrix basis for plane and modal waves in a Timoshenko beam.

PubMed

Claeyssen, Julio Cesar Ruiz; Tolfo, Daniela de Rosso; Tonetto, Leticia

2016-11-01

Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville's technique, these latter are well behaved at critical or static situations. Eigenanalysis is formulated for exponential and modal waves. Modal waves are superposition of four plane waves, but there are plane waves that cannot be modal waves. Reflected and transmitted waves at an interface point are formulated in matrix terms, regardless of having a conservative or a dissipative situation. The matrix representation of modal waves is used in a crack problem for determining the reflected and transmitted matrices. Their euclidean norms are seen to be dominated by certain components at low and high frequencies. The matrix basis technique is also used with a non-local Timoshenko model and with the wave interaction with a boundary. The matrix basis allows to characterize reflected and transmitted waves in spectral and non-spectral form.

A Riemann-Hilbert Approach to Complex Sharma-Tasso-Olver Equation on Half Line*

NASA Astrophysics Data System (ADS)

Zhang, Ning; Xia, Tie-Cheng; Hu, Bei-Bei

2017-11-01

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma-Tasso-Olver (cSTO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann-Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions \\{a(λ ),b(λ )\\} and \\{A(λ ),B(λ )\\} , which depending on initial data {u}0(x)=u(x,0) and boundary data {g}0(y)=u(0,y), {g}1(y)={u}x(0,y), {g}2(y)={u}{xx}(0,y). These spectral functions are not independent, they satisfy a global relation.

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

NASA Technical Reports Server (NTRS)

Maliassov, Serguei

1996-01-01

In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Semi-supervised spectral algorithms for community detection in complex networks based on equivalence of clustering methods

NASA Astrophysics Data System (ADS)

Ma, Xiaoke; Wang, Bingbo; Yu, Liang

2018-01-01

Community detection is fundamental for revealing the structure-functionality relationship in complex networks, which involves two issues-the quantitative function for community as well as algorithms to discover communities. Despite significant research on either of them, few attempt has been made to establish the connection between the two issues. To attack this problem, a generalized quantification function is proposed for community in weighted networks, which provides a framework that unifies several well-known measures. Then, we prove that the trace optimization of the proposed measure is equivalent with the objective functions of algorithms such as nonnegative matrix factorization, kernel K-means as well as spectral clustering. It serves as the theoretical foundation for designing algorithms for community detection. On the second issue, a semi-supervised spectral clustering algorithm is developed by exploring the equivalence relation via combining the nonnegative matrix factorization and spectral clustering. Different from the traditional semi-supervised algorithms, the partial supervision is integrated into the objective of the spectral algorithm. Finally, through extensive experiments on both artificial and real world networks, we demonstrate that the proposed method improves the accuracy of the traditional spectral algorithms in community detection.

Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

DOE PAGES

Smallwood, David O.

1997-01-01

The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general casemore » of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.« less

Development of a spectroscopic Mueller matrix imaging ellipsometer for nanostructure metrology

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

Chen, Xiuguo; Du, Weichao; Yuan, Kui

2016-05-15

In this paper, we describe the development of a spectroscopic Mueller matrix imaging ellipsometer (MMIE), which combines the great power of Mueller matrix ellipsometry with the high spatial resolution of optical microscopy. A dual rotating-compensator configuration is adopted to collect the full 4 × 4 imaging Mueller matrix in a single measurement. The light wavelengths are scanned in the range of 400–700 nm by a monochromator. The instrument has measurement accuracy and precision better than 0.01 for all the Mueller matrix elements in both the whole image and the whole spectral range. The instrument was then applied for the measurementmore » of nanostructures combined with an inverse diffraction problem solving technique. The experiment performed on a photoresist grating sample has demonstrated the great potential of MMIE for accurate grating reconstruction from spectral data collected by a single pixel of the camera and for efficient quantification of geometrical profile of the grating structure over a large area with pixel resolution. It is expected that MMIE will be a powerful tool for nanostructure metrology in future high-volume nanomanufacturing.« less

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

DOE PAGES

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

2015-01-01

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

A new family of high-order compact upwind difference schemes with good spectral resolution

NASA Astrophysics Data System (ADS)

Zhou, Qiang; Yao, Zhaohui; He, Feng; Shen, M. Y.

2007-12-01

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.

Confounder Detection in High-Dimensional Linear Models Using First Moments of Spectral Measures.

PubMed

Liu, Furui; Chan, Laiwan

2018-06-12

In this letter, we study the confounder detection problem in the linear model, where the target variable [Formula: see text] is predicted using its [Formula: see text] potential causes [Formula: see text]. Based on an assumption of a rotation-invariant generating process of the model, recent study shows that the spectral measure induced by the regression coefficient vector with respect to the covariance matrix of [Formula: see text] is close to a uniform measure in purely causal cases, but it differs from a uniform measure characteristically in the presence of a scalar confounder. Analyzing spectral measure patterns could help to detect confounding. In this letter, we propose to use the first moment of the spectral measure for confounder detection. We calculate the first moment of the regression vector-induced spectral measure and compare it with the first moment of a uniform spectral measure, both defined with respect to the covariance matrix of [Formula: see text]. The two moments coincide in nonconfounding cases and differ from each other in the presence of confounding. This statistical causal-confounding asymmetry can be used for confounder detection. Without the need to analyze the spectral measure pattern, our method avoids the difficulty of metric choice and multiple parameter optimization. Experiments on synthetic and real data show the performance of this method.

Matrix basis for plane and modal waves in a Timoshenko beam

PubMed Central

Tolfo, Daniela de Rosso; Tonetto, Leticia

2016-01-01

Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville’s technique, these latter are well behaved at critical or static situations. Eigenanalysis is formulated for exponential and modal waves. Modal waves are superposition of four plane waves, but there are plane waves that cannot be modal waves. Reflected and transmitted waves at an interface point are formulated in matrix terms, regardless of having a conservative or a dissipative situation. The matrix representation of modal waves is used in a crack problem for determining the reflected and transmitted matrices. Their euclidean norms are seen to be dominated by certain components at low and high frequencies. The matrix basis technique is also used with a non-local Timoshenko model and with the wave interaction with a boundary. The matrix basis allows to characterize reflected and transmitted waves in spectral and non-spectral form. PMID:28018668

Graph edit distance from spectral seriation.

PubMed

Robles-Kelly, Antonio; Hancock, Edwin R

2005-03-01

This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems.

A Poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Ma, Jun; Yang, Gang; Du, Bo; Zhang, Liangpei

2017-06-01

A new Bayesian method named Poisson Nonnegative Matrix Factorization with Parameter Subspace Clustering Constraint (PNMF-PSCC) has been presented to extract endmembers from Hyperspectral Imagery (HSI). First, the method integrates the liner spectral mixture model with the Bayesian framework and it formulates endmember extraction into a Bayesian inference problem. Second, the Parameter Subspace Clustering Constraint (PSCC) is incorporated into the statistical program to consider the clustering of all pixels in the parameter subspace. The PSCC could enlarge differences among ground objects and helps finding endmembers with smaller spectrum divergences. Meanwhile, the PNMF-PSCC method utilizes the Poisson distribution as the prior knowledge of spectral signals to better explain the quantum nature of light in imaging spectrometer. Third, the optimization problem of PNMF-PSCC is formulated into maximizing the joint density via the Maximum A Posterior (MAP) estimator. The program is finally solved by iteratively optimizing two sub-problems via the Alternating Direction Method of Multipliers (ADMM) framework and the FURTHESTSUM initialization scheme. Five state-of-the art methods are implemented to make comparisons with the performance of PNMF-PSCC on both the synthetic and real HSI datasets. Experimental results show that the PNMF-PSCC outperforms all the five methods in Spectral Angle Distance (SAD) and Root-Mean-Square-Error (RMSE), and especially it could identify good endmembers for ground objects with smaller spectrum divergences.

Handwritten text line segmentation by spectral clustering

NASA Astrophysics Data System (ADS)

Han, Xuecheng; Yao, Hui; Zhong, Guoqiang

2017-02-01

Since handwritten text lines are generally skewed and not obviously separated, text line segmentation of handwritten document images is still a challenging problem. In this paper, we propose a novel text line segmentation algorithm based on the spectral clustering. Given a handwritten document image, we convert it to a binary image first, and then compute the adjacent matrix of the pixel points. We apply spectral clustering on this similarity metric and use the orthogonal kmeans clustering algorithm to group the text lines. Experiments on Chinese handwritten documents database (HIT-MW) demonstrate the effectiveness of the proposed method.

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

Spectral-Spatial Shared Linear Regression for Hyperspectral Image Classification.

PubMed

Haoliang Yuan; Yuan Yan Tang

2017-04-01

Classification of the pixels in hyperspectral image (HSI) is an important task and has been popularly applied in many practical applications. Its major challenge is the high-dimensional small-sized problem. To deal with this problem, lots of subspace learning (SL) methods are developed to reduce the dimension of the pixels while preserving the important discriminant information. Motivated by ridge linear regression (RLR) framework for SL, we propose a spectral-spatial shared linear regression method (SSSLR) for extracting the feature representation. Comparing with RLR, our proposed SSSLR has the following two advantages. First, we utilize a convex set to explore the spatial structure for computing the linear projection matrix. Second, we utilize a shared structure learning model, which is formed by original data space and a hidden feature space, to learn a more discriminant linear projection matrix for classification. To optimize our proposed method, an efficient iterative algorithm is proposed. Experimental results on two popular HSI data sets, i.e., Indian Pines and Salinas demonstrate that our proposed methods outperform many SL methods.

Investigations of Some Liquid Matrixes for Analyte Quantification by MALDI

NASA Astrophysics Data System (ADS)

Moon, Jeong Hee; Park, Kyung Man; Ahn, Sung Hee; Lee, Seong Hoon; Kim, Myung Soo

2015-06-01

Sample inhomogeneity is one of the obstacles preventing the generation of reproducible mass spectra by MALDI and to their use for the purpose of analyte quantification. As a potential solution to this problem, we investigated MALDI with some liquid matrixes prepared by nonstoichiometric mixing of acids and bases. Out of 27 combinations of acids and bases, liquid matrixes could be produced from seven. When the overall spectral features were considered, two liquid matrixes using α-cyano-4-hydroxycinnamic acid as the acid and 3-aminoquinoline and N,N-diethylaniline as bases were the best choices. In our previous study of MALDI with solid matrixes, we found that three requirements had to be met for the generation of reproducible spectra and for analyte quantification: (1) controlling the temperature by fixing the total ion count, (2) plotting the analyte-to-matrix ion ratio versus the analyte concentration as the calibration curve, and (3) keeping the matrix suppression below a critical value. We found that the same requirements had to be met in MALDI with liquid matrixes as well. In particular, although the liquid matrixes tested here were homogeneous, they failed to display spot-to-spot spectral reproducibility unless the first requirement above was met. We also found that analyte-derived ions could not be produced efficiently by MALDI with the above liquid matrixes unless the analyte was sufficiently basic. In this sense, MALDI processes with solid and liquid matrixes should be regarded as complementary techniques rather than as competing ones.

Investigations of Some Liquid Matrixes for Analyte Quantification by MALDI.

PubMed

Moon, Jeong Hee; Park, Kyung Man; Ahn, Sung Hee; Lee, Seong Hoon; Kim, Myung Soo

2015-10-01

Sample inhomogeneity is one of the obstacles preventing the generation of reproducible mass spectra by MALDI and to their use for the purpose of analyte quantification. As a potential solution to this problem, we investigated MALDI with some liquid matrixes prepared by nonstoichiometric mixing of acids and bases. Out of 27 combinations of acids and bases, liquid matrixes could be produced from seven. When the overall spectral features were considered, two liquid matrixes using α-cyano-4-hydroxycinnamic acid as the acid and 3-aminoquinoline and N,N-diethylaniline as bases were the best choices. In our previous study of MALDI with solid matrixes, we found that three requirements had to be met for the generation of reproducible spectra and for analyte quantification: (1) controlling the temperature by fixing the total ion count, (2) plotting the analyte-to-matrix ion ratio versus the analyte concentration as the calibration curve, and (3) keeping the matrix suppression below a critical value. We found that the same requirements had to be met in MALDI with liquid matrixes as well. In particular, although the liquid matrixes tested here were homogeneous, they failed to display spot-to-spot spectral reproducibility unless the first requirement above was met. We also found that analyte-derived ions could not be produced efficiently by MALDI with the above liquid matrixes unless the analyte was sufficiently basic. In this sense, MALDI processes with solid and liquid matrixes should be regarded as complementary techniques rather than as competing ones.

Apparatus and system for multivariate spectral analysis

DOEpatents

Keenan, Michael R.; Kotula, Paul G.

2003-06-24

An apparatus and system for determining the properties of a sample from measured spectral data collected from the sample by performing a method of multivariate spectral analysis. The method can include: generating a two-dimensional matrix A containing measured spectral data; providing a weighted spectral data matrix D by performing a weighting operation on matrix A; factoring D into the product of two matrices, C and S.sup.T, by performing a constrained alternating least-squares analysis of D=CS.sup.T, where C is a concentration intensity matrix and S is a spectral shapes matrix; unweighting C and S by applying the inverse of the weighting used previously; and determining the properties of the sample by inspecting C and S. This method can be used by a spectrum analyzer to process X-ray spectral data generated by a spectral analysis system that can include a Scanning Electron Microscope (SEM) with an Energy Dispersive Detector and Pulse Height Analyzer.

Method of multivariate spectral analysis

DOEpatents

Keenan, Michael R.; Kotula, Paul G.

2004-01-06

A method of determining the properties of a sample from measured spectral data collected from the sample by performing a multivariate spectral analysis. The method can include: generating a two-dimensional matrix A containing measured spectral data; providing a weighted spectral data matrix D by performing a weighting operation on matrix A; factoring D into the product of two matrices, C and S.sup.T, by performing a constrained alternating least-squares analysis of D=CS.sup.T, where C is a concentration intensity matrix and S is a spectral shapes matrix; unweighting C and S by applying the inverse of the weighting used previously; and determining the properties of the sample by inspecting C and S. This method can be used to analyze X-ray spectral data generated by operating a Scanning Electron Microscope (SEM) with an attached Energy Dispersive Spectrometer (EDS).

Distributed Unmixing of Hyperspectral Datawith Sparsity Constraint

NASA Astrophysics Data System (ADS)

Khoshsokhan, S.; Rajabi, R.; Zayyani, H.

2017-09-01

Spectral unmixing (SU) is a data processing problem in hyperspectral remote sensing. The significant challenge in the SU problem is how to identify endmembers and their weights, accurately. For estimation of signature and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are used widely in the SU problem. One of the constraints which was added to NMF is sparsity constraint that was regularized by L1/2 norm. In this paper, a new algorithm based on distributed optimization has been used for spectral unmixing. In the proposed algorithm, a network including single-node clusters has been employed. Each pixel in hyperspectral images considered as a node in this network. The distributed unmixing with sparsity constraint has been optimized with diffusion LMS strategy, and then the update equations for fractional abundance and signature matrices are obtained. Simulation results based on defined performance metrics, illustrate advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods. The results show that the AAD and SAD of the proposed approach are improved respectively about 6 and 27 percent toward distributed unmixing in SNR=25dB.

New Results in {mathcal {N}}=2 N = 2 Theories from Non-perturbative String

NASA Astrophysics Data System (ADS)

Bonelli, Giulio; Grassi, Alba; Tanzini, Alessandro

2018-03-01

We describe the magnetic phase of SU(N) $\\mathcal{N}=2$ Super Yang-Mills theories in the self-dual Omega background in terms of a new class of multi-cut matrix models. These arise from a non-perturbative completion of topological strings in the dual four dimensional limit which engineers the gauge theory in the strongly coupled magnetic frame. The corresponding spectral determinants provide natural candidates for the tau functions of isomonodromy problems for flat spectral connections associated to the Seiberg-Witten geometry.

Algorithms for Solvents and Spectral Factors of Matrix Polynomials

DTIC Science & Technology

1981-01-01

spectral factors of matrix polynomials LEANG S. SHIEHt, YIH T. TSAYt and NORMAN P. COLEMANt A generalized Newton method , based on the contracted gradient...of a matrix poly- nomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial...estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right

A note on the upper bound of the spectral radius for SOR iteration matrix

NASA Astrophysics Data System (ADS)

Chang, D.-W. Da-Wei

2004-05-01

Recently, Wang and Huang (J. Comput. Appl. Math. 135 (2001) 325, Corollary 4.7) established the following estimation on the upper bound of the spectral radius for successive overrelaxation (SOR) iteration matrix:ρSOR≤1-ω+ωρGSunder the condition that the coefficient matrix A is a nonsingular M-matrix and ω≥1, where ρSOR and ρGS are the spectral radius of SOR iteration matrix and Gauss-Seidel iteration matrix, respectively. In this note, we would like to point out that the above estimation is not valid in general.

Spectral Unmixing With Multiple Dictionaries

NASA Astrophysics Data System (ADS)

Cohen, Jeremy E.; Gillis, Nicolas

2018-02-01

Spectral unmixing aims at recovering the spectral signatures of materials, called endmembers, mixed in a hyperspectral or multispectral image, along with their abundances. A typical assumption is that the image contains one pure pixel per endmember, in which case spectral unmixing reduces to identifying these pixels. Many fully automated methods have been proposed in recent years, but little work has been done to allow users to select areas where pure pixels are present manually or using a segmentation algorithm. Additionally, in a non-blind approach, several spectral libraries may be available rather than a single one, with a fixed number (or an upper or lower bound) of endmembers to chose from each. In this paper, we propose a multiple-dictionary constrained low-rank matrix approximation model that address these two problems. We propose an algorithm to compute this model, dubbed M2PALS, and its performance is discussed on both synthetic and real hyperspectral images.

Peak picking NMR spectral data using non-negative matrix factorization.

PubMed

Tikole, Suhas; Jaravine, Victor; Rogov, Vladimir; Dötsch, Volker; Güntert, Peter

2014-02-11

Simple peak-picking algorithms, such as those based on lineshape fitting, perform well when peaks are completely resolved in multidimensional NMR spectra, but often produce wrong intensities and frequencies for overlapping peak clusters. For example, NOESY-type spectra have considerable overlaps leading to significant peak-picking intensity errors, which can result in erroneous structural restraints. Precise frequencies are critical for unambiguous resonance assignments. To alleviate this problem, a more sophisticated peaks decomposition algorithm, based on non-negative matrix factorization (NMF), was developed. We produce peak shapes from Fourier-transformed NMR spectra. Apart from its main goal of deriving components from spectra and producing peak lists automatically, the NMF approach can also be applied if the positions of some peaks are known a priori, e.g. from consistently referenced spectral dimensions of other experiments. Application of the NMF algorithm to a three-dimensional peak list of the 23 kDa bi-domain section of the RcsD protein (RcsD-ABL-HPt, residues 688-890) as well as to synthetic HSQC data shows that peaks can be picked accurately also in spectral regions with strong overlap.

3D tensor-based blind multispectral image decomposition for tumor demarcation

NASA Astrophysics Data System (ADS)

Kopriva, Ivica; Peršin, Antun

2010-03-01

Blind decomposition of multi-spectral fluorescent image for tumor demarcation is formulated exploiting tensorial structure of the image. First contribution of the paper is identification of the matrix of spectral responses and 3D tensor of spatial distributions of the materials present in the image from Tucker3 or PARAFAC models of 3D image tensor. Second contribution of the paper is clustering based estimation of the number of the materials present in the image as well as matrix of their spectral profiles. 3D tensor of the spatial distributions of the materials is recovered through 3-mode multiplication of the multi-spectral image tensor and inverse of the matrix of spectral profiles. Tensor representation of the multi-spectral image preserves its local spatial structure that is lost, due to vectorization process, when matrix factorization-based decomposition methods (such as non-negative matrix factorization and independent component analysis) are used. Superior performance of the tensor-based image decomposition over matrix factorization-based decompositions is demonstrated on experimental red-green-blue (RGB) image with known ground truth as well as on RGB fluorescent images of the skin tumor (basal cell carcinoma).

On integrable boundaries in the 2 dimensional O(N) σ-models

NASA Astrophysics Data System (ADS)

Aniceto, Inês; Bajnok, Zoltán; Gombor, Tamás; Kim, Minkyoo; Palla, László

2017-09-01

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) σ-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve.

The application of trigonal curve to the Mikhailov-Shabat-Sokolov flows

NASA Astrophysics Data System (ADS)

He, Guoliang; Geng, Xianguo; Wu, Lihua

2016-08-01

Resorting to the characteristic polynomial of Lax matrix for the Mikhailov-Shabat-Sokolov hierarchy associated with a {3 × 3} matrix spectral problem, we introduce a trigonal curve, from which we deduce the associated Baker-Akhiezer function, meromorphic functions and Dubrovin-type equations. The straightening out of the Mikhailov-Shabat-Sokolov flows is exactly given through the Abel map. On the basis of these results and the theory of trigonal curve, we obtain the explicit theta function representations of the Baker-Akhiezer function, the meromorphic functions, and in particular, that of solutions for the entire Mikhailov-Shabat-Sokolov hierarchy.

Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra.

PubMed

Desbiens, Raphaël; Tremblay, Pierre; Genest, Jérôme; Bouchard, Jean-Pierre

2006-01-20

The instrument line shape (ILS) of a Fourier-transform spectrometer is expressed in a matrix form. For all line shape effects that scale with wavenumber, the ILS matrix is shown to be transposed in the spectral and interferogram domains. The novel representation of the ILS matrix in the interferogram domain yields an insightful physical interpretation of the underlying process producing self-apodization. Working in the interferogram domain circumvents the problem of taking into account the effects of finite optical path difference and permits a proper discretization of the equations. A fast algorithm in O(N log2 N), based on the fractional Fourier transform, is introduced that permits the application of a constant resolving power line shape to theoretical spectra or forward models. The ILS integration formalism is validated with experimental data.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

A novel edge-preserving nonnegative matrix factorization method for spectral unmixing

NASA Astrophysics Data System (ADS)

Bao, Wenxing; Ma, Ruishi

2015-12-01

Spectral unmixing technique is one of the key techniques to identify and classify the material in the hyperspectral image processing. A novel robust spectral unmixing method based on nonnegative matrix factorization(NMF) is presented in this paper. This paper used an edge-preserving function as hypersurface cost function to minimize the nonnegative matrix factorization. To minimize the hypersurface cost function, we constructed the updating functions for signature matrix of end-members and abundance fraction respectively. The two functions are updated alternatively. For evaluation purpose, synthetic data and real data have been used in this paper. Synthetic data is used based on end-members from USGS digital spectral library. AVIRIS Cuprite dataset have been used as real data. The spectral angle distance (SAD) and abundance angle distance(AAD) have been used in this research for assessment the performance of proposed method. The experimental results show that this method can obtain more ideal results and good accuracy for spectral unmixing than present methods.

The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

NASA Technical Reports Server (NTRS)

Haidvogel, D. B.; Zang, T.

1979-01-01

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

Digital techniques for ULF wave polarization analysis

NASA Technical Reports Server (NTRS)

Arthur, C. W.

1979-01-01

Digital power spectral and wave polarization analysis are powerful techniques for studying ULF waves in the earth's magnetosphere. Four different techniques for using the spectral matrix to perform such an analysis have been presented in the literature. Three of these techniques are similar in that they require transformation of the spectral matrix to the principal axis system prior to performing the polarization analysis. The differences in the three techniques lie in the manner in which determine this transformation. A comparative study of these three techniques using both simulated and real data has shown them to be approximately equal in quality of performance. The fourth technique does not require transformation of the spectral matrix. Rather, it uses the measured spectral matrix and state vectors for a desired wave type to design a polarization detector function in the frequency domain. The design of various detector functions and their application to both simulated and real data will be presented.

Peak picking NMR spectral data using non-negative matrix factorization

PubMed Central

2014-01-01

Background Simple peak-picking algorithms, such as those based on lineshape fitting, perform well when peaks are completely resolved in multidimensional NMR spectra, but often produce wrong intensities and frequencies for overlapping peak clusters. For example, NOESY-type spectra have considerable overlaps leading to significant peak-picking intensity errors, which can result in erroneous structural restraints. Precise frequencies are critical for unambiguous resonance assignments. Results To alleviate this problem, a more sophisticated peaks decomposition algorithm, based on non-negative matrix factorization (NMF), was developed. We produce peak shapes from Fourier-transformed NMR spectra. Apart from its main goal of deriving components from spectra and producing peak lists automatically, the NMF approach can also be applied if the positions of some peaks are known a priori, e.g. from consistently referenced spectral dimensions of other experiments. Conclusions Application of the NMF algorithm to a three-dimensional peak list of the 23 kDa bi-domain section of the RcsD protein (RcsD-ABL-HPt, residues 688-890) as well as to synthetic HSQC data shows that peaks can be picked accurately also in spectral regions with strong overlap. PMID:24511909

Spectral Elements Analysis for Viscoelastic Fluids at High Weissenberg Number Using Logarithmic conformation Tensor Model

NASA Astrophysics Data System (ADS)

Jafari, Azadeh; Deville, Michel O.; Fiétier, Nicolas

2008-09-01

This study discusses the capability of the constitutive laws for the matrix logarithm of the conformation tensor (LCT model) within the framework of the spectral elements method. The high Weissenberg number problems (HWNP) usually produce a lack of convergence of the numerical algorithms. Even though the question whether the HWNP is a purely numerical problem or rather a breakdown of the constitutive law of the model has remained somewhat of a mystery, it has been recognized that the selection of an appropriate constitutive equation constitutes a very crucial step although implementing a suitable numerical technique is still important for successful discrete modeling of non-Newtonian flows. The LCT model formulation of the viscoelastic equations originally suggested by Fattal and Kupferman is applied for 2-dimensional (2D) FENE-CR model. The Planar Poiseuille flow is considered as a benchmark problem to test this representation at high Weissenberg number. The numerical results are compared with numerical solution of the standard constitutive equation.

Correction of photoresponse nonuniformity for matrix detectors based on prior compensation for their nonlinear behavior.

PubMed

Ferrero, Alejandro; Campos, Joaquin; Pons, Alicia

2006-04-10

What we believe to be a novel procedure to correct the nonuniformity that is inherent in all matrix detectors has been developed and experimentally validated. This correction method, unlike other nonuniformity-correction algorithms, consists of two steps that separate two of the usual problems that affect characterization of matrix detectors, i.e., nonlinearity and the relative variation of the pixels' responsivity across the array. The correction of the nonlinear behavior remains valid for any illumination wavelength employed, as long as the nonlinearity is not due to power dependence of the internal quantum efficiency. This method of correction of nonuniformity permits the immediate calculation of the correction factor for any given power level and for any illuminant that has a known spectral content once the nonuniform behavior has been characterized for a sufficient number of wavelengths. This procedure has a significant advantage compared with other traditional calibration-based methods, which require that a full characterization be carried out for each spectral distribution pattern of the incident optical radiation. The experimental application of this novel method has achieved a 20-fold increase in the uniformity of a CCD array for response levels close to saturation.

Quasi-periodic solutions to the hierarchy of four-component Toda lattices

NASA Astrophysics Data System (ADS)

Wei, Jiao; Geng, Xianguo; Zeng, Xin

2016-08-01

Starting from a discrete 3×3 matrix spectral problem, the hierarchy of four-component Toda lattices is derived by using the stationary discrete zero-curvature equation. Resorting to the characteristic polynomial of the Lax matrix for the hierarchy, we introduce a trigonal curve Km-2 of genus m - 2 and present the related Baker-Akhiezer function and meromorphic function on it. Asymptotic expansions for the Baker-Akhiezer function and meromorphic function are given near three infinite points on the trigonal curve, from which explicit quasi-periodic solutions for the hierarchy of four-component Toda lattices are obtained in terms of the Riemann theta function.

Spectral Regularization Algorithms for Learning Large Incomplete Matrices.

PubMed

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-03-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 10(6) × 10(6) incomplete matrix with 10(5) observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques.

Spectral Regularization Algorithms for Learning Large Incomplete Matrices

PubMed Central

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-01-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 106 × 106 incomplete matrix with 105 observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques. PMID:21552465

Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution.

PubMed

Han, Fang; Liu, Han

2017-02-01

Correlation matrix plays a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good properties under Gaussian models, its not an effective estimator when facing heavy-tail distributions with possible outliers. As a robust alternative, Han and Liu (2013b) advocated the use of a transformed version of the Kendall's tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall's tau sample correlation matrix and its transformed version proposed in Han and Liu (2013b) for estimating the population Kendall's tau correlation matrix and the latent Pearson's correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of "effective rank" in quantifying the rate of convergence. With regard to the restricted spectral norm, we for the first time present a "sign subgaussian condition" which is sufficient to guarantee that the rank-based correlation matrix estimator attains the optimal rate of convergence. In both cases, we do not need any moment condition.

Design of multivariable feedback control systems via spectral assignment using reduced-order models and reduced-order observers

NASA Technical Reports Server (NTRS)

Mielke, R. R.; Tung, L. J.; Carraway, P. I., III

1984-01-01

The feasibility of using reduced order models and reduced order observers with eigenvalue/eigenvector assignment procedures is investigated. A review of spectral assignment synthesis procedures is presented. Then, a reduced order model which retains essential system characteristics is formulated. A constant state feedback matrix which assigns desired closed loop eigenvalues and approximates specified closed loop eigenvectors is calculated for the reduced order model. It is shown that the eigenvalue and eigenvector assignments made in the reduced order system are retained when the feedback matrix is implemented about the full order system. In addition, those modes and associated eigenvectors which are not included in the reduced order model remain unchanged in the closed loop full order system. The full state feedback design is then implemented by using a reduced order observer. It is shown that the eigenvalue and eigenvector assignments of the closed loop full order system rmain unchanged when a reduced order observer is used. The design procedure is illustrated by an actual design problem.

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

Ferraioli, Luigi; Hueller, Mauro; Vitale, Stefano

The scientific objectives of the LISA Technology Package experiment on board of the LISA Pathfinder mission demand accurate calibration and validation of the data analysis tools in advance of the mission launch. The level of confidence required in the mission outcomes can be reached only by intensively testing the tools on synthetically generated data. A flexible procedure allowing the generation of a cross-correlated stationary noise time series was set up. A multichannel time series with the desired cross-correlation behavior can be generated once a model for a multichannel cross-spectral matrix is provided. The core of the procedure comprises a noisemore » coloring, multichannel filter designed via a frequency-by-frequency eigendecomposition of the model cross-spectral matrix and a subsequent fit in the Z domain. The common problem of initial transients in a filtered time series is solved with a proper initialization of the filter recursion equations. The noise generator performance was tested in a two-dimensional case study of the closed-loop LISA Technology Package dynamics along the two principal degrees of freedom.« less

Design of multivariable feedback control systems via spectral assignment using reduced-order models and reduced-order observers

NASA Technical Reports Server (NTRS)

Mielke, R. R.; Tung, L. J.; Carraway, P. I., III

1985-01-01

The feasibility of using reduced order models and reduced order observers with eigenvalue/eigenvector assignment procedures is investigated. A review of spectral assignment synthesis procedures is presented. Then, a reduced order model which retains essential system characteristics is formulated. A constant state feedback matrix which assigns desired closed loop eigenvalues and approximates specified closed loop eigenvectors is calculated for the reduced order model. It is shown that the eigenvalue and eigenvector assignments made in the reduced order system are retained when the feedback matrix is implemented about the full order system. In addition, those modes and associated eigenvectors which are not included in the reduced order model remain unchanged in the closed loop full order system. The fulll state feedback design is then implemented by using a reduced order observer. It is shown that the eigenvalue and eigenvector assignments of the closed loop full order system remain unchanged when a reduced order observer is used. The design procedure is illustrated by an actual design problem.

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

DOE PAGES

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

2015-11-17

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

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

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

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

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

An adaptive angle-doppler compensation method for airborne bistatic radar based on PAST

NASA Astrophysics Data System (ADS)

Hang, Xu; Jun, Zhao

2018-05-01

Adaptive angle-Doppler compensation method extract the requisite information based on the data itself adaptively, thus avoiding the problem of performance degradation caused by inertia system error. However, this method requires estimation and egiendecomposition of sample covariance matrix, which has a high computational complexity and limits its real-time application. In this paper, an adaptive angle Doppler compensation method based on projection approximation subspace tracking (PAST) is studied. The method uses cyclic iterative processing to quickly estimate the positions of the spectral center of the maximum eigenvector of each range cell, and the computational burden of matrix estimation and eigen-decompositon is avoided, and then the spectral centers of all range cells is overlapped by two dimensional compensation. Simulation results show the proposed method can effectively reduce the no homogeneity of airborne bistatic radar, and its performance is similar to that of egien-decomposition algorithms, but the computation load is obviously reduced and easy to be realized.

Laser desorption/ionization mass spectrometry for direct profiling and imaging of small molecules from raw biological materials

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

Cha, Sangwon

2008-01-01

Matrix-assisted laser desorption/ionization(MALDI) mass spectrometry(MS) has been widely used for analysis of biological molecules, especially macromolecules such as proteins. However, MALDI MS has a problem in small molecule (less than 1 kDa) analysis because of the signal saturation by organic matrixes in the low mass region. In imaging MS (IMS), inhomogeneous surface formation due to the co-crystallization process by organic MALDI matrixes limits the spatial resolution of the mass spectral image. Therefore, to make laser desorption/ionization (LDI) MS more suitable for mass spectral profiling and imaging of small molecules directly from raw biological tissues, LDI MS protocols with various alternativemore » assisting materials were developed and applied to many biological systems of interest. Colloidal graphite was used as a matrix for IMS of small molecules for the first time and methodologies for analyses of small metabolites in rat brain tissues, fruits, and plant tissues were developed. With rat brain tissues, the signal enhancement for cerebroside species by colloidal graphite was observed and images of cerebrosides were successfully generated by IMS. In addition, separation of isobaric lipid ions was performed by imaging tandem MS. Directly from Arabidopsis flowers, flavonoids were successfully profiled and heterogeneous distribution of flavonoids in petals was observed for the first time by graphite-assisted LDI(GALDI) IMS.« less

Spectral functions of strongly correlated extended systems via an exact quantum embedding

NASA Astrophysics Data System (ADS)

Booth, George H.; Chan, Garnet Kin-Lic

2015-04-01

Density matrix embedding theory (DMET) [Phys. Rev. Lett. 109, 186404 (2012), 10.1103/PhysRevLett.109.186404], introduced an approach to quantum cluster embedding methods whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath states was rigorously formulated to exactly reproduce the entanglement of the ground state. The formalism provided similar physics to dynamical mean-field theory at a tiny fraction of the cost but was inherently limited by the construction of a bath designed to reproduce ground-state, static properties. Here, we generalize the concept of quantum embedding to dynamic properties and demonstrate accurate bulk spectral functions at similarly small computational cost. The proposed spectral DMET utilizes the Schmidt decomposition of a response vector, mapping the bulk dynamic correlation functions to that of a quantum impurity cluster coupled to a set of frequency-dependent bath states. The resultant spectral functions are obtained on the real-frequency axis, without bath discretization error, and allows for the construction of arbitrary dynamic correlation functions. We demonstrate the method on the one- (1D) and two-dimensional (2D) Hubbard model, where we obtain zero temperature and thermodynamic limit spectral functions, and show the trivial extension to two-particle Green's functions. This advance therefore extends the scope and applicability of DMET in condensed-matter problems as a computationally tractable route to correlated spectral functions of extended systems and provides a competitive alternative to dynamical mean-field theory for dynamic quantities.

FEL-FTIR spectroscopy of matrix-isolated formic acid

NASA Astrophysics Data System (ADS)

Henderson, Don O.; Mu, Richard; Silberman, Enrique; Berryman, Kenneth W.; Rella, Chris W.

1994-07-01

Infrared spectral hole burning studies have provided a wealth of information concerning site reorientation of defects in solids and vibrational relaxation dynamics. The most investigated systems appear to be impurities trapped in alkali halides. Limited studies on molecules trapped in noble gas matrices have demonstrated that these systems are good candidates for investigating persistent spectral holes. However, most infrared spectral hole burning studies have been limited by the tunability of commercially available infrared lasers which in turn restricts the spectral feature which can be burned. On the other hand, the tunability of Infrared Free Electron Lasers (IR-FELs) allows for targeting radiation into vibrational of the molecular system under study. We have used the Free Electron Laser-Fourier Transform Infrared Spectroscopy to investigate infrared hole burning of formic acid (HCOOD) isolated in an Ar matrix at a matrix/sample ratio of 4000/1. The results of the FEL radiation tuned to v2 mode of HCOOD are discussed together with matrix induced frequency shifts and matrix induced band splittings.

A space-time lower-upper symmetric Gauss-Seidel scheme for the time-spectral method

NASA Astrophysics Data System (ADS)

Zhan, Lei; Xiong, Juntao; Liu, Feng

2016-05-01

The time-spectral method (TSM) offers the advantage of increased order of accuracy compared to methods using finite-difference in time for periodic unsteady flow problems. Explicit Runge-Kutta pseudo-time marching and implicit schemes have been developed to solve iteratively the space-time coupled nonlinear equations resulting from TSM. Convergence of the explicit schemes is slow because of the stringent time-step limit. Many implicit methods have been developed for TSM. Their computational efficiency is, however, still limited in practice because of delayed implicit temporal coupling, multiple iterative loops, costly matrix operations, or lack of strong diagonal dominance of the implicit operator matrix. To overcome these shortcomings, an efficient space-time lower-upper symmetric Gauss-Seidel (ST-LU-SGS) implicit scheme with multigrid acceleration is presented. In this scheme, the implicit temporal coupling term is split as one additional dimension of space in the LU-SGS sweeps. To improve numerical stability for periodic flows with high frequency, a modification to the ST-LU-SGS scheme is proposed. Numerical results show that fast convergence is achieved using large or even infinite Courant-Friedrichs-Lewy (CFL) numbers for unsteady flow problems with moderately high frequency and with the use of moderately high numbers of time intervals. The ST-LU-SGS implicit scheme is also found to work well in calculating periodic flow problems where the frequency is not known a priori and needed to be determined by using a combined Fourier analysis and gradient-based search algorithm.

The Hölder continuity of spectral measures of an extended CMV matrix

NASA Astrophysics Data System (ADS)

Munger, Paul E.; Ong, Darren C.

2014-09-01

We prove results about the Hölder continuity of the spectral measures of the extended CMV matrix, given power law bounds of the solution of the eigenvalue equation. We thus arrive at a unitary analogue of the results of Damanik, Killip, and Lenz ["Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity," Commun. Math. Phys. 212, 191-204 (2000)] about the spectral measure of the discrete Schrödinger operator.

The Hölder continuity of spectral measures of an extended CMV matrix.

PubMed

Munger, Paul E; Ong, Darren C

2014-09-01

We prove results about the Hölder continuity of the spectral measures of the extended CMV matrix, given power law bounds of the solution of the eigenvalue equation. We thus arrive at a unitary analogue of the results of Damanik, Killip, and Lenz ["Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity," Commun. Math. Phys.55, 191-204 (2000)] about the spectral measure of the discrete Schrödinger operator.

Quantum spectral curve for ( q, t)-matrix model

NASA Astrophysics Data System (ADS)

Zenkevich, Yegor

2018-02-01

We derive quantum spectral curve equation for ( q, t)-matrix model, which turns out to be a certain difference equation. We show that in Nekrasov-Shatashvili limit this equation reproduces the Baxter TQ equation for the quantum XXZ spin chain. This chain is spectral dual to the Seiberg-Witten integrable system associated with the AGT dual gauge theory.

Quasi-periodic Solutions of the Kaup-Kupershmidt Hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Wu, Lihua; He, Guoliang

2013-08-01

Based on solving the Lenard recursion equations and the zero-curvature equation, we derive the Kaup-Kupershmidt hierarchy associated with a 3×3 matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix for the Kaup-Kupershmidt hierarchy, we introduce a trigonal curve {K}_{m-1} and present the corresponding Baker-Akhiezer function and meromorphic function on it. The Abel map is introduced to straighten out the Kaup-Kupershmidt flows. With the aid of the properties of the Baker-Akhiezer function and the meromorphic function and their asymptotic expansions, we arrive at their explicit Riemann theta function representations. The Riemann-Jacobi inversion problem is achieved by comparing the asymptotic expansion of the Baker-Akhiezer function and its Riemann theta function representation, from which quasi-periodic solutions of the entire Kaup-Kupershmidt hierarchy are obtained in terms of the Riemann theta functions.

Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution

PubMed Central

Han, Fang; Liu, Han

2016-01-01

Correlation matrix plays a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson’s sample correlation matrix. Although Pearson’s sample correlation matrix enjoys various good properties under Gaussian models, its not an effective estimator when facing heavy-tail distributions with possible outliers. As a robust alternative, Han and Liu (2013b) advocated the use of a transformed version of the Kendall’s tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall’s tau sample correlation matrix and its transformed version proposed in Han and Liu (2013b) for estimating the population Kendall’s tau correlation matrix and the latent Pearson’s correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of “effective rank” in quantifying the rate of convergence. With regard to the restricted spectral norm, we for the first time present a “sign subgaussian condition” which is sufficient to guarantee that the rank-based correlation matrix estimator attains the optimal rate of convergence. In both cases, we do not need any moment condition. PMID:28337068

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

High-precision solution to the moving load problem using an improved spectral element method

NASA Astrophysics Data System (ADS)

Wen, Shu-Rui; Wu, Zhi-Jing; Lu, Nian-Li

2018-02-01

In this paper, the spectral element method (SEM) is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem. In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases. Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.

A hierarchy of generalized Jaulent-Miodek equations and their explicit solutions

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Guan, Liang; Xue, Bo

A hierarchy of generalized Jaulent-Miodek (JM) equations related to a new spectral problem with energy-dependent potentials is proposed. Depending on the Lax matrix and elliptic variables, the generalized JM hierarchy is decomposed into two systems of solvable ordinary differential equations. Explicit theta function representations of the meromorphic function and the Baker-Akhiezer function are constructed, the solutions of the hierarchy are obtained based on the theory of algebraic curves.

Multiway spectral community detection in networks

NASA Astrophysics Data System (ADS)

Zhang, Xiao; Newman, M. E. J.

2015-11-01

One of the most widely used methods for community detection in networks is the maximization of the quality function known as modularity. Of the many maximization techniques that have been used in this context, some of the most conceptually attractive are the spectral methods, which are based on the eigenvectors of the modularity matrix. Spectral algorithms have, however, been limited, by and large, to the division of networks into only two or three communities, with divisions into more than three being achieved by repeated two-way division. Here we present a spectral algorithm that can directly divide a network into any number of communities. The algorithm makes use of a mapping from modularity maximization to a vector partitioning problem, combined with a fast heuristic for vector partitioning. We compare the performance of this spectral algorithm with previous approaches and find it to give superior results, particularly in cases where community sizes are unbalanced. We also give demonstrative applications of the algorithm to two real-world networks and find that it produces results in good agreement with expectations for the networks studied.

Quasi-periodic solutions of the Belov-Chaltikian lattice hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Zeng, Xin

Utilizing the characteristic polynomial of Lax matrix for the Belov-Chaltikian (BC) lattice hierarchy associated with a 3 × 3 discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker-Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.

Random matrix approach to plasmon resonances in the random impedance network model of disordered nanocomposites

NASA Astrophysics Data System (ADS)

Olekhno, N. A.; Beltukov, Y. M.

2018-05-01

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric and other two-component nanocomposites. In the present work, the spectral properties of resonances in random networks are studied within the framework of the random matrix theory. We have shown that the appropriate ensemble of random matrices for the considered problem is the Jacobi ensemble (the MANOVA ensemble). The obtained analytical expressions for the density of states in such resonant networks show a good agreement with the results of numerical simulations in a wide range of metal filling fractions 0

Euclidean commute time distance embedding and its application to spectral anomaly detection

NASA Astrophysics Data System (ADS)

Albano, James A.; Messinger, David W.

2012-06-01

Spectral image analysis problems often begin by performing a preprocessing step composed of applying a transformation that generates an alternative representation of the spectral data. In this paper, a transformation based on a Markov-chain model of a random walk on a graph is introduced. More precisely, we quantify the random walk using a quantity known as the average commute time distance and find a nonlinear transformation that embeds the nodes of a graph in a Euclidean space where the separation between them is equal to the square root of this quantity. This has been referred to as the Commute Time Distance (CTD) transformation and it has the important characteristic of increasing when the number of paths between two nodes decreases and/or the lengths of those paths increase. Remarkably, a closed form solution exists for computing the average commute time distance that avoids running an iterative process and is found by simply performing an eigendecomposition on the graph Laplacian matrix. Contained in this paper is a discussion of the particular graph constructed on the spectral data for which the commute time distance is then calculated from, an introduction of some important properties of the graph Laplacian matrix, and a subspace projection that approximately preserves the maximal variance of the square root commute time distance. Finally, RX anomaly detection and Topological Anomaly Detection (TAD) algorithms will be applied to the CTD subspace followed by a discussion of their results.

CO2 in solid para-hydrogen: spectral splitting and the CO2···(o-H2)n clusters.

PubMed

Du, Jun-He; Wan, Lei; Wu, Lei; Xu, Gang; Deng, Wen-Ping; Liu, An-Wen; Chen, Yang; Hu, Shui-Ming

2011-02-17

Complicated high-resolution spectral structures are often observed for molecules doped in solid molecular hydrogen. The structures can result from miscellaneous effects and are often interpreted differently in references. The spectrum of the ν(3) band of CO(2) in solid para-H(2) presents a model system which exhibits rich spectral structures. With the help of the potential energy simulation of the CO(2) molecule doped in para-hydrogen matrix, and extensive experiments with different CO(2) isotopologues and different ortho-hydrogen concentrations in the matrix, the spectral features observed in p-H(2) matrix are assigned to the CO(2)···(o-H(2))(n) clusters and also to energy level splitting that is due to different alignments of the doped CO(2) molecules in the matrix. The assignments are further supported by the dynamics analysis and also by the spectrum recorded with sample codoped with O(2) which serves as catalyst transferring o-H(2) to p-H(2) in the matrix at 4 K temperature. The observed spectral features of CO(2)/pH(2) can potentially be used as an alternative readout of the temperature and orthohydrogen concentration in the solid para-hydrogen.

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

NASA Astrophysics Data System (ADS)

Liu, X.; Banerjee, J. R.

2017-03-01

A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

Lanczos algorithm with matrix product states for dynamical correlation functions

NASA Astrophysics Data System (ADS)

Dargel, P. E.; Wöllert, A.; Honecker, A.; McCulloch, I. P.; Schollwöck, U.; Pruschke, T.

2012-05-01

The density-matrix renormalization group (DMRG) algorithm can be adapted to the calculation of dynamical correlation functions in various ways which all represent compromises between computational efficiency and physical accuracy. In this paper we reconsider the oldest approach based on a suitable Lanczos-generated approximate basis and implement it using matrix product states (MPS) for the representation of the basis states. The direct use of matrix product states combined with an ex post reorthogonalization method allows us to avoid several shortcomings of the original approach, namely the multitargeting and the approximate representation of the Hamiltonian inherent in earlier Lanczos-method implementations in the DMRG framework, and to deal with the ghost problem of Lanczos methods, leading to a much better convergence of the spectral weights and poles. We present results for the dynamic spin structure factor of the spin-1/2 antiferromagnetic Heisenberg chain. A comparison to Bethe ansatz results in the thermodynamic limit reveals that the MPS-based Lanczos approach is much more accurate than earlier approaches at minor additional numerical cost.

Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform.

PubMed

Kannan, R; Ievlev, A V; Laanait, N; Ziatdinov, M A; Vasudevan, R K; Jesse, S; Kalinin, S V

2018-01-01

Many spectral responses in materials science, physics, and chemistry experiments can be characterized as resulting from the superposition of a number of more basic individual spectra. In this context, unmixing is defined as the problem of determining the individual spectra, given measurements of multiple spectra that are spatially resolved across samples, as well as the determination of the corresponding abundance maps indicating the local weighting of each individual spectrum. Matrix factorization is a popular linear unmixing technique that considers that the mixture model between the individual spectra and the spatial maps is linear. Here, we present a tutorial paper targeted at domain scientists to introduce linear unmixing techniques, to facilitate greater understanding of spectroscopic imaging data. We detail a matrix factorization framework that can incorporate different domain information through various parameters of the matrix factorization method. We demonstrate many domain-specific examples to explain the expressivity of the matrix factorization framework and show how the appropriate use of domain-specific constraints such as non-negativity and sum-to-one abundance result in physically meaningful spectral decompositions that are more readily interpretable. Our aim is not only to explain the off-the-shelf available tools, but to add additional constraints when ready-made algorithms are unavailable for the task. All examples use the scalable open source implementation from https://github.com/ramkikannan/nmflibrary that can run from small laptops to supercomputers, creating a user-wide platform for rapid dissemination and adoption across scientific disciplines.

CHARACTERIZATION OF CRYPTOSPORIDIUM PARVUM BY MATRIX-ASSISTED LASER DESORPTION -- IONIZATION TIME OF FLIGHT MASS SPECTROMETRY

EPA Science Inventory

Matrix assisted laser desorption/ionization (MALDI) mass spectrometry was used to investigate whole and freeze thawed Cryptosporidium parvum oocysts. Whole oocysts revealed some mass spectral features. Reproducible patterns of spectral markers and increased sensitivity were obtai...

Characterization of Cryptosporidium parvum by Matrix-Assisted Laser Desorption Ionization–Time of Flight Mass Spectrometry

PubMed Central

Magnuson, Matthew L.; Owens, James H.; Kelty, Catherine A.

2000-01-01

Matrix-assisted laser desorption ionization–time of flight mass spectrometry (MALDI-TOF MS) was used to investigate whole and freeze-thawed Cryptosporidium parvum oocysts. Whole oocysts revealed some mass spectral features. Reproducible patterns of spectral markers and increased sensitivity were obtained after the oocysts were lysed with a freeze-thaw procedure. Spectral-marker patterns for C. parvum were distinguishable from those obtained for Cryptosporidium muris. One spectral marker appears specific for the genus, while others appear specific at the species level. Three different C. parvum lots were investigated, and similar spectral markers were observed in each. Disinfection of the oocysts reduced and/or eliminated the patterns of spectral markers. PMID:11055915

Relativistic elliptic matrix tops and finite Fourier transformations

NASA Astrophysics Data System (ADS)

Zotov, A.

2017-10-01

We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the “off-shell” Lax pairs, which do not satisfy the Lax equations in general case but become true Lax pairs under various conditions (reductions). At the level of the off-shell Lax matrix, there is a natural symmetry between the spectral parameter z and relativistic parameter η. It is generated by the finite Fourier transformation, which we describe in detail. The symmetry allows one to consider z and η on an equal footing. Depending on the type of integrable reduction, any of the parameters can be chosen to be the spectral one. Then another one is the relativistic deformation parameter. As a by-product, we describe the model of N2 interacting GL(M) matrix tops and/or M2 interacting GL(N) matrix tops depending on a choice of the spectral parameter.

An improved pulse coupled neural network with spectral residual for infrared pedestrian segmentation

NASA Astrophysics Data System (ADS)

He, Fuliang; Guo, Yongcai; Gao, Chao

2017-12-01

Pulse coupled neural network (PCNN) has become a significant tool for the infrared pedestrian segmentation, and a variety of relevant methods have been developed at present. However, these existing models commonly have several problems of the poor adaptability of infrared noise, the inaccuracy of segmentation results, and the fairly complex determination of parameters in current methods. This paper presents an improved PCNN model that integrates the simplified framework and spectral residual to alleviate the above problem. In this model, firstly, the weight matrix of the feeding input field is designed by the anisotropic Gaussian kernels (ANGKs), in order to suppress the infrared noise effectively. Secondly, the normalized spectral residual saliency is introduced as linking coefficient to enhance the edges and structural characteristics of segmented pedestrians remarkably. Finally, the improved dynamic threshold based on the average gray values of the iterative segmentation is employed to simplify the original PCNN model. Experiments on the IEEE OTCBVS benchmark and the infrared pedestrian image database built by our laboratory, demonstrate that the superiority of both subjective visual effects and objective quantitative evaluations in information differences and segmentation errors in our model, compared with other classic segmentation methods.

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

NASA Astrophysics Data System (ADS)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Map-invariant spectral analysis for the identification of DNA periodicities

PubMed Central

2012-01-01

Many signal processing based methods for finding hidden periodicities in DNA sequences have primarily focused on assigning numerical values to the symbolic DNA sequence and then applying spectral analysis tools such as the short-time discrete Fourier transform (ST-DFT) to locate these repeats. The key results pertaining to this approach are however obtained using a very specific symbolic to numerical map, namely the so-called Voss representation. An important research problem is to therefore quantify the sensitivity of these results to the choice of the symbolic to numerical map. In this article, a novel algebraic approach to the periodicity detection problem is presented and provides a natural framework for studying the role of the symbolic to numerical map in finding these repeats. More specifically, we derive a new matrix-based expression of the DNA spectrum that comprises most of the widely used mappings in the literature as special cases, shows that the DNA spectrum is in fact invariable under all these mappings, and generates a necessary and sufficient condition for the invariance of the DNA spectrum to the symbolic to numerical map. Furthermore, the new algebraic framework decomposes the periodicity detection problem into several fundamental building blocks that are totally independent of each other. Sophisticated digital filters and/or alternate fast data transforms such as the discrete cosine and sine transforms can therefore be always incorporated in the periodicity detection scheme regardless of the choice of the symbolic to numerical map. Although the newly proposed framework is matrix based, identification of these periodicities can be achieved at a low computational cost. PMID:23067324

A Comparative Study of Pairwise Learning Methods Based on Kernel Ridge Regression.

PubMed

Stock, Michiel; Pahikkala, Tapio; Airola, Antti; De Baets, Bernard; Waegeman, Willem

2018-06-12

Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction, or network inference problems. During the past decade, kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their behavior has been underexplored in the machine learning literature. In this work we review and unify kernel-based algorithms that are commonly used in different pairwise learning settings, ranging from matrix filtering to zero-shot learning. To this end, we focus on closed-form efficient instantiations of Kronecker kernel ridge regression. We show that independent task kernel ridge regression, two-step kernel ridge regression, and a linear matrix filter arise naturally as a special case of Kronecker kernel ridge regression, implying that all these methods implicitly minimize a squared loss. In addition, we analyze universality, consistency, and spectral filtering properties. Our theoretical results provide valuable insights into assessing the advantages and limitations of existing pairwise learning methods.

The spectral applications of Beer-Lambert law for some biological and dosimetric materials

NASA Astrophysics Data System (ADS)

Içelli, Orhan; Yalçin, Zeynel; Karakaya, Vatan; Ilgaz, Işıl P.

2014-08-01

The aim of this study is to conduct quantitative and qualitative analysis of biological and dosimetric materials which contain organic and inorganic materials and to make the determination by using the spectral theorem Beer-Lambert law. Beer-Lambert law is a system of linear equations for the spectral theory. It is possible to solve linear equations with a non-zero coefficient matrix determinant forming linear equations. Characteristic matrix of the linear equation with zero determinant is called point spectrum at the spectral theory.

Coherent mode decomposition using mixed Wigner functions of Hermite-Gaussian beams.

PubMed

Tanaka, Takashi

2017-04-15

A new method of coherent mode decomposition (CMD) is proposed that is based on a Wigner-function representation of Hermite-Gaussian beams. In contrast to the well-known method using the cross spectral density (CSD), it directly determines the mode functions and their weights without solving the eigenvalue problem. This facilitates the CMD of partially coherent light whose Wigner functions (and thus CSDs) are not separable, in which case the conventional CMD requires solving an eigenvalue problem with a large matrix and thus is numerically formidable. An example is shown regarding the CMD of synchrotron radiation, one of the most important applications of the proposed method.

Joint spatial-spectral hyperspectral image clustering using block-diagonal amplified affinity matrix

NASA Astrophysics Data System (ADS)

Fan, Lei; Messinger, David W.

2018-03-01

The large number of spectral channels in a hyperspectral image (HSI) produces a fine spectral resolution to differentiate between materials in a scene. However, difficult classes that have similar spectral signatures are often confused while merely exploiting information in the spectral domain. Therefore, in addition to spectral characteristics, the spatial relationships inherent in HSIs should also be considered for incorporation into classifiers. The growing availability of high spectral and spatial resolution of remote sensors provides rich information for image clustering. Besides the discriminating power in the rich spectrum, contextual information can be extracted from the spatial domain, such as the size and the shape of the structure to which one pixel belongs. In recent years, spectral clustering has gained popularity compared to other clustering methods due to the difficulty of accurate statistical modeling of data in high dimensional space. The joint spatial-spectral information could be effectively incorporated into the proximity graph for spectral clustering approach, which provides a better data representation by discovering the inherent lower dimensionality from the input space. We embedded both spectral and spatial information into our proposed local density adaptive affinity matrix, which is able to handle multiscale data by automatically selecting the scale of analysis for every pixel according to its neighborhood of the correlated pixels. Furthermore, we explored the "conductivity method," which aims at amplifying the block diagonal structure of the affinity matrix to further improve the performance of spectral clustering on HSI datasets.

Intrinsic fluorescence excitation-emission matrix spectral features of cottonseed protein fractions and the effects of denaturants

USDA-ARS?s Scientific Manuscript database

To better understand the functional and physicochemical properties of cottonseed protein, we investigated the intrinsic fluorescence excitation-emission matrix (EEM) spectral features of cottonseed protein isolate (CSPI) and sequentially extracted water (CSPw) and alkali (CSPa) protein fractions, an...

Analysis of Spectral Features of Seawaterbiooptical Components Fluorescence from the Excitation-emission Matrix

NASA Astrophysics Data System (ADS)

Salyuk, P. A.; Nagorny, I. G.

The paper presents the method for processing of excitation-emission matrix of sea water and the allocation of the spectral characteristics of different types of colored dissolved organic matter (CDOM) and phytoplankton cells in seawater. The method consists of identification of regularly observed fluorescence peaks of CDOM in marine waters of different type and definition of the spectral ranges, where the predominant influence of these peaks are observed.

On the cross-stream spectral method for the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Zorumski, William E.; Hodge, Steven L.

1993-01-01

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

A seismic coherency method using spectral amplitudes

NASA Astrophysics Data System (ADS)

Sui, Jing-Kun; Zheng, Xiao-Dong; Li, Yan-Dong

2015-09-01

Seismic coherence is used to detect discontinuities in underground media. However, strata with steeply dipping structures often produce false low coherence estimates and thus incorrect discontinuity characterization results. It is important to eliminate or reduce the effect of dipping on coherence estimates. To solve this problem, time-domain dip scanning is typically used to improve estimation of coherence in areas with steeply dipping structures. However, the accuracy of the time-domain estimation of dip is limited by the sampling interval. In contrast, the spectrum amplitude is not affected by the time delays in adjacent seismic traces caused by dipping structures. We propose a coherency algorithm that uses the spectral amplitudes of seismic traces within a predefined analysis window to construct the covariance matrix. The coherency estimates with the proposed algorithm is defined as the ratio between the dominant eigenvalue and the sum of all eigenvalues of the constructed covariance matrix. Thus, we eliminate the effect of dipping structures on coherency estimates. In addition, because different frequency bands of spectral amplitudes are used to estimate coherency, the proposed algorithm has multiscale features. Low frequencies are effective for characterizing large-scale faults, whereas high frequencies are better in characterizing small-scale faults. Application to synthetic and real seismic data show that the proposed algorithm can eliminate the effect of dip and produce better coherence estimates than conventional coherency algorithms in areas with steeply dipping structures.

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

PubMed Central

Wen, Xiaotong; Rangarajan, Govindan; Ding, Mingzhou

2013-01-01

Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix. PMID:23858479

Constrained low-rank matrix estimation: phase transitions, approximate message passing and applications

NASA Astrophysics Data System (ADS)

Lesieur, Thibault; Krzakala, Florent; Zdeborová, Lenka

2017-07-01

This article is an extended version of previous work of Lesieur et al (2015 IEEE Int. Symp. on Information Theory Proc. pp 1635-9 and 2015 53rd Annual Allerton Conf. on Communication, Control and Computing (IEEE) pp 680-7) on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic methods used in data analysis for unsupervised learning of relevant features and other types of dimensionality reduction. We present a framework to study the constrained low-rank matrix estimation for a general prior on the factors, and a general output channel through which the matrix is observed. We draw a parallel with the study of vector-spin glass models—presenting a unifying way to study a number of problems considered previously in separate statistical physics works. We present a number of applications for the problem in data analysis. We derive in detail a general form of the low-rank approximate message passing (Low-RAMP) algorithm, that is known in statistical physics as the TAP equations. We thus unify the derivation of the TAP equations for models as different as the Sherrington-Kirkpatrick model, the restricted Boltzmann machine, the Hopfield model or vector (xy, Heisenberg and other) spin glasses. The state evolution of the Low-RAMP algorithm is also derived, and is equivalent to the replica symmetric solution for the large class of vector-spin glass models. In the section devoted to result we study in detail phase diagrams and phase transitions for the Bayes-optimal inference in low-rank matrix estimation. We present a typology of phase transitions and their relation to performance of algorithms such as the Low-RAMP or commonly used spectral methods.

Ranking and combining multiple predictors without labeled data

PubMed Central

Parisi, Fabio; Strino, Francesco; Nadler, Boaz; Kluger, Yuval

2014-01-01

In a broad range of classification and decision-making problems, one is given the advice or predictions of several classifiers, of unknown reliability, over multiple questions or queries. This scenario is different from the standard supervised setting, where each classifier’s accuracy can be assessed using available labeled data, and raises two questions: Given only the predictions of several classifiers over a large set of unlabeled test data, is it possible to (i) reliably rank them and (ii) construct a metaclassifier more accurate than most classifiers in the ensemble? Here we present a spectral approach to address these questions. First, assuming conditional independence between classifiers, we show that the off-diagonal entries of their covariance matrix correspond to a rank-one matrix. Moreover, the classifiers can be ranked using the leading eigenvector of this covariance matrix, because its entries are proportional to their balanced accuracies. Second, via a linear approximation to the maximum likelihood estimator, we derive the Spectral Meta-Learner (SML), an unsupervised ensemble classifier whose weights are equal to these eigenvector entries. On both simulated and real data, SML typically achieves a higher accuracy than most classifiers in the ensemble and can provide a better starting point than majority voting for estimating the maximum likelihood solution. Furthermore, SML is robust to the presence of small malicious groups of classifiers designed to veer the ensemble prediction away from the (unknown) ground truth. PMID:24474744

Theoretical study on electronic excitation spectra: A matrix form of numerical algorithm for spectral shift

NASA Astrophysics Data System (ADS)

Ming, Mei-Jun; Xu, Long-Kun; Wang, Fan; Bi, Ting-Jun; Li, Xiang-Yuan

2017-07-01

In this work, a matrix form of numerical algorithm for spectral shift is presented based on the novel nonequilibrium solvation model that is established by introducing the constrained equilibrium manipulation. This form is convenient for the development of codes for numerical solution. By means of the integral equation formulation polarizable continuum model (IEF-PCM), a subroutine has been implemented to compute spectral shift numerically. Here, the spectral shifts of absorption spectra for several popular chromophores, N,N-diethyl-p-nitroaniline (DEPNA), methylenecyclopropene (MCP), acrolein (ACL) and p-nitroaniline (PNA) were investigated in different solvents with various polarities. The computed spectral shifts can explain the available experimental findings reasonably. Discussions were made on the contributions of solute geometry distortion, electrostatic polarization and other non-electrostatic interactions to spectral shift.

Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix

PubMed Central

Andreoli, Daria; Volpe, Giorgio; Popoff, Sébastien; Katz, Ori; Grésillon, Samuel; Gigan, Sylvain

2015-01-01

We present a method to measure the spectrally-resolved transmission matrix of a multiply scattering medium, thus allowing for the deterministic spatiospectral control of a broadband light source by means of wavefront shaping. As a demonstration, we show how the medium can be used to selectively focus one or many spectral components of a femtosecond pulse, and how it can be turned into a controllable dispersive optical element to spatially separate different spectral components to arbitrary positions. PMID:25965944

Invertible flexible matrices

NASA Astrophysics Data System (ADS)

Justino, Júlia

2017-06-01

Matrices with coefficients having uncertainties of type o (.) or O (.), called flexible matrices, are studied from the point of view of nonstandard analysis. The uncertainties of the afore-mentioned kind will be given in the form of the so-called neutrices, for instance the set of all infinitesimals. Since flexible matrices have uncertainties in their coefficients, it is not possible to define the identity matrix in an unique way and so the notion of spectral identity matrix arises. Not all nonsingular flexible matrices can be turned into a spectral identity matrix using Gauss-Jordan elimination method, implying that that not all nonsingular flexible matrices have the inverse matrix. Under certain conditions upon the size of the uncertainties appearing in a nonsingular flexible matrix, a general theorem concerning the boundaries of its minors is presented which guarantees the existence of the inverse matrix of a nonsingular flexible matrix.

Advantages of soft versus hard constraints in self-modeling curve resolution problems. Penalty alternating least squares (P-ALS) extension to multi-way problems.

PubMed

Richards, Selena; Miller, Robert; Gemperline, Paul

2008-02-01

An extension to the penalty alternating least squares (P-ALS) method, called multi-way penalty alternating least squares (NWAY P-ALS), is presented. Optionally, hard constraints (no deviation from predefined constraints) or soft constraints (small deviations from predefined constraints) were applied through the application of a row-wise penalty least squares function. NWAY P-ALS was applied to the multi-batch near-infrared (NIR) data acquired from the base catalyzed esterification reaction of acetic anhydride in order to resolve the concentration and spectral profiles of l-butanol with the reaction constituents. Application of the NWAY P-ALS approach resulted in the reduction of the number of active constraints at the solution point, while the batch column-wise augmentation allowed hard constraints in the spectral profiles and resolved rank deficiency problems of the measurement matrix. The results were compared with the multi-way multivariate curve resolution (MCR)-ALS results using hard and soft constraints to determine whether any advantages had been gained through using the weighted least squares function of NWAY P-ALS over the MCR-ALS resolution.

Verification of unfold error estimates in the unfold operator code

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

Fehl, D.L.; Biggs, F.

Spectral unfolding is an inverse mathematical operation that attempts to obtain spectral source information from a set of response functions and data measurements. Several unfold algorithms have appeared over the past 30 years; among them is the unfold operator (UFO) code written at Sandia National Laboratories. In addition to an unfolded spectrum, the UFO code also estimates the unfold uncertainty (error) induced by estimated random uncertainties in the data. In UFO the unfold uncertainty is obtained from the error matrix. This built-in estimate has now been compared to error estimates obtained by running the code in a Monte Carlo fashionmore » with prescribed data distributions (Gaussian deviates). In the test problem studied, data were simulated from an arbitrarily chosen blackbody spectrum (10 keV) and a set of overlapping response functions. The data were assumed to have an imprecision of 5{percent} (standard deviation). One hundred random data sets were generated. The built-in estimate of unfold uncertainty agreed with the Monte Carlo estimate to within the statistical resolution of this relatively small sample size (95{percent} confidence level). A possible 10{percent} bias between the two methods was unresolved. The Monte Carlo technique is also useful in underdetermined problems, for which the error matrix method does not apply. UFO has been applied to the diagnosis of low energy x rays emitted by Z-pinch and ion-beam driven hohlraums. {copyright} {ital 1997 American Institute of Physics.}« less

Pan-sharpening algorithm to remove thin cloud via mask dodging and nonsampled shift-invariant shearlet transform

NASA Astrophysics Data System (ADS)

Shi, Cheng; Liu, Fang; Li, Ling-Ling; Hao, Hong-Xia

2014-01-01

The goal of pan-sharpening is to get an image with higher spatial resolution and better spectral information. However, the resolution of the pan-sharpened image is seriously affected by the thin clouds. For a single image, filtering algorithms are widely used to remove clouds. These kinds of methods can remove clouds effectively, but the detail lost in the cloud removal image is also serious. To solve this problem, a pan-sharpening algorithm to remove thin cloud via mask dodging and nonsampled shift-invariant shearlet transform (NSST) is proposed. For the low-resolution multispectral (LR MS) and high-resolution panchromatic images with thin clouds, a mask dodging method is used to remove clouds. For the cloud removal LR MS image, an adaptive principal component analysis transform is proposed to balance the spectral information and spatial resolution in the pan-sharpened image. Since the clouds removal process causes the detail loss problem, a weight matrix is designed to enhance the details of the cloud regions in the pan-sharpening process, but noncloud regions remain unchanged. And the details of the image are obtained by NSST. Experimental results over visible and evaluation metrics demonstrate that the proposed method can keep better spectral information and spatial resolution, especially for the images with thin clouds.

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

PubMed

Mohr, Stephan; Dawson, William; Wagner, Michael; Caliste, Damien; Nakajima, Takahito; Genovese, Luigi

2017-10-10

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

Verifying the Presence of Low Levels of Neptunium in a Uranium Matrix with Electron Energy-Loss Spectroscopy

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

Buck, Edgar C.; Douglas, Matthew; Wittman, Richard S.

2010-01-01

This paper examines the problems associated with the analysis of low levels of neptunium (Np) in a uranium (U) matrix with electron energy-loss spectroscopy (EELS) on the transmission electron microscope (TEM). The detection of Np in a matrix of uranium (U) can be impeded by the occurrence of a plural scattering event from U (U-M5 + U-O4,5) that results in severe overlap on the Np-M5 edge at 3665 eV. Low levels (1600 - 6300 ppm) of Np can be detected in U solids by confirming the energy gap between the Np-M5 and Np-M4 edges is at 184 eV and showingmore » that the M4/M5 ratio for the Np is smaller than that for U. The Richardson-Lucy deconvolution method was applied to energy-loss spectral images and was shown to increase the signal to noise. This method also improves the limits of detection for Np in a U matrix.« less

Imaging of downward-looking linear array SAR using three-dimensional spatial smoothing MUSIC algorithm

NASA Astrophysics Data System (ADS)

Zhang, Siqian; Kuang, Gangyao

2014-10-01

In this paper, a novel three-dimensional imaging algorithm of downward-looking linear array SAR is presented. To improve the resolution, multiple signal classification (MUSIC) algorithm has been used. However, since the scattering centers are always correlated in real SAR system, the estimated covariance matrix becomes singular. To address the problem, a three-dimensional spatial smoothing method is proposed in this paper to restore the singular covariance matrix to a full-rank one. The three-dimensional signal matrix can be divided into a set of orthogonal three-dimensional subspaces. The main idea of the method is based on extracting the array correlation matrix as the average of all correlation matrices from the subspaces. In addition, the spectral height of the peaks contains no information with regard to the scattering intensity of the different scattering centers, thus it is difficulty to reconstruct the backscattering information. The least square strategy is used to estimate the amplitude of the scattering center in this paper. The above results of the theoretical analysis are verified by 3-D scene simulations and experiments on real data.

Application of the trigonal curve to the Blaszak-Marciniak lattice hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Zeng, Xin

2017-01-01

We develop a method for constructing algebro-geometric solutions of the Blaszak-Marciniak ( BM) lattice hierarchy based on the theory of trigonal curves. We first derive the BM lattice hierarchy associated with a discrete (3×3)- matrix spectral problem using Lenard recurrence relations. Using the characteristic polynomial of the Lax matrix for the BM lattice hierarchy, we introduce a trigonal curve with two infinite points, which we use to establish the associated Dubrovin-type equations. We then study the asymptotic properties of the algebraic function carrying the data of the divisor and the Baker-Akhiezer function near the two infinite points on the trigonal curve. We finally obtain algebro-geometric solutions of the entire BM lattice hierarchy in terms of the Riemann theta function.

Active constrained clustering by examining spectral Eigenvectors

NASA Technical Reports Server (NTRS)

Wagstaff, Kiri L.; desJardins, Marie; Xu, Qianjun

2005-01-01

This work focuses on the active selection of pairwise constraints for spectral clustering. We develop and analyze a technique for Active Constrained Clustering by Examining Spectral eigenvectorS (ACCESS) derived from a similarity matrix.

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

NASA Astrophysics Data System (ADS)

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

2000-10-01

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

Spectral function from Reduced Density Matrix Functional Theory

NASA Astrophysics Data System (ADS)

Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia

2015-03-01

In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

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

NASA Astrophysics Data System (ADS)

Kang, Hyun-Gyu; Cheong, Hyeong-Bin

2017-03-01

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

Geometric phase and o -mode blueshift in a chiral anisotropic medium inside a Fabry-Pérot cavity

NASA Astrophysics Data System (ADS)

Timofeev, Ivan V.; Gunyakov, Vladimir A.; Sutormin, Vitaly S.; Myslivets, Sergey A.; Arkhipkin, Vasily G.; Vetrov, Stepan Ya.; Lee, Wei; Zyryanov, Victor Ya.

2015-11-01

Anomalous spectral shift of transmission peaks is observed in a Fabry-Pérot cavity filled with a chiral anisotropic medium. The effective refractive index value resides out of the interval between the ordinary and the extraordinary refractive indices. The spectral shift is explained by contribution of a geometric phase. The problem is solved analytically using the approximate Jones matrix method, numerically using the accurate Berreman method, and geometrically using the generalized Mauguin-Poincaré rolling cone method. The o -mode blueshift is measured for a 4-methoxybenzylidene-4 '-n -butylaniline twisted-nematic layer inside the Fabry-Pérot cavity. The twist is electrically induced due to the homeoplanar-twisted configuration transition in an ionic-surfactant-doped liquid crystal layer. Experimental evidence confirms the validity of the theoretical model.

A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Van Gorder, Robert A.

2014-12-01

The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrödinger equation (T-FSE) and the space-fractional Schrödinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrödinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.

Utilization of all Spectral Channels of IASI for the Retrieval of the Atmospheric State

NASA Astrophysics Data System (ADS)

Del Bianco, S.; Cortesi, U.; Carli, B.

2010-12-01

The retrieval of atmospheric state parameters from broadband measurements acquired by high spectral resolution sensors, such as the Infrared Atmospheric Sounding Interferometer (IASI) onboard the Meteorological Operational (MetOp) platform, generally requires to deal with a prohibitively large number of spectral elements available from a single observation (8461 samples in the case of IASI, covering the 645-2760 cm-1 range with a resolution of 0.5 cm-1 and a spectral sampling of 0.25 cm-1). Most inversion algorithms developed for both operational and scientific analysis of IASI spectra perform a reduction of the data - typically based on channel selection, super-channel clustering or Principal Component Analysis (PCA) techniques - in order to handle the high dimensionality of the problem. Accordingly, simultaneous processing of all IASI channels received relatively low attention. Here we prove the feasibility of a retrieval approach exploiting all spectral channels of IASI, to extract information on water vapor, temperature and ozone profiles. This multi-target retrieval removes the systematic errors due to interfering parameters and makes the channel selection no longer necessary. The challenging computation is made possible by the use of a coarse spectral grid for the forward model calculation and by the abatement of the associated modeling errors through the use of a variance-covariance matrix of the residuals that takes into account all the forward model errors.

Quantitative methods and detection techniques in hyperspectral imaging involving medical and other applications

NASA Astrophysics Data System (ADS)

Roy, Ankita

2007-12-01

This research using Hyperspectral imaging involves recognizing targets through spatial and spectral matching and spectral un-mixing of data ranging from remote sensing to medical imaging kernels for clinical studies based on Hyperspectral data-sets generated using the VFTHSI [Visible Fourier Transform Hyperspectral Imager], whose high resolution Si detector makes the analysis achievable. The research may be broadly classified into (I) A Physically Motivated Correlation Formalism (PMCF), which places both spatial and spectral data on an equivalent mathematical footing in the context of a specific Kernel and (II) An application in RF plasma specie detection during carbon nanotube growing process. (III) Hyperspectral analysis for assessing density and distribution of retinopathies like age related macular degeneration (ARMD) and error estimation enabling the early recognition of ARMD, which is treated as an ill-conditioned inverse imaging problem. The broad statistical scopes of this research are two fold-target recognition problems and spectral unmixing problems. All processes involve experimental and computational analysis of Hyperspectral data sets is presented, which is based on the principle of a Sagnac Interferometer, calibrated to obtain high SNR levels. PMCF computes spectral/spatial/cross moments and answers the question of how optimally the entire hypercube should be sampled and finds how many spatial-spectral pixels are required precisely for a particular target recognition. Spectral analysis of RF plasma radicals, typically Methane plasma and Argon plasma using VFTHSI has enabled better process monitoring during growth of vertically aligned multi-walled carbon nanotubes by instant registration of the chemical composition or density changes temporally, which is key since a significant correlation can be found between plasma state and structural properties. A vital focus of this dissertation is towards medical Hyperspectral imaging applied to retinopathies like age related macular degeneration targets taken with a Fundus imager, which is akin to the VFTHSI. Detection of the constituent components in the diseased hyper-pigmentation area is also computed. The target or reflectance matrix is treated as a highly ill-conditioned spectral un-mixing problem, to which methodologies like inverse techniques, principal component analysis (PCA) and receiver operating curves (ROC) for precise spectral recognition of infected area. The region containing ARMD was easily distinguishable from the spectral mesh plots over the entire band-pass area. Once the location was detected the PMCF coefficients were calculated by cross correlating a target of normal oxygenated retina with the deoxygenated one. The ROCs generated using PMCF shows 30% higher detection probability with improved accuracy than ROCs based on Spectral Angle Mapper (SAM). By spectral unmixing methods, the important endmembers/carotenoids of the MD pigment were found to be Xanthophyl and lutein, while beta-carotene which showed a negative correlation in the unconstrained inverse problem is a supplement given to ARMD patients to prevent the disease and does not occur in the eye. Literature also shows degeneration of meso-zeaxanthin. Ophthalmologists may assert the presence of ARMD and commence the diagnosis process if the Xanthophyl pigment have degenerated 89.9%, while the lutein has decayed almost 80%, as found deduced computationally. This piece of current research takes it to the next level of precise investigation in the continuing process of improved clinical findings by correlating the microanatomy of the diseased fovea and shows promise of an early detection of this disease.

Solution of the neutronics code dynamic benchmark by finite element method

NASA Astrophysics Data System (ADS)

Avvakumov, A. V.; Vabishchevich, P. N.; Vasilev, A. O.; Strizhov, V. F.

2016-10-01

The objective is to analyze the dynamic benchmark developed by Atomic Energy Research for the verification of best-estimate neutronics codes. The benchmark scenario includes asymmetrical ejection of a control rod in a water-type hexagonal reactor at hot zero power. A simple Doppler feedback mechanism assuming adiabatic fuel temperature heating is proposed. The finite element method on triangular calculation grids is used to solve the three-dimensional neutron kinetics problem. The software has been developed using the engineering and scientific calculation library FEniCS. The matrix spectral problem is solved using the scalable and flexible toolkit SLEPc. The solution accuracy of the dynamic benchmark is analyzed by condensing calculation grid and varying degree of finite elements.

G W calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods

DOE PAGES

Pham, T. Anh; Nguyen, Huy -Viet; Rocca, Dario; ...

2013-04-26

Inmore » a recent paper we presented an approach to evaluate quasiparticle energies based on the spectral decomposition of the static dielectric matrix. This method does not require the calculation of unoccupied electronic states or the direct diagonalization of large dielectric matrices, and it avoids the use of plasmon-pole models. The numerical accuracy of the approach is controlled by a single parameter, i.e., the number of eigenvectors used in the spectral decomposition of the dielectric matrix. Here we present a comprehensive validation of the method, encompassing calculations of ionization potentials and electron affinities of various molecules and of band gaps for several crystalline and disordered semiconductors. Lastly, we demonstrate the efficiency of our approach by carrying out G W calculations for systems with several hundred valence electrons.« less

Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions

NASA Astrophysics Data System (ADS)

Kraberger, Gernot J.; Triebl, Robert; Zingl, Manuel; Aichhorn, Markus

2017-10-01

We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.

Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory

NASA Astrophysics Data System (ADS)

Kos, Pavel; Ljubotina, Marko; Prosen, Tomaž

2018-04-01

A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985), 10.1098/rspa.1985.0078] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K (t ) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004), 10.1103/PhysRevLett.93.014103]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the "many-body localized phase" and "ergodic phase." In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K (t ) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1 /2 models in a periodically kicking transverse field. In particular, we relate K (t ) to partition functions of a class of twisted classical Ising models on a ring of size t ; hence, the leading-order RMT behavior K (t )≃2 t is a consequence of translation and reflection symmetry of the Ising partition function.

A component prediction method for flue gas of natural gas combustion based on nonlinear partial least squares method.

PubMed

Cao, Hui; Yan, Xingyu; Li, Yaojiang; Wang, Yanxia; Zhou, Yan; Yang, Sanchun

2014-01-01

Quantitative analysis for the flue gas of natural gas-fired generator is significant for energy conservation and emission reduction. The traditional partial least squares method may not deal with the nonlinear problems effectively. In the paper, a nonlinear partial least squares method with extended input based on radial basis function neural network (RBFNN) is used for components prediction of flue gas. For the proposed method, the original independent input matrix is the input of RBFNN and the outputs of hidden layer nodes of RBFNN are the extension term of the original independent input matrix. Then, the partial least squares regression is performed on the extended input matrix and the output matrix to establish the components prediction model of flue gas. A near-infrared spectral dataset of flue gas of natural gas combustion is used for estimating the effectiveness of the proposed method compared with PLS. The experiments results show that the root-mean-square errors of prediction values of the proposed method for methane, carbon monoxide, and carbon dioxide are, respectively, reduced by 4.74%, 21.76%, and 5.32% compared to those of PLS. Hence, the proposed method has higher predictive capabilities and better robustness.

A spectrally tunable LED sphere source enables accurate calibration of tristimulus colorimeters

NASA Astrophysics Data System (ADS)

Fryc, I.; Brown, S. W.; Ohno, Y.

2006-02-01

The Four-Color Matrix method (FCM) was developed to improve the accuracy of chromaticity measurements of various display colors. The method is valid for each type of display having similar spectra. To develop the Four-Color correction matrix, spectral measurements of primary red, green, blue, and white colors of a display are needed. Consequently, a calibration facility should be equipped with a number of different displays. This is very inconvenient and expensive. A spectrally tunable light source (STS) that can mimic different display spectral distributions would eliminate the need for maintaining a wide variety of displays and would enable a colorimeter to be calibrated for a number of different displays using the same setup. Simulations show that an STS that can create red, green, blue and white distributions that are close to the real spectral power distribution (SPD) of a display works well with the FCM for the calibration of colorimeters.

Calibration of the ROSAT HRI Spectral Response

NASA Technical Reports Server (NTRS)

Prestwich, Andrea H.; Silverman, John; McDowell, Jonathan; Callanan, Paul; Snowden, Steve

2000-01-01

The ROSAT High Resolution Imager has a limited (2-band) spectral response. This spectral capability can give X-ray hardness ratios on spatial scales of 5 arcseconds. The spectral response of the center of the detector was calibrated before the launch of ROSAT, but the gain decreases with time and also is a function of position on the detector. To complicate matters further, the satellite is 'wobbled', possibly moving a source across several spatial gain states. These difficulties have prevented the spectral response of the ROSAT High Resolution Imager (HRI) from being used for scientific measurements. We have used Bright Earth data and in-flight calibration sources to map the spatial and temporal gain changes, and written software which will allow ROSAT users to generate a calibrated XSPEC (an x ray spectral fitting package) response matrix and hence determine a calibrated hardness ratio. In this report, we describe the calibration procedure and show how to obtain a response matrix. In Section 2 we give an overview of the calibration procedure, in Section 3 we give a summary of HRI spatial and temporal gain variations. Section 4 describes the routines used to determine the gain distribution of a source. In Sections 5 and 6, we describe in detail how, the Bright Earth database and calibration sources are used to derive a corrected response matrix for a given observation. Finally, Section 7 describes how to use the software.

Partitioning sparse matrices with eigenvectors of graphs

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

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

PubMed

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

2011-11-01

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

Sensitivity test of derivative matrix isopotential synchronous fluorimetry and least squares fitting methods.

PubMed

Makkai, Géza; Buzády, Andrea; Erostyák, János

2010-01-01

Determination of concentrations of spectrally overlapping compounds has special difficulties. Several methods are available to calculate the constituents' concentrations in moderately complex mixtures. A method which can provide information about spectrally hidden components in mixtures is very useful. Two methods powerful in resolving spectral components are compared in this paper. The first method tested is the Derivative Matrix Isopotential Synchronous Fluorimetry (DMISF). It is based on derivative analysis of MISF spectra, which are constructed using isopotential trajectories in the Excitation-Emission Matrix (EEM) of background solution. For DMISF method, a mathematical routine fitting the 3D data of EEMs was developed. The other method tested uses classical Least Squares Fitting (LSF) algorithm, wherein Rayleigh- and Raman-scattering bands may lead to complications. Both methods give excellent sensitivity and have advantages against each other. Detection limits of DMISF and LSF have been determined at very different concentration and noise levels.

QCD-inspired spectra from Blue's functions

NASA Astrophysics Data System (ADS)

Nowak, Maciej A.; Papp, Gábor; Zahed, Ismail

1996-02-01

We use the law of addition in random matrix theory to analyze the spectral distributions of a variety of chiral random matrix models as inspired from QCD whether through symmetries or models. In terms of the Blue's functions recently discussed by Zee, we show that most of the spectral distributions in the macroscopic limit and the quenched approximation, follow algebraically from the discontinuity of a pertinent solution to a cubic (Cardano) or a quartic (Ferrari) equation. We use the end-point equation of the energy spectra in chiral random matrix models to argue for novel phase structures, in which the Dirac density of states plays the role of an order parameter.

A loop-counting method for covariate-corrected low-rank biclustering of gene-expression and genome-wide association study data.

PubMed

Rangan, Aaditya V; McGrouther, Caroline C; Kelsoe, John; Schork, Nicholas; Stahl, Eli; Zhu, Qian; Krishnan, Arjun; Yao, Vicky; Troyanskaya, Olga; Bilaloglu, Seda; Raghavan, Preeti; Bergen, Sarah; Jureus, Anders; Landen, Mikael

2018-05-14

A common goal in data-analysis is to sift through a large data-matrix and detect any significant submatrices (i.e., biclusters) that have a low numerical rank. We present a simple algorithm for tackling this biclustering problem. Our algorithm accumulates information about 2-by-2 submatrices (i.e., 'loops') within the data-matrix, and focuses on rows and columns of the data-matrix that participate in an abundance of low-rank loops. We demonstrate, through analysis and numerical-experiments, that this loop-counting method performs well in a variety of scenarios, outperforming simple spectral methods in many situations of interest. Another important feature of our method is that it can easily be modified to account for aspects of experimental design which commonly arise in practice. For example, our algorithm can be modified to correct for controls, categorical- and continuous-covariates, as well as sparsity within the data. We demonstrate these practical features with two examples; the first drawn from gene-expression analysis and the second drawn from a much larger genome-wide-association-study (GWAS).

Raney Distributions and Random Matrix Theory

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Liu, Dang-Zheng

2015-03-01

Recent works have shown that the family of probability distributions with moments given by the Fuss-Catalan numbers permit a simple parameterized form for their density. We extend this result to the Raney distribution which by definition has its moments given by a generalization of the Fuss-Catalan numbers. Such computations begin with an algebraic equation satisfied by the Stieltjes transform, which we show can be derived from the linear differential equation satisfied by the characteristic polynomial of random matrix realizations of the Raney distribution. For the Fuss-Catalan distribution, an equilibrium problem characterizing the density is identified. The Stieltjes transform for the limiting spectral density of the singular values squared of the matrix product formed from inverse standard Gaussian matrices, and standard Gaussian matrices, is shown to satisfy a variant of the algebraic equation relating to the Raney distribution. Supported on , we show that it too permits a simple functional form upon the introduction of an appropriate choice of parameterization. As an application, the leading asymptotic form of the density as the endpoints of the support are approached is computed, and is shown to have some universal features.

Verification of unfold error estimates in the UFO code

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

Fehl, D.L.; Biggs, F.

Spectral unfolding is an inverse mathematical operation which attempts to obtain spectral source information from a set of tabulated response functions and data measurements. Several unfold algorithms have appeared over the past 30 years; among them is the UFO (UnFold Operator) code. In addition to an unfolded spectrum, UFO also estimates the unfold uncertainty (error) induced by running the code in a Monte Carlo fashion with prescribed data distributions (Gaussian deviates). In the problem studied, data were simulated from an arbitrarily chosen blackbody spectrum (10 keV) and a set of overlapping response functions. The data were assumed to have anmore » imprecision of 5% (standard deviation). 100 random data sets were generated. The built-in estimate of unfold uncertainty agreed with the Monte Carlo estimate to within the statistical resolution of this relatively small sample size (95% confidence level). A possible 10% bias between the two methods was unresolved. The Monte Carlo technique is also useful in underdetemined problems, for which the error matrix method does not apply. UFO has been applied to the diagnosis of low energy x rays emitted by Z-Pinch and ion-beam driven hohlraums.« less

Spectral Analysis of Rich Network Topology in Social Networks

ERIC Educational Resources Information Center

Wu, Leting

2013-01-01

Social networks have received much attention these days. Researchers have developed different methods to study the structure and characteristics of the network topology. Our focus is on spectral analysis of the adjacency matrix of the underlying network. Recent work showed good properties in the adjacency spectral space but there are few…

Sharp Estimates in Ruelle Theorems for Matrix Transfer Operators

NASA Astrophysics Data System (ADS)

Campbell, J.; Latushkin, Y.

A matrix coefficient transfer operator , on the space of -sections of an m-dimensional vector bundle over n-dimensional compact manifold is considered. The spectral radius of is estimated bya; and the essential spectral radius by Here is the set of ergodic f-invariant measures, and for is the measure-theoretic entropy of f, is the largest Lyapunov exponent of the cocycle over f generated by , and is the smallest Lyapunov exponent of the differential of f.

A novel alignment-free method to classify protein folding types by combining spectral graph clustering with Chou's pseudo amino acid composition.

PubMed

Tripathi, Pooja; Pandey, Paras N

2017-07-07

The present work employs pseudo amino acid composition (PseAAC) for encoding the protein sequences in their numeric form. Later this will be arranged in the similarity matrix, which serves as input for spectral graph clustering method. Spectral methods are used previously also for clustering of protein sequences, but they uses pair wise alignment scores of protein sequences, in similarity matrix. The alignment score depends on the length of sequences, so clustering short and long sequences together may not good idea. Therefore the idea of introducing PseAAC with spectral clustering algorithm came into scene. We extensively tested our method and compared its performance with other existing machine learning methods. It is consistently observed that, the number of clusters that we obtained for a given set of proteins is close to the number of superfamilies in that set and PseAAC combined with spectral graph clustering shows the best classification results. Copyright © 2017 Elsevier Ltd. All rights reserved.

A-TEEMTM, a new molecular fingerprinting technique: simultaneous absorbance-transmission and fluorescence excitation-emission matrix method

NASA Astrophysics Data System (ADS)

Quatela, Alessia; Gilmore, Adam M.; Steege Gall, Karen E.; Sandros, Marinella; Csatorday, Karoly; Siemiarczuk, Alex; (Ben Yang, Boqian; Camenen, Loïc

2018-04-01

We investigate the new simultaneous absorbance-transmission and fluorescence excitation-emission matrix method for rapid and effective characterization of the varying components from a mixture. The absorbance-transmission and fluorescence excitation-emission matrix method uniquely facilitates correction of fluorescence inner-filter effects to yield quantitative fluorescence spectral information that is largely independent of component concentration. This is significant because it allows one to effectively monitor quantitative component changes using multivariate methods and to generate and evaluate spectral libraries. We present the use of this novel instrument in different fields: i.e. tracking changes in complex mixtures including natural water, wine as well as monitoring stability and aggregation of hormones for biotherapeutics.

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

NASA Astrophysics Data System (ADS)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems

NASA Technical Reports Server (NTRS)

Streett, C. L.

1987-01-01

Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.

Calibration of the ROSAT HRI Spectral Response

NASA Technical Reports Server (NTRS)

Prestwich, Andrea

1998-01-01

The ROSAT High Resolution Imager has a limited (2-band) spectral response. This spectral capability can give X-ray hardness ratios on spatial scales of 5 arcseconds. The spectral response of the center of the detector was calibrated before the launch of ROSAT, but the gain decreases-with time and also is a function of position on the detector. To complicate matters further, the satellite is "wobbled", possibly moving a source across several spatial gain states. These difficulties have prevented the spectral response of the ROSAT HRI from being used for scientific measurements. We have used Bright Earth data and in-flight calibration sources to map the spatial and temporal gain changes, and written software which will allow ROSAT users to generate a calibrated XSPEC response matrix and hence determine a calibrated hardness ratio. In this report, we describe the calibration procedure and show how to obtain a response matrix. In Section 2 we give an overview of the calibration procedure, in Section 3 we give a summary of HRI spatial and temporal gain variations. Section 4 describes the routines used to determine the gain distribution of a source. In Sections 5 and 6, we describe in detail how the Bright Earth database and calibration sources are used to derive a corrected response matrix for a given observation. Finally, Section 7 describes how to use the software.

Aspects géométriques et intégrables des modèles de matrices aléatoires

NASA Astrophysics Data System (ADS)

Marchal, Olivier

2010-12-01

This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of integrable systems. The variety of these applications shows why matrix models are important from a mathematical point of view. First, the thesis will focus on the study of the merging of two intervals of the eigenvalues density near a singular point. Specifically, we will show why this special limit gives universal equations from the Painlevé II hierarchy of integrable systems theory. Then, following the approach of (bi) orthogonal polynomials introduced by Mehta to compute partition functions, we will find Riemann-Hilbert and isomonodromic problems connected to matrix models, making the link with the theory of Jimbo, Miwa and Ueno. In particular, we will describe how the hermitian two-matrix models provide a degenerate case of Jimbo-Miwa-Ueno's theory that we will generalize in this context. Furthermore, the loop equations method, with its central notions of spectral curve and topological expansion, will lead to the symplectic invariants of algebraic geometry recently proposed by Eynard and Orantin. This last point will be generalized to the case of non-hermitian matrix models (arbitrary beta) paving the way to "quantum algebraic geometry" and to the generalization of symplectic invariants to "quantum curves". Finally, this set up will be applied to combinatorics in the context of topological string theory, with the explicit computation of an hermitian random matrix model enumerating the Gromov-Witten invariants of a toric Calabi-Yau threefold.

HiC-spector: a matrix library for spectral and reproducibility analysis of Hi-C contact maps.

PubMed

Yan, Koon-Kiu; Yardimci, Galip Gürkan; Yan, Chengfei; Noble, William S; Gerstein, Mark

2017-07-15

Genome-wide proximity ligation based assays like Hi-C have opened a window to the 3D organization of the genome. In so doing, they present data structures that are different from conventional 1D signal tracks. To exploit the 2D nature of Hi-C contact maps, matrix techniques like spectral analysis are particularly useful. Here, we present HiC-spector, a collection of matrix-related functions for analyzing Hi-C contact maps. In particular, we introduce a novel reproducibility metric for quantifying the similarity between contact maps based on spectral decomposition. The metric successfully separates contact maps mapped from Hi-C data coming from biological replicates, pseudo-replicates and different cell types. Source code in Julia and Python, and detailed documentation is available at https://github.com/gersteinlab/HiC-spector . koonkiu.yan@gmail.com or mark@gersteinlab.org. Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.

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

Smallwood, D.O.

In a previous paper Smallwood and Paez (1991) showed how to generate realizations of partially coherent stationary normal time histories with a specified cross-spectral density matrix. This procedure is generalized for the case of multiple inputs with a specified cross-spectral density function and a specified marginal probability density function (pdf) for each of the inputs. The specified pdfs are not required to be Gaussian. A zero memory nonlinear (ZMNL) function is developed for each input to transform a Gaussian or normal time history into a time history with a specified non-Gaussian distribution. The transformation functions have the property that amore » transformed time history will have nearly the same auto spectral density as the original time history. A vector of Gaussian time histories are then generated with the specified cross-spectral density matrix. These waveforms are then transformed into the required time history realizations using the ZMNL function.« less

WE-FG-207B-02: Material Reconstruction for Spectral Computed Tomography with Detector Response Function

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

Liu, J; Gao, H

2016-06-15

Purpose: Different from the conventional computed tomography (CT), spectral CT based on energy-resolved photon-counting detectors is able to provide the unprecedented material composition. However, an important missing piece for accurate spectral CT is to incorporate the detector response function (DRF), which is distorted by factors such as pulse pileup and charge-sharing. In this work, we propose material reconstruction methods for spectral CT with DRF. Methods: The polyenergetic X-ray forward model takes the DRF into account for accurate material reconstruction. Two image reconstruction methods are proposed: a direct method based on the nonlinear data fidelity from DRF-based forward model; a linear-data-fidelitymore » based method that relies on the spectral rebinning so that the corresponding DRF matrix is invertible. Then the image reconstruction problem is regularized with the isotropic TV term and solved by alternating direction method of multipliers. Results: The simulation results suggest that the proposed methods provided more accurate material compositions than the standard method without DRF. Moreover, the proposed method with linear data fidelity had improved reconstruction quality from the proposed method with nonlinear data fidelity. Conclusion: We have proposed material reconstruction methods for spectral CT with DRF, whichprovided more accurate material compositions than the standard methods without DRF. Moreover, the proposed method with linear data fidelity had improved reconstruction quality from the proposed method with nonlinear data fidelity. Jiulong Liu and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000), and the Shanghai Pujiang Talent Program (#14PJ1404500).« less

Hyperspectral image compressing using wavelet-based method

NASA Astrophysics Data System (ADS)

Yu, Hui; Zhang, Zhi-jie; Lei, Bo; Wang, Chen-sheng

2017-10-01

Hyperspectral imaging sensors can acquire images in hundreds of continuous narrow spectral bands. Therefore each object presented in the image can be identified from their spectral response. However, such kind of imaging brings a huge amount of data, which requires transmission, processing, and storage resources for both airborne and space borne imaging. Due to the high volume of hyperspectral image data, the exploration of compression strategies has received a lot of attention in recent years. Compression of hyperspectral data cubes is an effective solution for these problems. Lossless compression of the hyperspectral data usually results in low compression ratio, which may not meet the available resources; on the other hand, lossy compression may give the desired ratio, but with a significant degradation effect on object identification performance of the hyperspectral data. Moreover, most hyperspectral data compression techniques exploits the similarities in spectral dimensions; which requires bands reordering or regrouping, to make use of the spectral redundancy. In this paper, we explored the spectral cross correlation between different bands, and proposed an adaptive band selection method to obtain the spectral bands which contain most of the information of the acquired hyperspectral data cube. The proposed method mainly consist three steps: First, the algorithm decomposes the original hyperspectral imagery into a series of subspaces based on the hyper correlation matrix of the hyperspectral images between different bands. And then the Wavelet-based algorithm is applied to the each subspaces. At last the PCA method is applied to the wavelet coefficients to produce the chosen number of components. The performance of the proposed method was tested by using ISODATA classification method.

Heterogeneous continuous-time random walks

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.; Tupikina, Liubov

2018-01-01

We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.

Matrix Interdiction Problem

NASA Astrophysics Data System (ADS)

Kasiviswanathan, Shiva Prasad; Pan, Feng

In the matrix interdiction problem, a real-valued matrix and an integer k is given. The objective is to remove a set of k matrix columns that minimizes in the residual matrix the sum of the row values, where the value of a row is defined to be the largest entry in that row. This combinatorial problem is closely related to bipartite network interdiction problem that can be applied to minimize the probability that an adversary can successfully smuggle weapons. After introducing the matrix interdiction problem, we study the computational complexity of this problem. We show that the matrix interdiction problem is NP-hard and that there exists a constant γ such that it is even NP-hard to approximate this problem within an n γ additive factor. We also present an algorithm for this problem that achieves an (n - k) multiplicative approximation ratio.

Efficient geostatistical inversion of transient groundwater flow using preconditioned nonlinear conjugate gradients

NASA Astrophysics Data System (ADS)

Klein, Ole; Cirpka, Olaf A.; Bastian, Peter; Ippisch, Olaf

2017-04-01

In the geostatistical inverse problem of subsurface hydrology, continuous hydraulic parameter fields, in most cases hydraulic conductivity, are estimated from measurements of dependent variables, such as hydraulic heads, under the assumption that the parameter fields are autocorrelated random space functions. Upon discretization, the continuous fields become large parameter vectors with O (104 -107) elements. While cokriging-like inversion methods have been shown to be efficient for highly resolved parameter fields when the number of measurements is small, they require the calculation of the sensitivity of each measurement with respect to all parameters, which may become prohibitive with large sets of measured data such as those arising from transient groundwater flow. We present a Preconditioned Conjugate Gradient method for the geostatistical inverse problem, in which a single adjoint equation needs to be solved to obtain the gradient of the objective function. Using the autocovariance matrix of the parameters as preconditioning matrix, expensive multiplications with its inverse can be avoided, and the number of iterations is significantly reduced. We use a randomized spectral decomposition of the posterior covariance matrix of the parameters to perform a linearized uncertainty quantification of the parameter estimate. The feasibility of the method is tested by virtual examples of head observations in steady-state and transient groundwater flow. These synthetic tests demonstrate that transient data can reduce both parameter uncertainty and time spent conducting experiments, while the presented methods are able to handle the resulting large number of measurements.

Asymmetric correlation matrices: an analysis of financial data

NASA Astrophysics Data System (ADS)

Livan, G.; Rebecchi, L.

2012-06-01

We analyse the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non-symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrix to distinguish between noise and non-trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non-symmetric correlation matrix. We find several non trivial results when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.

Spectral analysis of localized rotating waves in parabolic systems.

PubMed

Beyn, Wolf-Jürgen; Otten, Denny

2018-04-13

In this paper, we study the spectra and Fredholm properties of Ornstein-Uhlenbeck operators [Formula: see text]where [Formula: see text] is the profile of a rotating wave satisfying [Formula: see text] as [Formula: see text], the map [Formula: see text] is smooth and the matrix [Formula: see text] has eigenvalues with positive real parts and commutes with the limit matrix [Formula: see text] The matrix [Formula: see text] is assumed to be skew-symmetric with eigenvalues (λ 1 ,…,λ d )=(±i σ 1 ,…,±i σ k ,0,…,0). The spectra of these linearized operators are crucial for the nonlinear stability of rotating waves in reaction-diffusion systems. We prove under appropriate conditions that every [Formula: see text] satisfying the dispersion relation [Formula: see text]belongs to the essential spectrum [Formula: see text] in L p For values Re λ to the right of the spectral bound for [Formula: see text], we show that the operator [Formula: see text] is Fredholm of index 0, solve the identification problem for the adjoint operator [Formula: see text] and formulate the Fredholm alternative. Moreover, we show that the set [Formula: see text]belongs to the point spectrum [Formula: see text] in L p We determine the associated eigenfunctions and show that they decay exponentially in space. As an application, we analyse spinning soliton solutions which occur in the Ginzburg-Landau equation and compute their numerical spectra as well as associated eigenfunctions. Our results form the basis for investigating the nonlinear stability of rotating waves in higher space dimensions and truncations to bounded domains. This article is part of the themed issue 'Stability of nonlinear waves and patterns and related topics'. © 2018 The Author(s).

Spectral methods for time dependent problems

NASA Technical Reports Server (NTRS)

Tadmor, Eitan

1990-01-01

Spectral approximations are reviewed for time dependent problems. Some basic ingredients from the spectral Fourier and Chebyshev approximations theory are discussed. A brief survey was made of hyperbolic and parabolic time dependent problems which are dealt with by both the energy method and the related Fourier analysis. The ideas presented above are combined in the study of accuracy stability and convergence of the spectral Fourier approximation to time dependent problems.

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

LIFT a future atmospheric chemistry sensor

NASA Astrophysics Data System (ADS)

Pailharey, E.; Châteauneuf, F.; Aminou, D.

2017-11-01

Natural and anthropogenic trace constituents play an important role for the ozone budget and climate as well as in other problems of the environment. In order to prevent the dramatic impact of any climate change, exchange processes between the stratosphere and troposphere as well as the distribution and deposition of tropospheric trace constituents are investigated. The Limb Infrared Fourier Transform spectrometer (LIFT) will globally provide calibrated spectra of the atmosphere as a function of the tangent altitude. LIFT field of view will be 30 km × 30 km. The resolution is 30 km in azimuth corresponding to the full field of view, and 2 km in elevation, obtained by using a matrix of 15×15 detectors. The instrument will cover the spectral domain 5.7-14.7 μm through 2 different bands respectively 13.0-9.5 μm, 9.5-5.7 μm. With a spectral resolution of 0.1 cm-1, LIFT is a high class Fourier Transform Spectrometer compliant with the challenging constraints of limb viewing and spaceborne implementation.

Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

2017-12-01

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

q-Poincaré supersymmetry in AdS5/CFT4

NASA Astrophysics Data System (ADS)

Borsato, Riccardo; Torrielli, Alessandro

2018-03-01

We consider the exact S-matrix governing the planar spectral problem for strings on AdS5 ×S5 and N = 4 super Yang-Mills, and we show that it is invariant under a novel "boost" symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended psu (2 | 2) symmetry, and to conclude that the S-matrix is invariant under a q-Poincaré supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct) that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory) and weak-coupling (spin-chain description of the gauge theory) limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincaré symmetry, by contraction of the quantum affine algebra Uq (sl2 ˆ) in Drinfeld's second realisation.

Spectral statistics of random geometric graphs

NASA Astrophysics Data System (ADS)

Dettmann, C. P.; Georgiou, O.; Knight, G.

2017-04-01

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short-range correlations in the level spacings of the spectrum via the nearest-neighbour and next-nearest-neighbour spacing distribution and long-range correlations via the spectral rigidity Δ3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter-dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdős-Rényi, Barabási-Albert and Watts-Strogatz random graphs.

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

Clark, Darin P.; Badea, Cristian T., E-mail: cristian.badea@duke.edu; Lee, Chang-Lung

Purpose: X-ray computed tomography (CT) is widely used, both clinically and preclinically, for fast, high-resolution anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. The authors propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D + dual energy + time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols. Methods: The authors approach the 5D reconstruction problem withinmore » the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, the authors establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a nonlinear, image domain filtration approach, the authors refer to as rank-sparse kernel regression, the authors transfer image structure from the well-sampled time and energy averaged reconstruction to the spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction subproblems, enabling substantial undersampling. The authors solved the 5D reconstruction problem using the split Bregman method and GPU-based implementations of backprojection, reprojection, and kernel regression. Using a preclinical mouse model, the authors apply the proposed algorithm to study myocardial injury following radiation treatment of breast cancer. Results: Quantitative 5D simulations are performed using the MOBY mouse phantom. Twenty data sets (ten cardiac phases, two energies) are reconstructed with 88 μm, isotropic voxels from 450 total projections acquired over a single 360° rotation. In vivo 5D myocardial injury data sets acquired in two mice injected with gold and iodine nanoparticles are also reconstructed with 20 data sets per mouse using the same acquisition parameters (dose: ∼60 mGy). For both the simulations and the in vivo data, the reconstruction quality is sufficient to perform material decomposition into gold and iodine maps to localize the extent of myocardial injury (gold accumulation) and to measure cardiac functional metrics (vascular iodine). Their 5D CT imaging protocol represents a 95% reduction in radiation dose per cardiac phase and energy and a 40-fold decrease in projection sampling time relative to their standard imaging protocol. Conclusions: Their 5D CT data acquisition and reconstruction protocol efficiently exploits the rank-sparse nature of spectral and temporal CT data to provide high-fidelity reconstruction results without increased radiation dose or sampling time.« less

Spectrotemporal CT data acquisition and reconstruction at low dose

PubMed Central

Clark, Darin P.; Lee, Chang-Lung; Kirsch, David G.; Badea, Cristian T.

2015-01-01

Purpose: X-ray computed tomography (CT) is widely used, both clinically and preclinically, for fast, high-resolution anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. The authors propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D + dual energy + time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols. Methods: The authors approach the 5D reconstruction problem within the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, the authors establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a nonlinear, image domain filtration approach, the authors refer to as rank-sparse kernel regression, the authors transfer image structure from the well-sampled time and energy averaged reconstruction to the spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction subproblems, enabling substantial undersampling. The authors solved the 5D reconstruction problem using the split Bregman method and GPU-based implementations of backprojection, reprojection, and kernel regression. Using a preclinical mouse model, the authors apply the proposed algorithm to study myocardial injury following radiation treatment of breast cancer. Results: Quantitative 5D simulations are performed using the MOBY mouse phantom. Twenty data sets (ten cardiac phases, two energies) are reconstructed with 88 μm, isotropic voxels from 450 total projections acquired over a single 360° rotation. In vivo 5D myocardial injury data sets acquired in two mice injected with gold and iodine nanoparticles are also reconstructed with 20 data sets per mouse using the same acquisition parameters (dose: ∼60 mGy). For both the simulations and the in vivo data, the reconstruction quality is sufficient to perform material decomposition into gold and iodine maps to localize the extent of myocardial injury (gold accumulation) and to measure cardiac functional metrics (vascular iodine). Their 5D CT imaging protocol represents a 95% reduction in radiation dose per cardiac phase and energy and a 40-fold decrease in projection sampling time relative to their standard imaging protocol. Conclusions: Their 5D CT data acquisition and reconstruction protocol efficiently exploits the rank-sparse nature of spectral and temporal CT data to provide high-fidelity reconstruction results without increased radiation dose or sampling time. PMID:26520724

Quantum Linear System Algorithm for Dense Matrices.

PubMed

Wossnig, Leonard; Zhao, Zhikuan; Prakash, Anupam

2018-02-02

Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix A and a vector b the task is to find the vector x such that Ax=b. We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of O(κ^{2}sqrt[n]polylog(n)/ε) for an n×n dimensional A with bounded spectral norm, where κ denotes the condition number of A, and ε is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of A and the vector of Euclidean norms of the rows of A.

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

NASA Technical Reports Server (NTRS)

Coutsias, Evangelos A.; Torres, David; Hagstrom, Thomas

1994-01-01

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Serum Peptide Changes in Chickens with Metabolic Skeletal Problems Associated with Lameness

NASA Astrophysics Data System (ADS)

Rasaputra, Komal S.; Liyanage, Rohana; Okimoto, Ron; Lay, Jackson O.; Rath, Narayan C.

2011-06-01

Serum proteins and peptides have potential as biomarkers since they form the structural and functional basis of tissues and are involved in metabolic and regulatory processes. Changes in their profiles or their breakdown products have been of interest as potential biomarkers. Tibial dyschondroplasia (TD) and femoral head separation (FHS) are two metabolic skeletal problems in poultry that cause lameness. The objective of this study was to identify serum peptide changes associated with lameness in poultry that may be predictive of the disease and may help in eliminating these hereditary defects from the genetic pool. Serum peptides were extracted from six-wk-old chickens with or without the above leg problems using C18 magnetic beads and analyzed by MALDI-TOF mass spectrometry. Differentially expressed peptides were analyzed in the m/z range of 1,000-10,000 using ClinproTool™ software. Twenty two peaks from TD and 20 from FHS affected chickens were compared with their respective controls. The spectral peaks were identified using mass spectrometry followed by a data base search. Some of the peptides identified were hemostasis associated breakdown products. No differentially expressed peptide was detected in FHS but a peptide with m/z 5308.1 was elevated in chickens with TD (p⩽0.05). It was identified as a fragment of alpha 1 type-XI isoform 1. Type XI collagen is a cartilage specific extracellular matrix protein that is involved in the organization of other collagens and maintains extracellular matrix integrity. Its breakdown product may indicate cartilage degeneration in tibial dyschondroplasia thus may serve as a surrogate marker for this problem.

Resolving fluorophores by unmixing multispectral fluorescence tomography with independent component analysis

NASA Astrophysics Data System (ADS)

Pu, Huangsheng; Zhang, Guanglei; He, Wei; Liu, Fei; Guang, Huizhi; Zhang, Yue; Bai, Jing; Luo, Jianwen

2014-09-01

It is a challenging problem to resolve and identify drug (or non-specific fluorophore) distribution throughout the whole body of small animals in vivo. In this article, an algorithm of unmixing multispectral fluorescence tomography (MFT) images based on independent component analysis (ICA) is proposed to solve this problem. ICA is used to unmix the data matrix assembled by the reconstruction results from MFT. Then the independent components (ICs) that represent spatial structures and the corresponding spectrum courses (SCs) which are associated with spectral variations can be obtained. By combining the ICs with SCs, the recovered MFT images can be generated and fluorophore concentration can be calculated. Simulation studies, phantom experiments and animal experiments with different concentration contrasts and spectrum combinations are performed to test the performance of the proposed algorithm. Results demonstrate that the proposed algorithm can not only provide the spatial information of fluorophores, but also recover the actual reconstruction of MFT images.

Density-Aware Clustering Based on Aggregated Heat Kernel and Its Transformation

DOE PAGES

Huang, Hao; Yoo, Shinjae; Yu, Dantong; ...

2015-06-01

Current spectral clustering algorithms suffer from the sensitivity to existing noise, and parameter scaling, and may not be aware of different density distributions across clusters. If these problems are left untreated, the consequent clustering results cannot accurately represent true data patterns, in particular, for complex real world datasets with heterogeneous densities. This paper aims to solve these problems by proposing a diffusion-based Aggregated Heat Kernel (AHK) to improve the clustering stability, and a Local Density Affinity Transformation (LDAT) to correct the bias originating from different cluster densities. AHK statistically\\ models the heat diffusion traces along the entire time scale, somore » it ensures robustness during clustering process, while LDAT probabilistically reveals local density of each instance and suppresses the local density bias in the affinity matrix. Our proposed framework integrates these two techniques systematically. As a result, not only does it provide an advanced noise-resisting and density-aware spectral mapping to the original dataset, but also demonstrates the stability during the processing of tuning the scaling parameter (which usually controls the range of neighborhood). Furthermore, our framework works well with the majority of similarity kernels, which ensures its applicability to many types of data and problem domains. The systematic experiments on different applications show that our proposed algorithms outperform state-of-the-art clustering algorithms for the data with heterogeneous density distributions, and achieve robust clustering performance with respect to tuning the scaling parameter and handling various levels and types of noise.« less

Spectral multigrid methods for elliptic equations 2

NASA Technical Reports Server (NTRS)

Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.

1983-01-01

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.; Kwak, Dochan (Technical Monitor)

2002-01-01

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Evaluation of a six-DOF electrodynamic shaker system.

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

Gregory, Danny Lynn; Smallwood, David Ora

2009-03-01

The paper describes the preliminary evaluation of a 6 degree of freedom electrodynamic shaker system. The 8 by 8 inch (20.3 cm) table is driven by 12 electrodynamic shakers producing motion in all 6 rigid body modes. A small electrodynamic shaker system suitable for small component testing is described. The principal purpose of the system is to demonstrate the technology. The shaker is driven by 12 electrodynamic shakers each with a force capability of about 50 lbs (220 N). The system was developed through an informal cooperative agreement between Sandia National Laboratories, Team Corp. and Spectral Dynamics Corporation. Sandia providedmore » the laboratory space and some development funds. Team provided the mechanical system, and Spectral Dynamics provided the control system. Spectral Dynamics was chosen to provide the control system partly because of their experience in MIMO control and partly because Sandia already had part of the system in house. The shaker system was conceived and manufactured by TEAM Corp. Figure 1 shows the overall system. The vibration table, electrodynamic shakers, hydraulic pumps, and amplifiers are all housed in a single cabinet. Figure 2 is a drawing showing how the electrodynamic shakers are coupled to the table. The shakers are coupled to the table through a hydraulic spherical pad bearing providing 5 degrees of freedom and one stiff degree of freedom. The pad bearing must be preloaded with a static force as they are unable to provide any tension forces. The horizontal bearings are preloaded with steel springs. The drawing shows a spring providing the vertical preload. This was changed in the final design. The vertical preload is provided by multiple strands of an O-ring material as shown in Figure 4. Four shakers provide excitation in each of the three orthogonal axes. The specifications of the shaker are outlined in Table 1. Four shakers provide inputs in each of the three orthogonal directions. By choosing the phase relationships between the shakers all six rigid body modes (three translation, and three rotations) can be excited. The system is over determined. There are more shakers than degrees of freedom. This provided an interesting control problem. The problem was approached using the input-output transformation matrices provided in the Spectral control system. Twelve accelerometers were selected for the control accelerometers (a tri-axial accelerometer at each corner of the table (see Figure 5). Figure 6 shows the nomenclature used to identify the shakers and control accelerometers. A fifth tri-axial accelerometer was placed at the center of the table, but it was not used for control. Thus we had 12 control accelerometers and 12 shakers to control a 6-dof shaker. The 12 control channels were reduced to a 6-dof control using a simple input transformation matrix. The control was defined by a 6x6 spectral density matrix. The six outputs in the control variable coordinates were transformed to twelve physical drive signals using another simple output transformation matrix. It was assumed that the accelerometers and shakers were well matched such that the transformation matrices were independent of frequency and could be deduced from rigid body considerations. The input/output transformations are shown in Equations 1 and 2.« less

Spectral statistics and scattering resonances of complex primes arrays

NASA Astrophysics Data System (ADS)

Wang, Ren; Pinheiro, Felipe A.; Dal Negro, Luca

2018-01-01

We introduce a class of aperiodic arrays of electric dipoles generated from the distribution of prime numbers in complex quadratic fields (Eisenstein and Gaussian primes) as well as quaternion primes (Hurwitz and Lifschitz primes), and study the nature of their scattering resonances using the vectorial Green's matrix method. In these systems we demonstrate several distinctive spectral properties, such as the absence of level repulsion in the strongly scattering regime, critical statistics of level spacings, and the existence of critical modes, which are extended fractal modes with long lifetimes not supported by either random or periodic systems. Moreover, we show that one can predict important physical properties, such as the existence spectral gaps, by analyzing the eigenvalue distribution of the Green's matrix of the arrays in the complex plane. Our results unveil the importance of aperiodic correlations in prime number arrays for the engineering of gapped photonic media that support far richer mode localization and spectral properties compared to usual periodic and random media.

Atomic spectral-product representations of molecular electronic structure: metric matrices and atomic-product composition of molecular eigenfunctions.

PubMed

Ben-Nun, M; Mills, J D; Hinde, R J; Winstead, C L; Boatz, J A; Gallup, G A; Langhoff, P W

2009-07-02

Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectral-product basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H(2), CH) and triatomic (H(3), CH(2)) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstate-product representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or linear dependence of its explicitly antisymmetrized form, the convergence of the apparently disparate atomic-product and explicitly antisymmetrized atomic-product forms to a common invariant subspace, and the nature of a chemical bonding descriptor provided by the atomic-product compositions of molecular eigenstates. Concluding remarks indicate additional studies in progress and the prognosis for performing atomic spectral-product calculations more generally and efficiently.

A new approach for the calculation of response spectral density of a linear stationary random multidegree of freedom system

NASA Astrophysics Data System (ADS)

Sharan, A. M.; Sankar, S.; Sankar, T. S.

1982-08-01

A new approach for the calculation of response spectral density for a linear stationary random multidegree of freedom system is presented. The method is based on modifying the stochastic dynamic equations of the system by using a set of auxiliary variables. The response spectral density matrix obtained by using this new approach contains the spectral densities and the cross-spectral densities of the system generalized displacements and velocities. The new method requires significantly less computation time as compared to the conventional method for calculating response spectral densities. Two numerical examples are presented to compare quantitatively the computation time.

Intermediate quantum maps for quantum computation

NASA Astrophysics Data System (ADS)

Giraud, O.; Georgeot, B.

2005-10-01

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically and yields pseudorandom operators with original properties, enabling, for example, one to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.

Use of immobilized exopeptidases and volatile buffers for analysis of peptides by fast atom bombardment mass spectrometry.

PubMed

Wagner, R M; Fraser, B A

1987-05-01

beta-Lipotrophin (62-77) or Ac-gastrin releasing peptide was incubated with immobilized carboxypeptidase Y or aminopeptidase M. Subsequent aliquots of each incubation mixture were analysed by fast atom bombardment mass spectrometry using a dithiothreitol/dithioerythritol liquid matrix. The use of immobilized enzymes and volatile buffers for exopeptidase digestions enabled rapid and facile separation of enzyme from digestion products. This approach to mass spectral peptide analysis reduced spectral background arising from a glycerol matrix, buffer salts, or enzyme proteins and contaminants, enabling analysis of as little as 200 picomoles of a suitable peptide.

Textural signatures for wetland vegetation

NASA Technical Reports Server (NTRS)

Whitman, R. I.; Marcellus, K. L.

1973-01-01

This investigation indicates that unique textural signatures do exist for specific wetland communities at certain times in the growing season. When photographs with the proper resolution are obtained, the textural features can identify the spectral features of the vegetation community seen with lower resolution mapping data. The development of a matrix of optimum textural signatures is the goal of this research. Seasonal variations of spectral and textural features are particularly important when performing a vegetations analysis of fresh water marshes. This matrix will aid in flight planning, since expected seasonal variations and resolution requirements can be established prior to a given flight mission.

Analysis of spectrally resolved autofluorescence images by support vector machines

NASA Astrophysics Data System (ADS)

Mateasik, A.; Chorvat, D.; Chorvatova, A.

2013-02-01

Spectral analysis of the autofluorescence images of isolated cardiac cells was performed to evaluate and to classify the metabolic state of the cells in respect to the responses to metabolic modulators. The classification was done using machine learning approach based on support vector machine with the set of the automatically calculated features from recorded spectral profile of spectral autofluorescence images. This classification method was compared with the classical approach where the individual spectral components contributing to cell autofluorescence were estimated by spectral analysis, namely by blind source separation using non-negative matrix factorization. Comparison of both methods showed that machine learning can effectively classify the spectrally resolved autofluorescence images without the need of detailed knowledge about the sources of autofluorescence and their spectral properties.

Implementation and Assessment of Advanced Analog Vector-Matrix Processor

NASA Technical Reports Server (NTRS)

Gary, Charles K.; Bualat, Maria G.; Lum, Henry, Jr. (Technical Monitor)

1994-01-01

This paper discusses the design and implementation of an analog optical vecto-rmatrix coprocessor with a throughput of 128 Mops for a personal computer. Vector matrix calculations are inherently parallel, providing a promising domain for the use of optical calculators. However, to date, digital optical systems have proven too cumbersome to replace electronics, and analog processors have not demonstrated sufficient accuracy in large scale systems. The goal of the work described in this paper is to demonstrate a viable optical coprocessor for linear operations. The analog optical processor presented has been integrated with a personal computer to provide full functionality and is the first demonstration of an optical linear algebra processor with a throughput greater than 100 Mops. The optical vector matrix processor consists of a laser diode source, an acoustooptical modulator array to input the vector information, a liquid crystal spatial light modulator to input the matrix information, an avalanche photodiode array to read out the result vector of the vector matrix multiplication, as well as transport optics and the electronics necessary to drive the optical modulators and interface to the computer. The intent of this research is to provide a low cost, highly energy efficient coprocessor for linear operations. Measurements of the analog accuracy of the processor performing 128 Mops are presented along with an assessment of the implications for future systems. A range of noise sources, including cross-talk, source amplitude fluctuations, shot noise at the detector, and non-linearities of the optoelectronic components are measured and compared to determine the most significant source of error. The possibilities for reducing these sources of error are discussed. Also, the total error is compared with that expected from a statistical analysis of the individual components and their relation to the vector-matrix operation. The sufficiency of the measured accuracy of the processor is compared with that required for a range of typical problems. Calculations resolving alloy concentrations from spectral plume data of rocket engines are implemented on the optical processor, demonstrating its sufficiency for this problem. We also show how this technology can be easily extended to a 100 x 100 10 MHz (200 Cops) processor.

Application of blood cadmium determination to industry using a punched disc technique.

PubMed Central

Cernik, A A; Sayers, M P

1975-01-01

A paper disc flameless atomic absorption spectroscopy (AAS) method is described for the determination of cadmium (Cd) in blood, enabling difficulties in sample preparation to be minimized. By control of the ashing step the matrix can be removed without loss of cadmium. Problems with the fast signal response during atomization can be met by spectral band width and temperature control. At the 106 pg level (471 nmol Cd/1 blood; 5-3 mug/100 ml) the relative standard deviation (RSD) was 0-06. Results in four industrial situations are reported. This description of the method should facilitate further investigation of its application to industry using capillary or venous blood. PMID:1131342

Crossover ensembles of random matrices and skew-orthogonal polynomials

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

Kumar, Santosh, E-mail: skumar.physics@gmail.com; Pandey, Akhilesh, E-mail: ap0700@mail.jnu.ac.in

2011-08-15

Highlights: > We study crossover ensembles of Jacobi family of random matrices. > We consider correlations for orthogonal-unitary and symplectic-unitary crossovers. > We use the method of skew-orthogonal polynomials and quaternion determinants. > We prove universality of spectral correlations in crossover ensembles. > We discuss applications to quantum conductance and communication theory problems. - Abstract: In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we givemore » details of the work. We start with Dyson's Brownian motion description of random matrix ensembles and obtain universal hierarchic relations among the unfolded correlation functions. For arbitrary dimensions we derive the joint probability density (jpd) of eigenvalues for all transitions leading to unitary ensembles as equilibrium ensembles. We focus on the orthogonal-unitary and symplectic-unitary crossovers and give generic expressions for jpd of eigenvalues, two-point kernels and n-level correlation functions. This involves generalization of the theory of skew-orthogonal polynomials to crossover ensembles. We also consider crossovers in the circular ensembles to show the generality of our method. In the large dimensionality limit, correlations in spectra with arbitrary initial density are shown to be universal when expressed in terms of a rescaled symmetry breaking parameter. Applications of our crossover results to communication theory and quantum conductance problems are also briefly discussed.« less

The spectrum of a vertex model and related spin one chain sitting in a genus five curve

NASA Astrophysics Data System (ADS)

Martins, M. J.

2017-11-01

We derive the transfer matrix eigenvalues of a three-state vertex model whose weights are based on a R-matrix not of difference form with spectral parameters lying on a genus five curve. We have shown that the basic building blocks for both the transfer matrix eigenvalues and Bethe equations can be expressed in terms of meromorphic functions on an elliptic curve. We discuss the properties of an underlying spin one chain originated from a particular choice of the R-matrix second spectral parameter. We present numerical and analytical evidences that the respective low-energy excitations can be gapped or massless depending on the strength of the interaction coupling. In the massive phase we provide analytical and numerical evidences in favor of an exact expression for the lowest energy gap. We point out that the critical point separating these two distinct physical regimes coincides with the one in which the weights geometry degenerate into union of genus one curves.

Spectral interferences in the determination of rhenium in molybdenum and copper concentrates by inductively coupled plasma optical emission spectrometry (ICP-OES)

NASA Astrophysics Data System (ADS)

Karadjov, Metody; Velitchkova, Nikolaya; Veleva, Olga; Velichkov, Serafim; Markov, Pavel; Daskalova, Nonka

2016-05-01

This paper deals with spectral interferences of complex matrix containing Mo, Al, Ti, Fe, Mg, Ca and Cu in the determination of rhenium in molybdenum and copper concentrates by inductively coupled plasma optical emission spectrometry (ICP-OES). By radial viewing 40.68 MHz ICP equipped with a high resolution spectrometer (spectral bandwidth = 5 pm) the hyperfine structure (HFS) of the most prominent lines of rhenium (Re II 197.248 nm, Re II 221.426 nm and Re II 227.525 nm) was registered. The HFS components under high resolution conditions were used as separate prominent line in order to circumvent spectral interferences. The Q-concept was applied for quantification of spectral interferences. The quantitative databases for the type and the magnitude of the spectral interferences in the presence of above mentioned matrix constituents were obtained by using a radial viewing 40.68 MHz ICP with high resolution and an axial viewing 27.12 MHz ICP with middle resolution. The data for the both ICP-OES systems were collected chiefly with a view to spectrochemical analysis for comparing the magnitude of line and wing (background) spectral interference and the true detection limits with spectroscopic apparatus with different spectral resolution. The sample pretreatment methods by sintering with magnesium oxide and oxidizing agents as well as a microwave acid digestion were applied. The feasibility, accuracy and precision of the analytical results were experimentally demonstrated by certified reference materials.

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Non-Markovian modification of the golden rule rate expression

NASA Astrophysics Data System (ADS)

Basilevsky, M. V.; Davidovich, G. V.; Titov, S. V.; Voronin, A. I.

2006-11-01

The reformulation of the standard golden rule approach considered in this paper for treating reactive tunneling reduces the computation of the reaction rate to a derivation of band shapes for energy levels of reactant and product states. This treatment is based on the assumption that the medium environment is actively involved as a partner in the energy exchange with the reactive subsystem but its reorganization effect is negligible. Starting from the quantum relaxation equation for the density matrix, the required band shapes are represented in terms of the spectral density function, exhibiting the continuum spectrum inherent to the interaction between the reactants and the medium in the total reactive system. The simplest Lorentzian spectral bands, obtained under Redfield approximation, proved to be unsatisfactory because they produced a divergent rate expression at low temperature. The problem is resolved by invoking a refined spectral band shape, which behaves as Lorentzian one at the band center but decays exponentially at its tails. The corresponding closed non-Markovian rate expression is derived and investigated taking as an example the photochemical H-transfer reaction between fluorene and acridine proceeding in the fluorene molecular crystal. The kinetics in this reactive system was thoroughly studied experimentally in a wide temperature range [B. Prass et al., Ber. Bunsenges. Phys. Chem. 102, 498 (1998)].

Factorization-based texture segmentation

DOE PAGES

Yuan, Jiangye; Wang, Deliang; Cheriyadat, Anil M.

2015-06-17

This study introduces a factorization-based approach that efficiently segments textured images. We use local spectral histograms as features, and construct an M × N feature matrix using M-dimensional feature vectors in an N-pixel image. Based on the observation that each feature can be approximated by a linear combination of several representative features, we factor the feature matrix into two matrices-one consisting of the representative features and the other containing the weights of representative features at each pixel used for linear combination. The factorization method is based on singular value decomposition and nonnegative matrix factorization. The method uses local spectral histogramsmore » to discriminate region appearances in a computationally efficient way and at the same time accurately localizes region boundaries. Finally, the experiments conducted on public segmentation data sets show the promise of this simple yet powerful approach.« less

Use Of The Diamond Cell In An Industrial Laboratory

NASA Astrophysics Data System (ADS)

Barbour, Rachael L.; Stephens, J. D.; Cameron, David G.

1989-12-01

The traditional method for recording the IR spectra of solids has been KBr pellet transmission spectroscopy. This technique has several disadvantages: sample preparation time, matrix contamination, spectral distortion, ion exchange, a limited spectral range, scattering, loss of sample integrity during grinding, etc. In recent years, diffuse reflectance, ATR, photoacoustic reflectance, and external reflectance have been used increasingly, facilitated by the high SNR of FT instruments. In many cases, the diamond cell is an attractive alternative to all of these. The spectral range is -100 -1 to the UV, excluding the 2200-2000 cm -1 region. Spectral distortion, usually a great problem with inorganics, is greatly reduced as a result of sample homogeneity (from a spectral point of view) and refractive index matching. There is no matrix contamination: scattering, background slope, and all absorption bands are from the sample. There is no ion exchange. The sample size requirements are minimal. Finally, sample preparation requires the somewhat lost. but powerful, art of microscopic examination. In some instances, there may be sample orientation or pressure induced phase changes associated with the use of the diamond cell. A common misconception is that an IR microscope is needed to use the diamond cell. In fact, ~5 minutes will suffice without a beam condenser; 1 minute is all that is needed with one. In part, this is because one usually has excellent control of the optical thickness; with experience, the cell can easily be assembled to give bands in the 0.7-1.5 absorbance range, and making the sample thinner merely involves pressing the diamonds together. Given the above, the microscope should only be used for inhomogeneous samples as one loses all information below 700 cm-1, the region of greatest value when studying inorganics. We also note that the cell can readily be moved from a mid-IR to a far-IR bench. We have moved to the point where this is the dominant sampling technique, with ATR being the next most important. Diffuse reflectance and KBr pellets are seldom used. The cell has been used on inorganics (mid and far IR) including extremely small pure mineral samples selected by hand. It is also used for polymers, polymer inclusions, filter deposits, pure (and not so puce) organics, and general "what is this stuff" samples. Examples of a wide variety of analyses will be given.

T -matrix approach to quark-gluon plasma

NASA Astrophysics Data System (ADS)

Liu, Shuai Y. F.; Rapp, Ralf

2018-03-01

A self-consistent thermodynamic T -matrix approach is deployed to study the microscopic properties of the quark-gluon plasma (QGP), encompassing both light- and heavy-parton degrees of freedom in a unified framework. The starting point is a relativistic effective Hamiltonian with a universal color force. The input in-medium potential is quantitatively constrained by computing the heavy-quark (HQ) free energy from the static T -matrix and fitting it to pertinent lattice-QCD (lQCD) data. The corresponding T -matrix is then applied to compute the equation of state (EoS) of the QGP in a two-particle irreducible formalism, including the full off-shell properties of the selfconsistent single-parton spectral functions and their two-body interaction. In particular, the skeleton diagram functional is fully resummed to account for emerging bound and scattering states as the critical temperature is approached from above. We find that the solution satisfying three sets of lQCD data (EoS, HQ free energy, and quarkonium correlator ratios) is not unique. As limiting cases we discuss a weakly coupled solution, which features color potentials close to the free energy, relatively sharp quasiparticle spectral functions and weak hadronic resonances near Tc, and a strongly coupled solution with a strong color potential (much larger than the free energy), resulting in broad nonquasiparticle parton spectral functions and strong hadronic resonance states which dominate the EoS when approaching Tc.

Visible-infrared micro-spectrometer based on a preaggregated silver nanoparticle monolayer film and an infrared sensor card

NASA Astrophysics Data System (ADS)

Yang, Tao; Peng, Jing-xiao; Ho, Ho-pui; Song, Chun-yuan; Huang, Xiao-li; Zhu, Yong-yuan; Li, Xing-ao; Huang, Wei

2018-01-01

By using a preaggregated silver nanoparticle monolayer film and an infrared sensor card, we demonstrate a miniature spectrometer design that covers a broad wavelength range from visible to infrared with high spectral resolution. The spectral contents of an incident probe beam are reconstructed by solving a matrix equation with a smoothing simulated annealing algorithm. The proposed spectrometer offers significant advantages over current instruments that are based on Fourier transform and grating dispersion, in terms of size, resolution, spectral range, cost and reliability. The spectrometer contains three components, which are used for dispersion, frequency conversion and detection. Disordered silver nanoparticles in dispersion component reduce the fabrication complexity. An infrared sensor card in the conversion component broaden the operational spectral range of the system into visible and infrared bands. Since the CCD used in the detection component provides very large number of intensity measurements, one can reconstruct the final spectrum with high resolution. An additional feature of our algorithm for solving the matrix equation, which is suitable for reconstructing both broadband and narrowband signals, we have adopted a smoothing step based on a simulated annealing algorithm. This algorithm improve the accuracy of the spectral reconstruction.

Application of Wave Distribution Function Method to the ERG/PWE Data

NASA Astrophysics Data System (ADS)

Ota, M.; Kasahara, Y.; Matsuda, S.; Kojima, H.; Matsuoka, A.; Hikishima, M.; Kasaba, Y.; Ozaki, M.; Yagitani, S.; Tsuchiya, F.; Kumamoto, A.

2017-12-01

The ERG (Arase) satellite was launched on 20 December 2016 to study acceleration and loss mechanisms of relativistic electrons in the Earth's magnetosphere. The Plasma Wave Experiment (PWE), which is one of the science instruments on board the ERG satellite, measures electric field and magnetic field. The PWE consists of three sub-systems; EFD (Electric Field Detector), OFA/WFC (Onboard Frequency Analyzer and Waveform Capture), and HFA (High Frequency Analyzer).The OFA/WFC measures electromagnetic field spectra and raw waveforms in the frequency range from few Hz to 20 kHz. The OFA produces three kind of data; OFA-SPEC (power spectrum), OFA-MATRIX (spectral matrix), and OFA-COMPLEX (complex spectrum). The OFA-MATRIX measures ensemble averaged complex cross-spectra of two electric field components, and of three magnetic field components. The OFA-COMPLEX measures instantaneous complex spectra of electric and magnetic fields. These data are produced every 8 seconds in the nominal mode, and it can be used for polarization analysis and wave propagation direction finding.In general, spectral matrix composed by cross-spectra of observed signals is used for direction finding, and many algorithms have been proposed. For example, Means method and SVD method can be applied on the assumption that the spectral matrix is consists of a single plane wave, while wave distribution function (WDF) method is applicable even to the data in which multiple numbers of plane waves are simultaneously included. In this presentation, we introduce the results when the WDF method is applied to the ERG/PWE data.

CONSTRUCTING A FLEXIBLE LIKELIHOOD FUNCTION FOR SPECTROSCOPIC INFERENCE

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

Czekala, Ian; Andrews, Sean M.; Mandel, Kaisey S.

2015-10-20

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints (pixels) into the residual spectrum. For the high signal-to-noise data with large spectral range that is commonly employed in stellar astrophysics, that covariant structure can lead to dramatically underestimated parameter uncertainties (and, in some cases, biases). We construct a likelihood function that accounts for the structure of the covariance matrix, utilizing the machinery of Gaussian process kernels. This framework specifically addresses the common problem of mismatches in model spectralmore » line strengths (with respect to data) due to intrinsic model imperfections (e.g., in the atomic/molecular databases or opacity prescriptions) by developing a novel local covariance kernel formalism that identifies and self-consistently downweights pathological spectral line “outliers.” By fitting many spectra in a hierarchical manner, these local kernels provide a mechanism to learn about and build data-driven corrections to synthetic spectral libraries. An open-source software implementation of this approach is available at http://iancze.github.io/Starfish, including a sophisticated probabilistic scheme for spectral interpolation when using model libraries that are sparsely sampled in the stellar parameters. We demonstrate some salient features of the framework by fitting the high-resolution V-band spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate-resolution K-band spectrum of Gliese 51, an M5 field dwarf.« less

PCA determination of the radiometric noise of high spectral resolution infrared observations from spectral residuals: Application to IASI

NASA Astrophysics Data System (ADS)

Serio, C.; Masiello, G.; Camy-Peyret, C.; Jacquette, E.; Vandermarcq, O.; Bermudo, F.; Coppens, D.; Tobin, D.

2018-02-01

The problem of characterizing and estimating the instrumental or radiometric noise of satellite high spectral resolution infrared spectrometers directly from Earth observations is addressed in this paper. An approach has been developed, which relies on the Principal Component Analysis (PCA) with a suitable criterion to select the optimal number of PC scores. Different selection criteria have been set up and analysed, which is based on the estimation theory of Least Squares and/or Maximum Likelihood Principle. The approach is independent of any forward model and/or radiative transfer calculations. The PCA is used to define an orthogonal basis, which, in turn, is used to derive an optimal linear reconstruction of the observations. The residual vector that is the observation vector minus the calculated or reconstructed one is then used to estimate the instrumental noise. It will be shown that the use of the spectral residuals to assess the radiometric instrumental noise leads to efficient estimators, which are largely independent of possible departures of the true noise from that assumed a priori to model the observational covariance matrix. Application to the Infrared Atmospheric Sounder Interferometer (IASI) has been considered. A series of case studies has been set up, which make use of IASI observations. As a major result, the analysis confirms the high stability and radiometric performance of IASI. The approach also proved to be efficient in characterizing noise features due to mechanical micro-vibrations of the beam splitter of the IASI instrument.

Optimal fluorescence waveband determination for detecting defect cherry tomatoes using fluorescence excitation-emission matrix

USDA-ARS?s Scientific Manuscript database

A multi-spectral fluorescence imaging technique was used to detect defect cherry tomatoes. The fluorescence excitation and emission matrix was used to measure for defects, sound surface, and stem areas to determine the optimal fluorescence excitation and emission wavelengths for discrimination. Two-...

Using Perturbed QR Factorizations To Solve Linear Least-Squares Problems

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

Avron, Haim; Ng, Esmond G.; Toledo, Sivan

2008-03-21

We propose and analyze a new tool to help solve sparse linear least-squares problems min{sub x} {parallel}Ax-b{parallel}{sub 2}. Our method is based on a sparse QR factorization of a low-rank perturbation {cflx A} of A. More precisely, we show that the R factor of {cflx A} is an effective preconditioner for the least-squares problem min{sub x} {parallel}Ax-b{parallel}{sub 2}, when solved using LSQR. We propose applications for the new technique. When A is rank deficient we can add rows to ensure that the preconditioner is well-conditioned without column pivoting. When A is sparse except for a few dense rows we canmore » drop these dense rows from A to obtain {cflx A}. Another application is solving an updated or downdated problem. If R is a good preconditioner for the original problem A, it is a good preconditioner for the updated/downdated problem {cflx A}. We can also solve what-if scenarios, where we want to find the solution if a column of the original matrix is changed/removed. We present a spectral theory that analyzes the generalized spectrum of the pencil (A*A,R*R) and analyze the applications.« less

Birefringence measurement of retinal nerve fiber layer using polarization-sensitive spectral domain optical coherence tomography with Jones matrix based analysis

NASA Astrophysics Data System (ADS)

Yamanari, Masahiro; Miura, Masahiro; Makita, Shuichi; Yatagai, Toyohiko; Yasuno, Yoshiaki

2007-02-01

Birefringence of retinal nerve fiber layer is measured by polarization-sensitive spectral domain optical coherence tomography using the B-scan-oriented polarization modulation method. Birefringence of the optical fiber and the cornea is compensated by Jones matrix based analysis. Three-dimensional phase retardation map around the optic nerve head and en-face phase retardation map of the retinal nerve fiber layer are shown. Unlike scanning laser polarimetry, our system can measure the phase retardation quantitatively without using bow-tie pattern of the birefringence in the macular region, which enables diagnosis of glaucoma even if the patients have macular disease.

An analytical X-ray CdTe detector response matrix for incomplete charge collection correction for photon energies up to 300 keV

NASA Astrophysics Data System (ADS)

Kurková, Dana; Judas, Libor

2018-05-01

Gamma and X-ray energy spectra measured with semiconductor detectors suffer from various distortions, one of them being so-called "tailing" caused by an incomplete charge collection. Using the Hecht equation, a response matrix of size 321 × 321 was constructed which was used to correct the effect of incomplete charge collection. The correction matrix was constructed analytically for an arbitrary energy bin and the size of the energy bin thus defines the width of the spectral window. The correction matrix can be applied separately from other possible spectral corrections or it can be incorporated into an already existing response matrix of the detector. The correction was tested and its adjustable parameters were optimized on the line spectra of 57Co measured with a cadmium telluride (CdTe) detector in a spectral range from 0 up to 160 keV. The best results were obtained when the values of the free path of holes were spread over a range from 0.4 to 1.0 cm and weighted by a Gauss function. The model with the optimized parameter values was then used to correct the line spectra of 152Eu in a spectral range from 0 up to 530 keV. An improvement in the energy resolution at full width at half maximum from 2.40 % ± 0.28 % to 0.96 % ± 0.28 % was achieved at 344.27 keV. Spectra of "narrow spectrum series" beams, N120, N150, N200, N250 and N300, generated with tube voltages of 120 kV, 150 kV, 200 kV, 250 kV and 300 kV respectively, and measured with the CdTe detector, were corrected in the spectral range from 0 to 160 keV (N120 and N150) and from 0 to 530 keV (N200, N250, N300). All the measured spectra correspond both qualitatively and quantitatively to the available reference data after the correction. To obtain better correspondence between N150, N200, N250 and N300 spectra and the reference data, lower values of the free paths of holes (range from 0.16 to 0.65 cm) were used for X-ray spectra correction, which suggests energy dependence of the phenomenon.

Undecidability of the spectral gap.

PubMed

Cubitt, Toby S; Perez-Garcia, David; Wolf, Michael M

2015-12-10

The spectral gap--the energy difference between the ground state and first excited state of a system--is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped topological spin liquid phases, and the Yang-Mills gap conjecture, concern spectral gaps. These and other problems are particular cases of the general spectral gap problem: given the Hamiltonian of a quantum many-body system, is it gapped or gapless? Here we prove that this is an undecidable problem. Specifically, we construct families of quantum spin systems on a two-dimensional lattice with translationally invariant, nearest-neighbour interactions, for which the spectral gap problem is undecidable. This result extends to undecidability of other low-energy properties, such as the existence of algebraically decaying ground-state correlations. The proof combines Hamiltonian complexity techniques with aperiodic tilings, to construct a Hamiltonian whose ground state encodes the evolution of a quantum phase-estimation algorithm followed by a universal Turing machine. The spectral gap depends on the outcome of the corresponding 'halting problem'. Our result implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless, and that there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics.

Inductively Coupled Plasma Optical Emission Spectrometry for Rare Earth Elements Analysis

NASA Astrophysics Data System (ADS)

He, Man; Hu, Bin; Chen, Beibei; Jiang, Zucheng

2017-01-01

Inductively coupled plasma optical emission spectrometry (ICP-OES) merits multielements capability, high sensitivity, good reproducibility, low matrix effect and wide dynamic linear range for rare earth elements (REEs) analysis. But the spectral interference in trace REEs analysis by ICP-OES is a serious problem due to the complicated emission spectra of REEs, which demands some correction technology including interference factor method, derivative spectrum, Kalman filtering algorithm and partial least-squares (PLS) method. Matrix-matching calibration, internal standard, correction factor and sample dilution are usually employed to overcome or decrease the matrix effect. Coupled with various sample introduction techniques, the analytical performance of ICP-OES for REEs analysis would be improved. Compared with conventional pneumatic nebulization (PN), acid effect and matrix effect are decreased to some extent in flow injection ICP-OES, with higher tolerable matrix concentration and better reproducibility. By using electrothermal vaporization as sample introduction system, direct analysis of solid samples by ICP-OES is achieved and the vaporization behavior of refractory REEs with high boiling point, which can easily form involatile carbides in the graphite tube, could be improved by using chemical modifier, such as polytetrafluoroethylene and 1-phenyl-3-methyl-4-benzoyl-5-pyrazone. Laser ablation-ICP-OES is suitable for the analysis of both conductive and nonconductive solid samples, with the absolute detection limit of ng-pg level and extremely low sample consumption (0.2 % of that in conventional PN introduction). ICP-OES has been extensively employed for trace REEs analysis in high-purity materials, and environmental and biological samples.

Effective approach to spectroscopy and spectral analysis techniques using Matlab

NASA Astrophysics Data System (ADS)

Li, Xiang; Lv, Yong

2017-08-01

With the development of electronic information, computer and network, modern education technology has entered new era, which would give a great impact on teaching process. Spectroscopy and spectral analysis is an elective course for Optoelectronic Information Science and engineering. The teaching objective of this course is to master the basic concepts and principles of spectroscopy, spectral analysis and testing of basic technical means. Then, let the students learn the principle and technology of the spectrum to study the structure and state of the material and the developing process of the technology. MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and fourth-generation programming language. A proprietary programming language developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, Based on the teaching practice, this paper summarizes the new situation of applying Matlab to the teaching of spectroscopy. This would be suitable for most of the current school multimedia assisted teaching

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

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

None, None

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE PAGES

None, None

2016-11-21

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Extending the Dynamic Range of the Ion Trap by Differential Mobility Filtration

PubMed Central

Hall, Adam B.; Coy, Stephen L.; Kafle, Amol; Glick, James; Nazarov, Erkinjon

2013-01-01

A miniature, planar, differential ion mobility spectrometer (DMS) was interfaced to an LCQ classic ion trap to conduct selective ion filtration prior to mass analysis in order to extend the dynamic range of the trap. Space charge effects are known to limit the functional ion storage capacity of ion trap mass analyzers and this, in turn, can affect the quality of the mass spectral data generated. This problem is further exacerbated in the analysis of mixtures where the indiscriminate introduction of matrix ions results in premature trap saturation with non-targeted species, thereby reducing the number of parent ions that may be used to conduct MS/MS experiments for quantitation or other diagnostic studies. We show that conducting differential mobility-based separations prior to mass analysis allows the isolation of targeted analytes from electrosprayed mixtures preventing the indiscriminate introduction of matrix ions and premature trap saturation with analytically unrelated species. Coupling these two analytical techniques is shown to enhance the detection of a targeted drug metabolite from a biological matrix. In its capacity as a selective ion filter, the DMS can improve the analytical performance of analyzers such as quadrupole (3-D or linear) and ion cyclotron resonance (FT-ICR) ion traps that depend on ion accumulation. PMID:23797861

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

Staring 2-D hadamard transform spectral imager

DOEpatents

Gentry, Stephen M [Albuquerque, NM; Wehlburg, Christine M [Albuquerque, NM; Wehlburg, Joseph C [Albuquerque, NM; Smith, Mark W [Albuquerque, NM; Smith, Jody L [Albuquerque, NM

2006-02-07

A staring imaging system inputs a 2D spatial image containing multi-frequency spectral information. This image is encoded in one dimension of the image with a cyclic Hadamarid S-matrix. The resulting image is detecting with a spatial 2D detector; and a computer applies a Hadamard transform to recover the encoded image.

Representations of the quantum doubles of finite group algebras and spectral parameter dependent solutions of the Yang-Baxter equation

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

Dancer, K. A.; Isac, P. S.; Links, J.

2006-10-15

Quantum doubles of finite group algebras form a class of quasitriangular Hopf algebras that algebraically solve the Yang-Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang-Baxter equation. Such solutions do not depend on a spectral parameter, and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter. Here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups D{sub n}. These results may be used to determine constant solutions of the Yang-Baxtermore » equation. We then discuss Baxterization ansaetze to obtain solutions of the Yang-Baxter equation with a spectral parameter and give several examples, including a new 21-vertex model. We also describe this approach in terms of minimal-dimensional representations of the quantum doubles of the alternating group A{sub 4} and the symmetric group S{sub 4}.« less

Assessment of Infrared Sounder Radiometric Noise from Analysis of Spectral Residuals

NASA Astrophysics Data System (ADS)

Dufour, E.; Klonecki, A.; Standfuss, C.; Tournier, B.; Serio, C.; Masiello, G.; Tjemkes, S.; Stuhlmann, R.

2016-08-01

For the preparation and performance monitoring of the future generation of hyperspectral InfraRed sounders dedicated to the precise vertical profiling of the atmospheric state, such as the Meteosat Third Generation hyperspectral InfraRed Sounder, a reliable assessment of the instrument radiometric error covariance matrix is needed.Ideally, an inflight estimation of the radiometrric noise is recommended as certain sources of noise can be driven by the spectral signature of the observed Earth/ atmosphere radiance. Also, unknown correlated noise sources, generally related to incomplete knowledge of the instrument state, can be present, so a caracterisation of the noise spectral correlation is also neeed.A methodology, relying on the analysis of post-retreival spectral residuals, is designed and implemented to derive in-flight the covariance matrix on the basis of Earth scenes measurements. This methodology is successfully demonstrated using IASI observations as MTG-IRS proxy data and made it possible to highlight anticipated correlation structures explained by apodization and micro-vibration effects (ghost). This analysis is corroborated by a parallel estimation based on an IASI black body measurement dataset and the results of an independent micro-vibration model.

Estimation of beam material random field properties via sensitivity-based model updating using experimental frequency response functions

NASA Astrophysics Data System (ADS)

Machado, M. R.; Adhikari, S.; Dos Santos, J. M. C.; Arruda, J. R. F.

2018-03-01

Structural parameter estimation is affected not only by measurement noise but also by unknown uncertainties which are present in the system. Deterministic structural model updating methods minimise the difference between experimentally measured data and computational prediction. Sensitivity-based methods are very efficient in solving structural model updating problems. Material and geometrical parameters of the structure such as Poisson's ratio, Young's modulus, mass density, modal damping, etc. are usually considered deterministic and homogeneous. In this paper, the distributed and non-homogeneous characteristics of these parameters are considered in the model updating. The parameters are taken as spatially correlated random fields and are expanded in a spectral Karhunen-Loève (KL) decomposition. Using the KL expansion, the spectral dynamic stiffness matrix of the beam is expanded as a series in terms of discretized parameters, which can be estimated using sensitivity-based model updating techniques. Numerical and experimental tests involving a beam with distributed bending rigidity and mass density are used to verify the proposed method. This extension of standard model updating procedures can enhance the dynamic description of structural dynamic models.

Endmember extraction from hyperspectral image based on discrete firefly algorithm (EE-DFA)

NASA Astrophysics Data System (ADS)

Zhang, Chengye; Qin, Qiming; Zhang, Tianyuan; Sun, Yuanheng; Chen, Chao

2017-04-01

This study proposed a novel method to extract endmembers from hyperspectral image based on discrete firefly algorithm (EE-DFA). Endmembers are the input of many spectral unmixing algorithms. Hence, in this paper, endmember extraction from hyperspectral image is regarded as a combinational optimization problem to get best spectral unmixing results, which can be solved by the discrete firefly algorithm. Two series of experiments were conducted on the synthetic hyperspectral datasets with different SNR and the AVIRIS Cuprite dataset, respectively. The experimental results were compared with the endmembers extracted by four popular methods: the sequential maximum angle convex cone (SMACC), N-FINDR, Vertex Component Analysis (VCA), and Minimum Volume Constrained Nonnegative Matrix Factorization (MVC-NMF). What's more, the effect of the parameters in the proposed method was tested on both synthetic hyperspectral datasets and AVIRIS Cuprite dataset, and the recommended parameters setting was proposed. The results in this study demonstrated that the proposed EE-DFA method showed better performance than the existing popular methods. Moreover, EE-DFA is robust under different SNR conditions.

Normal modes of the shallow water system on the cubed sphere

NASA Astrophysics Data System (ADS)

Kang, H. G.; Cheong, H. B.; Lee, C. H.

2017-12-01

Spherical harmonics expressed as the Rossby-Haurwitz waves are the normal modes of non-divergent barotropic model. Among the normal modes in the numerical models, the most unstable mode will contaminate the numerical results, and therefore the investigation of normal mode for a given grid system and a discretiztaion method is important. The cubed-sphere grid which consists of six identical faces has been widely adopted in many atmospheric models. This grid system is non-orthogonal grid so that calculation of the normal mode is quiet challenge problem. In the present study, the normal modes of the shallow water system on the cubed sphere discretized by the spectral element method employing the Gauss-Lobatto Lagrange interpolating polynomials as orthogonal basis functions is investigated. The algebraic equations for the shallow water equation on the cubed sphere are derived, and the huge global matrix is constructed. The linear system representing the eigenvalue-eigenvector relations is solved by numerical libraries. The normal mode calculated for the several horizontal resolution and lamb parameters will be discussed and compared to the normal mode from the spherical harmonics spectral method.

Combining NMR spectral and structural data to form models of polychlorinated dibenzodioxins, dibenzofurans, and biphenyls binding to the AhR

NASA Astrophysics Data System (ADS)

Beger, Richard D.; Buzatu, Dan A.; Wilkes, Jon G.

2002-10-01

A three-dimensional quantitative spectrometric data-activity relationship (3D-QSDAR) modeling technique which uses NMR spectral and structural information that is combined in a 3D-connectivity matrix has been developed. A 3D-connectivity matrix was built by displaying all possible assigned carbon NMR chemical shifts, carbon-to-carbon connections, and distances between the carbons. Two-dimensional 13C-13C COSY and 2D slices from the distance dimension of the 3D-connectivity matrix were used to produce a relationship among the 2D spectral patterns for polychlorinated dibenzofurans, dibenzodioxins, and biphenyls (PCDFs, PCDDs, and PCBs respectively) binding to the aryl hydrocarbon receptor (AhR). We refer to this technique as comparative structural connectivity spectral analysis (CoSCoSA) modeling. All CoSCoSA models were developed using forward multiple linear regression analysis of the predicted 13C NMR structure-connectivity spectral bins. A CoSCoSA model for 26 PCDFs had an explained variance (r2) of 0.93 and an average leave-four-out cross-validated variance (q4 2) of 0.89. A CoSCoSA model for 14 PCDDs produced an r2 of 0.90 and an average leave-two-out cross-validated variance (q2 2) of 0.79. One CoSCoSA model for 12 PCBs gave an r2 of 0.91 and an average q2 2 of 0.80. Another CoSCoSA model for all 52 compounds had an r2 of 0.85 and an average q4 2 of 0.52. Major benefits of CoSCoSA modeling include ease of development since the technique does not use molecular docking routines.

VizieR Online Data Catalog: Vela Junior (RX J0852.0-4622) HESS image (HESS+, 2018)

NASA Astrophysics Data System (ADS)

H. E. S. S. Collaboration; Abdalla, H.; Abramowski, A.; Aharonian, F.; Ait Benkhali, F.; Akhperjanian, A. G.; Andersson, T.; Anguener, E. O.; Arakawa, M.; Arrieta, M.; Aubert, P.; Backes, M.; Balzer, A.; Barnard, M.; Becherini, Y.; Becker Tjus, J.; Berge, D.; Bernhard, S.; Bernloehr, K.; Blackwell, R.; Boettcher, M.; Boisson, C.; Bolmont, J.; Bordas, P.; Bregeon, J.; Brun, F.; Brun, P.; Bryan, M.; Buechele, M.; Bulik, T.; Capasso, M.; Carr, J.; Casanova, S.; Cerruti, M.; Chakraborty, N.; Chalme-Calvet, R.; Chaves, R. C. G.; Chen, A.; Chevalier, J.; Chretien, M.; Coffaro, M.; Colafrancesco, S.; Cologna, G.; Condon, B.; Conrad, J.; Cui, Y.; Davids, I. D.; Decock, J.; Degrange, B.; Deil, C.; Devin, J.; Dewilt, P.; Dirson, L.; Djannati-Atai, A.; Domainko, W.; Donath, A.; Drury, L. O'c.; Dutson, K.; Dyks, J.; Edwards, T.; Egberts, K.; Eger, P.; Ernenwein, J.-P.; Eschbach, S.; Farnier, C.; Fegan, S.; Fernandes, M. V.; Fiasson, A.; Fontaine, G.; Foerster, A.; Funk, S.; Fuessling, M.; Gabici, S.; Gajdus, M.; Gallant, Y. A.; Garrigoux, T.; Giavitto, G.; Giebels, B.; Glicenstein, J. F.; Gottschall, D.; Goyal, A.; Grondin, M.-H.; Hahn, J.; Haupt, M.; Hawkes, J.; Heinzelmann, G.; Henri, G.; Hermann, G.; Hervet, O.; Hinton, J. A.; Hofmann, W.; Hoischen, C.; Holler, M.; Horns, D.; Ivascenko, A.; Iwasaki, H.; Jacholkowska, A.; Jamrozy, M.; Janiak, M.; Jankowsky, D.; Jankowsky, F.; Jingo, M.; Jogler, T.; Jouvin, L.; Jung-Richardt, I.; Kastendieck, M. A.; Katarzynski, K.; Katsuragawa, M.; Katz, U.; Kerszberg, D.; Khangulyan, D.; Khelifi, B.; Kieffer, M.; King, J.; Klepser, S.; Klochkov, D.; Kluzniak, W.; Kolitzus, D.; Komin, Nu.; Kosack, K.; Krakau, S.; Kraus, M.; Krueger, P. P.; Laffon, H.; Lamanna, G.; Lau, J.; Lees, J.-P.; Lefaucheur, J.; Lefranc, V.; Lemiere, A.; Lemoine-Goumard, M.; Lenain, J.-P.; Leser, E.; Lohse, T.; Lorentz, M.; Liu, R.; Lopez-Coto, R.; Lypova, I.; Marandon, V.; Marcowith, A.; Mariaud, C.; Marx, R.; Maurin, G.; Maxted, N.; Mayer, M.; Meintjes, P. J.; Meyer, M.; Mitchell, A. M. W.; Moderski, R.; Mohamed, M.; Mohrmann, L.; Mora, K.; Moulin, E.; Murach, T.; Nakashima, S.; de Naurois, M.; Niederwanger, F.; Niemiec J.; Oakes, L.; O'Brien, P.; Odaka, H.; Oettl, S.; Ohm, S.; Ostrowski, M.; Oya, I.; Padovani, M.; Panter, M.; Parsons, R. D.; Paz Arribas, M.; Pekeur, N. W.; Pelletier, G.; Perennes, C.; Petrucci, P.-O.; Peyaud, B.; Piel, Q.; Pita, S.; Poon, H.; Prokhorov, D.; Prokoph, H.; Puehlhofer, G.; Punch, M.; Quirrenbach, A.; Raab, S.; Reimer, A.; Reimer, O.; Renaud, M.; de Los Reyes, R.; Richter, S.; Rieger, F.; Romoli, C.; Rowell, G.; Rudak, B.; Rulten, C. B.; Sahakian, V.; Saito, S.; Salek, D.; Sanchez, D. A.; Santangelo, A.; Sasaki, M.; Schlickeiser, R.; Schuessler, F.; Schulz, A.; Schwanke, U.; Schwemmer, S.; Seglar-Arroyo, M.; Settimo, M.; Seyffert, A. S.; Shafi, N.; Shilon, I.; Simoni, R.; Sol, H.; Spanier, F.; Spengler, G.; Spies, F.; Stawarz, L.; Steenkamp, R.; Stegmann, C.; Stycz, K.; Sushch, I.; Takahashi, T.; Tavernet, J.-P.; Tavernier, T.; Taylor, A. M.; Terrier, R.; Tibaldo, L.; Tiziani, D.; Tluczykont, M.; Trichard, C.; Tsuji, N.; Tuffs, R.; Uchiyama, Y.; van der, Walt D. J.; van Eldik, C.; van Rensburg, C.; van Soelen, B.; Vasileiadis, G.; Veh, J.; Venter, C.; Viana, A.; Vincent, P.; Vink, J.; Voisin, F.; Voelk, H. J.; Vuillaume, T.; Wadiasingh, Z.; Wagner, S. J.; Wagner, P.; Wagner, R. M.; White, R.; Wierzcholska, A.; Willmann, P.; Woernlein, A.; Wouters, D.; Yang, R.; Zabalza, V.; Zaborov, D.; Zacharias, M.; Zanin, R.; Zdziarski, A. A.; Zech, A.; Zefi, F.; Ziegler, A.; Zywucka, N.

2018-03-01

skymap.fit: H.E.S.S. excess skymap in FITS format of the region comprising Vela Junior and its surroundings. The excess map has been corrected for the gradient of exposure and smoothed with a Gaussian function of width 0.08° to match the analysis point spread function, matching the procedure applied to derive the maps in Fig. 1. sp_stat.txt: H.E.S.S. spectral points and fit parameters for Vela Junior (H.E.S.S. data points in Fig. 3 and Tab. A.2 and H.E.S.S. spectral fit parameters in Tab. 4). The errors in this file represent statistical uncertainties at 1 sigma confidence level. The covariance matrix of the fit is also included in the format: c11 c12 c_13 c21 c22 c_23 c31 c32 c_33 where the subindices represent the following parameters of the power-law with exponential cut-off (ECPL) formula in Tab. 2: 1: flux normalization (Phi0) 2: spectral index (Gamma) 3: inverse of the cutoff energy (lambda=1/Ecut) The units for the covariance matrix are the same as for the fit parameters. Notice that, while the fit parameters section of the file shows E_cut as parameter, the fit was done in lambda=1/Ecut; hence the covariance matrix shows the values for lambda in TeV-1. sp_syst.txt: H.E.S.S. spectral points and fit parameters for Vela Junior (H.E.S.S. data points in Fig. 3 and Tab. A.2 and H.E.S.S. spectral fit parameters in Tab. 4). The errors in this file represent systematic uncertainties at 1 sigma confidence level. The integral fluxes for several energy ranges are also included. (4 data files).

Simultaneous screening of targeted and non-targeted contaminants using an LC-QTOF-MS system and automated MS/MS library searching.

PubMed

Herrera-Lopez, S; Hernando, M D; García-Calvo, E; Fernández-Alba, A R; Ulaszewska, M M

2014-09-01

Simultaneous high-resolution full-scan and tandem mass spectrometry (MS/MS) analysis using time of flight mass spectrometry brings an answer for increasing demand of retrospective and non-targeted data analysis. Such analysis combined with spectral library searching is a promising tool for targeted and untargeted screening of small molecules. Despite considerable extension of the panel of compounds of tandem mass spectral libraries, the heterogeneity of spectral data poses a major challenge against the effective usage of spectral libraries. Performance evaluation of available LC-MS/MS libraries will significantly increase credibility in the search results. The present work was aimed to evaluate fluctuation of MS/MS pattern, in the peak intensities distribution together with mass accuracy measurements, and in consequence, performance compliant with ion ratio and mass error criteria as principles in identification processes for targeted and untargeted contaminants at trace levels. Matrix effect and ultra-trace levels of concentration (from 50 ng l(-1) to 1000 ng l(-1) were evaluated as potential source of inaccuracy in the performance of spectral matching. Matrix-matched samples and real samples were screened for proof of applicability. By manual review of data and application of ion ratio and ppm error criteria, false negatives were obtained; this number diminished when in-house library was used, while with on-line MS/MS databases 100% of positive samples were found. In our experience, intensity of peaks across spectra was highly correlated to the concentration effect and matrix complexity. In turn, analysis of spectra acquired at trace concentrations and in different matrices results in better performance in providing correct and reliable identification. Copyright © 2014 John Wiley & Sons, Ltd.

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

NASA Astrophysics Data System (ADS)

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

2018-05-01

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 +1 dimensions. We have found that, close to the ground state E ≈0 , discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N , which we compute analytically and numerically, grows exponentially with N for E ≈0 . However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈0 , the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first O (N ) eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N . Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor g (t ), obtained from the connected two-level correlation function of the unfolded spectrum, decays as 1 /t2 for times shorter but comparable to the Thouless time with g (0 ) related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

Confined One Dimensional Harmonic Oscillator as a Two-Mode System

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

Gueorguiev, V G; Rau, A P; Draayer, J P

2005-07-11

The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in anymore » other way. An alternative to casting the problem in terms of one or the other basis set consists of using an ''oblique'' basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful.« less

Spectral resolution of SU(3)-invariant solutions of the Yang-Baxter equation

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

Alishauskas, S.I.; Kulish, P.P.

1986-11-20

The spectral resolution of invariant R-matrices is computed on the basis of solution of the defining equation. Multiple representations in the Clebsch-Gordon series are considered by means of the classifying operator A: a linear combination of known operators of third and fourth degrees in the group generators. The matrix elements of A in a nonorthonormal basis are found. Explicit expressions are presented for the spectral resolutions for a number of representations.

Spectral resolution of SU(3)-invariant solutions of the Yang-Baxter equation

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

Alishavskas, S.I.; Kulish, P.P.

1986-11-01

The spectral resolution of invariant R-matrices is computed on the basis of solution of the defining equation. Multiple representations in the Clebsch-Gordon series are considered by means of the classifying operator A: a linear combination of known operators of third and fourth degrees in the group generators. The matrix elements of A in a nonorthonormal basis are found. Explicit expressions are presented for the spectral resolutions for a number of representations.

Characterization of cancer and normal tissue fluorescence through wavelet transform and singular value decomposition

NASA Astrophysics Data System (ADS)

Gharekhan, Anita H.; Biswal, Nrusingh C.; Gupta, Sharad; Pradhan, Asima; Sureshkumar, M. B.; Panigrahi, Prasanta K.

2008-02-01

The statistical and characteristic features of the polarized fluorescence spectra from cancer, normal and benign human breast tissues are studied through wavelet transform and singular value decomposition. The discrete wavelets enabled one to isolate high and low frequency spectral fluctuations, which revealed substantial randomization in the cancerous tissues, not present in the normal cases. In particular, the fluctuations fitted well with a Gaussian distribution for the cancerous tissues in the perpendicular component. One finds non-Gaussian behavior for normal and benign tissues' spectral variations. The study of the difference of intensities in parallel and perpendicular channels, which is free from the diffusive component, revealed weak fluorescence activity in the 630nm domain, for the cancerous tissues. This may be ascribable to porphyrin emission. The role of both scatterers and fluorophores in the observed minor intensity peak for the cancer case is experimentally confirmed through tissue-phantom experiments. Continuous Morlet wavelet also highlighted this domain for the cancerous tissue fluorescence spectra. Correlation in the spectral fluctuation is further studied in different tissue types through singular value decomposition. Apart from identifying different domains of spectral activity for diseased and non-diseased tissues, we found random matrix support for the spectral fluctuations. The small eigenvalues of the perpendicular polarized fluorescence spectra of cancerous tissues fitted remarkably well with random matrix prediction for Gaussian random variables, confirming our observations about spectral fluctuations in the wavelet domain.

Research on the application of a decoupling algorithm for structure analysis

NASA Technical Reports Server (NTRS)

Denman, E. D.

1980-01-01

The mathematical theory for decoupling mth-order matrix differential equations is presented. It is shown that the decoupling precedure can be developed from the algebraic theory of matrix polynomials. The role of eigenprojectors and latent projectors in the decoupling process is discussed and the mathematical relationships between eigenvalues, eigenvectors, latent roots, and latent vectors are developed. It is shown that the eigenvectors of the companion form of a matrix contains the latent vectors as a subset. The spectral decomposition of a matrix and the application to differential equations is given.

Spectroscopic studies of clusterization of methanol molecules isolated in a nitrogen matrix

NASA Astrophysics Data System (ADS)

Vaskivskyi, Ye.; Doroshenko, I.; Chernolevska, Ye.; Pogorelov, V.; Pitsevich, G.

2017-12-01

IR absorption spectra of methanol isolated in a nitrogen matrix are recorded at temperatures ranging from 9 to 34 K. The changes in the spectra with increasing matrix temperature are analyzed. Based on quantum-chemical calculations of the geometric and spectral parameters of different methanol clusters, the observed absorption bands are identified. The cluster composition of the sample is determined at each temperature. It is shown that as the matrix is heated there is a redistribution among the different cluster structures in the sample, from smaller to larger clusters.

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

Campbell, Keri R.; Judge, Elizabeth J.; Barefield, James E.

We show the analysis of light water reactor simulated used nuclear fuel using laser-induced breakdown spectroscopy (LIBS) is explored using a simplified version of the main oxide phase. The main oxide phase consists of the actinides, lanthanides, and zirconium. The purpose of this study is to develop a rapid, quantitative technique for measuring zirconium in a uranium dioxide matrix without the need to dissolve the material. A second set of materials including cerium oxide is also analyzed to determine precision and limit of detection (LOD) using LIBS in a complex matrix. Two types of samples are used in this study:more » binary and ternary oxide pellets. The ternary oxide, (U,Zr,Ce)O 2 pellets used in this study are a simplified version the main oxide phase of used nuclear fuel. The binary oxides, (U,Ce)O 2 and (U,Zr)O 2 are also examined to determine spectral emission lines for Ce and Zr, potential spectral interferences with uranium and baseline LOD values for Ce and Zr in a UO 2 matrix. In the spectral range of 200 to 800 nm, 33 cerium lines and 25 zirconium lines were identified and shown to have linear correlation values (R 2) > 0.97 for both the binary and ternary oxides. The cerium LOD in the (U,Ce)O 2 matrix ranged from 0.34 to 1.08 wt% and 0.94 to 1.22 wt% in (U,Ce,Zr)O 2 for 33 of Ce emission lines. The zirconium limit of detection in the (U,Zr)O 2 matrix ranged from 0.84 to 1.15 wt% and 0.99 to 1.10 wt% in (U,Ce,Zr)O 2 for 25 Zr lines. Finally, the effect of multiple elements in the plasma and the impact on the LOD is discussed.« less

Determination of 18 kinds of trace impurities in the vanadium battery grade vanadyl sulfate by ICP-OES

NASA Astrophysics Data System (ADS)

Yong, Cheng

2018-03-01

The method that direct determination of 18 kinds of trace impurities in the vanadium battery grade vanadyl sulfate by inductively coupled plasma atomic emission spectrometry (ICP-OES) was established, and the detection range includes 0.001% ∼ 0.100% of Fe, Cr, Ni, Cu, Mn, Mo, Pb, As, Co, P, Ti, Zn and 0.005% ∼ 0.100% of K, Na, Ca, Mg, Si, Al. That the influence of the matrix effects, spectral interferences and background continuum superposition in the high concentrations of vanadium ions and sulfate coexistence system had been studied, and then the following conclusions were obtained: the sulfate at this concentration had no effect on the determination, but the matrix effects or continuous background superposition which were generated by high concentration of vanadium ions had negative interference on the determination of potassium and sodium, and it produced a positive interference on the determination of the iron and other impurity elements, so that the impacts of high vanadium matrix were eliminated by the matrix matching and combining synchronous background correction measures. Through the spectral interference test, the paper classification summarized the spectral interferences of vanadium matrix and between the impurity elements, and the analytical lines, the background correction regions and working parameters of the spectrometer were all optimized. The technical performance index of the analysis method is that the background equivalent concentration -0.0003%(Na)~0.0004%(Cu), the detection limit of the element is 0.0001%∼ 0.0003%, RSD<10% when the element content is in the range from 0.001% to 0.007%, RSD< 20% even if the element content is in the range from 0.0001% to 0.001% that is beyond the scope of the method of detection, recoveries is 91.0% ∼ 110.0%.

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

Conformational effects on cationization of poly(ethylene glycol) by alkali metal ions in matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

NASA Astrophysics Data System (ADS)

Shimada, Kayori; Matsuyama, Shigetomo; Saito, Takeshi; Kinugasa, Shinichi; Nagahata, Ritsuko; Kawabata, Shin-Ichirou

2005-12-01

Conformational effects of polymer chains on matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) were studied by using an equimolar mixture of uniform poly(ethylene glycol)s (PEGs) and by molecular dynamics simulations. Uniform PEGs with degrees of polymerization n = 8-39 were separated from commercial PEG samples by preparative supercritical fluid chromatography. MALDI-TOFMS spectra of an equimolar mixture of the uniform PEGs in aqueous ethanol were measured by adding a mixture of 2,5-dihydroxybenzoic acid (as a matrix reagent) and five alkali metal chlorides (LiCl, NaCl, KCl, RbCl, and CsCl). After optimization of the matrix concentration and laser power, five types of adduct cationized by Li+, Na+, K+, Rb+, and Cs+ could be identified simultaneously in the same spectrum. In the lower molecular-mass region around 103, the spectral intensity increase rapidly with increasing molecular mass of PEG; this rapid increase in the spectral intensity started at a lower molecular mass for smaller adduct cations. Molecular dynamics simulations were used to calculated the affinity of PEG for the adduct cations. These experimental and simulated results showed that the observed spectral intensities in MALDI-TOFMS were markedly affected by the species of adduct cations and the degree of polymerization of the PEG, and that they were dependent on the stability of the PEG-cation complex.

Linear Spectral Analysis of Plume Emissions Using an Optical Matrix Processor

NASA Technical Reports Server (NTRS)

Gary, C. K.

1992-01-01

Plume spectrometry provides a means to monitor the health of a burning rocket engine, and optical matrix processors provide a means to analyze the plume spectra in real time. By observing the spectrum of the exhaust plume of a rocket engine, researchers have detected anomalous behavior of the engine and have even determined the failure of some equipment before it would normally have been noticed. The spectrum of the plume is analyzed by isolating information in the spectrum about the various materials present to estimate what materials are being burned in the engine. Scientists at the Marshall Space Flight Center (MSFC) have implemented a high resolution spectrometer to discriminate the spectral peaks of the many species present in the plume. Researchers at the Stennis Space Center Demonstration Testbed Facility (DTF) have implemented a high resolution spectrometer observing a 1200-lb. thrust engine. At this facility, known concentrations of contaminants can be introduced into the burn, allowing for the confirmation of diagnostic algorithms. While the high resolution of the measured spectra has allowed greatly increased insight into the functioning of the engine, the large data flows generated limit the ability to perform real-time processing. The use of an optical matrix processor and the linear analysis technique described below may allow for the detailed real-time analysis of the engine's health. A small optical matrix processor can perform the required mathematical analysis both quicker and with less energy than a large electronic computer dedicated to the same spectral analysis routine.

Circular Mixture Modeling of Color Distribution for Blind Stain Separation in Pathology Images.

PubMed

Li, Xingyu; Plataniotis, Konstantinos N

2017-01-01

In digital pathology, to address color variation and histological component colocalization in pathology images, stain decomposition is usually performed preceding spectral normalization and tissue component segmentation. This paper examines the problem of stain decomposition, which is a naturally nonnegative matrix factorization (NMF) problem in algebra, and introduces a systematical and analytical solution consisting of a circular color analysis module and an NMF-based computation module. Unlike the paradigm of existing stain decomposition algorithms where stain proportions are computed from estimated stain spectra using a matrix inverse operation directly, the introduced solution estimates stain spectra and stain depths via probabilistic reasoning individually. Since the proposed method pays extra attentions to achromatic pixels in color analysis and stain co-occurrence in pixel clustering, it achieves consistent and reliable stain decomposition with minimum decomposition residue. Particularly, aware of the periodic and angular nature of hue, we propose the use of a circular von Mises mixture model to analyze the hue distribution, and provide a complete color-based pixel soft-clustering solution to address color mixing introduced by stain overlap. This innovation combined with saturation-weighted computation makes our study effective for weak stains and broad-spectrum stains. Extensive experimentation on multiple public pathology datasets suggests that our approach outperforms state-of-the-art blind stain separation methods in terms of decomposition effectiveness.

Orthogonal Polynomials on the Unit Circle with Fibonacci Verblunsky Coefficients, II. Applications

NASA Astrophysics Data System (ADS)

Damanik, David; Munger, Paul; Yessen, William N.

2013-10-01

We consider CMV matrices with Verblunsky coefficients determined in an appropriate way by the Fibonacci sequence and present two applications of the spectral theory of such matrices to problems in mathematical physics. In our first application we estimate the spreading rates of quantum walks on the line with time-independent coins following the Fibonacci sequence. The estimates we obtain are explicit in terms of the parameters of the system. In our second application, we establish a connection between the classical nearest neighbor Ising model on the one-dimensional lattice in the complex magnetic field regime, and CMV operators. In particular, given a sequence of nearest-neighbor interaction couplings, we construct a sequence of Verblunsky coefficients, such that the support of the Lee-Yang zeros of the partition function for the Ising model in the thermodynamic limit coincides with the essential spectrum of the CMV matrix with the constructed Verblunsky coefficients. Under certain technical conditions, we also show that the zeros distribution measure coincides with the density of states measure for the CMV matrix.

Quantum Linear System Algorithm for Dense Matrices

NASA Astrophysics Data System (ADS)

Wossnig, Leonard; Zhao, Zhikuan; Prakash, Anupam

2018-02-01

Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix A and a vector b the task is to find the vector x such that A x =b . We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of O (κ2√{n }polylog(n )/ɛ ) for an n ×n dimensional A with bounded spectral norm, where κ denotes the condition number of A , and ɛ is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of A and the vector of Euclidean norms of the rows of A .

Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides

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

Abdel-Rehim, A M; Stathopoulos, Andreas; Orginos, Kostas

2014-08-01

The technique that was used to build the EigCG algorithm for sparse symmetric linear systems is extended to the nonsymmetric case using the BiCG algorithm. We show that, similarly to the symmetric case, we can build an algorithm that is capable of computing a few smallest magnitude eigenvalues and their corresponding left and right eigenvectors of a nonsymmetric matrix using only a small window of the BiCG residuals while simultaneously solving a linear system with that matrix. For a system with multiple right-hand sides, we give an algorithm that computes incrementally more eigenvalues while solving the first few systems andmore » then uses the computed eigenvectors to deflate BiCGStab for the remaining systems. Our experiments on various test problems, including Lattice QCD, show the remarkable ability of EigBiCG to compute spectral approximations with accuracy comparable to that of the unrestarted, nonsymmetric Lanczos. Furthermore, our incremental EigBiCG followed by appropriately restarted and deflated BiCGStab provides a competitive method for systems with multiple right-hand sides.« less

Emergent spectral properties of river network topology: an optimal channel network approach.

PubMed

Abed-Elmdoust, Armaghan; Singh, Arvind; Yang, Zong-Liang

2017-09-13

Characterization of river drainage networks has been a subject of research for many years. However, most previous studies have been limited to quantities which are loosely connected to the topological properties of these networks. In this work, through a graph-theoretic formulation of drainage river networks, we investigate the eigenvalue spectra of their adjacency matrix. First, we introduce a graph theory model for river networks and explore the properties of the network through its adjacency matrix. Next, we show that the eigenvalue spectra of such complex networks follow distinct patterns and exhibit striking features including a spectral gap in which no eigenvalue exists as well as a finite number of zero eigenvalues. We show that such spectral features are closely related to the branching topology of the associated river networks. In this regard, we find an empirical relation for the spectral gap and nullity in terms of the energy dissipation exponent of the drainage networks. In addition, the eigenvalue distribution is found to follow a finite-width probability density function with certain skewness which is related to the drainage pattern. Our results are based on optimal channel network simulations and validated through examples obtained from physical experiments on landscape evolution. These results suggest the potential of the spectral graph techniques in characterizing and modeling river networks.

Artifacts reduction in VIR/Dawn data.

PubMed

Carrozzo, F G; Raponi, A; De Sanctis, M C; Ammannito, E; Giardino, M; D'Aversa, E; Fonte, S; Tosi, F

2016-12-01

Remote sensing images are generally affected by different types of noise that degrade the quality of the spectral data (i.e., stripes and spikes). Hyperspectral images returned by a Visible and InfraRed (VIR) spectrometer onboard the NASA Dawn mission exhibit residual systematic artifacts. VIR is an imaging spectrometer coupling high spectral and spatial resolutions in the visible and infrared spectral domain (0.25-5.0 μm). VIR data present one type of noise that may mask or distort real features (i.e., spikes and stripes), which may lead to misinterpretation of the surface composition. This paper presents a technique for the minimization of artifacts in VIR data that include a new instrument response function combining ground and in-flight radiometric measurements, correction of spectral spikes, odd-even band effects, systematic vertical stripes, high-frequency noise, and comparison with ground telescopic spectra of Vesta and Ceres. We developed a correction of artifacts in a two steps process: creation of the artifacts matrix and application of the same matrix to the VIR dataset. In the approach presented here, a polynomial function is used to fit the high frequency variations. After applying these corrections, the resulting spectra show improvements of the quality of the data. The new calibrated data enhance the significance of results from the spectral analysis of Vesta and Ceres.

Classification of fresh and frozen-thawed pork muscles using visible and near infrared hyperspectral imaging and textural analysis.

PubMed

Pu, Hongbin; Sun, Da-Wen; Ma, Ji; Cheng, Jun-Hu

2015-01-01

The potential of visible and near infrared hyperspectral imaging was investigated as a rapid and nondestructive technique for classifying fresh and frozen-thawed meats by integrating critical spectral and image features extracted from hyperspectral images in the region of 400-1000 nm. Six feature wavelengths (400, 446, 477, 516, 592 and 686 nm) were identified using uninformative variable elimination and successive projections algorithm. Image textural features of the principal component images from hyperspectral images were obtained using histogram statistics (HS), gray level co-occurrence matrix (GLCM) and gray level-gradient co-occurrence matrix (GLGCM). By these spectral and textural features, probabilistic neural network (PNN) models for classification of fresh and frozen-thawed pork meats were established. Compared with the models using the optimum wavelengths only, optimum wavelengths with HS image features, and optimum wavelengths with GLCM image features, the model integrating optimum wavelengths with GLGCM gave the highest classification rate of 93.14% and 90.91% for calibration and validation sets, respectively. Results indicated that the classification accuracy can be improved by combining spectral features with textural features and the fusion of critical spectral and textural features had better potential than single spectral extraction in classifying fresh and frozen-thawed pork meat. Copyright © 2014 Elsevier Ltd. All rights reserved.

Scattering theory of stochastic electromagnetic light waves.

PubMed

Wang, Tao; Zhao, Daomu

2010-07-15

We generalize scattering theory to stochastic electromagnetic light waves. It is shown that when a stochastic electromagnetic light wave is scattered from a medium, the properties of the scattered field can be characterized by a 3 x 3 cross-spectral density matrix. An example of scattering of a spatially coherent electromagnetic light wave from a deterministic medium is discussed. Some interesting phenomena emerge, including the changes of the spectral degree of coherence and of the spectral degree of polarization of the scattered field.

On the matrix Fourier filtering problem for a class of models of nonlinear optical systems with a feedback

NASA Astrophysics Data System (ADS)

Razgulin, A. V.; Sazonova, S. V.

2017-09-01

A novel statement of the Fourier filtering problem based on the use of matrix Fourier filters instead of conventional multiplier filters is considered. The basic properties of the matrix Fourier filtering for the filters in the Hilbert-Schmidt class are established. It is proved that the solutions with a finite energy to the periodic initial boundary value problem for the quasi-linear functional differential diffusion equation with the matrix Fourier filtering Lipschitz continuously depend on the filter. The problem of optimal matrix Fourier filtering is formulated, and its solvability for various classes of matrix Fourier filters is proved. It is proved that the objective functional is differentiable with respect to the matrix Fourier filter, and the convergence of a version of the gradient projection method is also proved.

Improving color constancy by discounting the variation of camera spectral sensitivity

NASA Astrophysics Data System (ADS)

Gao, Shao-Bing; Zhang, Ming; Li, Chao-Yi; Li, Yong-Jie

2017-08-01

It is an ill-posed problem to recover the true scene colors from a color biased image by discounting the effects of scene illuminant and camera spectral sensitivity (CSS) at the same time. Most color constancy (CC) models have been designed to first estimate the illuminant color, which is then removed from the color biased image to obtain an image taken under white light, without the explicit consideration of CSS effect on CC. This paper first studies the CSS effect on illuminant estimation arising in the inter-dataset-based CC (inter-CC), i.e., training a CC model on one dataset and then testing on another dataset captured by a distinct CSS. We show the clear degradation of existing CC models for inter-CC application. Then a simple way is proposed to overcome such degradation by first learning quickly a transform matrix between the two distinct CSSs (CSS-1 and CSS-2). The learned matrix is then used to convert the data (including the illuminant ground truth and the color biased images) rendered under CSS-1 into CSS-2, and then train and apply the CC model on the color biased images under CSS-2, without the need of burdensome acquiring of training set under CSS-2. Extensive experiments on synthetic and real images show that our method can clearly improve the inter-CC performance for traditional CC algorithms. We suggest that by taking the CSS effect into account, it is more likely to obtain the truly color constant images invariant to the changes of both illuminant and camera sensors.

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

Hybrid parallelization of the XTOR-2F code for the simulation of two-fluid MHD instabilities in tokamaks

NASA Astrophysics Data System (ADS)

Marx, Alain; Lütjens, Hinrich

2017-03-01

A hybrid MPI/OpenMP parallel version of the XTOR-2F code [Lütjens and Luciani, J. Comput. Phys. 229 (2010) 8130] solving the two-fluid MHD equations in full tokamak geometry by means of an iterative Newton-Krylov matrix-free method has been developed. The present work shows that the code has been parallelized significantly despite the numerical profile of the problem solved by XTOR-2F, i.e. a discretization with pseudo-spectral representations in all angular directions, the stiffness of the two-fluid stability problem in tokamaks, and the use of a direct LU decomposition to invert the physical pre-conditioner at every Krylov iteration of the solver. The execution time of the parallelized version is an order of magnitude smaller than the sequential one for low resolution cases, with an increasing speedup when the discretization mesh is refined. Moreover, it allows to perform simulations with higher resolutions, previously forbidden because of memory limitations.

Partitioning technique for open systems

NASA Astrophysics Data System (ADS)

Brändas, Erkki J.

2010-11-01

The focus of the present contribution is essentially confined to three research areas carried out during the author's turns as visiting (assistant, associate and full) professor at the University of Florida's Quantum Theory Project, QTP. The first two topics relate to perturbation theory and spectral theory for self-adjoint operators in Hilbert space. The third subject concerns analytic extensions to non-self-adjoint problems, where particular consequences of the occurrence of continuous energy spectra are measured. In these studies general partitioning methods serve as general cover for perturbation-, variational- and general matrix theory. In addition we follow up associated inferences for the time dependent problem as well as recent results and conclusions of a rather general yet surprising character. Although the author spent most of his times at QTP during visits in the 1970s and 1980s, collaborations with department members and shorter stays continued through later decades. Nevertheless the impact must be somewhat fragmentary, yet it is hoped that the present account is sufficiently self-contained to be realistic and constructive.

Global analysis of an impulsive delayed Lotka-Volterra competition system

NASA Astrophysics Data System (ADS)

Xia, Yonghui

2011-03-01

In this paper, a retarded impulsive n-species Lotka-Volterra competition system with feedback controls is studied. Some sufficient conditions are obtained to guarantee the global exponential stability and global asymptotic stability of a unique equilibrium for such a high-dimensional biological system. The problem considered in this paper is in many aspects more general and incorporates as special cases various problems which have been extensively studied in the literature. Moreover, applying the obtained results to some special cases, I derive some new criteria which generalize and greatly improve some well known results. A method is proposed to investigate biological systems subjected to the effect of both impulses and delays. The method is based on Banach fixed point theory and matrix's spectral theory as well as Lyapunov function. Moreover, some novel analytic techniques are employed to study GAS and GES. It is believed that the method can be extended to other high-dimensional biological systems and complex neural networks. Finally, two examples show the feasibility of the results.

A SIMPLE AND RAPID MATRIX-ASSISTED LASER DESORPTION/IONIZATION TIME OF FLIGHT MASS SPECTROMETRY METHOD TO SCREEN FISH PLASMA SAMPLES FOR ESTROGEN-RESPONSIVE BIOMARKERS

EPA Science Inventory

In this study, we describe and evaluate the performance of a simple and rapid mass spectral method for screening fish plasma for estrogen-responsive biomarkers using matrix assisted laster desorption/ionization time of flight mass spectrometry (MALDI-TOF-MS) couopled with a short...

Toda theories as contractions of affine Toda theories

NASA Astrophysics Data System (ADS)

Aghamohammadi, A.; Khorrami, M.; Shariati, A.

1996-02-01

Using a contraction procedure, we obtain Toda theories and their structures, from affine Toda theories and their corresponding structures. By structures, we mean the equation of motion, the classical Lax pair, the boundary term for half line theories, and the quantum transfer matrix. The Lax pair and the transfer matrix so obtained, depend nontrivially on the spectral parameter.

A simple and low cost dual-wavelength β-correction spectrophotometric determination and speciation of mercury(II) in water using chromogenic reagent 4-(2-thiazolylazo) resorcinol

NASA Astrophysics Data System (ADS)

Al-Bagawi, A. H.; Ahmad, W.; Saigl, Z. M.; Alwael, H.; Al-Harbi, E. A.; El-Shahawi, M. S.

2017-12-01

The most common problems in spectrophotometric determination of various complex species originate from the background spectral interference. Thus, the present study aimed to overcome the spectral matrix interference for the precise analysis and speciation of mercury(II) in water by dual-wavelength β-correction spectrophotometry using 4-(2-thiazolylazo) resorcinol (TAR) as chromogenic reagent. The principle was based on measuring the correct absorbance for the formed complex of mercury(II) ions with TAR reagent at 547 nm (lambda max). Under optimized conditions, a linear dynamic range of 0.1-2.0 μg mL- 1 with correlation coefficient (R2) of 0.997 were obtained with lower limits of detection (LOD) of 0.024 μg mL- 1 and limit of quantification (LOQ) of 0.081 μg mL- 1. The values of RSD and relative error (RE) obtained for β-correction method and single wavelength spectrophotometry were 1.3, 1.32% and 4.7, 5.9%, respectively. The method was validated in tap and sea water in terms of the data obtained from inductively coupled plasma-optical emission spectrometry (ICP-OES) using student's t and F tests. The developed methodology satisfactorily overcomes the spectral interference in trace determination and speciation of mercury(II) ions in water.

[Monitoring of Crack Propagation in Repaired Structures Based on Characteristics of FBG Sensors Reflecting Spectra].

PubMed

Yuan, Shen-fang; Jin, Xin; Qiu, Lei; Huang, Hong-mei

2015-03-01

In order to improve the security of aircraft repaired structures, a method of crack propagation monitoring in repaired structures is put forward basing on characteristics of Fiber Bragg Grating (FBG) reflecting spectra in this article. With the cyclic loading effecting on repaired structure, cracks propagate, while non-uniform strain field appears nearby the tip of crack which leads to the FBG sensors' reflecting spectra deformations. The crack propagating can be monitored by extracting the characteristics of FBG sensors' reflecting spectral deformations. A finite element model (FEM) of the specimen is established. Meanwhile, the distributions of strains which are under the action of cracks of different angles and lengths are obtained. The characteristics, such as main peak wavelength shift, area of reflecting spectra, second and third peak value and so on, are extracted from the FBGs' reflecting spectral which are calculated by transfer matrix algorithm. An artificial neural network is built to act as the model between the characteristics of the reflecting spectral and the propagation of crack. As a result, the crack propagation of repaired structures is monitored accurately and the error of crack length is less than 0.5 mm, the error of crack angle is less than 5 degree. The accurately monitoring problem of crack propagation of repaired structures is solved by taking use of this method. It has important significance in aircrafts safety improvement and maintenance cost reducing.

Observation-Based Dissipation and Input Terms for Spectral Wave Models, with End-User Testing

DTIC Science & Technology

2014-09-30

scale influence of the Great barrier reef matrix on wave attenuation, Coral Reefs [published, refereed] Ghantous, M., and A.V. Babanin, 2014: One...Observation-Based Dissipation and Input Terms for Spectral Wave Models...functions, based on advanced understanding of physics of air-sea interactions, wave breaking and swell attenuation, in wave - forecast models. OBJECTIVES The

An augmented classical least squares method for quantitative Raman spectral analysis against component information loss.

PubMed

Zhou, Yan; Cao, Hui

2013-01-01

We propose an augmented classical least squares (ACLS) calibration method for quantitative Raman spectral analysis against component information loss. The Raman spectral signals with low analyte concentration correlations were selected and used as the substitutes for unknown quantitative component information during the CLS calibration procedure. The number of selected signals was determined by using the leave-one-out root-mean-square error of cross-validation (RMSECV) curve. An ACLS model was built based on the augmented concentration matrix and the reference spectral signal matrix. The proposed method was compared with partial least squares (PLS) and principal component regression (PCR) using one example: a data set recorded from an experiment of analyte concentration determination using Raman spectroscopy. A 2-fold cross-validation with Venetian blinds strategy was exploited to evaluate the predictive power of the proposed method. The one-way variance analysis (ANOVA) was used to access the predictive power difference between the proposed method and existing methods. Results indicated that the proposed method is effective at increasing the robust predictive power of traditional CLS model against component information loss and its predictive power is comparable to that of PLS or PCR.

Application of partial least squares near-infrared spectral classification in diabetic identification

NASA Astrophysics Data System (ADS)

Yan, Wen-juan; Yang, Ming; He, Guo-quan; Qin, Lin; Li, Gang

2014-11-01

In order to identify the diabetic patients by using tongue near-infrared (NIR) spectrum - a spectral classification model of the NIR reflectivity of the tongue tip is proposed, based on the partial least square (PLS) method. 39sample data of tongue tip's NIR spectra are harvested from healthy people and diabetic patients , respectively. After pretreatment of the reflectivity, the spectral data are set as the independent variable matrix, and information of classification as the dependent variables matrix, Samples were divided into two groups - i.e. 53 samples as calibration set and 25 as prediction set - then the PLS is used to build the classification model The constructed modelfrom the 53 samples has the correlation of 0.9614 and the root mean square error of cross-validation (RMSECV) of 0.1387.The predictions for the 25 samples have the correlation of 0.9146 and the RMSECV of 0.2122.The experimental result shows that the PLS method can achieve good classification on features of healthy people and diabetic patients.

QCD dirac operator at nonzero chemical potential: lattice data and matrix model.

PubMed

Akemann, Gernot; Wettig, Tilo

2004-03-12

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at a nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.

Active subspace: toward scalable low-rank learning.

PubMed

Liu, Guangcan; Yan, Shuicheng

2012-12-01

We address the scalability issues in low-rank matrix learning problems. Usually these problems resort to solving nuclear norm regularized optimization problems (NNROPs), which often suffer from high computational complexities if based on existing solvers, especially in large-scale settings. Based on the fact that the optimal solution matrix to an NNROP is often low rank, we revisit the classic mechanism of low-rank matrix factorization, based on which we present an active subspace algorithm for efficiently solving NNROPs by transforming large-scale NNROPs into small-scale problems. The transformation is achieved by factorizing the large solution matrix into the product of a small orthonormal matrix (active subspace) and another small matrix. Although such a transformation generally leads to nonconvex problems, we show that a suboptimal solution can be found by the augmented Lagrange alternating direction method. For the robust PCA (RPCA) (Candès, Li, Ma, & Wright, 2009 ) problem, a typical example of NNROPs, theoretical results verify the suboptimality of the solution produced by our algorithm. For the general NNROPs, we empirically show that our algorithm significantly reduces the computational complexity without loss of optimality.

Optimal network modification for spectral radius dependent phase transitions

NASA Astrophysics Data System (ADS)

Rosen, Yonatan; Kirsch, Lior; Louzoun, Yoram

2016-09-01

The dynamics of contact processes on networks is often determined by the spectral radius of the networks adjacency matrices. A decrease of the spectral radius can prevent the outbreak of an epidemic, or impact the synchronization among systems of coupled oscillators. The spectral radius is thus tightly linked to network dynamics and function. As such, finding the minimal change in network structure necessary to reach the intended spectral radius is important theoretically and practically. Given contemporary big data resources such as large scale communication or social networks, this problem should be solved with a low runtime complexity. We introduce a novel method for the minimal decrease in weights of edges required to reach a given spectral radius. The problem is formulated as a convex optimization problem, where a global optimum is guaranteed. The method can be easily adjusted to an efficient discrete removal of edges. We introduce a variant of the method which finds optimal decrease with a focus on weights of vertices. The proposed algorithm is exceptionally scalable, solving the problem for real networks of tens of millions of edges in a short time.

Multi-spectrometer calibration transfer based on independent component analysis.

PubMed

Liu, Yan; Xu, Hao; Xia, Zhenzhen; Gong, Zhiyong

2018-02-26

Calibration transfer is indispensable for practical applications of near infrared (NIR) spectroscopy due to the need for precise and consistent measurements across different spectrometers. In this work, a method for multi-spectrometer calibration transfer is described based on independent component analysis (ICA). A spectral matrix is first obtained by aligning the spectra measured on different spectrometers. Then, by using independent component analysis, the aligned spectral matrix is decomposed into the mixing matrix and the independent components of different spectrometers. These differing measurements between spectrometers can then be standardized by correcting the coefficients within the independent components. Two NIR datasets of corn and edible oil samples measured with three and four spectrometers, respectively, were used to test the reliability of this method. The results of both datasets reveal that spectra measurements across different spectrometers can be transferred simultaneously and that the partial least squares (PLS) models built with the measurements on one spectrometer can predict that the spectra can be transferred correctly on another.

Dynamics of fractional condensation of a substance on a probe for spectral analysis

NASA Astrophysics Data System (ADS)

Zakharov, Yu. A.; Kokorina, O. B.; Lysogorskiĭ, Yu. V.; Sevastianov, A. A.

2008-11-01

The fractional separation of trace metals on a cold tungsten probe from salt matrix vapor, which interferes with the spectral analysis, is studied. The spatial structure of the vapor flows of sodium chloride, potassium sulfate, and indium atoms is visualized at characteristic wavelengths as they interact with the probe. The vapor flow rate and the probe orientation were varied. It is found that the smoke of the matrix does not prevent the deposition of the metal on the probe because of spatial separation of these fractions and that the detrimental effect of thermal gas expansion and other factors is eliminated. The sensitivity of the atomic absorption analysis of indium impurities in these salts is increased by an order of magnitude.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Super-resolution Doppler beam sharpening method using fast iterative adaptive approach-based spectral estimation

NASA Astrophysics Data System (ADS)

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

2018-01-01

Doppler beam sharpening (DBS) is a critical technology for airborne radar ground mapping in forward-squint region. In conventional DBS technology, the narrow-band Doppler filter groups formed by fast Fourier transform (FFT) method suffer from low spectral resolution and high side lobe levels. The iterative adaptive approach (IAA), based on the weighted least squares (WLS), is applied to the DBS imaging applications, forming narrower Doppler filter groups than the FFT with lower side lobe levels. Regrettably, the IAA is iterative, and requires matrix multiplication and inverse operation when forming the covariance matrix, its inverse and traversing the WLS estimate for each sampling point, resulting in a notably high computational complexity for cubic time. We propose a fast IAA (FIAA)-based super-resolution DBS imaging method, taking advantage of the rich matrix structures of the classical narrow-band filtering. First, we formulate the covariance matrix via the FFT instead of the conventional matrix multiplication operation, based on the typical Fourier structure of the steering matrix. Then, by exploiting the Gohberg-Semencul representation, the inverse of the Toeplitz covariance matrix is computed by the celebrated Levinson-Durbin (LD) and Toeplitz-vector algorithm. Finally, the FFT and fast Toeplitz-vector algorithm are further used to traverse the WLS estimates based on the data-dependent trigonometric polynomials. The method uses the Hermitian feature of the echo autocorrelation matrix R to achieve its fast solution and uses the Toeplitz structure of R to realize its fast inversion. The proposed method enjoys a lower computational complexity without performance loss compared with the conventional IAA-based super-resolution DBS imaging method. The results based on simulations and measured data verify the imaging performance and the operational efficiency.

The method of trend analysis of parameters time series of gas-turbine engine state

NASA Astrophysics Data System (ADS)

Hvozdeva, I.; Myrhorod, V.; Derenh, Y.

2017-10-01

This research substantiates an approach to interval estimation of time series trend component. The well-known methods of spectral and trend analysis are used for multidimensional data arrays. The interval estimation of trend component is proposed for the time series whose autocorrelation matrix possesses a prevailing eigenvalue. The properties of time series autocorrelation matrix are identified.

Spectral grading and Gleason grading of malignant prostate tissue using Stokes shift spectra

NASA Astrophysics Data System (ADS)

Al Salhi, M.; Masilamani, V.; Rabah, D.; Farhat, K.; Liu, C. H.; Pu, Y.; Alfano, R. R.

2012-01-01

Gleason score is the most common method of grading the virulence of prostate malignancy and is based on the pathological assessment of morphology of cellular matrix. Since this involves the excision of the tissue, we are working on a new, minimally invasive, non contact, procedure of spectral diagnosis of prostate malignancy. In this preliminary in vitro study reported here, we have analyzed 27 tissue samples (normal control =7: benign=8: malignant =12) by Stokes' shift spectra (SSS) to establish a one- to- one correlation between spectral grading and Gleason grading.

Spectral statistics of the uni-modular ensemble

NASA Astrophysics Data System (ADS)

Joyner, Christopher H.; Smilansky, Uzy; Weidenmüller, Hans A.

2017-09-01

We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U(1) , called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a supersymmetric integration method, a combinatorial graph-theoretical analysis and a Brownian motion approach, we are able to derive expressions for 1 / N corrections to the mean spectral moments and also analyse the fluctuations about this mean. By addressing the same ensemble from three different point of view, we can critically compare their relative advantages and derive some new results.

Solution of electromagnetic scattering and radiation problems using a spectral domain approach - A review

NASA Technical Reports Server (NTRS)

Mittra, R.; Ko, W. L.; Rahmat-Samii, Y.

1979-01-01

This paper presents a brief review of some recent developments on the use of the spectral-domain approach for deriving high-frequency solutions to electromagnetics scattering and radiation problems. The spectral approach is not only useful for interpreting the well-known Keller formulas based on the geometrical theory of diffraction (GTD), it can also be employed for verifying the accuracy of GTD and other asymptotic solutions and systematically improving the results when such improvements are needed. The problem of plane wave diffraction by a finite screen or a strip is presented as an example of the application of the spectral-domain approach.

Conditional Spectral Analysis of Replicated Multiple Time Series with Application to Nocturnal Physiology.

PubMed

Krafty, Robert T; Rosen, Ori; Stoffer, David S; Buysse, Daniel J; Hall, Martica H

2017-01-01

This article considers the problem of analyzing associations between power spectra of multiple time series and cross-sectional outcomes when data are observed from multiple subjects. The motivating application comes from sleep medicine, where researchers are able to non-invasively record physiological time series signals during sleep. The frequency patterns of these signals, which can be quantified through the power spectrum, contain interpretable information about biological processes. An important problem in sleep research is drawing connections between power spectra of time series signals and clinical characteristics; these connections are key to understanding biological pathways through which sleep affects, and can be treated to improve, health. Such analyses are challenging as they must overcome the complicated structure of a power spectrum from multiple time series as a complex positive-definite matrix-valued function. This article proposes a new approach to such analyses based on a tensor-product spline model of Cholesky components of outcome-dependent power spectra. The approach exibly models power spectra as nonparametric functions of frequency and outcome while preserving geometric constraints. Formulated in a fully Bayesian framework, a Whittle likelihood based Markov chain Monte Carlo (MCMC) algorithm is developed for automated model fitting and for conducting inference on associations between outcomes and spectral measures. The method is used to analyze data from a study of sleep in older adults and uncovers new insights into how stress and arousal are connected to the amount of time one spends in bed.

Common Prairie feeds with different soluble and insoluble fractions used for CPM diet formulation in dairy cattle: impact of carbohydrate-protein matrix structure on protein and other primary nutrient digestion.

PubMed

Peng, Quanhui; Wang, Zhisheng; Zhang, Xuewei; Yu, Peiqiang

2014-01-01

An experiment was conducted to investigate the relationship of carbohydrates molecular spectral characteristics to rumen degradability of primary nutrients in Prairie feeds in dairy cattle. In total, 12 different types of feeds were selected, each type of feed was from three different source with total 37 samples. Six types of them were energy-sourced feeds and the others were protein-sourced feeds. The carbohydrates molecular spectral intensity of various functional groups were collected using Fourier transform infrared attenuated total reflectance (ATR-FT/IR) spectroscopy. In the in situ study, the results showed that the rumen digestibility and digestible fractions of primary nutrients (DM, OM, NCP, and CP) were significantly different (P<0.05) among the feeds. The spectral bands features were significantly different (P<0.05) among the feeds. Spectral intensities of A_Cell, H_1415 and H_1370 were weakly positively correlated with in situ rumen digestibility and digestible fractions of DM, OM and NCP. Spectral intensities of H_1150, H_1015, A_1, and A_3 were weakly negatively associated with in situ rumen degradation of CP. Spectral intensities of A_1240 and H_1240, mainly associated with cellulosic compounds, were correlated with rumen CP degradation. The multiple regression analysis demonstrated that the spectral intensities of A_3 and H_1415 played the most important role and could be used as a potential tool to predict rumen protein degradation of feeds in dairy cattle. In conclusion, this study showed that the carbohydrates as a whole have an effect on protein rumen degradation, rather than cellulose alone, indicating carbohydrate-protein matrix structure impact protein utilization in dairy cattle. The non-invasive molecular spectral technique (ATR-FT/IR) could be used as a rapid potential tool to predict rumen protein degradation of feedstuffs by using molecular spectral bands intensities in carbohydrate fingerprint region. Copyright © 2013 Elsevier B.V. All rights reserved.

Common Prairie feeds with different soluble and insoluble fractions used for CPM diet formulation in dairy cattle: Impact of carbohydrate-protein matrix structure on protein and other primary nutrient digestion

NASA Astrophysics Data System (ADS)

Peng, Quanhui; Wang, Zhisheng; Zhang, Xuewei; Yu, Peiqiang

2014-03-01

An experiment was conducted to investigate the relationship of carbohydrates molecular spectral characteristics to rumen degradability of primary nutrients in Prairie feeds in dairy cattle. In total, 12 different types of feeds were selected, each type of feed was from three different source with total 37 samples. Six types of them were energy-sourced feeds and the others were protein-sourced feeds. The carbohydrates molecular spectral intensity of various functional groups were collected using Fourier transform infrared attenuated total reflectance (ATR-FT/IR) spectroscopy. In the in situ study, the results showed that the rumen digestibility and digestible fractions of primary nutrients (DM, OM, NCP, and CP) were significantly different (P < 0.05) among the feeds. The spectral bands features were significantly different (P < 0.05) among the feeds. Spectral intensities of A_Cell, H_1415 and H_1370 were weakly positively correlated with in situ rumen digestibility and digestible fractions of DM, OM and NCP. Spectral intensities of H_1150, H_1015, A_1, and A_3 were weakly negatively associated with in situ rumen degradation of CP. Spectral intensities of A_1240 and H_1240, mainly associated with cellulosic compounds, were correlated with rumen CP degradation. The multiple regression analysis demonstrated that the spectral intensities of A_3 and H_1415 played the most important role and could be used as a potential tool to predict rumen protein degradation of feeds in dairy cattle. In conclusion, this study showed that the carbohydrates as a whole have an effect on protein rumen degradation, rather than cellulose alone, indicating carbohydrate-protein matrix structure impact protein utilization in dairy cattle. The non-invasive molecular spectral technique (ATR-FT/IR) could be used as a rapid potential tool to predict rumen protein degradation of feedstuffs by using molecular spectral bands intensities in carbohydrate fingerprint region.

Convergence analysis of modulus-based matrix splitting iterative methods for implicit complementarity problems.

PubMed

Wang, An; Cao, Yang; Shi, Quan

2018-01-01

In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra Appl. 23:629-641, 2016). New convergence conditions are presented when the system matrix is a positive-definite matrix and an [Formula: see text]-matrix, respectively.

The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities

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

Pavlenko, V N; Potapov, D K

2015-09-30

This paper is concerned with the existence of semiregular solutions to the Dirichlet problem for an equation of elliptic type with discontinuous nonlinearity and when the differential operator is not assumed to be formally self-adjoint. Theorems on the existence of semiregular (positive and negative) solutions for the problem under consideration are given, and a principle of upper and lower solutions giving the existence of semiregular solutions is established. For positive values of the spectral parameter, elliptic spectral problems with discontinuous nonlinearities are shown to have nontrivial semiregular (positive and negative) solutions. Bibliography: 32 titles.

Validation of Spectral Unmixing Results from Informed Non-Negative Matrix Factorization (INMF) of Hyperspectral Imagery

NASA Astrophysics Data System (ADS)

Wright, L.; Coddington, O.; Pilewskie, P.

2017-12-01

Hyperspectral instruments are a growing class of Earth observing sensors designed to improve remote sensing capabilities beyond discrete multi-band sensors by providing tens to hundreds of continuous spectral channels. Improved spectral resolution, range and radiometric accuracy allow the collection of large amounts of spectral data, facilitating thorough characterization of both atmospheric and surface properties. We describe the development of an Informed Non-Negative Matrix Factorization (INMF) spectral unmixing method to exploit this spectral information and separate atmospheric and surface signals based on their physical sources. INMF offers marked benefits over other commonly employed techniques including non-negativity, which avoids physically impossible results; and adaptability, which tailors the method to hyperspectral source separation. The INMF algorithm is adapted to separate contributions from physically distinct sources using constraints on spectral and spatial variability, and library spectra to improve the initial guess. Using this INMF algorithm we decompose hyperspectral imagery from the NASA Hyperspectral Imager for the Coastal Ocean (HICO), with a focus on separating surface and atmospheric signal contributions. HICO's coastal ocean focus provides a dataset with a wide range of atmospheric and surface conditions. These include atmospheres with varying aerosol optical thicknesses and cloud cover. HICO images also provide a range of surface conditions including deep ocean regions, with only minor contributions from the ocean surfaces; and more complex shallow coastal regions with contributions from the seafloor or suspended sediments. We provide extensive comparison of INMF decomposition results against independent measurements of physical properties. These include comparison against traditional model-based retrievals of water-leaving, aerosol, and molecular scattering radiances and other satellite products, such as aerosol optical thickness from the Moderate Resolution Imaging Spectroradiometer (MODIS).

Physical and Hydrological Meaning of the Spectral Information from Hydrodynamic Signals at Karst Springs

NASA Astrophysics Data System (ADS)

Dufoyer, A.; Lecoq, N.; Massei, N.; Marechal, J. C.

2017-12-01

Physics-based modeling of karst systems remains almost impossible without enough accurate information about the inner physical characteristics. Usually, the only available hydrodynamic information is the flow rate at the karst outlet. Numerous works in the past decades have used and proven the usefulness of time-series analysis and spectral techniques applied to spring flow, precipitations or even physico-chemical parameters, for interpreting karst hydrological functioning. However, identifying or interpreting the karst systems physical features that control statistical or spectral characteristics of spring flow variations is still challenging, not to say sometimes controversial. The main objective of this work is to determine how the statistical and spectral characteristics of the hydrodynamic signal at karst springs can be related to inner physical and hydraulic properties. In order to address this issue, we undertake an empirical approach based on the use of both distributed and physics-based models, and on synthetic systems responses. The first step of the research is to conduct a sensitivity analysis of time-series/spectral methods to karst hydraulic and physical properties. For this purpose, forward modeling of flow through several simple, constrained and synthetic cases in response to precipitations is undertaken. It allows us to quantify how the statistical and spectral characteristics of flow at the outlet are sensitive to changes (i) in conduit geometries, and (ii) in hydraulic parameters of the system (matrix/conduit exchange rate, matrix hydraulic conductivity and storativity). The flow differential equations resolved by MARTHE, a computer code developed by the BRGM, allows karst conduits modeling. From signal processing on simulated spring responses, we hope to determine if specific frequencies are always modified, thanks to Fourier series and multi-resolution analysis. We also hope to quantify which parameters are the most variable with auto-correlation analysis: first results seem to show higher variations due to conduit conductivity than the ones due to matrix/conduit exchange rate. Future steps will be using another computer code, based on double-continuum approach and allowing turbulent conduit flow, and modeling a natural system.

Iterative spectral methods and spectral solutions to compressible flows

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Zang, T. A.

1982-01-01

A spectral multigrid scheme is described which can solve pseudospectral discretizations of self-adjoint elliptic problems in O(N log N) operations. An iterative technique for efficiently implementing semi-implicit time-stepping for pseudospectral discretizations of Navier-Stokes equations is discussed. This approach can handle variable coefficient terms in an effective manner. Pseudospectral solutions of compressible flow problems are presented. These include one dimensional problems and two dimensional Euler solutions. Results are given both for shock-capturing approaches and for shock-fitting ones.

M-matrices with prescribed elementary divisors

NASA Astrophysics Data System (ADS)

Soto, Ricardo L.; Díaz, Roberto C.; Salas, Mario; Rojo, Oscar

2017-09-01

A real matrix A is said to be an M-matrix if it is of the form A=α I-B, where B is a nonnegative matrix with Perron eigenvalue ρ (B), and α ≥slant ρ (B) . This paper provides sufficient conditions for the existence and construction of an M-matrix A with prescribed elementary divisors, which are the characteristic polynomials of the Jordan blocks of the Jordan canonical form of A. This inverse problem on M-matrices has not been treated until now. We solve the inverse elementary divisors problem for diagonalizable M-matrices and the symmetric generalized doubly stochastic inverse M-matrix problem for lists of real numbers and for lists of complex numbers of the form Λ =\\{λ 1, a+/- bi, \\ldots, a+/- bi\\} . The constructive nature of our results allows for the computation of a solution matrix. The paper also discusses an application of M-matrices to a capacity problem in wireless communications.

Geometrical calibration of an AOTF hyper-spectral imaging system

NASA Astrophysics Data System (ADS)

Špiclin, Žiga; Katrašnik, Jaka; Bürmen, Miran; Pernuš, Franjo; Likar, Boštjan

2010-02-01

Optical aberrations present an important problem in optical measurements. Geometrical calibration of an imaging system is therefore of the utmost importance for achieving accurate optical measurements. In hyper-spectral imaging systems, the problem of optical aberrations is even more pronounced because optical aberrations are wavelength dependent. Geometrical calibration must therefore be performed over the entire spectral range of the hyper-spectral imaging system, which is usually far greater than that of the visible light spectrum. This problem is especially adverse in AOTF (Acousto- Optic Tunable Filter) hyper-spectral imaging systems, as the diffraction of light in AOTF filters is dependent on both wavelength and angle of incidence. Geometrical calibration of hyper-spectral imaging system was performed by stable caliber of known dimensions, which was imaged at different wavelengths over the entire spectral range. The acquired images were then automatically registered to the caliber model by both parametric and nonparametric transformation based on B-splines and by minimizing normalized correlation coefficient. The calibration method was tested on an AOTF hyper-spectral imaging system in the near infrared spectral range. The results indicated substantial wavelength dependent optical aberration that is especially pronounced in the spectral range closer to the infrared part of the spectrum. The calibration method was able to accurately characterize the aberrations and produce transformations for efficient sub-pixel geometrical calibration over the entire spectral range, finally yielding better spatial resolution of hyperspectral imaging system.

Segmentation of High Angular Resolution Diffusion MRI using Sparse Riemannian Manifold Clustering

PubMed Central

Wright, Margaret J.; Thompson, Paul M.; Vidal, René

2015-01-01

We address the problem of segmenting high angular resolution diffusion imaging (HARDI) data into multiple regions (or fiber tracts) with distinct diffusion properties. We use the orientation distribution function (ODF) to represent HARDI data and cast the problem as a clustering problem in the space of ODFs. Our approach integrates tools from sparse representation theory and Riemannian geometry into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for each ODF and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. In cases where regions with similar (resp. distinct) diffusion properties belong to different (resp. same) fiber tracts, we obtain the segmentation by incorporating spatial and user-specified pairwise relationships into the formulation. Experiments on synthetic data evaluate the sensitivity of our method to image noise and the presence of complex fiber configurations, and show its superior performance compared to alternative segmentation methods. Experiments on phantom and real data demonstrate the accuracy of the proposed method in segmenting simulated fibers, as well as white matter fiber tracts of clinical importance in the human brain. PMID:24108748

Implementation of webcam-based hyperspectral imaging system

NASA Astrophysics Data System (ADS)

Balooch, Ali; Nazeri, Majid; Abbasi, Hamed

2018-02-01

In the present work, a hyperspectral imaging system (imaging spectrometer) using a commercial webcam has been designed and developed. This system was able to capture two-dimensional spectra (in emission, transmission and reflection modes) directly from the scene in the desired wavelengths. Imaging of the object is done directly by linear sweep (pushbroom method). To do so, the spectrometer is equipped with a suitable collecting lens and a linear travel stage. A 1920 x 1080 pixel CMOS webcam was used as a detector. The spectrometer has been calibrated by the reference spectral lines of standard lamps. The spectral resolution of this system was about 2nm and its spatial resolution was about 1 mm for a 10 cm long object. The hardware solution is based on data acquisition working on the USB platform and controlled by a LabVIEW program. In this system, the initial output was a three-dimensional matrix in which two dimensions of the matrix were related to the spatial information of the object and the third dimension was the spectrum of any point of the object. Finally, the images in different wavelengths were created by reforming the data of the matrix. The free spectral range (FSR) of the system was 400 to 1100 nm. The system was successfully tested for some applications, such as plasma diagnosis as well as applications in food and agriculture sciences.

POLARIZED LINE FORMATION WITH LOWER-LEVEL POLARIZATION AND PARTIAL FREQUENCY REDISTRIBUTION

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

Supriya, H. D.; Sampoorna, M.; Nagendra, K. N.

2016-09-10

In the well-established theories of polarized line formation with partial frequency redistribution (PRD) for a two-level and two-term atom, it is generally assumed that the lower level of the scattering transition is unpolarized. However, the existence of unexplained spectral features in some lines of the Second Solar Spectrum points toward a need to relax this assumption. There exists a density matrix theory that accounts for the polarization of all the atomic levels, but it is based on the flat-spectrum approximation (corresponding to complete frequency redistribution). In the present paper we propose a numerical algorithm to solve the problem of polarizedmore » line formation in magnetized media, which includes both the effects of PRD and the lower level polarization (LLP) for a two-level atom. First we derive a collisionless redistribution matrix that includes the combined effects of the PRD and the LLP. We then solve the relevant transfer equation using a two-stage approach. For illustration purposes, we consider two case studies in the non-magnetic regime, namely, the J {sub a} = 1, J {sub b} = 0 and J {sub a} = J {sub b} = 1, where J {sub a} and J {sub b} represent the total angular momentum quantum numbers of the lower and upper states, respectively. Our studies show that the effects of LLP are significant only in the line core. This leads us to propose a simplified numerical approach to solve the concerned radiative transfer problem.« less

Laser-induced breakdown spectroscopy of light water reactor simulated used nuclear fuel: Main oxide phase

DOE PAGES

Campbell, Keri R.; Judge, Elizabeth J.; Barefield, James E.; ...

2017-04-22

We show the analysis of light water reactor simulated used nuclear fuel using laser-induced breakdown spectroscopy (LIBS) is explored using a simplified version of the main oxide phase. The main oxide phase consists of the actinides, lanthanides, and zirconium. The purpose of this study is to develop a rapid, quantitative technique for measuring zirconium in a uranium dioxide matrix without the need to dissolve the material. A second set of materials including cerium oxide is also analyzed to determine precision and limit of detection (LOD) using LIBS in a complex matrix. Two types of samples are used in this study:more » binary and ternary oxide pellets. The ternary oxide, (U,Zr,Ce)O 2 pellets used in this study are a simplified version the main oxide phase of used nuclear fuel. The binary oxides, (U,Ce)O 2 and (U,Zr)O 2 are also examined to determine spectral emission lines for Ce and Zr, potential spectral interferences with uranium and baseline LOD values for Ce and Zr in a UO 2 matrix. In the spectral range of 200 to 800 nm, 33 cerium lines and 25 zirconium lines were identified and shown to have linear correlation values (R 2) > 0.97 for both the binary and ternary oxides. The cerium LOD in the (U,Ce)O 2 matrix ranged from 0.34 to 1.08 wt% and 0.94 to 1.22 wt% in (U,Ce,Zr)O 2 for 33 of Ce emission lines. The zirconium limit of detection in the (U,Zr)O 2 matrix ranged from 0.84 to 1.15 wt% and 0.99 to 1.10 wt% in (U,Ce,Zr)O 2 for 25 Zr lines. Finally, the effect of multiple elements in the plasma and the impact on the LOD is discussed.« less

A well-posed optimal spectral element approximation for the Stokes problem

NASA Technical Reports Server (NTRS)

Maday, Y.; Patera, A. T.; Ronquist, E. M.

1987-01-01

A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.

[Review of digital ground object spectral library].

PubMed

Zhou, Xiao-Hu; Zhou, Ding-Wu

2009-06-01

A higher spectral resolution is the main direction of developing remote sensing technology, and it is quite important to set up the digital ground object reflectance spectral database library, one of fundamental research fields in remote sensing application. Remote sensing application has been increasingly relying on ground object spectral characteristics, and quantitative analysis has been developed to a new stage. The present article summarized and systematically introduced the research status quo and development trend of digital ground object reflectance spectral libraries at home and in the world in recent years. Introducing the spectral libraries has been established, including desertification spectral database library, plants spectral database library, geological spectral database library, soil spectral database library, minerals spectral database library, cloud spectral database library, snow spectral database library, the atmosphere spectral database library, rocks spectral database library, water spectral database library, meteorites spectral database library, moon rock spectral database library, and man-made materials spectral database library, mixture spectral database library, volatile compounds spectral database library, and liquids spectral database library. In the process of establishing spectral database libraries, there have been some problems, such as the lack of uniform national spectral database standard and uniform standards for the ground object features as well as the comparability between different databases. In addition, data sharing mechanism can not be carried out, etc. This article also put forward some suggestions on those problems.

New Possibilities for the Accurate in Situ Determination of Chalcophile and Siderophile Trace Elements by Laser Ablation Collision and Reaction Cell ICP-MS

NASA Astrophysics Data System (ADS)

Mason, P. R.

2004-05-01

Our knowledge of how chalcophile and siderophile elements partition in minerals is limited, mainly due to the lack of suitable techniques for their accurate in situ determination. Host minerals (e.g. sulphides) are typically of small size (<30 μ m) and highly heterogeneous in composition, requiring analysis of high spatial resolution. Concentrations of chalcophile elements in silicates and oxides are low (sub μ gg-1) and thus challenging to measure. Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS), offering high sensitivity and good spatial resolution (10-100 μ m) is thus highly suited for this purpose. Unfortunately, the widespread use of this technique has been limited by enhanced problems specific to chalcophile and siderophile elements. These include inaccuracy due to the presence of spectral interferences, elemental fractionation during ablation/ionization and the lack of suitable calibration standards. Polyatomic spectral interferences, present either as a background component (e.g. O2+, ArAr+) or based around the recombination of matrix elements with argon (e.g. ArS+, ArNi+) hinder accurate analysis. These depend upon the relative concentrations of major matrix components and trace elements to be measured and are significant in many relevant minerals (e.g. sulphides). The use of a collision and reaction cells in ICP-MS is a new method for selective interference attenuation, significantly improving detection limits for elements such as Fe, S and Se by between 1 and 4 orders of magnitude. ArNi+ and ArCu+ interferences in sulphides can be attenuated by at least an order of magnitude leading to improved accuracy for the measurement of the Platinum Group elements Rh and Ru. Sulphur isotopes can be measured interference-free at m/z=32 and 34 by eliminating background O2+. These improvements open up new possibilities for the use of LA-ICP-MS in trace element and isotopic studies at the lowest concentration levels or where sample preparation creates additional problems (e.g. NiS fire assay beads). I will give examples of applications for this technique in the study of ore minerals, meteorites and precipitates from hydrothermal vents.

Rapid Identification of Cryptococcus neoformans and Cryptococcus gattii by Matrix-Assisted Laser Desorption Ionization–Time of Flight Mass Spectrometry ▿

PubMed Central

McTaggart, Lisa R.; Lei, Eric; Richardson, Susan E.; Hoang, Linda; Fothergill, Annette; Zhang, Sean X.

2011-01-01

Compared to DNA sequence analysis, matrix-assisted laser desorption ionization–time of flight mass spectrometry (MALDI-TOF MS) correctly identified 100% of Cryptococcus species, distinguishing the notable pathogens Cryptococcus neoformans and C. gattii. Identification was greatly enhanced by supplementing a commercial spectral library with additional entries to account for subspecies variability. PMID:21653762

Sensitivity of coronal loop sausage mode frequencies and decay rates to radial and longitudinal density inhomogeneities: a spectral approach

NASA Astrophysics Data System (ADS)

Cally, Paul S.; Xiong, Ming

2018-01-01

Fast sausage modes in solar magnetic coronal loops are only fully contained in unrealistically short dense loops. Otherwise they are leaky, losing energy to their surrounds as outgoing waves. This causes any oscillation to decay exponentially in time. Simultaneous observations of both period and decay rate therefore reveal the eigenfrequency of the observed mode, and potentially insight into the tubes’ nonuniform internal structure. In this article, a global spectral description of the oscillations is presented that results in an implicit matrix eigenvalue equation where the eigenvalues are associated predominantly with the diagonal terms of the matrix. The off-diagonal terms vanish identically if the tube is uniform. A linearized perturbation approach, applied with respect to a uniform reference model, is developed that makes the eigenvalues explicit. The implicit eigenvalue problem is easily solved numerically though, and it is shown that knowledge of the real and imaginary parts of the eigenfrequency is sufficient to determine the width and density contrast of a boundary layer over which the tubes’ enhanced internal densities drop to ambient values. Linearized density kernels are developed that show sensitivity only to the extreme outside of the loops for radial fundamental modes, especially for small density enhancements, with no sensitivity to the core. Higher radial harmonics do show some internal sensitivity, but these will be more difficult to observe. Only kink modes are sensitive to the tube centres. Variation in internal and external Alfvén speed along the loop is shown to have little effect on the fundamental dimensionless eigenfrequency, though the associated eigenfunction becomes more compact at the loop apex as stratification increases, or may even displace from the apex.

Solving matrix-effects exploiting the second order advantage in the resolution and determination of eight tetracycline antibiotics in effluent wastewater by modelling liquid chromatography data with multivariate curve resolution-alternating least squares and unfolded-partial least squares followed by residual bilinearization algorithms I. Effect of signal pre-treatment.

PubMed

De Zan, M M; Gil García, M D; Culzoni, M J; Siano, R G; Goicoechea, H C; Martínez Galera, M

2008-02-01

The effect of piecewise direct standardization (PDS) and baseline correction approaches was evaluated in the performance of multivariate curve resolution (MCR-ALS) algorithm for the resolution of three-way data sets from liquid chromatography with diode-array detection (LC-DAD). First, eight tetracyclines (tetracycline, oxytetracycline, chlorotetracycline, demeclocycline, methacycline, doxycycline, meclocycline and minocycline) were isolated from 250 mL effluent wastewater samples by solid-phase extraction (SPE) with Oasis MAX 500 mg/6 mL cartridges and then separated on an Aquasil C18 150 mm x 4.6mm (5 microm particle size) column by LC and detected by DAD. Previous experiments, carried out with Milli-Q water samples, showed a considerable loss of the most polar analytes (minocycline, oxitetracycline and tetracycline) due to breakthrough. PDS was applied to overcome this important drawback. Conversion of chromatograms obtained from standards prepared in solvent was performed obtaining a high correlation with those corresponding to the real situation (r2 = 0.98). Although the enrichment and clean-up steps were carefully optimized, the sample matrix caused a large baseline drift, and also additive interferences were present at the retention times of the analytes. These problems were solved with the baseline correction method proposed by Eilers. MCR-ALS was applied to the corrected and uncorrected three-way data sets to obtain spectral and chromatographic profiles of each tetracycline, as well as those corresponding to the co-eluting interferences. The complexity of the calibration model built from uncorrected data sets was higher, as expected, and the quality of the spectral and chromatographic profiles was worse.

Origin of the quasiparticle peak in the spectral density of Cr(001) surfaces

NASA Astrophysics Data System (ADS)

Peters, L.; Jacob, D.; Karolak, M.; Lichtenstein, A. I.; Katsnelson, M. I.

2017-12-01

In the spectral density of Cr(001) surfaces, a sharp resonance close to the Fermi level is observed in both experiment and theory. For the physical origin of this peak, two mechanisms were proposed: a single-particle dz2 surface state renormalized by electron-phonon coupling and an orbital Kondo effect due to the degenerate dx z/dy z states. Despite several experimental and theoretical investigations, the origin is still under debate. In this work, we address this problem by two different approaches of the dynamical mean-field theory: first, by the spin-polarized T -matrix fluctuation exchange approximation suitable for weakly and moderately correlated systems; second, by the noncrossing approximation derived in the limit of weak hybridization (i.e., for strongly correlated systems) capturing Kondo-type processes. By using recent continuous-time quantum Monte Carlo calculations as a benchmark, we find that the high-energy features, everything except the resonance, of the spectrum are captured within the spin-polarized T -matrix fluctuation exchange approximation. More precisely, the particle-particle processes provide the main contribution. For the noncrossing approximation, it appears that spin-polarized calculations suffer from spurious behavior at the Fermi level. Then, we turned to non-spin-polarized calculations to avoid this unphysical behavior. By employing two plausible starting hybridization functions, it is observed that the characteristics of the resonance are crucially dependent on the starting point. It appears that only one of these starting hybridizations could result in an orbital Kondo resonance in the presence of a strong magnetic field like in the Cr(001) surface. It is for a future investigation to first resolve the unphysical behavior within the spin-polarized noncrossing approximation and then check for an orbital Kondo resonance.

Spectral methods for partial differential equations

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Streett, C. L.; Zang, T. A.

1983-01-01

Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid dynamical applications are emphasized.

Recent applications of spectral methods in fluid dynamics

NASA Technical Reports Server (NTRS)

Zang, T. A.; Hussaini, M. Y.

1985-01-01

Origins of spectral methods, especially their relation to the method of weighted residuals, are surveyed. Basic Fourier and Chebyshev spectral concepts are reviewed and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic and mixzed type. Fluid dynamical applications are emphasized.

Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem

NASA Astrophysics Data System (ADS)

Belinschi, Serban; Nowak, Maciej A.; Speicher, Roland; Tarnowski, Wojciech

2017-03-01

We extend the so-called ‘single ring theorem’ (Feinberg and Zee 1997 Nucl. Phys. B 504 579), also known as the Haagerup-Larsen theorem (Haagerup and Larsen 2000 J. Funct. Anal. 176 331). We do this by showing that in the limit when the size of the matrix goes to infinity a particular correlator between left and right eigenvectors of the relevant non-hermitian matrix X, being the spectral density weighted by the squared eigenvalue condition number, is given by a simple formula involving only the radial spectral cumulative distribution function of X. We show that this object allows the calculation of the conditional expectation of the squared eigenvalue condition number. We give examples and provide a cross-check of the analytic prediction by the large scale numerics.

Anderson Localization in Quark-Gluon Plasma

NASA Astrophysics Data System (ADS)

Kovács, Tamás G.; Pittler, Ferenc

2010-11-01

At low temperature the low end of the QCD Dirac spectrum is well described by chiral random matrix theory. In contrast, at high temperature there is no similar statistical description of the spectrum. We show that at high temperature the lowest part of the spectrum consists of a band of statistically uncorrelated eigenvalues obeying essentially Poisson statistics and the corresponding eigenvectors are extremely localized. Going up in the spectrum the spectral density rapidly increases and the eigenvectors become more and more delocalized. At the same time the spectral statistics gradually crosses over to the bulk statistics expected from the corresponding random matrix ensemble. This phenomenon is reminiscent of Anderson localization in disordered conductors. Our findings are based on staggered Dirac spectra in quenched lattice simulations with the SU(2) gauge group.

A minimum drives automatic target definition procedure for multi-axis random control testing

NASA Astrophysics Data System (ADS)

Musella, Umberto; D'Elia, Giacomo; Carrella, Alex; Peeters, Bart; Mucchi, Emiliano; Marulo, Francesco; Guillaume, Patrick

2018-07-01

Multiple-Input Multiple-Output (MIMO) vibration control tests are able to closely replicate, via shakers excitation, the vibration environment that a structure needs to withstand during its operational life. This feature is fundamental to accurately verify the experienced stress state, and ultimately the fatigue life, of the tested structure. In case of MIMO random tests, the control target is a full reference Spectral Density Matrix in the frequency band of interest. The diagonal terms are the Power Spectral Densities (PSDs), representative for the acceleration operational levels, and the off-diagonal terms are the Cross Spectral Densities (CSDs). The specifications of random vibration tests are however often given in terms of PSDs only, coming from a legacy of single axis testing. Information about the CSDs is often missing. An accurate definition of the CSD profiles can further enhance the MIMO random testing practice, as these terms influence both the responses and the shaker's voltages (the so-called drives). The challenges are linked to the algebraic constraint that the full reference matrix must be positive semi-definite in the entire bandwidth, with no flexibility in modifying the given PSDs. This paper proposes a newly developed method that automatically provides the full reference matrix without modifying the PSDs, considered as test specifications. The innovative feature is the capability of minimizing the drives required to match the reference PSDs and, at the same time, to directly guarantee that the obtained full matrix is positive semi-definite. The drives minimization aims on one hand to reach the fixed test specifications without stressing the delicate excitation system; on the other hand it potentially allows to further increase the test levels. The detailed analytic derivation and implementation steps of the proposed method are followed by real-life testing considering different scenarios.

Accuracy enhancement of laser induced breakdown spectra using permittivity and size optimized plasma confinement rings.

PubMed

Li, An; Guo, Shuai; Wazir, Nasrullah; Chai, Ke; Liang, Liang; Zhang, Min; Hao, Yan; Nan, Pengfei; Liu, Ruibin

2017-10-30

The inevitable problems in laser induced breakdown spectroscopy are matrix effect and statistical fluctuation of the spectral signal, which can be partly avoided by utilizing a proper confined unit. The dependences of spectral signal enhancement on relative permittivity were studied by varying materials to confine the plasma, which include polytetrafluoroethylene(PTFE), nylon/dacron, silicagel, and nitrile-butadiene rubber (NBR) with the relative permittivity 2.2, ~3.3, 3.6, 8~13, 15~22. We found that higher relative permittivity rings induce stronger enhancement ability, which restricts the energy dissipation of plasma better and due to the reflected electromagnetic wave from the wall of different materials, the electromagnetic field of plasma can be well confined and makes the distribution of plasma more orderly. The spectral intensities of the characteristic lines Si I 243.5 nm and Si I 263.1 nm increased approximately 2 times with relative permittivity values from 2.2 to ~20. The size dependent enhancement of PTFE was further checked and the maximum gain was realized by using a confinement ring with a diameter size of 5 mm and a height of 3 mm (D5mmH3mm), and the rings with D2mmH1mm and D3mmH2mm also show higher enhancement factor. In view of peak shift, peak lost and accidental peaks in the obtained spectra were properly treated in data progressing; the spectral fluctuation decreased drastically for various materials with different relative permittivities as confined units, which means the core of plasma is stabilized, attributing to the confinement effect. Furthermore, the quantitative analysis in coal shows wonderful results-the prediction fitting coefficient R 2 reaches 0.98 for ash and 0.99 for both volatile and carbon.

A Spectral Element Discretisation on Unstructured Triangle / Tetrahedral Meshes for Elastodynamics

NASA Astrophysics Data System (ADS)

May, Dave A.; Gabriel, Alice-A.

2017-04-01

The spectral element method (SEM) defined over quadrilateral and hexahedral element geometries has proven to be a fast, accurate and scalable approach to study wave propagation phenomena. In the context of regional scale seismology and or simulations incorporating finite earthquake sources, the geometric restrictions associated with hexahedral elements can limit the applicability of the classical quad./hex. SEM. Here we describe a continuous Galerkin spectral element discretisation defined over unstructured meshes composed of triangles (2D), or tetrahedra (3D). The method uses a stable, nodal basis constructed from PKD polynomials and thus retains the spectral accuracy and low dispersive properties of the classical SEM, in addition to the geometric versatility provided by unstructured simplex meshes. For the particular basis and quadrature rule we have adopted, the discretisation results in a mass matrix which is not diagonal, thereby mandating linear solvers be utilised. To that end, we have developed efficient solvers and preconditioners which are robust with respect to the polynomial order (p), and possess high arithmetic intensity. Furthermore, we also consider using implicit time integrators, together with a p-multigrid preconditioner to circumvent the CFL condition. Implicit time integrators become particularly relevant when considering solving problems on poor quality meshes, or meshes containing elements with a widely varying range of length scales - both of which frequently arise when meshing non-trivial geometries. We demonstrate the applicability of the new method by examining a number of two- and three-dimensional wave propagation scenarios. These scenarios serve to characterise the accuracy and cost of the new method. Lastly, we will assess the potential benefits of using implicit time integrators for regional scale wave propagation simulations.

Solvers for $$\\mathcal{O} (N)$$ Electronic Structure in the Strong Scaling Limit

DOE PAGES

Bock, Nicolas; Challacombe, William M.; Kale, Laxmikant

2016-01-26

Here we present a hybrid OpenMP/Charm\\tt++ framework for solving themore » $$\\mathcal{O} (N)$$ self-consistent-field eigenvalue problem with parallelism in the strong scaling regime, $$P\\gg{N}$$, where $P$ is the number of cores, and $N$ is a measure of system size, i.e., the number of matrix rows/columns, basis functions, atoms, molecules, etc. This result is achieved with a nested approach to spectral projection and the sparse approximate matrix multiply [Bock and Challacombe, SIAM J. Sci. Comput., 35 (2013), pp. C72--C98], and involves a recursive, task-parallel algorithm, often employed by generalized $N$-Body solvers, to occlusion and culling of negligible products in the case of matrices with decay. Lastly, employing classic technologies associated with generalized $N$-Body solvers, including overdecomposition, recursive task parallelism, orderings that preserve locality, and persistence-based load balancing, we obtain scaling beyond hundreds of cores per molecule for small water clusters ([H$${}_2$$O]$${}_N$$, $$N \\in \\{ 30, 90, 150 \\}$$, $$P/N \\approx \\{ 819, 273, 164 \\}$$) and find support for an increasingly strong scalability with increasing system size $N$.« less

Speckle Noise Reduction in Optical Coherence Tomography Using Two-dimensional Curvelet-based Dictionary Learning.

PubMed

Esmaeili, Mahdad; Dehnavi, Alireza Mehri; Rabbani, Hossein; Hajizadeh, Fedra

2017-01-01

The process of interpretation of high-speed optical coherence tomography (OCT) images is restricted due to the large speckle noise. To address this problem, this paper proposes a new method using two-dimensional (2D) curvelet-based K-SVD algorithm for speckle noise reduction and contrast enhancement of intra-retinal layers of 2D spectral-domain OCT images. For this purpose, we take curvelet transform of the noisy image. In the next step, noisy sub-bands of different scales and rotations are separately thresholded with an adaptive data-driven thresholding method, then, each thresholded sub-band is denoised based on K-SVD dictionary learning with a variable size initial dictionary dependent on the size of curvelet coefficients' matrix in each sub-band. We also modify each coefficient matrix to enhance intra-retinal layers, with noise suppression at the same time. We demonstrate the ability of the proposed algorithm in speckle noise reduction of 100 publically available OCT B-scans with and without non-neovascular age-related macular degeneration (AMD), and improvement of contrast-to-noise ratio from 1.27 to 5.12 and mean-to-standard deviation ratio from 3.20 to 14.41 are obtained.

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

PubMed

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

2018-04-23

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

Sunspot Pattern Classification using PCA and Neural Networks (Poster)

NASA Technical Reports Server (NTRS)

Rajkumar, T.; Thompson, D. E.; Slater, G. L.

2005-01-01

The sunspot classification scheme presented in this paper is considered as a 2-D classification problem on archived datasets, and is not a real-time system. As a first step, it mirrors the Zuerich/McIntosh historical classification system and reproduces classification of sunspot patterns based on preprocessing and neural net training datasets. Ultimately, the project intends to move from more rudimentary schemes, to develop spatial-temporal-spectral classes derived by correlating spatial and temporal variations in various wavelengths to the brightness fluctuation spectrum of the sun in those wavelengths. Once the approach is generalized, then the focus will naturally move from a 2-D to an n-D classification, where "n" includes time and frequency. Here, the 2-D perspective refers both to the actual SOH0 Michelson Doppler Imager (MDI) images that are processed, but also refers to the fact that a 2-D matrix is created from each image during preprocessing. The 2-D matrix is the result of running Principal Component Analysis (PCA) over the selected dataset images, and the resulting matrices and their eigenvalues are the objects that are stored in a database, classified, and compared. These matrices are indexed according to the standard McIntosh classification scheme.

New algorithms for field-theoretic block copolymer simulations: Progress on using adaptive-mesh refinement and sparse matrix solvers in SCFT calculations

NASA Astrophysics Data System (ADS)

Sides, Scott; Jamroz, Ben; Crockett, Robert; Pletzer, Alexander

2012-02-01

Self-consistent field theory (SCFT) for dense polymer melts has been highly successful in describing complex morphologies in block copolymers. Field-theoretic simulations such as these are able to access large length and time scales that are difficult or impossible for particle-based simulations such as molecular dynamics. The modified diffusion equations that arise as a consequence of the coarse-graining procedure in the SCF theory can be efficiently solved with a pseudo-spectral (PS) method that uses fast-Fourier transforms on uniform Cartesian grids. However, PS methods can be difficult to apply in many block copolymer SCFT simulations (eg. confinement, interface adsorption) in which small spatial regions might require finer resolution than most of the simulation grid. Progress on using new solver algorithms to address these problems will be presented. The Tech-X Chompst project aims at marrying the best of adaptive mesh refinement with linear matrix solver algorithms. The Tech-X code PolySwift++ is an SCFT simulation platform that leverages ongoing development in coupling Chombo, a package for solving PDEs via block-structured AMR calculations and embedded boundaries, with PETSc, a toolkit that includes a large assortment of sparse linear solvers.

Visualizing Intrapopulation Hematopoietic Cell Heterogeneity with Self-Organizing Maps of SIMS Data.

PubMed

Mirshafiee, Vahid; Harley, Brendan A C; Kraft, Mary L

2018-05-07

Characterization of the heterogeneity within stem cell populations, which affects their differentiation potential, is necessary for the design of artificial cultures for stem cell expansion. In this study, we assessed whether self-organizing maps (SOMs) of single-cell time-of-flight secondary ion mass spectrometry (TOF-SIMS) data provide insight into the spectral, and thus the related functional heterogeneity between and within three hematopoietic cell populations. SOMs were created of TOF-SIMS data from individual hematopoietic stem and progenitor cells (HSPCs), lineage-committed common lymphoid progenitors (CLPs), and fully differentiated B cells that had been isolated from murine bone marrow via conventional flow cytometry. The positions of these cells on the SOMs and the spectral variation between adjacent map units, shown on the corresponding unified distance matrix (U-matrix), indicated the CLPs exhibited the highest intrapopulation spectral variation, regardless of the age of the donor mice. SOMs of HSPCs, CLPs, and B cells isolated from young and old mice using the same surface antigen profiles revealed the HSPCs exhibited the most age-related spectral variation, whereas B cells exhibited the least. These results demonstrate that SOMs of single-cell spectra enable characterizing the heterogeneity between and within cell populations that lie along distinct differentiation pathways.

Chebyshev polynomials in the spectral Tau method and applications to Eigenvalue problems

NASA Technical Reports Server (NTRS)

Johnson, Duane

1996-01-01

Chebyshev Spectral methods have received much attention recently as a technique for the rapid solution of ordinary differential equations. This technique also works well for solving linear eigenvalue problems. Specific detail is given to the properties and algebra of chebyshev polynomials; the use of chebyshev polynomials in spectral methods; and the recurrence relationships that are developed. These formula and equations are then applied to several examples which are worked out in detail. The appendix contains an example FORTRAN program used in solving an eigenvalue problem.

Modelling of Carbon Monoxide Air Pollution in Larg Cities by Evaluetion of Spectral LANDSAT8 Images

NASA Astrophysics Data System (ADS)

Hamzelo, M.; Gharagozlou, A.; Sadeghian, S.; Baikpour, S. H.; Rajabi, A.

2015-12-01

Air pollution in large cities is one of the major problems that resolve and reduce it need multiple applications and environmental management. Of The main sources of this pollution is industrial activities, urban and transport that enter large amounts of contaminants into the air and reduces its quality. With Variety of pollutants and high volume manufacturing, local distribution of manufacturing centers, Testing and measuring emissions is difficult. Substances such as carbon monoxide, sulfur dioxide, and unburned hydrocarbons and lead compounds are substances that cause air pollution and carbon monoxide is most important. Today, data exchange systems, processing, analysis and modeling is of important pillars of management system and air quality control. In this study, using the spectral signature of carbon monoxide gas as the most efficient gas pollution LANDSAT8 images in order that have better spatial resolution than appropriate spectral bands and weather meters،SAM classification algorithm and Geographic Information System (GIS ), spatial distribution of carbon monoxide gas in Tehran over a period of one year from the beginning of 2014 until the beginning of 2015 at 11 map have modeled and then to the model valuation ،created maps were compared with the map provided by the Tehran quality comparison air company. Compare involved plans did with the error matrix and results in 4 types of care; overall, producer, user and kappa coefficient was investigated. Results of average accuracy were about than 80%, which indicates the fit method and data used for modeling.

Beyond Low-Rank Representations: Orthogonal clustering basis reconstruction with optimized graph structure for multi-view spectral clustering.

PubMed

Wang, Yang; Wu, Lin

2018-07-01

Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data similarity embedded in high-dimensional space, to yield a better graph partition than their single-view counterparts. In this paper we revisit it with a fundamentally different perspective by discovering LRR as essentially a latent clustered orthogonal projection based representation winged with an optimized local graph structure for spectral clustering; each column of the representation is fundamentally a cluster basis orthogonal to others to indicate its members, which intuitively projects the view-specific feature representation to be the one spanned by all orthogonal basis to characterize the cluster structures. Upon this finding, we propose our technique with the following: (1) We decompose LRR into latent clustered orthogonal representation via low-rank matrix factorization, to encode the more flexible cluster structures than LRR over primal data objects; (2) We convert the problem of LRR into that of simultaneously learning orthogonal clustered representation and optimized local graph structure for each view; (3) The learned orthogonal clustered representations and local graph structures enjoy the same magnitude for multi-view, so that the ideal multi-view consensus can be readily achieved. The experiments over multi-view datasets validate its superiority, especially over recent state-of-the-art LRR models. Copyright © 2018 Elsevier Ltd. All rights reserved.

Solitons of shallow-water models from energy-dependent spectral problems

NASA Astrophysics Data System (ADS)

Haberlin, Jack; Lyons, Tony

2018-01-01

The current work investigates the soliton solutions of the Kaup-Boussinesq equation using the inverse scattering transform method. We outline the construction of the Riemann-Hilbert problem for a pair of energy-dependent spectral problems for the system, which we then use to construct the solution of this hydrodynamic system.

Uniform high order spectral methods for one and two dimensional Euler equations

NASA Technical Reports Server (NTRS)

Cai, Wei; Shu, Chi-Wang

1991-01-01

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two dimensional shock wave and a rotating vortex is simulated.

Singlet and doublet states UV-vis spectrum and electronic properties of 3-methylchrysene and 4-methylchrysene in glass matrix.

PubMed

Husain, Mudassir M; Tandon, H C; Varadwaj, Pradeep R

2008-03-01

The ultraviolet-visual spectrum of 3-methylchrysene, 4-methylchrysene and their radical cations formed by ultraviolet radiations, were measured in glass matrix at the room temperature. In the measured singlet state spectrum we were able to identify the alpha, p, beta, beta' (Clar's) or (1)L(b), (1)L(a)(1)B(b), (1)B(a) (Platt's notation) bands. The presence of alpha, beta or (1)L(b), (1)B(b) was confirmed by calculating their wavelength ratio lambda(alpha)/lambda(beta). Since matrix induces perturbation in the measured spectrum; it becomes necessary to take into account the perturbation while computing the spectrum. An effort has been made in this work to simulate the electronic spectrum in the same environment as is measured. This study presents the first calculated spectrum of these systems and their cations in glass matrix by semi empirical methods. To observe the magnitude of perturbation and hence to see the spectral shift in glass matrix, the spectrum was calculated in the free state as well. Spectral properties such as frontier orbitals gap, dipole moment, mean polarizabilities and its tensors were also computed both in glass matrix and free state using semiemperical method. The measured bands of 3-methylchrysene cation at wavelength 416.50 and 473.85 nm closely match with the available diffuse intersteallar bands (DIBs) at 417.55 and 472.64 nm, respectively. Also the observed 474.85 nm band of 4-methylchrysene cation matches the DIB at 476.00 nm.

Structure-function correlations in glaucoma using matrix and standard automated perimetry versus time-domain and spectral-domain OCT devices.

PubMed

Pinto, Luciano Moreira; Costa, Elaine Fiod; Melo, Luiz Alberto S; Gross, Paula Blasco; Sato, Eduardo Toshio; Almeida, Andrea Pereira; Maia, Andre; Paranhos, Augusto

2014-04-10

We examined the structure-function relationship between two perimetric tests, the frequency doubling technology (FDT) matrix and standard automated perimetry (SAP), and two optical coherence tomography (OCT) devices (time-domain and spectral-domain). This cross-sectional study included 97 eyes from 29 healthy individuals, and 68 individuals with early, moderate, or advanced primary open-angle glaucoma. The correlations between overall and sectorial parameters of retinal nerve fiber layer thickness (RNFL) measured with Stratus and Spectralis OCT, and the visual field sensitivity obtained with FDT matrix and SAP were assessed. The relationship also was evaluated using a previously described linear model. The correlation coefficients for the threshold sensitivity measured with SAP and Stratus OCT ranged from 0.44 to 0.79, and those for Spectralis OCT ranged from 0.30 to 0.75. Regarding FDT matrix, the correlation ranged from 0.40 to 0.79 with Stratus OCT and from 0.39 to 0.79 with Spectralis OCT. Stronger correlations were found in the overall measurements and the arcuate sectors for both visual fields and OCT devices. A linear relationship was observed between FDT matrix sensitivity and the OCT devices. The previously described linear model fit the data from SAP and the OCT devices well, particularly in the inferotemporal sector. The FDT matrix and SAP visual sensitivities were related strongly to the RNFL thickness measured with the Stratus and Spectralis OCT devices, particularly in the overall and arcuate sectors. Copyright 2014 The Association for Research in Vision and Ophthalmology, Inc.

Manifold regularized matrix completion for multi-label learning with ADMM.

PubMed

Liu, Bin; Li, Yingming; Xu, Zenglin

2018-05-01

Multi-label learning is a common machine learning problem arising from numerous real-world applications in diverse fields, e.g, natural language processing, bioinformatics, information retrieval and so on. Among various multi-label learning methods, the matrix completion approach has been regarded as a promising approach to transductive multi-label learning. By constructing a joint matrix comprising the feature matrix and the label matrix, the missing labels of test samples are regarded as missing values of the joint matrix. With the low-rank assumption of the constructed joint matrix, the missing labels can be recovered by minimizing its rank. Despite its success, most matrix completion based approaches ignore the smoothness assumption of unlabeled data, i.e., neighboring instances should also share a similar set of labels. Thus they may under exploit the intrinsic structures of data. In addition, the matrix completion problem can be less efficient. To this end, we propose to efficiently solve the multi-label learning problem as an enhanced matrix completion model with manifold regularization, where the graph Laplacian is used to ensure the label smoothness over it. To speed up the convergence of our model, we develop an efficient iterative algorithm, which solves the resulted nuclear norm minimization problem with the alternating direction method of multipliers (ADMM). Experiments on both synthetic and real-world data have shown the promising results of the proposed approach. Copyright © 2018 Elsevier Ltd. All rights reserved.

Rigorous quantitative elemental microanalysis by scanning electron microscopy/energy dispersive x-ray spectrometry (SEM/EDS) with spectrum processing by NIST DTSA-II

NASA Astrophysics Data System (ADS)

Newbury, Dale E.; Ritchie, Nicholas W. M.

2014-09-01

Quantitative electron-excited x-ray microanalysis by scanning electron microscopy/silicon drift detector energy dispersive x-ray spectrometry (SEM/SDD-EDS) is capable of achieving high accuracy and high precision equivalent to that of the high spectral resolution wavelength dispersive x-ray spectrometer even when severe peak interference occurs. The throughput of the SDD-EDS enables high count spectra to be measured that are stable in calibration and resolution (peak shape) across the full deadtime range. With this high spectral stability, multiple linear least squares peak fitting is successful for separating overlapping peaks and spectral background. Careful specimen preparation is necessary to remove topography on unknowns and standards. The standards-based matrix correction procedure embedded in the NIST DTSA-II software engine returns quantitative results supported by a complete error budget, including estimates of the uncertainties from measurement statistics and from the physical basis of the matrix corrections. NIST DTSA-II is available free for Java-platforms at: http://www.cstl.nist.gov/div837/837.02/epq/dtsa2/index.html).

Anomaly-specified virtual dimensionality

NASA Astrophysics Data System (ADS)

Chen, Shih-Yu; Paylor, Drew; Chang, Chein-I.

2013-09-01

Virtual dimensionality (VD) has received considerable interest where VD is used to estimate the number of spectral distinct signatures, denoted by p. Unfortunately, no specific definition is provided by VD for what a spectrally distinct signature is. As a result, various types of spectral distinct signatures determine different values of VD. There is no one value-fit-all for VD. In order to address this issue this paper presents a new concept, referred to as anomaly-specified VD (AS-VD) which determines the number of anomalies of interest present in the data. Specifically, two types of anomaly detection algorithms are of particular interest, sample covariance matrix K-based anomaly detector developed by Reed and Yu, referred to as K-RXD and sample correlation matrix R-based RXD, referred to as R-RXD. Since K-RXD is only determined by 2nd order statistics compared to R-RXD which is specified by statistics of the first two orders including sample mean as the first order statistics, the values determined by K-RXD and R-RXD will be different. Experiments are conducted in comparison with widely used eigen-based approaches.

Phylogeny of metabolic networks: a spectral graph theoretical approach.

PubMed

Deyasi, Krishanu; Banerjee, Anirban; Deb, Bony

2015-10-01

Many methods have been developed for finding the commonalities between different organisms in order to study their phylogeny. The structure of metabolic networks also reveals valuable insights into metabolic capacity of species as well as into the habitats where they have evolved. We constructed metabolic networks of 79 fully sequenced organisms and compared their architectures. We used spectral density of normalized Laplacian matrix for comparing the structure of networks. The eigenvalues of this matrix reflect not only the global architecture of a network but also the local topologies that are produced by different graph evolutionary processes like motif duplication or joining. A divergence measure on spectral densities is used to quantify the distances between various metabolic networks, and a split network is constructed to analyse the phylogeny from these distances. In our analysis, we focused on the species that belong to different classes, but appear more related to each other in the phylogeny. We tried to explore whether they have evolved under similar environmental conditions or have similar life histories. With this focus, we have obtained interesting insights into the phylogenetic commonality between different organisms.

Multivariate Analysis of Mixed Lipid Aggregate Phase Transitions Monitored Using Raman Spectroscopy.

PubMed

Neal, Sharon L

2018-01-01

The phase behavior of aqueous 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC)/1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) mixtures between 8.0 ℃ and 41.0 ℃ were monitored using Raman spectroscopy. Temperature-dependent Raman matrices were assembled from series of spectra and subjected to multivariate analysis. The consensus of pseudo-rank estimation results is that seven to eight components account for the temperature-dependent changes observed in the spectra. The spectra and temperature response profiles of the mixture components were resolved by applying a variant of the non-negative matrix factorization (NMF) algorithm described by Lee and Seung (1999). The rotational ambiguity of the data matrix was reduced by augmenting the original temperature-dependent spectral matrix with its cumulative counterpart, i.e., the matrix formed by successive integration of the spectra across the temperature index (columns). Successive rounds of constrained NMF were used to isolate component spectra from a significant fluorescence background. Five major components exhibiting varying degrees of gel and liquid crystalline lipid character were resolved. Hydrogen-bonded water networks exhibiting varying degrees of organization are associated with the lipid components. Spectral parameters were computed to compare the chain conformation, packing, and hydration indicated by the resolved spectra. Based on spectral features and relative amounts of the components observed, four components reflect long chain lipid response. The fifth component could reflect the response of the short chain lipid, DHPC, but there were no definitive spectral features confirming this assignment. A minor component of uncertain assignment that exhibits a striking response to the DMPC pre-transition and chain melting transition also was recovered. While none of the spectra resolved exhibit features unequivocally attributable to a specific aggregate morphology or step in the gelation process, the results are consistent with the evolution of mixed phase bicelles (nanodisks) and small amounts of worm-like DMPC/DHPC aggregates, and perhaps DHPC micelles, at low temperature to suspensions of branched and entangled worm-like aggregates above the DMPC gel phase transition and perforated multi-lamellar aggregates at high temperature.

Asynchronous Gossip for Averaging and Spectral Ranking

NASA Astrophysics Data System (ADS)

Borkar, Vivek S.; Makhijani, Rahul; Sundaresan, Rajesh

2014-08-01

We consider two variants of the classical gossip algorithm. The first variant is a version of asynchronous stochastic approximation. We highlight a fundamental difficulty associated with the classical asynchronous gossip scheme, viz., that it may not converge to a desired average, and suggest an alternative scheme based on reinforcement learning that has guaranteed convergence to the desired average. We then discuss a potential application to a wireless network setting with simultaneous link activation constraints. The second variant is a gossip algorithm for distributed computation of the Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant draws upon a reinforcement learning algorithm for an average cost controlled Markov decision problem, the second variant draws upon a reinforcement learning algorithm for risk-sensitive control. We then discuss potential applications of the second variant to ranking schemes, reputation networks, and principal component analysis.

Characterization of Window Functions for Regularization of Electrical Capacitance Tomography Image Reconstruction

NASA Astrophysics Data System (ADS)

Jiang, Peng; Peng, Lihui; Xiao, Deyun

2007-06-01

This paper presents a regularization method by using different window functions as regularization for electrical capacitance tomography (ECT) image reconstruction. Image reconstruction for ECT is a typical ill-posed inverse problem. Because of the small singular values of the sensitivity matrix, the solution is sensitive to the measurement noise. The proposed method uses the spectral filtering properties of different window functions to make the solution stable by suppressing the noise in measurements. The window functions, such as the Hanning window, the cosine window and so on, are modified for ECT image reconstruction. Simulations with respect to five typical permittivity distributions are carried out. The reconstructions are better and some of the contours are clearer than the results from the Tikhonov regularization. Numerical results show that the feasibility of the image reconstruction algorithm using different window functions as regularization.

The Augmented Lagrange Multipliers Method for Matrix Completion from Corrupted Samplings with Application to Mixed Gaussian-Impulse Noise Removal

PubMed Central

Meng, Fan; Yang, Xiaomei; Zhou, Chenghu

2014-01-01

This paper studies the problem of the restoration of images corrupted by mixed Gaussian-impulse noise. In recent years, low-rank matrix reconstruction has become a research hotspot in many scientific and engineering domains such as machine learning, image processing, computer vision and bioinformatics, which mainly involves the problem of matrix completion and robust principal component analysis, namely recovering a low-rank matrix from an incomplete but accurate sampling subset of its entries and from an observed data matrix with an unknown fraction of its entries being arbitrarily corrupted, respectively. Inspired by these ideas, we consider the problem of recovering a low-rank matrix from an incomplete sampling subset of its entries with an unknown fraction of the samplings contaminated by arbitrary errors, which is defined as the problem of matrix completion from corrupted samplings and modeled as a convex optimization problem that minimizes a combination of the nuclear norm and the -norm in this paper. Meanwhile, we put forward a novel and effective algorithm called augmented Lagrange multipliers to exactly solve the problem. For mixed Gaussian-impulse noise removal, we regard it as the problem of matrix completion from corrupted samplings, and restore the noisy image following an impulse-detecting procedure. Compared with some existing methods for mixed noise removal, the recovery quality performance of our method is dominant if images possess low-rank features such as geometrically regular textures and similar structured contents; especially when the density of impulse noise is relatively high and the variance of Gaussian noise is small, our method can outperform the traditional methods significantly not only in the simultaneous removal of Gaussian noise and impulse noise, and the restoration ability for a low-rank image matrix, but also in the preservation of textures and details in the image. PMID:25248103

The fast algorithm of spark in compressive sensing

NASA Astrophysics Data System (ADS)

Xie, Meihua; Yan, Fengxia

2017-01-01

Compressed Sensing (CS) is an advanced theory on signal sampling and reconstruction. In CS theory, the reconstruction condition of signal is an important theory problem, and spark is a good index to study this problem. But the computation of spark is NP hard. In this paper, we study the problem of computing spark. For some special matrixes, for example, the Gaussian random matrix and 0-1 random matrix, we obtain some conclusions. Furthermore, for Gaussian random matrix with fewer rows than columns, we prove that its spark equals to the number of its rows plus one with probability 1. For general matrix, two methods are given to compute its spark. One is the method of directly searching and the other is the method of dual-tree searching. By simulating 24 Gaussian random matrixes and 18 0-1 random matrixes, we tested the computation time of these two methods. Numerical results showed that the dual-tree searching method had higher efficiency than directly searching, especially for those matrixes which has as much as rows and columns.

Liquid crystal-based Mueller matrix spectral imaging polarimetry for parameterizing mineral structural organization.

PubMed

Gladish, James C; Duncan, Donald D

2017-01-20

Herein, we discuss the remote assessment of the subwavelength organizational structure of a medium. Specifically, we use spectral imaging polarimetry, as the vector nature of polarized light enables it to interact with optical anisotropies within a medium, while the spectral aspect of polarization is sensitive to small-scale structure. The ability to image these effects allows for inference of spatial structural organization parameters. This work describes a methodology for revealing structural organization by exploiting the Stokes/Mueller formalism and by utilizing measurements from a spectral imaging polarimeter constructed from liquid crystal variable retarders and a liquid crystal tunable filter. We provide results to validate the system and then show results from measurements on a mineral sample.

The magnifying glass - A feature space local expansion for visual analysis. [and image enhancement

NASA Technical Reports Server (NTRS)

Juday, R. D.

1981-01-01

The Magnifying Glass Transformation (MGT) technique is proposed, as a multichannel spectral operation yielding visual imagery which is enhanced in a specified spectral vicinity, guided by the statistics of training samples. An application example is that in which the discrimination among spectral neighbors within an interactive display may be increased without altering distant object appearances or overall interpretation. A direct histogram specification technique is applied to the channels within the multispectral image so that a subset of the spectral domain occupies an increased fraction of the domain. The transformation is carried out by obtaining the training information, establishing the condition of the covariance matrix, determining the influenced solid, and initializing the lookup table. Finally, the image is transformed.

Preliminary Geologic/spectral Analysis of LANDSAT-4 Thematic Mapper Data, Wind River/bighorn Basin Area, Wyoming

NASA Technical Reports Server (NTRS)

Lang, H. R.; Conel, J. E.; Paylor, E. D.

1984-01-01

A LIDQA evaluation for geologic applications of a LANDSAT TM scene covering the Wind River/Bighorn Basin area, Wyoming, is examined. This involves a quantitative assessment of data quality including spatial and spectral characteristics. Analysis is concentrated on the 6 visible, near infrared, and short wavelength infrared bands. Preliminary analysis demonstrates that: (1) principal component images derived from the correlation matrix provide the most useful geologic information. To extract surface spectral reflectance, the TM radiance data must be calibrated. Scatterplots demonstrate that TM data can be calibrated and sensor response is essentially linear. Low instrumental offset and gain settings result in spectral data that do not utilize the full dynamic range of the TM system.

Table-sized matrix model in fractional learning

NASA Astrophysics Data System (ADS)

Soebagyo, J.; Wahyudin; Mulyaning, E. C.

2018-05-01

This article provides an explanation of the fractional learning model i.e. a Table-Sized Matrix model in which fractional representation and its operations are symbolized by the matrix. The Table-Sized Matrix are employed to develop problem solving capabilities as well as the area model. The Table-Sized Matrix model referred to in this article is used to develop an understanding of the fractional concept to elementary school students which can then be generalized into procedural fluency (algorithm) in solving the fractional problem and its operation.

Structural analysis and design of multivariable control systems: An algebraic approach

NASA Technical Reports Server (NTRS)

Tsay, Yih Tsong; Shieh, Leang-San; Barnett, Stephen

1988-01-01

The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.

Local terahertz microspectroscopy with λ/100 spatial resolution.

PubMed

Glotin, F; Ortega, J-M; Prazeres, R

2013-12-15

We have extended the spectral range of a differential method of infrared microspectroscopy in order to operate in the terahertz spectral region. We show on samples of graphite embedded in a matrix of polymers that the spatial resolution is practically independent of the wavelength and is at least λ/100. This method aims at performing "chemical mapping" of various objects since it is sensitive only to the imaginary part of the index of refraction.

Spectrum-to-Spectrum Searching Using a Proteome-wide Spectral Library*

PubMed Central

Yen, Chia-Yu; Houel, Stephane; Ahn, Natalie G.; Old, William M.

2011-01-01

The unambiguous assignment of tandem mass spectra (MS/MS) to peptide sequences remains a key unsolved problem in proteomics. Spectral library search strategies have emerged as a promising alternative for peptide identification, in which MS/MS spectra are directly compared against a reference library of confidently assigned spectra. Two problems relate to library size. First, reference spectral libraries are limited to rediscovery of previously identified peptides and are not applicable to new peptides, because of their incomplete coverage of the human proteome. Second, problems arise when searching a spectral library the size of the entire human proteome. We observed that traditional dot product scoring methods do not scale well with spectral library size, showing reduction in sensitivity when library size is increased. We show that this problem can be addressed by optimizing scoring metrics for spectrum-to-spectrum searches with large spectral libraries. MS/MS spectra for the 1.3 million predicted tryptic peptides in the human proteome are simulated using a kinetic fragmentation model (MassAnalyzer version2.1) to create a proteome-wide simulated spectral library. Searches of the simulated library increase MS/MS assignments by 24% compared with Mascot, when using probabilistic and rank based scoring methods. The proteome-wide coverage of the simulated library leads to 11% increase in unique peptide assignments, compared with parallel searches of a reference spectral library. Further improvement is attained when reference spectra and simulated spectra are combined into a hybrid spectral library, yielding 52% increased MS/MS assignments compared with Mascot searches. Our study demonstrates the advantages of using probabilistic and rank based scores to improve performance of spectrum-to-spectrum search strategies. PMID:21532008

Direct Solve of Electrically Large Integral Equations for Problem Sizes to 1M Unknowns

NASA Technical Reports Server (NTRS)

Shaeffer, John

2008-01-01

Matrix methods for solving integral equations via direct solve LU factorization are presently limited to weeks to months of very expensive supercomputer time for problems sizes of several hundred thousand unknowns. This report presents matrix LU factor solutions for electromagnetic scattering problems for problem sizes to one million unknowns with thousands of right hand sides that run in mere days on PC level hardware. This EM solution is accomplished by utilizing the numerical low rank nature of spatially blocked unknowns using the Adaptive Cross Approximation for compressing the rank deficient blocks of the system Z matrix, the L and U factors, the right hand side forcing function and the final current solution. This compressed matrix solution is applied to a frequency domain EM solution of Maxwell's equations using standard Method of Moments approach. Compressed matrix storage and operations count leads to orders of magnitude reduction in memory and run time.

A penny shaped crack in a filament-reinforced matrix. 2: The crack problem

NASA Technical Reports Server (NTRS)

Pacella, A. H.; Erdogan, F.

1973-01-01

The elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix was formulated. For a single filament as well as multiple identical filaments located symmetrically around the crack the problem is shown to reduce to a singular integral equation. The solution of the problem is obtained for various geometries and filament-to-matrix stiffness ratios, and the results relating to the angular variation of the stress intensity factor and the maximum filament stress are presented.

Chaos and random matrices in supersymmetric SYK

NASA Astrophysics Data System (ADS)

Hunter-Jones, Nicholas; Liu, Junyu

2018-05-01

We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.

The covariance matrix for the solution vector of an equality-constrained least-squares problem

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1976-01-01

Methods are given for computing the covariance matrix for the solution vector of an equality-constrained least squares problem. The methods are matched to the solution algorithms given in the book, 'Solving Least Squares Problems.'

Spectra of random networks in the weak clustering regime

NASA Astrophysics Data System (ADS)

Peron, Thomas K. DM.; Ji, Peng; Kurths, Jürgen; Rodrigues, Francisco A.

2018-03-01

The asymptotic behavior of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values of the clustering coefficient. Here we study effects of cycles of order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectral distribution of the network adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Implications to network dynamics are discussed. Our findings can shed light in the study of how particular kinds of subgraphs influence network dynamics.

Direct detection of the plant pathogens Burkholderia glumae, Burkholderia gladioli pv. gladioli, and Erwinia chrysanthemi pv. zeae in infected rice seedlings using matrix assisted laser desorption/ionization time-of-flight mass spectrometry.

PubMed

Kajiwara, Hideyuki

2016-01-01

The plant pathogens Burkholderia glumae, Burkholderia gladioli pv. gladioli, and Erwinia chrysanthemi pv. zeae were directly detected in extracts from infected rice seedlings by matrix assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). This method did not require culturing of the pathogens on artificial medium. In the MALDI-TOF MS analysis, peaks originating from bacteria were found in extracts from infected rice seedlings. The spectral peaks showed significantly high scores, in spite of minor differences in spectra. The spectral peaks originating from host plant tissues did not affect this direct MALDI-TOF MS analysis for the rapid identification of plant pathogens. Copyright © 2015 Elsevier B.V. All rights reserved.

Pixelated filters for spatial imaging

NASA Astrophysics Data System (ADS)

Mathieu, Karine; Lequime, Michel; Lumeau, Julien; Abel-Tiberini, Laetitia; Savin De Larclause, Isabelle; Berthon, Jacques

2015-10-01

Small satellites are often used by spatial agencies to meet scientific spatial mission requirements. Their payloads are composed of various instruments collecting an increasing amount of data, as well as respecting the growing constraints relative to volume and mass; So small-sized integrated camera have taken a favored place among these instruments. To ensure scene specific color information sensing, pixelated filters seem to be more attractive than filter wheels. The work presented here, in collaboration with Institut Fresnel, deals with the manufacturing of this kind of component, based on thin film technologies and photolithography processes. CCD detectors with a pixel pitch about 30 μm were considered. In the configuration where the matrix filters are positioned the closest to the detector, the matrix filters are composed of 2x2 macro pixels (e.g. 4 filters). These 4 filters have a bandwidth about 40 nm and are respectively centered at 550, 700, 770 and 840 nm with a specific rejection rate defined on the visible spectral range [500 - 900 nm]. After an intense design step, 4 thin-film structures have been elaborated with a maximum thickness of 5 μm. A run of tests has allowed us to choose the optimal micro-structuration parameters. The 100x100 matrix filters prototypes have been successfully manufactured with lift-off and ion assisted deposition processes. High spatial and spectral characterization, with a dedicated metrology bench, showed that initial specifications and simulations were globally met. These excellent performances knock down the technological barriers for high-end integrated specific multi spectral imaging.

Second-order standard addition for deconvolution and quantification of fatty acids of fish oil using GC-MS.

PubMed

Vosough, Maryam; Salemi, Amir

2007-08-15

In the present work two second-order calibration methods, generalized rank annihilation method (GRAM) and multivariate curve resolution-alternating least square (MCR-ALS) have been applied on standard addition data matrices obtained by gas chromatography-mass spectrometry (GC-MS) to characterize and quantify four unsaturated fatty acids cis-9-hexadecenoic acid (C16:1omega7c), cis-9-octadecenoic acid (C18:1omega9c), cis-11-eicosenoic acid (C20:1omega9) and cis-13-docosenoic acid (C22:1omega9) in fish oil considering matrix interferences. With these methods, the area does not need to be directly measured and predictions are more accurate. Because of non-trilinear conditions of GC-MS data matrices, at first MCR-ALS and GRAM have been used on uncorrected data matrices. In comparison to MCR-ALS, biased and imprecise concentrations (%R.S.D.=27.3) were obtained using GRAM without correcting the retention time-shift. As trilinearity is the essential requirement for implementing GRAM, the data need to be corrected. Multivariate rank alignment objectively corrects the run-to-run retention time variations between sample GC-MS data matrix and a standard addition GC-MS data matrix. Then, two second-order algorithms have been compared with each other. The above algorithms provided similar mean predictions, pure concentrations and spectral profiles. The results validated using standard mass spectra of target compounds. In addition, some of the quantification results were compared with the concentration values obtained using the selected mass chromatograms. As in the case of strong peak-overlap and the matrix effect, the classical univariate method of determination of the area of the peaks of the analytes will fail, the "second-order advantage" has solved this problem successfully.

Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations

NASA Astrophysics Data System (ADS)

Awata, Hidetoshi; Kanno, Hiroaki; Mironov, Andrei; Morozov, Alexei; Morozov, Andrey; Ohkubo, Yusuke; Zenkevich, Yegor

2016-10-01

R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. Calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the Yangian case by A. Smirnov but less general. We investigate the interplay between the R-matrix structure and the structure of DIM algebra intertwiners, i.e. of refined topological vertices and show that the R-matrix is diagonalized by the action of the spectral duality belonging to the SL(2, ℤ) group of DIM algebra automorphisms. We also construct the T-operators satisfying the RTT relations with the R-matrix from refined amplitudes on resolved conifold. We thus show that topological string theories on the toric Calabi-Yau threefolds can be naturally interpreted as lattice integrable models. Integrals of motion for these systems are related to q-deformation of the reflection matrices of the Liouville/Toda theories.

Pure endmember extraction using robust kernel archetypoid analysis for hyperspectral imagery

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

The Problem of Spectral Mimicry of Supergiants

NASA Astrophysics Data System (ADS)

Klochkova, V. G.; Chentsov, E. L.

2018-01-01

The phenomenon of spectral mimicry refers to the fact that hypergiants and post-AGB supergiants—stars of different masses in fundamentally different stages of their evolution—have similar optical spectra, and also share certain other characteristics (unstable extended atmospheres, expanding dust-gas envelopes, high IR excesses). As a consequence, it is not always possible to distinguish post-AGB stars from hypergiants based on individual spectral observations in the optical. Examples of spectral mimicry are analyzed using uniform, high-quality spectral material obtained on the 6-m telescope of the Special Astrophysical Observatory in the course of long-term monitoring of high-luminosity stars. It is shown that unambiguously resolving the mimicry problem for individual stars requires the determination of a whole set of parameters: luminosity, wind parameters, spectral energy distribution, spectral features, velocity field in the atmosphere and circumstellar medium, behavior of the parameters with time, and the chemical composition of the atmosphere.

Spectral methods for time dependent partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

A multidomain spectral collocation method for the Stokes problem

NASA Technical Reports Server (NTRS)

Landriani, G. Sacchi; Vandeven, H.

1989-01-01

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.

Airborne spectroradiometry: The application of AIS data to detecting subtle mineral absorption features

NASA Technical Reports Server (NTRS)

Cocks, T. D.; Green, A. A.

1986-01-01

Analysis of Airborne Imaging Spectrometer (AIS) data acquired in Australia has revealed a number of operational problems. Horizontal striping in AIS imagery and spectral distortions due to order overlap were investigated. Horizontal striping, caused by grating position errors can be removed with little or no effect on spectral details. Order overlap remains a problem that seriously compromises identification of subtle mineral absorption features within AIS spectra. A spectrometric model of the AIS was developed to assist in identifying spurious spectral features, and will be used in efforts to restore the spectral integrity of the data.

Analytical modeling of polarization transformation of laser radiation of various spectral ranges by birefringent structures

NASA Astrophysics Data System (ADS)

Motrich, A. V.; Ushenko, O. G.

2018-01-01

The results of statistical dependence and correlation structures of two-dimensional Mueller matrix elements in various spectral regions of laser radiation by changes in the distribution of orientations of optical axes and birefringence of protein crystals. Namely, a two-wave ("red-blue") approach - layer of biological tissues irradiated by He-Ne laser (λ1 = 0,63μm ) and He-Cd laser (λ1 = 0,41μm )was used Conducted analysis of polarimetric sensitivity was made, a state of polarization points that contain volumetric structures of biological objects to spectral region of laser radiation was detected.

Changes in the Spectral Features of Zinc Phthalocyanine Induced by Nitrogen Dioxide Gas in Solution and in Solid Polymer Nanofiber Media.

PubMed

Zugle, Ruphino; Tetteh, Samuel

2017-03-01

The changes in the spectral features of zinc phthalocyanine in the visible domain as a result of its interaction with nitrogen dioxide gas were assessed in this work. This was done both in solution and when the phthalocyanine was incorporated into a solid polystyrene polymer nanofiber matrix. The spectral changes were found to be spontaneous and marked in both cases suggesting a rapid response criterion for the detection of the gas. In particular, the functionalised nano-fabric material could serve as a practical fire alarm system as it rapidly detects the nitrogen dioxide gas generated during burning.

Single-particle spectral functions in the normal phase of a strongly attractive Bose-Fermi mixture

NASA Astrophysics Data System (ADS)

Fratini, E.; Pieri, P.

2013-07-01

We calculate the single-particle spectral functions and quasiparticle dispersions for a Bose-Fermi mixture when the boson-fermion attraction is sufficiently strong to suppress completely the condensation of bosons at zero temperature. Within a T-matrix diagrammatic approach, we vary the boson-fermion attraction from the critical value where the boson condensate first disappears to the strongly attractive (molecular) regime and study the effect of both mass and density imbalance on the spectral weights and dispersions. An interesting spectrum of particle-hole excitations mixing two different Fermi surfaces is found. These unconventional excitations could be produced and explored experimentally with radio-frequency spectroscopy.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

NASA Technical Reports Server (NTRS)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

The Rigid Orthogonal Procrustes Rotation Problem

ERIC Educational Resources Information Center

ten Berge, Jos M. F.

2006-01-01

The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has…

Identification and modification of dominant noise sources in diesel engines

NASA Astrophysics Data System (ADS)

Hayward, Michael D.

Determination of dominant noise sources in diesel engines is an integral step in the creation of quiet engines, but is a process which can involve an extensive series of expensive, time-consuming fired and motored tests. The goal of this research is to determine dominant noise source characteristics of a diesel engine in the near and far-fields with data from fewer tests than is currently required. Pre-conditioning and use of numerically robust methods to solve a set of cross-spectral density equations results in accurate calculation of the transfer paths between the near- and far-field measurement points. Application of singular value decomposition to an input cross-spectral matrix determines the spectral characteristics of a set of independent virtual sources, that, when scaled and added, result in the input cross spectral matrix. Each virtual source power spectral density is a singular value resulting from the decomposition performed over a range of frequencies. The complex relationship between virtual and physical sources is estimated through determination of virtual source contributions to each input measurement power spectral density. The method is made more user-friendly through use of a percentage contribution color plotting technique, where different normalizations can be used to help determine the presence of sources and the strengths of their contributions. Convolution of input measurements with the estimated path impulse responses results in a set of far-field components, to which the same singular value contribution plotting technique can be applied, thus allowing dominant noise source characteristics in the far-field to also be examined. Application of the methods presented results in determination of the spectral characteristics of dominant noise sources both in the near- and far-fields from one fired test, which significantly reduces the need for extensive fired and motored testing. Finally, it is shown that the far-field noise time history of a physically altered engine can be simulated through modification of singular values and recalculation of transfer paths between input and output measurements of previously recorded data.

Practical Implementation of Multiple Model Adaptive Estimation Using Neyman-Pearson Based Hypothesis Testing and Spectral Estimation Tools

DTIC Science & Technology

1996-09-01

Generalized Likelihood Ratio (GLR) and voting techniques. The third class consisted of multiple hypothesis filter detectors, specifically the MMAE. The...vector version, versus a tensor if we use the matrix version of the power spectral density estimate. Using this notation, we will derive an...as MATLAB , have an intrinsic sample covariance computation available, which makes this method quite easy to implement. In practice, the mean for the

A grid matrix-based Raman spectroscopic method to characterize different cell milieu in biopsied axillary sentinel lymph nodes of breast cancer patients.

PubMed

Som, Dipasree; Tak, Megha; Setia, Mohit; Patil, Asawari; Sengupta, Amit; Chilakapati, C Murali Krishna; Srivastava, Anurag; Parmar, Vani; Nair, Nita; Sarin, Rajiv; Badwe, R

2016-01-01

Raman spectroscopy which is based upon inelastic scattering of photons has a potential to emerge as a noninvasive bedside in vivo or ex vivo molecular diagnostic tool. There is a need to improve the sensitivity and predictability of Raman spectroscopy. We developed a grid matrix-based tissue mapping protocol to acquire cellular-specific spectra that also involved digital microscopy for localizing malignant and lymphocytic cells in sentinel lymph node biopsy sample. Biosignals acquired from specific cellular milieu were subjected to an advanced supervised analytical method, i.e., cross-correlation and peak-to-peak ratio in addition to PCA and PC-LDA. We observed decreased spectral intensity as well as shift in the spectral peaks of amides and lipid bands in the completely metastatic (cancer cells) lymph nodes with high cellular density. Spectral library of normal lymphocytes and metastatic cancer cells created using the cellular specific mapping technique can be utilized to create an automated smart diagnostic tool for bench side screening of sampled lymph nodes. Spectral library of normal lymphocytes and metastatic cancer cells created using the cellular specific mapping technique can be utilized to develop an automated smart diagnostic tool for bench side screening of sampled lymph nodes supported by ongoing global research in developing better technology and signal and big data processing algorithms.

Spectral Interferences Manganese (Mn) - Europium (Eu) Lines in X-Ray Fluorescence Spectrometry Spectrum

NASA Astrophysics Data System (ADS)

Tanc, Beril; Kaya, Mustafa; Gumus, Lokman; Kumral, Mustafa

2016-04-01

X-ray fluorescence (XRF) spectrometry is widely used for quantitative and semi quantitative analysis of many major, minor and trace elements in geological samples. Some advantages of the XRF method are; non-destructive sample preparation, applicability for powder, solid, paste and liquid samples and simple spectrum that are independent from chemical state. On the other hand, there are some disadvantages of the XRF methods such as poor sensitivity for low atomic number elements, matrix effect (physical matrix effects, such as fine versus course grain materials, may impact XRF performance) and interference effect (the spectral lines of elements may overlap distorting results for one or more elements). Especially, spectral interferences are very significant factors for accurate results. In this study, semi-quantitative analyzed manganese (II) oxide (MnO, 99.99%) was examined. Samples were pelleted and analyzed with XRF spectrometry (Bruker S8 Tiger). Unexpected peaks were obtained at the side of the major Mn peaks. Although sample does not contain Eu element, in results 0,3% Eu2O3 was observed. These result can occur high concentration of MnO and proximity of Mn and Eu lines. It can be eliminated by using correction equation or Mn concentration can confirm with other methods (such as Atomic absorption spectroscopy). Keywords: Spectral Interferences; Manganese (Mn); Europium (Eu); X-Ray Fluorescence Spectrometry Spectrum.

Estimation of positive semidefinite correlation matrices by using convex quadratic semidefinite programming.

PubMed

Fushiki, Tadayoshi

2009-07-01

The correlation matrix is a fundamental statistic that is used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used in the Gram matrix in kernel methods. However, the estimated correlation matrix sometimes has a serious defect: although the correlation matrix is originally positive semidefinite, the estimated one may not be positive semidefinite when not all ratings are observed. To obtain a positive semidefinite correlation matrix, the nearest correlation matrix problem has recently been studied in the fields of numerical analysis and optimization. However, statistical properties are not explicitly used in such studies. To obtain a positive semidefinite correlation matrix, we assume the approximate model. By using the model, an estimate is obtained as the optimal point of an optimization problem formulated with information on the variances of the estimated correlation coefficients. The problem is solved by a convex quadratic semidefinite program. A penalized likelihood approach is also examined. The MovieLens data set is used to test our approach.

Effects of calibration methods on quantitative material decomposition in photon-counting spectral computed tomography using a maximum a posteriori estimator.

PubMed

Curtis, Tyler E; Roeder, Ryan K

2017-10-01

Advances in photon-counting detectors have enabled quantitative material decomposition using multi-energy or spectral computed tomography (CT). Supervised methods for material decomposition utilize an estimated attenuation for each material of interest at each photon energy level, which must be calibrated based upon calculated or measured values for known compositions. Measurements using a calibration phantom can advantageously account for system-specific noise, but the effect of calibration methods on the material basis matrix and subsequent quantitative material decomposition has not been experimentally investigated. Therefore, the objective of this study was to investigate the influence of the range and number of contrast agent concentrations within a modular calibration phantom on the accuracy of quantitative material decomposition in the image domain. Gadolinium was chosen as a model contrast agent in imaging phantoms, which also contained bone tissue and water as negative controls. The maximum gadolinium concentration (30, 60, and 90 mM) and total number of concentrations (2, 4, and 7) were independently varied to systematically investigate effects of the material basis matrix and scaling factor calibration on the quantitative (root mean squared error, RMSE) and spatial (sensitivity and specificity) accuracy of material decomposition. Images of calibration and sample phantoms were acquired using a commercially available photon-counting spectral micro-CT system with five energy bins selected to normalize photon counts and leverage the contrast agent k-edge. Material decomposition of gadolinium, calcium, and water was performed for each calibration method using a maximum a posteriori estimator. Both the quantitative and spatial accuracy of material decomposition were most improved by using an increased maximum gadolinium concentration (range) in the basis matrix calibration; the effects of using a greater number of concentrations were relatively small in magnitude by comparison. The material basis matrix calibration was more sensitive to changes in the calibration methods than the scaling factor calibration. The material basis matrix calibration significantly influenced both the quantitative and spatial accuracy of material decomposition, while the scaling factor calibration influenced quantitative but not spatial accuracy. Importantly, the median RMSE of material decomposition was as low as ~1.5 mM (~0.24 mg/mL gadolinium), which was similar in magnitude to that measured by optical spectroscopy on the same samples. The accuracy of quantitative material decomposition in photon-counting spectral CT was significantly influenced by calibration methods which must therefore be carefully considered for the intended diagnostic imaging application. © 2017 American Association of Physicists in Medicine.

Quantitative fluorescence and elastic scattering tissue polarimetry using an Eigenvalue calibrated spectroscopic Mueller matrix system.

PubMed

Soni, Jalpa; Purwar, Harsh; Lakhotia, Harshit; Chandel, Shubham; Banerjee, Chitram; Kumar, Uday; Ghosh, Nirmalya

2013-07-01

A novel spectroscopic Mueller matrix system has been developed and explored for both fluorescence and elastic scattering polarimetric measurements from biological tissues. The 4 × 4 Mueller matrix measurement strategy is based on sixteen spectrally resolved (λ = 400 - 800 nm) measurements performed by sequentially generating and analyzing four elliptical polarization states. Eigenvalue calibration of the system ensured high accuracy of Mueller matrix measurement over a broad wavelength range, either for forward or backscattering geometry. The system was explored for quantitative fluorescence and elastic scattering spectroscopic polarimetric studies on normal and precancerous tissue sections from human uterine cervix. The fluorescence spectroscopic Mueller matrices yielded an interesting diattenuation parameter, exhibiting differences between normal and precancerous tissues.

Informed Source Separation of Atmospheric and Surface Signal Contributions in Shortwave Hyperspectral Imagery using Non-negative Matrix Factorization

NASA Astrophysics Data System (ADS)

Wright, L.; Coddington, O.; Pilewskie, P.

2015-12-01

Current challenges in Earth remote sensing require improved instrument spectral resolution, spectral coverage, and radiometric accuracy. Hyperspectral instruments, deployed on both aircraft and spacecraft, are a growing class of Earth observing sensors designed to meet these challenges. They collect large amounts of spectral data, allowing thorough characterization of both atmospheric and surface properties. The higher accuracy and increased spectral and spatial resolutions of new imagers require new numerical approaches for processing imagery and separating surface and atmospheric signals. One potential approach is source separation, which allows us to determine the underlying physical causes of observed changes. Improved signal separation will allow hyperspectral instruments to better address key science questions relevant to climate change, including land-use changes, trends in clouds and atmospheric water vapor, and aerosol characteristics. In this work, we investigate a Non-negative Matrix Factorization (NMF) method for the separation of atmospheric and land surface signal sources. NMF offers marked benefits over other commonly employed techniques, including non-negativity, which avoids physically impossible results, and adaptability, which allows the method to be tailored to hyperspectral source separation. We adapt our NMF algorithm to distinguish between contributions from different physically distinct sources by introducing constraints on spectral and spatial variability and by using library spectra to inform separation. We evaluate our NMF algorithm with simulated hyperspectral images as well as hyperspectral imagery from several instruments including, the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), NASA Hyperspectral Imager for the Coastal Ocean (HICO) and National Ecological Observatory Network (NEON) Imaging Spectrometer.

Digital staining for histopathology multispectral images by the combined application of spectral enhancement and spectral transformation.

PubMed

Bautista, Pinky A; Yagi, Yukako

2011-01-01

In this paper we introduced a digital staining method for histopathology images captured with an n-band multispectral camera. The method consisted of two major processes: enhancement of the original spectral transmittance and the transformation of the enhanced transmittance to its target spectral configuration. Enhancement is accomplished by shifting the original transmittance with the scaled difference between the original transmittance and the transmittance estimated with m dominant principal component (PC) vectors;the m-PC vectors were determined from the transmittance samples of the background image. Transformation of the enhanced transmittance to the target spectral configuration was done using an nxn transformation matrix, which was derived by applying a least square method to the enhanced and target spectral training data samples of the different tissue components. Experimental results on the digital conversion of a hematoxylin and eosin (H&E) stained multispectral image to its Masson's trichrome stained (MT) equivalent shows the viability of the method.

Structuring Word Problems for Diagnostic Teaching: Helping Teachers Meet the Needs of Children with Mild Disabilities.

ERIC Educational Resources Information Center

Parmar, Rene S.; Cawley, John F.

1994-01-01

Matrix organization can be used to construct math word problems for children with mild disabilities. Matrix organization specifies the characteristics of problems, such as problem theme or setting, operations, level of computation complexity, reading vocabulary level, and need for classification. A sample scope and sequence and 16 sample word…

Evaluation of methods for trace-element determination with emphasis on their usability in the clinical routine laboratory.

PubMed

Bolann, B J; Rahil-Khazen, R; Henriksen, H; Isrenn, R; Ulvik, R J

2007-01-01

Commonly used techniques for trace-element analysis in human biological material are flame atomic absorption spectrometry (FAAS), graphite furnace atomic absorption spectrometry (GFAAS), inductively coupled plasma atomic emission spectrometry (ICP-AES) and inductively coupled plasma mass spectrometry (ICP-MS). Elements that form volatile hydrides, first of all mercury, are analysed by hydride generation techniques. In the absorption techniques the samples are vaporized into free, neutral atoms and illuminated by a light source that emits the atomic spectrum of the element under analysis. The absorbance gives a quantitative measure of the concentration of the element. ICP-AES and ICP-MS are multi-element techniques. In ICP-AES the atoms of the sample are excited by, for example, argon plasma at very high temperatures. The emitted light is directed to a detector, and the optical signals are processed to values for the concentrations of the elements. In ICP-MS a mass spectrometer separates and detects ions produced by the ICP, according to their mass-to-charge ratio. Dilution of biological fluids is commonly needed to reduce the effect of the matrix. Digestion using acids and microwave energy in closed vessels at elevated pressure is often used. Matrix and spectral interferences may cause problems. Precautions should be taken against trace-element contamination during collection, storage and processing of samples. For clinical problems requiring the analysis of only one or a few elements, the use of FAAS may be sufficient, unless the higher sensitivity of GFAAS is required. For screening of multiple elements, however, the ICP techniques are preferable.

Random Matrix Approach for Primal-Dual Portfolio Optimization Problems

NASA Astrophysics Data System (ADS)

Tada, Daichi; Yamamoto, Hisashi; Shinzato, Takashi

2017-12-01

In this paper, we revisit the portfolio optimization problems of the minimization/maximization of investment risk under constraints of budget and investment concentration (primal problem) and the maximization/minimization of investment concentration under constraints of budget and investment risk (dual problem) for the case that the variances of the return rates of the assets are identical. We analyze both optimization problems by the Lagrange multiplier method and the random matrix approach. Thereafter, we compare the results obtained from our proposed approach with the results obtained in previous work. Moreover, we use numerical experiments to validate the results obtained from the replica approach and the random matrix approach as methods for analyzing both the primal and dual portfolio optimization problems.

Users manual for the Variable dimension Automatic Synthesis Program (VASP)

NASA Technical Reports Server (NTRS)

White, J. S.; Lee, H. Q.

1971-01-01

A dictionary and some problems for the Variable Automatic Synthesis Program VASP are submitted. The dictionary contains a description of each subroutine and instructions on its use. The example problems give the user a better perspective on the use of VASP for solving problems in modern control theory. These example problems include dynamic response, optimal control gain, solution of the sampled data matrix Ricatti equation, matrix decomposition, and pseudo inverse of a matrix. Listings of all subroutines are also included. The VASP program has been adapted to run in the conversational mode on the Ames 360/67 computer.

Statistical analysis and machine learning algorithms for optical biopsy

NASA Astrophysics Data System (ADS)

Wu, Binlin; Liu, Cheng-hui; Boydston-White, Susie; Beckman, Hugh; Sriramoju, Vidyasagar; Sordillo, Laura; Zhang, Chunyuan; Zhang, Lin; Shi, Lingyan; Smith, Jason; Bailin, Jacob; Alfano, Robert R.

2018-02-01

Analyzing spectral or imaging data collected with various optical biopsy methods is often times difficult due to the complexity of the biological basis. Robust methods that can utilize the spectral or imaging data and detect the characteristic spectral or spatial signatures for different types of tissue is challenging but highly desired. In this study, we used various machine learning algorithms to analyze a spectral dataset acquired from human skin normal and cancerous tissue samples using resonance Raman spectroscopy with 532nm excitation. The algorithms including principal component analysis, nonnegative matrix factorization, and autoencoder artificial neural network are used to reduce dimension of the dataset and detect features. A support vector machine with a linear kernel is used to classify the normal tissue and cancerous tissue samples. The efficacies of the methods are compared.

Spectral difference Lanczos method for efficient time propagation in quantum control theory

NASA Astrophysics Data System (ADS)

Farnum, John D.; Mazziotti, David A.

2004-04-01

Spectral difference methods represent the real-space Hamiltonian of a quantum system as a banded matrix which possesses the accuracy of the discrete variable representation (DVR) and the efficiency of finite differences. When applied to time-dependent quantum mechanics, spectral differences enhance the efficiency of propagation methods for evolving the Schrödinger equation. We develop a spectral difference Lanczos method which is computationally more economical than the sinc-DVR Lanczos method, the split-operator technique, and even the fast-Fourier-Transform Lanczos method. Application of fast propagation is made to quantum control theory where chirped laser pulses are designed to dissociate both diatomic and polyatomic molecules. The specificity of the chirped laser fields is also tested as a possible method for molecular identification and discrimination.

Dual-camera design for coded aperture snapshot spectral imaging.

PubMed

Wang, Lizhi; Xiong, Zhiwei; Gao, Dahua; Shi, Guangming; Wu, Feng

2015-02-01

Coded aperture snapshot spectral imaging (CASSI) provides an efficient mechanism for recovering 3D spectral data from a single 2D measurement. However, since the reconstruction problem is severely underdetermined, the quality of recovered spectral data is usually limited. In this paper we propose a novel dual-camera design to improve the performance of CASSI while maintaining its snapshot advantage. Specifically, a beam splitter is placed in front of the objective lens of CASSI, which allows the same scene to be simultaneously captured by a grayscale camera. This uncoded grayscale measurement, in conjunction with the coded CASSI measurement, greatly eases the reconstruction problem and yields high-quality 3D spectral data. Both simulation and experimental results demonstrate the effectiveness of the proposed method.

RF Wave Simulation Using the MFEM Open Source FEM Package

NASA Astrophysics Data System (ADS)

Stillerman, J.; Shiraiwa, S.; Bonoli, P. T.; Wright, J. C.; Green, D. L.; Kolev, T.

2016-10-01

A new plasma wave simulation environment based on the finite element method is presented. MFEM, a scalable open-source FEM library, is used as the basis for this capability. MFEM allows for assembling an FEM matrix of arbitrarily high order in a parallel computing environment. A 3D frequency domain RF physics layer was implemented using a python wrapper for MFEM and a cold collisional plasma model was ported. This physics layer allows for defining the plasma RF wave simulation model without user knowledge of the FEM weak-form formulation. A graphical user interface is built on πScope, a python-based scientific workbench, such that a user can build a model definition file interactively. Benchmark cases have been ported to this new environment, with results being consistent with those obtained using COMSOL multiphysics, GENRAY, and TORIC/TORLH spectral solvers. This work is a first step in bringing to bear the sophisticated computational tool suite that MFEM provides (e.g., adaptive mesh refinement, solver suite, element types) to the linear plasma-wave interaction problem, and within more complicated integrated workflows, such as coupling with core spectral solver, or incorporating additional physics such as an RF sheath potential model or kinetic effects. USDoE Awards DE-FC02-99ER54512, DE-FC02-01ER54648.

Discrimination of organic coffee via Fourier transform infrared-photoacoustic spectroscopy.

PubMed

Gordillo-Delgado, Fernando; Marín, Ernesto; Cortés-Hernández, Diego Mauricio; Mejía-Morales, Claudia; García-Salcedo, Angela Janet

2012-08-30

Procedures for the evaluation of the origin and quality of ground and roasted coffee are constantly needed for the associated industry due to complexity of the related market. Conventional Fourier transform infrared (FTIR) spectroscopy can be used for detecting changes in functional groups of compounds, such as coffee. However, dispersion, reflection and non-homogeneity of the sample matrix can cause problems resulting in low spectral quality. On the other hand, sample preparation frequently takes place in a destructive way. To overcome these difficulties, in this work a photoacoustic cell has been adapted as a detector in a FTIR spectrophotometer to perform a study of roasted and ground coffee from three varieties of Coffea arabica grown by organic and conventional methods. Comparison between spectra of coffee recorded by FTIR-photoacoustic spectrometry (PAS) and by FTIR spectrophotometry showed a better resolution of the former method, which, aided by principal components analysis, allowed the identification of some absorption bands that allow the discrimination between organic and conventional coffee. The results obtained provide information about the spectral behavior of coffee powder which can be useful for establishing discrimination criteria. It has been demonstrated that FTIR-PAS can be a useful experimental tool for the characterization of coffee. Copyright © 2012 Society of Chemical Industry.

Rational Variety Mapping for Contrast-Enhanced Nonlinear Unsupervised Segmentation of Multispectral Images of Unstained Specimen

PubMed Central

Kopriva, Ivica; Hadžija, Mirko; Popović Hadžija, Marijana; Korolija, Marina; Cichocki, Andrzej

2011-01-01

A methodology is proposed for nonlinear contrast-enhanced unsupervised segmentation of multispectral (color) microscopy images of principally unstained specimens. The methodology exploits spectral diversity and spatial sparseness to find anatomical differences between materials (cells, nuclei, and background) present in the image. It consists of rth-order rational variety mapping (RVM) followed by matrix/tensor factorization. Sparseness constraint implies duality between nonlinear unsupervised segmentation and multiclass pattern assignment problems. Classes not linearly separable in the original input space become separable with high probability in the higher-dimensional mapped space. Hence, RVM mapping has two advantages: it takes implicitly into account nonlinearities present in the image (ie, they are not required to be known) and it increases spectral diversity (ie, contrast) between materials, due to increased dimensionality of the mapped space. This is expected to improve performance of systems for automated classification and analysis of microscopic histopathological images. The methodology was validated using RVM of the second and third orders of the experimental multispectral microscopy images of unstained sciatic nerve fibers (nervus ischiadicus) and of unstained white pulp in the spleen tissue, compared with a manually defined ground truth labeled by two trained pathophysiologists. The methodology can also be useful for additional contrast enhancement of images of stained specimens. PMID:21708116

Spectral Approaches to Learning Predictive Representations

DTIC Science & Technology

2012-09-01

conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed...to the mean to form an initial prediction of x̂(ht). Similarly, Equation 2.3b can be interpreted as using the dynamics matrix A and error covarianceQ...in the sense of Lyapunov if its dynamics matrix A is. Thus, the Lyapunov criterion can be interpreted as holding for an LDS if, for a given covariance

Performance comparisons on spatial lattice algorithm and direct matrix inverse method with application to adaptive arrays processing

NASA Technical Reports Server (NTRS)

An, S. H.; Yao, K.

1986-01-01

Lattice algorithm has been employed in numerous adaptive filtering applications such as speech analysis/synthesis, noise canceling, spectral analysis, and channel equalization. In this paper the application to adaptive-array processing is discussed. The advantages are fast convergence rate as well as computational accuracy independent of the noise and interference conditions. The results produced by this technique are compared to those obtained by the direct matrix inverse method.

Analysis of trichothecene mycotoxins in contaminated grains by gas chromatography/matrix isolation/Fourier transform infrared spectroscopy and gas chromatography/mass spectrometry.

PubMed

Mossoba, M M; Adams, S; Roach, J A; Trucksess, M W

1996-01-01

Gas chromatography/matrix isolation/Fourier transform infrared (GC/MI/FTIR) spectroscopy and GC/mass spectrometry (MS) were used to confirm the identities of trimethylsilyl (TMS) derivatives of trichothecene mycotoxins in naturally contaminated grains. Infrared spectral bands observed in the fingerprint region were unique for 10 trichothecene standards. Characteristic absorption bands were observed for the ester (near 1750 cm-1) and ketone (near 1700 cm-1) carbonyl stretching vibrations, the acetate CH3 symmetric bend (1370 cm-1), the epoxide ring (1262 cm-1), the trimethylsilyl CH3 in-plane deformation (1253 cm-1), the ester (O)C-O asymmetric stretching vibration (near 1244 cm-1), and several other bands including intense features due to the TMS function. Infrared bands observed under cryogenic matrix isolation conditions were compared with those found at room temperature in a potassium bromide matrix for 5 of these standards. Identities of deoxynivalenol (DON) from barley and mixed feed, nivalenol from wheat and barley, and DON and fusarenon-x from sweet corn were confirmed by comparison of their infrared spectral bands with those of standards. The identity of DON in the same test samples of sweet corn was confirmed further by GC/MS. GC/MS was also used to quantitate the levels of DON (67-455 ppm) in sweet corn test samples.

Intra- and intermolecular H-bond mediated tautomerization and dimerization of 3-methyl-1,2-cyclopentanedione: Infrared spectroscopy in argon matrix and CCl 4 solution

NASA Astrophysics Data System (ADS)

Samanta, Amit K.; Pandey, Prasenjit; Bandyopadhyay, Biman; Mukhopadhyay, Anamika; Chakraborty, Tapas

2011-05-01

Mid-infrared spectra of 3-methyl-1,2-cyclopentanedione (3-MeCPD) have been recorded by isolating the molecule in a cold argon matrix (8 K) and also in CCl 4 solution at room temperature. The spectral features reveal that in both media, the molecule exists exclusively in an enol tautomeric form, which is stabilized by an intramolecular O sbnd H⋯O hydrogen bond. NBO analysis shows that the preferred conformer is further stabilized because of hyperconjugation interaction between the methyl and vinyl group of the enol tautomer. In CCl 4 solution, the molecule undergoes extensive self association and generates a doubly hydrogen bonded centrosymmetric dimer. The dimerization constant ( K d) is estimated to have a value of ˜9 L mol -1 at room temperature (25 °C) and the thermodynamic parameters, Δ H°, Δ S° and Δ G°, of dimerization are estimated by measuring K d at several temperatures within the range 22-60 °C. The same dimer is also produced when the matrix is annealed at a higher temperature. In addition, a non-centrosymmetric singly hydrogen bonded dimer is also identified in the argon matrix. A comparison between the spectral features of the two dimers indicates that the dimerization effect on doubly H-bonded case is influenced by cooperative interaction between the two H-bonds.

Dependence of Sum Frequency Generation (SFG) Spectral Features on the Mesoscale Arrangement of SFG-Active Crystalline Domains Interspersed in SFG-Inactive Matrix: A Case Study with Cellulose in Uniaxially Aligned Control Samples and Alkali-Treated Secondary Cell Walls of Plants

DOE PAGES

Makarem, Mohamadamin; Sawada, Daisuke; O'Neill, Hugh M.; ...

2017-04-21

Vibrational sum frequency generation (SFG) spectroscopy can selectively detect not only molecules at two-dimensional (2D) interfaces but also noncentrosymmetric domains interspersed in amorphous three-dimensional (3D) matrixes. However, the SFG analysis of 3D systems is more complicated than 2D systems because more variables are involved. One such variable is the distance between SFG-active domains in SFG-inactive matrixes. In this study, we fabricated control samples in which SFG-active cellulose crystals were uniaxially aligned in an amorphous matrix. Assuming uniform separation distances between cellulose crystals, the relative intensities of alkyl (CH) and hydroxyl (OH) SFG peaks of cellulose could be related to themore » intercrystallite distance. The experimentally measured CH/OH intensity ratio as a function of the intercrystallite distance could be explained reasonably well with a model constructed using the theoretically calculated hyperpolarizabilities of cellulose and the symmetry cancellation principle of dipoles antiparallel to each other. In conclusion, this comparison revealed physical insights into the intercrystallite distance dependence of the CH/OH SFG intensity ratio of cellulose, which can be used to interpret the SFG spectral features of plant cell walls in terms of mesoscale packing of cellulose microfibrils.« less

Advanced Background Subtraction Applied to Aeroacoustic Wind Tunnel Testing

NASA Technical Reports Server (NTRS)

Bahr, Christopher J.; Horne, William C.

2015-01-01

An advanced form of background subtraction is presented and applied to aeroacoustic wind tunnel data. A variant of this method has seen use in other fields such as climatology and medical imaging. The technique, based on an eigenvalue decomposition of the background noise cross-spectral matrix, is robust against situations where isolated background auto-spectral levels are measured to be higher than levels of combined source and background signals. It also provides an alternate estimate of the cross-spectrum, which previously might have poor definition for low signal-to-noise ratio measurements. Simulated results indicate similar performance to conventional background subtraction when the subtracted spectra are weaker than the true contaminating background levels. Superior performance is observed when the subtracted spectra are stronger than the true contaminating background levels. Experimental results show limited success in recovering signal behavior for data where conventional background subtraction fails. They also demonstrate the new subtraction technique's ability to maintain a proper coherence relationship in the modified cross-spectral matrix. Beam-forming and de-convolution results indicate the method can successfully separate sources. Results also show a reduced need for the use of diagonal removal in phased array processing, at least for the limited data sets considered.

A rapid excitation-emission matrix fluorometer utilizing supercontinuum white light and acousto-optic tunable filters

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

Wang, Wenbo; Department of Dermatology and Skin Science, University of British Columbia, 835 West 10th Avenue, Vancouver, British Columbia V5Z 4E8; Department of Biomedical Engineering, University of British Columbia, KAIS 5500, 2332 Main Mall, Vancouver, British Columbia V6T 1Z4

Scanning speed and coupling efficiency of excitation light to optic fibres are two major technical challenges that limit the potential of fluorescence excitation-emission matrix (EEM) spectrometer for on-line applications and in vivo studies. In this paper, a novel EEM system, utilizing a supercontinuum white light source and acousto-optic tunable filters (AOTFs), was introduced and evaluated. The supercontinuum white light, generated by pumping a nonlinear photonic crystal fiber with an 800 nm femtosecond laser, was efficiently coupled into a bifurcated optic fiber bundle. High speed EEM spectral scanning was achieved using AOTFs both for selecting excitation wavelength and scanning emission spectra.more » Using calibration lamps (neon and mercury argon), wavelength deviations were determined to vary from 0.18 nm to −0.70 nm within the spectral range of 500–850 nm. Spectral bandwidth for filtered excitation light broadened by twofold compared to that measured with monochromatic light between 650 nm and 750 nm. The EEM spectra for methanol solutions of laser dyes were successfully acquired with this rapid fluorometer using an integration time of 5 s.« less

Luminescence of CdSe/ZnS quantum dots infiltrated into an opal matrix

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

Gruzintsev, A. N.; Emelchenko, G. A.; Masalov, V. M.

The effect of the photonic band gap in the photonic crystal, the synthesized SiO{sub 2} opal with embedded CdSe/ZnS quantum dots, on its luminescence in the visible spectral region is studied. It is shown that the position of the photonic band gap in the luminescence and reflectance spectra for the infiltrated opal depends on the diameter of the constituent nanospheres and on the angle of recording the signal. The optimal conditions for embedding the CdSe/ZnS quantum dots from the solution into the opal matrix are determined. It is found that, for the opal-CdSe/ZnS nanocomposites, the emission intensity decreases and themore » luminescence decay time increases in the spatial directions, in which the spectral positions of the photonic band gap and the luminescence peak of the quantum dots coincide.« less

Quantum adiabatic computation with a constant gap is not useful in one dimension.

PubMed

Hastings, M B

2009-07-31

We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state. The proof relies on a recently proven area law for such systems, implying the existence of a good matrix product representation of the ground state, combined with an appropriate algorithm to update the matrix product state as the Hamiltonian is changed. This implies that adiabatic evolution with such Hamiltonians is not useful for universal quantum computation. Therefore, adiabatic algorithms which are useful for universal quantum computation either require a spectral gap tending to zero or need to be implemented in more than one dimension (we leave open the question of the computational power of adiabatic simulation with a constant gap in more than one dimension).

Photochromic properties of the N-Salicylideneaniline in Polyvinyl Butyral matrix: Experimental and theoretical investigations

NASA Astrophysics Data System (ADS)

Shahab, Siyamak; Filippovich, Liudmila; Aharodnikova, M.; Almodarresiyeh, Hora A.; Hajikolaee, Fatemeh Haji; Kumar, Rakesh; Mashayekhi, Mahsa

2017-04-01

In the present work, isomerization, photophysical properties, thermal conductivity (λ) and spectral study of the N-Salicylideneaniline: 2-[(E)-(phenylimino)methyl]phenol (SA) under the action of UV radiation in the Polyvinyl Butyral (PVB) matrix were studied using the Indicator method and Density Functional Theory (DFT). The electronic absorption spectra of SA and its isomers (SA1 and SA2) in dimethylformamide (DMF) solutions were also calculated. The nature of absorption bands of SA, SA1 and SA2 in the visible and near ultraviolet spectral regions was interpreted. The excitation energies, electronic transitions and oscillator strengths for SA, SA1 and SA2 have also been calculated. Thermal Conductivity of PVB-films containing SA before and after UV radiation was also measured. A Photochromic PVB - film on the basis of SA for application in optical devices and display technologies was made.

The difference between two random mixed quantum states: exact and asymptotic spectral analysis

NASA Astrophysics Data System (ADS)

Mejía, José; Zapata, Camilo; Botero, Alonso

2017-01-01

We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson’s theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance.

A spectral k-means approach to bright-field cell image segmentation.

PubMed

Bradbury, Laura; Wan, Justin W L

2010-01-01

Automatic segmentation of bright-field cell images is important to cell biologists, but difficult to complete due to the complex nature of the cells in bright-field images (poor contrast, broken halo, missing boundaries). Standard approaches such as level set segmentation and active contours work well for fluorescent images where cells appear as round shape, but become less effective when optical artifacts such as halo exist in bright-field images. In this paper, we present a robust segmentation method which combines the spectral and k-means clustering techniques to locate cells in bright-field images. This approach models an image as a matrix graph and segment different regions of the image by computing the appropriate eigenvectors of the matrix graph and using the k-means algorithm. We illustrate the effectiveness of the method by segmentation results of C2C12 (muscle) cells in bright-field images.

Finite-temperature dynamic structure factor of the spin-1 XXZ chain with single-ion anisotropy

NASA Astrophysics Data System (ADS)

Lange, Florian; Ejima, Satoshi; Fehske, Holger

2018-02-01

Improving matrix-product state techniques based on the purification of the density matrix, we are able to accurately calculate the finite-temperature dynamic response of the infinite spin-1 XXZ chain with single-ion anisotropy in the Haldane, large-D , and antiferromagnetic phases. Distinct thermally activated scattering processes make a significant contribution to the spectral weight in all cases. In the Haldane phase, intraband magnon scattering is prominent, and the on-site anisotropy causes the magnon to split into singlet and doublet branches. In the large-D phase response, the intraband signal is separated from an exciton-antiexciton continuum. In the antiferromagnetic phase, holons are the lowest-lying excitations, with a gap that closes at the transition to the Haldane state. At finite temperatures, scattering between domain-wall excitations becomes especially important and strongly enhances the spectral weight for momentum transfer π .

Retrievals of Aerosol and Cloud Particle Microphysics Using Polarization and Depolarization Techniques

NASA Technical Reports Server (NTRS)

Mishchenko, Michael; Hansen, James E. (Technical Monitor)

2001-01-01

The recent availability of theoretical techniques for computing single and multiple scattering of light by realistic polydispersions of spherical and nonspherical particles and the strong dependence of the Stokes scattering matrix on particle size, shape, and refractive index make polarization and depolarization measurements a powerful particle characterization tool. In this presentation I will describe recent applications of photopolarimetric and lidar depolarization measurements to remote sensing characterization of tropospheric aerosols, polar stratospheric clouds (PSCs), and contrails. The talk will include (1) a short theoretical overview of the effects of particle microphysics on particle single-scattering characteristics; (2) the use of multi-angle multi-spectral photopolarimetry to retrieve the optical thickness, size distribution, refractive index, and number concentration of tropospheric aerosols over the ocean surface; and (3) the application of the T-matrix method to constraining the PSC and contrail particle microphysics using multi-spectral measurements of lidar backscatter and depolarization.

Almost sure convergence in quantum spin glasses

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

Buzinski, David, E-mail: dab197@case.edu; Meckes, Elizabeth, E-mail: elizabeth.meckes@case.edu

2015-12-15

Recently, Keating, Linden, and Wells [Markov Processes Relat. Fields 21(3), 537-555 (2015)] showed that the density of states measure of a nearest-neighbor quantum spin glass model is approximately Gaussian when the number of particles is large. The density of states measure is the ensemble average of the empirical spectral measure of a random matrix; in this paper, we use concentration of measure and entropy techniques together with the result of Keating, Linden, and Wells to show that in fact the empirical spectral measure of such a random matrix is almost surely approximately Gaussian itself with no ensemble averaging. We alsomore » extend this result to a spherical quantum spin glass model and to the more general coupling geometries investigated by Erdős and Schröder [Math. Phys., Anal. Geom. 17(3-4), 441–464 (2014)].« less

Stability Analysis of Multi-Sensor Kalman Filtering over Lossy Networks

PubMed Central

Gao, Shouwan; Chen, Pengpeng; Huang, Dan; Niu, Qiang

2016-01-01

This paper studies the remote Kalman filtering problem for a distributed system setting with multiple sensors that are located at different physical locations. Each sensor encapsulates its own measurement data into one single packet and transmits the packet to the remote filter via a lossy distinct channel. For each communication channel, a time-homogeneous Markov chain is used to model the normal operating condition of packet delivery and losses. Based on the Markov model, a necessary and sufficient condition is obtained, which can guarantee the stability of the mean estimation error covariance. Especially, the stability condition is explicitly expressed as a simple inequality whose parameters are the spectral radius of the system state matrix and transition probabilities of the Markov chains. In contrast to the existing related results, our method imposes less restrictive conditions on systems. Finally, the results are illustrated by simulation examples. PMID:27104541

Compressed-sensing wavenumber-scanning interferometry

NASA Astrophysics Data System (ADS)

Bai, Yulei; Zhou, Yanzhou; He, Zhaoshui; Ye, Shuangli; Dong, Bo; Xie, Shengli

2018-01-01

The Fourier transform (FT), the nonlinear least-squares algorithm (NLSA), and eigenvalue decomposition algorithm (EDA) are used to evaluate the phase field in depth-resolved wavenumber-scanning interferometry (DRWSI). However, because the wavenumber series of the laser's output is usually accompanied by nonlinearity and mode-hop, FT, NLSA, and EDA, which are only suitable for equidistant interference data, often lead to non-negligible phase errors. In this work, a compressed-sensing method for DRWSI (CS-DRWSI) is proposed to resolve this problem. By using the randomly spaced inverse Fourier matrix and solving the underdetermined equation in the wavenumber domain, CS-DRWSI determines the nonuniform sampling and spectral leakage of the interference spectrum. Furthermore, it can evaluate interference data without prior knowledge of the object. The experimental results show that CS-DRWSI improves the depth resolution and suppresses sidelobes. It can replace the FT as a standard algorithm for DRWSI.

Parallel Preconditioning for CFD Problems on the CM-5

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

The phase transition of matrix recovery from Gaussian measurements matches the minimax MSE of matrix denoising.

PubMed

Donoho, David L; Gavish, Matan; Montanari, Andrea

2013-05-21

Let X(0) be an unknown M by N matrix. In matrix recovery, one takes n < MN linear measurements y(1),…,y(n) of X(0), where y(i) = Tr(A(T)iX(0)) and each A(i) is an M by N matrix. A popular approach for matrix recovery is nuclear norm minimization (NNM): solving the convex optimization problem min ||X||*subject to y(i) =Tr(A(T)(i)X) for all 1 ≤ i ≤ n, where || · ||* denotes the nuclear norm, namely, the sum of singular values. Empirical work reveals a phase transition curve, stated in terms of the undersampling fraction δ(n,M,N) = n/(MN), rank fraction ρ=rank(X0)/min {M,N}, and aspect ratio β=M/N. Specifically when the measurement matrices Ai have independent standard Gaussian random entries, a curve δ*(ρ) = δ*(ρ;β) exists such that, if δ > δ*(ρ), NNM typically succeeds for large M,N, whereas if δ < δ*(ρ), it typically fails. An apparently quite different problem is matrix denoising in Gaussian noise, in which an unknown M by N matrix X(0) is to be estimated based on direct noisy measurements Y =X(0) + Z, where the matrix Z has independent and identically distributed Gaussian entries. A popular matrix denoising scheme solves the unconstrained optimization problem min|| Y-X||(2)(F)/2+λ||X||*. When optimally tuned, this scheme achieves the asymptotic minimax mean-squared error M(ρ;β) = lim(M,N → ∞)inf(λ)sup(rank(X) ≤ ρ · M)MSE(X,X(λ)), where M/N → . We report extensive experiments showing that the phase transition δ*(ρ) in the first problem, matrix recovery from Gaussian measurements, coincides with the minimax risk curve M(ρ)=M(ρ;β) in the second problem, matrix denoising in Gaussian noise: δ*(ρ)=M(ρ), for any rank fraction 0 < ρ < 1 (at each common aspect ratio β). Our experiments considered matrices belonging to two constraint classes: real M by N matrices, of various ranks and aspect ratios, and real symmetric positive-semidefinite N by N matrices, of various ranks.

An advanced plasmonic cermet solar absorber for high temperature solar energy conversion applications

NASA Astrophysics Data System (ADS)

Bilokur, M.; Gentle, A.; Arnold, M.; Cortie, M.; Smith, G.

2017-08-01

Cermet coatings based on nanoparticles of Au or Ag in a stable dielectric matrix provide a combination of spectral-selectivity and microstructural stability at elevated temperatures. The nanoparticles provide an absorption peak due to their localized surface plasmon resonance and the dielectric matrix provides red-shifting and intrinsic absorption from defects. The matrix and two separated cermet layers combined add mechanical support, greater thermal stability and extra absorptance. The coatings may be prepared by magnetron sputtering. They have solar absorptance ranging between 91% and 97% with low thermal emittance making them suitable for application in solar thermal conversion installations.

Automated acoustic matrix deposition for MALDI sample preparation.

PubMed

Aerni, Hans-Rudolf; Cornett, Dale S; Caprioli, Richard M

2006-02-01

Novel high-throughput sample preparation strategies for MALDI imaging mass spectrometry (IMS) and profiling are presented. An acoustic reagent multispotter was developed to provide improved reproducibility for depositing matrix onto a sample surface, for example, such as a tissue section. The unique design of the acoustic droplet ejector and its optimization for depositing matrix solution are discussed. Since it does not contain a capillary or nozzle for fluid ejection, issues with clogging of these orifices are avoided. Automated matrix deposition provides better control of conditions affecting protein extraction and matrix crystallization with the ability to deposit matrix accurately onto small surface features. For tissue sections, matrix spots of 180-200 microm in diameter were obtained and a procedure is described for generating coordinate files readable by a mass spectrometer to permit automated profile acquisition. Mass spectral quality and reproducibility was found to be better than that obtained with manual pipet spotting. The instrument can also deposit matrix spots in a dense array pattern so that, after analysis in a mass spectrometer, two-dimensional ion images may be constructed. Example ion images from a mouse brain are presented.

Parametric number covariance in quantum chaotic spectra.

PubMed

Vinayak; Kumar, Sandeep; Pandey, Akhilesh

2016-03-01

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.

Fast Algorithms for Structured Least Squares and Total Least Squares Problems

PubMed Central

Kalsi, Anoop; O’Leary, Dianne P.

2006-01-01

We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z1 and Z2. We develop formulas for the generators of the matrix M HM in terms of the generators of M and show that the Cholesky factorization of the matrix M HM can be computed quickly if Z1 is close to unitary and Z2 is triangular and nilpotent. These conditions are satisfied for several classes of matrices, including Toeplitz, block Toeplitz, Hankel, and block Hankel, and for matrices whose blocks have such structure. Fast Cholesky factorization enables fast solution of least squares problems, total least squares problems, and regularized total least squares problems involving these classes of matrices. PMID:27274922

Fast Algorithms for Structured Least Squares and Total Least Squares Problems.

PubMed

Kalsi, Anoop; O'Leary, Dianne P

2006-01-01

We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z 1 and Z 2. We develop formulas for the generators of the matrix M (H) M in terms of the generators of M and show that the Cholesky factorization of the matrix M (H) M can be computed quickly if Z 1 is close to unitary and Z 2 is triangular and nilpotent. These conditions are satisfied for several classes of matrices, including Toeplitz, block Toeplitz, Hankel, and block Hankel, and for matrices whose blocks have such structure. Fast Cholesky factorization enables fast solution of least squares problems, total least squares problems, and regularized total least squares problems involving these classes of matrices.

Optimization of compressive 4D-spatio-spectral snapshot imaging

NASA Astrophysics Data System (ADS)

Zhao, Xia; Feng, Weiyi; Lin, Lihua; Su, Wu; Xu, Guoqing

2017-10-01

In this paper, a modified 3D computational reconstruction method in the compressive 4D-spectro-volumetric snapshot imaging system is proposed for better sensing spectral information of 3D objects. In the design of the imaging system, a microlens array (MLA) is used to obtain a set of multi-view elemental images (EIs) of the 3D scenes. Then, these elemental images with one dimensional spectral information and different perspectives are captured by the coded aperture snapshot spectral imager (CASSI) which can sense the spectral data cube onto a compressive 2D measurement image. Finally, the depth images of 3D objects at arbitrary depths, like a focal stack, are computed by inversely mapping the elemental images according to geometrical optics. With the spectral estimation algorithm, the spectral information of 3D objects is also reconstructed. Using a shifted translation matrix, the contrast of the reconstruction result is further enhanced. Numerical simulation results verify the performance of the proposed method. The system can obtain both 3D spatial information and spectral data on 3D objects using only one single snapshot, which is valuable in the agricultural harvesting robots and other 3D dynamic scenes.

BASIC Matrix Operations.

ERIC Educational Resources Information Center

Digital Equipment Corp., Maynard, MA.

The curriculum materials and computer programs in this booklet introduce the idea of a matrix. They go on to discuss matrix operations of addition, subtraction, multiplication by a scalar, and matrix multiplication. The last section covers several contemporary applications of matrix multiplication, including problems of communication…

Complex mode indication function and its applications to spatial domain parameter estimation

NASA Astrophysics Data System (ADS)

Shih, C. Y.; Tsuei, Y. G.; Allemang, R. J.; Brown, D. L.

1988-10-01

This paper introduces the concept of the Complex Mode Indication Function (CMIF) and its application in spatial domain parameter estimation. The concept of CMIF is developed by performing singular value decomposition (SVD) of the Frequency Response Function (FRF) matrix at each spectral line. The CMIF is defined as the eigenvalues, which are the square of the singular values, solved from the normal matrix formed from the FRF matrix, [ H( jω)] H[ H( jω)], at each spectral line. The CMIF appears to be a simple and efficient method for identifying the modes of the complex system. The CMIF identifies modes by showing the physical magnitude of each mode and the damped natural frequency for each root. Since multiple reference data is applied in CMIF, repeated roots can be detected. The CMIF also gives global modal parameters, such as damped natural frequencies, mode shapes and modal participation vectors. Since CMIF works in the spatial domain, uneven frequency spacing data such as data from spatial sine testing can be used. A second-stage procedure for accurate damped natural frequency and damping estimation as well as mode shape scaling is also discussed in this paper.

A semi-Lagrangian advection scheme for radioactive tracers in a regional spectral model

NASA Astrophysics Data System (ADS)

Chang, E.-C.; Yoshimura, K.

2015-06-01

In this study, the non-iteration dimensional-split semi-Lagrangian (NDSL) advection scheme is applied to the National Centers for Environmental Prediction (NCEP) regional spectral model (RSM) to alleviate the Gibbs phenomenon. The Gibbs phenomenon is a problem wherein negative values of positive-definite quantities (e.g., moisture and tracers) are generated by the spectral space transformation in a spectral model system. To solve this problem, the spectral prognostic specific humidity and radioactive tracer advection scheme is replaced by the NDSL advection scheme, which considers advection of tracers in a grid system without spectral space transformations. A regional version of the NDSL is developed in this study and is applied to the RSM. Idealized experiments show that the regional version of the NDSL is successful. The model runs for an actual case study suggest that the NDSL can successfully advect radioactive tracers (iodine-131 and cesium-137) without noise from the Gibbs phenomenon. The NDSL can also remove negative specific humidity values produced in spectral calculations without losing detailed features.

Fiber-based polarization-sensitive OCT of the human retina with correction of system polarization distortions

PubMed Central

Braaf, Boy; Vermeer, Koenraad A.; de Groot, Mattijs; Vienola, Kari V.; de Boer, Johannes F.

2014-01-01

In polarization-sensitive optical coherence tomography (PS-OCT) the use of single-mode fibers causes unpredictable polarization distortions which can result in increased noise levels and erroneous changes in calculated polarization parameters. In the current paper this problem is addressed by a new Jones matrix analysis method that measures and corrects system polarization distortions as a function of wavenumber by spectral analysis of the sample surface polarization state and deeper located birefringent tissue structures. This method was implemented on a passive-component depth-multiplexed swept-source PS-OCT system at 1040 nm which was theoretically modeled using Jones matrix calculus. High-resolution B-scan images are presented of the double-pass phase retardation, diattenuation, and relative optic axis orientation to show the benefits of the new analysis method for in vivo imaging of the human retina. The correction of system polarization distortions yielded reduced phase retardation noise, and better estimates of the diattenuation and the relative optic axis orientation in weakly birefringent tissues. The clinical potential of the system is shown by en face visualization of the phase retardation and optic axis orientation of the retinal nerve fiber layer in a healthy volunteer and a glaucoma patient with nerve fiber loss. PMID:25136498

Fingerprint recognition of alien invasive weeds based on the texture character and machine learning

NASA Astrophysics Data System (ADS)

Yu, Jia-Jia; Li, Xiao-Li; He, Yong; Xu, Zheng-Hao

2008-11-01

Multi-spectral imaging technique based on texture analysis and machine learning was proposed to discriminate alien invasive weeds with similar outline but different categories. The objectives of this study were to investigate the feasibility of using Multi-spectral imaging, especially the near-infrared (NIR) channel (800 nm+/-10 nm) to find the weeds' fingerprints, and validate the performance with specific eigenvalues by co-occurrence matrix. Veronica polita Pries, Veronica persica Poir, longtube ground ivy, Laminum amplexicaule Linn. were selected in this study, which perform different effect in field, and are alien invasive species in China. 307 weed leaves' images were randomly selected for the calibration set, while the remaining 207 samples for the prediction set. All images were pretreated by Wallis filter to adjust the noise by uneven lighting. Gray level co-occurrence matrix was applied to extract the texture character, which shows density, randomness correlation, contrast and homogeneity of texture with different algorithms. Three channels (green channel by 550 nm+/-10 nm, red channel by 650 nm+/-10 nm and NIR channel by 800 nm+/-10 nm) were respectively calculated to get the eigenvalues.Least-squares support vector machines (LS-SVM) was applied to discriminate the categories of weeds by the eigenvalues from co-occurrence matrix. Finally, recognition ratio of 83.35% by NIR channel was obtained, better than the results by green channel (76.67%) and red channel (69.46%). The prediction results of 81.35% indicated that the selected eigenvalues reflected the main characteristics of weeds' fingerprint based on multi-spectral (especially by NIR channel) and LS-SVM model.

A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Danabasoglu, G.; Biringen, S.

1989-01-01

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Estimating the Inertia Matrix of a Spacecraft

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Keim, Jason; Shields, Joel

2007-01-01

A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

Theory and implementation of H-matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels

NASA Astrophysics Data System (ADS)

Chaillat, Stéphanie; Desiderio, Luca; Ciarlet, Patrick

2017-12-01

In this work, we study the accuracy and efficiency of hierarchical matrix (H-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known in the literature that standard H-matrix based methods, although very efficient tools for asymptotically smooth kernels, are not optimal for oscillatory kernels. H2-matrix and directional approaches have been proposed to overcome this problem. However the implementation of such methods is much more involved than the standard H-matrix representation. The central questions we address are twofold. (i) What is the frequency-range in which the H-matrix format is an efficient representation for 3D elastodynamic problems? (ii) What can be expected of such an approach to model problems in mechanical engineering? We show that even though the method is not optimal (in the sense that more involved representations can lead to faster algorithms) an efficient solver can be easily developed. The capabilities of the method are illustrated on numerical examples using the Boundary Element Method.

A spectral mimetic least-squares method

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

Bochev, Pavel; Gerritsma, Marc

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

A spectral mimetic least-squares method

DOE PAGES

Bochev, Pavel; Gerritsma, Marc

2014-09-01

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

Phase diagram of matrix compressed sensing

NASA Astrophysics Data System (ADS)

Schülke, Christophe; Schniter, Philip; Zdeborová, Lenka

2016-12-01

In the problem of matrix compressed sensing, we aim to recover a low-rank matrix from a few noisy linear measurements. In this contribution, we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model where the matrix to be recovered is a product of random matrices. The results that we obtain using the replica method describe the state evolution of the Parametric Bilinear Generalized Approximate Message Passing (P-BiG-AMP) algorithm, recently introduced in J. T. Parker and P. Schniter [IEEE J. Select. Top. Signal Process. 10, 795 (2016), 10.1109/JSTSP.2016.2539123]. We show the existence of two different types of phase transition and their implications for the solvability of the problem, and we compare the results of our theoretical analysis to the numerical performance reached by P-BiG-AMP. Remarkably, the asymptotic replica equations for matrix compressed sensing are the same as those for a related but formally different problem of matrix factorization.

Calculation and experimental validation of spectral properties of microsize grains surrounded by nanoparticles.

PubMed

Yu, Haitong; Liu, Dong; Duan, Yuanyuan; Wang, Xiaodong

2014-04-07

Opacified aerogels are particulate thermal insulating materials in which micrometric opacifier mineral grains are surrounded by silica aerogel nanoparticles. A geometric model was developed to characterize the spectral properties of such microsize grains surrounded by much smaller particles. The model represents the material's microstructure with the spherical opacifier's spectral properties calculated using the multi-sphere T-matrix (MSTM) algorithm. The results are validated by comparing the measured reflectance of an opacified aerogel slab against the value predicted using the discrete ordinate method (DOM) based on calculated optical properties. The results suggest that the large particles embedded in the nanoparticle matrices show different scattering and absorption properties from the single scattering condition and that the MSTM and DOM algorithms are both useful for calculating the spectral and radiative properties of this particulate system.

Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.

2005-09-01

We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

Spectral properties of Google matrix of Wikipedia and other networks

NASA Astrophysics Data System (ADS)

Ermann, Leonardo; Frahm, Klaus M.; Shepelyansky, Dima L.

2013-05-01

We study the properties of eigenvalues and eigenvectors of the Google matrix of the Wikipedia articles hyperlink network and other real networks. With the help of the Arnoldi method, we analyze the distribution of eigenvalues in the complex plane and show that eigenstates with significant eigenvalue modulus are located on well defined network communities. We also show that the correlator between PageRank and CheiRank vectors distinguishes different organizations of information flow on BBC and Le Monde web sites.

Cluster-enriched Yang-Baxter equation from SUSY gauge theories

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-04-01

We propose a new generalization of the Yang-Baxter equation, where the R-matrix depends on cluster y-variables in addition to the spectral parameters. We point out that we can construct solutions to this new equation from the recently found correspondence between Yang-Baxter equations and supersymmetric gauge theories. The S^2 partition function of a certain 2d N=(2,2) quiver gauge theory gives an R-matrix, whereas its FI parameters can be identified with the cluster y-variables.

Characterization of ceramic matrix composite degradation using Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Henry, Christine; Criner, Amanda Keck; Imel, Megan; King, Derek

2018-04-01

Data collected with a handheld Fourier Transform Infrared (FTIR) device is analyzed and considered as a useful method for detecting and quantifying oxidation on the surface of ceramic matrix composite (CMC) materials. Experiments examine silicon carbide (SiC) coupons, looking for changes in chemical composition before and after thermal exposure. Using mathematical, physical and statistical models for FTIR reflectance data, this research seeks to quantify any detected spectral changes as an indicator of surface oxidation on the CMC coupon.

Inversion of Robin coefficient by a spectral stochastic finite element approach

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

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Extracting spectral contrast in Landsat Thematic Mapper image data using selective principal component analysis

USGS Publications Warehouse

Chavez, P.S.; Kwarteng, A.Y.

1989-01-01

A challenge encountered with Landsat Thematic Mapper (TM) data, which includes data from size reflective spectral bands, is displaying as much information as possible in a three-image set for color compositing or digital analysis. Principal component analysis (PCA) applied to the six TM bands simultaneously is often used to address this problem. However, two problems that can be encountered using the PCA method are that information of interest might be mathematically mapped to one of the unused components and that a color composite can be difficult to interpret. "Selective' PCA can be used to minimize both of these problems. The spectral contrast among several spectral regions was mapped for a northern Arizona site using Landsat TM data. Field investigations determined that most of the spectral contrast seen in this area was due to one of the following: the amount of iron and hematite in the soils and rocks, vegetation differences, standing and running water, or the presence of gypsum, which has a higher moisture retention capability than do the surrounding soils and rocks. -from Authors

Spectral Learning for Supervised Topic Models.

PubMed

Ren, Yong; Wang, Yining; Zhu, Jun

2018-03-01

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte Carlo sampling, which often suffers from the local minimum defect. Spectral methods have been applied to learn unsupervised topic models, such as latent Dirichlet allocation (LDA), with provable guarantees. This paper investigates the possibility of applying spectral methods to recover the parameters of supervised LDA (sLDA). We first present a two-stage spectral method, which recovers the parameters of LDA followed by a power update method to recover the regression model parameters. Then, we further present a single-phase spectral algorithm to jointly recover the topic distribution matrix as well as the regression weights. Our spectral algorithms are provably correct and computationally efficient. We prove a sample complexity bound for each algorithm and subsequently derive a sufficient condition for the identifiability of sLDA. Thorough experiments on synthetic and real-world datasets verify the theory and demonstrate the practical effectiveness of the spectral algorithms. In fact, our results on a large-scale review rating dataset demonstrate that our single-phase spectral algorithm alone gets comparable or even better performance than state-of-the-art methods, while previous work on spectral methods has rarely reported such promising performance.

Theoretical Stark broadening parameters for spectral lines arising from the 2p5ns, 2p5np and 2p5nd electronic configurations of Mg III

NASA Astrophysics Data System (ADS)

Colón, C.; Moreno-Díaz, C.; Alonso-Medina, A.

2013-10-01

In the present work we report theoretical Stark widths and shifts calculated using the Griem semi-empirical approach, corresponding to 237 spectral lines of Mg III. Data are presented for an electron density of 1017 cm-3 and temperatures T = 0.5-10.0 (104K). The matrix elements used in these calculations have been determined from 23 configurations of Mg III: 2s22p6, 2s22p53p, 2s22p54p, 2s22p54f and 2s22p55f for even parity and 2s22p5ns (n = 3-6), 2s22p5nd (n = 3-9), 2s22p55g and 2s2p6np (n = 3-8) for odd parity. For the intermediate coupling (IC) calculations, we use the standard method of least-squares fitting from experimental energy levels by means of the Cowan computer code. Also, in order to test the matrix elements used in our calculations, we present calculated values of 70 transition probabilities of Mg III spectral lines and 14 calculated values of radiative lifetimes of Mg III levels. There is good agreement between our calculations and experimental radiative lifetimes. Spectral lines of Mg III are relevant in astrophysics and also play an important role in the spectral analysis of laboratory plasma. Theoretical trends of the Stark broadening parameter versus the temperature for relevant lines are presented. No values of Stark parameters can be found in the bibliography.

Extension of modified power method to two-dimensional problems

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

Zhang, Peng; Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919; Lee, Hyunsuk

2016-09-01

In this study, the generalized modified power method was extended to two-dimensional problems. A direct application of the method to two-dimensional problems was shown to be unstable when the number of requested eigenmodes is larger than a certain problem dependent number. The root cause of this instability has been identified as the degeneracy of the transfer matrix. In order to resolve this instability, the number of sub-regions for the transfer matrix was increased to be larger than the number of requested eigenmodes; and a new transfer matrix was introduced accordingly which can be calculated by the least square method. Themore » stability of the new method has been successfully demonstrated with a neutron diffusion eigenvalue problem and the 2D C5G7 benchmark problem. - Graphical abstract:.« less

Bayesian hierarchical model for large-scale covariance matrix estimation.

PubMed

Zhu, Dongxiao; Hero, Alfred O

2007-12-01

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.

Palagonitic Mars: A Basalt Centric View of Surface Composition and Aqueous Alteration

NASA Technical Reports Server (NTRS)

Morris, R. V.; Graff, T. G.; Ming, D. W.; Bell, J. F., III; Le, L.; Mertzman, S. A.; Christensen, P. R.

2004-01-01

Palagonitic tephra from certain areas on Mauna Kea Volcano (Hawaii) are well-established spectral and magnetic analogues of high-albedo regions on Mars. By definition, palagonite is "a yellow or orange isotropic mineraloid formed by hydration and devitrification of basaltic glass." The yellow to orange pigment is nanometer-sized ferric oxide particles (np-Ox) dispersed throughout the hydrated basaltic glass matrix. The hydration state of the np-Ox particles and the matrix is not known, but the best Martian spectral analogues contain allophane-like materials and not crystalline phyllosilicates. Martian low-albedo regions are also characterized by a palagonite-like ferric absorption edge, but, unlike the highalbedo regions, they also show evidence for absorption by ferrous iron. Thermal emission spectra (TES) obtained by the Mars Global Surveyor Thermal Emission Spectrometer suggest that basaltic (surface Type 1) and andesitic (surface Type 2) volcanic compositions preferentially occur in southern (Syrtis Major) and northern (Acidalia) hemispheres, respectively. The absence of a ferric-bearing component in the modeling of TES spectra is in apparent conflict with VNIR spectra of Martian dark regions, as discussed above. However, the andesitic spectra have also been interpreted as oxidized basalt using phyllosilicates instead of high-SiO2 glass as endmembers in the spectral deconvolution of surface Type 2 TES spectra. We show here that laboratory VNIR and TES spectra of rinds on basaltic rocks are spectral endmembers that provide a consistent explanation for both VNIR and TES data of Martian dark regions.

Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

NASA Astrophysics Data System (ADS)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2015-10-01

In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

A review of spectral methods

NASA Technical Reports Server (NTRS)

Lustman, L.

1984-01-01

An outline for spectral methods for partial differential equations is presented. The basic spectral algorithm is defined, collocation are emphasized and the main advantage of the method, the infinite order of accuracy in problems with smooth solutions are discussed. Examples of theoretical numerical analysis of spectral calculations are presented. An application of spectral methods to transonic flow is presented. The full potential transonic equation is among the best understood among nonlinear equations.

[Research on partial least squares for determination of impurities in the presence of high concentration of matrix by ICP-AES].

PubMed

Wang, Yan-peng; Gong, Qi; Yu, Sheng-rong; Liu, You-yan

2012-04-01

A method for detecting trace impurities in high concentration matrix by ICP-AES based on partial least squares (PLS) was established. The research showed that PLS could effectively correct the interference caused by high level of matrix concentration error and could withstand higher concentrations of matrix than multicomponent spectral fitting (MSF). When the mass ratios of matrix to impurities were from 1 000 : 1 to 20 000 : 1, the recoveries of standard addition were between 95% and 105% by PLS. For the system in which interference effect has nonlinear correlation with the matrix concentrations, the prediction accuracy of normal PLS method was poor, but it can be improved greatly by using LIN-PPLS, which was based on matrix transformation of sample concentration. The contents of Co, Pb and Ga in stream sediment (GBW07312) were detected by MSF, PLS and LIN-PPLS respectively. The results showed that the prediction accuracy of LIN-PPLS was better than PLS, and the prediction accuracy of PLS was better than MSF.

Multispectral analysis tools can increase utility of RGB color images in histology

NASA Astrophysics Data System (ADS)

Fereidouni, Farzad; Griffin, Croix; Todd, Austin; Levenson, Richard

2018-04-01

Multispectral imaging (MSI) is increasingly finding application in the study and characterization of biological specimens. However, the methods typically used come with challenges on both the acquisition and the analysis front. MSI can be slow and photon-inefficient, leading to long imaging times and possible phototoxicity and photobleaching. The resulting datasets can be large and complex, prompting the development of a number of mathematical approaches for segmentation and signal unmixing. We show that under certain circumstances, just three spectral channels provided by standard color cameras, coupled with multispectral analysis tools, including a more recent spectral phasor approach, can efficiently provide useful insights. These findings are supported with a mathematical model relating spectral bandwidth and spectral channel number to achievable spectral accuracy. The utility of 3-band RGB and MSI analysis tools are demonstrated on images acquired using brightfield and fluorescence techniques, as well as a novel microscopy approach employing UV-surface excitation. Supervised linear unmixing, automated non-negative matrix factorization and phasor analysis tools all provide useful results, with phasors generating particularly helpful spectral display plots for sample exploration.

Selecting algorithms, sensors, and linear bases for optimum spectral recovery of skylight.

PubMed

López-Alvarez, Miguel A; Hernández-Andrés, Javier; Valero, Eva M; Romero, Javier

2007-04-01

In a previous work [Appl. Opt.44, 5688 (2005)] we found the optimum sensors for a planned multispectral system for measuring skylight in the presence of noise by adapting a linear spectral recovery algorithm proposed by Maloney and Wandell [J. Opt. Soc. Am. A3, 29 (1986)]. Here we continue along these lines by simulating the responses of three to five Gaussian sensors and recovering spectral information from noise-affected sensor data by trying out four different estimation algorithms, three different sizes for the training set of spectra, and various linear bases. We attempt to find the optimum combination of sensors, recovery method, linear basis, and matrix size to recover the best skylight spectral power distributions from colorimetric and spectral (in the visible range) points of view. We show how all these parameters play an important role in the practical design of a real multispectral system and how to obtain several relevant conclusions from simulating the behavior of sensors in the presence of noise.

[An improved low spectral distortion PCA fusion method].

PubMed

Peng, Shi; Zhang, Ai-Wu; Li, Han-Lun; Hu, Shao-Xing; Meng, Xian-Gang; Sun, Wei-Dong

2013-10-01

Aiming at the spectral distortion produced in PCA fusion process, the present paper proposes an improved low spectral distortion PCA fusion method. This method uses NCUT (normalized cut) image segmentation algorithm to make a complex hyperspectral remote sensing image into multiple sub-images for increasing the separability of samples, which can weaken the spectral distortions of traditional PCA fusion; Pixels similarity weighting matrix and masks were produced by using graph theory and clustering theory. These masks are used to cut the hyperspectral image and high-resolution image into some sub-region objects. All corresponding sub-region objects between the hyperspectral image and high-resolution image are fused by using PCA method, and all sub-regional integration results are spliced together to produce a new image. In the experiment, Hyperion hyperspectral data and Rapid Eye data were used. And the experiment result shows that the proposed method has the same ability to enhance spatial resolution and greater ability to improve spectral fidelity performance.

Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows

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

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau

2008-07-01

A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” familymore » of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.« less

Multilabel user classification using the community structure of online networks

PubMed Central

Papadopoulos, Symeon; Kompatsiaris, Yiannis

2017-01-01

We study the problem of semi-supervised, multi-label user classification of networked data in the online social platform setting. We propose a framework that combines unsupervised community extraction and supervised, community-based feature weighting before training a classifier. We introduce Approximate Regularized Commute-Time Embedding (ARCTE), an algorithm that projects the users of a social graph onto a latent space, but instead of packing the global structure into a matrix of predefined rank, as many spectral and neural representation learning methods do, it extracts local communities for all users in the graph in order to learn a sparse embedding. To this end, we employ an improvement of personalized PageRank algorithms for searching locally in each user’s graph structure. Then, we perform supervised community feature weighting in order to boost the importance of highly predictive communities. We assess our method performance on the problem of user classification by performing an extensive comparative study among various recent methods based on graph embeddings. The comparison shows that ARCTE significantly outperforms the competition in almost all cases, achieving up to 35% relative improvement compared to the second best competing method in terms of F1-score. PMID:28278242

A discrete spherical harmonics method for radiative transfer analysis in inhomogeneous polarized planar atmosphere

NASA Astrophysics Data System (ADS)

Tapimo, Romuald; Tagne Kamdem, Hervé Thierry; Yemele, David

2018-03-01

A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands both the Stokes vector and the phase matrix in a finite series of generalized spherical functions and the resulting vector radiative transfer equation is expressed in a set of polar directions. Hence, the polarized characteristics of the radiance within the atmosphere at any polar direction and azimuthal angle can be determined without linearization and/or interpolations. The spatial dependent of the problem is solved using the spectral Chebyshev method. The emergent and transmitted radiative intensity and the degree of polarization are predicted for both Rayleigh and Mie scattering. The discrete spherical harmonics method predictions for optical thin atmosphere using 36 streams are found in good agreement with benchmark literature results. The maximum deviation between the proposed method and literature results and for polar directions \\vert μ \\vert ≥0.1 is less than 0.5% and 0.9% for the Rayleigh and Mie scattering, respectively. These deviations for directions close to zero are about 3% and 10% for Rayleigh and Mie scattering, respectively.

Multilabel user classification using the community structure of online networks.

PubMed

Rizos, Georgios; Papadopoulos, Symeon; Kompatsiaris, Yiannis

2017-01-01

We study the problem of semi-supervised, multi-label user classification of networked data in the online social platform setting. We propose a framework that combines unsupervised community extraction and supervised, community-based feature weighting before training a classifier. We introduce Approximate Regularized Commute-Time Embedding (ARCTE), an algorithm that projects the users of a social graph onto a latent space, but instead of packing the global structure into a matrix of predefined rank, as many spectral and neural representation learning methods do, it extracts local communities for all users in the graph in order to learn a sparse embedding. To this end, we employ an improvement of personalized PageRank algorithms for searching locally in each user's graph structure. Then, we perform supervised community feature weighting in order to boost the importance of highly predictive communities. We assess our method performance on the problem of user classification by performing an extensive comparative study among various recent methods based on graph embeddings. The comparison shows that ARCTE significantly outperforms the competition in almost all cases, achieving up to 35% relative improvement compared to the second best competing method in terms of F1-score.

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

Supra-organization and optical anisotropies of the extracellular matrix in the amniotic membrane and limbal stroma before and after explant culture

PubMed Central

Valdetaro, Gisele P.; Aldrovani, Marcela; Padua, Ivan R. M.; Cristovam, Priscila C.; Gomes, José A. P.; Laus, José L.

2016-01-01

In this research we evaluated the supramolecular organizations and the optical anisotropical properties of the de-epithelialized human amniotic membrane and rabbit limbal stroma, before and after explant culture. Birefringence, monochromatic light spectral absorption and linear dichroism of the main extracellular matrix biopolymers, that is, the fibrillar collagens and proteoglycans, were investigated by polarized light microscopy combined with image analysis. Our results demonstrated that the culture procedure–induced stimuli altered the supra-organizational characteristics (in terms of collagens/proteoglycans spatial orientation and ordered-aggregational state) of the amniotic and limbal extracellular matrix, which led to changes in optical anisotropical properties. PMID:28018719

Convergence Results on Iteration Algorithms to Linear Systems

PubMed Central

Wang, Zhuande; Yang, Chuansheng; Yuan, Yubo

2014-01-01

In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods. PMID:24991640

Spectral properties of nanocomposites based on fluorine-containing polymer and gold nanoparticles

NASA Astrophysics Data System (ADS)

Barmina, E. V.; Mel’nik, N. N.; Rakov, I. I.; Ivanov, V. E.; Simakin, A. V.; Gudkov, S. V.; Shafeev, G. A.

2018-04-01

The optical properties of nanocomposites of gold nanoparticles and fluorine-containing polymer have been studied. Gold nanoparticles were obtained by laser ablation of gold or terbium targets in organic solvents. The thus formed colloidal solutions were used to prepare nanocomposites of gold nanoparticles in polymer matrices of transparent and colorless fluorine-containing polymer. The polymer matrix is found to promote aggregation of nanoparticles of metal under study into elongated chains. In turn, metal nanoparticles influence on the polymer matrix. Gold nanoparticles amplify the Raman signal of the polymer matrix. In addition, the Raman spectra of nanocomposites indicate aggregation of disordered carbon around the nanoparticles obtained by laser ablation in organic solvents.

Workshop report on large-scale matrix diagonalization methods in chemistry theory institute

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

Bischof, C.H.; Shepard, R.L.; Huss-Lederman, S.

The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems asmore » well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configuration interaction (CI), intramolecular vibrational relaxation (IVR), and scattering problems. In atomic structure calculations using the Hartree-Fock method (SCF), the symmetric matrices can range from order hundreds to thousands. These matrices often include large clusters of eigenvalues which can be as much as 25% of the spectrum. However, if Cl methods are also used, the matrix size can be between 10{sup 4} and 10{sup 9} where only one or a few extremal eigenvalues and eigenvectors are needed. Working with very large matrices has lead to the development of« less

Covariance expressions for eigenvalue and eigenvector problems

NASA Astrophysics Data System (ADS)

Liounis, Andrew J.

There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.

Hyperspectral cytometry.

PubMed

Grégori, Gérald; Rajwa, Bartek; Patsekin, Valery; Jones, James; Furuki, Motohiro; Yamamoto, Masanobu; Paul Robinson, J

2014-01-01

Hyperspectral cytometry is an emerging technology for single-cell analysis that combines ultrafast optical spectroscopy and flow cytometry. Spectral cytometry systems utilize diffraction gratings or prism-based monochromators to disperse fluorescence signals from multiple labels (organic dyes, nanoparticles, or fluorescent proteins) present in each analyzed bioparticle onto linear detector arrays such as multianode photomultipliers or charge-coupled device sensors. The resultant data, consisting of a series of characterizing every analyzed cell, are not compensated by employing the traditional cytometry approach, but rather are spectrally unmixed utilizing algorithms such as constrained Poisson regression or non-negative matrix factorization. Although implementations of spectral cytometry were envisioned as early as the 1980s, only recently has the development of highly sensitive photomultiplier tube arrays led to design and construction of functional prototypes and subsequently to introduction of commercially available systems. This chapter summarizes the historical efforts and work in the field of spectral cytometry performed at Purdue University Cytometry Laboratories and describes the technology developed by Sony Corporation that resulted in release of the first commercial spectral cytometry system-the Sony SP6800. A brief introduction to spectral data analysis is also provided, with emphasis on the differences between traditional polychromatic and spectral cytometry approaches.

Computing sparse derivatives and consecutive zeros problem

NASA Astrophysics Data System (ADS)

Chandra, B. V. Ravi; Hossain, Shahadat

2013-02-01

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

A Matrix-Free Algorithm for Multidisciplinary Design Optimization

NASA Astrophysics Data System (ADS)

Lambe, Andrew Borean

Multidisciplinary design optimization (MDO) is an approach to engineering design that exploits the coupling between components or knowledge disciplines in a complex system to improve the final product. In aircraft design, MDO methods can be used to simultaneously design the outer shape of the aircraft and the internal structure, taking into account the complex interaction between the aerodynamic forces and the structural flexibility. Efficient strategies are needed to solve such design optimization problems and guarantee convergence to an optimal design. This work begins with a comprehensive review of MDO problem formulations and solution algorithms. First, a fundamental MDO problem formulation is defined from which other formulations may be obtained through simple transformations. Using these fundamental problem formulations, decomposition methods from the literature are reviewed and classified. All MDO methods are presented in a unified mathematical notation to facilitate greater understanding. In addition, a novel set of diagrams, called extended design structure matrices, are used to simultaneously visualize both data communication and process flow between the many software components of each method. For aerostructural design optimization, modern decomposition-based MDO methods cannot efficiently handle the tight coupling between the aerodynamic and structural states. This fact motivates the exploration of methods that can reduce the computational cost. A particular structure in the direct and adjoint methods for gradient computation motivates the idea of a matrix-free optimization method. A simple matrix-free optimizer is developed based on the augmented Lagrangian algorithm. This new matrix-free optimizer is tested on two structural optimization problems and one aerostructural optimization problem. The results indicate that the matrix-free optimizer is able to efficiently solve structural and multidisciplinary design problems with thousands of variables and constraints. On the aerostructural test problem formulated with thousands of constraints, the matrix-free optimizer is estimated to reduce the total computational time by up to 90% compared to conventional optimizers.

A Matrix-Free Algorithm for Multidisciplinary Design Optimization

NASA Astrophysics Data System (ADS)

Lambe, Andrew Borean

Multidisciplinary design optimization (MDO) is an approach to engineering design that exploits the coupling between components or knowledge disciplines in a complex system to improve the final product. In aircraft design, MDO methods can be used to simultaneously design the outer shape of the aircraft and the internal structure, taking into account the complex interaction between the aerodynamic forces and the structural flexibility. Efficient strategies are needed to solve such design optimization problems and guarantee convergence to an optimal design. This work begins with a comprehensive review of MDO problem formulations and solution algorithms. First, a fundamental MDO problem formulation is defined from which other formulations may be obtained through simple transformations. Using these fundamental problem formulations, decomposition methods from the literature are reviewed and classified. All MDO methods are presented in a unified mathematical notation to facilitate greater understanding. In addition, a novel set of diagrams, called extended design structure matrices, are used to simultaneously visualize both data communication and process flow between the many software components of each method. For aerostructural design optimization, modern decomposition-based MDO methods cannot efficiently handle the tight coupling between the aerodynamic and structural states. This fact motivates the exploration of methods that can reduce the computational cost. A particular structure in the direct and adjoint methods for gradient computation. motivates the idea of a matrix-free optimization method. A simple matrix-free optimizer is developed based on the augmented Lagrangian algorithm. This new matrix-free optimizer is tested on two structural optimization problems and one aerostructural optimization problem. The results indicate that the matrix-free optimizer is able to efficiently solve structural and multidisciplinary design problems with thousands of variables and constraints. On the aerostructural test problem formulated with thousands of constraints, the matrix-free optimizer is estimated to reduce the total computational time by up to 90% compared to conventional optimizers.

A semi-Lagrangian advection scheme for radioactive tracers in the NCEP Regional Spectral Model (RSM)

NASA Astrophysics Data System (ADS)

Chang, E.-C.; Yoshimura, K.

2015-10-01

In this study, the non-iteration dimensional-split semi-Lagrangian (NDSL) advection scheme is applied to the National Centers for Environmental Prediction (NCEP) Regional Spectral Model (RSM) to alleviate the Gibbs phenomenon. The Gibbs phenomenon is a problem wherein negative values of positive-definite quantities (e.g., moisture and tracers) are generated by the spectral space transformation in a spectral model system. To solve this problem, the spectral prognostic specific humidity and radioactive tracer advection scheme is replaced by the NDSL advection scheme, which considers advection of tracers in a grid system without spectral space transformations. A regional version of the NDSL is developed in this study and is applied to the RSM. Idealized experiments show that the regional version of the NDSL is successful. The model runs for an actual case study suggest that the NDSL can successfully advect radioactive tracers (iodine-131 and cesium-137) without noise from the Gibbs phenomenon. The NDSL can also remove negative specific humidity values produced in spectral calculations without losing detailed features.

Accurate ω-ψ Spectral Solution of the Singular Driven Cavity Problem

NASA Astrophysics Data System (ADS)

Auteri, F.; Quartapelle, L.; Vigevano, L.

2002-08-01

This article provides accurate spectral solutions of the driven cavity problem, calculated in the vorticity-stream function representation without smoothing the corner singularities—a prima facie impossible task. As in a recent benchmark spectral calculation by primitive variables of Botella and Peyret, closed-form contributions of the singular solution for both zero and finite Reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form. The method employed is based on a split approach to the vorticity and stream function equations, a Galerkin-Legendre approximation of the problem for the perturbation, and an evaluation of the nonlinear terms by Gauss-Legendre numerical integration. Results computed for Re=0, 100, and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation-Chebyshev projection method. The validity of the proposed singularity subtraction scheme for computing time-dependent solutions is also established.

Estimation of tissue optical parameters with hyperspectral imaging and spectral unmixing

NASA Astrophysics Data System (ADS)

Lu, Guolan; Qin, Xulei; Wang, Dongsheng; Chen, Zhuo G.; Fei, Baowei

2015-03-01

Early detection of oral cancer and its curable precursors can improve patient survival and quality of life. Hyperspectral imaging (HSI) holds the potential for noninvasive early detection of oral cancer. The quantification of tissue chromophores by spectral unmixing of hyperspectral images could provide insights for evaluating cancer progression. In this study, non-negative matrix factorization has been applied for decomposing hyperspectral images into physiologically meaningful chromophore concentration maps. The approach has been validated by computer-simulated hyperspectral images and in vivo tumor hyperspectral images from a head and neck cancer animal model.

Multi-Centrality Graph Spectral Decompositions and Their Application to Cyber Intrusion Detection

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

Chen, Pin-Yu; Choudhury, Sutanay; Hero, Alfred

Many modern datasets can be represented as graphs and hence spectral decompositions such as graph principal component analysis (PCA) can be useful. Distinct from previous graph decomposition approaches based on subspace projection of a single topological feature, e.g., the centered graph adjacency matrix (graph Laplacian), we propose spectral decomposition approaches to graph PCA and graph dictionary learning that integrate multiple features, including graph walk statistics, centrality measures and graph distances to reference nodes. In this paper we propose a new PCA method for single graph analysis, called multi-centrality graph PCA (MC-GPCA), and a new dictionary learning method for ensembles ofmore » graphs, called multi-centrality graph dictionary learning (MC-GDL), both based on spectral decomposition of multi-centrality matrices. As an application to cyber intrusion detection, MC-GPCA can be an effective indicator of anomalous connectivity pattern and MC-GDL can provide discriminative basis for attack classification.« less

Persistence of uranium emission in laser-produced plasmas

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

LaHaye, N. L.; Harilal, S. S., E-mail: hari@purdue.edu; Diwakar, P. K.

2014-04-28

Detection of uranium and other nuclear materials is of the utmost importance for nuclear safeguards and security. Optical emission spectroscopy of laser-ablated U plasmas has been presented as a stand-off, portable analytical method that can yield accurate qualitative and quantitative elemental analysis of a variety of samples. In this study, optimal laser ablation and ambient conditions are explored, as well as the spatio-temporal evolution of the plasma for spectral analysis of excited U species in a glass matrix. Various Ar pressures were explored to investigate the role that plasma collisional effects and confinement have on spectral line emission enhancement andmore » persistence. The plasma-ambient gas interaction was also investigated using spatially resolved spectra and optical time-of-flight measurements. The results indicate that ambient conditions play a very important role in spectral emission intensity as well as the persistence of excited neutral U emission lines, influencing the appropriate spectral acquisition conditions.« less

Road simulation for four-wheel vehicle whole input power spectral density

NASA Astrophysics Data System (ADS)

Wang, Jiangbo; Qiang, Baomin

2017-05-01

As the vibration of running vehicle mainly comes from road and influence vehicle ride performance. So the road roughness power spectral density simulation has great significance to analyze automobile suspension vibration system parameters and evaluate ride comfort. Firstly, this paper based on the mathematical model of road roughness power spectral density, established the integral white noise road random method. Then in the MATLAB/Simulink environment, according to the research method of automobile suspension frame from simple two degree of freedom single-wheel vehicle model to complex multiple degrees of freedom vehicle model, this paper built the simple single incentive input simulation model. Finally the spectrum matrix was used to build whole vehicle incentive input simulation model. This simulation method based on reliable and accurate mathematical theory and can be applied to the random road simulation of any specified spectral which provides pavement incentive model and foundation to vehicle ride performance research and vibration simulation.

Spectral Diffusion: An Algorithm for Robust Material Decomposition of Spectral CT Data

PubMed Central

Clark, Darin P.; Badea, Cristian T.

2014-01-01

Clinical successes with dual energy CT, aggressive development of energy discriminating x-ray detectors, and novel, target-specific, nanoparticle contrast agents promise to establish spectral CT as a powerful functional imaging modality. Common to all of these applications is the need for a material decomposition algorithm which is robust in the presence of noise. Here, we develop such an algorithm which uses spectrally joint, piece-wise constant kernel regression and the split Bregman method to iteratively solve for a material decomposition which is gradient sparse, quantitatively accurate, and minimally biased. We call this algorithm spectral diffusion because it integrates structural information from multiple spectral channels and their corresponding material decompositions within the framework of diffusion-like denoising algorithms (e.g. anisotropic diffusion, total variation, bilateral filtration). Using a 3D, digital bar phantom and a material sensitivity matrix calibrated for use with a polychromatic x-ray source, we quantify the limits of detectability (CNR = 5) afforded by spectral diffusion in the triple-energy material decomposition of iodine (3.1 mg/mL), gold (0.9 mg/mL), and gadolinium (2.9 mg/mL) concentrations. We then apply spectral diffusion to the in vivo separation of these three materials in the mouse kidneys, liver, and spleen. PMID:25296173

Spectral diffusion: an algorithm for robust material decomposition of spectral CT data.

PubMed

Clark, Darin P; Badea, Cristian T

2014-11-07

Clinical successes with dual energy CT, aggressive development of energy discriminating x-ray detectors, and novel, target-specific, nanoparticle contrast agents promise to establish spectral CT as a powerful functional imaging modality. Common to all of these applications is the need for a material decomposition algorithm which is robust in the presence of noise. Here, we develop such an algorithm which uses spectrally joint, piecewise constant kernel regression and the split Bregman method to iteratively solve for a material decomposition which is gradient sparse, quantitatively accurate, and minimally biased. We call this algorithm spectral diffusion because it integrates structural information from multiple spectral channels and their corresponding material decompositions within the framework of diffusion-like denoising algorithms (e.g. anisotropic diffusion, total variation, bilateral filtration). Using a 3D, digital bar phantom and a material sensitivity matrix calibrated for use with a polychromatic x-ray source, we quantify the limits of detectability (CNR = 5) afforded by spectral diffusion in the triple-energy material decomposition of iodine (3.1 mg mL(-1)), gold (0.9 mg mL(-1)), and gadolinium (2.9 mg mL(-1)) concentrations. We then apply spectral diffusion to the in vivo separation of these three materials in the mouse kidneys, liver, and spleen.

New algorithms to compute the nearness symmetric solution of the matrix equation.

PubMed

Peng, Zhen-Yun; Fang, Yang-Zhi; Xiao, Xian-Wei; Du, Dan-Dan

2016-01-01

In this paper we consider the nearness symmetric solution of the matrix equation AXB = C to a given matrix [Formula: see text] in the sense of the Frobenius norm. By discussing equivalent form of the considered problem, we derive some necessary and sufficient conditions for the matrix [Formula: see text] is a solution of the considered problem. Based on the idea of the alternating variable minimization with multiplier method, we propose two iterative methods to compute the solution of the considered problem, and analyze the global convergence results of the proposed algorithms. Numerical results illustrate the proposed methods are more effective than the existing two methods proposed in Peng et al. (Appl Math Comput 160:763-777, 2005) and Peng (Int J Comput Math 87: 1820-1830, 2010).

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Effect of Computer-Presented Organizational/Memory Aids on Problem Solving Behavior.

ERIC Educational Resources Information Center

Steinberg, Esther R.; And Others

This research studied the effects of computer-presented organizational/memory aids on problem solving behavior. The aids were either matrix or verbal charts shown on the display screen next to the problem. The 104 college student subjects were randomly assigned to one of the four conditions: type of chart (matrix or verbal chart) and use of charts…

Deep UV Narrow-Band Photodetector Based on Ion Beam Synthesized Indium Oxide Quantum Dots in Al2O3 Matrix.

PubMed

Rajamani, Saravanan; Arora, Kanika; Konakov, Anton; Belov, Alexey; Korolev, Dmitry; Nikolskaya, Alyona; Mikhaylov, Alexey N; Surodin, Sergey; Kryukov, Ruslan; Nikolichev, Dmitri; Sushkov, Artem; Pavlov, Dmitry; Tetelbaum, David; Kumar, Mukesh; Kumar, Mahesh

2018-04-20

Semiconductor quantum dots (QDs) have attracted tremendous attention owing to their novel electrical and optical properties due to the size dependent quantum confinement effects. This provides an advantage of tunable wavelength detection, which is essential to realize spectrally selective photodetectors. We report the fabrication and characterization of high performance narrow band ultraviolet photodetector (UV-B) based on In2O3 nanocrystals embedded in Al2O3 matrices. The In2O3 nanocrystals are synthesized in Al2O3 matrix by sequential implantation of In+ and N2+ ions and post-implantation annealing. The photodetector exhibits excellent optoelectronic performances with high spectral responsivity and external quantum efficiency. The spectral response showed a band-selective nature with a full width half maximum of ∼ 60 nm, and the responsivity reaches up to 70 A/W under 290 nm at 5 V bias. The corresponding rejection ratio to visible region was as high as 8400. The high performance of this photodetector makes it highly suitable for practical applications such as narrow-band spectrum-selective photodetectors. The device design based on ion-synthesized nanocrystals would provide a new approach for realizing a visible-blind photodetector. © 2018 IOP Publishing Ltd.

An improved V-Lambda solution of the matrix Riccati equation

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Markley, F. Landis

1988-01-01

The authors present an improved algorithm for computing the V-Lambda solution of the matrix Riccati equation. The improvement is in the reduction of the computational load, results from the orthogonality of the eigenvector matrix that has to be solved for. The orthogonality constraint reduces the number of independent parameters which define the matrix from n-squared to n (n - 1)/2. The authors show how to specify the parameters, how to solve for them and how to form from them the needed eigenvector matrix. In the search for suitable parameters, the analogy between the present problem and the problem of attitude determination is exploited, resulting in the choice of Rodrigues parameters.

A Note on Alternating Minimization Algorithm for the Matrix Completion Problem

DOE PAGES

Gamarnik, David; Misra, Sidhant

2016-06-06

Here, we consider the problem of reconstructing a low-rank matrix from a subset of its entries and analyze two variants of the so-called alternating minimization algorithm, which has been proposed in the past.We establish that when the underlying matrix has rank one, has positive bounded entries, and the graph underlying the revealed entries has diameter which is logarithmic in the size of the matrix, both algorithms succeed in reconstructing the matrix approximately in polynomial time starting from an arbitrary initialization.We further provide simulation results which suggest that the second variant which is based on the message passing type updates performsmore » significantly better.« less

Matrix Completion Optimization for Localization in Wireless Sensor Networks for Intelligent IoT

PubMed Central

Nguyen, Thu L. N.; Shin, Yoan

2016-01-01

Localization in wireless sensor networks (WSNs) is one of the primary functions of the intelligent Internet of Things (IoT) that offers automatically discoverable services, while the localization accuracy is a key issue to evaluate the quality of those services. In this paper, we develop a framework to solve the Euclidean distance matrix completion problem, which is an important technical problem for distance-based localization in WSNs. The sensor network localization problem is described as a low-rank dimensional Euclidean distance completion problem with known nodes. The task is to find the sensor locations through recovery of missing entries of a squared distance matrix when the dimension of the data is small compared to the number of data points. We solve a relaxation optimization problem using a modification of Newton’s method, where the cost function depends on the squared distance matrix. The solution obtained in our scheme achieves a lower complexity and can perform better if we use it as an initial guess for an interactive local search of other higher precision localization scheme. Simulation results show the effectiveness of our approach. PMID:27213378

On the classification of the spectrally stable standing waves of the Hartree problem

NASA Astrophysics Data System (ADS)

Georgiev, Vladimir; Stefanov, Atanas

2018-05-01

We consider the fractional Hartree model, with general power non-linearity and arbitrary spatial dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model-in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.

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

PubMed

Fan, Jicong; Chow, Tommy W S

2017-09-01

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

Investigation and Implementation of Matrix Permanent Algorithms for Identity Resolution

DTIC Science & Technology

2014-12-01

calculation of the permanent of a matrix whose dimension is a function of target count [21]. However, the optimal approach for computing the permanent is...presently unclear. The primary objective of this project was to determine the optimal computing strategy(-ies) for the matrix permanent in tactical and...solving various combinatorial problems (see [16] for details and appli- cations to a wide variety of problems) and thus can be applied to compute a

Spectral collocation methods

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.

1987-01-01

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.

Conversion of a Rhotrix to a "Coupled Matrix"

ERIC Educational Resources Information Center

Sani, B.

2008-01-01

In this note, a method of converting a rhotrix to a special form of matrix termed a "coupled matrix" is proposed. The special matrix can be used to solve various problems involving n x n and (n - 1) x (n - 1) matrices simultaneously.

The supersymmetric method in random matrix theory and applications to QCD

NASA Astrophysics Data System (ADS)

Verbaarschot, Jacobus

2004-12-01

The supersymmetric method is a powerful method for the nonperturbative evaluation of quenched averages in disordered systems. Among others, this method has been applied to the statistical theory of S-matrix fluctuations, the theory of universal conductance fluctuations and the microscopic spectral density of the QCD Dirac operator. We start this series of lectures with a general review of Random Matrix Theory and the statistical theory of spectra. An elementary introduction of the supersymmetric method in Random Matrix Theory is given in the second and third lecture. We will show that a Random Matrix Theory can be rewritten as an integral over a supermanifold. This integral will be worked out in detail for the Gaussian Unitary Ensemble that describes level correlations in systems with broken time-reversal invariance. We especially emphasize the role of symmetries. As a second example of the application of the supersymmetric method we discuss the calculation of the microscopic spectral density of the QCD Dirac operator. This is the eigenvalue density near zero on the scale of the average level spacing which is known to be given by chiral Random Matrix Theory. Also in this case we use symmetry considerations to rewrite the generating function for the resolvent as an integral over a supermanifold. The main topic of the second last lecture is the recent developments on the relation between the supersymmetric partition function and integrable hierarchies (in our case the Toda lattice hierarchy). We will show that this relation is an efficient way to calculate superintegrals. Several examples that were given in previous lectures will be worked out by means of this new method. Finally, we will discuss the quenched QCD Dirac spectrum at nonzero chemical potential. Because of the nonhermiticity of the Dirac operator the usual supersymmetric method has not been successful in this case. However, we will show that the supersymmetric partition function can be evaluated by means of the replica limit of the Toda lattice equation.

An Algebraic Construction of Duality Functions for the Stochastic {U_q( A_n^{(1)})} Vertex Model and Its Degenerations

NASA Astrophysics Data System (ADS)

Kuan, Jeffrey

2018-03-01

A recent paper (Kuniba in Nucl Phys B 913:248-277, 2016) introduced the stochastic U}_q(A_n^{(1)})} vertex model. The stochastic S-matrix is related to the R-matrix of the quantum group {U_q(A_n^{(1)})} by a gauge transformation. We will show that a certain function {D^+_{m intertwines with the transfer matrix and its space reversal. When interpreting the transfer matrix as the transition matrix of a discrete-time totally asymmetric particle system on the one-dimensional lattice Z , the function {D^+m} becomes a Markov duality function {Dm} which only depends on q and the vertical spin parameters μ_x. By considering degenerations in the spectral parameter, the duality results also hold on a finite lattice with closed boundary conditions, and for a continuous-time degeneration. This duality function had previously appeared in a multi-species ASEP(q, j) process (Kuan in A multi-species ASEP(q, j) and q-TAZRP with stochastic duality, 2017). The proof here uses that the R-matrix intertwines with the co-product, but does not explicitly use the Yang-Baxter equation. It will also be shown that the stochastic U}_q(A_n^{(1)})} is a multi-species version of a stochastic vertex model studied in Borodin and Petrov (Higher spin six vertex model and symmetric rational functions, 2016) and Corwin and Petrov (Commun Math Phys 343:651-700, 2016). This will be done by generalizing the fusion process of Corwin and Petrov (2016) and showing that it matches the fusion of Kulish and yu (Lett Math Phys 5:393-403, 1981) up to the gauge transformation. We also show, by direct computation, that the multi-species q-Hahn Boson process (which arises at a special value of the spectral parameter) also satisfies duality with respect to D_∞, generalizing the single-species result of Corwin (Int Math Res Not 2015:5577-5603, 2015).

A note on the estimation of the Pareto efficient set for multiobjective matrix permutation problems.

PubMed

Brusco, Michael J; Steinley, Douglas

2012-02-01

There are a number of important problems in quantitative psychology that require the identification of a permutation of the n rows and columns of an n × n proximity matrix. These problems encompass applications such as unidimensional scaling, paired-comparison ranking, and anti-Robinson forms. The importance of simultaneously incorporating multiple objective criteria in matrix permutation applications is well recognized in the literature; however, to date, there has been a reliance on weighted-sum approaches that transform the multiobjective problem into a single-objective optimization problem. Although exact solutions to these single-objective problems produce supported Pareto efficient solutions to the multiobjective problem, many interesting unsupported Pareto efficient solutions may be missed. We illustrate the limitation of the weighted-sum approach with an example from the psychological literature and devise an effective heuristic algorithm for estimating both the supported and unsupported solutions of the Pareto efficient set. © 2011 The British Psychological Society.

Levy Matrices and Financial Covariances

NASA Astrophysics Data System (ADS)

Burda, Zdzislaw; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, Gabor; Zahed, Ismail

2003-10-01

In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.

PubMed

Sztepanacz, Jacqueline L; Blows, Mark W

2017-07-01

The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix. Copyright © 2017 by the Genetics Society of America.

A Green's function method for two-dimensional reactive solute transport in a parallel fracture-matrix system

NASA Astrophysics Data System (ADS)

Chen, Kewei; Zhan, Hongbin

2018-06-01

The reactive solute transport in a single fracture bounded by upper and lower matrixes is a classical problem that captures the dominant factors affecting transport behavior beyond pore scale. A parallel fracture-matrix system which considers the interaction among multiple paralleled fractures is an extension to a single fracture-matrix system. The existing analytical or semi-analytical solution for solute transport in a parallel fracture-matrix simplifies the problem to various degrees, such as neglecting the transverse dispersion in the fracture and/or the longitudinal diffusion in the matrix. The difficulty of solving the full two-dimensional (2-D) problem lies in the calculation of the mass exchange between the fracture and matrix. In this study, we propose an innovative Green's function approach to address the 2-D reactive solute transport in a parallel fracture-matrix system. The flux at the interface is calculated numerically. It is found that the transverse dispersion in the fracture can be safely neglected due to the small scale of fracture aperture. However, neglecting the longitudinal matrix diffusion would overestimate the concentration profile near the solute entrance face and underestimate the concentration profile at the far side. The error caused by neglecting the longitudinal matrix diffusion decreases with increasing Peclet number. The longitudinal matrix diffusion does not have obvious influence on the concentration profile in long-term. The developed model is applied to a non-aqueous-phase-liquid (DNAPL) contamination field case in New Haven Arkose of Connecticut in USA to estimate the Trichloroethylene (TCE) behavior over 40 years. The ratio of TCE mass stored in the matrix and the injected TCE mass increases above 90% in less than 10 years.

Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem*

PubMed Central

Katsevich, E.; Katsevich, A.; Singer, A.

2015-01-01

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly oriented copies of a molecule. The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy two-dimensional projection images taken at unknown directions to reconstruct the three-dimensional (3D) structure of the molecule. In some situations, the molecule under examination exhibits structural variability, which poses a fundamental challenge in SPR. The heterogeneity problem is the task of mapping the space of conformational states of a molecule. It has been previously suggested that the leading eigenvectors of the covariance matrix of the 3D molecules can be used to solve the heterogeneity problem. Estimating the covariance matrix is challenging, since only projections of the molecules are observed, but not the molecules themselves. In this paper, we formulate a general problem of covariance estimation from noisy projections of samples. This problem has intimate connections with matrix completion problems and high-dimensional principal component analysis. We propose an estimator and prove its consistency. When there are finitely many heterogeneity classes, the spectrum of the estimated covariance matrix reveals the number of classes. The estimator can be found as the solution to a certain linear system. In the cryo-EM case, the linear operator to be inverted, which we term the projection covariance transform, is an important object in covariance estimation for tomographic problems involving structural variation. Inverting it involves applying a filter akin to the ramp filter in tomography. We design a basis in which this linear operator is sparse and thus can be tractably inverted despite its large size. We demonstrate via numerical experiments on synthetic datasets the robustness of our algorithm to high levels of noise. PMID:25699132

Forest tree species clssification based on airborne hyper-spectral imagery

NASA Astrophysics Data System (ADS)

Dian, Yuanyong; Li, Zengyuan; Pang, Yong

2013-10-01

Forest precision classification products were the basic data for surveying of forest resource, updating forest subplot information, logging and design of forest. However, due to the diversity of stand structure, complexity of the forest growth environment, it's difficult to discriminate forest tree species using multi-spectral image. The airborne hyperspectral images can achieve the high spatial and spectral resolution imagery of forest canopy, so it will good for tree species level classification. The aim of this paper was to test the effective of combining spatial and spectral features in airborne hyper-spectral image classification. The CASI hyper spectral image data were acquired from Liangshui natural reserves area. Firstly, we use the MNF (minimum noise fraction) transform method for to reduce the hyperspectral image dimensionality and highlighting variation. And secondly, we use the grey level co-occurrence matrix (GLCM) to extract the texture features of forest tree canopy from the hyper-spectral image, and thirdly we fused the texture and the spectral features of forest canopy to classify the trees species using support vector machine (SVM) with different kernel functions. The results showed that when using the SVM classifier, MNF and texture-based features combined with linear kernel function can achieve the best overall accuracy which was 85.92%. It was also confirm that combine the spatial and spectral information can improve the accuracy of tree species classification.

Spectrum recovery method based on sparse representation for segmented multi-Gaussian model

NASA Astrophysics Data System (ADS)

Teng, Yidan; Zhang, Ye; Ti, Chunli; Su, Nan

2016-09-01

Hyperspectral images can realize crackajack features discriminability for supplying diagnostic characteristics with high spectral resolution. However, various degradations may generate negative influence on the spectral information, including water absorption, bands-continuous noise. On the other hand, the huge data volume and strong redundancy among spectrums produced intense demand on compressing HSIs in spectral dimension, which also leads to the loss of spectral information. The reconstruction of spectral diagnostic characteristics has irreplaceable significance for the subsequent application of HSIs. This paper introduces a spectrum restoration method for HSIs making use of segmented multi-Gaussian model (SMGM) and sparse representation. A SMGM is established to indicating the unsymmetrical spectral absorption and reflection characteristics, meanwhile, its rationality and sparse property are discussed. With the application of compressed sensing (CS) theory, we implement sparse representation to the SMGM. Then, the degraded and compressed HSIs can be reconstructed utilizing the uninjured or key bands. Finally, we take low rank matrix recovery (LRMR) algorithm for post processing to restore the spatial details. The proposed method was tested on the spectral data captured on the ground with artificial water absorption condition and an AVIRIS-HSI data set. The experimental results in terms of qualitative and quantitative assessments demonstrate that the effectiveness on recovering the spectral information from both degradations and loss compression. The spectral diagnostic characteristics and the spatial geometry feature are well preserved.

Spectral statistics of the acoustic stadium

NASA Astrophysics Data System (ADS)

Méndez-Sánchez, R. A.; Báez, G.; Leyvraz, F.; Seligman, T. H.

2014-01-01

We calculate the normal-mode frequencies and wave amplitudes of the two-dimensional acoustical stadium. We also obtain the statistical properties of the acoustical spectrum and show that they agree with the results given by random matrix theory. Some normal-mode wave amplitudes showing scarring are presented.

Geoelectrical Response of Surfactant Solutions in a Quartzitic Sand Analog Aquifer

EPA Science Inventory

In this project, the resistivity and phase shift of ten surfactant aqueous solutions in a sand matrix were measured using spectral induced polarization (SIP). In addition, specific conductivity, pH, dissolved oxygen, and dielectric constant measurements of the solutions were also...

Tasked-based quantification of measurement utility for ex vivo multi-spectral Mueller polarimetry of the uterine cervix

NASA Astrophysics Data System (ADS)

Kupinski, Meredith; Rehbinder, Jean; Haddad, Huda; Deby, Stanislas; Vizet, Jérémy; Teig, Benjamin; Nazac, André; Pierangelo, Angelo; Moreau, François; Novikova, Tatiana

2017-07-01

Significant contrast in visible wavelength Mueller matrix images for healthy and pre-cancerous regions of excised cervical tissue is shown. A novel classification algorithm is used to compute a test statistic from a small patient population.

Dispersion of speckle suppression efficiency for binary DOE structures: spectral domain and coherent matrix approaches.

PubMed

Lapchuk, Anatoliy; Prygun, Olexandr; Fu, Minglei; Le, Zichun; Xiong, Qiyuan; Kryuchyn, Andriy

2017-06-26

We present the first general theoretical description of speckle suppression efficiency based on an active diffractive optical element (DOE). The approach is based on spectral analysis of diffracted beams and a coherent matrix. Analytical formulae are obtained for the dispersion of speckle suppression efficiency using different DOE structures and different DOE activation methods. We show that a one-sided 2D DOE structure has smaller speckle suppression range than a two-sided 1D DOE structure. Both DOE structures have sufficient speckle suppression range to suppress low-order speckles in the entire visible range, but only the two-sided 1D DOE can suppress higher-order speckles. We also show that a linear shift 2D DOE in a laser projector with a large numerical aperture has higher effective speckle suppression efficiency than the method using switching or step-wise shift DOE structures. The generalized theoretical models elucidate the mechanism and practical realization of speckle suppression.

Matching algorithm of missile tail flame based on back-propagation neural network

NASA Astrophysics Data System (ADS)

Huang, Da; Huang, Shucai; Tang, Yidong; Zhao, Wei; Cao, Wenhuan

2018-02-01

This work presents a spectral matching algorithm of missile plume detection that based on neural network. The radiation value of the characteristic spectrum of the missile tail flame is taken as the input of the network. The network's structure including the number of nodes and layers is determined according to the number of characteristic spectral bands and missile types. We can get the network weight matrixes and threshold vectors through training the network using training samples, and we can determine the performance of the network through testing the network using the test samples. A small amount of data cause the network has the advantages of simple structure and practicality. Network structure composed of weight matrix and threshold vector can complete task of spectrum matching without large database support. Network can achieve real-time requirements with a small quantity of data. Experiment results show that the algorithm has the ability to match the precise spectrum and strong robustness.

Charging effects in single InP/GaInP baby dots

NASA Astrophysics Data System (ADS)

Persson, Jonas

2001-03-01

It has recently been demonstrated that the matrix material plays a major role for the physical behavior of self-assembled InP/GaInP quantum dots. As the "intrinsically" n-type GaInP matrix fills the quantum dot with electrons the spectral behavior of the dot dramatically changes. For the larger, fully developed dots, the charging gives rise to several broad lines. With an external bias it is possible to reduce the electron population of the dot. For smaller dots, baby dots, we show the possibility of dramatically changing the appearance of the dot spectrum by a precise tuning of the size of the quantum dot. When the dot is small enough it is uncharged and the spectrum is very similar to other material systems, whereas a slightly larger dot is charged and the number of lines is dramatically increased. We present high spectral resolution photoluminescence measurements of individual InP/GaInP baby-dots and k\\cdotp calculations including direct and exchange interactions.

Mesonic enhancement of the weak axial charge and its effect on the half-lives and spectral shapes of first-forbidden J+↔J- decays

NASA Astrophysics Data System (ADS)

Kostensalo, Joel; Suhonen, Jouni

2018-06-01

The effects of the enhancement of the axial-charge matrix element γ5 were studied in medium heavy and heavy nuclei for first-forbidden J+ ↔J- decay transitions using the nuclear shell model. Noticeable dependence on the enhancement ɛMEC of the axial-charge matrix element, as well as on the value of the axial-vector coupling constant gA was found in the spectral shapes of 93Y, 95Sr, and 97Y. The importance of the spectrum of 138Cs in the determination of gA is discussed. Half-life analyses in the A ≈ 95 and A ≈ 135 regions were done, and consistent results gA ≈ 0.90, 0.75, and 0.65, corresponding to the three enhancement scenarios ɛMEC = 1.4, 1.7, and 2.0, were obtained. Connection to the reactor-antineutrino anomaly is pointed out.

A high-accuracy optical linear algebra processor for finite element applications

NASA Technical Reports Server (NTRS)

Casasent, D.; Taylor, B. K.

1984-01-01

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

A penny-shaped crack in a filament-reinforced matrix. I - The filament model. II - The crack problem

NASA Technical Reports Server (NTRS)

Erdogan, F.; Pacella, A. H.

1974-01-01

The study deals with the elastostatic problem of a penny-shaped crack in an elastic matrix which is reinforced by filaments or fibers perpendicular to the plane of the crack. An elastic filament model is first developed, followed by consideration of the application of the model to the penny-shaped crack problem in which the filaments of finite length are asymmetrically distributed around the crack. Since the primary interest is in the application of the results to studies relating to the fracture of fiber or filament-reinforced composites and reinforced concrete, the main emphasis of the study is on the evaluation of the stress intensity factor along the periphery of the crack, the stresses in the filaments or fibers, and the interface shear between the matrix and the filaments or fibers. Using the filament model developed, the elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix is formulated.

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

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

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

Efficient l1 -norm-based low-rank matrix approximations for large-scale problems using alternating rectified gradient method.

PubMed

Kim, Eunwoo; Lee, Minsik; Choi, Chong-Ho; Kwak, Nojun; Oh, Songhwai

2015-02-01

Low-rank matrix approximation plays an important role in the area of computer vision and image processing. Most of the conventional low-rank matrix approximation methods are based on the l2 -norm (Frobenius norm) with principal component analysis (PCA) being the most popular among them. However, this can give a poor approximation for data contaminated by outliers (including missing data), because the l2 -norm exaggerates the negative effect of outliers. Recently, to overcome this problem, various methods based on the l1 -norm, such as robust PCA methods, have been proposed for low-rank matrix approximation. Despite the robustness of the methods, they require heavy computational effort and substantial memory for high-dimensional data, which is impractical for real-world problems. In this paper, we propose two efficient low-rank factorization methods based on the l1 -norm that find proper projection and coefficient matrices using the alternating rectified gradient method. The proposed methods are applied to a number of low-rank matrix approximation problems to demonstrate their efficiency and robustness. The experimental results show that our proposals are efficient in both execution time and reconstruction performance unlike other state-of-the-art methods.

Spectral methods for CFD

NASA Technical Reports Server (NTRS)

Zang, Thomas A.; Streett, Craig L.; Hussaini, M. Yousuff

1989-01-01

One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched.

Plutonium oxalate precipitation for trace elemental determination in plutonium materials

DOE PAGES

Xu, Ning; Gallimore, David; Lujan, Elmer; ...

2015-05-26

In this study, an analytical chemistry method has been developed that removes the plutonium (Pu) matrix from the dissolved Pu metal or oxide solution prior to the determination of trace impurities that are present in the metal or oxide. In this study, a Pu oxalate approach was employed to separate Pu from trace impurities. After Pu(III) was precipitated with oxalic acid and separated by centrifugation, trace elemental constituents in the supernatant were analyzed by inductively coupled plasma-optical emission spectroscopy with minimized spectral interferences from the sample matrix.

Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices.

PubMed

Luis, Alfredo

2007-04-01

We assess the degree of coherence of vectorial electromagnetic fields in the space-frequency domain as the distance between the cross-spectral density matrix and the identity matrix representing completely incoherent light. This definition is compared with previous approaches. It is shown that this distance provides an upper bound for the degree of coherence and visibility for any pair of scalar waves obtained by linear combinations of the original fields. This same approach emerges when applying a previous definition of global coherence to a Young interferometer.

Analysis of solar spectra in the middle ultraviolet and visible for atmospheric trace constituents measurements. [hydroxyl radicals

NASA Technical Reports Server (NTRS)

Goldman, A.

1980-01-01

Individual spectral line parameters including line positions, strengths, and intensities were generated for the sq Alpha Sigma - sq Chi Pi (0,0) band of OH, applicable to atmospheric and high temperatures. Energy levels and transition frequencies are calculated by numerically diagonalizing the Hamiltonian. Line strengths are calculated using the dipole matrix and eigenvectors derived from energy matrix diagonalization. The line strengths are compared to those calculated from previously published algebraic line strength formulas. Tables of line parameters are presented for 240 K and 4600 K.

Performance and cost analysis of matrix-assisted laser desorption ionization-time of flight mass spectrometry for routine identification of yeast.

PubMed

Dhiman, Neelam; Hall, Leslie; Wohlfiel, Sherri L; Buckwalter, Seanne P; Wengenack, Nancy L

2011-04-01

Matrix-assisted laser desorption ionization-time of flight (MALDI-TOF) mass spectrometry was compared to phenotypic testing for yeast identification. MALDI-TOF mass spectrometry yielded 96.3% and 84.5% accurate species level identifications (spectral scores, ≥ 1.8) for 138 common and 103 archived strains of yeast. MALDI-TOF mass spectrometry is accurate, rapid (5.1 min of hands-on time/identification), and cost-effective ($0.50/sample) for yeast identification in the clinical laboratory.

RADIATIVE TRANSFER MODELING OF THE ENIGMATIC SCATTERING POLARIZATION IN THE SOLAR Na i D{sub 1} LINE

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

Belluzzi, Luca; Bueno, Javier Trujillo; Degl’Innocenti, Egidio Landi

2015-12-01

The modeling of the peculiar scattering polarization signals observed in some diagnostically important solar resonance lines requires the consideration of the detailed spectral structure of the incident radiation field as well as the possibility of ground level polarization, along with the atom's hyperfine structure and quantum interference between hyperfine F-levels pertaining either to the same fine structure J-level, or to different J-levels of the same term. Here we present a theoretical and numerical approach suitable for solving this complex non-LTE radiative transfer problem. This approach is based on the density-matrix metalevel theory (where each level is viewed as a continuousmore » distribution of sublevels) and on accurate formal solvers of the transfer equations and efficient iterative methods. We show an application to the D-lines of Na i, with emphasis on the enigmatic D{sub 1} line, pointing out the observable signatures of the various physical mechanisms considered. We demonstrate that the linear polarization observed in the core of the D{sub 1} line may be explained by the effect that one gets when the detailed spectral structure of the anisotropic radiation responsible for the optical pumping is taken into account. This physical ingredient is capable of introducing significant scattering polarization in the core of the Na i D{sub 1} line without the need for ground-level polarization.« less

Rational variety mapping for contrast-enhanced nonlinear unsupervised segmentation of multispectral images of unstained specimen.

PubMed

Kopriva, Ivica; Hadžija, Mirko; Popović Hadžija, Marijana; Korolija, Marina; Cichocki, Andrzej

2011-08-01

A methodology is proposed for nonlinear contrast-enhanced unsupervised segmentation of multispectral (color) microscopy images of principally unstained specimens. The methodology exploits spectral diversity and spatial sparseness to find anatomical differences between materials (cells, nuclei, and background) present in the image. It consists of rth-order rational variety mapping (RVM) followed by matrix/tensor factorization. Sparseness constraint implies duality between nonlinear unsupervised segmentation and multiclass pattern assignment problems. Classes not linearly separable in the original input space become separable with high probability in the higher-dimensional mapped space. Hence, RVM mapping has two advantages: it takes implicitly into account nonlinearities present in the image (ie, they are not required to be known) and it increases spectral diversity (ie, contrast) between materials, due to increased dimensionality of the mapped space. This is expected to improve performance of systems for automated classification and analysis of microscopic histopathological images. The methodology was validated using RVM of the second and third orders of the experimental multispectral microscopy images of unstained sciatic nerve fibers (nervus ischiadicus) and of unstained white pulp in the spleen tissue, compared with a manually defined ground truth labeled by two trained pathophysiologists. The methodology can also be useful for additional contrast enhancement of images of stained specimens. Copyright © 2011 American Society for Investigative Pathology. Published by Elsevier Inc. All rights reserved.

Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations

NASA Astrophysics Data System (ADS)

Guo, Xiu-Rong

2016-06-01

We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, including the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Shandong Provincial Natural Science Foundation of China under Grant Nos. ZR2012AQ011, ZR2013AL016, ZR2015EM042, National Social Science Foundation of China under Grant No. 13BJY026, the Development of Science and Technology Project under Grant No. 2015NS1048 and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58

Multilevel Hierarchical Kernel Spectral Clustering for Real-Life Large Scale Complex Networks

PubMed Central

Mall, Raghvendra; Langone, Rocco; Suykens, Johan A. K.

2014-01-01

Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual level. The dual formulation allows to build a model on a representative subgraph of the large scale network in the training phase and the model parameters are estimated in the validation stage. The KSC model has a powerful out-of-sample extension property which allows cluster affiliation for the unseen nodes of the big data network. In this paper we exploit the structure of the projections in the eigenspace during the validation stage to automatically determine a set of increasing distance thresholds. We use these distance thresholds in the test phase to obtain multiple levels of hierarchy for the large scale network. The hierarchical structure in the network is determined in a bottom-up fashion. We empirically showcase that real-world networks have multilevel hierarchical organization which cannot be detected efficiently by several state-of-the-art large scale hierarchical community detection techniques like the Louvain, OSLOM and Infomap methods. We show that a major advantage of our proposed approach is the ability to locate good quality clusters at both the finer and coarser levels of hierarchy using internal cluster quality metrics on 7 real-life networks. PMID:24949877

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Spacecraft inertia estimation via constrained least squares

NASA Technical Reports Server (NTRS)

Keim, Jason A.; Acikmese, Behcet A.; Shields, Joel F.

2006-01-01

This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

The distribution of genetic variance across phenotypic space and the response to selection.

PubMed

Blows, Mark W; McGuigan, Katrina

2015-05-01

The role of adaptation in biological invasions will depend on the availability of genetic variation for traits under selection in the new environment. Although genetic variation is present for most traits in most populations, selection is expected to act on combinations of traits, not individual traits in isolation. The distribution of genetic variance across trait combinations can be characterized by the empirical spectral distribution of the genetic variance-covariance (G) matrix. Empirical spectral distributions of G from a range of trait types and taxa all exhibit a characteristic shape; some trait combinations have large levels of genetic variance, while others have very little genetic variance. In this study, we review what is known about the empirical spectral distribution of G and show how it predicts the response to selection across phenotypic space. In particular, trait combinations that form a nearly null genetic subspace with little genetic variance respond only inconsistently to selection. We go on to set out a framework for understanding how the empirical spectral distribution of G may differ from the random expectations that have been developed under random matrix theory (RMT). Using a data set containing a large number of gene expression traits, we illustrate how hypotheses concerning the distribution of multivariate genetic variance can be tested using RMT methods. We suggest that the relative alignment between novel selection pressures during invasion and the nearly null genetic subspace is likely to be an important component of the success or failure of invasion, and for the likelihood of rapid adaptation in small populations in general. © 2014 John Wiley & Sons Ltd.

Digital Equivalent Data System for XRF Labeling of Objects

NASA Technical Reports Server (NTRS)

Schramm, Harry F.; Kaiser, Bruce

2005-01-01

A digital equivalent data system (DEDS) is a system for identifying objects by means of the x-ray fluorescence (XRF) spectra of labeling elements that are encased in or deposited on the objects. As such, a DEDS is a revolutionary new major subsystem of an XRF system. A DEDS embodies the means for converting the spectral data output of an XRF scanner to an ASCII alphanumeric or barcode label that can be used to identify (or verify the assumed or apparent identity of) an XRF-scanned object. A typical XRF spectrum of interest contains peaks at photon energies associated with specific elements on the Periodic Table (see figure). The height of each spectral peak above the local background spectral intensity is proportional to the relative abundance of the corresponding element. Alphanumeric values are assigned to the relative abundances of the elements. Hence, if an object contained labeling elements in suitably chosen proportions, an alphanumeric representation of the object could be extracted from its XRF spectrum. The mixture of labeling elements and for reading the XRF spectrum would be compatible with one of the labeling conventions now used for bar codes and binary matrix patterns (essentially, two-dimensional bar codes that resemble checkerboards). A further benefit of such compatibility is that it would enable the conversion of the XRF spectral output to a bar or matrix-coded label, if needed. In short, a process previously used only for material composition analysis has been reapplied to the world of identification. This new level of verification is now being used for "authentication."

A Ranking Analysis/An Interlinking Approach of New Triangular Fuzzy Cognitive Maps and Combined Effective Time Dependent Matrix

NASA Astrophysics Data System (ADS)

Adiga, Shreemathi; Saraswathi, A.; Praveen Prakash, A.

2018-04-01

This paper aims an interlinking approach of new Triangular Fuzzy Cognitive Maps (TrFCM) and Combined Effective Time Dependent (CETD) matrix to find the ranking of the problems of Transgenders. Section one begins with an introduction that briefly describes the scope of Triangular Fuzzy Cognitive Maps (TrFCM) and CETD Matrix. Section two provides the process of causes of problems faced by Transgenders using Fuzzy Triangular Fuzzy Cognitive Maps (TrFCM) method and performs the calculations using the collected data among the Transgender. In Section 3, the reasons for the main causes for the problems of the Transgenders. Section 4 describes the Charles Spearmans coefficients of rank correlation method by interlinking of Triangular Fuzzy Cognitive Maps (TrFCM) Method and CETD Matrix. Section 5 shows the results based on our study.

Solving large sparse eigenvalue problems on supercomputers

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef

1988-01-01

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

VASP- VARIABLE DIMENSION AUTOMATIC SYNTHESIS PROGRAM

NASA Technical Reports Server (NTRS)

White, J. S.

1994-01-01

VASP is a variable dimension Fortran version of the Automatic Synthesis Program, ASP. The program is used to implement Kalman filtering and control theory. Basically, it consists of 31 subprograms for solving most modern control problems in linear, time-variant (or time-invariant) control systems. These subprograms include operations of matrix algebra, computation of the exponential of a matrix and its convolution integral, and the solution of the matrix Riccati equation. The user calls these subprograms by means of a FORTRAN main program, and so can easily obtain solutions to most general problems of extremization of a quadratic functional of the state of the linear dynamical system. Particularly, these problems include the synthesis of the Kalman filter gains and the optimal feedback gains for minimization of a quadratic performance index. VASP, as an outgrowth of the Automatic Synthesis Program, has the following improvements: more versatile programming language; more convenient input/output format; some new subprograms which consolidate certain groups of statements that are often repeated; and variable dimensioning. The pertinent difference between the two programs is that VASP has variable dimensioning and more efficient storage. The documentation for the VASP program contains a VASP dictionary and example problems. The dictionary contains a description of each subroutine and instructions on its use. The example problems include dynamic response, optimal control gain, solution of the sampled data matrix Riccati equation, matrix decomposition, and a pseudo-inverse of a matrix. This program is written in FORTRAN IV and has been implemented on the IBM 360. The VASP program was developed in 1971.

Numerical methods on some structured matrix algebra problems

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

Jessup, E.R.

1996-06-01

This proposal concerned the design, analysis, and implementation of serial and parallel algorithms for certain structured matrix algebra problems. It emphasized large order problems and so focused on methods that can be implemented efficiently on distributed-memory MIMD multiprocessors. Such machines supply the computing power and extensive memory demanded by the large order problems. We proposed to examine three classes of matrix algebra problems: the symmetric and nonsymmetric eigenvalue problems (especially the tridiagonal cases) and the solution of linear systems with specially structured coefficient matrices. As all of these are of practical interest, a major goal of this work was tomore » translate our research in linear algebra into useful tools for use by the computational scientists interested in these and related applications. Thus, in addition to software specific to the linear algebra problems, we proposed to produce a programming paradigm and library to aid in the design and implementation of programs for distributed-memory MIMD computers. We now report on our progress on each of the problems and on the programming tools.« less

Black box multigrid

NASA Technical Reports Server (NTRS)

Dendy, J. E., Jr.

1981-01-01

The black box multigrid (BOXMG) code, which only needs specification of the matrix problem for application in the multigrid method was investigated. It is contended that a major problem with the multigrid method is that each new grid configuration requires a major programming effort to develop a code that specifically handles that grid configuration. The SOR and ICCG methods only specify the matrix problem, no matter what the grid configuration. It is concluded that the BOXMG does everything else necessary to set up the auxiliary coarser problems to achieve a multigrid solution.

Estimating gene function with least squares nonnegative matrix factorization.

PubMed

Wang, Guoli; Ochs, Michael F

2007-01-01

Nonnegative matrix factorization is a machine learning algorithm that has extracted information from data in a number of fields, including imaging and spectral analysis, text mining, and microarray data analysis. One limitation with the method for linking genes through microarray data in order to estimate gene function is the high variance observed in transcription levels between different genes. Least squares nonnegative matrix factorization uses estimates of the uncertainties on the mRNA levels for each gene in each condition, to guide the algorithm to a local minimum in normalized chi2, rather than a Euclidean distance or divergence between the reconstructed data and the data itself. Herein, application of this method to microarray data is demonstrated in order to predict gene function.

Interval-valued distributed preference relation and its application to group decision making

PubMed Central

Liu, Yin; Xue, Min; Chang, Wenjun; Yang, Shanlin

2018-01-01

As an important way to help express the preference relation between alternatives, distributed preference relation (DPR) can represent the preferred, non-preferred, indifferent, and uncertain degrees of one alternative over another simultaneously. DPR, however, is unavailable in some situations where a decision maker cannot provide the precise degrees of one alternative over another due to lack of knowledge, experience, and data. In this paper, to address this issue, we propose interval-valued DPR (IDPR) and present its properties of validity and normalization. Through constructing two optimization models, an IDPR matrix is transformed into a score matrix to facilitate the comparison between any two alternatives. The properties of the score matrix are analyzed. To guarantee the rationality of the comparisons between alternatives derived from the score matrix, the additive consistency of the score matrix is developed. In terms of these, IDPR is applied to model and solve multiple criteria group decision making (MCGDM) problem. Particularly, the relationship between the parameters for the consistency of the score matrix associated with each decision maker and those for the consistency of the score matrix associated with the group of decision makers is analyzed. A manager selection problem is investigated to demonstrate the application of IDPRs to MCGDM problems. PMID:29889871

Soft-landing ion mobility of silver clusters for small-molecule matrix-assisted laser desorption ionization mass spectrometry and imaging of latent fingerprints.

PubMed

Walton, Barbara L; Verbeck, Guido F

2014-08-19

Matrix-assisted laser desorption ionization (MALDI) imaging is gaining popularity, but matrix effects such as mass spectral interference and damage to the sample limit its applications. Replacing traditional matrices with silver particles capable of equivalent or increased photon energy absorption from the incoming laser has proven to be beneficial for low mass analysis. Not only can silver clusters be advantageous for low mass compound detection, but they can be used for imaging as well. Conventional matrix application methods can obstruct samples, such as fingerprints, rendering them useless after mass analysis. The ability to image latent fingerprints without causing damage to the ridge pattern is important as it allows for further characterization of the print. The application of silver clusters by soft-landing ion mobility allows for enhanced MALDI and preservation of fingerprint integrity.

Matrix Results and Techniques in Quantum Information Science and Related Topics

NASA Astrophysics Data System (ADS)

Pelejo, Diane Christine

In this dissertation, we present several matrix-related problems and results motivated by quantum information theory. Some background material of quantum information science will be discussed in chapter 1, while chapter 7 gives a summary of results and concluding remarks. In chapter 2, we look at 2n x 2 n unitary matrices, which describe operations on a closed n-qubit system. We define a set of simple quantum gates, called controlled single qubit gates, and their associated operational cost. We then present a recurrence scheme to decompose a general 2n x 2n unitary matrix to the product of no more than 2n-12n-1 single qubit gates with small number of controls. In chapter 3, we address the problem of finding a specific element phi among a given set of quantum channels S that will produce the optimal value of a scalar function D(rho 1,phi(rho2)), on two fixed quantum states rho 1 and rho2. Some of the functions we considered for D(·,·) are the trace distance, quantum fidelity and quantum relative entropy. We discuss the optimal solution when S is the set of unitary quantum channels, the set of mixed unitary channels, the set of unital quantum channels, and the set of all quantum channels. In chapter 4, we focus on the spectral properties of qubit-qudit bipartite states with a maximally mixed qudit subsystem. More specifically, given positive numbers a1 ≥ ... ≥ a 2n ≥ 0, we want to determine if there exist a 2n x 2n density matrix rho having eigenvalues a1,..., a2n and satisfying tr 1(rho)=1/n In. This problem is a special case of the more general quantum marginal problem. We give the minimal necessary and sufficient conditions on a1,..., a2n for n ≤ 6 and state some observations on general values of n.. In chapter 5, we discuss the numerical method of alternating projections and illustrate its usefulness in: (a) constructing a quantum channel, if it exists, such that phi(rho(1))=sigma(1),...,phi(rho (k))=sigma(k) for given rho (1),...,rho(k) ∈ Dn and sigma(1),...,sigma (k) ∈ Dm, (b) constructing a multipartite state rho having a prescribed set of reduced states rho1,..., rhor on r of its subsystems, (c) constructing a multipartite staterho having prescribed reduced states and additional properties such as having prescribed eigenvalues, prescribed rank or low von Neuman entropy; and (d) determining if a square matrix A can be written as a product of two positive semidefinite contractions. In chapter 6, we examine the shape of the Minkowski product of convex subsets K1 and K2 of C given by K1K 2 = {ab: a ∈ K1, b ∈ K2}, which has applications in the study of the product numerical range and quantum error-correction. In Karol, it was conjectured that K1K 2 is star-shaped when K1 and K2 are convex. We give counterexamples to show that this conjecture does not hold in general but we show that the set K 1K2 is star-shaped if K 1 is a line segment or a circular disk.

Monitoring temporal microstructural variations of skeletal muscle tissues by multispectral Mueller matrix polarimetry

NASA Astrophysics Data System (ADS)

Dong, Yang; He, Honghui; He, Chao; Ma, Hui

2017-02-01

Mueller matrix polarimetry is a powerful tool for detecting microscopic structures, therefore can be used to monitor physiological changes of tissue samples. Meanwhile, spectral features of scattered light can also provide abundant microstructural information of tissues. In this paper, we take the 2D multispectral backscattering Mueller matrix images of bovine skeletal muscle tissues, and analyze their temporal variation behavior using multispectral Mueller matrix parameters. The 2D images of the Mueller matrix elements are reduced to the multispectral frequency distribution histograms (mFDHs) to reveal the dominant structural features of the muscle samples more clearly. For quantitative analysis, the multispectral Mueller matrix transformation (MMT) parameters are calculated to characterize the microstructural variations during the rigor mortis and proteolysis processes of the skeletal muscle tissue samples. The experimental results indicate that the multispectral MMT parameters can be used to judge different physiological stages for bovine skeletal muscle tissues in 24 hours, and combining with the multispectral technique, the Mueller matrix polarimetry and FDH analysis can monitor the microstructural variation features of skeletal muscle samples. The techniques may be used for quick assessment and quantitative monitoring of meat qualities in food industry.

Spectral Knowledge (SK-UTALCA): Software for Exploratory Analysis of High-Resolution Spectral Reflectance Data on Plant Breeding

PubMed Central

Lobos, Gustavo A.; Poblete-Echeverría, Carlos

2017-01-01

This article describes public, free software that provides efficient exploratory analysis of high-resolution spectral reflectance data. Spectral reflectance data can suffer from problems such as poor signal to noise ratios in various wavebands or invalid measurements due to changes in incoming solar radiation or operator fatigue leading to poor orientation of sensors. Thus, exploratory data analysis is essential to identify appropriate data for further analyses. This software overcomes the problem that analysis tools such as Excel are cumbersome to use for the high number of wavelengths and samples typically acquired in these studies. The software, Spectral Knowledge (SK-UTALCA), was initially developed for plant breeding, but it is also suitable for other studies such as precision agriculture, crop protection, ecophysiology plant nutrition, and soil fertility. Various spectral reflectance indices (SRIs) are often used to relate crop characteristics to spectral data and the software is loaded with 255 SRIs which can be applied quickly to the data. This article describes the architecture and functions of SK-UTALCA and the features of the data that led to the development of each of its modules. PMID:28119705

Spectral Knowledge (SK-UTALCA): Software for Exploratory Analysis of High-Resolution Spectral Reflectance Data on Plant Breeding.

PubMed

Lobos, Gustavo A; Poblete-Echeverría, Carlos

2016-01-01

This article describes public, free software that provides efficient exploratory analysis of high-resolution spectral reflectance data. Spectral reflectance data can suffer from problems such as poor signal to noise ratios in various wavebands or invalid measurements due to changes in incoming solar radiation or operator fatigue leading to poor orientation of sensors. Thus, exploratory data analysis is essential to identify appropriate data for further analyses. This software overcomes the problem that analysis tools such as Excel are cumbersome to use for the high number of wavelengths and samples typically acquired in these studies. The software, Spectral Knowledge (SK-UTALCA), was initially developed for plant breeding, but it is also suitable for other studies such as precision agriculture, crop protection, ecophysiology plant nutrition, and soil fertility. Various spectral reflectance indices (SRIs) are often used to relate crop characteristics to spectral data and the software is loaded with 255 SRIs which can be applied quickly to the data. This article describes the architecture and functions of SK-UTALCA and the features of the data that led to the development of each of its modules.

Utilization of matrix-assisted laser desorption/ionization time-of-flight mass spectrometry for structural studies related to biology and disease

NASA Astrophysics Data System (ADS)

Costello, Catherine E.; Helin, Jari; Ngoka, Lambert C. M.

1996-04-01

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS), because of its high sensitivity and relatively straightforward requirements for sample preparation, is contributing to the solution of structural problems in biology and to the development of therapeutic approaches through increased understanding of pharmacology and enhanced capabilities for quality control of pharmaceuticals. We are using a reflectron TOF- MS for the determination of molecular weights of individual compounds and the components of mixtures that are naturally occurring or are generated through enzymic digests, and employing the post-source decay mode to elucidate structural details. To maximize the sensitivity and information content of the spectra, varied matrices, derivative, and stepwise degradation procedures are being explored. Present studies include investigations of oligosaccharides, neutral glycolipids, gangliosides, glycoproteins, neuropeptides and proteins. Rules for fragmentation are being developed with model compounds and used for the structural elucidation of unknowns. When adequate sample amounts are available, the results are compared with low- and high-energy collision-induced decomposition spectra obtained with tandem MS in order to provide a data base for the correlation of spectral features and guidance in selection of approaches for scarce biological samples. Current projects include biophysical studies of glycoplipids, glycoproteins and oligosaccharides and investigations of the substance P receptor, transthyretin genetic variants and cisplatin-DNA interactions.

The KS Method in Light of Generalized Euler Parameters.

DTIC Science & Technology

1980-01-01

motion for the restricted two-body problem is trans- formed via the Kustaanheimo - Stiefel transformation method (KS) into a dynamical equation in the... Kustaanheimo - Stiefel2 transformation method (KS) in the two-body problem. Many papers have appeared in which specific problems or applications have... TRANSFORMATION MATRIX P. Kustaanheimo and E. Stiefel2 proposed a regularization method by intro- ducing a 4 x 4 transformation matrix and four-component

A Problem-Centered Approach to Canonical Matrix Forms

ERIC Educational Resources Information Center

Sylvestre, Jeremy

2014-01-01

This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…

Automated MALDI Matrix Coating System for Multiple Tissue Samples for Imaging Mass Spectrometry

NASA Astrophysics Data System (ADS)

Mounfield, William P.; Garrett, Timothy J.

2012-03-01

Uniform matrix deposition on tissue samples for matrix-assisted laser desorption/ionization (MALDI) is key for reproducible analyte ion signals. Current methods often result in nonhomogenous matrix deposition, and take time and effort to produce acceptable ion signals. Here we describe a fully-automated method for matrix deposition using an enclosed spray chamber and spray nozzle for matrix solution delivery. A commercial air-atomizing spray nozzle was modified and combined with solenoid controlled valves and a Programmable Logic Controller (PLC) to control and deliver the matrix solution. A spray chamber was employed to contain the nozzle, sample, and atomized matrix solution stream, and to prevent any interference from outside conditions as well as allow complete control of the sample environment. A gravity cup was filled with MALDI matrix solutions, including DHB in chloroform/methanol (50:50) at concentrations up to 60 mg/mL. Various samples (including rat brain tissue sections) were prepared using two deposition methods (spray chamber, inkjet). A linear ion trap equipped with an intermediate-pressure MALDI source was used for analyses. Optical microscopic examination showed a uniform coating of matrix crystals across the sample. Overall, the mass spectral images gathered from tissues coated using the spray chamber system were of better quality and more reproducible than from tissue specimens prepared by the inkjet deposition method.

Automated MALDI matrix coating system for multiple tissue samples for imaging mass spectrometry.

PubMed

Mounfield, William P; Garrett, Timothy J

2012-03-01

Uniform matrix deposition on tissue samples for matrix-assisted laser desorption/ionization (MALDI) is key for reproducible analyte ion signals. Current methods often result in nonhomogenous matrix deposition, and take time and effort to produce acceptable ion signals. Here we describe a fully-automated method for matrix deposition using an enclosed spray chamber and spray nozzle for matrix solution delivery. A commercial air-atomizing spray nozzle was modified and combined with solenoid controlled valves and a Programmable Logic Controller (PLC) to control and deliver the matrix solution. A spray chamber was employed to contain the nozzle, sample, and atomized matrix solution stream, and to prevent any interference from outside conditions as well as allow complete control of the sample environment. A gravity cup was filled with MALDI matrix solutions, including DHB in chloroform/methanol (50:50) at concentrations up to 60 mg/mL. Various samples (including rat brain tissue sections) were prepared using two deposition methods (spray chamber, inkjet). A linear ion trap equipped with an intermediate-pressure MALDI source was used for analyses. Optical microscopic examination showed a uniform coating of matrix crystals across the sample. Overall, the mass spectral images gathered from tissues coated using the spray chamber system were of better quality and more reproducible than from tissue specimens prepared by the inkjet deposition method.

Hyperspectral remote sensing image retrieval system using spectral and texture features.

PubMed

Zhang, Jing; Geng, Wenhao; Liang, Xi; Li, Jiafeng; Zhuo, Li; Zhou, Qianlan

2017-06-01

Although many content-based image retrieval systems have been developed, few studies have focused on hyperspectral remote sensing images. In this paper, a hyperspectral remote sensing image retrieval system based on spectral and texture features is proposed. The main contributions are fourfold: (1) considering the "mixed pixel" in the hyperspectral image, endmembers as spectral features are extracted by an improved automatic pixel purity index algorithm, then the texture features are extracted with the gray level co-occurrence matrix; (2) similarity measurement is designed for the hyperspectral remote sensing image retrieval system, in which the similarity of spectral features is measured with the spectral information divergence and spectral angle match mixed measurement and in which the similarity of textural features is measured with Euclidean distance; (3) considering the limited ability of the human visual system, the retrieval results are returned after synthesizing true color images based on the hyperspectral image characteristics; (4) the retrieval results are optimized by adjusting the feature weights of similarity measurements according to the user's relevance feedback. The experimental results on NASA data sets can show that our system can achieve comparable superior retrieval performance to existing hyperspectral analysis schemes.

Spectral analysis of the Crab Nebula and GRB 160530A with the Compton Spectrometer and Imager

NASA Astrophysics Data System (ADS)

Sleator, Clio; Boggs, Steven E.; Chiu, Jeng-Lun; Kierans, Carolyn; Lowell, Alexander; Tomsick, John; Zoglauer, Andreas; Amman, Mark; Chang, Hsiang-Kuang; Tseng, Chao-Hsiung; Yang, Chien-Ying; Lin, Chih H.; Jean, Pierre; von Ballmoos, Peter

2017-08-01

The Compton Spectrometer and Imager (COSI) is a balloon-borne soft gamma-ray (0.2-5 MeV) telescope designed to study astrophysical sources including gamma-ray bursts and compact objects. As a compact Compton telescope, COSI has inherent sensitivity to polarization. COSI utilizes 12 germanium detectors to provide excellent spectral resolution. On May 17, 2016, COSI was launched from Wanaka, New Zealand and completed a successful 46-day flight on NASA’s new Superpressure balloon. To perform spectral analysis with COSI, we have developed an accurate instrument model as required for the response matrix. With carefully chosen background regions, we are able to fit the background-subtracted spectra in XSPEC. We have developed a model of the atmosphere above COSI based on the NRLMSISE-00 Atmosphere Model to include in our spectral fits. The Crab and GRB 160530A are among the sources detected during the 2016 flight. We present spectral analysis of these two point sources. Our GRB 160530A results are consistent with those from other instruments, confirming COSI’s spectral abilities. Furthermore, we discuss prospects for measuring the Crab polarization with COSI.

Matrix differentiation formulas

NASA Technical Reports Server (NTRS)

Usikov, D. A.; Tkhabisimov, D. K.

1983-01-01

A compact differentiation technique (without using indexes) is developed for scalar functions that depend on complex matrix arguments which are combined by operations of complex conjugation, transposition, addition, multiplication, matrix inversion and taking the direct product. The differentiation apparatus is developed in order to simplify the solution of extremum problems of scalar functions of matrix arguments.

A reconstruction algorithm for three-dimensional object-space data using spatial-spectral multiplexing

NASA Astrophysics Data System (ADS)

Wu, Zhejun; Kudenov, Michael W.

2017-05-01

This paper presents a reconstruction algorithm for the Spatial-Spectral Multiplexing (SSM) optical system. The goal of this algorithm is to recover the three-dimensional spatial and spectral information of a scene, given that a one-dimensional spectrometer array is used to sample the pupil of the spatial-spectral modulator. The challenge of the reconstruction is that the non-parametric representation of the three-dimensional spatial and spectral object requires a large number of variables, thus leading to an underdetermined linear system that is hard to uniquely recover. We propose to reparameterize the spectrum using B-spline functions to reduce the number of unknown variables. Our reconstruction algorithm then solves the improved linear system via a least- square optimization of such B-spline coefficients with additional spatial smoothness regularization. The ground truth object and the optical model for the measurement matrix are simulated with both spatial and spectral assumptions according to a realistic field of view. In order to test the robustness of the algorithm, we add Poisson noise to the measurement and test on both two-dimensional and three-dimensional spatial and spectral scenes. Our analysis shows that the root mean square error of the recovered results can be achieved within 5.15%.

Infrared spectral imaging as a novel approach for histopathological recognition in colon cancer diagnosis

NASA Astrophysics Data System (ADS)

Nallala, Jayakrupakar; Gobinet, Cyril; Diebold, Marie-Danièle; Untereiner, Valérie; Bouché, Olivier; Manfait, Michel; Sockalingum, Ganesh Dhruvananda; Piot, Olivier

2012-11-01

Innovative diagnostic methods are the need of the hour that could complement conventional histopathology for cancer diagnosis. In this perspective, we propose a new concept based on spectral histopathology, using IR spectral micro-imaging, directly applied to paraffinized colon tissue array stabilized in an agarose matrix without any chemical pre-treatment. In order to correct spectral interferences from paraffin and agarose, a mathematical procedure is implemented. The corrected spectral images are then processed by a multivariate clustering method to automatically recover, on the basis of their intrinsic molecular composition, the main histological classes of the normal and the tumoral colon tissue. The spectral signatures from different histological classes of the colonic tissues are analyzed using statistical methods (Kruskal-Wallis test and principal component analysis) to identify the most discriminant IR features. These features allow characterizing some of the biomolecular alterations associated with malignancy. Thus, via a single analysis, in a label-free and nondestructive manner, main changes associated with nucleotide, carbohydrates, and collagen features can be identified simultaneously between the compared normal and the cancerous tissues. The present study demonstrates the potential of IR spectral imaging as a complementary modern tool, to conventional histopathology, for an objective cancer diagnosis directly from paraffin-embedded tissue arrays.

Spectral K-edge subtraction imaging

NASA Astrophysics Data System (ADS)

Zhu, Y.; Samadi, N.; Martinson, M.; Bassey, B.; Wei, Z.; Belev, G.; Chapman, D.

2014-05-01

We describe a spectral x-ray transmission method to provide images of independent material components of an object using a synchrotron x-ray source. The imaging system and process is similar to K-edge subtraction (KES) imaging where two imaging energies are prepared above and below the K-absorption edge of a contrast element and a quantifiable image of the contrast element and a water equivalent image are obtained. The spectral method, termed ‘spectral-KES’ employs a continuous spectrum encompassing an absorption edge of an element within the object. The spectrum is prepared by a bent Laue monochromator with good focal and energy dispersive properties. The monochromator focuses the spectral beam at the object location, which then diverges onto an area detector such that one dimension in the detector is an energy axis. A least-squares method is used to interpret the transmitted spectral data with fits to either measured and/or calculated absorption of the contrast and matrix material-water. The spectral-KES system is very simple to implement and is comprised of a bent Laue monochromator, a stage for sample manipulation for projection and computed tomography imaging, and a pixelated area detector. The imaging system and examples of its applications to biological imaging are presented. The system is particularly well suited for a synchrotron bend magnet beamline with white beam access.

Breaking Megrelishvili protocol using matrix diagonalization

NASA Astrophysics Data System (ADS)

Arzaki, Muhammad; Triantoro Murdiansyah, Danang; Adi Prabowo, Satrio

2018-03-01

In this article we conduct a theoretical security analysis of Megrelishvili protocol—a linear algebra-based key agreement between two participants. We study the computational complexity of Megrelishvili vector-matrix problem (MVMP) as a mathematical problem that strongly relates to the security of Megrelishvili protocol. In particular, we investigate the asymptotic upper bounds for the running time and memory requirement of the MVMP that involves diagonalizable public matrix. Specifically, we devise a diagonalization method for solving the MVMP that is asymptotically faster than all of the previously existing algorithms. We also found an important counterintuitive result: the utilization of primitive matrix in Megrelishvili protocol makes the protocol more vulnerable to attacks.

Angle-resolved Auger electron spectra induced by neon ion impact on aluminum

NASA Technical Reports Server (NTRS)

Pepper, S. V.; Aron, P. R.

1986-01-01

Auger electron emission from aluminum bombarded with 1 to 5 keV neon ions was studied by angle-resolved electron spectroscopy. The position and shape of the spectral features depended on the incident ion energy, angle of ion incidence, and electron take-off angle with respect to the aluminum surface. These spectral dependencies were interpreted in terms of the Doppler shift given to the Auger electron velocity by the excited atom ejected into the vacuum. For oblique ion incidence it is concluded that a flux of high energy atoms are ejected in a direction close to the projection of the ion beam on the target surface. In addition, a new spectral feature was found and identified as due to Auger emission from excited neon in the aluminum matrix.

Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity.

PubMed

Samsonov, Boris F

2013-04-28

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.

Time-resolved lidar fluorosensor for sea pollution detection

NASA Technical Reports Server (NTRS)

Ferrario, A.; Pizzolati, P. L.; Zanzottera, E.

1986-01-01

A contemporary time and spectral analysis of oil fluorescence is useful for the detection and the characterization of oil spills on the sea surface. Nevertheless the fluorosensor lidars, which were realized up to now, have only partial capability to perform this double analysis. The main difficulties are the high resolution required (of the order of 1 nanosecond) and the complexity of the detection system for the recording of a two-dimensional matrix of data for each laser pulse. An airborne system whose major specifications were: time range, 30 to 75 ns; time resolution, 1 ns; spectral range, 350 to 700 nm; and spectral resolution, 10 nm was designed and constructed. The designed system of a short pulse ultraviolet laser source and a streak camera based detector are described.