International Nuclear Information System (INIS)
Tanaka, Yuho; Uruma, Kazunori; Furukawa, Toshihiro; Nakao, Tomoki; Izumi, Kenya; Utsumi, Hiroaki
2017-01-01
This paper deals with an analysis problem for diffusion-ordered NMR spectroscopy (DOSY). DOSY is formulated as a matrix factorization problem of a given observed matrix. In order to solve this problem, a direct exponential curve resolution algorithm (DECRA) is well known. DECRA is based on singular value decomposition; the advantage of this algorithm is that the initial value is not required. However, DECRA requires a long calculating time, depending on the size of the given observed matrix due to the singular value decomposition, and this is a serious problem in practical use. Thus, this paper proposes a new analysis algorithm for DOSY to achieve a short calculating time. In order to solve matrix factorization for DOSY without using singular value decomposition, this paper focuses on the size of the given observed matrix. The observed matrix in DOSY is also a rectangular matrix with more columns than rows, due to limitation of the measuring time; thus, the proposed algorithm transforms the given observed matrix into a small observed matrix. The proposed algorithm applies the eigenvalue decomposition and the difference approximation to the small observed matrix, and the matrix factorization problem for DOSY is solved. The simulation and a data analysis show that the proposed algorithm achieves a lower calculating time than DECRA as well as similar analysis result results to DECRA. (author)
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-07
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-05
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul
2015-01-01
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul
2015-01-01
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika; Amato, Nancy M.; Lu, Yanyan; Lien, Jyh-Ming
2013-01-01
Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika
2013-02-01
Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.
Approximate modal analysis using Fourier decomposition
International Nuclear Information System (INIS)
Kozar, Ivica; Jericevic, Zeljko; Pecak, Tatjana
2010-01-01
The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures with special attention on plate structures. The approach is based on Fourier transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculation. After calculation eigenvectors are expanded and transformed back into time domain. The principles are presented in Jericevic [1]. Fourier transform can be formulated in a way that some parts of the matrix that should not be approximated are not transformed but are fully preserved. In this paper we present formulation that preserves central or edge parts of the matrix and compare it with the formulation that performs transform on the whole matrix. Numerical experiments on transformed structural dynamic matrices describe quality of the approximations obtained in modal analysis of structures. On the basis of the numerical experiments, from the three approaches to matrix reduction one is recommended.
Salient Object Detection via Structured Matrix Decomposition.
Peng, Houwen; Li, Bing; Ling, Haibin; Hu, Weiming; Xiong, Weihua; Maybank, Stephen J
2016-05-04
Low-rank recovery models have shown potential for salient object detection, where a matrix is decomposed into a low-rank matrix representing image background and a sparse matrix identifying salient objects. Two deficiencies, however, still exist. First, previous work typically assumes the elements in the sparse matrix are mutually independent, ignoring the spatial and pattern relations of image regions. Second, when the low-rank and sparse matrices are relatively coherent, e.g., when there are similarities between the salient objects and background or when the background is complicated, it is difficult for previous models to disentangle them. To address these problems, we propose a novel structured matrix decomposition model with two structural regularizations: (1) a tree-structured sparsity-inducing regularization that captures the image structure and enforces patches from the same object to have similar saliency values, and (2) a Laplacian regularization that enlarges the gaps between salient objects and the background in feature space. Furthermore, high-level priors are integrated to guide the matrix decomposition and boost the detection. We evaluate our model for salient object detection on five challenging datasets including single object, multiple objects and complex scene images, and show competitive results as compared with 24 state-of-the-art methods in terms of seven performance metrics.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying
2015-01-01
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-11-30
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
Unambiguous results from variational matrix Pade approximants
International Nuclear Information System (INIS)
Pindor, Maciej.
1979-10-01
Variational Matrix Pade Approximants are studied as a nonlinear variational problem. It is shown that although a stationary value of the Schwinger functional is a stationary value of VMPA, the latter has also another stationary value. It is therefore proposed that instead of looking for a stationary point of VMPA, one minimizes some non-negative functional and then one calculates VMPA at the point where the former has the absolute minimum. This approach, which we call the Method of the Variational Gradient (MVG) gives unambiguous results and is also shown to minimize a distance between the approximate and the exact stationary values of the Schwinger functional
Solving network design problems via decomposition, aggregation and approximation
Bärmann, Andreas
2016-01-01
Andreas Bärmann develops novel approaches for the solution of network design problems as they arise in various contexts of applied optimization. At the example of an optimal expansion of the German railway network until 2030, the author derives a tailor-made decomposition technique for multi-period network design problems. Next, he develops a general framework for the solution of network design problems via aggregation of the underlying graph structure. This approach is shown to save much computation time as compared to standard techniques. Finally, the author devises a modelling framework for the approximation of the robust counterpart under ellipsoidal uncertainty, an often-studied case in the literature. Each of these three approaches opens up a fascinating branch of research which promises a better theoretical understanding of the problem and an increasing range of solvable application settings at the same time. Contents Decomposition for Multi-Period Network Design Solving Network Design Problems via Ag...
International Nuclear Information System (INIS)
Lee, Yoon Hee; Cho, Nam Zin
2016-01-01
The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.
Energy Technology Data Exchange (ETDEWEB)
Lee, Yoon Hee; Cho, Nam Zin [KAERI, Daejeon (Korea, Republic of)
2016-05-15
The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.
Aquilante, Francesco; Gagliardi, Laura; Pedersen, Thomas Bondo; Lindh, Roland
2009-04-01
Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante et al., J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.
rCUR: an R package for CUR matrix decomposition
Directory of Open Access Journals (Sweden)
Bodor András
2012-05-01
Full Text Available Abstract Background Many methods for dimensionality reduction of large data sets such as those generated in microarray studies boil down to the Singular Value Decomposition (SVD. Although singular vectors associated with the largest singular values have strong optimality properties and can often be quite useful as a tool to summarize the data, they are linear combinations of up to all of the data points, and thus it is typically quite hard to interpret those vectors in terms of the application domain from which the data are drawn. Recently, an alternative dimensionality reduction paradigm, CUR matrix decompositions, has been proposed to address this problem and has been applied to genetic and internet data. CUR decompositions are low-rank matrix decompositions that are explicitly expressed in terms of a small number of actual columns and/or actual rows of the data matrix. Since they are constructed from actual data elements, CUR decompositions are interpretable by practitioners of the field from which the data are drawn. Results We present an implementation to perform CUR matrix decompositions, in the form of a freely available, open source R-package called rCUR. This package will help users to perform CUR-based analysis on large-scale data, such as those obtained from different high-throughput technologies, in an interactive and exploratory manner. We show two examples that illustrate how CUR-based techniques make it possible to reduce significantly the number of probes, while at the same time maintaining major trends in data and keeping the same classification accuracy. Conclusions The package rCUR provides functions for the users to perform CUR-based matrix decompositions in the R environment. In gene expression studies, it gives an additional way of analysis of differential expression and discriminant gene selection based on the use of statistical leverage scores. These scores, which have been used historically in diagnostic regression
An analogue of Wagner's theorem for decompositions of matrix algebras
International Nuclear Information System (INIS)
Ivanov, D N
2004-01-01
Wagner's celebrated theorem states that a finite affine plane whose collineation group is transitive on lines is a translation plane. The notion of an orthogonal decomposition (OD) of a classically semisimple associative algebra introduced by the author allows one to draw an analogy between finite affine planes of order n and ODs of the matrix algebra M n (C) into a sum of subalgebras conjugate to the diagonal subalgebra. These ODs are called WP-decompositions and are equivalent to the well-known ODs of simple Lie algebras of type A n-1 into a sum of Cartan subalgebras. In this paper we give a detailed and improved proof of the analogue of Wagner's theorem for WP-decompositions of the matrix algebra of odd non-square order an outline of which was earlier published in a short note in 'Russian Math. Surveys' in 1994. In addition, in the framework of the theory of ODs of associative algebras, based on the method of idempotent bases, we obtain an elementary proof of the well-known Kostrikin-Tiep theorem on irreducible ODs of Lie algebras of type A n-1 in the case where n is a prime-power.
ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Keyes, David E.
2016-01-01
In this work the task is to use the available measurements to estimate unknown hyper-parameters (variance, smoothness parameter and covariance length) of the covariance function. We do it by maximizing the joint log-likelihood function. This is a non-convex and non-linear problem. To overcome cubic complexity in linear algebra, we approximate the discretised covariance function in the hierarchical (ℋ-) matrix format. The ℋ-matrix format has a log-linear computational cost and storage O(knlogn), where rank k is a small integer. On each iteration step of the optimization procedure the covariance matrix itself, its determinant and its Cholesky decomposition are recomputed within ℋ-matrix format. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters
Litvinenko, Alexander
2016-10-25
In this work the task is to use the available measurements to estimate unknown hyper-parameters (variance, smoothness parameter and covariance length) of the covariance function. We do it by maximizing the joint log-likelihood function. This is a non-convex and non-linear problem. To overcome cubic complexity in linear algebra, we approximate the discretised covariance function in the hierarchical (ℋ-) matrix format. The ℋ-matrix format has a log-linear computational cost and storage O(knlogn), where rank k is a small integer. On each iteration step of the optimization procedure the covariance matrix itself, its determinant and its Cholesky decomposition are recomputed within ℋ-matrix format. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
Decomposition of spectra in EPR dosimetry using the matrix method
International Nuclear Information System (INIS)
Sholom, S.V.; Chumak, V.V.
2003-01-01
The matrix method of EPR spectra decomposition is developed and adapted for routine application in retrospective EPR dosimetry with teeth. According to this method, the initial EPR spectra are decomposed (using methods of matrix algebra) into several reference components (reference matrices) that are specific for each material. Proposed procedure has been tested on the example of tooth enamel. Reference spectra were a spectrum of an empty sample tube and three standard signals of enamel (two at g=2.0045, both for the native signal and one at g perpendicular =2.0018, g parallel =1.9973 for the dosimetric signal). Values of dosimetric signals obtained using the given method have been compared with data obtained by manual manipulation of spectra, and good coincidence was observed. This allows considering the proposed method as potent for application in routine EPR dosimetry
Approximate Solution of LR Fuzzy Sylvester Matrix Equations
Directory of Open Access Journals (Sweden)
Xiaobin Guo
2013-01-01
Full Text Available The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.
S-AMP: Approximate Message Passing for General Matrix Ensembles
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2014-01-01
the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its......We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends...
A domian Decomposition Method for Transient Neutron Transport with Pomrning-Eddington Approximation
International Nuclear Information System (INIS)
Hendi, A.A.; Abulwafa, E.E.
2008-01-01
The time-dependent neutron transport problem is approximated using the Pomraning-Eddington approximation. This approximation is two-flux approximation that expands the angular intensity in terms of the energy density and the net flux. This approximation converts the integro-differential Boltzmann equation into two first order differential equations. The A domian decomposition method that used to solve the linear or nonlinear differential equations is used to solve the resultant two differential equations to find the neutron energy density and net flux, which can be used to calculate the neutron angular intensity through the Pomraning-Eddington approximation
Rules for matrix element evaluations in JWKB approximation
International Nuclear Information System (INIS)
Giler, S.
1990-01-01
Using the properties of the so-called fundamental solutions to the one-dimensional Schroedinger equation having Froeman and Froeman form the rules are formulated which allow one to evaluate matrix elements in the JWKB approximation and its generalizations. The rules apply to operators M(x, d/dx), M being polynomial functions of their arguments. The applicability of the rules depends on the properties of the so-called canonical indices introduced in this paper. The canonical indices are global characteristics of underlying Stokes graphs. If sufficiently small in comparison with unity they allow one to apply safely the JWKB approximation within the so-called ε-reduced canonical domains of a given Stokes graph. The Oth canonical index for the nth energy level Stokes graph corresponding to the harmonic oscillator potential is found to be ε CAN = 0.678/(2n+1). If the application of the rules is allowed then approximated matrix elements are obtained in an unambiguous way and with an accuracy controlled by corresponding canonical indices. Several examples of matrix elements are considered to illustrate how the rules should be used. Limitations to the rules are also discussed with the aid of suitably chosen examples. (author)
Gao, Pengzhi; Wang, Meng; Chow, Joe H.; Ghiocel, Scott G.; Fardanesh, Bruce; Stefopoulos, George; Razanousky, Michael P.
2016-11-01
This paper presents a new framework of identifying a series of cyber data attacks on power system synchrophasor measurements. We focus on detecting "unobservable" cyber data attacks that cannot be detected by any existing method that purely relies on measurements received at one time instant. Leveraging the approximate low-rank property of phasor measurement unit (PMU) data, we formulate the identification problem of successive unobservable cyber attacks as a matrix decomposition problem of a low-rank matrix plus a transformed column-sparse matrix. We propose a convex-optimization-based method and provide its theoretical guarantee in the data identification. Numerical experiments on actual PMU data from the Central New York power system and synthetic data are conducted to verify the effectiveness of the proposed method.
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe
2010-01-01
Roč. 5910, - (2010), s. 76-83 ISSN 0302-9743. [International Conference on Large-Scale Scientific Computations, LSSC 2009 /7./. Sozopol, 04.06.2009-08.06.2009] R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z30860518 Keywords : additive matrix * condition number * domain decomposition Subject RIV: BA - General Mathematics www.springerlink.com
Directory of Open Access Journals (Sweden)
Elias D. Nino-Ruiz
2017-07-01
Full Text Available In this paper, a matrix-free posterior ensemble Kalman filter implementation based on a modified Cholesky decomposition is proposed. The method works as follows: the precision matrix of the background error distribution is estimated based on a modified Cholesky decomposition. The resulting estimator can be expressed in terms of Cholesky factors which can be updated based on a series of rank-one matrices in order to approximate the precision matrix of the analysis distribution. By using this matrix, the posterior ensemble can be built by either sampling from the posterior distribution or using synthetic observations. Furthermore, the computational effort of the proposed method is linear with regard to the model dimension and the number of observed components from the model domain. Experimental tests are performed making use of the Lorenz-96 model. The results reveal that, the accuracy of the proposed implementation in terms of root-mean-square-error is similar, and in some cases better, to that of a well-known ensemble Kalman filter (EnKF implementation: the local ensemble transform Kalman filter. In addition, the results are comparable to those obtained by the EnKF with large ensemble sizes.
Ford, Neville J.; Connolly, Joseph A.
2009-07-01
We give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi-term fractional differential equations using the Caputo form of the fractional derivative. The schemes we compare are based on conversion of the original problem into a system of equations. We review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation.
Approximate L0 constrained Non-negative Matrix and Tensor Factorization
DEFF Research Database (Denmark)
Mørup, Morten; Madsen, Kristoffer Hougaard; Hansen, Lars Kai
2008-01-01
Non-negative matrix factorization (NMF), i.e. V = WH where both V, W and H are non-negative has become a widely used blind source separation technique due to its part based representation. The NMF decomposition is not in general unique and a part based representation not guaranteed. However...... constraint. In general, solving for a given L0 norm is an NP hard problem thus convex relaxatin to regularization by the L1 norm is often considered, i.e., minimizing ( 1/2 ||V-WHk||^2+lambda|H|_1). An open problem is to control the degree of sparsity imposed. We here demonstrate that a full regularization......, the L1 regularization strength lambda that best approximates a given L0 can be directly accessed and in effect used to control the sparsity of H. The MATLAB code for the NLARS algorithm is available for download....
Bryant, C. M.; Prudhomme, S.; Wildey, T.
2015-01-01
In this work, we investigate adaptive approaches to control errors in response surface approximations computed from numerical approximations of differential equations with uncertain or random data and coefficients. The adaptivity of the response surface approximation is based on a posteriori error estimation, and the approach relies on the ability to decompose the a posteriori error estimate into contributions from the physical discretization and the approximation in parameter space. Errors are evaluated in terms of linear quantities of interest using adjoint-based methodologies. We demonstrate that a significant reduction in the computational cost required to reach a given error tolerance can be achieved by refining the dominant error contributions rather than uniformly refining both the physical and stochastic discretization. Error decomposition is demonstrated for a two-dimensional flow problem, and adaptive procedures are tested on a convection-diffusion problem with discontinuous parameter dependence and a diffusion problem, where the diffusion coefficient is characterized by a 10-dimensional parameter space.
Directory of Open Access Journals (Sweden)
Xiao-Ying Qin
2014-01-01
Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.
Mussard, Bastien; Rocca, Dario; Jansen, Georg; Ángyán, János G
2016-05-10
Starting from the general expression for the ground state correlation energy in the adiabatic-connection fluctuation-dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case, the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed, and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental for improvement over direct RPA results.
International Nuclear Information System (INIS)
Song Lina; Wang Weiguo
2010-01-01
In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.
Energy Technology Data Exchange (ETDEWEB)
Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)
1996-12-31
An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.
HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.
Fan, Jianqing; Liao, Yuan; Mincheva, Martina
2011-01-01
The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.
Low-rank matrix approximation with manifold regularization.
Zhang, Zhenyue; Zhao, Keke
2013-07-01
This paper proposes a new model of low-rank matrix factorization that incorporates manifold regularization to the matrix factorization. Superior to the graph-regularized nonnegative matrix factorization, this new regularization model has globally optimal and closed-form solutions. A direct algorithm (for data with small number of points) and an alternate iterative algorithm with inexact inner iteration (for large scale data) are proposed to solve the new model. A convergence analysis establishes the global convergence of the iterative algorithm. The efficiency and precision of the algorithm are demonstrated numerically through applications to six real-world datasets on clustering and classification. Performance comparison with existing algorithms shows the effectiveness of the proposed method for low-rank factorization in general.
Decomposition of continuum {gamma}-ray spectra using synthesized response matrix
Energy Technology Data Exchange (ETDEWEB)
Jandel, M.; Morhac, M.; Kliman, J.; Krupa, L.; Matousek, V. E-mail: vladislav.matousek@savba.sk; Hamilton, J.H.; Ramayya, A.V
2004-01-01
The efficient methods of decomposition of {gamma}-ray spectra, based on the Gold algorithm, are presented. They use a response matrix of Gammasphere, which was obtained by synthesis of simulated and interpolated response functions using a new developed interpolation algorithm. The decomposition method has been applied to the measured spectra of {sup 152}Eu and {sup 56}Co. The results show a very effective removal of the background counts and their concentration into the corresponding photopeaks. The peak-to-total ratio in the spectra achieved after applying the decomposition method is in the interval 0.95-0.99. In addition, a new advanced algorithm of the 'boosted' decomposition has been proposed. In the spectra obtained after applying the boosted decomposition to the measured spectra, very narrow photopeaks are observed with the counts concentrated to several channels.
Structured decomposition design of partial Mueller matrix polarimeters.
Alenin, Andrey S; Scott Tyo, J
2015-07-01
Partial Mueller matrix polarimeters (pMMPs) are active sensing instruments that probe a scattering process with a set of polarization states and analyze the scattered light with a second set of polarization states. Unlike conventional Mueller matrix polarimeters, pMMPs do not attempt to reconstruct the entire Mueller matrix. With proper choice of generator and analyzer states, a subset of the Mueller matrix space can be reconstructed with fewer measurements than that of the full Mueller matrix polarimeter. In this paper we consider the structure of the Mueller matrix and our ability to probe it using a reduced number of measurements. We develop analysis tools that allow us to relate the particular choice of generator and analyzer polarization states to the portion of Mueller matrix space that the instrument measures, as well as develop an optimization method that is based on balancing the signal-to-noise ratio of the resulting instrument with the ability of that instrument to accurately measure a particular set of desired polarization components with as few measurements as possible. In the process, we identify 10 classes of pMMP systems, for which the space coverage is immediately known. We demonstrate the theory with a numerical example that designs partial polarimeters for the task of monitoring the damage state of a material as presented earlier by Hoover and Tyo [Appl. Opt.46, 8364 (2007)10.1364/AO.46.008364APOPAI1559-128X]. We show that we can reduce the polarimeter to making eight measurements while still covering the Mueller matrix subspace spanned by the objects.
Subspace-Based Noise Reduction for Speech Signals via Diagonal and Triangular Matrix Decompositions
DEFF Research Database (Denmark)
Hansen, Per Christian; Jensen, Søren Holdt
We survey the definitions and use of rank-revealing matrix decompositions in single-channel noise reduction algorithms for speech signals. Our algorithms are based on the rank-reduction paradigm and, in particular, signal subspace techniques. The focus is on practical working algorithms, using both...... diagonal (eigenvalue and singular value) decompositions and rank-revealing triangular decompositions (ULV, URV, VSV, ULLV and ULLIV). In addition we show how the subspace-based algorithms can be evaluated and compared by means of simple FIR filter interpretations. The algorithms are illustrated...... with working Matlab code and applications in speech processing....
International Nuclear Information System (INIS)
Mery, P.
1977-01-01
The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed
Zhang, Hongqin; Tian, Xiangjun
2018-04-01
Ensemble-based data assimilation methods often use the so-called localization scheme to improve the representation of the ensemble background error covariance (Be). Extensive research has been undertaken to reduce the computational cost of these methods by using the localized ensemble samples to localize Be by means of a direct decomposition of the local correlation matrix C. However, the computational costs of the direct decomposition of the local correlation matrix C are still extremely high due to its high dimension. In this paper, we propose an efficient local correlation matrix decomposition approach based on the concept of alternating directions. This approach is intended to avoid direct decomposition of the correlation matrix. Instead, we first decompose the correlation matrix into 1-D correlation matrices in the three coordinate directions, then construct their empirical orthogonal function decomposition at low resolution. This procedure is followed by the 1-D spline interpolation process to transform the above decompositions to the high-resolution grid. Finally, an efficient correlation matrix decomposition is achieved by computing the very similar Kronecker product. We conducted a series of comparison experiments to illustrate the validity and accuracy of the proposed local correlation matrix decomposition approach. The effectiveness of the proposed correlation matrix decomposition approach and its efficient localization implementation of the nonlinear least-squares four-dimensional variational assimilation are further demonstrated by several groups of numerical experiments based on the Advanced Research Weather Research and Forecasting model.
A cluster approximation for the transfer-matrix method
International Nuclear Information System (INIS)
Surda, A.
1990-08-01
A cluster approximation for the transfer-method is formulated. The calculation of the partition function of lattice models is transformed to a nonlinear mapping problem. The method yields the free energy, correlation functions and the phase diagrams for a large class of lattice models. The high accuracy of the method is exemplified by the calculation of the critical temperature of the Ising model. (author). 14 refs, 2 figs, 1 tab
Least-Squares Approximation of an Improper Correlation Matrix by a Proper One.
Knol, Dirk L.; ten Berge, Jos M. F.
1989-01-01
An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…
On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm
Czech Academy of Sciences Publication Activity Database
Liesen, J.; Tichý, Petr
2009-01-01
Roč. 31, č. 2 (2009), s. 853-863 ISSN 0895-4798 R&D Projects: GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : matrix approximation problems * polynomials in matrices * matrix functions * matrix 2-norm * GMRES * Arnoldi's method Subject RIV: BA - General Mathematics Impact factor: 2.411, year: 2009
Subspace-Based Noise Reduction for Speech Signals via Diagonal and Triangular Matrix Decompositions
DEFF Research Database (Denmark)
Hansen, Per Christian; Jensen, Søren Holdt
2007-01-01
We survey the definitions and use of rank-revealing matrix decompositions in single-channel noise reduction algorithms for speech signals. Our algorithms are based on the rank-reduction paradigm and, in particular, signal subspace techniques. The focus is on practical working algorithms, using both...... with working Matlab code and applications in speech processing....
A Taxonomy of Latent Structure Assumptions for Probability Matrix Decomposition Models.
Meulders, Michel; De Boeck, Paul; Van Mechelen, Iven
2003-01-01
Proposed a taxonomy of latent structure assumptions for probability matrix decomposition (PMD) that includes the original PMD model and a three-way extension of the multiple classification latent class model. Simulation study results show the usefulness of the taxonomy. (SLD)
Localized motion in random matrix decomposition of complex financial systems
Jiang, Xiong-Fei; Zheng, Bo; Ren, Fei; Qiu, Tian
2017-04-01
With the random matrix theory, we decompose the multi-dimensional time series of complex financial systems into a set of orthogonal eigenmode functions, which are classified into the market mode, sector mode, and random mode. In particular, the localized motion generated by the business sectors, plays an important role in financial systems. Both the business sectors and their impact on the stock market are identified from the localized motion. We clarify that the localized motion induces different characteristics of the time correlations for the stock-market index and individual stocks. With a variation of a two-factor model, we reproduce the return-volatility correlations of the eigenmodes.
Bienvenu, François; Akçay, Erol; Legendre, Stéphane; McCandlish, David M
2017-06-01
Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units. Copyright © 2017 Elsevier Inc. All rights reserved.
Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method
Directory of Open Access Journals (Sweden)
Hooman Fatoorehchi
2014-10-01
Full Text Available In this paper, we put forth a combined method for calculation of all real zeroes of a polynomial equation through the Adomian decomposition method equipped with a number of developed theorems from matrix algebra. These auxiliary theorems are associated with eigenvalues of matrices and enable convergence of the Adomian decomposition method toward different real roots of the target polynomial equation. To further improve the computational speed of our technique, a nonlinear convergence accelerator known as the Shanks transform has optionally been employed. For the sake of illustration, a number of numerical examples are given.
Bisetti, Fabrizio
2012-01-01
with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix
Least-squares approximation of an improper correlation matrix by a proper one
Knol, Dirk L.; ten Berge, Jos M.F.
1989-01-01
An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and
Near-lossless multichannel EEG compression based on matrix and tensor decompositions.
Dauwels, Justin; Srinivasan, K; Reddy, M Ramasubba; Cichocki, Andrzej
2013-05-01
A novel near-lossless compression algorithm for multichannel electroencephalogram (MC-EEG) is proposed based on matrix/tensor decomposition models. MC-EEG is represented in suitable multiway (multidimensional) forms to efficiently exploit temporal and spatial correlations simultaneously. Several matrix/tensor decomposition models are analyzed in view of efficient decorrelation of the multiway forms of MC-EEG. A compression algorithm is built based on the principle of “lossy plus residual coding,” consisting of a matrix/tensor decomposition-based coder in the lossy layer followed by arithmetic coding in the residual layer. This approach guarantees a specifiable maximum absolute error between original and reconstructed signals. The compression algorithm is applied to three different scalp EEG datasets and an intracranial EEG dataset, each with different sampling rate and resolution. The proposed algorithm achieves attractive compression ratios compared to compressing individual channels separately. For similar compression ratios, the proposed algorithm achieves nearly fivefold lower average error compared to a similar wavelet-based volumetric MC-EEG compression algorithm.
Random matrix theory and acoustic resonances in plates with an approximate symmetry
DEFF Research Database (Denmark)
Andersen, Anders Peter; Ellegaard, C.; Jackson, A.D.
2001-01-01
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum and...
Split-and-Combine Singular Value Decomposition for Large-Scale Matrix
Directory of Open Access Journals (Sweden)
Jengnan Tzeng
2013-01-01
Full Text Available The singular value decomposition (SVD is a fundamental matrix decomposition in linear algebra. It is widely applied in many modern techniques, for example, high- dimensional data visualization, dimension reduction, data mining, latent semantic analysis, and so forth. Although the SVD plays an essential role in these fields, its apparent weakness is the order three computational cost. This order three computational cost makes many modern applications infeasible, especially when the scale of the data is huge and growing. Therefore, it is imperative to develop a fast SVD method in modern era. If the rank of matrix is much smaller than the matrix size, there are already some fast SVD approaches. In this paper, we focus on this case but with the additional condition that the data is considerably huge to be stored as a matrix form. We will demonstrate that this fast SVD result is sufficiently accurate, and most importantly it can be derived immediately. Using this fast method, many infeasible modern techniques based on the SVD will become viable.
Directory of Open Access Journals (Sweden)
Norhasimah Mahiddin
2014-01-01
Full Text Available The modified decomposition method (MDM and homotopy perturbation method (HPM are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.
Grassmann integral and Balian–Brézin decomposition in Hartree–Fock–Bogoliubov matrix elements
Energy Technology Data Exchange (ETDEWEB)
Mizusaki, Takahiro, E-mail: mizusaki@isc.senshu-u.ac.jp [Institute of Natural Sciences, Senshu University, 3-8-1 Kanda-Jinbocho, Chiyoda-ku, Tokyo 101-8425 (Japan); Oi, Makito [Institute of Natural Sciences, Senshu University, 3-8-1 Kanda-Jinbocho, Chiyoda-ku, Tokyo 101-8425 (Japan); Chen, Fang-Qi [Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Sun, Yang [Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China)
2013-08-09
We present a new formula to calculate matrix elements of a general unitary operator with respect to Hartree–Fock–Bogoliubov states allowing multiple quasi-particle excitations. The Balian–Brézin decomposition of the unitary operator [R. Balian, E. Brézin, Il Nuovo Cimento B 64 (1969) 37] is employed in the derivation. We found that this decomposition is extremely suitable for an application of Fermion coherent state and Grassmann integrals in the quasi-particle basis. The resultant formula is compactly expressed in terms of the Pfaffian, and shows the similar bipartite structure to the formula that we have previously derived in the bare-particles basis [T. Mizusaki, M. Oi, Phys. Lett. B 715 (2012) 219].
Energy Technology Data Exchange (ETDEWEB)
Druskin, V.; Lee, Ping [Schlumberger-Doll Research, Ridgefield, CT (United States); Knizhnerman, L. [Central Geophysical Expedition, Moscow (Russian Federation)
1996-12-31
There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.
Litvinenko, Alexander
2017-01-01
and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters
Litvinenko, Alexander
2017-01-01
matrices. Therefore covariance matrices are approximated in the hierarchical ($\\H$-) matrix format with computational cost $\\mathcal{O}(k^2n \\log^2 n/p)$ and storage $\\mathcal{O}(kn \\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p
Multidisciplinary Product Decomposition and Analysis Based on Design Structure Matrix Modeling
DEFF Research Database (Denmark)
Habib, Tufail
2014-01-01
Design structure matrix (DSM) modeling in complex system design supports to define physical and logical configuration of subsystems, components, and their relationships. This modeling includes product decomposition, identification of interfaces, and structure analysis to increase the architectural...... interactions across subsystems and components. For this purpose, Cambridge advanced modeler (CAM) software tool is used to develop the system matrix. The analysis of the product (printer) architecture includes clustering, partitioning as well as structure analysis of the system. The DSM analysis is helpful...... understanding of the system. Since product architecture has broad implications in relation to product life cycle issues, in this paper, mechatronic product is decomposed into subsystems and components, and then, DSM model is developed to examine the extent of modularity in the system and to manage multiple...
Number-conserving random phase approximation with analytically integrated matrix elements
International Nuclear Information System (INIS)
Kyotoku, M.; Schmid, K.W.; Gruemmer, F.; Faessler, A.
1990-01-01
In the present paper a number conserving random phase approximation is derived as a special case of the recently developed random phase approximation in general symmetry projected quasiparticle mean fields. All the occurring integrals induced by the number projection are performed analytically after writing the various overlap and energy matrices in the random phase approximation equation as polynomials in the gauge angle. In the limit of a large number of particles the well-known pairing vibration matrix elements are recovered. We also present a new analytically number projected variational equation for the number conserving pairing problem
Leone, Frank A., Jr.
2015-01-01
A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.
Implementation of the CCGM approximation for surface diffraction using Wigner R-matrix theory
International Nuclear Information System (INIS)
Lauderdale, J.G.; McCurdy, C.W.
1983-01-01
The CCGM approximation for surface scattering proposed by Cabrera, Celli, Goodman, and Manson [Surf. Sci. 19, 67 (1970)] is implemented for realistic surface interaction potentials using Wigner R-matrix theory. The resulting procedure is highly efficient computationally and is in no way limited to hard wall or purely repulsive potentials. Comparison is made with the results of close-coupling calculations of other workers which include the same diffraction channels in order to fairly evaluate the CCGM approximation which is an approximation to the coupled channels Lippman--Schwinger equation for the T matrix. The shapes of selective adsorption features, whether maxima or minima, in the scattered intensity are well represented in this approach for cases in which the surface corrugation is not too strong
Calculations of the properties of superconducting alloys via the average T-matrix approximation
International Nuclear Information System (INIS)
Chatterjee, P.
1980-01-01
The theoretical formula of McMillan, modified via the multiple-scattering theory by Gomersall and Gyorffy, has been very successful in computing the electron-phonon coupling constant (lambda) and the transition temperature (Tsub(c)) of many superconducting elements and compounds. For disordered solids, such as substitutional alloys, however, this theory fails because of the breakdown of the translational symmetry used in the multiple-scattering theory. Under these conditions the problem can still be solved if the t-matrix is averaged in the random phase approximation (average T-matrix approximation). Gomersall and Gyorffy's expression is reformulated for lambda in the random phase approximation. This theory is applied to calculate lambda and Tsub(c) of the binary substitutional NbMo alloy system at different concentrations. The results appear to be in fair agreement with experiments. (author)
International Nuclear Information System (INIS)
Barrios, Dolores; Lopez, Guillermo L; Martinez-Finkelshtein, A; Torrano, Emilio
1999-01-01
The approximability of the resolvent of an operator induced by a band matrix by the resolvents of its finite-dimensional sections is studied. For bounded perturbations of self-adjoint matrices a positive result is obtained. The convergence domain of the sequence of resolvents can be described in this case in terms of matrices involved in the representation. This result is applied to tridiagonal complex matrices to establish conditions for the convergence of Chebyshev continued fractions on sets in the complex domain. In the particular case of compact perturbations this result is improved and a connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is established
2017-09-27
100 times larger for the minimal Krylov subspace. 0 5 10 15 20 25 Krylov subspace dimension 10-2 10-1 100 101 102 103 104 jjĜ ¡ 1 jj F SVD...approximation Kn (G;u(0) ) 0 5 10 15 20 25 Krylov subspace dimension 10-2 10-1 100 101 102 103 104 jjx jj fo r m in x jjĜ x ¡ bjj SVD approximation Kn (G;u(0
Real-time dynamics of matrix quantum mechanics beyond the classical approximation
Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas
2018-03-01
We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.
A rational approximation to Reich-Moore collision matrix of non-fissile nuclides
International Nuclear Information System (INIS)
Devan, K.; Keshavamurthy, R.S.
1999-01-01
The cross sections of many important nuclides are represented in Reich-Moore (RM) formalism in the recent American Evaluated Nuclear Data file, ENDF/B-VI. Processing of cross sections with RM resonance parameters is much more difficult than the other multilevel formalisms such as MLBW and Adler-Adler. In this paper, we derive a rational approximation to the RM collision matrix in the vicinity of a resonance. This simplifies the cross section processing. The energy range of the validity of this approximation in the vicinity of a resonance is also derived. Choosing Ni 58 as an example, results of our approximation for a non-fissile nuclide are given for two typical s-wave resonances. Our rational approximation method is found to work with good accuracies in the vicinity of resonances
Matrix model approximations of fuzzy scalar field theories and their phase diagrams
Energy Technology Data Exchange (ETDEWEB)
Tekel, Juraj [Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, Bratislava, 842 48 (Slovakia)
2015-12-29
We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.
A S-matrix-like approximation in the charged particle scattering by the hydrogen atom
International Nuclear Information System (INIS)
Mignaco, J.A.; Tort, A.C.
1979-01-01
The Born approximation for charged particle scattering by the hydrogen atom is unfit at low energies. From a S-matrix-like consideration on the dominance of the neighbour singularities, the calculation of other contributions is suggested. The inclusion of bound states is made, following Eden's and his colaborators' ideas, which are described by their interest and likeness with procedures in the intermediate energy physics. (Author) [pt
Czech Academy of Sciences Publication Activity Database
Náprstek, Jiří; Fischer, Cyril
2017-01-01
Roč. 180, February (2017), s. 3-12 ISSN 0045-7949 R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : Dynamic Stiffness Matrix * lambda matrices * self-adjoint operators * approximation in frequency domain * Wittrick-Williams algorithm Subject RIV: JM - Building Engineering OBOR OECD: Construction engineering, Municipal and structural engineering Impact factor: 2.847, year: 2016 http://www.sciencedirect.com/science/article/pii/S0045794916310495
A Class of Weighted Low Rank Approximation of the Positive Semidefinite Hankel Matrix
Directory of Open Access Journals (Sweden)
Jianchao Bai
2015-01-01
Full Text Available We consider the weighted low rank approximation of the positive semidefinite Hankel matrix problem arising in signal processing. By using the Vandermonde representation, we firstly transform the problem into an unconstrained optimization problem and then use the nonlinear conjugate gradient algorithm with the Armijo line search to solve the equivalent unconstrained optimization problem. Numerical examples illustrate that the new method is feasible and effective.
Litvinenko, Alexander
2017-09-26
The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Mat\\\\\\'ern covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\H$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.
Litvinenko, Alexander
2017-09-24
The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Mat\\\\\\'ern covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\mathcal{H}$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.
Maitra, Rahul; Nakajima, Takahito
2017-11-28
We present an accurate single reference coupled cluster theory in which the conventional Fock operator matrix is suitably dressed to simulate the effect of triple and higher excitations within a singles and doubles framework. The dressing thus invoked originates from a second-order perturbative approximation of a similarity transformed Hamiltonian and induces higher rank excitations through local renormalization of individual occupied and unoccupied orbital lines. Such a dressing is able to recover a significant amount of correlation effects beyond singles and doubles approximation, but only with an economic n 5 additional cost. Due to the inclusion of higher rank excitations via the Fock matrix dressing, this method is a natural improvement over conventional coupled cluster theory with singles and doubles approximation, and this method would be demonstrated via applications on some challenging systems. This highly promising scheme has a conceptually simple structure which is also easily generalizable to a multi-reference coupled cluster scheme for treating strong degeneracy. We shall demonstrate that this method is a natural lowest order perturbative approximation to the recently developed iterative n-body excitation inclusive coupled cluster singles and doubles scheme [R. Maitra et al., J. Chem. Phys. 147, 074103 (2017)].
van Aggelen, Helen; Yang, Yang; Yang, Weitao
2014-05-14
Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H2, and eliminates delocalization errors in H2(+) and other single-bond systems. It gives surprisingly good non-bonded interaction energies--competitive with the ph-RPA--with the correct R(-6) asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations.
International Nuclear Information System (INIS)
Aggelen, Helen van; Yang, Yang; Yang, Weitao
2014-01-01
Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H 2 , and eliminates delocalization errors in H 2 + and other single-bond systems. It gives surprisingly good non-bonded interaction energies – competitive with the ph-RPA – with the correct R −6 asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components. © 2012 Copyright Taylor and Francis Group, LLC.
Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation
International Nuclear Information System (INIS)
Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi
2015-01-01
Highlights: • We propose a new numerical solution of matrix exponential in burn-up depletion calculations. • The depletion calculation with extremely short half-lived nuclides can be done numerically stable with this method. • The computational time is shorter than the other conventional methods. - Abstract: Nuclear fuel burn-up depletion calculations are essential to compute the nuclear fuel composition transition. In the burn-up calculations, the matrix exponential method has been widely used. In the present paper, we propose a new numerical solution of the matrix exponential, a Mini-Max Polynomial Approximation (MMPA) method. This method is numerically stable for burn-up matrices with extremely short half-lived nuclides as the Chebyshev Rational Approximation Method (CRAM), and it has several advantages over CRAM. We also propose a multi-step calculation, a computational time reduction scheme of the MMPA method, which can perform simultaneously burn-up calculations with several time periods. The applicability of these methods has been theoretically and numerically proved for general burn-up matrices. The numerical verification has been performed, and it has been shown that these methods have high precision equivalent to CRAM
Correlated random-phase approximation from densities and in-medium matrix elements
Energy Technology Data Exchange (ETDEWEB)
Trippel, Richard; Roth, Robert [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany)
2016-07-01
The random-phase approximation (RPA) as well as the second RPA (SRPA) are established tools for the study of collective excitations in nuclei. Addressing the well known lack of correlations, we derived a universal framework for a fully correlated RPA based on the use of one- and two-body densities. We apply densities from coupled cluster theory and investigate the impact of correlations. As an alternative approach to correlations we use matrix elements transformed via in-medium similarity renormalization group (IM-SRG) in combination with RPA and SRPA. We find that within SRPA the use of IM-SRG matrix elements leads to the disappearance of instabilities of low-lying states. For the calculations we use normal-ordered two- plus three-body interactions derived from chiral effective field theory. We apply different Hamiltonians to a number of doubly-magic nuclei and calculate electric transition strengths.
Luenser, Arne; Schurkus, Henry F; Ochsenfeld, Christian
2017-04-11
A reformulation of the random phase approximation within the resolution-of-the-identity (RI) scheme is presented, that is competitive to canonical molecular orbital RI-RPA already for small- to medium-sized molecules. For electronically sparse systems drastic speedups due to the reduced scaling behavior compared to the molecular orbital formulation are demonstrated. Our reformulation is based on two ideas, which are independently useful: First, a Cholesky decomposition of density matrices that reduces the scaling with basis set size for a fixed-size molecule by one order, leading to massive performance improvements. Second, replacement of the overlap RI metric used in the original AO-RPA by an attenuated Coulomb metric. Accuracy is significantly improved compared to the overlap metric, while locality and sparsity of the integrals are retained, as is the effective linear scaling behavior.
Time dependent mean field approximation to the many-body S-matrix
International Nuclear Information System (INIS)
Alhassid, Y.; Koonin, S.E.
1980-01-01
Time-dependent Hartree-Fock (TDHF) calculations are a good description of some inclusive properties of deep inelastic heavy-ion collisions. The first steps toward a mean-field theory that approximates specific elements of the many-body S matrix are presented. A many-body system with pairwise interactions excited by an external, time-dependent one-body field is considered. The methods are used to solve the forced Lipkin model. The moduli of elastic and excitation amplitudes are plotted. 3 figures
Sparse and smooth canonical correlation analysis through rank-1 matrix approximation
Aïssa-El-Bey, Abdeldjalil; Seghouane, Abd-Krim
2017-12-01
Canonical correlation analysis (CCA) is a well-known technique used to characterize the relationship between two sets of multidimensional variables by finding linear combinations of variables with maximal correlation. Sparse CCA and smooth or regularized CCA are two widely used variants of CCA because of the improved interpretability of the former and the better performance of the later. So far, the cross-matrix product of the two sets of multidimensional variables has been widely used for the derivation of these variants. In this paper, two new algorithms for sparse CCA and smooth CCA are proposed. These algorithms differ from the existing ones in their derivation which is based on penalized rank-1 matrix approximation and the orthogonal projectors onto the space spanned by the two sets of multidimensional variables instead of the simple cross-matrix product. The performance and effectiveness of the proposed algorithms are tested on simulated experiments. On these results, it can be observed that they outperform the state of the art sparse CCA algorithms.
Directory of Open Access Journals (Sweden)
Tzu-Chien Hsiao
2013-11-01
Full Text Available Excitation-emission matrix (EEM fluorescence spectroscopy is a noninvasive method for tissue diagnosis and has become important in clinical use. However, the intrinsic characterization of EEM fluorescence remains unclear. Photobleaching and the complexity of the chemical compounds make it difficult to distinguish individual compounds due to overlapping features. Conventional studies use principal component analysis (PCA for EEM fluorescence analysis, and the relationship between the EEM features extracted by PCA and diseases has been examined. The spectral features of different tissue constituents are not fully separable or clearly defined. Recently, a non-stationary method called multi-dimensional ensemble empirical mode decomposition (MEEMD was introduced; this method can extract the intrinsic oscillations on multiple spatial scales without loss of information. The aim of this study was to propose a fluorescence spectroscopy system for EEM measurements and to describe a method for extracting the intrinsic characteristics of EEM by MEEMD. The results indicate that, although PCA provides the principal factor for the spectral features associated with chemical compounds, MEEMD can provide additional intrinsic features with more reliable mapping of the chemical compounds. MEEMD has the potential to extract intrinsic fluorescence features and improve the detection of biochemical changes.
Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction
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.
Ahmed, Raheel; Edwards, Michael G.; Lamine, Sadok; Huisman, Bastiaan A. H.; Pal, Mayur
2017-11-01
Two novel control-volume methods are presented for flow in fractured media, and involve coupling the control-volume distributed multi-point flux approximation (CVD-MPFA) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation for simulation on unstructured grids; (i) involving hybrid grids and (ii) a lower dimensional fracture model. Flow is governed by Darcy's law together with mass conservation both in the matrix and the fractures, where large discontinuities in permeability tensors can occur. Finite-volume FPS schemes are more robust than the earlier CVD-MPFA triangular pressure support (TPS) schemes for problems involving highly anisotropic homogeneous and heterogeneous full-tensor permeability fields. We use a cell-centred hybrid-grid method, where fractures are modelled by lower-dimensional interfaces between matrix cells in the physical mesh but expanded to equi-dimensional cells in the computational domain. We present a simple procedure to form a consistent hybrid-grid locally for a dual-cell. We also propose a novel hybrid-grid for intersecting fractures, for the FPS method, which reduces the condition number of the global linear system and leads to larger time steps for tracer transport. The transport equation for tracer flow is coupled with the pressure equation and provides flow parameter assessment of the fracture models. Transport results obtained via TPS and FPS hybrid-grid formulations are compared with the corresponding results of fine-scale explicit equi-dimensional formulations. The results show that the hybrid-grid FPS method applies to general full-tensor fields and provides improved robust approximations compared to the hybrid-grid TPS method for fractured domains, for both weakly anisotropic permeability fields and very strong anisotropic full-tensor permeability fields where the TPS scheme exhibits spurious oscillations. The hybrid-grid FPS formulation is extended to compressible flow and the
International Nuclear Information System (INIS)
Perez-Alvarez, R.; Rodriguez-Coppola, H.; Lopez-Gondar, J.; Izquierdo, M.L.
1987-11-01
We develop the quasiclassical approximation for the effective Hamiltonians describing nonhomogeneous systems and we deduce the wave function, the applicability conditions and the connection rules around the turning points. Based on the transfer matrix (TM) formalism we obtain expressions for the transmission coefficient of multiple barriers, the energy levels of multiple wells and the quasistationary levels of a well open by one, and by the two sides. The dispersion relation of a periodic potential profile with variable mass problem is also given. We discuss resonant tunneling for a system of multiple barriers. The transmission coefficient of such a barrier is maximum at energies close to the levels of the inner well when the end barriers are high enough and symmetric. (author). 20 refs, 1 fig
Knol, Dirk L.; ten Berge, Jos M.F.
1987-01-01
An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based on a solution for C. I. Mosier's oblique Procrustes rotation problem offered by J. M. F. ten Berge and K. Nevels (1977).
Energy Technology Data Exchange (ETDEWEB)
Chen, H.; Li, B.; Zhang, B. [Chinese Academy of Sciences, Taiyuan (China). Institute of Coal Chemistry
1999-07-01
The thermal decomposition and reduction behaviour of pure pyrite crystals were studied under nitrogen and hydrogen atmospheres. Decomposition of pyrite in coal during pyrolysis and hydropyrolysis, and the behaviour of organic sulphur, are discussed. Temperature and pressure effects are considered. 7 refs., 6 figs., 1 tab.
Chew, Peter A; Bader, Brett W
2012-10-16
A technique for information retrieval includes parsing a corpus to identify a number of wordform instances within each document of the corpus. A weighted morpheme-by-document matrix is generated based at least in part on the number of wordform instances within each document of the corpus and based at least in part on a weighting function. The weighted morpheme-by-document matrix separately enumerates instances of stems and affixes. Additionally or alternatively, a term-by-term alignment matrix may be generated based at least in part on the number of wordform instances within each document of the corpus. At least one lower rank approximation matrix is generated by factorizing the weighted morpheme-by-document matrix and/or the term-by-term alignment matrix.
Directory of Open Access Journals (Sweden)
Yasuhiro Nakamura
2012-07-01
Full Text Available The present study introduces the four-component scattering power decomposition (4-CSPD algorithm with rotation of covariance matrix, and presents an experimental proof of the equivalence between the 4-CSPD algorithms based on rotation of covariance matrix and coherency matrix. From a theoretical point of view, the 4-CSPD algorithms with rotation of the two matrices are identical. Although it seems obvious, no experimental evidence has yet been presented. In this paper, using polarimetric synthetic aperture radar (POLSAR data acquired by Phased Array L-band SAR (PALSAR on board of Advanced Land Observing Satellite (ALOS, an experimental proof is presented to show that both algorithms indeed produce identical results.
Niederegger, Senta; Schermer, Julia; Höfig, Juliane; Mall, Gita
2015-01-01
Estimating time of death of buried human bodies is a very difficult task. Casper's rule from 1860 is still widely used which illustrates the lack of suitable methods. In this case study excavations in an arbor revealed the crouching body of a human being, dressed only in boxer shorts and socks. Witnesses were not able to generate a concise answer as to when the person in question was last seen alive; the pieces of information opened a window of 2-6 weeks for the possible time of death. To determine the post mortem interval (PMI) an experiment using a pig carcass was conducted to set up a decomposition matrix. Fitting the autopsy findings of the victim into the decomposition matrix yielded a time of death estimation of 2-3 weeks. This time frame was later confirmed by a new witness. The authors feel confident that a widespread conduction of decomposition matrices using pig carcasses can lead to a great increase of experience and knowledge in PMI estimation of buried bodies and will eventually lead to applicable new methods. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
Decomposing tensors with structured matrix factors reduces to rank-1 approximations
DEFF Research Database (Denmark)
Comon, Pierre; Sørensen, Mikael; Tsigaridas, Elias
2010-01-01
Tensor decompositions permit to estimate in a deterministic way the parameters in a multi-linear model. Applications have been already pointed out in antenna array processing and digital communications, among others, and are extremely attractive provided some diversity at the receiver is availabl....... As opposed to the widely used ALS algorithm, non-iterative algorithms are proposed in this paper to compute the required tensor decomposition into a sum of rank-1 terms, when some factor matrices enjoy some structure, such as block-Hankel, triangular, band, etc....
Zhang, Du; Su, Neil Qiang; Yang, Weitao
2017-07-20
The GW self-energy, especially G 0 W 0 based on the particle-hole random phase approximation (phRPA), is widely used to study quasiparticle (QP) energies. Motivated by the desirable features of the particle-particle (pp) RPA compared to the conventional phRPA, we explore the pp counterpart of GW, that is, the T-matrix self-energy, formulated with the eigenvectors and eigenvalues of the ppRPA matrix. We demonstrate the accuracy of the T-matrix method for molecular QP energies, highlighting the importance of the pp channel for calculating QP spectra.
Performance of Scattering Matrix Decomposition and Color Spaces for Synthetic Aperture Radar Imagery
2010-03-01
Color Spaces and Synthetic Aperture Radar (SAR) Multicolor Imaging. 15 2.3.1 Colorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.2...III. Decomposition Techniques on SAR Polarimetry and Colorimetry applied to SAR Imagery...space polarimetric SAR systems. Colorimetry is also introduced in this chapter, presenting the fundamentals of the RGB and CMY color spaces, defined for
International Nuclear Information System (INIS)
Zhang, L.
1981-08-01
A method based on the tight-binding approximation is developed to calculate the electron-phonon matrix element for the disordered transition metals. With the method as a basis the experimental Tsub(c) data of the amorphous transition metal superconductors are re-analysed. Some comments on the superconductivity of the disordered materials are given
van den Akker, Jeroen; Pistea, Adrian; Bakker, Erik N. T. P.; VanBavel, Ed
2008-01-01
Microvascular remodeling is known to depend on cellular interactions with matrix tissue. However, it is difficult to study the role of specific cells or matrix elements in an in vivo setting. The aim of this study is to develop an automated technique that can be employed to obtain and analyze local
Wang, Lu; Albera, Laurent; Kachenoura, Amar; Shu, Huazhong; Senhadji, Lotfi
2014-12-01
Semi-symmetric three-way arrays are essential tools in blind source separation (BSS) particularly in independent component analysis (ICA). These arrays can be built by resorting to higher order statistics of the data. The canonical polyadic (CP) decomposition of such semi-symmetric three-way arrays allows us to identify the so-called mixing matrix, which contains the information about the intensities of some latent source signals present in the observation channels. In addition, in many applications, such as the magnetic resonance spectroscopy (MRS), the columns of the mixing matrix are viewed as relative concentrations of the spectra of the chemical components. Therefore, the two loading matrices of the three-way array, which are equal to the mixing matrix, are nonnegative. Most existing CP algorithms handle the symmetry and the nonnegativity separately. Up to now, very few of them consider both the semi-nonnegativity and the semi-symmetry structure of the three-way array. Nevertheless, like all the methods based on line search, trust region strategies, and alternating optimization, they appear to be dependent on initialization, requiring in practice a multi-initialization procedure. In order to overcome this drawback, we propose two new methods, called [InlineEquation not available: see fulltext.] and [InlineEquation not available: see fulltext.], to solve the problem of CP decomposition of semi-nonnegative semi-symmetric three-way arrays. Firstly, we rewrite the constrained optimization problem as an unconstrained one. In fact, the nonnegativity constraint of the two symmetric modes is ensured by means of a square change of variable. Secondly, a Jacobi-like optimization procedure is adopted because of its good convergence property. More precisely, the two new methods use LU and QR matrix factorizations, respectively, which consist in formulating high-dimensional optimization problems into several sequential polynomial and rational subproblems. By using both LU
International Nuclear Information System (INIS)
Yuan, Dong-hai; Guo, Xu-jing; Wen, Li; He, Lian-sheng; Wang, Jing-gang; Li, Jun-qi
2015-01-01
Fluorescence excitation-emission matrix (EEM) spectra coupled with parallel factor analysis (PARAFAC) was used to characterize dissolved organic matter (DOM) derived from macrophyte decomposition, and to study its complexation with Cu (II) and Cd (II). Both the protein-like and the humic-like components showed a marked quenching effect by Cu (II). Negligible quenching effects were found for Cd (II) by components 1, 5 and 6. The stability constants and the fraction of the binding fluorophores for humic-like components and Cu (II) can be influenced by macrophyte decomposition of various weight gradients in aquatic plants. Macrophyte decomposition within the scope of the appropriate aquatic phytomass can maximize the stability constant of DOM-metal complexes. A large amount of organic matter was introduced into the aquatic environment by macrophyte decomposition, suggesting that the potential risk of DOM as a carrier of heavy metal contamination in macrophytic lakes should not be ignored. - Highlights: • Macrophyte decomposition increases fluorescent DOM components in the upper sediment. • Protein-like components are quenched or enhanced by adding Cu (II) and Cd (II). • Macrophyte decomposition DOM can impact the affinity of Cu (II) and Cd (II). • The log K M and f values showed a marked change due to macrophyte decomposition. • Macrophyte decomposition can maximize the stability constant of DOM-Cu (II) complexes. - Macrophyte decomposition DOM can influence on the binding affinity of metal ions in macrophytic lakes
International Nuclear Information System (INIS)
Chan, C.K.; Hoffman, D.K.; Evans, J.W.
1985-01-01
Local, i.e., multiplicative, operators satisfy well-known linear factorization relations wherein matrix elements (between states associated with a complete set of wave functions) can be obtained as a linear combination of those out of the ground state (the input data). Analytic derivation of factorization relations for general state input data results in singular integral expressions for the coefficients, which can, however, be regularized using consistency conditions between matrix elements out of a single (nonground) state. Similar results hold for suitable ''symmetry class'' averaged matrix elements where the symmetry class projection operators are ''complete.'' In several cases where the wave functions or projection operators incorporate orthogonal polynomial dependence, we show that the ground state factorization relations have a simplified structure allowing an alternative derivation of the general factorization relations via an infinite matrix inversion procedure. This form is shown to have some advantages over previous versions. In addition, this matrix inversion procedure obtains all consistency conditions (which is not always the case from regularization of singular integrals)
Directory of Open Access Journals (Sweden)
W. Łenski
2015-01-01
Full Text Available The results generalizing some theorems on N, pnE, γ summability are shown. The same degrees of pointwise approximation as in earlier papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results, the estimation on norm approximation is derived. Some special cases as corollaries are also formulated.
Zhang, Haicang; Gao, Yujuan; Deng, Minghua; Wang, Chao; Zhu, Jianwei; Li, Shuai Cheng; Zheng, Wei-Mou; Bu, Dongbo
2016-03-25
Strategies for correlation analysis in protein contact prediction often encounter two challenges, namely, the indirect coupling among residues, and the background correlations mainly caused by phylogenetic biases. While various studies have been conducted on how to disentangle indirect coupling, the removal of background correlations still remains unresolved. Here, we present an approach for removing background correlations via low-rank and sparse decomposition (LRS) of a residue correlation matrix. The correlation matrix can be constructed using either local inference strategies (e.g., mutual information, or MI) or global inference strategies (e.g., direct coupling analysis, or DCA). In our approach, a correlation matrix was decomposed into two components, i.e., a low-rank component representing background correlations, and a sparse component representing true correlations. Finally the residue contacts were inferred from the sparse component of correlation matrix. We trained our LRS-based method on the PSICOV dataset, and tested it on both GREMLIN and CASP11 datasets. Our experimental results suggested that LRS significantly improves the contact prediction precision. For example, when equipped with the LRS technique, the prediction precision of MI and mfDCA increased from 0.25 to 0.67 and from 0.58 to 0.70, respectively (Top L/10 predicted contacts, sequence separation: 5 AA, dataset: GREMLIN). In addition, our LRS technique also consistently outperforms the popular denoising technique APC (average product correction), on both local (MI_LRS: 0.67 vs MI_APC: 0.34) and global measures (mfDCA_LRS: 0.70 vs mfDCA_APC: 0.67). Interestingly, we found out that when equipped with our LRS technique, local inference strategies performed in a comparable manner to that of global inference strategies, implying that the application of LRS technique narrowed down the performance gap between local and global inference strategies. Overall, our LRS technique greatly facilitates
Analytic approximation to the largest eigenvalue distribution of a white Wishart matrix
CSIR Research Space (South Africa)
Vlok, JD
2012-08-14
Full Text Available offers largely simplified computation and provides statistics such as the mean value and region of support of the largest eigenvalue distribution. Numeric results from the literature are compared with the approximation and Monte Carlo simulation results...
International Nuclear Information System (INIS)
Jowzani-Moghaddam, A.
1981-01-01
An integral transport method of calculating the geometrical shadowing factor in multiregion annular cells for infinite closely packed lattices in cylindrical geometry is developed. This analytical method has been programmed in the TPGS code. This method is based upon a consideration of the properties of the integral transport method for a nonuniform body, which together with Bonalumi's approximations allows the determination of the approximate multiregion collision probability matrix for infinite closely packed lattices with sufficient accuracy. The multiregion geometrical shadowing factors have been calculated for variations in fuel pin annular segment rings in a geometry of annular cells. These shadowing factors can then be used in the calculation of neutron transport from one annulus to another in an infinite lattice. The result of this new geometrical shadowing and collision probability matrix are compared with the Dancoff-Ginsburg correction and the probability matrix using constant shadowing on Yankee fuel elements in an infinite lattice. In these cases the Dancoff-Ginsburg correction factor and collision probability matrix using constant shadowing are in difference by at most 6.2% and 6%, respectively
The coupled-channel T-matrix: its lowest-order Born + Lanczos approximants
International Nuclear Information System (INIS)
Znojil, M.
1995-01-01
Three iterative methods of solution of the Lippmann-Schwinger equations (viz., the method of continued fractions by J.Horacek and T.Sasakawa), its Born-remainder modification and a coupled-channel matrix-continued-fraction generalization are all interpreted as special cases of a common iterative matrix prescription. Firstly, in terms of certain asymmetric projectors P≠P + , we re-derive the three particular older methods as different realizations of the well-known Lanczos inversion. Then, a generalized iteration method is proposed as a Born-like re-arrangement of any intermediate Lanczos iteration step. A maximal flexibility is achieved in the formalism which might compete with the standard Pade re-summations in practice. Its first few truncations are listed, therefore. 26 refs., 1 tab
Direct formulation to Cholesky decomposition of a general nonsingular correlation matrix.
Madar, Vered
2015-08-01
We present two novel and explicit parametrizations of Cholesky factor of a nonsingular correlation matrix. One that uses semi-partial correlation coefficients, and a second that utilizes differences between the successive ratios of two determinants. To each, we offer a useful application.
International Nuclear Information System (INIS)
Zimmerman, R.W.; Bodvarsson, G.S.
1994-03-01
A theoretical study is presented of the effect of matrix block shape and matrix block size distribution on liquid imbibition and solute absorption in a fractured rock mass. It is shown that the behavior of an individual irregularly-shaped matrix block can be modeled with reasonable accuracy by using the results for a spherical matrix block, if one uses an effective radius a = 3V/A, where V is the volume of the block and A is its surface area. In the early-time regime of matrix imbibition, it is shown that a collection of blocks of different sizes can be modeled by a single equivalent block, with an equivalent radius of -1 > -1 , where the average is taken on a volumetrically-weighted basis. In an intermediate time regime, it is shown for the case where the radii are normally distributed that the equivalent radius is reasonably well approximated by the mean radius . In the long-time limit, where no equivalent radius can be rigorously defined, an asymptotic expression is derived for the cumulative diffusion as a function of the mean and the standard deviation of the radius distribution function
Relativistic atomic matrix elements of rq for arbitrary states in the quantum-defect approximation
International Nuclear Information System (INIS)
Owono Owono, L.C.; Owona Angue, M.L.C.; Kwato Njock, M.G.; Oumarou, B.
2004-01-01
Recurrence relations used in the calculation of matrix elements of r q for arbitrary q and states of the relativistic one-electron atom with a point-like ionic core are obtained with Dirac and quasirelativistic effective radial Hamiltonians. The phenomenological and supersymmetry-inspired quantum-defect approaches introduced in previous works to model the electron-core interactions are employed. The formulas worked out on the basis of a hypervirial inspired method may be viewed as a generalization to off-diagonal cases of our recently reported results on the evaluation of expectation values of r q
International Nuclear Information System (INIS)
Krishnaswami, Govind S.
2006-01-01
Large-N multi-matrix loop equations are formulated as quadratic difference equations in concatenation of gluon correlations. Though non-linear, they involve highest rank correlations linearly. They are underdetermined in many cases. Additional linear equations for gluon correlations, associated to symmetries of action and measure are found. Loop equations aren't differential equations as they involve left annihilation, which doesn't satisfy the Leibnitz rule with concatenation. But left annihilation is a derivation of the commutative shuffle product. Moreover shuffle and concatenation combine to define a bialgebra. Motivated by deformation quantization, we expand concatenation around shuffle in powers of q, whose physical value is 1. At zeroth order the loop equations become quadratic PDEs in the shuffle algebra. If the variation of the action is linear in iterated commutators of left annihilations, these quadratic PDEs linearize by passage to shuffle reciprocal of correlations. Remarkably, this is true for regularized versions of the Yang-Mills, Chern-Simons and Gaussian actions. But the linear equations are underdetermined just as the loop equations were. For any particular solution, the shuffle reciprocal is explicitly inverted to get the zeroth order gluon correlations. To go beyond zeroth order, we find a Poisson bracket on the shuffle algebra and associative q-products interpolating between shuffle and concatenation. This method, and a complementary one of deforming annihilation rather than product are shown to give over and underestimates for correlations of a gaussian matrix model
Orbital-Optimized MP3 and MP2.5 with Density-Fitting and Cholesky Decomposition Approximations.
Bozkaya, Uğur
2016-03-08
Efficient implementations of the orbital-optimized MP3 and MP2.5 methods with the density-fitting (DF-OMP3 and DF-OMP2.5) and Cholesky decomposition (CD-OMP3 and CD-OMP2.5) approaches are presented. The DF/CD-OMP3 and DF/CD-OMP2.5 methods are applied to a set of alkanes to compare the computational cost with the conventional orbital-optimized MP3 (OMP3) [Bozkaya J. Chem. Phys. 2011, 135, 224103] and the orbital-optimized MP2.5 (OMP2.5) [Bozkaya and Sherrill J. Chem. Phys. 2014, 141, 204105]. Our results demonstrate that the DF-OMP3 and DF-OMP2.5 methods provide considerably lower computational costs than OMP3 and OMP2.5. Further application results show that the orbital-optimized methods are very helpful for the study of open-shell noncovalent interactions, aromatic bond dissociation energies, and hydrogen transfer reactions. We conclude that the DF-OMP3 and DF-OMP2.5 methods are very promising for molecular systems with challenging electronic structures.
Das, Nandan Kumar; Dey, Rajib; Chakraborty, Semanti; Panigrahi, Prasanta K.; Meglinski, Igor; Ghosh, Nirmalya
2018-04-01
A number of tissue-like disordered media exhibit local anisotropy of scattering in the scaling behavior. Scaling behavior contains wealth of fractal or multifractal properties. We demonstrate that the spatial dielectric fluctuations in a sample of biological tissue exhibit multifractal anisotropy. Multifractal anisotropy encoded in the wavelength variation of the light scattering Mueller matrix and manifesting as an intriguing spectral diattenuation effect. We developed an inverse method for the quantitative assessment of the multifractal anisotropy. The method is based on the processing of relevant Mueller matrix elements in Fourier domain by using Born approximation, followed by the multifractal analysis. The approach promises for probing subtle micro-structural changes in biological tissues associated with the cancer and precancer, as well as for non-destructive characterization of a wide range of scattering materials.
Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation
Yokota, Rio
2018-01-03
There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. The first half of this paper has the form of a survey paper, to achieve the former objective. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.
Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation
Yokota, Rio; Ibeid, Huda; Keyes, David E.
2018-01-01
There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. The first half of this paper has the form of a survey paper, to achieve the former objective. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.
Efficient GW calculations using eigenvalue-eigenvector decomposition of the dielectric matrix
Nguyen, Huy-Viet; Pham, T. Anh; Rocca, Dario; Galli, Giulia
2011-03-01
During the past 25 years, the GW method has been successfully used to compute electronic quasi-particle excitation spectra of a variety of materials. It is however a computationally intensive technique, as it involves summations over occupied and empty electronic states, to evaluate both the Green function (G) and the dielectric matrix (DM) entering the expression of the screened Coulomb interaction (W). Recent developments have shown that eigenpotentials of DMs can be efficiently calculated without any explicit evaluation of empty states. In this work, we will present a computationally efficient approach to the calculations of GW spectra by combining a representation of DMs in terms of its eigenpotentials and a recently developed iterative algorithm. As a demonstration of the efficiency of the method, we will present calculations of the vertical ionization potentials of several systems. Work was funnded by SciDAC-e DE-FC02-06ER25777.
International Nuclear Information System (INIS)
Holas, A.; Cinal, M.
2005-01-01
Three approximate exchange potentials of high accuracy v x Y (r), Y=A,B,C, for the density-functional theory applications are obtained by replacing the matrix elements of the exact potential between the Kohn-Sham (KS) orbitals with such elements of the Fock exchange operator (within the virtual-occupied subset only) in three representations found for any local potential. A common identity is the base of these representations. The potential v x C happens to be the same as that derived by Harbola and Sahni, and v x A as that derived by Gritsenko and Baerends, and Della Sala and Goerling. The potentials obtained can be expressed in terms of occupied KS orbitals only. At large r, their asymptotic form -1/r is the same as that of the exact potential. The high quality of these three approximations is demonstrated by direct comparison with the exact potential and using various consistency tests. A common root established for the three approximations could be helpful in finding new and better approximations via modification of identities employed in the present investigation
Lorin, E.; Yang, X.; Antoine, X.
2016-06-01
The paper is devoted to develop efficient domain decomposition methods for the linear Schrödinger equation beyond the semiclassical regime, which does not carry a small enough rescaled Planck constant for asymptotic methods (e.g. geometric optics) to produce a good accuracy, but which is too computationally expensive if direct methods (e.g. finite difference) are applied. This belongs to the category of computing middle-frequency wave propagation, where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy. Motivated by recent works of the authors on absorbing boundary conditions (Antoine et al. (2014) [13] and Yang and Zhang (2014) [43]), we introduce Semiclassical Schwarz Waveform Relaxation methods (SSWR), which are seamless integrations of semiclassical approximation to Schwarz Waveform Relaxation methods. Two versions are proposed respectively based on Herman-Kluk propagation and geometric optics, and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods.
Harris, W F
1989-03-01
The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.
International Nuclear Information System (INIS)
Aoyama, Tatsumi; Kawai, Hikaru; Shibusa, Yuuichiro
2006-01-01
We investigate the origin of our four-dimensional space-time by considering dynamical aspects of the IIB matrix model using the improved mean field approximation. Previous works have focused on the specific choices of configurations as ansatz which preserve SO(d) rotational symmetry. In this report, an extended ansatz is proposed and examined up to a third-order approximation which includes both the SO(4) ansatz and the SO(7) ansatz in their respective limits. From the solutions of the self-consistency condition represented by the extrema of the free energy of the system, it is found that some of the solutions found in the SO(4) or SO(7) ansatz disappear in the extended ansatz. This implies that the extension of ansatz can be used to distinguish stable solutions from unstable solutions. It is also found that there is a non-trivial accumulation of extrema including the SO(4)-preserving solution, which may lead to the formation of a plateau. (author)
Directory of Open Access Journals (Sweden)
Shuan-Feng Zhao
2017-01-01
Full Text Available In the driver fatigue monitoring technology, the essence is to capture and analyze the driver behavior information, such as eyes, face, heart, and EEG activity during driving. However, ECG and EEG monitoring are limited by the installation electrodes and are not commercially available. The most common fatigue detection method is the analysis of driver behavior, that is, to determine whether the driver is tired by recording and analyzing the behavior characteristics of steering wheel and brake. The driver usually adjusts his or her actions based on the observed road conditions. Obviously the road path information is directly contained in the vehicle driving state; if you want to judge the driver’s driving behavior by vehicle driving status information, the first task is to remove the road information from the vehicle driving state data. Therefore, this paper proposes an effective intrinsic mode function selection method for the approximate entropy of empirical mode decomposition considering the characteristics of the frequency distribution of road and vehicle information and the unsteady and nonlinear characteristics of the driver closed-loop driving system in vehicle driving state data. The objective is to extract the effective component of the driving behavior information and to weaken the road information component. Finally the effectiveness of the proposed method is verified by simulating driving experiments.
Tarai, Madhumita; Kumar, Keshav; Divya, O.; Bairi, Partha; Mishra, Kishor Kumar; Mishra, Ashok Kumar
2017-09-01
The present work compares the dissimilarity and covariance based unsupervised chemometric classification approaches by taking the total synchronous fluorescence spectroscopy data sets acquired for the cumin and non-cumin based herbal preparations. The conventional decomposition method involves eigenvalue-eigenvector analysis of the covariance of the data set and finds the factors that can explain the overall major sources of variation present in the data set. The conventional approach does this irrespective of the fact that the samples belong to intrinsically different groups and hence leads to poor class separation. The present work shows that classification of such samples can be optimized by performing the eigenvalue-eigenvector decomposition on the pair-wise dissimilarity matrix.
Tarai, Madhumita; Kumar, Keshav; Divya, O; Bairi, Partha; Mishra, Kishor Kumar; Mishra, Ashok Kumar
2017-09-05
The present work compares the dissimilarity and covariance based unsupervised chemometric classification approaches by taking the total synchronous fluorescence spectroscopy data sets acquired for the cumin and non-cumin based herbal preparations. The conventional decomposition method involves eigenvalue-eigenvector analysis of the covariance of the data set and finds the factors that can explain the overall major sources of variation present in the data set. The conventional approach does this irrespective of the fact that the samples belong to intrinsically different groups and hence leads to poor class separation. The present work shows that classification of such samples can be optimized by performing the eigenvalue-eigenvector decomposition on the pair-wise dissimilarity matrix. Copyright © 2017 Elsevier B.V. All rights reserved.
Cotrufo, M Francesca; Wallenstein, Matthew D; Boot, Claudia M; Denef, Karolien; Paul, Eldor
2013-04-01
The decomposition and transformation of above- and below-ground plant detritus (litter) is the main process by which soil organic matter (SOM) is formed. Yet, research on litter decay and SOM formation has been largely uncoupled, failing to provide an effective nexus between these two fundamental processes for carbon (C) and nitrogen (N) cycling and storage. We present the current understanding of the importance of microbial substrate use efficiency and C and N allocation in controlling the proportion of plant-derived C and N that is incorporated into SOM, and of soil matrix interactions in controlling SOM stabilization. We synthesize this understanding into the Microbial Efficiency-Matrix Stabilization (MEMS) framework. This framework leads to the hypothesis that labile plant constituents are the dominant source of microbial products, relative to input rates, because they are utilized more efficiently by microbes. These microbial products of decomposition would thus become the main precursors of stable SOM by promoting aggregation and through strong chemical bonding to the mineral soil matrix. © 2012 Blackwell Publishing Ltd.
DEFF Research Database (Denmark)
Yang, Yukay
I consider multivariate (vector) time series models in which the error covariance matrix may be time-varying. I derive a test of constancy of the error covariance matrix against the alternative that the covariance matrix changes over time. I design a new family of Lagrange-multiplier tests against...... to consider multivariate volatility modelling....
International Nuclear Information System (INIS)
Jasielska, A.; Wiktor, S.
1977-01-01
The table of two-particle matrix elements calculated according to the formalism of MSDI approximation for the orbits 1fsub(7/2), 2psub(3/2), 2psub(1/2) and 1fsub(5/2) and published previously is now supplemented by inclusion of the 1gsub(9/2) orbit. (author)
Energy Technology Data Exchange (ETDEWEB)
Martini, Till; Uwer, Peter [Humboldt-Universität zu Berlin, Institut für Physik,Newtonstraße 15, 12489 Berlin (Germany)
2015-09-14
In this article we illustrate how event weights for jet events can be calculated efficiently at next-to-leading order (NLO) accuracy in QCD. This is a crucial prerequisite for the application of the Matrix Element Method in NLO. We modify the recombination procedure used in jet algorithms, to allow a factorisation of the phase space for the real corrections into resolved and unresolved regions. Using an appropriate infrared regulator the latter can be integrated numerically. As illustration, we reproduce differential distributions at NLO for two sample processes. As further application and proof of concept, we apply the Matrix Element Method in NLO accuracy to the mass determination of top quarks produced in e{sup +}e{sup −} annihilation. This analysis is relevant for a future Linear Collider. We observe a significant shift in the extracted mass depending on whether the Matrix Element Method is used in leading or next-to-leading order.
International Nuclear Information System (INIS)
Martini, Till; Uwer, Peter
2015-01-01
In this article we illustrate how event weights for jet events can be calculated efficiently at next-to-leading order (NLO) accuracy in QCD. This is a crucial prerequisite for the application of the Matrix Element Method in NLO. We modify the recombination procedure used in jet algorithms, to allow a factorisation of the phase space for the real corrections into resolved and unresolved regions. Using an appropriate infrared regulator the latter can be integrated numerically. As illustration, we reproduce differential distributions at NLO for two sample processes. As further application and proof of concept, we apply the Matrix Element Method in NLO accuracy to the mass determination of top quarks produced in e"+e"− annihilation. This analysis is relevant for a future Linear Collider. We observe a significant shift in the extracted mass depending on whether the Matrix Element Method is used in leading or next-to-leading order.
Sanz, J M; Saiz, J M; González, F; Moreno, F
2011-07-20
In this research, the polar decomposition (PD) method is applied to experimental Mueller matrices (MMs) measured on two-dimensional microstructured surfaces. Polarization information is expressed through a set of parameters of easier physical interpretation. It is shown that evaluating the first derivative of the retardation parameter, δ, a clear indication of the presence of defects either built on or dug in the scattering flat surface (a silicon wafer in our case) can be obtained. Although the rule of thumb thus obtained is established through PD, it can be easily implemented on conventional surface polarimetry. These results constitute an example of the capabilities of the PD approach to MM analysis, and show a direct application in surface characterization. © 2011 Optical Society of America
Moraes Rêgo, Patrícia Helena; Viana da Fonseca Neto, João; Ferreira, Ernesto M.
2015-08-01
The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor-critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.
Cioslowski, Jerzy; Strasburger, Krzysztof
2018-04-01
Electronic properties of several states of the five- and six-electron harmonium atoms are obtained from large-scale calculations employing explicitly correlated basis functions. The high accuracy of the computed energies (including their components), natural spinorbitals, and their occupation numbers makes them suitable for testing, calibration, and benchmarking of approximate formalisms of quantum chemistry and solid state physics. In the case of the five-electron species, the availability of the new data for a wide range of the confinement strengths ω allows for confirmation and generalization of the previously reached conclusions concerning the performance of the presently known approximations for the electron-electron repulsion energy in terms of the 1-matrix that are at heart of the density matrix functional theory (DMFT). On the other hand, the properties of the three low-lying states of the six-electron harmonium atom, computed at ω = 500 and ω = 1000, uncover deficiencies of the 1-matrix functionals not revealed by previous studies. In general, the previously published assessment of the present implementations of DMFT being of poor accuracy is found to hold. Extending the present work to harmonically confined systems with even more electrons is most likely counterproductive as the steep increase in computational cost required to maintain sufficient accuracy of the calculated properties is not expected to be matched by the benefits of additional information gathered from the resulting benchmarks.
Physically asymptotic Hartree-Fock stationary-phase approximant to the many-body S-matrix
International Nuclear Information System (INIS)
Griffin, J.J.; Dworzecka, M.
1982-01-01
The Asymptotic Hartree-Fock Approximant replaces the physically non-asymptotic (and dynamically nontrivial) external translation of the FISP result with the asymptotic and dynamically trivial translational evolution of Dirac-TDHF by adding an explicit restriction upon the acceptable channel states. It is therefore preferable under the principle of commensurability, which judges the expected output of physical descriptions in terms of the physical assumptions they incorporate. Further insight into the relationship between the TDSHF and FISP methods will reward careful comparison of the respective expressions, in specific cases
International Nuclear Information System (INIS)
Tyynelae, Jani; Nousiainen, Timo; Goeke, Sabine; Muinonen, Karri
2009-01-01
We study the applicability of the discrete-dipole approximation by modeling centimeter (C-band) radar echoes for hydrometeors, and compare the results to exact theories. We use ice and water particles of various shapes with varying water-content to investigate how the backscattering, extinction, and absorption cross sections change as a function of particle radius. We also compute radar parameters, such as the differential reflectivity, the linear depolarization ratio, and the copolarized correlation coefficient. We find that using discrete-dipole approximation (DDA) to model pure ice and pure water particles at the C-band, is a lot more accurate than particles containing both ice and water. For coated particles, a large grid-size is recommended so that the coating is modeled adequately. We also find that the absorption cross section is significantly less accurate than the scattering and backscattering cross sections. The accuracy of DDA can be increased by increasing the number of dipoles, but also by using the filtered coupled dipole-option for the polarizability. This halved the relative errors in cross sections.
2017-01-01
In the current era of big data, the amount of data available is continuously increasing. Both the number and types of samples, or features, are on the rise. The mixing of distinct features often makes interpretation more difficult. However, separate analysis of individual types requires subsequent integration. A tensor is a useful framework to deal with distinct types of features in an integrated manner without mixing them. On the other hand, tensor data is not easy to obtain since it requires the measurements of huge numbers of combinations of distinct features; if there are m kinds of features, each of which has N dimensions, the number of measurements needed are as many as Nm, which is often too large to measure. In this paper, I propose a new method where a tensor is generated from individual features without combinatorial measurements, and the generated tensor was decomposed back to matrices, by which unsupervised feature extraction was performed. In order to demonstrate the usefulness of the proposed strategy, it was applied to synthetic data, as well as three omics datasets. It outperformed other matrix-based methodologies. PMID:28841719
Clustering via Kernel Decomposition
DEFF Research Database (Denmark)
Have, Anna Szynkowiak; Girolami, Mark A.; Larsen, Jan
2006-01-01
Methods for spectral clustering have been proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this work it is proposed that the affinity matrix is created based on the elements of a non-parametric density estimator. This matrix is then decomposed to obtain...... posterior probabilities of class membership using an appropriate form of nonnegative matrix factorization. The troublesome selection of hyperparameters such as kernel width and number of clusters can be obtained using standard cross-validation methods as is demonstrated on a number of diverse data sets....
Directory of Open Access Journals (Sweden)
Ichitaro Yamazaki
2015-01-01
of their low-rank properties. To compute a low-rank approximation of a dense matrix, in this paper, we study the performance of QR factorization with column pivoting or with restricted pivoting on multicore CPUs with a GPU. We first propose several techniques to reduce the postprocessing time, which is required for restricted pivoting, on a modern CPU. We then examine the potential of using a GPU to accelerate the factorization process with both column and restricted pivoting. Our performance results on two eight-core Intel Sandy Bridge CPUs with one NVIDIA Kepler GPU demonstrate that using the GPU, the factorization time can be reduced by a factor of more than two. In addition, to study the performance of our implementations in practice, we integrate them into a recently developed software StruMF which algebraically exploits such low-rank structures for solving a general sparse linear system of equations. Our performance results for solving Poisson's equations demonstrate that the proposed techniques can significantly reduce the preconditioner construction time of StruMF on the CPUs, and the construction time can be further reduced by 10%–50% using the GPU.
Genton, Marc G.
2017-09-07
We present a hierarchical decomposition scheme for computing the n-dimensional integral of multivariate normal probabilities that appear frequently in statistics. The scheme exploits the fact that the formally dense covariance matrix can be approximated by a matrix with a hierarchical low rank structure. It allows the reduction of the computational complexity per Monte Carlo sample from O(n2) to O(mn+knlog(n/m)), where k is the numerical rank of off-diagonal matrix blocks and m is the size of small diagonal blocks in the matrix that are not well-approximated by low rank factorizations and treated as dense submatrices. This hierarchical decomposition leads to substantial efficiencies in multivariate normal probability computations and allows integrations in thousands of dimensions to be practical on modern workstations.
Genton, Marc G.; Keyes, David E.; Turkiyyah, George
2017-01-01
We present a hierarchical decomposition scheme for computing the n-dimensional integral of multivariate normal probabilities that appear frequently in statistics. The scheme exploits the fact that the formally dense covariance matrix can be approximated by a matrix with a hierarchical low rank structure. It allows the reduction of the computational complexity per Monte Carlo sample from O(n2) to O(mn+knlog(n/m)), where k is the numerical rank of off-diagonal matrix blocks and m is the size of small diagonal blocks in the matrix that are not well-approximated by low rank factorizations and treated as dense submatrices. This hierarchical decomposition leads to substantial efficiencies in multivariate normal probability computations and allows integrations in thousands of dimensions to be practical on modern workstations.
EISPACK, Subroutines for Eigenvalues, Eigenvectors, Matrix Operations
International Nuclear Information System (INIS)
Garbow, Burton S.; Cline, A.K.; Meyering, J.
1993-01-01
: Driver subroutine for a nonsym. tridiag. matrix; SVD: Singular value decomposition of rectangular matrix; TINVIT: Find some vectors of sym. tridiag. matrix; TQLRAT: Find all values of sym. tridiag. matrix; TQL1: Find all values of sym. tridiag. matrix; TQL2: Find all values/vectors of sym. tridiag. matrix; TRBAK1: Back transform vectors of matrix formed by TRED1; TRBAK3: Back transform vectors of matrix formed by TRED3; TRED1: Reduce sym. matrix to sym. tridiag. matrix; TRED2: Reduce sym. matrix to sym. tridiag. matrix; TRED3: Reduce sym. packed matrix to sym. tridiag. matrix; TRIDIB: Find some values of sym. tridiag. matrix; TSTURM: Find some values/vectors of sym. tridiag. matrix. 2 - Method of solution: Almost all the algorithms used in EISPACK are based on similarity transformations. Similarity transformations based on orthogonal and unitary matrices are particularly attractive from a numerical point of view because they do not magnify any errors present in the input data or introduced during the computation. Most of the techniques employed are constructive realizations of variants of Schur's theorem, 'Any matrix can be triangularized by a unitary similarity transformation'. It is usually not possible to compute Schur's transformation with a finite number of rational arithmetic operations. Instead, the algorithms employ a potentially infinite sequence of similarity transformations in which the resultant matrix approaches an upper triangular matrix. The sequence is terminated when all of the sub-diagonal elements of the resulting matrix are less than the roundoff errors involved in the computation. The diagonal elements are then the desired approximations to the eigenvalues of the original matrix and the corresponding eigenvectors can be calculated. Special algorithms deal with symmetric matrices. QR, LR, QL, rational QR, bisection QZ, and inverse iteration methods are used
Decomposing Nekrasov decomposition
Energy Technology Data Exchange (ETDEWEB)
Morozov, A. [ITEP,25 Bolshaya Cheremushkinskaya, Moscow, 117218 (Russian Federation); Institute for Information Transmission Problems,19-1 Bolshoy Karetniy, Moscow, 127051 (Russian Federation); National Research Nuclear University MEPhI,31 Kashirskoe highway, Moscow, 115409 (Russian Federation); Zenkevich, Y. [ITEP,25 Bolshaya Cheremushkinskaya, Moscow, 117218 (Russian Federation); National Research Nuclear University MEPhI,31 Kashirskoe highway, Moscow, 115409 (Russian Federation); Institute for Nuclear Research of Russian Academy of Sciences,6a Prospekt 60-letiya Oktyabrya, Moscow, 117312 (Russian Federation)
2016-02-16
AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions — this is immediately seen when conformal block is represented in the form of a matrix model. However, the q-deformation of the same block has a deeper decomposition — into a sum over a quadruple of Young diagrams of a product of four topological vertices. We analyze the interplay between these two decompositions, their properties and their generalization to multi-point conformal blocks. In the latter case we explain how Dotsenko-Fateev all-with-all (star) pair “interaction” is reduced to the quiver model nearest-neighbor (chain) one. We give new identities for q-Selberg averages of pairs of generalized Macdonald polynomials. We also translate the slicing invariance of refined topological strings into the language of conformal blocks and interpret it as abelianization of generalized Macdonald polynomials.
Decomposing Nekrasov decomposition
International Nuclear Information System (INIS)
Morozov, A.; Zenkevich, Y.
2016-01-01
AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions — this is immediately seen when conformal block is represented in the form of a matrix model. However, the q-deformation of the same block has a deeper decomposition — into a sum over a quadruple of Young diagrams of a product of four topological vertices. We analyze the interplay between these two decompositions, their properties and their generalization to multi-point conformal blocks. In the latter case we explain how Dotsenko-Fateev all-with-all (star) pair “interaction” is reduced to the quiver model nearest-neighbor (chain) one. We give new identities for q-Selberg averages of pairs of generalized Macdonald polynomials. We also translate the slicing invariance of refined topological strings into the language of conformal blocks and interpret it as abelianization of generalized Macdonald polynomials.
On low-rank updates to the singular value and Tucker decompositions
Energy Technology Data Exchange (ETDEWEB)
O' Hara, M J
2009-10-06
The singular value decomposition is widely used in signal processing and data mining. Since the data often arrives in a stream, the problem of updating matrix decompositions under low-rank modification has been widely studied. Brand developed a technique in 2006 that has many advantages. However, the technique does not directly approximate the updated matrix, but rather its previous low-rank approximation added to the new update, which needs justification. Further, the technique is still too slow for large information processing problems. We show that the technique minimizes the change in error per update, so if the error is small initially it remains small. We show that an updating algorithm for large sparse matrices should be sub-linear in the matrix dimension in order to be practical for large problems, and demonstrate a simple modification to the original technique that meets the requirements.
Note on Symplectic SVD-Like Decomposition
Directory of Open Access Journals (Sweden)
AGOUJIL Said
2016-02-01
Full Text Available The aim of this study was to introduce a constructive method to compute a symplectic singular value decomposition (SVD-like decomposition of a 2n-by-m rectangular real matrix A, based on symplectic refectors.This approach used a canonical Schur form of skew-symmetric matrix and it allowed us to compute eigenvalues for the structured matrices as Hamiltonian matrix JAA^T.
Directory of Open Access Journals (Sweden)
Batakliev Todor
2014-06-01
Full Text Available Catalytic ozone decomposition is of great significance because ozone is a toxic substance commonly found or generated in human environments (aircraft cabins, offices with photocopiers, laser printers, sterilizers. Considerable work has been done on ozone decomposition reported in the literature. This review provides a comprehensive summary of the literature, concentrating on analysis of the physico-chemical properties, synthesis and catalytic decomposition of ozone. This is supplemented by a review on kinetics and catalyst characterization which ties together the previously reported results. Noble metals and oxides of transition metals have been found to be the most active substances for ozone decomposition. The high price of precious metals stimulated the use of metal oxide catalysts and particularly the catalysts based on manganese oxide. It has been determined that the kinetics of ozone decomposition is of first order importance. A mechanism of the reaction of catalytic ozone decomposition is discussed, based on detailed spectroscopic investigations of the catalytic surface, showing the existence of peroxide and superoxide surface intermediates
Decomposition methods for unsupervised learning
DEFF Research Database (Denmark)
Mørup, Morten
2008-01-01
This thesis presents the application and development of decomposition methods for Unsupervised Learning. It covers topics from classical factor analysis based decomposition and its variants such as Independent Component Analysis, Non-negative Matrix Factorization and Sparse Coding...... methods and clustering problems is derived both in terms of classical point clustering but also in terms of community detection in complex networks. A guiding principle throughout this thesis is the principle of parsimony. Hence, the goal of Unsupervised Learning is here posed as striving for simplicity...... in the decompositions. Thus, it is demonstrated how a wide range of decomposition methods explicitly or implicitly strive to attain this goal. Applications of the derived decompositions are given ranging from multi-media analysis of image and sound data, analysis of biomedical data such as electroencephalography...
High Performance Polar Decomposition on Distributed Memory Systems
Sukkari, Dalal E.; Ltaief, Hatem; Keyes, David E.
2016-01-01
The polar decomposition of a dense matrix is an important operation in linear algebra. It can be directly calculated through the singular value decomposition (SVD) or iteratively using the QR dynamically-weighted Halley algorithm (QDWH). The former
Matrix with Prescribed Eigenvectors
Ahmad, Faiz
2011-01-01
It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…
Chao, T.T.; Sanzolone, R.F.
1992-01-01
Sample decomposition is a fundamental and integral step in the procedure of geochemical analysis. It is often the limiting factor to sample throughput, especially with the recent application of the fast and modern multi-element measurement instrumentation. The complexity of geological materials makes it necessary to choose the sample decomposition technique that is compatible with the specific objective of the analysis. When selecting a decomposition technique, consideration should be given to the chemical and mineralogical characteristics of the sample, elements to be determined, precision and accuracy requirements, sample throughput, technical capability of personnel, and time constraints. This paper addresses these concerns and discusses the attributes and limitations of many techniques of sample decomposition along with examples of their application to geochemical analysis. The chemical properties of reagents as to their function as decomposition agents are also reviewed. The section on acid dissolution techniques addresses the various inorganic acids that are used individually or in combination in both open and closed systems. Fluxes used in sample fusion are discussed. The promising microwave-oven technology and the emerging field of automation are also examined. A section on applications highlights the use of decomposition techniques for the determination of Au, platinum group elements (PGEs), Hg, U, hydride-forming elements, rare earth elements (REEs), and multi-elements in geological materials. Partial dissolution techniques used for geochemical exploration which have been treated in detail elsewhere are not discussed here; nor are fire-assaying for noble metals and decomposition techniques for X-ray fluorescence or nuclear methods be discussed. ?? 1992.
Multilinear operators for higher-order decompositions.
Energy Technology Data Exchange (ETDEWEB)
Kolda, Tamara Gibson
2006-04-01
We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to concisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outer-products of the columns of N matrices and allows a divorce from a matricized representation and a very concise expression of the PARAFAC decomposition. We explore the properties of the Tucker and Kruskal operators independently of the related decompositions. Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.
DEFF Research Database (Denmark)
Petersen, Kaare Brandt; Pedersen, Michael Syskind
Matrix identities, relations and approximations. A desktop reference for quick overview of mathematics of matrices.......Matrix identities, relations and approximations. A desktop reference for quick overview of mathematics of matrices....
Singular value decomposition for collaborative filtering on a GPU
Kato, Kimikazu; Hosino, Tikara
2010-06-01
A collaborative filtering predicts customers' unknown preferences from known preferences. In a computation of the collaborative filtering, a singular value decomposition (SVD) is needed to reduce the size of a large scale matrix so that the burden for the next phase computation will be decreased. In this application, SVD means a roughly approximated factorization of a given matrix into smaller sized matrices. Webb (a.k.a. Simon Funk) showed an effective algorithm to compute SVD toward a solution of an open competition called "Netflix Prize". The algorithm utilizes an iterative method so that the error of approximation improves in each step of the iteration. We give a GPU version of Webb's algorithm. Our algorithm is implemented in the CUDA and it is shown to be efficient by an experiment.
Singular value decomposition for collaborative filtering on a GPU
International Nuclear Information System (INIS)
Kato, Kimikazu; Hosino, Tikara
2010-01-01
A collaborative filtering predicts customers' unknown preferences from known preferences. In a computation of the collaborative filtering, a singular value decomposition (SVD) is needed to reduce the size of a large scale matrix so that the burden for the next phase computation will be decreased. In this application, SVD means a roughly approximated factorization of a given matrix into smaller sized matrices. Webb (a.k.a. Simon Funk) showed an effective algorithm to compute SVD toward a solution of an open competition called 'Netflix Prize'. The algorithm utilizes an iterative method so that the error of approximation improves in each step of the iteration. We give a GPU version of Webb's algorithm. Our algorithm is implemented in the CUDA and it is shown to be efficient by an experiment.
Lie bialgebras with triangular decomposition
International Nuclear Information System (INIS)
Andruskiewitsch, N.; Levstein, F.
1992-06-01
Lie bialgebras originated in a triangular decomposition of the underlying Lie algebra are discussed. The explicit formulas for the quantization of the Heisenberg Lie algebra and some motion Lie algebras are given, as well as the algebra of rational functions on the quantum Heisenberg group and the formula for the universal R-matrix. (author). 17 refs
Biclustering via Sparse Singular Value Decomposition
Lee, Mihee
2010-02-16
Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.
Biomass pyrolysis: Thermal decomposition mechanisms of furfural and benzaldehyde
Vasiliou, AnGayle K.; Kim, Jong Hyun; Ormond, Thomas K.; Piech, Krzysztof M.; Urness, Kimberly N.; Scheer, Adam M.; Robichaud, David J.; Mukarakate, Calvin; Nimlos, Mark R.; Daily, John W.; Guan, Qi; Carstensen, Hans-Heinrich; Ellison, G. Barney
2013-09-01
The thermal decompositions of furfural and benzaldehyde have been studied in a heated microtubular flow reactor. The pyrolysis experiments were carried out by passing a dilute mixture of the aromatic aldehydes (roughly 0.1%-1%) entrained in a stream of buffer gas (either He or Ar) through a pulsed, heated SiC reactor that is 2-3 cm long and 1 mm in diameter. Typical pressures in the reactor are 75-150 Torr with the SiC tube wall temperature in the range of 1200-1800 K. Characteristic residence times in the reactor are 100-200 μsec after which the gas mixture emerges as a skimmed molecular beam at a pressure of approximately 10 μTorr. Products were detected using matrix infrared absorption spectroscopy, 118.2 nm (10.487 eV) photoionization mass spectroscopy and resonance enhanced multiphoton ionization. The initial steps in the thermal decomposition of furfural and benzaldehyde have been identified. Furfural undergoes unimolecular decomposition to furan + CO: C4H3O-CHO (+ M) → CO + C4H4O. Sequential decomposition of furan leads to the production of HC≡CH, CH2CO, CH3C≡CH, CO, HCCCH2, and H atoms. In contrast, benzaldehyde resists decomposition until higher temperatures when it fragments to phenyl radical plus H atoms and CO: C6H5CHO (+ M) → C6H5CO + H → C6H5 + CO + H. The H atoms trigger a chain reaction by attacking C6H5CHO: H + C6H5CHO → [C6H6CHO]* → C6H6 + CO + H. The net result is the decomposition of benzaldehyde to produce benzene and CO.
Separable decompositions of bipartite mixed states
Li, Jun-Li; Qiao, Cong-Feng
2018-04-01
We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8:1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then, we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.
Eigenvalue Decomposition-Based Modified Newton Algorithm
Directory of Open Access Journals (Sweden)
Wen-jun Wang
2013-01-01
Full Text Available When the Hessian matrix is not positive, the Newton direction may not be the descending direction. A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction. The new searching direction is always the descending direction. The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively. Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.
Bodewig, E
1959-01-01
Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Schmidt, Wolfgang M
1980-01-01
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.
Indecomposability of polynomials via Jacobian matrix
International Nuclear Information System (INIS)
Cheze, G.; Najib, S.
2007-12-01
Uni-multivariate decomposition of polynomials is a special case of absolute factorization. Recently, thanks to the Ruppert's matrix some effective results about absolute factorization have been improved. Here we show that with a jacobian matrix we can get sharper bounds for the special case of uni-multivariate decomposition. (author)
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Belitsky, A. V.
2017-10-01
The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang-Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4) matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.
Directory of Open Access Journals (Sweden)
A.V. Belitsky
2017-10-01
Full Text Available The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang–Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4 matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.
International Nuclear Information System (INIS)
Dongarra, J.J.
1982-01-01
SICEDR is a FORTRAN subroutine for improving the accuracy of a computed real eigenvalue and improving or computing the associated eigenvector. It is first used to generate information during the determination of the eigenvalues by the Schur decomposition technique. In particular, the Schur decomposition technique results in an orthogonal matrix Q and an upper quasi-triangular matrix T, such that A = QTQ/sup T/. Matrices A, Q, and T and the approximate eigenvalue, say lambda, are then used in the improvement phase. SICEDR uses an iterative method similar to iterative improvement for linear systems to improve the accuracy of lambda and improve or compute the eigenvector x in O(n 2 ) work, where n is the order of the matrix A
Parallelism in matrix computations
Gallopoulos, Efstratios; Sameh, Ahmed H
2016-01-01
This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of pa...
Attractive electron-electron interactions within robust local fitting approximations.
Merlot, Patrick; Kjærgaard, Thomas; Helgaker, Trygve; Lindh, Roland; Aquilante, Francesco; Reine, Simen; Pedersen, Thomas Bondo
2013-06-30
An analysis of Dunlap's robust fitting approach reveals that the resulting two-electron integral matrix is not manifestly positive semidefinite when local fitting domains or non-Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four-center two-electron integrals based on the resolution-of-the-identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair-atomic resolution-of-the-identity (PARI) approach, atomic-orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree-Fock and Kohn-Sham calculations, the indefinite integral matrix causes nonconvergence in the self-consistent-field iterations. In these cases, the two-electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb-metric RI method. The speed-up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple-zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky-decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations. Copyright © 2013 Wiley Periodicals, Inc.
Optimal matrix product states for the Heisenberg spin chain
International Nuclear Information System (INIS)
Latorre, Jose I; Pico, Vicent
2009-01-01
We present some exact results for the optimal matrix product state (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce the problem of approximating for the ground state of a spin chain to an analytical minimization. This allows one to show that results of standard simulations, e.g. density matrix renormalization group and infinite time evolving block decimation, do correspond to the result obtained by this minimization strategy and, thus, both methods deliver optimal MPS with the same energy but, otherwise, different properties. We also find that translational and rotational symmetries cannot be maintained simultaneously by the MPS ansatz of minimum energy and present explicit constructions for each case. Furthermore, we analyze symmetry restoration and quantify it to uncover new scaling relations. The method we propose can be extended to any translational invariant Hamiltonian
Thermal decomposition of biphenyl (1963); Decomposition thermique du biphenyle (1963)
Energy Technology Data Exchange (ETDEWEB)
Clerc, M [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1962-06-15
The rates of formation of the decomposition products of biphenyl; hydrogen, methane, ethane, ethylene, as well as triphenyl have been measured in the vapour and liquid phases at 460 deg. C. The study of the decomposition products of biphenyl at different temperatures between 400 and 460 deg. C has provided values of the activation energies of the reactions yielding the main products of pyrolysis in the vapour phase. Product and Activation energy: Hydrogen 73 {+-} 2 kCal/Mole; Benzene 76 {+-} 2 kCal/Mole; Meta-triphenyl 53 {+-} 2 kCal/Mole; Biphenyl decomposition 64 {+-} 2 kCal/Mole; The rate of disappearance of biphenyl is only very approximately first order. These results show the major role played at the start of the decomposition by organic impurities which are not detectable by conventional physico-chemical analysis methods and the presence of which accelerates noticeably the decomposition rate. It was possible to eliminate these impurities by zone-melting carried out until the initial gradient of the formation curves for the products became constant. The composition of the high-molecular weight products (over 250) was deduced from the mean molecular weight and the dosage of the aromatic C - H bonds by infrared spectrophotometry. As a result the existence in tars of hydrogenated tetra, penta and hexaphenyl has been demonstrated. (author) [French] Les vitesses de formation des produits de decomposition du biphenyle: hydrogene, methane, ethane, ethylene, ainsi que des triphenyles, ont ete mesurees en phase vapeur et en phase liquide a 460 deg. C. L'etude des produits de decomposition du biphenyle a differentes temperatures comprises entre 400 et 460 deg. C, a fourni les valeurs des energies d'activation des reactions conduisant aux principaux produits de la pyrolyse en phase vapeur. Produit et Energie d'activation: Hydrogene 73 {+-} 2 kcal/Mole; Benzene 76 {+-} 2 kcal/Mole; Metatriphenyle, 53 {+-} 2 kcal/Mole; Decomposition du biphenyle 64 {+-} 2 kcal/Mole; La
QR-decomposition based SENSE reconstruction using parallel architecture.
Ullah, Irfan; Nisar, Habab; Raza, Haseeb; Qasim, Malik; Inam, Omair; Omer, Hammad
2018-04-01
Magnetic Resonance Imaging (MRI) is a powerful medical imaging technique that provides essential clinical information about the human body. One major limitation of MRI is its long scan time. Implementation of advance MRI algorithms on a parallel architecture (to exploit inherent parallelism) has a great potential to reduce the scan time. Sensitivity Encoding (SENSE) is a Parallel Magnetic Resonance Imaging (pMRI) algorithm that utilizes receiver coil sensitivities to reconstruct MR images from the acquired under-sampled k-space data. At the heart of SENSE lies inversion of a rectangular encoding matrix. This work presents a novel implementation of GPU based SENSE algorithm, which employs QR decomposition for the inversion of the rectangular encoding matrix. For a fair comparison, the performance of the proposed GPU based SENSE reconstruction is evaluated against single and multicore CPU using openMP. Several experiments against various acceleration factors (AFs) are performed using multichannel (8, 12 and 30) phantom and in-vivo human head and cardiac datasets. Experimental results show that GPU significantly reduces the computation time of SENSE reconstruction as compared to multi-core CPU (approximately 12x speedup) and single-core CPU (approximately 53x speedup) without any degradation in the quality of the reconstructed images. Copyright © 2018 Elsevier Ltd. All rights reserved.
Spectral Decomposition Algorithm (SDA)
National Aeronautics and Space Administration — Spectral Decomposition Algorithm (SDA) is an unsupervised feature extraction technique similar to PCA that was developed to better distinguish spectral features in...
Thermal decomposition of pyrite
International Nuclear Information System (INIS)
Music, S.; Ristic, M.; Popovic, S.
1992-01-01
Thermal decomposition of natural pyrite (cubic, FeS 2 ) has been investigated using X-ray diffraction and 57 Fe Moessbauer spectroscopy. X-ray diffraction analysis of pyrite ore from different sources showed the presence of associated minerals, such as quartz, szomolnokite, stilbite or stellerite, micas and hematite. Hematite, maghemite and pyrrhotite were detected as thermal decomposition products of natural pyrite. The phase composition of the thermal decomposition products depends on the terature, time of heating and starting size of pyrite chrystals. Hematite is the end product of the thermal decomposition of natural pyrite. (author) 24 refs.; 6 figs.; 2 tabs
Directory of Open Access Journals (Sweden)
Hugo Lara
2014-12-01
Full Text Available The matrix completion problem (MC has been approximated by using the nuclear norm relaxation. Some algorithms based on this strategy require the computationally expensive singular value decomposition (SVD at each iteration. One way to avoid SVD calculations is to use alternating methods, which pursue the completion through matrix factorization with a low rank condition. In this work an augmented Lagrangean-type alternating algorithm is proposed. The new algorithm uses duality information to define the iterations, in contrast to the solely primal LMaFit algorithm, which employs a Successive Over Relaxation scheme. The convergence result is studied. Some numerical experiments are given to compare numerical performance of both proposals.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Optical bistability without the rotating wave approximation
Energy Technology Data Exchange (ETDEWEB)
Sharaby, Yasser A., E-mail: Yasser_Sharaby@hotmail.co [Physics Department, Faculty of Applied Sciences, Suez Canal University, Suez (Egypt); Joshi, Amitabh, E-mail: ajoshi@eiu.ed [Department of Physics, Eastern Illinois University, Charleston, IL 61920 (United States); Hassan, Shoukry S., E-mail: Shoukryhassan@hotmail.co [Mathematics Department, College of Science, University of Bahrain, P.O. Box 32038 (Bahrain)
2010-04-26
Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.
Optical bistability without the rotating wave approximation
International Nuclear Information System (INIS)
Sharaby, Yasser A.; Joshi, Amitabh; Hassan, Shoukry S.
2010-01-01
Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.
Reduced-rank approximations to the far-field transform in the gridded fast multipole method
Hesford, Andrew J.; Waag, Robert C.
2011-05-01
The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.
Dynamic mode decomposition for plasma diagnostics and validation
Taylor, Roy; Kutz, J. Nathan; Morgan, Kyle; Nelson, Brian A.
2018-05-01
We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix decomposition that correlates spatial features of computational or experimental data while simultaneously associating the spatial activity with periodic temporal behavior. DMD can produce low-rank, reduced order surrogate models that can be used to reconstruct the state of the system with high fidelity. This allows for a reduction in the computational cost and, at the same time, accurate approximations of the problem, even if the data are sparsely sampled. We demonstrate the use of the method on both numerical and experimental data, showing that it is a successful mathematical architecture for characterizing the helicity injected torus with steady inductive (HIT-SI) magnetohydrodynamics. Importantly, the DMD produces interpretable, dominant mode structures, including a stationary mode consistent with our understanding of a HIT-SI spheromak accompanied by a pair of injector-driven modes. In combination, the 3-mode DMD model produces excellent dynamic reconstructions across the domain of analyzed data.
Multiresolution signal decomposition schemes
J. Goutsias (John); H.J.A.M. Heijmans (Henk)
1998-01-01
textabstract[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis
Decomposition of Sodium Tetraphenylborate
International Nuclear Information System (INIS)
Barnes, M.J.
1998-01-01
The chemical decomposition of aqueous alkaline solutions of sodium tetraphenylborate (NaTPB) has been investigated. The focus of the investigation is on the determination of additives and/or variables which influence NaTBP decomposition. This document describes work aimed at providing better understanding into the relationship of copper (II), solution temperature, and solution pH to NaTPB stability
Efficient approximation of random fields for numerical applications
Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus
2015-01-01
We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.
Efficient approximation of random fields for numerical applications
Harbrecht, Helmut
2015-01-07
We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.
Multilevel domain decomposition for electronic structure calculations
International Nuclear Information System (INIS)
Barrault, M.; Cances, E.; Hager, W.W.; Le Bris, C.
2007-01-01
We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and density functional theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of domain decomposition methods. Using this approach, calculations have been successfully performed on several linear polymer chains containing up to 40,000 atoms and 200,000 atomic orbitals. Both the computational cost and the memory requirement scale linearly with the number of atoms. Additional speed-up can easily be obtained by parallelization. We show that this domain decomposition method outperforms the density matrix minimization (DMM) method for poor initial guesses. Our method provides an efficient preconditioner for DMM and other linear scaling methods, variational in nature, such as the orbital minimization (OM) procedure
Azimuthal decomposition of optical modes
CSIR Research Space (South Africa)
Dudley, Angela L
2012-07-01
Full Text Available This presentation analyses the azimuthal decomposition of optical modes. Decomposition of azimuthal modes need two steps, namely generation and decomposition. An azimuthally-varying phase (bounded by a ring-slit) placed in the spatial frequency...
Massively Parallel Polar Decomposition on Distributed-Memory Systems
Ltaief, Hatem; Sukkari, Dalal E.; Esposito, Aniello; Nakatsukasa, Yuji; Keyes, David E.
2018-01-01
We present a high-performance implementation of the Polar Decomposition (PD) on distributed-memory systems. Building upon on the QR-based Dynamically Weighted Halley (QDWH) algorithm, the key idea lies in finding the best rational approximation
Square well approximation to the optical potential
International Nuclear Information System (INIS)
Jain, A.K.; Gupta, M.C.; Marwadi, P.R.
1976-01-01
Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)
Tensor Decompositions for Learning Latent Variable Models
2012-12-08
and eigenvectors of tensors is generally significantly more complicated than their matrix counterpart (both algebraically [Qi05, CS11, Lim05] and...The reduction First, let W ∈ Rd×k be a linear transformation such that M2(W,W ) = W M2W = I where I is the k × k identity matrix (i.e., W whitens ...approximate the whitening matrix W ∈ Rd×k from second-moment matrix M2 ∈ Rd×d. To do this, one first multiplies M2 by a random matrix R ∈ Rd×k′ for some k′ ≥ k
Cellular decomposition in vikalloys
International Nuclear Information System (INIS)
Belyatskaya, I.S.; Vintajkin, E.Z.; Georgieva, I.Ya.; Golikov, V.A.; Udovenko, V.A.
1981-01-01
Austenite decomposition in Fe-Co-V and Fe-Co-V-Ni alloys at 475-600 deg C is investigated. The cellular decomposition in ternary alloys results in the formation of bcc (ordered) and fcc structures, and in quaternary alloys - bcc (ordered) and 12R structures. The cellular 12R structure results from the emergence of stacking faults in the fcc lattice with irregular spacing in four layers. The cellular decomposition results in a high-dispersion structure and magnetic properties approaching the level of well-known vikalloys [ru
Daverman, Robert J
2007-01-01
Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to eve
Numerical CP Decomposition of Some Difficult Tensors
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2017-01-01
Roč. 317, č. 1 (2017), s. 362-370 ISSN 0377-0427 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : Small matrix multiplication * Canonical polyadic tensor decomposition * Levenberg-Marquardt method Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0468385. pdf
Vector domain decomposition schemes for parabolic equations
Vabishchevich, P. N.
2017-09-01
A new class of domain decomposition schemes for finding approximate solutions of timedependent problems for partial differential equations is proposed and studied. A boundary value problem for a second-order parabolic equation is used as a model problem. The general approach to the construction of domain decomposition schemes is based on partition of unity. Specifically, a vector problem is set up for solving problems in individual subdomains. Stability conditions for vector regionally additive schemes of first- and second-order accuracy are obtained.
Approximate quantum Markov chains
Sutter, David
2018-01-01
This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...
Jia, Zhongxiao; Yang, Yanfei
2018-05-01
In this paper, we propose new randomization based algorithms for large scale linear discrete ill-posed problems with general-form regularization: subject to , where L is a regularization matrix. Our algorithms are inspired by the modified truncated singular value decomposition (MTSVD) method, which suits only for small to medium scale problems, and randomized SVD (RSVD) algorithms that generate good low rank approximations to A. We use rank-k truncated randomized SVD (TRSVD) approximations to A by truncating the rank- RSVD approximations to A, where q is an oversampling parameter. The resulting algorithms are called modified TRSVD (MTRSVD) methods. At every step, we use the LSQR algorithm to solve the resulting inner least squares problem, which is proved to become better conditioned as k increases so that LSQR converges faster. We present sharp bounds for the approximation accuracy of the RSVDs and TRSVDs for severely, moderately and mildly ill-posed problems, and substantially improve a known basic bound for TRSVD approximations. We prove how to choose the stopping tolerance for LSQR in order to guarantee that the computed and exact best regularized solutions have the same accuracy. Numerical experiments illustrate that the best regularized solutions by MTRSVD are as accurate as the ones by the truncated generalized singular value decomposition (TGSVD) algorithm, and at least as accurate as those by some existing truncated randomized generalized singular value decomposition (TRGSVD) algorithms. This work was supported in part by the National Science Foundation of China (Nos. 11771249 and 11371219).
Photochemical decomposition of catecholamines
International Nuclear Information System (INIS)
Mol, N.J. de; Henegouwen, G.M.J.B. van; Gerritsma, K.W.
1979-01-01
During photochemical decomposition (lambda=254 nm) adrenaline, isoprenaline and noradrenaline in aqueous solution were converted to the corresponding aminochrome for 65, 56 and 35% respectively. In determining this conversion, photochemical instability of the aminochromes was taken into account. Irradiations were performed in such dilute solutions that the neglect of the inner filter effect is permissible. Furthermore, quantum yields for the decomposition of the aminochromes in aqueous solution are given. (Author)
Application of spectral Lanczos decomposition method to large scale problems arising geophysics
Energy Technology Data Exchange (ETDEWEB)
Tamarchenko, T. [Western Atlas Logging Services, Houston, TX (United States)
1996-12-31
This paper presents an application of Spectral Lanczos Decomposition Method (SLDM) to numerical modeling of electromagnetic diffusion and elastic waves propagation in inhomogeneous media. SLDM approximates an action of a matrix function as a linear combination of basis vectors in Krylov subspace. I applied the method to model electromagnetic fields in three-dimensions and elastic waves in two dimensions. The finite-difference approximation of the spatial part of differential operator reduces the initial boundary-value problem to a system of ordinary differential equations with respect to time. The solution to this system requires calculating exponential and sine/cosine functions of the stiffness matrices. Large scale numerical examples are in a good agreement with the theoretical error bounds and stability estimates given by Druskin, Knizhnerman, 1987.
Barth, Timothy J.; Chan, Tony F.; Tang, Wei-Pai
1998-01-01
This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.
Decomposition of forest products buried in landfills
International Nuclear Information System (INIS)
Wang, Xiaoming; Padgett, Jennifer M.; Powell, John S.; Barlaz, Morton A.
2013-01-01
Highlights: • This study tracked chemical changes of wood and paper in landfills. • A decomposition index was developed to quantify carbohydrate biodegradation. • Newsprint biodegradation as measured here is greater than previous reports. • The field results correlate well with previous laboratory measurements. - Abstract: The objective of this study was to investigate the decomposition of selected wood and paper products in landfills. The decomposition of these products under anaerobic landfill conditions results in the generation of biogenic carbon dioxide and methane, while the un-decomposed portion represents a biogenic carbon sink. Information on the decomposition of these municipal waste components is used to estimate national methane emissions inventories, for attribution of carbon storage credits, and to assess the life-cycle greenhouse gas impacts of wood and paper products. Hardwood (HW), softwood (SW), plywood (PW), oriented strand board (OSB), particleboard (PB), medium-density fiberboard (MDF), newsprint (NP), corrugated container (CC) and copy paper (CP) were buried in landfills operated with leachate recirculation, and were excavated after approximately 1.5 and 2.5 yr. Samples were analyzed for cellulose (C), hemicellulose (H), lignin (L), volatile solids (VS), and organic carbon (OC). A holocellulose decomposition index (HOD) and carbon storage factor (CSF) were calculated to evaluate the extent of solids decomposition and carbon storage. Samples of OSB made from HW exhibited cellulose plus hemicellulose (C + H) loss of up to 38%, while loss for the other wood types was 0–10% in most samples. The C + H loss was up to 81%, 95% and 96% for NP, CP and CC, respectively. The CSFs for wood and paper samples ranged from 0.34 to 0.47 and 0.02 to 0.27 g OC g −1 dry material, respectively. These results, in general, correlated well with an earlier laboratory-scale study, though NP and CC decomposition measured in this study were higher than
Decomposition of forest products buried in landfills
Energy Technology Data Exchange (ETDEWEB)
Wang, Xiaoming, E-mail: xwang25@ncsu.edu [Department of Civil, Construction, and Environmental Engineering, Campus Box 7908, North Carolina State University, Raleigh, NC 27695-7908 (United States); Padgett, Jennifer M. [Department of Civil, Construction, and Environmental Engineering, Campus Box 7908, North Carolina State University, Raleigh, NC 27695-7908 (United States); Powell, John S. [Department of Chemical and Biomolecular Engineering, Campus Box 7905, North Carolina State University, Raleigh, NC 27695-7905 (United States); Barlaz, Morton A. [Department of Civil, Construction, and Environmental Engineering, Campus Box 7908, North Carolina State University, Raleigh, NC 27695-7908 (United States)
2013-11-15
Highlights: • This study tracked chemical changes of wood and paper in landfills. • A decomposition index was developed to quantify carbohydrate biodegradation. • Newsprint biodegradation as measured here is greater than previous reports. • The field results correlate well with previous laboratory measurements. - Abstract: The objective of this study was to investigate the decomposition of selected wood and paper products in landfills. The decomposition of these products under anaerobic landfill conditions results in the generation of biogenic carbon dioxide and methane, while the un-decomposed portion represents a biogenic carbon sink. Information on the decomposition of these municipal waste components is used to estimate national methane emissions inventories, for attribution of carbon storage credits, and to assess the life-cycle greenhouse gas impacts of wood and paper products. Hardwood (HW), softwood (SW), plywood (PW), oriented strand board (OSB), particleboard (PB), medium-density fiberboard (MDF), newsprint (NP), corrugated container (CC) and copy paper (CP) were buried in landfills operated with leachate recirculation, and were excavated after approximately 1.5 and 2.5 yr. Samples were analyzed for cellulose (C), hemicellulose (H), lignin (L), volatile solids (VS), and organic carbon (OC). A holocellulose decomposition index (HOD) and carbon storage factor (CSF) were calculated to evaluate the extent of solids decomposition and carbon storage. Samples of OSB made from HW exhibited cellulose plus hemicellulose (C + H) loss of up to 38%, while loss for the other wood types was 0–10% in most samples. The C + H loss was up to 81%, 95% and 96% for NP, CP and CC, respectively. The CSFs for wood and paper samples ranged from 0.34 to 0.47 and 0.02 to 0.27 g OC g{sup −1} dry material, respectively. These results, in general, correlated well with an earlier laboratory-scale study, though NP and CC decomposition measured in this study were higher than
Pérez López, César
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Matrix Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic and numeric variables, with an emphasis on vector and matrix variables, you will go on to examine functions and operations that support vectors and matrices as arguments, including those based on analytic parent functions. Computational methods for finding eigenvalues and eigenvectors of matrices are detailed, leading to various matrix decompositions. Applications such as change of bases, the classification of quadratic forms and ...
Microbial Signatures of Cadaver Gravesoil During Decomposition.
Finley, Sheree J; Pechal, Jennifer L; Benbow, M Eric; Robertson, B K; Javan, Gulnaz T
2016-04-01
Genomic studies have estimated there are approximately 10(3)-10(6) bacterial species per gram of soil. The microbial species found in soil associated with decomposing human remains (gravesoil) have been investigated and recognized as potential molecular determinants for estimates of time since death. The nascent era of high-throughput amplicon sequencing of the conserved 16S ribosomal RNA (rRNA) gene region of gravesoil microbes is allowing research to expand beyond more subjective empirical methods used in forensic microbiology. The goal of the present study was to evaluate microbial communities and identify taxonomic signatures associated with the gravesoil human cadavers. Using 16S rRNA gene amplicon-based sequencing, soil microbial communities were surveyed from 18 cadavers placed on the surface or buried that were allowed to decompose over a range of decomposition time periods (3-303 days). Surface soil microbial communities showed a decreasing trend in taxon richness, diversity, and evenness over decomposition, while buried cadaver-soil microbial communities demonstrated increasing taxon richness, consistent diversity, and decreasing evenness. The results show that ubiquitous Proteobacteria was confirmed as the most abundant phylum in all gravesoil samples. Surface cadaver-soil communities demonstrated a decrease in Acidobacteria and an increase in Firmicutes relative abundance over decomposition, while buried soil communities were consistent in their community composition throughout decomposition. Better understanding of microbial community structure and its shifts over time may be important for advancing general knowledge of decomposition soil ecology and its potential use during forensic investigations.
Uniform analytic approximation of Wigner rotation matrices
Hoffmann, Scott E.
2018-02-01
We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.
Approximate Inverse Preconditioners with Adaptive Dropping
Czech Academy of Sciences Publication Activity Database
Kopal, J.; Rozložník, Miroslav; Tůma, Miroslav
2015-01-01
Roč. 84, June (2015), s. 13-20 ISSN 0965-9978 R&D Projects: GA ČR(CZ) GAP108/11/0853; GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : approximate inverse * Gram-Schmidt orthogonalization * incomplete decomposition * preconditioned conjugate gradient method * algebraic preconditioning * pivoting Subject RIV: BA - General Mathematics Impact factor: 1.673, year: 2015
International Nuclear Information System (INIS)
Strobel, E.L.
1985-01-01
Given the many conflicting experimental results, examination is made of the neutrino mass matrix in order to determine possible masses and mixings. It is assumed that the Dirac mass matrix for the electron, muon, and tau neutrinos is similar in form to those of the quarks and charged leptons, and that the smallness of the observed neutrino masses results from the Gell-Mann-Ramond-Slansky mechanism. Analysis of masses and mixings for the neutrinos is performed using general structures for the Majorana mass matrix. It is shown that if certain tentative experimental results concerning the neutrino masses and mixing angles are confirmed, significant limitations may be placed on the Majorana mass matrix. The most satisfactory simple assumption concerning the Majorana mass matrix is that it is approximately proportional to the Dirac mass matrix. A very recent experimental neutrino mass result and its implications are discussed. Some general properties of matrices with structure similar to the Dirac mass matrices are discussed
Analysis of Nonlinear Dynamics by Square Matrix Method
Energy Technology Data Exchange (ETDEWEB)
Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II
2016-07-25
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
Approximating the minimum cycle mean
Directory of Open Access Journals (Sweden)
Krishnendu Chatterjee
2013-07-01
Full Text Available We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1 First we show that the algorithmic question is reducible in O(n^2 time to the problem of a logarithmic number of min-plus matrix multiplications of n-by-n matrices, where n is the number of vertices of the graph. (2 Second, when the weights are nonnegative, we present the first (1 + ε-approximation algorithm for the problem and the running time of our algorithm is ilde(O(n^ω log^3(nW/ε / ε, where O(n^ω is the time required for the classic n-by-n matrix multiplication and W is the maximum value of the weights.
International Nuclear Information System (INIS)
Macasek, F.; Buriova, E.
2004-01-01
In this presentation authors present the results of analysis of decomposition products of [ 18 ]fluorodexyglucose. It is concluded that the coupling of liquid chromatography - mass spectrometry with electrospray ionisation is a suitable tool for quantitative analysis of FDG radiopharmaceutical, i.e. assay of basic components (FDG, glucose), impurities (Kryptofix) and decomposition products (gluconic and glucuronic acids etc.); 2-[ 18 F]fluoro-deoxyglucose (FDG) is sufficiently stable and resistant towards autoradiolysis; the content of radiochemical impurities (2-[ 18 F]fluoro-gluconic and 2-[ 18 F]fluoro-glucuronic acids in expired FDG did not exceed 1%
Approximate Inference for Wireless Communications
DEFF Research Database (Denmark)
Hansen, Morten
This thesis investigates signal processing techniques for wireless communication receivers. The aim is to improve the performance or reduce the computationally complexity of these, where the primary focus area is cellular systems such as Global System for Mobile communications (GSM) (and extensions...... to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum...
Fragmentation of extracellular matrix by hypochlorous acid
DEFF Research Database (Denmark)
Woods, Alan A; Davies, Michael Jonathan
2003-01-01
/chloramide decomposition, with copper and iron ions being effective catalysts, and decreased by compounds which scavenge chloramines/chloramides, or species derived from them. The effect of such matrix modifications on cellular behaviour is poorly understood, though it is known that changes in matrix materials can have...... profound effects on cell adhesion, proliferation, growth and phenotype. The observed matrix modifications reported here may therefore modulate cellular behaviour in diseases such as atherosclerosis where MPO-derived oxidants are generated....
International Nuclear Information System (INIS)
Ginsburg, C.A.
1980-01-01
In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)
Parallel decompositions of Mueller matrices and polarimetric subtraction
Directory of Open Access Journals (Sweden)
Gil J.J.
2010-06-01
Full Text Available From a general formulation of the physically realizable parallel decompositions of the Mueller matrix M of a given depolarizing system, a procedure for determining the set of pure Mueller matrices susceptible to be subtracted from M is presented. This procedure provides a way to check if a given pure Mueller matrix N can be subtracted from M or not. If this check is positive, the value of the relative cross section of the subtracted component is also determined.
A PARALLEL NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR STOKES PROBLEMS
Institute of Scientific and Technical Information of China (English)
Mei-qun Jiang; Pei-liang Dai
2006-01-01
A nonoverlapping domain decomposition iterative procedure is developed and analyzed for generalized Stokes problems and their finite element approximate problems in RN(N=2,3). The method is based on a mixed-type consistency condition with two parameters as a transmission condition together with a derivative-free transmission data updating technique on the artificial interfaces. The method can be applied to a general multi-subdomain decomposition and implemented on parallel machines with local simple communications naturally.
On the correspondence between data revision and trend-cycle decomposition
Dungey, M.; Jacobs, J. P. A. M.; Tian, J.; van Norden, S.
2013-01-01
This article places the data revision model of Jacobs and van Norden (2011) within a class of trend-cycle decompositions relating directly to the Beveridge-Nelson decomposition. In both these approaches, identifying restrictions on the covariance matrix under simple and realistic conditions may
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
TRUST MODEL FOR SOCIAL NETWORK USING SINGULAR VALUE DECOMPOSITION
Directory of Open Access Journals (Sweden)
Davis Bundi Ntwiga
2016-06-01
Full Text Available For effective interactions to take place in a social network, trust is important. We model trust of agents using the peer to peer reputation ratings in the network that forms a real valued matrix. Singular value decomposition discounts the reputation ratings to estimate the trust levels as trust is the subjective probability of future expectations based on current reputation ratings. Reputation and trust are closely related and singular value decomposition can estimate trust using the real valued matrix of the reputation ratings of the agents in the network. Singular value decomposition is an ideal technique in error elimination when estimating trust from reputation ratings. Reputation estimation of trust is optimal at the discounting of 20 %.
Decomposition theory of chemical reactions
International Nuclear Information System (INIS)
Rabitz, S.; Rabitz, H.
1977-01-01
The coupled channel formulation is utilized to variationally derive approximate closed-form expressions for reactive transition matrices. In conjunction with this effort it is shown that the effect of differing choices of possible channel coupling arrays becomes important when incomplete channel basis sets are used. Generalized techniques are employed to derive the necessary variational principles. The inherent coupling of the Green's functions in the resulting expression for the transition matrix makes inclusion of continuum states in the basis sets less crucial. The practical viability of this formulation as a computational scheme for chemical systems is discussed
Electrochemical and Infrared Absorption Spectroscopy Detection of SF₆ Decomposition Products.
Dong, Ming; Zhang, Chongxing; Ren, Ming; Albarracín, Ricardo; Ye, Rixin
2017-11-15
Sulfur hexafluoride (SF₆) gas-insulated electrical equipment is widely used in high-voltage (HV) and extra-high-voltage (EHV) power systems. Partial discharge (PD) and local heating can occur in the electrical equipment because of insulation faults, which results in SF₆ decomposition and ultimately generates several types of decomposition products. These SF₆ decomposition products can be qualitatively and quantitatively detected with relevant detection methods, and such detection contributes to diagnosing the internal faults and evaluating the security risks of the equipment. At present, multiple detection methods exist for analyzing the SF₆ decomposition products, and electrochemical sensing (ES) and infrared (IR) spectroscopy are well suited for application in online detection. In this study, the combination of ES with IR spectroscopy is used to detect SF₆ gas decomposition. First, the characteristics of these two detection methods are studied, and the data analysis matrix is established. Then, a qualitative and quantitative analysis ES-IR model is established by adopting a two-step approach. A SF₆ decomposition detector is designed and manufactured by combining an electrochemical sensor and IR spectroscopy technology. The detector is used to detect SF₆ gas decomposition and is verified to reliably and accurately detect the gas components and concentrations.
Qian, Weixian; Zhou, Xiaojun; Lu, Yingcheng; Xu, Jiang
2015-09-15
Both the Jones and Mueller matrices encounter difficulties when physically modeling mixed materials or rough surfaces due to the complexity of light-matter interactions. To address these issues, we derived a matrix called the paths correlation matrix (PCM), which is a probabilistic mixture of Jones matrices of every light propagation path. Because PCM is related to actual light propagation paths, it is well suited for physical modeling. Experiments were performed, and the reflection PCM of a mixture of polypropylene and graphite was measured. The PCM of the mixed sample was accurately decomposed into pure polypropylene's single reflection, pure graphite's single reflection, and depolarization caused by multiple reflections, which is consistent with the theoretical derivation. Reflection parameters of rough surface can be calculated from PCM decomposition, and the results fit well with the theoretical calculations provided by the Fresnel equations. These theoretical and experimental analyses verify that PCM is an efficient way to physically model light-matter interactions.
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Inverse scale space decomposition
DEFF Research Database (Denmark)
Schmidt, Marie Foged; Benning, Martin; Schönlieb, Carola-Bibiane
2018-01-01
We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and even and positively one-homogeneous regularisation functionals, can decompose data represented...... by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums...... of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range...
Cacciatori, Sergio L; Marrani, Alessio
2013-01-01
By exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square, two types of coset decompositions are analyzed for the non-compact special K\\"ahler symmetric rank-3 coset E7(-25)/[(E6(-78) x U(1))/Z_3], occurring in supergravity as the vector multiplets' scalar manifold in N=2, D=4 exceptional Maxwell-Einstein theory. The first decomposition exhibits maximal manifest covariance, whereas the second (triality-symmetric) one is of Iwasawa type, with maximal SO(8) covariance. Generalizations to conformal non-compact, real forms of non-degenerate, simple groups "of type E7" are presented for both classes of coset parametrizations, and relations to rank-3 simple Euclidean Jordan algebras and normed trialities over division algebras are also discussed.
Low Rank Approximation Algorithms, Implementation, Applications
Markovsky, Ivan
2012-01-01
Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...
Approximating distributions from moments
Pawula, R. F.
1987-11-01
A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.
Franklin, Joel N
2003-01-01
Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.
CONTRIBUTIONS TO RATIONAL APPROXIMATION,
Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Robust regularized singular value decomposition with application to mortality data
Zhang, Lingsong
2013-09-01
We develop a robust regularized singular value decomposition (RobRSVD) method for analyzing two-way functional data. The research is motivated by the application of modeling human mortality as a smooth two-way function of age group and year. The RobRSVD is formulated as a penalized loss minimization problem where a robust loss function is used to measure the reconstruction error of a low-rank matrix approximation of the data, and an appropriately defined two-way roughness penalty function is used to ensure smoothness along each of the two functional domains. By viewing the minimization problem as two conditional regularized robust regressions, we develop a fast iterative reweighted least squares algorithm to implement the method. Our implementation naturally incorporates missing values. Furthermore, our formulation allows rigorous derivation of leaveone- row/column-out cross-validation and generalized cross-validation criteria, which enable computationally efficient data-driven penalty parameter selection. The advantages of the new robust method over nonrobust ones are shown via extensive simulation studies and the mortality rate application. © Institute of Mathematical Statistics, 2013.
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Energy Technology Data Exchange (ETDEWEB)
Pan, Feng [Los Alamos National Laboratory; Kasiviswanathan, Shiva [Los Alamos National Laboratory
2010-01-01
In the matrix interdiction problem, a real-valued matrix and an integer k is given. The objective is to remove k columns such that the sum over all rows of the maximum entry in each row is minimized. This combinatorial problem is closely related to bipartite network interdiction problem which can be applied to prioritize the border checkpoints in order to minimize the probability that an adversary can successfully cross the border. After introducing the matrix interdiction problem, we will prove the problem is NP-hard, and even NP-hard to approximate with an additive n{gamma} factor for a fixed constant {gamma}. We also present an algorithm for this problem that achieves a factor of (n-k) mUltiplicative approximation ratio.
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
International Nuclear Information System (INIS)
Khoromskij, B.N.; Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.
2009-01-01
In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h 3 ) convergence in the grid-size h=O(n -1 ). Moreover, this requires O(3rn+r 3 ) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH 4 molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10 -6 hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.
M3: Matrix Multiplication on MapReduce
DEFF Research Database (Denmark)
Silvestri, Francesco; Ceccarello, Matteo
2015-01-01
M3 is an Hadoop library for performing dense and sparse matrix multiplication in MapReduce. The library is based on multi-round algorithms exploiting the 3D decomposition of the problem.......M3 is an Hadoop library for performing dense and sparse matrix multiplication in MapReduce. The library is based on multi-round algorithms exploiting the 3D decomposition of the problem....
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximate and renormgroup symmetries
International Nuclear Information System (INIS)
Ibragimov, Nail H.; Kovalev, Vladimir F.
2009-01-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximations of Fuzzy Systems
Directory of Open Access Journals (Sweden)
Vinai K. Singh
2013-03-01
Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions
Potvin, Guy
2015-10-01
We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.
Danburite decomposition by sulfuric acid
International Nuclear Information System (INIS)
Mirsaidov, U.; Mamatov, E.D.; Ashurov, N.A.
2011-01-01
Present article is devoted to decomposition of danburite of Ak-Arkhar Deposit of Tajikistan by sulfuric acid. The process of decomposition of danburite concentrate by sulfuric acid was studied. The chemical nature of decomposition process of boron containing ore was determined. The influence of temperature on the rate of extraction of boron and iron oxides was defined. The dependence of decomposition of boron and iron oxides on process duration, dosage of H 2 SO 4 , acid concentration and size of danburite particles was determined. The kinetics of danburite decomposition by sulfuric acid was studied as well. The apparent activation energy of the process of danburite decomposition by sulfuric acid was calculated. The flowsheet of danburite processing by sulfuric acid was elaborated.
Thermal decomposition of lutetium propionate
DEFF Research Database (Denmark)
Grivel, Jean-Claude
2010-01-01
The thermal decomposition of lutetium(III) propionate monohydrate (Lu(C2H5CO2)3·H2O) in argon was studied by means of thermogravimetry, differential thermal analysis, IR-spectroscopy and X-ray diffraction. Dehydration takes place around 90 °C. It is followed by the decomposition of the anhydrous...... °C. Full conversion to Lu2O3 is achieved at about 1000 °C. Whereas the temperatures and solid reaction products of the first two decomposition steps are similar to those previously reported for the thermal decomposition of lanthanum(III) propionate monohydrate, the final decomposition...... of the oxycarbonate to the rare-earth oxide proceeds in a different way, which is here reminiscent of the thermal decomposition path of Lu(C3H5O2)·2CO(NH2)2·2H2O...
The influence of preburial insect access on the decomposition rate.
Bachmann, Jutta; Simmons, Tal
2010-07-01
This study compared total body score (TBS) in buried remains (35 cm depth) with and without insect access prior to burial. Sixty rabbit carcasses were exhumed at 50 accumulated degree day (ADD) intervals. Weight loss, TBS, intra-abdominal decomposition, carcass/soil interface temperature, and below-carcass soil pH were recorded and analyzed. Results showed significant differences (p decomposition rates between carcasses with and without insect access prior to burial. An approximately 30% enhanced decomposition rate with insects was observed. TBS was the most valid tool in postmortem interval (PMI) estimation. All other variables showed only weak relationships to decomposition stages, adding little value to PMI estimation. Although progress in estimating the PMI for surface remains has been made, no previous studies have accomplished this for buried remains. This study builds a framework to which further comparable studies can contribute, to produce predictive models for PMI estimation in buried human remains.
Geometric approximation algorithms
Har-Peled, Sariel
2011-01-01
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
International Nuclear Information System (INIS)
Knobloch, A.F.
1980-01-01
A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
The Products of the Thermal Decomposition of CH3CHO
Energy Technology Data Exchange (ETDEWEB)
Vasiliou, AnGayle; Piech, Krzysztof M.; Zhang, Xu; Nimlos, Mark R.; Ahmed, Musahid; Golan, Amir; Kostko, Oleg; Osborn, David L.; Daily, John W.; Stanton, John F.; Ellison, G. Barney
2011-04-06
We have used a heated 2 cm x 1 mm SiC microtubular (mu tubular) reactor to decompose acetaldehyde: CH3CHO + DELTA --> products. Thermal decomposition is followed at pressures of 75 - 150 Torr and at temperatures up to 1700 K, conditions that correspond to residence times of roughly 50 - 100 mu sec in the mu tubular reactor. The acetaldehyde decomposition products are identified by two independent techniques: VUV photoionization mass spectroscopy (PIMS) and infrared (IR) absorption spectroscopy after isolation in a cryogenic matrix. Besides CH3CHO, we have studied three isotopologues, CH3CDO, CD3CHO, and CD3CDO. We have identified the thermal decomposition products CH3(PIMS), CO (IR, PIMS), H (PIMS), H2 (PIMS), CH2CO (IR, PIMS), CH2=CHOH (IR, PIMS), H2O (IR, PIMS), and HC=CH (IR, PIMS). Plausible evidence has been found to support the idea that there are at least three different thermal decomposition pathways for CH3CHO: Radical decomposition: CH3CHO + DELTA --> CH3 + [HCO] --> CH3 + H + CO Elimination: CH3CHO + DELTA --> H2 + CH2=C=O. Isomerization/elimination: CH3CHO + DELTA --> [CH2=CH-OH] --> HC=CH + H2O. Both PIMS and IR spectroscopy show compelling evidence for the participation of vinylidene, CH2=C:, as an intermediate in the decomposition of vinyl alchohol: CH2=CH-OH + DELTA --> [CH2=C:] + H2O --> HC=CH + H2O.
International Nuclear Information System (INIS)
Krenciglowa, E.M.; Kung, C.L.; Kuo, T.T.S.; Osnes, E.; and Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794)
1976-01-01
Different definitions of the reaction matrix G appropriate to the calculation of nuclear structure are reviewed and discussed. Qualitative physical arguments are presented in support of a two-step calculation of the G-matrix for finite nuclei. In the first step the high-energy excitations are included using orthogonalized plane-wave intermediate states, and in the second step the low-energy excitations are added in, using harmonic oscillator intermediate states. Accurate calculations of G-matrix elements for nuclear structure calculations in the Aapprox. =18 region are performed following this procedure and treating the Pauli exclusion operator Q 2 /sub p/ by the method of Tsai and Kuo. The treatment of Q 2 /sub p/, the effect of the intermediate-state spectrum and the energy dependence of the reaction matrix are investigated in detail. The present matrix elements are compared with various matrix elements given in the literature. In particular, close agreement is obtained with the matrix elements calculated by Kuo and Brown using approximate methods
Fast wavelet based sparse approximate inverse preconditioner
Energy Technology Data Exchange (ETDEWEB)
Wan, W.L. [Univ. of California, Los Angeles, CA (United States)
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
Carlberg, Kevin
2010-10-28
A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.
Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel
2010-01-01
A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.
Subtracting a best rank-1 approximation may increase tensor rank
Stegeman, Alwin; Comon, Pierre
2010-01-01
It has been shown that a best rank-R approximation of an order-k tensor may not exist when R >= 2 and k >= 3. This poses a serious problem to data analysts using tensor decompositions it has been observed numerically that, generally, this issue cannot be solved by consecutively computing and
Approximate Method for Solving the Linear Fuzzy Delay Differential Equations
Directory of Open Access Journals (Sweden)
S. Narayanamoorthy
2015-01-01
Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.
Sparse Localization with a Mobile Beacon Based on LU Decomposition in Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Chunhui Zhao
2015-09-01
Full Text Available Node localization is the core in wireless sensor network. It can be solved by powerful beacons, which are equipped with global positioning system devices to know their location information. In this article, we present a novel sparse localization approach with a mobile beacon based on LU decomposition. Our scheme firstly translates node localization problem into a 1-sparse vector recovery problem by establishing sparse localization model. Then, LU decomposition pre-processing is adopted to solve the problem that measurement matrix does not meet the re¬stricted isometry property. Later, the 1-sparse vector can be exactly recovered by compressive sensing. Finally, as the 1-sparse vector is approximate sparse, weighted Cen¬troid scheme is introduced to accurately locate the node. Simulation and analysis show that our scheme has better localization performance and lower requirement for the mobile beacon than MAP+GC, MAP-M, and MAP-MN schemes. In addition, the obstacles and DOI have little effect on the novel scheme, and it has great localization performance under low SNR, thus, the scheme proposed is robust.
Randomized interpolative decomposition of separated representations
Biagioni, David J.; Beylkin, Daniel; Beylkin, Gregory
2015-01-01
We introduce an algorithm to compute tensor interpolative decomposition (dubbed CTD-ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ɛ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the Alternating Least Squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank.
On Covering Approximation Subspaces
Directory of Open Access Journals (Sweden)
Xun Ge
2009-06-01
Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.
Thermal Decomposition of Radiation-Damaged Polystyrene
International Nuclear Information System (INIS)
J Abrefah, J.; Klinger, G.S.
2000-01-01
The radiation-damaged polystyrene material (''polycube'') used in this study was synthesized by mixing a high-density polystyrene (''Dylene Fines No. 100'') with plutonium and uranium oxides. The polycubes were used on the Hanford Site in the 1960s for criticality studies to determine the hydrogen-to-fissile atom ratios for neutron moderation during processing of spent nuclear fuel. Upon completion of the studies, two methods were developed to reclaim the transuranic (TRU) oxides from the polymer matrix: (1) burning the polycubes in air at 873 K; and (2) heating the polycubes in the absence of oxygen and scrubbing the released monomer and other volatile organics using carbon tetrachloride. Neither of these methods was satisfactory in separating the TRU oxides from the polystyrene. Consequently, the remaining polycubes were sent to the Hanford Plutonium Finishing Plant (PFP) for storage. Over time, the high dose of alpha and gamma radiation has resulted in a polystyrene matrix that is highly cross-linked and hydrogen deficient and a stabilization process is being developed in support of Defense Nuclear Facility Safety Board Recommendation 94-1. Baseline processes involve thermal treatment to pyrolyze the polycubes in a furnace to decompose the polystyrene and separate out the TRU oxides. Thermal decomposition products from this degraded polystyrene matrix were characterized by Pacific Northwest National Laboratory to provide information for determining the environmental impact of the process and for optimizing the process parameters. A gas chromatography/mass spectrometry (GC/MS) system coupled to a horizontal tube furnace was used for the characterization studies. The decomposition studies were performed both in air and helium atmospheres at 773 K, the planned processing temperature. The volatile and semi-volatile organic products identified for the radiation-damaged polystyrene were different from those observed for virgin polystyrene. The differences were in the
Yang, Yi-Bo; Chen, Ying; Draper, Terrence; Liang, Jian; Liu, Keh-Fei
2018-03-01
We report the results on the proton mass decomposition and also on the related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of Nf = 2 + 1 DWF configurations with three lattice spacings and volumes, and several pion masses including the physical pion mass. With 1-loop pertur-bative calculation and proper normalization of the glue operator, we find that the u, d, and s quark masses contribute 9(2)% to the proton mass. The quark energy and glue field energy contribute 31(5)% and 37(5)% respectively in the MS scheme at µ = 2 GeV. The trace anomaly gives the remaining 23(1)% contribution. The u, d, s and glue momentum fractions in the MS scheme are consistent with the global analysis at µ = 2 GeV.
Erbium hydride decomposition kinetics.
Energy Technology Data Exchange (ETDEWEB)
Ferrizz, Robert Matthew
2006-11-01
Thermal desorption spectroscopy (TDS) is used to study the decomposition kinetics of erbium hydride thin films. The TDS results presented in this report are analyzed quantitatively using Redhead's method to yield kinetic parameters (E{sub A} {approx} 54.2 kcal/mol), which are then utilized to predict hydrogen outgassing in vacuum for a variety of thermal treatments. Interestingly, it was found that the activation energy for desorption can vary by more than 7 kcal/mol (0.30 eV) for seemingly similar samples. In addition, small amounts of less-stable hydrogen were observed for all erbium dihydride films. A detailed explanation of several approaches for analyzing thermal desorption spectra to obtain kinetic information is included as an appendix.
International Nuclear Information System (INIS)
Chen Xiangsong; Sun Weimin; Wang Fan; Goldman, T.
2011-01-01
We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular-momentum eigenstates. We split, from the total angular-momentum operator, a proper part which can be separately conserved for a stationary state. This part commutes with the total Hamiltonian and thus specifies the quantum angular momentum. We first show how this can be done in a gauge-dependent way, by seeking a specific gauge in which part of the total angular-momentum operator vanishes identically. We then construct a gauge-invariant operator with the desired property. Our analysis clarifies what is the most pertinent choice among the various proposals for decomposing the nucleon spin. A similar analysis is performed for extracting a proper part from the total Hamiltonian to construct energy eigenstates.
A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics
Gingold, H.
1991-01-01
A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.
SAM revisited: uniform semiclassical approximation with absorption
International Nuclear Information System (INIS)
Hussein, M.S.; Pato, M.P.
1986-01-01
The uniform semiclassical approximation is modified to take into account strong absorption. The resulting theory, very similar to the one developed by Frahn and Gross is used to discuss heavy-ion elastic scattering at intermediate energies. The theory permits a reasonably unambiguos separation of refractive and diffractive effects. The systems 12 C+ 12 C and 12 C+ 16 O, which seem to exhibit a remnant of a nuclear rainbow at E=20 Mev/N, are analysed with theory which is built directly on a model for the S-matrix. Simple relations between the fit S-matrix and the underlying complex potential are derived. (Author) [pt
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Prestack wavefield approximations
Alkhalifah, Tariq
2013-01-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
DEFF Research Database (Denmark)
Madsen, Rasmus Elsborg
2005-01-01
The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
An improved saddlepoint approximation.
Gillespie, Colin S; Renshaw, Eric
2007-08-01
Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Approximate Bayesian recursive estimation
Czech Academy of Sciences Publication Activity Database
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Approximating Preemptive Stochastic Scheduling
Megow Nicole; Vredeveld Tjark
2009-01-01
We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...
Optimization and approximation
Pedregal, Pablo
2017-01-01
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.
Transition matrices and orbitals from reduced density matrix theory
Energy Technology Data Exchange (ETDEWEB)
Etienne, Thibaud [Université de Lorraine – Nancy, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); CNRS, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); Unité de Chimie Physique Théorique et Structurale, Université de Namur, Rue de Bruxelles 61, 5000 Namur (Belgium)
2015-06-28
In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.
Seismic wave extrapolation using lowrank symbol approximation
Fomel, Sergey
2012-04-30
We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Energy Technology Data Exchange (ETDEWEB)
Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
High Performance Polar Decomposition on Distributed Memory Systems
Sukkari, Dalal E.
2016-08-08
The polar decomposition of a dense matrix is an important operation in linear algebra. It can be directly calculated through the singular value decomposition (SVD) or iteratively using the QR dynamically-weighted Halley algorithm (QDWH). The former is difficult to parallelize due to the preponderant number of memory-bound operations during the bidiagonal reduction. We investigate the latter scenario, which performs more floating-point operations but exposes at the same time more parallelism, and therefore, runs closer to the theoretical peak performance of the system, thanks to more compute-bound matrix operations. Profiling results show the performance scalability of QDWH for calculating the polar decomposition using around 9200 MPI processes on well and ill-conditioned matrices of 100K×100K problem size. We study then the performance impact of the QDWH-based polar decomposition as a pre-processing step toward calculating the SVD itself. The new distributed-memory implementation of the QDWH-SVD solver achieves up to five-fold speedup against current state-of-the-art vendor SVD implementations. © Springer International Publishing Switzerland 2016.
Praeger, Cheryl; Tao, Terence
2018-01-01
MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: Higher Structures in Geometry and Physics (Chapters 1-5 and 18-21); Winter of Disconnectedness (Chapter 6 and 22-26); Approximation and Optimisation (Chapters 7-8); Refining C*-Algebraic Invariants for Dynamics using KK-theory (Chapters 9-13); Interactions between Topological Recursion, Modularity, Quantum Invariants and Low-dimensional Topology (Chapters 14-17 and 27). The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The artic...
Danburite decomposition by hydrochloric acid
International Nuclear Information System (INIS)
Mamatov, E.D.; Ashurov, N.A.; Mirsaidov, U.
2011-01-01
Present article is devoted to decomposition of danburite of Ak-Arkhar Deposit of Tajikistan by hydrochloric acid. The interaction of boron containing ores of Ak-Arkhar Deposit of Tajikistan with mineral acids, including hydrochloric acid was studied. The optimal conditions of extraction of valuable components from danburite composition were determined. The chemical composition of danburite of Ak-Arkhar Deposit was determined as well. The kinetics of decomposition of calcined danburite by hydrochloric acid was studied. The apparent activation energy of the process of danburite decomposition by hydrochloric acid was calculated.
Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander; Sun, Ying; Genton, Marc G.; Keyes, David E.
2017-01-01
algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The H
AUTONOMOUS GAUSSIAN DECOMPOSITION
Energy Technology Data Exchange (ETDEWEB)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)
2015-04-15
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
AUTONOMOUS GAUSSIAN DECOMPOSITION
International Nuclear Information System (INIS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-01-01
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes
Cyclic approximation to stasis
Directory of Open Access Journals (Sweden)
Stewart D. Johnson
2009-06-01
Full Text Available Neighborhoods of points in $mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.
International Nuclear Information System (INIS)
El Sawi, M.
1983-07-01
A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)
The relaxation time approximation
International Nuclear Information System (INIS)
Gairola, R.P.; Indu, B.D.
1991-01-01
A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs
Polynomial approximation on polytopes
Totik, Vilmos
2014-01-01
Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Trace Norm Regularized CANDECOMP/PARAFAC Decomposition With Missing Data.
Liu, Yuanyuan; Shang, Fanhua; Jiao, Licheng; Cheng, James; Cheng, Hong
2015-11-01
In recent years, low-rank tensor completion (LRTC) problems have received a significant amount of attention in computer vision, data mining, and signal processing. The existing trace norm minimization algorithms for iteratively solving LRTC problems involve multiple singular value decompositions of very large matrices at each iteration. Therefore, they suffer from high computational cost. In this paper, we propose a novel trace norm regularized CANDECOMP/PARAFAC decomposition (TNCP) method for simultaneous tensor decomposition and completion. We first formulate a factor matrix rank minimization model by deducing the relation between the rank of each factor matrix and the mode- n rank of a tensor. Then, we introduce a tractable relaxation of our rank function, and then achieve a convex combination problem of much smaller-scale matrix trace norm minimization. Finally, we develop an efficient algorithm based on alternating direction method of multipliers to solve our problem. The promising experimental results on synthetic and real-world data validate the effectiveness of our TNCP method. Moreover, TNCP is significantly faster than the state-of-the-art methods and scales to larger problems.
Nanoscale decomposition of Nb-Ru-O
Music, Denis; Geyer, Richard W.; Chen, Yen-Ting
2016-11-01
A correlative theoretical and experimental methodology has been employed to explore the decomposition of amorphous Nb-Ru-O at elevated temperatures. Density functional theory based molecular dynamics simulations reveal that amorphous Nb-Ru-O is structurally modified within 10 ps at 800 K giving rise to an increase in the planar metal - oxygen and metal - metal population and hence formation of large clusters, which signifies atomic segregation. The driving force for this atomic segregation process is 0.5 eV/atom. This is validated by diffraction experiments and transmission electron microscopy of sputter-synthesized Nb-Ru-O thin films. Room temperature samples are amorphous, while at 800 K nanoscale rutile RuO2 grains, self-organized in an amorphous Nb-O matrix, are observed, which is consistent with our theoretical predictions. This amorphous/crystalline interplay may be of importance for next generation of thermoelectric devices.
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
NRSA enzyme decomposition model data
U.S. Environmental Protection Agency — Microbial enzyme activities measured at more than 2000 US streams and rivers. These enzyme data were then used to predict organic matter decomposition and microbial...
Some nonlinear space decomposition algorithms
Energy Technology Data Exchange (ETDEWEB)
Tai, Xue-Cheng; Espedal, M. [Univ. of Bergen (Norway)
1996-12-31
Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.
The random phase approximation
International Nuclear Information System (INIS)
Schuck, P.
1985-01-01
RPA is the adequate theory to describe vibrations of the nucleus of very small amplitudes. These vibrations can either be forced by an external electromagnetic field or can be eigenmodes of the nucleus. In a one dimensional analogue the potential corresponding to such eigenmodes of very small amplitude should be rather stiff otherwise the motion risks to be a large amplitude one and to enter a region where the approximation is not valid. This means that nuclei which are supposedly well described by RPA must have a very stable groundstate configuration (must e.g. be very stiff against deformation). This is usually the case for doubly magic nuclei or close to magic nuclei which are in the middle of proton and neutron shells which develop a very stable groundstate deformation; we take the deformation as an example but there are many other possible degrees of freedom as, for example, compression modes, isovector degrees of freedom, spin degrees of freedom, and many more
The quasilocalized charge approximation
International Nuclear Information System (INIS)
Kalman, G J; Golden, K I; Donko, Z; Hartmann, P
2005-01-01
The quasilocalized charge approximation (QLCA) has been used for some time as a formalism for the calculation of the dielectric response and for determining the collective mode dispersion in strongly coupled Coulomb and Yukawa liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a short-time scale in local potential fluctuations. We review the conceptual basis and theoretical structure of the QLC approach and together with recent results from molecular dynamics simulations that corroborate and quantify the theoretical concepts. We also summarize the major applications of the QLCA to various physical systems, combined with the corresponding results of the molecular dynamics simulations and point out the general agreement and instances of disagreement between the two
International Nuclear Information System (INIS)
Craps, Ben; Evnin, Oleg; Nguyen, Kévin
2017-01-01
Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.
Craps, Ben; Evnin, Oleg; Nguyen, Kévin
2017-02-01
Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.
Energy Technology Data Exchange (ETDEWEB)
Craps, Ben [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Evnin, Oleg [Department of Physics, Faculty of Science, Chulalongkorn University, Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Nguyen, Kévin [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)
2017-02-08
Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.
Hössjer, Ola; Tyvand, Peder A; Miloh, Touvia
2016-02-01
The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates. Copyright © 2015 Elsevier Inc. All rights reserved.
Model-free method for isothermal and non-isothermal decomposition kinetics analysis of PET sample
International Nuclear Information System (INIS)
Saha, B.; Maiti, A.K.; Ghoshal, A.K.
2006-01-01
Pyrolysis, one possible alternative to recover valuable products from waste plastics, has recently been the subject of renewed interest. In the present study, the isoconversion methods, i.e., Vyazovkin model-free approach is applied to study non-isothermal decomposition kinetics of waste PET samples using various temperature integral approximations such as Coats and Redfern, Gorbachev, and Agrawal and Sivasubramanian approximation and direct integration (recursive adaptive Simpson quadrature scheme) to analyze the decomposition kinetics. The results show that activation energy (E α ) is a weak but increasing function of conversion (α) in case of non-isothermal decomposition and strong and decreasing function of conversion in case of isothermal decomposition. This indicates possible existence of nucleation, nuclei growth and gas diffusion mechanism during non-isothermal pyrolysis and nucleation and gas diffusion mechanism during isothermal pyrolysis. Optimum E α dependencies on α obtained for non-isothermal data showed similar nature for all the types of temperature integral approximations
Real interest parity decomposition
Directory of Open Access Journals (Sweden)
Alex Luiz Ferreira
2009-09-01
Full Text Available The aim of this paper is to investigate the general causes of real interest rate differentials (rids for a sample of emerging markets for the period of January 1996 to August 2007. To this end, two methods are applied. The first consists of breaking the variance of rids down into relative purchasing power pariety and uncovered interest rate parity and shows that inflation differentials are the main source of rids variation; while the second method breaks down the rids and nominal interest rate differentials (nids into nominal and real shocks. Bivariate autoregressive models are estimated under particular identification conditions, having been adequately treated for the identified structural breaks. Impulse response functions and error variance decomposition result in real shocks as being the likely cause of rids.O objetivo deste artigo é investigar as causas gerais dos diferenciais da taxa de juros real (rids para um conjunto de países emergentes, para o período de janeiro de 1996 a agosto de 2007. Para tanto, duas metodologias são aplicadas. A primeira consiste em decompor a variância dos rids entre a paridade do poder de compra relativa e a paridade de juros a descoberto e mostra que os diferenciais de inflação são a fonte predominante da variabilidade dos rids; a segunda decompõe os rids e os diferenciais de juros nominais (nids em choques nominais e reais. Sob certas condições de identificação, modelos autorregressivos bivariados são estimados com tratamento adequado para as quebras estruturais identificadas e as funções de resposta ao impulso e a decomposição da variância dos erros de previsão são obtidas, resultando em evidências favoráveis a que os choques reais são a causa mais provável dos rids.
Bessel collocation approach for approximate solutions of Hantavirus infection model
Directory of Open Access Journals (Sweden)
Suayip Yuzbasi
2017-11-01
Full Text Available In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.
The Bloch Approximation in Periodically Perforated Media
International Nuclear Information System (INIS)
Conca, C.; Gomez, D.; Lobo, M.; Perez, E.
2005-01-01
We consider a periodically heterogeneous and perforated medium filling an open domain Ω of R N . Assuming that the size of the periodicity of the structure and of the holes is O(ε),we study the asymptotic behavior, as ε → 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in Ω ε (Ω ε being Ω minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and the first Bloch eigenfunction. We first consider the case where Ωis R N and then localize the problem for abounded domain Ω, considering a homogeneous Dirichlet condition on the boundary of Ω
Approximate analytical modeling of leptospirosis infection
Ismail, Nur Atikah; Azmi, Amirah; Yusof, Fauzi Mohamed; Ismail, Ahmad Izani
2017-11-01
Leptospirosis is an infectious disease carried by rodents which can cause death in humans. The disease spreads directly through contact with feces, urine or through bites of infected rodents and indirectly via water contaminated with urine and droppings from them. Significant increase in the number of leptospirosis cases in Malaysia caused by the recent severe floods were recorded during heavy rainfall season. Therefore, to understand the dynamics of leptospirosis infection, a mathematical model based on fractional differential equations have been developed and analyzed. In this paper an approximate analytical method, the multi-step Laplace Adomian decomposition method, has been used to conduct numerical simulations so as to gain insight on the spread of leptospirosis infection.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Efficient morse decompositions of vector fields.
Chen, Guoning; Mischaikow, Konstantin; Laramee, Robert S; Zhang, Eugene
2008-01-01
Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits, and separatrices that are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG). While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCG's, while fast, are overly conservative and usually results in MCG's that are too coarse to be useful for the applications. To address this issue, we present a new technique for performing Morse decomposition based on the concept of tau-maps, which typically provides finer MCG's than existing techniques. Furthermore, the choice of tau provides a natural tradeoff between the fineness of the MCG's and the computational costs. We provide efficient implementations of Morse decomposition based on tau-maps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles in the meshes used for simulation.. Furthermore, we propose the use of spatial tau-maps in addition to the original temporal tau-maps. These techniques provide additional trade-offs between the quality of the MCGs and the speed of computation. We demonstrate the utility of our technique with various examples in the plane and on surfaces including engine simulation data sets.
Approximating centrality in evolving graphs: toward sublinearity
Priest, Benjamin W.; Cybenko, George
2017-05-01
The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.
Thermal decomposition of potassium metaperiodate doped with trivalent ions
Energy Technology Data Exchange (ETDEWEB)
Muraleedharan, K., E-mail: kmuralika@gmail.com [Department of Chemistry, University of Calicut, Calicut, Kerala 673 635 (India); Kannan, M.P.; Gangadevi, T. [Department of Chemistry, University of Calicut, Calicut, Kerala 673 635 (India)
2010-04-20
The kinetics of isothermal decomposition of potassium metaperiodate (KIO{sub 4}), doped with phosphate and aluminium has been studied by thermogravimetry (TG). We introduced a custom-made thermobalance that is able to record weight decrease with time under pure isothermal conditions. The decomposition proceeds mainly through two stages: an acceleratory stages up to {alpha} = 0.50 and the decay stage beyond. The decomposition data for aluminium and phosphate doped KIO{sub 4} were found to be best described by the Prout-Tompkins equation. Separate kinetic analyses of the {alpha}-t data corresponding to the acceleratory region and decay region showed that the acceleratory stage gave the best fit with Prout-Tompkins equation itself whereas the decay stage fitted better to the contracting area equation. The rate of decomposition of phosphate doped KIO{sub 4} increases approximately linearly with an increase in the dopant concentration. In the case of aluminium doped KIO{sub 4}, the rate passes through a maximum with increase in the dopant concentration. The {alpha}-t data of pure and doped KIO{sub 4} were also subjected to isoconversional studies for the determination of activation energy values. Doping did not change the activation energy of the reaction. The results favour an electron-transfer mechanism for the isothermal decomposition of KIO{sub 4}, agreeing well with our earlier observations.
Singular Value Decomposition and Ligand Binding Analysis
Directory of Open Access Journals (Sweden)
André Luiz Galo
2013-01-01
Full Text Available Singular values decomposition (SVD is one of the most important computations in linear algebra because of its vast application for data analysis. It is particularly useful for resolving problems involving least-squares minimization, the determination of matrix rank, and the solution of certain problems involving Euclidean norms. Such problems arise in the spectral analysis of ligand binding to macromolecule. Here, we present a spectral data analysis method using SVD (SVD analysis and nonlinear fitting to determine the binding characteristics of intercalating drugs to DNA. This methodology reduces noise and identifies distinct spectral species similar to traditional principal component analysis as well as fitting nonlinear binding parameters. We applied SVD analysis to investigate the interaction of actinomycin D and daunomycin with native DNA. This methodology does not require prior knowledge of ligand molar extinction coefficients (free and bound, which potentially limits binding analysis. Data are acquired simply by reconstructing the experimental data and by adjusting the product of deconvoluted matrices and the matrix of model coefficients determined by the Scatchard and McGee and von Hippel equation.
Global sensitivity analysis by polynomial dimensional decomposition
Energy Technology Data Exchange (ETDEWEB)
Rahman, Sharif, E-mail: rahman@engineering.uiowa.ed [College of Engineering, The University of Iowa, Iowa City, IA 52242 (United States)
2011-07-15
This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol's method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent.
Decomposition of incomplete fusion
International Nuclear Information System (INIS)
Sobotka, L.B.; Sarantities, D.G.; Stracener, D.W.; Majka, Z.; Abenante, V.; Semkow, T.M.; Hensley, D.C.; Beene, J.R.; Halbert, M.L.
1989-01-01
The velocity distribution of fusion-like products formed in the reaction 701 MeV 28 Si+ 100 Mo is decomposed into 26 incomplete fusion channels. The momentum deficit of the residue per nonevaporative mass unit is approximately equal to the beam momentum per nucleon. The yields of the incomplete fusion channels correlate with the Q-value for projectile fragmentation rather than that for incomplete fusion. The backward angle multiplicities of light particles and heavy ions increase with momentum transfer, however, the heavy ion multiplicities also depend on the extent of the fragmentation of the incomplete fusion channel. These data indicate that at fixed linear momentum transfer, increased fragmentation of the unfused component is related to a reduced transferred angular momentum. 22 refs., 6 figs., 1 tab
Adaptive ACMS: A robust localized Approximated Component Mode Synthesis Method
Madureira, Alexandre L.; Sarkis, Marcus
2017-01-01
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\\infty$ coefficients. The methods are of Galerkin type and follows the Variational Multiscale and Localized Orthogonal Decomposition--LOD approaches in the sense that it decouples spaces into multiscale and fine subspaces. In a first method, the multiscale basis functions are obtained by mapping coarse basis functions, based...
Approximate motion integrals and the quantum chaos problem
International Nuclear Information System (INIS)
Bunakov, V.E.; Ivanov, I.B.
2001-01-01
One discusses the problem of occurrence and seek for the motion integrals in the stationary quantum mechanics and its relation to the quantum chaos. One studies decomposition of quantum numbers and derives the criterion of chaos. To seek the motion integrals one applies the convergence method. One derived the approximate integrals in the Hennone-Hales problem. One discusses the problem of compatibility of chaos and integrability [ru
Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications
Directory of Open Access Journals (Sweden)
Raúl Merino
2017-01-01
Full Text Available We obtain a Hull and White type option price decomposition for a general local volatility model. We apply the obtained formula to CEV model. As an application we give an approximated closed formula for the call option price under a CEV model and an approximated short term implied volatility surface. These approximated formulas are used to estimate model parameters. Numerical comparison is performed for our new method with exact and approximated formulas existing in the literature.
Self-similar factor approximants
International Nuclear Information System (INIS)
Gluzman, S.; Yukalov, V.I.; Sornette, D.
2003-01-01
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties
On the hadron mass decomposition
Lorcé, Cédric
2018-02-01
We argue that the standard decompositions of the hadron mass overlook pressure effects, and hence should be interpreted with great care. Based on the semiclassical picture, we propose a new decomposition that properly accounts for these pressure effects. Because of Lorentz covariance, we stress that the hadron mass decomposition automatically comes along with a stability constraint, which we discuss for the first time. We show also that if a hadron is seen as made of quarks and gluons, one cannot decompose its mass into more than two contributions without running into trouble with the consistency of the physical interpretation. In particular, the so-called quark mass and trace anomaly contributions appear to be purely conventional. Based on the current phenomenological values, we find that in average quarks exert a repulsive force inside nucleons, balanced exactly by the gluon attractive force.
On the hadron mass decomposition
Energy Technology Data Exchange (ETDEWEB)
Lorce, Cedric [Universite Paris-Saclay, Centre de Physique Theorique, Ecole Polytechnique, CNRS, Palaiseau (France)
2018-02-15
We argue that the standard decompositions of the hadron mass overlook pressure effects, and hence should be interpreted with great care. Based on the semiclassical picture, we propose a new decomposition that properly accounts for these pressure effects. Because of Lorentz covariance, we stress that the hadron mass decomposition automatically comes along with a stability constraint, which we discuss for the first time. We show also that if a hadron is seen as made of quarks and gluons, one cannot decompose its mass into more than two contributions without running into trouble with the consistency of the physical interpretation. In particular, the so-called quark mass and trace anomaly contributions appear to be purely conventional. Based on the current phenomenological values, we find that in average quarks exert a repulsive force inside nucleons, balanced exactly by the gluon attractive force. (orig.)
Zhan, Xingzhi
2002-01-01
The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.
Generalized Benders’ Decomposition for topology optimization problems
DEFF Research Database (Denmark)
Munoz Queupumil, Eduardo Javier; Stolpe, Mathias
2011-01-01
) problems with discrete design variables to global optimality. We present the theoretical aspects of the method, including a proof of finite convergence and conditions for obtaining global optimal solutions. The method is also linked to, and compared with, an Outer-Approximation approach and a mixed 0......–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality.......This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness...
Decomposition of childhood malnutrition in Cambodia.
Sunil, Thankam S; Sagna, Marguerite
2015-10-01
Childhood malnutrition is a major problem in developing countries, and in Cambodia, it is estimated that approximately 42% of the children are stunted, which is considered to be very high. In the present study, we examined the effects of proximate and socio-economic determinants on childhood malnutrition in Cambodia. In addition, we examined the effects of the changes in these proximate determinants on childhood malnutrition between 2000 and 2005. Our analytical approach included descriptive, logistic regression and decomposition analyses. Separate analyses are estimated for 2000 and 2005 survey. The primary component of the difference in stunting is attributable to the rates component, indicating that the decrease of stunting is due mainly to the decrease in stunting rates between 2000 and 2005. While majority of the differences in childhood malnutrition between 2000 and 2005 can be attributed to differences in the distribution of malnutrition determinants between 2000 and 2005, differences in their effects also showed some significance. © 2013 John Wiley & Sons Ltd.
Domain decomposition and multilevel integration for fermions
International Nuclear Information System (INIS)
Ce, Marco; Giusti, Leonardo; Schaefer, Stefan
2016-01-01
The numerical computation of many hadronic correlation functions is exceedingly difficult due to the exponentially decreasing signal-to-noise ratio with the distance between source and sink. Multilevel integration methods, using independent updates of separate regions in space-time, are known to be able to solve such problems but have so far been available only for pure gauge theory. We present first steps into the direction of making such integration schemes amenable to theories with fermions, by factorizing a given observable via an approximated domain decomposition of the quark propagator. This allows for multilevel integration of the (large) factorized contribution to the observable, while its (small) correction can be computed in the standard way.
Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations
International Nuclear Information System (INIS)
FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov
2002-01-01
The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations
Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations
Fan, W C; Powell, J L
2002-01-01
The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.
Ranking Support Vector Machine with Kernel Approximation
Directory of Open Access Journals (Sweden)
Kai Chen
2017-01-01
Full Text Available Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels can give higher accuracy than linear RankSVM (RankSVM with a linear kernel for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.
Ranking Support Vector Machine with Kernel Approximation.
Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi
2017-01-01
Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.
Abstract decomposition theorem and applications
Grossberg, R; Grossberg, Rami; Lessmann, Olivier
2005-01-01
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).
Asynchronous Task-Based Polar Decomposition on Manycore Architectures
Sukkari, Dalal
2016-10-25
This paper introduces the first asynchronous, task-based implementation of the polar decomposition on manycore architectures. Based on a new formulation of the iterative QR dynamically-weighted Halley algorithm (QDWH) for the calculation of the polar decomposition, the proposed implementation replaces the original and hostile LU factorization for the condition number estimator by the more adequate QR factorization to enable software portability across various architectures. Relying on fine-grained computations, the novel task-based implementation is also capable of taking advantage of the identity structure of the matrix involved during the QDWH iterations, which decreases the overall algorithmic complexity. Furthermore, the artifactual synchronization points have been severely weakened compared to previous implementations, unveiling look-ahead opportunities for better hardware occupancy. The overall QDWH-based polar decomposition can then be represented as a directed acyclic graph (DAG), where nodes represent computational tasks and edges define the inter-task data dependencies. The StarPU dynamic runtime system is employed to traverse the DAG, to track the various data dependencies and to asynchronously schedule the computational tasks on the underlying hardware resources, resulting in an out-of-order task scheduling. Benchmarking experiments show significant improvements against existing state-of-the-art high performance implementations (i.e., Intel MKL and Elemental) for the polar decomposition on latest shared-memory vendors\\' systems (i.e., Intel Haswell/Broadwell/Knights Landing, NVIDIA K80/P100 GPUs and IBM Power8), while maintaining high numerical accuracy.
An optimization approach for fitting canonical tensor decompositions.
Energy Technology Data Exchange (ETDEWEB)
Dunlavy, Daniel M. (Sandia National Laboratories, Albuquerque, NM); Acar, Evrim; Kolda, Tamara Gibson
2009-02-01
Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methods have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.
Nuclear Matrix Elements for the $\\beta\\beta$ Decay of the $^{76}$Ge
Brown, B A; Horoi, M
2015-01-01
The nuclear matrix elements for two-neutrino double-beta (2 n$\\beta\\beta$ ) and zero-neutrino double-beta (0 n$\\beta\\beta$) decay of 76 Ge are evaluated in terms of the configuration interaction (CI), quasiparticle random phase approximation (QRPA) and interacting boson model (IBM) methods. We show that the decomposition of the matrix elements in terms of interemediate states in 74 Ge is dominated by ground state of this nucleus. We consider corrections to the CI results that arise from configurations admixtures involving orbitals out-side of the CI configuration space by using results from QRPA, many-body-perturbation theory, and the connections to related observables. The CI two-neutrino matrix element is reduced due to the inclusion of spin-orbit partners, and to many-body correlations connected with Gamow-Teller beta decay. The CI zero-neutrino matrix element for the heavy neutrino is enhanced due to particle-particle correlations that are connected with the odd-even oscillations in the nuclear masse...
Role of electrodes in ambient electrolytic decomposition of hydroxylammonium nitrate (HAN solutions
Directory of Open Access Journals (Sweden)
Kai Seng Koh
2013-09-01
Full Text Available Decomposition of hydroxylammonium nitrate (HAN solution with electrolytic decomposition method has attracted much attention in recent years due to its efficiencies and practicability. However, the phenomenon has not been well-studied till now. By utilizing mathematical model currently available, the effect of water content and power used for decomposition was studied. Experiment data shows that sacrificial material such as copper or aluminum outperforms inert electrodes in the decomposition of HAN solution. In the case of using copper wire to electrolyse HAN solutions, approximately 10 seconds is required to reach 100 °C regardless of concentration of HAN. In term of power consumption, 100 W–300 W was found to be the range in which decomposition could be triggered effectively using copper wire as electrodes.
International Conference Approximation Theory XV
Schumaker, Larry
2017-01-01
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Directory of Open Access Journals (Sweden)
Veyis Turut
2013-01-01
Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.
Decomposition of metal nitrate solutions
International Nuclear Information System (INIS)
Haas, P.A.; Stines, W.B.
1982-01-01
Oxides in powder form are obtained from aqueous solutions of one or more heavy metal nitrates (e.g. U, Pu, Th, Ce) by thermal decomposition at 300 to 800 deg C in the presence of about 50 to 500% molar concentration of ammonium nitrate to total metal. (author)
Probability inequalities for decomposition integrals
Czech Academy of Sciences Publication Activity Database
Agahi, H.; Mesiar, Radko
2017-01-01
Roč. 315, č. 1 (2017), s. 240-248 ISSN 0377-0427 Institutional support: RVO:67985556 Keywords : Decomposition integral * Superdecomposition integral * Probability inequalities Subject RIV: BA - General Mathematics OBOR OECD: Statistics and probability Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/E/mesiar-0470959.pdf
Thermal decomposition of ammonium hexachloroosmate
DEFF Research Database (Denmark)
Asanova, T I; Kantor, Innokenty; Asanov, I. P.
2016-01-01
Structural changes of (NH4)2[OsCl6] occurring during thermal decomposition in a reduction atmosphere have been studied in situ using combined energy-dispersive X-ray absorption spectroscopy (ED-XAFS) and powder X-ray diffraction (PXRD). According to PXRD, (NH4)2[OsCl6] transforms directly to meta...
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-01
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Near-infrared Mueller matrix imaging for colonic cancer detection
Wang, Jianfeng; Zheng, Wei; Lin, Kan; Huang, Zhiwei
2016-03-01
Mueller matrix imaging along with polar decomposition method was employed for the colonic cancer detection by polarized light in the near-infrared spectral range (700-1100 nm). A high-speed (colonic tissues (i.e., normal and caner) were acquired. Polar decomposition was further implemented on the 16 images to derive the diattentuation, depolarization, and the retardance images. The decomposed images showed clear margin between the normal and cancerous colon tissue samples. The work shows the potential of near-infrared Mueller matrix imaging for the early diagnosis and detection of malignant lesions in the colon.
Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander
2017-09-03
We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, since H-matrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.
Bhatia, Rajendra
1997-01-01
A good part of matrix theory is functional analytic in spirit. This statement can be turned around. There are many problems in operator theory, where most of the complexities and subtleties are present in the finite-dimensional case. My purpose in writing this book is to present a systematic treatment of methods that are useful in the study of such problems. This book is intended for use as a text for upper division and gradu ate courses. Courses based on parts of the material have been given by me at the Indian Statistical Institute and at the University of Toronto (in collaboration with Chandler Davis). The book should also be useful as a reference for research workers in linear algebra, operator theory, mathe matical physics and numerical analysis. A possible subtitle of this book could be Matrix Inequalities. A reader who works through the book should expect to become proficient in the art of deriving such inequalities. Other authors have compared this art to that of cutting diamonds. One first has to...
Efficient Matrix Models for Relational Learning
2009-10-01
base learners and h1:r is the ensemble learner. For example, consider the case where h1, . . . , hr are linear discriminants. The weighted vote of...a multilinear form naturally leads one to consider tensor factorization: e.g., UAV T is a special case of Tucker decomposition [129] on a 2D- tensor , a...matrix. Our five modeling choices can also be used to differentiate tensor factorizations, but the choices may be subtler for tensors than for
Forms of Approximate Radiation Transport
Brunner, G
2002-01-01
Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
Investigating hydrogel dosimeter decomposition by chemical methods
International Nuclear Information System (INIS)
Jordan, Kevin
2015-01-01
The chemical oxidative decomposition of leucocrystal violet micelle hydrogel dosimeters was investigated using the reaction of ferrous ions with hydrogen peroxide or sodium bicarbonate with hydrogen peroxide. The second reaction is more effective at dye decomposition in gelatin hydrogels. Additional chemical analysis is required to determine the decomposition products
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Fast heap transform-based QR-decomposition of real and complex matrices: algorithms and codes
Grigoryan, Artyom M.
2015-03-01
In this paper, we describe a new look on the application of Givens rotations to the QR-decomposition problem, which is similar to the method of Householder transformations. We apply the concept of the discrete heap transform, or signal-induced unitary transforms which had been introduced by Grigoryan (2006) and used in signal and image processing. Both cases of real and complex nonsingular matrices are considered and examples of performing QR-decomposition of square matrices are given. The proposed method of QR-decomposition for the complex matrix is novel and differs from the known method of complex Givens rotation and is based on analytical equations for the heap transforms. Many examples illustrated the proposed heap transform method of QR-decomposition are given, algorithms are described in detail, and MATLAB-based codes are included.
Implementation of QR-decomposition based on CORDIC for unitary MUSIC algorithm
Lounici, Merwan; Luan, Xiaoming; Saadi, Wahab
2013-07-01
The DOA (Direction Of Arrival) estimation with subspace methods such as MUSIC (MUltiple SIgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique) is based on an accurate estimation of the eigenvalues and eigenvectors of covariance matrix. QR decomposition is implemented with the Coordinate Rotation DIgital Computer (CORDIC) algorithm. QRD requires only additions and shifts [6], so it is faster and more regular than other methods. In this article the hardware architecture of an EVD (Eigen Value Decomposition) processor based on TSA (triangular systolic array) for QR decomposition is proposed. Using Xilinx System Generator (XSG), the design is implemented and the estimated logic device resource values are presented for different matrix sizes.
Applications of tensor (multiway array) factorizations and decompositions in data mining
DEFF Research Database (Denmark)
Mørup, Morten
2011-01-01
Tensor (multiway array) factorization and decomposition has become an important tool for data mining. Fueled by the computational power of modern computer researchers can now analyze large-scale tensorial structured data that only a few years ago would have been impossible. Tensor factorizations...... have several advantages over two-way matrix factorizations including uniqueness of the optimal solution and component identification even when most of the data is missing. Furthermore, multiway decomposition techniques explicitly exploit the multiway structure that is lost when collapsing some...... of the modes of the tensor in order to analyze the data by regular matrix factorization approaches. Multiway decomposition is being applied to new fields every year and there is no doubt that the future will bring many exciting new applications. The aim of this overview is to introduce the basic concepts...
Using many pilot points and singular value decomposition in groundwater model calibration
DEFF Research Database (Denmark)
Christensen, Steen; Doherty, John
2008-01-01
over the model area. Singular value decomposition (SVD) of the normal matrix is used to reduce the large number of pilot point parameters to a smaller number of so-called super parameters that can be estimated by nonlinear regression from the available observations. A number of eigenvectors...
Reducing condition number by appropriate current decomposition on a multiplet of several wires
CSIR Research Space (South Africa)
Lysko, AA
2011-07-01
Full Text Available This paper discusses a numerical investigation in connection with the dependency of the condition number of the impedance matrix on the decomposition of current on a junction with several attached wires (multiplet). It is shown that the condition...
Electrochemical and Infrared Absorption Spectroscopy Detection of SF6 Decomposition Products
Directory of Open Access Journals (Sweden)
Ming Dong
2017-11-01
Full Text Available Sulfur hexafluoride (SF6 gas-insulated electrical equipment is widely used in high-voltage (HV and extra-high-voltage (EHV power systems. Partial discharge (PD and local heating can occur in the electrical equipment because of insulation faults, which results in SF6 decomposition and ultimately generates several types of decomposition products. These SF6 decomposition products can be qualitatively and quantitatively detected with relevant detection methods, and such detection contributes to diagnosing the internal faults and evaluating the security risks of the equipment. At present, multiple detection methods exist for analyzing the SF6 decomposition products, and electrochemical sensing (ES and infrared (IR spectroscopy are well suited for application in online detection. In this study, the combination of ES with IR spectroscopy is used to detect SF6 gas decomposition. First, the characteristics of these two detection methods are studied, and the data analysis matrix is established. Then, a qualitative and quantitative analysis ES-IR model is established by adopting a two-step approach. A SF6 decomposition detector is designed and manufactured by combining an electrochemical sensor and IR spectroscopy technology. The detector is used to detect SF6 gas decomposition and is verified to reliably and accurately detect the gas components and concentrations.
Electrochemical and Infrared Absorption Spectroscopy Detection of SF6 Decomposition Products
Dong, Ming; Ren, Ming; Ye, Rixin
2017-01-01
Sulfur hexafluoride (SF6) gas-insulated electrical equipment is widely used in high-voltage (HV) and extra-high-voltage (EHV) power systems. Partial discharge (PD) and local heating can occur in the electrical equipment because of insulation faults, which results in SF6 decomposition and ultimately generates several types of decomposition products. These SF6 decomposition products can be qualitatively and quantitatively detected with relevant detection methods, and such detection contributes to diagnosing the internal faults and evaluating the security risks of the equipment. At present, multiple detection methods exist for analyzing the SF6 decomposition products, and electrochemical sensing (ES) and infrared (IR) spectroscopy are well suited for application in online detection. In this study, the combination of ES with IR spectroscopy is used to detect SF6 gas decomposition. First, the characteristics of these two detection methods are studied, and the data analysis matrix is established. Then, a qualitative and quantitative analysis ES-IR model is established by adopting a two-step approach. A SF6 decomposition detector is designed and manufactured by combining an electrochemical sensor and IR spectroscopy technology. The detector is used to detect SF6 gas decomposition and is verified to reliably and accurately detect the gas components and concentrations. PMID:29140268
Limited-memory adaptive snapshot selection for proper orthogonal decomposition
Energy Technology Data Exchange (ETDEWEB)
Oxberry, Geoffrey M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kostova-Vassilevska, Tanya [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Arrighi, Bill [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Chand, Kyle [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-04-02
Reduced order models are useful for accelerating simulations in many-query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floating-point operation costs in high-performance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive time-stepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decomposition-based reduced order models, and memory usage is minimized by computing the singular value decomposition using a single-pass incremental algorithm. Results for a viscous Burgers’ test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full order model is recovered to within discretization error. The resulting method can be used on supercomputers to generate proper orthogonal decomposition-based reduced order models, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space.
Liu, Yongbin; He, Bing; Liu, Fang; Lu, Siliang; Zhao, Yilei
2016-12-01
Fault pattern identification is a crucial step for the intelligent fault diagnosis of real-time health conditions in monitoring a mechanical system. However, many challenges exist in extracting the effective feature from vibration signals for fault recognition. A new feature fusion method is proposed in this study to extract new features using kernel joint approximate diagonalization of eigen-matrices (KJADE). In the method, the input space that is composed of original features is mapped into a high-dimensional feature space by nonlinear mapping. Then, the new features can be estimated through the eigen-decomposition of the fourth-order cumulative kernel matrix obtained from the feature space. Therefore, the proposed method could be used to reduce data redundancy because it extracts the inherent pattern structure of different fault classes as it is nonlinear by nature. The integration evaluation factor of between-class and within-class scatters (SS) is employed to depict the clustering performance quantitatively, and the new feature subset extracted by the proposed method is fed into a multi-class support vector machine for fault pattern identification. Finally, the effectiveness of the proposed method is verified by experimental vibration signals with different bearing fault types and severities. Results of several cases show that the KJADE algorithm is efficient in feature fusion for bearing fault identification.
Dictionary-Based Tensor Canonical Polyadic Decomposition
Cohen, Jeremy Emile; Gillis, Nicolas
2018-04-01
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.
Decomposition of diesel oil by various microorganisms
Energy Technology Data Exchange (ETDEWEB)
Suess, A; Netzsch-Lehner, A
1969-01-01
Previous experiments demonstrated the decomposition of diesel oil in different soils. In this experiment the decomposition of /sup 14/C-n-Hexadecane labelled diesel oil by special microorganisms was studied. The results were as follows: (1) In the experimental soils the microorganisms Mycoccus ruber, Mycobacterium luteum and Trichoderma hamatum are responsible for the diesel oil decomposition. (2) By adding microorganisms to the soil an increase of the decomposition rate was found only in the beginning of the experiments. (3) Maximum decomposition of diesel oil was reached 2-3 weeks after incubation.
Variance decomposition in stochastic simulators.
Le Maître, O P; Knio, O M; Moraes, A
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Energy Technology Data Exchange (ETDEWEB)
Le Maître, O. P., E-mail: olm@limsi.fr [LIMSI-CNRS, UPR 3251, Orsay (France); Knio, O. M., E-mail: knio@duke.edu [Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708 (United States); Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa [King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maî tre, O. P.; Knio, O. M.; Moraes, Alvaro
2015-01-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Central limit theorems for large graphs: Method of quantum decomposition
International Nuclear Information System (INIS)
Hashimoto, Yukihiro; Hora, Akihito; Obata, Nobuaki
2003-01-01
A new method is proposed for investigating spectral distribution of the combinatorial Laplacian (adjacency matrix) of a large regular graph on the basis of quantum decomposition and quantum central limit theorem. General results are proved for Cayley graphs of discrete groups and for distance-regular graphs. The Coxeter groups and the Johnson graphs are discussed in detail by way of illustration. In particular, the limit distributions obtained from the Johnson graphs are characterized by the Meixner polynomials which form a one-parameter deformation of the Laguerre polynomials
Non-negative Matrix Factorization for Binary Data
DEFF Research Database (Denmark)
Larsen, Jacob Søgaard; Clemmensen, Line Katrine Harder
We propose the Logistic Non-negative Matrix Factorization for decomposition of binary data. Binary data are frequently generated in e.g. text analysis, sensory data, market basket data etc. A common method for analysing non-negative data is the Non-negative Matrix Factorization, though...... this is in theory not appropriate for binary data, and thus we propose a novel Non-negative Matrix Factorization based on the logistic link function. Furthermore we generalize the method to handle missing data. The formulation of the method is compared to a previously proposed method (Tome et al., 2015). We compare...... the performance of the Logistic Non-negative Matrix Factorization to Least Squares Non-negative Matrix Factorization and Kullback-Leibler (KL) Non-negative Matrix Factorization on sets of binary data: a synthetic dataset, a set of student comments on their professors collected in a binary term-document matrix...
Excimer laser decomposition of silicone
International Nuclear Information System (INIS)
Laude, L.D.; Cochrane, C.; Dicara, Cl.; Dupas-Bruzek, C.; Kolev, K.
2003-01-01
Excimer laser irradiation of silicone foils is shown in this work to induce decomposition, ablation and activation of such materials. Thin (100 μm) laminated silicone foils are irradiated at 248 nm as a function of impacting laser fluence and number of pulsed irradiations at 1 s intervals. Above a threshold fluence of 0.7 J/cm 2 , material starts decomposing. At higher fluences, this decomposition develops and gives rise to (i) swelling of the irradiated surface and then (ii) emission of matter (ablation) at a rate that is not proportioned to the number of pulses. Taking into consideration the polymer structure and the foil lamination process, these results help defining the phenomenology of silicone ablation. The polymer decomposition results in two parts: one which is organic and volatile, and another part which is inorganic and remains, forming an ever thickening screen to light penetration as the number of light pulses increases. A mathematical model is developed that accounts successfully for this physical screening effect
The approximate Loebl-Komlós-Sós Conjecture I: The sparse decomposition
Czech Academy of Sciences Publication Activity Database
Hladký, Jan; Komlós, J.; Piguet, Diana; Simonovits, M.; Stein, M.; Szemerédi, E.
2017-01-01
Roč. 31, č. 2 (2017), s. 945-982 ISSN 0895-4801 R&D Projects: GA MŠk(CZ) 1M0545 EU Projects: European Commission(XE) 628974 - PAECIDM Institutional support: RVO:67985840 ; RVO:67985807 Keywords : extremal graph theory * Loebl–Komlós–Sós conjecture * regularity lemma Subject RIV: BA - General Mathematics; BA - General Mathematics (UIVT-O) OBOR OECD: Pure mathematics; Pure mathematics (UIVT-O) Impact factor: 0.755, year: 2016 http://epubs.siam.org/doi/10.1137/140982842
The approximate Loebl-Komlós-Sós Conjecture I: The sparse decomposition
Czech Academy of Sciences Publication Activity Database
Hladký, Jan; Komlós, J.; Piguet, Diana; Simonovits, M.; Stein, M.; Szemerédi, E.
2017-01-01
Roč. 31, č. 2 (2017), s. 945-982 ISSN 0895-4801 R&D Projects: GA MŠk(CZ) 1M0545 EU Projects: European Commission(XE) 628974 - PAECIDM Institutional support: RVO:67985840 ; RVO:67985807 Keywords : extremal graph theory * Loebl–Komlós–Sós conjecture * regularity lemma Subject RIV: BA - General Mathematics ; BA - General Mathematics (UIVT-O) OBOR OECD: Pure mathematics ; Pure mathematics (UIVT-O) Impact factor: 0.755, year: 2016 http://epubs.siam.org/doi/10.1137/140982842
ARMA Cholesky Factor Models for the Covariance Matrix of Linear Models.
Lee, Keunbaik; Baek, Changryong; Daniels, Michael J
2017-11-01
In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these limitations, two Cholesky decomposition approaches have been proposed: modified Cholesky decomposition for autoregressive (AR) structure and moving average Cholesky decomposition for moving average (MA) structure, respectively. However, the correlations of repeated outcomes are often not captured parsimoniously using either approach separately. In this paper, we propose a class of flexible, nonstationary, heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the covariance matrix that we denote as ARMACD. We analyze a recent lung cancer study to illustrate the power of our proposed methods.
Some results in Diophantine approximation
DEFF Research Database (Denmark)
Pedersen, Steffen Højris
the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...
Limitations of shallow nets approximation.
Lin, Shao-Bo
2017-10-01
In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.
Hierarchical matrix techniques for the solution of elliptic equations
Chá vez, Gustavo; Turkiyyah, George; Yokota, Rio; Keyes, David E.
2014-01-01
Hierarchical matrix approximations are a promising tool for approximating low-rank matrices given the compactness of their representation and the economy of the operations between them. Integral and differential operators have been the major
Approximating the Analytic Fourier Transform with the Discrete Fourier Transform
Axelrod, Jeremy
2015-01-01
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.
International Nuclear Information System (INIS)
Zerr, R.J.; Azmy, Y.Y.
2010-01-01
A spatial domain decomposition with a parallel block Jacobi solution algorithm has been developed based on the integral transport matrix formulation of the discrete ordinates approximation for solving the within-group transport equation. The new methodology abandons the typical source iteration scheme and solves directly for the fully converged scalar flux. Four matrix operators are constructed based upon the integral form of the discrete ordinates equations. A single differential mesh sweep is performed to construct these operators. The method is parallelized by decomposing the problem domain into several smaller sub-domains, each treated as an independent problem. The scalar flux of each sub-domain is solved exactly given incoming angular flux boundary conditions. Sub-domain boundary conditions are updated iteratively, and convergence is achieved when the scalar flux error in all cells meets a pre-specified convergence criterion. The method has been implemented in a computer code that was then employed for strong scaling studies of the algorithm's parallel performance via a fixed-size problem in tests ranging from one domain up to one cell per sub-domain. Results indicate that the best parallel performance compared to source iterations occurs for optically thick, highly scattering problems, the variety that is most difficult for the traditional SI scheme to solve. Moreover, the minimum execution time occurs when each sub-domain contains a total of four cells. (authors)
Thermic decomposition of biphenyl; Decomposition thermique du biphenyle
Energy Technology Data Exchange (ETDEWEB)
Lutz, M [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1966-03-01
Liquid and vapour phase pyrolysis of very pure biphenyl obtained by methods described in the text was carried out at 400 C in sealed ampoules, the fraction transformed being always less than 0.1 per cent. The main products were hydrogen, benzene, terphenyls, and a deposit of polyphenyls strongly adhering to the walls. Small quantities of the lower aliphatic hydrocarbons were also found. The variation of the yields of these products with a) the pyrolysis time, b) the state (gas or liquid) of the biphenyl, and c) the pressure of the vapour was measured. Varying the area and nature of the walls showed that in the absence of a liquid phase, the pyrolytic decomposition takes place in the adsorbed layer, and that metallic walls promote the reaction more actively than do those of glass (pyrex or silica). A mechanism is proposed to explain the results pertaining to this decomposition in the adsorbed phase. The adsorption seems to obey a Langmuir isotherm, and the chemical act which determines the overall rate of decomposition is unimolecular. (author) [French] Du biphenyle tres pur, dont la purification est decrite, est pyrolyse a 400 C en phase vapeur et en phase liquide dans des ampoules scellees sous vide, a des taux de decomposition n'ayant jamais depasse 0,1 pour cent. Les produits provenant de la pyrolyse sont essentiellement: l' hydrogene, le benzene, les therphenyles, et un depot de polyphenyles adherant fortement aux parois. En plus il se forme de faibles quantites d'hydrocarbures aliphatiques gazeux. On indique la variation des rendements des differents produits avec la duree de pyrolyse, l'etat gazeux ou liquide du biphenyle, et la pression de la vapeur. Variant la superficie et la nature des parois, on montre qu'en absence de liquide la pyrolyse se fait en phase adsorbee. La pyrolyse est plus active au contact de parois metalliques que de celles de verres (pyrex ou silice). A partir des resultats experimentaux un mecanisme de degradation du biphenyle en phase
A novel method for EMG decomposition based on matched filters
Directory of Open Access Journals (Sweden)
Ailton Luiz Dias Siqueira Júnior
Full Text Available Introduction Decomposition of electromyography (EMG signals into the constituent motor unit action potentials (MUAPs can allow for deeper insights into the underlying processes associated with the neuromuscular system. The vast majority of the methods for EMG decomposition found in the literature depend on complex algorithms and specific instrumentation. As an attempt to contribute to solving these issues, we propose a method based on a bank of matched filters for the decomposition of EMG signals. Methods Four main units comprise our method: a bank of matched filters, a peak detector, a motor unit classifier and an overlapping resolution module. The system’s performance was evaluated with simulated and real EMG data. Classification accuracy was measured by comparing the responses of the system with known data from the simulator and with the annotations of a human expert. Results The results show that decomposition of non-overlapping MUAPs can be achieved with up to 99% accuracy for signals with up to 10 active motor units and a signal-to-noise ratio (SNR of 10 dB. For overlapping MUAPs with up to 10 motor units per signal and a SNR of 20 dB, the technique allows for correct classification of approximately 71% of the MUAPs. The method is capable of processing, decomposing and classifying a 50 ms window of data in less than 5 ms using a standard desktop computer. Conclusion This article contributes to the ongoing research on EMG decomposition by describing a novel technique capable of delivering high rates of success by means of a fast algorithm, suggesting its possible use in future real-time embedded applications, such as myoelectric prostheses control and biofeedback systems.
Interacting effects of insects and flooding on wood decomposition.
Directory of Open Access Journals (Sweden)
Michael D Ulyshen
Full Text Available Saproxylic arthropods are thought to play an important role in wood decomposition but very few efforts have been made to quantify their contributions to the process and the factors controlling their activities are not well understood. In the current study, mesh exclusion bags were used to quantify how arthropods affect loblolly pine (Pinus taeda L. decomposition rates in both seasonally flooded and unflooded forests over a 31-month period in the southeastern United States. Wood specific gravity (based on initial wood volume was significantly lower in bolts placed in unflooded forests and for those unprotected from insects. Approximately 20.5% and 13.7% of specific gravity loss after 31 months was attributable to insect activity in flooded and unflooded forests, respectively. Importantly, minimal between-treatment differences in water content and the results from a novel test carried out separately suggest the mesh bags had no significant impact on wood mass loss beyond the exclusion of insects. Subterranean termites (Isoptera: Rhinotermitidae: Reticulitermes spp. were 5-6 times more active below-ground in unflooded forests compared to flooded forests based on wooden monitoring stakes. They were also slightly more active above-ground in unflooded forests but these differences were not statistically significant. Similarly, seasonal flooding had no detectable effect on above-ground beetle (Coleoptera richness or abundance. Although seasonal flooding strongly reduced Reticulitermes activity below-ground, it can be concluded from an insignificant interaction between forest type and exclusion treatment that reduced above-ground decomposition rates in seasonally flooded forests were due largely to suppressed microbial activity at those locations. The findings from this study indicate that southeastern U.S. arthropod communities accelerate above-ground wood decomposition significantly and to a similar extent in both flooded and unflooded forests
Spherical Approximation on Unit Sphere
Directory of Open Access Journals (Sweden)
Eman Samir Bhaya
2018-01-01
Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of functions in spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in spaces for by modulus of smoothness of functions.
Underdetermined Blind Audio Source Separation Using Modal Decomposition
Directory of Open Access Journals (Sweden)
Abdeldjalil Aïssa-El-Bey
2007-03-01
Full Text Available This paper introduces new algorithms for the blind separation of audio sources using modal decomposition. Indeed, audio signals and, in particular, musical signals can be well approximated by a sum of damped sinusoidal (modal components. Based on this representation, we propose a two-step approach consisting of a signal analysis (extraction of the modal components followed by a signal synthesis (grouping of the components belonging to the same source using vector clustering. For the signal analysis, two existing algorithms are considered and compared: namely the EMD (empirical mode decomposition algorithm and a parametric estimation algorithm using ESPRIT technique. A major advantage of the proposed method resides in its validity for both instantaneous and convolutive mixtures and its ability to separate more sources than sensors. Simulation results are given to compare and assess the performance of the proposed algorithms.
Underdetermined Blind Audio Source Separation Using Modal Decomposition
Directory of Open Access Journals (Sweden)
Aïssa-El-Bey Abdeldjalil
2007-01-01
Full Text Available This paper introduces new algorithms for the blind separation of audio sources using modal decomposition. Indeed, audio signals and, in particular, musical signals can be well approximated by a sum of damped sinusoidal (modal components. Based on this representation, we propose a two-step approach consisting of a signal analysis (extraction of the modal components followed by a signal synthesis (grouping of the components belonging to the same source using vector clustering. For the signal analysis, two existing algorithms are considered and compared: namely the EMD (empirical mode decomposition algorithm and a parametric estimation algorithm using ESPRIT technique. A major advantage of the proposed method resides in its validity for both instantaneous and convolutive mixtures and its ability to separate more sources than sensors. Simulation results are given to compare and assess the performance of the proposed algorithms.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Modal analysis of fluid flows using variants of proper orthogonal decomposition
Rowley, Clarence; Dawson, Scott
2017-11-01
This talk gives an overview of several methods for analyzing fluid flows, based on variants of proper orthogonal decomposition. These methods may be used to determine simplified, approximate models that capture the essential features of these flows, in order to better understand the dominant physical mechanisms, and potentially to develop appropriate strategies for model-based flow control. We discuss balanced proper orthogonal decomposition as an approximation of balanced truncation, and explain connections with system identification methods such as the eigensystem realization algorithm. We demonstrate the methods on several canonical examples, including a linearized channel flow and the flow past a circular cylinder. Supported by AFOSR, Grant FA9550-14-1-0289.
A Tensor Decomposition-Based Approach for Detecting Dynamic Network States From EEG.
Mahyari, Arash Golibagh; Zoltowski, David M; Bernat, Edward M; Aviyente, Selin
2017-01-01
Functional connectivity (FC), defined as the statistical dependency between distinct brain regions, has been an important tool in understanding cognitive brain processes. Most of the current works in FC have focused on the assumption of temporally stationary networks. However, recent empirical work indicates that FC is dynamic due to cognitive functions. The purpose of this paper is to understand the dynamics of FC for understanding the formation and dissolution of networks of the brain. In this paper, we introduce a two-step approach to characterize the dynamics of functional connectivity networks (FCNs) by first identifying change points at which the network connectivity across subjects shows significant changes and then summarizing the FCNs between consecutive change points. The proposed approach is based on a tensor representation of FCNs across time and subjects yielding a four-mode tensor. The change points are identified using a subspace distance measure on low-rank approximations to the tensor at each time point. The network summarization is then obtained through tensor-matrix projections across the subject and time modes. The proposed framework is applied to electroencephalogram (EEG) data collected during a cognitive control task. The detected change-points are consistent with a priori known ERN interval. The results show significant connectivities in medial-frontal regions which are consistent with widely observed ERN amplitude measures. The tensor-based method outperforms conventional matrix-based methods such as singular value decomposition in terms of both change-point detection and state summarization. The proposed tensor-based method captures the topological structure of FCNs which provides more accurate change-point-detection and state summarization.
Approximating the constellation constrained capacity of the MIMO channel with discrete input
DEFF Research Database (Denmark)
Yankov, Metodi Plamenov; Forchhammer, Søren; Larsen, Knud J.
2015-01-01
In this paper the capacity of a Multiple Input Multiple Output (MIMO) channel is considered, subject to average power constraint, for multi-dimensional discrete input, in the case when no channel state information is available at the transmitter. We prove that when the constellation size grows, t...... for the equivalent orthogonal channel, obtained by the singular value decomposition. Furthermore, lower bounds on the constrained capacity are derived for the cases of square and tall MIMO matrix, by optimizing the constellation for the equivalent channel, obtained by QR decomposition....
Matrix Krylov subspace methods for image restoration
Directory of Open Access Journals (Sweden)
khalide jbilou
2015-09-01
Full Text Available In the present paper, we consider some matrix Krylov subspace methods for solving ill-posed linear matrix equations and in those problems coming from the restoration of blurred and noisy images. Applying the well known Tikhonov regularization procedure leads to a Sylvester matrix equation depending the Tikhonov regularized parameter. We apply the matrix versions of the well known Krylov subspace methods, namely the Least Squared (LSQR and the conjugate gradient (CG methods to get approximate solutions representing the restored images. Some numerical tests are presented to show the effectiveness of the proposed methods.
Variational random phase approximation for the anharmonic oscillator
International Nuclear Information System (INIS)
Dukelsky, J.; Schuck, P.
1990-04-01
The recently derived Variational Random Phase Approximation is examined using the anharmonic oscillator model. Special attention is paid to the ground state RPA wave function and the convergence of the proposed truncation scheme to obtain the diagonal density matrix. Comparison with the standard Coupled Cluster method is made
On the rational approximation of the bidimensional potentials
International Nuclear Information System (INIS)
Niculescu, V.I.R; Catana, D.
1997-01-01
In the present letter we introduced a symmetrical bidimensional potential with Woods-Saxon tail. The potential approximation has permitted to replace in the matrix the evaluation of double integration by a product of two integrals. That implied a complexity reduction in the Hamiltonian eigenvalue and eigenvector evaluation. Also, the harmonic bidimensional basis simplifies significantly the evaluation of electric multipole operators. (authors)
Approximation of reliability of direct genomic breeding values
Two methods to efficiently approximate theoretical genomic reliabilities are presented. The first method is based on the direct inverse of the left hand side (LHS) of mixed model equations. It uses the genomic relationship matrix for a small subset of individuals with the highest genomic relationshi...
Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.
Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E
2018-06-01
An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.
Dolomite decomposition under CO2
International Nuclear Information System (INIS)
Guerfa, F.; Bensouici, F.; Barama, S.E.; Harabi, A.; Achour, S.
2004-01-01
Full text.Dolomite (MgCa (CO 3 ) 2 is one of the most abundant mineral species on the surface of the planet, it occurs in sedimentary rocks. MgO, CaO and Doloma (Phase mixture of MgO and CaO, obtained from the mineral dolomite) based materials are attractive steel-making refractories because of their potential cost effectiveness and world wide abundance more recently, MgO is also used as protective layers in plasma screen manufacture ceel. The crystal structure of dolomite was determined as rhombohedral carbonates, they are layers of Mg +2 and layers of Ca +2 ions. It dissociates depending on the temperature variations according to the following reactions: MgCa (CO 3 ) 2 → MgO + CaO + 2CO 2 .....MgCa (CO 3 ) 2 → MgO + Ca + CaCO 3 + CO 2 .....This latter reaction may be considered as a first step for MgO production. Differential thermal analysis (DTA) are used to control dolomite decomposition and the X-Ray Diffraction (XRD) was used to elucidate thermal decomposition of dolomite according to the reaction. That required samples were heated to specific temperature and holding times. The average particle size of used dolomite powders is 0.3 mm, as where, the heating temperature was 700 degree celsius, using various holding times (90 and 120 minutes). Under CO 2 dolomite decomposed directly to CaCO 3 accompanied by the formation of MgO, no evidence was offered for the MgO formation of either CaO or MgCO 3 , under air, simultaneous formation of CaCO 3 , CaO and accompanied dolomite decomposition
The efficiency of Flory approximation
International Nuclear Information System (INIS)
Obukhov, S.P.
1984-01-01
The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)
Nuclear power plant risk assembly and decomposition for risk management
International Nuclear Information System (INIS)
Iden, D.C.
1985-01-01
The state-of-the-art method for analyzing the risk from nuclear power plants is probabilistic risk assessment (PRA). The intermediate results of a PRA are first assembled to quantify the risk from operating a nuclear power plant in the form of (1) core damage (or core melt) frequency, (2) plant damage state frequencies, (3) release category frequencies, and (4) the frequency of exceeding specific levels of offsite consequences. Once the overall PRA results have been quantified, the next step is to decompose those results into the individual contributors to each of the four forms of risk in some rank order. The way in which the PRA model is set up to assemble and decompose the plant risk determines the ease and usefulness of the PRA model as a risk management tool for evaluating perturbations to the PRA model. These perturbations can take the form of technical specification changes, hardware modifications, procedural changes, etc. The matrix formalism developed by Dr. Stan Kaplan for risk assembly and decomposition represents a significant breakthrough in making the PRA model an effective risk management tool. The key to understanding the matrix formalism and making it a useful tool for managing nuclear power plant risk is the structure of the PRA model. PRA risk model structure and decomposition of the risk results are discussed with the Seabrook PRA as an example
Simultaneous tensor decomposition and completion using factor priors.
Chen, Yi-Lei; Hsu, Chiou-Ting; Liao, Hong-Yuan Mark
2014-03-01
The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion, which is a high-order extension of matrix completion, has also generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called simultaneous tensor decomposition and completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.
International Nuclear Information System (INIS)
Gavrilov, V.I.; Gumerov, N.S.; Rakhmatullin, R.R.
1989-01-01
By the method of conductometry decomposition kinetics of 10-methyl-10phenylphenoxarsonium iodide in methanol, ethanol, 2-propanol, 1-butanol, 1-pentanol and methyl ethyl ketone at initial concentration of the salt 0.00024-0.003 mol/l, is studied. It is shown that at the temperatures up to 80-95 deg C practically no decomposition of arsonium salt in methanol and ethanol is observed. With an increase in the length of alcohol alkyl radical the decomposition rate increases. The values of activation enrgy both for alcohols and ketone are approximately the same. At the same time, decomposition rate in alcohol proved much slower than in ketone, which is related to iodide-ion solvation in protic solvents
Energy Technology Data Exchange (ETDEWEB)
Gavrilov, V I; Gumerov, N S; Rakhmatullin, R R [Kazanskij Khimiko-Tekhnologicheskij Inst., Kazan (USSR)
1989-03-01
By the method of conductometry decomposition kinetics of 10-methyl-10phenylphenoxarsonium iodide in methanol, ethanol, 2-propanol, 1-butanol, 1-pentanol and methyl ethyl ketone at initial concentration of the salt 0.00024-0.003 mol/l, is studied. It is shown that at the temperatures up to 80-95 deg C practically no decomposition of arsonium salt in methanol and ethanol is observed. With an increase in the length of alcohol alkyl radical the decomposition rate increases. The values of activation enrgy both for alcohols and ketone are approximately the same. At the same time, decomposition rate in alcohol proved much slower than in ketone, which is related to iodide-ion solvation in protic solvents.
DEFF Research Database (Denmark)
Wu, Hao; Jespersen, Jacob Boll; Jappe Frandsen, Flemming
2013-01-01
Ferric sulfate is used as an additive in biomass combustion to convert the released potassium chloride to the less harmful potassium sulfate. The decomposition of ferric sulfate is studied in a fast heating rate thermogravimetric analyzer and a volumetric reaction model is proposed to describe...... the process. The yields of sulfur oxides from ferric sulfate decomposition under boiler conditions are investigated experimentally, revealing a distribution of approximately 40% SO3 and 60% SO2. The ferric sulfate decomposition model is combined with a detailed kinetic model of gas‐phase KCl sulfation...... and a model of K2SO4 condensation to simulate the sulfation of KCl by ferric sulfate addition. The simulation results show good agreements with experiments conducted in a biomass grate‐firing reactor. The results indicate that the SO3 released from ferric sulfate decomposition is the main contributor to KCl...
3D quantitative analysis of early decomposition changes of the human face.
Caplova, Zuzana; Gibelli, Daniele Maria; Poppa, Pasquale; Cummaudo, Marco; Obertova, Zuzana; Sforza, Chiarella; Cattaneo, Cristina
2018-03-01
Decomposition of the human body and human face is influenced, among other things, by environmental conditions. The early decomposition changes that modify the appearance of the face may hamper the recognition and identification of the deceased. Quantitative assessment of those changes may provide important information for forensic identification. This report presents a pilot 3D quantitative approach of tracking early decomposition changes of a single cadaver in controlled environmental conditions by summarizing the change with weekly morphological descriptions. The root mean square (RMS) value was used to evaluate the changes of the face after death. The results showed a high correlation (r = 0.863) between the measured RMS and the time since death. RMS values of each scan are presented, as well as the average weekly RMS values. The quantification of decomposition changes could improve the accuracy of antemortem facial approximation and potentially could allow the direct comparisons of antemortem and postmortem 3D scans.
A Hybrid Model Based on Wavelet Decomposition-Reconstruction in Track Irregularity State Forecasting
Directory of Open Access Journals (Sweden)
Chaolong Jia
2015-01-01
Full Text Available Wavelet is able to adapt to the requirements of time-frequency signal analysis automatically and can focus on any details of the signal and then decompose the function into the representation of a series of simple basis functions. It is of theoretical and practical significance. Therefore, this paper does subdivision on track irregularity time series based on the idea of wavelet decomposition-reconstruction and tries to find the best fitting forecast model of detail signal and approximate signal obtained through track irregularity time series wavelet decomposition, respectively. On this ideology, piecewise gray-ARMA recursive based on wavelet decomposition and reconstruction (PG-ARMARWDR and piecewise ANN-ARMA recursive based on wavelet decomposition and reconstruction (PANN-ARMARWDR models are proposed. Comparison and analysis of two models have shown that both these models can achieve higher accuracy.
International Nuclear Information System (INIS)
Sotiriou, Georgios A.; Singh, Dilpreet; Zhang, Fang; Chalbot, Marie-Cecile G.; Spielman-Sun, Eleanor; Hoering, Lutz; Kavouras, Ilias G.; Lowry, Gregory V.; Wohlleben, Wendel; Demokritou, Philip
2016-01-01
Highlights: • Nano-enabled products might reach their end-of-life by thermal decomposition. • Thermal decomposition provides two by-products: released aerosol and residual ash. • Is there any nanofiller release in byproducts? • Risk assessment of potential environmental health implications. - Abstract: Nano-enabled products (NEPs) are currently part of our life prompting for detailed investigation of potential nano-release across their life-cycle. Particularly interesting is their end-of-life thermal decomposition scenario. Here, we examine the thermal decomposition of widely used NEPs, namely thermoplastic nanocomposites, and assess the properties of the byproducts (released aerosol and residual ash) and possible environmental health and safety implications. We focus on establishing a fundamental understanding on the effect of thermal decomposition parameters, such as polymer matrix, nanofiller properties, decomposition temperature, on the properties of byproducts using a recently-developed lab-based experimental integrated platform. Our results indicate that thermoplastic polymer matrix strongly influences size and morphology of released aerosol, while there was minimal but detectable nano-release, especially when inorganic nanofillers were used. The chemical composition of the released aerosol was found not to be strongly influenced by the presence of nanofiller at least for the low, industry-relevant loadings assessed here. Furthermore, the morphology and composition of residual ash was found to be strongly influenced by the presence of nanofiller. The findings presented here on thermal decomposition/incineration of NEPs raise important questions and concerns regarding the potential fate and transport of released engineered nanomaterials in environmental media and potential environmental health and safety implications.
Energy Technology Data Exchange (ETDEWEB)
Sotiriou, Georgios A.; Singh, Dilpreet; Zhang, Fang [Center for Nanotechnology and Nanotoxicology, Department of Environmental Health, T.H. Chan School of Public Health, Harvard University, 665 Huntington Ave., Boston, MA 02115 (United States); Chalbot, Marie-Cecile G. [Department of Environmental and Occupational Health, College of Public Health, University of Arkansas for Medical Sciences, Little Rock, AR 72205 (United States); Spielman-Sun, Eleanor [Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 (United States); Hoering, Lutz [BASF SE, Material Physics, 67056 Ludwigshafen (Germany); Kavouras, Ilias G. [Department of Environmental and Occupational Health, College of Public Health, University of Arkansas for Medical Sciences, Little Rock, AR 72205 (United States); Lowry, Gregory V. [Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 (United States); Wohlleben, Wendel [Center for Nanotechnology and Nanotoxicology, Department of Environmental Health, T.H. Chan School of Public Health, Harvard University, 665 Huntington Ave., Boston, MA 02115 (United States); BASF SE, Material Physics, 67056 Ludwigshafen (Germany); Demokritou, Philip, E-mail: pdemokri@hsph.harvard.edu [Center for Nanotechnology and Nanotoxicology, Department of Environmental Health, T.H. Chan School of Public Health, Harvard University, 665 Huntington Ave., Boston, MA 02115 (United States)
2016-03-15
Highlights: • Nano-enabled products might reach their end-of-life by thermal decomposition. • Thermal decomposition provides two by-products: released aerosol and residual ash. • Is there any nanofiller release in byproducts? • Risk assessment of potential environmental health implications. - Abstract: Nano-enabled products (NEPs) are currently part of our life prompting for detailed investigation of potential nano-release across their life-cycle. Particularly interesting is their end-of-life thermal decomposition scenario. Here, we examine the thermal decomposition of widely used NEPs, namely thermoplastic nanocomposites, and assess the properties of the byproducts (released aerosol and residual ash) and possible environmental health and safety implications. We focus on establishing a fundamental understanding on the effect of thermal decomposition parameters, such as polymer matrix, nanofiller properties, decomposition temperature, on the properties of byproducts using a recently-developed lab-based experimental integrated platform. Our results indicate that thermoplastic polymer matrix strongly influences size and morphology of released aerosol, while there was minimal but detectable nano-release, especially when inorganic nanofillers were used. The chemical composition of the released aerosol was found not to be strongly influenced by the presence of nanofiller at least for the low, industry-relevant loadings assessed here. Furthermore, the morphology and composition of residual ash was found to be strongly influenced by the presence of nanofiller. The findings presented here on thermal decomposition/incineration of NEPs raise important questions and concerns regarding the potential fate and transport of released engineered nanomaterials in environmental media and potential environmental health and safety implications.
Directory of Open Access Journals (Sweden)
Elena Vasil'evna Chetina
2010-01-01
Conclusion. The effect of CP on gene expression and collagen decomposition activity depends on the morphotype of embryonic chondrocytes. Lack of effect of CP on collagen decomposition activity in both the embryonic hypertrophic chondrocytes and the cartilage explants from OA patients supports the hypothesis that the hypertrophic morphotype is a dominant morphotype of articular chondrocytes in OA. Moreover, collagen decomposition products can be involved in the resorption of matrix in OA and in the maintenance of chronic nature of the pathology.
Extended quasiparticle approximation for relativistic electrons in plasmas
Directory of Open Access Journals (Sweden)
V.G.Morozov
2006-01-01
Full Text Available Starting with Dyson equations for the path-ordered Green's function, it is shown that the correlation functions for relativistic electrons (positrons in a weakly coupled non-equilibrium plasmas can be decomposed into sharply peaked quasiparticle parts and off-shell parts in a rather general form. To leading order in the electromagnetic coupling constant, this decomposition yields the extended quasiparticle approximation for the correlation functions, which can be used for the first principle calculation of the radiation scattering rates in QED plasmas.
Data-Driven Model Reduction and Transfer Operator Approximation
Klus, Stefan; Nüske, Feliks; Koltai, Péter; Wu, Hao; Kevrekidis, Ioannis; Schütte, Christof; Noé, Frank
2018-06-01
In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.
Decomposition of Multi-player Games
Zhao, Dengji; Schiffel, Stephan; Thielscher, Michael
Research in General Game Playing aims at building systems that learn to play unknown games without human intervention. We contribute to this endeavour by generalising the established technique of decomposition from AI Planning to multi-player games. To this end, we present a method for the automatic decomposition of previously unknown games into independent subgames, and we show how a general game player can exploit a successful decomposition for game tree search.
Constructive quantum Shannon decomposition from Cartan involutions
International Nuclear Information System (INIS)
Drury, Byron; Love, Peter
2008-01-01
The work presented here extends upon the best known universal quantum circuit, the quantum Shannon decomposition proposed by Shende et al (2006 IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 25 1000). We obtain the basis of the circuit's design in a pair of Cartan decompositions. This insight gives a simple constructive factoring algorithm in terms of the Cartan involutions corresponding to these decompositions
Constructive quantum Shannon decomposition from Cartan involutions
Energy Technology Data Exchange (ETDEWEB)
Drury, Byron; Love, Peter [Department of Physics, 370 Lancaster Ave., Haverford College, Haverford, PA 19041 (United States)], E-mail: plove@haverford.edu
2008-10-03
The work presented here extends upon the best known universal quantum circuit, the quantum Shannon decomposition proposed by Shende et al (2006 IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 25 1000). We obtain the basis of the circuit's design in a pair of Cartan decompositions. This insight gives a simple constructive factoring algorithm in terms of the Cartan involutions corresponding to these decompositions.
Mathematical modelling of the decomposition of explosives
International Nuclear Information System (INIS)
Smirnov, Lev P
2010-01-01
Studies on mathematical modelling of the molecular and supramolecular structures of explosives and the elementary steps and overall processes of their decomposition are analyzed. Investigations on the modelling of combustion and detonation taking into account the decomposition of explosives are also considered. It is shown that solution of problems related to the decomposition kinetics of explosives requires the use of a complex strategy based on the methods and concepts of chemical physics, solid state physics and theoretical chemistry instead of empirical approach.
Rollout sampling approximate policy iteration
Dimitrakakis, C.; Lagoudakis, M.G.
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Framework for sequential approximate optimization
Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.
2004-01-01
An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python
Random-phase approximation and broken symmetry
International Nuclear Information System (INIS)
Davis, E.D.; Heiss, W.D.
1986-01-01
The validity of the random-phase approximation (RPA) in broken-symmetry bases is tested in an appropriate many-body system for which exact solutions are available. Initially the regions of stability of the self-consistent quasiparticle bases in this system are established and depicted in a 'phase' diagram. It is found that only stable bases can be used in an RPA calculation. This is particularly true for those RPA modes which are not associated with the onset of instability of the basis; it is seen that these modes do not describe any excited state when the basis is unstable, although from a formal point of view they remain acceptable. The RPA does well in a stable broken-symmetry basis provided one is not too close to a point where a phase transition occurs. This is true for both energies and matrix elements. (author)
Xylanase and cellulase activities during anaerobic decomposition of three aquatic macrophytes.
Nunes, Maíra F; da Cunha-Santino, Marcela B; Bianchini, Irineu
2011-01-01
Enzymatic activity during decomposition is extremely important to hydrolyze molecules that are assimilated by microorganisms. During aquatic macrophytes decomposition, enzymes act mainly in the breakdown of lignocellulolytic matrix fibers (i.e. cellulose, hemicellulose and lignin) that encompass the refractory fraction from organic matter. Considering the importance of enzymatic activities role in decomposition processes, this study aimed to describe the temporal changes of xylanase and cellulose activities during anaerobic decomposition of Ricciocarpus natans (freely-floating), Oxycaryum cubense (emergent) and Cabomba furcata (submersed). The aquatic macrophytes were collected in Óleo Lagoon, Luiz Antonio, São Paulo, Brazil and bioassays were accomplished. Decomposition chambers from each species (n = 10) were set up with dried macrophyte fragments and filtered Óleo Lagoon water. The chambers were incubated at 22.5°C, in the dark and under anaerobic conditions. Enzymatic activities and remaining organic matter were measured periodically during 90 days. The temporal variation of enzymes showed that C. furcata presented the highest decay and the highest maximum enzyme production. Xylanase production was higher than cellulase production for the decomposition of the three aquatic macrophytes species.
Directory of Open Access Journals (Sweden)
Katelynn A. Perrault
2014-07-01
Full Text Available Odour profiling of decomposed remains is important for understanding the mechanisms that cadaver dogs and forensically-relevant insects use to locate decomposed remains. The decomposition odour profile is complex and has been documented in outdoor terrestrial environments. The purpose of this study was to perform longitudinal analysis of the volatile organic compound (VOC profile in soils associated with decomposed remains across all stages of decomposition. Two VOC collection techniques (sorbent tubes and solid phase microextraction were used to collect a wider analyte range and to investigate differences in collection techniques. Pig carcasses were placed in an outdoor research facility in Australia to model the decomposition process and VOCs were collected intermittently over two months. VOCs of interest were identified over the duration of the trial, showing distinct trends in compound evolution and disappearance. The collection techniques were complementary, representing different subsets of VOCs from the overall profile. Sorbent tubes collected more decomposition-specific VOCs and these compounds were more effective at characterising the matrix over an extended period. Using both collection techniques improves the likelihood of identifying the complete VOC profile of decomposition odour. Such information is important for the search and recovery of victim remains in various stages of decomposition.
Speech Denoising in White Noise Based on Signal Subspace Low-rank Plus Sparse Decomposition
Directory of Open Access Journals (Sweden)
yuan Shuai
2017-01-01
Full Text Available In this paper, a new subspace speech enhancement method using low-rank and sparse decomposition is presented. In the proposed method, we firstly structure the corrupted data as a Toeplitz matrix and estimate its effective rank for the underlying human speech signal. Then the low-rank and sparse decomposition is performed with the guidance of speech rank value to remove the noise. Extensive experiments have been carried out in white Gaussian noise condition, and experimental results show the proposed method performs better than conventional speech enhancement methods, in terms of yielding less residual noise and lower speech distortion.
Matrix regularization of 4-manifolds
Trzetrzelewski, M.
2012-01-01
We consider products of two 2-manifolds such as S^2 x S^2, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S...
Decomposition in pelagic marine ecosytems
International Nuclear Information System (INIS)
Lucas, M.I.
1986-01-01
During the decomposition of plant detritus, complex microbial successions develop which are dominated in the early stages by a number of distinct bacterial morphotypes. The microheterotrophic community rapidly becomes heterogenous and may include cyanobacteria, fungi, yeasts and bactivorous protozoans. Microheterotrophs in the marine environment may have a biomass comparable to that of all other heterotrophs and their significance as a resource to higher trophic orders, and in the regeneration of nutrients, particularly nitrogen, that support 'regenerated' primary production, has aroused both attention and controversy. Numerous methods have been employed to measure heterotrophic bacterial production and activity. The most widely used involve estimates of 14 C-glucose uptake; the frequency of dividing cells; the incorporation of 3 H-thymidine and exponential population growth in predator-reduced filtrates. Recent attempts to model decomposition processes and C and N fluxes in pelagic marine ecosystems are described. This review examines the most sensitive components and predictions of the models with particular reference to estimates of bacterial production, net growth yield and predictions of N cycling determined by 15 N methodology. Directed estimates of nitrogen (and phosphorus) flux through phytoplanktonic and bacterioplanktonic communities using 15 N (and 32 P) tracer methods are likely to provide more realistic measures of nitrogen flow through planktonic communities
Infrared multiphoton absorption and decomposition
International Nuclear Information System (INIS)
Evans, D.K.; McAlpine, R.D.
1984-01-01
The discovery of infrared laser induced multiphoton absorption (IRMPA) and decomposition (IRMPD) by Isenor and Richardson in 1971 generated a great deal of interest in these phenomena. This interest was increased with the discovery by Ambartzumian, Letokhov, Ryadbov and Chekalin that isotopically selective IRMPD was possible. One of the first speculations about these phenomena was that it might be possible to excite a particular mode of a molecule with the intense infrared laser beam and cause decomposition or chemical reaction by channels which do not predominate thermally, thus providing new synthetic routes for complex chemicals. The potential applications to isotope separation and novel chemistry stimulated efforts to understand the underlying physics and chemistry of these processes. At ICOMP I, in 1977 and at ICOMP II in 1980, several authors reviewed the current understandings of IRMPA and IRMPD as well as the particular aspect of isotope separation. There continues to be a great deal of effort into understanding IRMPA and IRMPD and we will briefly review some aspects of these efforts with particular emphasis on progress since ICOMP II. 31 references
Decomposition of Diethylstilboestrol in Soil
DEFF Research Database (Denmark)
Gregers-Hansen, Birte
1964-01-01
The rate of decomposition of DES-monoethyl-1-C14 in soil was followed by measurement of C14O2 released. From 1.6 to 16% of the added C14 was recovered as C14O2 during 3 months. After six months as much as 12 to 28 per cent was released as C14O2.Determination of C14 in the soil samples after the e...... not inhibit the CO2 production from the soil.Experiments with γ-sterilized soil indicated that enzymes present in the soil are able to attack DES.......The rate of decomposition of DES-monoethyl-1-C14 in soil was followed by measurement of C14O2 released. From 1.6 to 16% of the added C14 was recovered as C14O2 during 3 months. After six months as much as 12 to 28 per cent was released as C14O2.Determination of C14 in the soil samples after...
Efficient solution of parabolic equations by Krylov approximation methods
Gallopoulos, E.; Saad, Y.
1990-01-01
Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.
Kumar, Ravi; Bhaduri, Basanta; Nishchal, Naveen K.
2018-01-01
In this study, we propose a quick response (QR) code based nonlinear optical image encryption technique using spiral phase transform (SPT), equal modulus decomposition (EMD) and singular value decomposition (SVD). First, the primary image is converted into a QR code and then multiplied with a spiral phase mask (SPM). Next, the product is spiral phase transformed with particular spiral phase function, and further, the EMD is performed on the output of SPT, which results into two complex images, Z 1 and Z 2. Among these, Z 1 is further Fresnel propagated with distance d, and Z 2 is reserved as a decryption key. Afterwards, SVD is performed on Fresnel propagated output to get three decomposed matrices i.e. one diagonal matrix and two unitary matrices. The two unitary matrices are modulated with two different SPMs and then, the inverse SVD is performed using the diagonal matrix and modulated unitary matrices to get the final encrypted image. Numerical simulation results confirm the validity and effectiveness of the proposed technique. The proposed technique is robust against noise attack, specific attack, and brutal force attack. Simulation results are presented in support of the proposed idea.
An approximation method for diffusion based leaching models
International Nuclear Information System (INIS)
Shukla, B.S.; Dignam, M.J.
1987-01-01
In connection with the fixation of nuclear waste in a glassy matrix equations have been derived for leaching models based on a uniform concentration gradient approximation, and hence a uniform flux, therefore requiring the use of only Fick's first law. In this paper we improve on the uniform flux approximation, developing and justifying the approach. The resulting set of equations are solved to a satisfactory approximation for a matrix dissolving at a constant rate in a finite volume of leachant to give analytical expressions for the time dependence of the thickness of the leached layer, the diffusional and dissolutional contribution to the flux, and the leachant composition. Families of curves are presented which cover the full range of all the physical parameters for this system. The same procedure can be readily extended to more complex systems. (author)
COMPOSITION OF FOWLPOX VIRUS AND INCLUSION MATRIX.
RANDALL, C C; GAFFORD, L G; DARLINGTON, R W; HYDE, J
1964-04-01
Randall, Charles C. (University of Mississippi School of Medicine, Jackson), Lanelle G. Gafford, Robert W. Darlington, and James M. Hyde. Composition of fowlpox virus and inclusion matrix. J. Bacteriol. 87:939-944. 1964.-Inclusion bodies of fowlpox virus infection are especially favorable starting material for the isolation of virus and inclusion matrix. Electron micrographs of viral particles and matrix indicated a high degree of purification. Density-gradient centrifugation of virus in cesium chloride and potassium tartrate was unsatisfactory because of inactivation, and clumping or disintegration. Chemical analyses of virus and matrix revealed significant amounts of lipid, protein, and deoxyribonucleic acid, but no ribonucleic acid or carbohydrate. Approximately 47% of the weight of the virus and 83% of the matrix were extractable in chloroform-methanol. The lipid partitions of the petroleum ether extracts were similar, except that the phospholipid content of the matrix was 2.2 times that of the virus. Viral particles were sensitive to diethyl ether and chloroform.
Vegetation exerts a greater control on litter decomposition than climate warming in peatlands.
Ward, Susan E; Orwin, Kate H; Ostle, Nicholas J; Briones, J I; Thomson, Bruce C; Griffiths, Robert I; Oakley, Simon; Quirk, Helen; Bardget, Richard D
2015-01-01
Historically, slow decomposition rates have resulted in the accumulation of large amounts of carbon in northern peatlands. Both climate warming and vegetation change can alter rates of decomposition, and hence affect rates of atmospheric CO2 exchange, with consequences for climate change feedbacks. Although warming and vegetation change are happening concurrently, little is known about their relative and interactive effects on decomposition processes. To test the effects of warming and vegetation change on decomposition rates, we placed litter of three dominant species (Calluna vulgaris, Eriophorum vaginatum, Hypnum jutlandicum) into a peatland field experiment that combined warming.with plant functional group removals, and measured mass loss over two years. To identify potential mechanisms behind effects, we also measured nutrient cycling and soil biota. We found that plant functional group removals exerted a stronger control over short-term litter decomposition than did approximately 1 degrees C warming, and that the plant removal effect depended on litter species identity. Specifically, rates of litter decomposition were faster when shrubs were removed from the plant community, and these effects were strongest for graminoid and bryophyte litter. Plant functional group removals also had strong effects on soil biota and nutrient cycling associated with decomposition, whereby shrub removal had cascading effects on soil fungal community composition, increased enchytraeid abundance, and increased rates of N mineralization. Our findings demonstrate that, in addition to litter quality, changes in vegetation composition play a significant role in regulating short-term litter decomposition and belowground communities in peatland, and that these impacts can be greater than moderate warming effects. Our findings, albeit from a relatively short-term study, highlight the need to consider both vegetation change and its impacts below ground alongside climatic effects when
Reliable Function Approximation and Estimation
2016-08-16
compressed sensing results to a wide class of infinite -dimensional problems. We discuss four key application domains for the methods developed in this... infinite -dimensional problems. We discuss four key findings arising from this project, as related to uncertainty quantification, image processing, matrix...compressed sensing results to a wide class of infinite -dimensional problems. We discuss four key application domains for the methods developed in this project
Thermal decomposition of anhydrous zinc and cadmium salicylates
International Nuclear Information System (INIS)
Kharitonov, Yu.Ya.; Tujebakhova, Z.K.
1984-01-01
On the basis of studying thermograms, thermogravigrams, IR absorption spectra, X-rayograms of anhydrous znc and cadmium salicylate complexes of the M(HSal) 2 composition, (where M=Zn, Cd; HSal is an anion of once deprotonated salicyclic acid H 2 Sal) and products of their thermal transformations, the processes are characterized of stage-by-stage thermal decomposition of these compounds under continuous heating in the air from room temperature to approximately 1000 deg C. It is shown that the Cd(HSal) 2 pyrolysis proceeds with the formation of CdSal at 170-250 deg C and CdO - at 320-460 deg C
Nuclear Hartree-Fock approximation testing and other related approximations
International Nuclear Information System (INIS)
Cohenca, J.M.
1970-01-01
Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt
Decomposition kinetics of plutonium hydride
Energy Technology Data Exchange (ETDEWEB)
Haschke, J.M.; Stakebake, J.L.
1979-01-01
Kinetic data for decomposition of PuH/sub 1/ /sub 95/ provides insight into a possible mechanism for the hydriding and dehydriding reactions of plutonium. The fact that the rate of the hydriding reaction, K/sub H/, is proportional to P/sup 1/2/ and the rate of the dehydriding process, K/sub D/, is inversely proportional to P/sup 1/2/ suggests that the forward and reverse reactions proceed by opposite paths of the same mechanism. The P/sup 1/2/ dependence of hydrogen solubility in metals is characteristic of the dissociative absorption of hydrogen; i.e., the reactive species is atomic hydrogen. It is reasonable to assume that the rates of the forward and reverse reactions are controlled by the surface concentration of atomic hydrogen, (H/sub s/), that K/sub H/ = c'(H/sub s/), and that K/sub D/ = c/(H/sub s/), where c' and c are proportionality constants. For this surface model, the pressure dependence of K/sub D/ is related to (H/sub s/) by the reaction (H/sub s/) reversible 1/2H/sub 2/(g) and by its equilibrium constant K/sub e/ = (H/sub 2/)/sup 1/2//(H/sub s/). In the pressure range of ideal gas behavior, (H/sub s/) = K/sub e//sup -1/(RT)/sup -1/2/ and the decomposition rate is given by K/sub D/ = cK/sub e/(RT)/sup -1/2/P/sup 1/2/. For an analogous treatment of the hydriding process with this model, it can be readily shown that K/sub H/ = c'K/sub e//sup -1/(RT)/sup -1/2/P/sup 1/2/. The inverse pressure dependence and direct temperature dependence of the decomposition rate are correctly predicted by this mechanism which is most consistent with the observed behavior of the Pu--H system.
Flat norm decomposition of integral currents
Directory of Open Access Journals (Sweden)
Sharif Ibrahim
2016-05-01
Full Text Available Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary and integer multiplicities, to arbitrary elements of the dual space of differential forms. The flat norm provides a natural distance in the space of currents, and works by decomposing a $d$-dimensional current into $d$- and (the boundary of $(d+1$-dimensional pieces in an optimal way.Given an integral current, can we expect its at norm decomposition to be integral as well? This is not known in general, except in the case of $d$-currents that are boundaries of $(d+1$-currents in $\\mathbb{R}^{d+1}$ (following results from a corresponding problem on the $L^1$ total variation ($L^1$TV of functionals. On the other hand, for a discretized at norm on a finite simplicial complex, the analogous statement holds even when the inputs are not boundaries. This simplicial version relies on the total unimodularity of the boundary matrix of the simplicial complex; a result distinct from the $L^1$TV approach.We develop an analysis framework that extends the result in the simplicial setting to one for $d$-currents in $\\mathbb{R}^{d+1}$, provided a suitable triangulation result holds. In $\\mathbb{R}^2$, we use a triangulation result of Shewchuk (bounding both the size and location of small angles, and apply the framework to show that the discrete result implies the continuous result for $1$-currents in $\\mathbb{R}^2$ .
Shearlets and Optimally Sparse Approximations
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
2012-01-01
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....
Diophantine approximation and Dirichlet series
Queffélec, Hervé
2013-01-01
This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...
Approximations to camera sensor noise
Jin, Xiaodan; Hirakawa, Keigo
2013-02-01
Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.
Rational approximations for tomographic reconstructions
International Nuclear Information System (INIS)
Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas
2013-01-01
We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. (paper)
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Spinodal decomposition in fluid mixtures
International Nuclear Information System (INIS)
Kawasaki, Kyozi; Koga, Tsuyoshi
1993-01-01
We study the late stage dynamics of spinodal decomposition in binary fluids by the computer simulation of the time-dependent Ginzburg-Landau equation. We obtain a temporary linear growth law of the characteristic length of domains in the late stage. This growth law has been observed in many real experiments of binary fluids and indicates that the domain growth proceeds by the flow caused by the surface tension of interfaces. We also find that the dynamical scaling law is satisfied in this hydrodynamic domain growth region. By comparing the scaling functions for fluids with that for the case without hydrodynamic effects, we find that the scaling functions for the two systems are different. (author)
Approximate reasoning in physical systems
International Nuclear Information System (INIS)
Mutihac, R.
1991-01-01
The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)
Face Recognition using Approximate Arithmetic
DEFF Research Database (Denmark)
Marso, Karol
Face recognition is image processing technique which aims to identify human faces and found its use in various diﬀerent ﬁelds for example in security. Throughout the years this ﬁeld evolved and there are many approaches and many diﬀerent algorithms which aim to make the face recognition as eﬀective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....
Early stage litter decomposition across biomes
Ika Djukic; Sebastian Kepfer-Rojas; Inger Kappel Schmidt; Klaus Steenberg Larsen; Claus Beier; Björn Berg; Kris Verheyen; Adriano Caliman; Alain Paquette; Alba Gutiérrez-Girón; Alberto Humber; Alejandro Valdecantos; Alessandro Petraglia; Heather Alexander; Algirdas Augustaitis; Amélie Saillard; Ana Carolina Ruiz Fernández; Ana I. Sousa; Ana I. Lillebø; Anderson da Rocha Gripp; André-Jean Francez; Andrea Fischer; Andreas Bohner; Andrey Malyshev; Andrijana Andrić; Andy Smith; Angela Stanisci; Anikó Seres; Anja Schmidt; Anna Avila; Anne Probst; Annie Ouin; Anzar A. Khuroo; Arne Verstraeten; Arely N. Palabral-Aguilera; Artur Stefanski; Aurora Gaxiola; Bart Muys; Bernard Bosman; Bernd Ahrends; Bill Parker; Birgit Sattler; Bo Yang; Bohdan Juráni; Brigitta Erschbamer; Carmen Eugenia Rodriguez Ortiz; Casper T. Christiansen; E. Carol Adair; Céline Meredieu; Cendrine Mony; Charles A. Nock; Chi-Ling Chen; Chiao-Ping Wang; Christel Baum; Christian Rixen; Christine Delire; Christophe Piscart; Christopher Andrews; Corinna Rebmann; Cristina Branquinho; Dana Polyanskaya; David Fuentes Delgado; Dirk Wundram; Diyaa Radeideh; Eduardo Ordóñez-Regil; Edward Crawford; Elena Preda; Elena Tropina; Elli Groner; Eric Lucot; Erzsébet Hornung; Esperança Gacia; Esther Lévesque; Evanilde Benedito; Evgeny A. Davydov; Evy Ampoorter; Fabio Padilha Bolzan; Felipe Varela; Ferdinand Kristöfel; Fernando T. Maestre; Florence Maunoury-Danger; Florian Hofhansl; Florian Kitz; Flurin Sutter; Francisco Cuesta; Francisco de Almeida Lobo; Franco Leandro de Souza; Frank Berninger; Franz Zehetner; Georg Wohlfahrt; George Vourlitis; Geovana Carreño-Rocabado; Gina Arena; Gisele Daiane Pinha; Grizelle González; Guylaine Canut; Hanna Lee; Hans Verbeeck; Harald Auge; Harald Pauli; Hassan Bismarck Nacro; Héctor A. Bahamonde; Heike Feldhaar; Heinke Jäger; Helena C. Serrano; Hélène Verheyden; Helge Bruelheide; Henning Meesenburg; Hermann Jungkunst; Hervé Jactel; Hideaki Shibata; Hiroko Kurokawa; Hugo López Rosas; Hugo L. Rojas Villalobos; Ian Yesilonis; Inara Melece; Inge Van Halder; Inmaculada García Quirós; Isaac Makelele; Issaka Senou; István Fekete; Ivan Mihal; Ivika Ostonen; Jana Borovská; Javier Roales; Jawad Shoqeir; Jean-Christophe Lata; Jean-Paul Theurillat; Jean-Luc Probst; Jess Zimmerman; Jeyanny Vijayanathan; Jianwu Tang; Jill Thompson; Jiří Doležal; Joan-Albert Sanchez-Cabeza; Joël Merlet; Joh Henschel; Johan Neirynck; Johannes Knops; John Loehr; Jonathan von Oppen; Jónína Sigríður Þorláksdóttir; Jörg Löffler; José-Gilberto Cardoso-Mohedano; José-Luis Benito-Alonso; Jose Marcelo Torezan; Joseph C. Morina; Juan J. Jiménez; Juan Dario Quinde; Juha Alatalo; Julia Seeber; Jutta Stadler; Kaie Kriiska; Kalifa Coulibaly; Karibu Fukuzawa; Katalin Szlavecz; Katarína Gerhátová; Kate Lajtha; Kathrin Käppeler; Katie A. Jennings; Katja Tielbörger; Kazuhiko Hoshizaki; Ken Green; Lambiénou Yé; Laryssa Helena Ribeiro Pazianoto; Laura Dienstbach; Laura Williams; Laura Yahdjian; Laurel M. Brigham; Liesbeth van den Brink; Lindsey Rustad; al. et
2018-01-01
Through litter decomposition enormous amounts of carbon is emitted to the atmosphere. Numerous large-scale decomposition experiments have been conducted focusing on this fundamental soil process in order to understand the controls on the terrestrial carbon transfer to the atmosphere. However, previous studies were mostly based on site-specific litter and methodologies...
Nutrient Dynamics and Litter Decomposition in Leucaena ...
African Journals Online (AJOL)
Nutrient contents and rate of litter decomposition were investigated in Leucaena leucocephala plantation in the University of Agriculture, Abeokuta, Ogun State, Nigeria. Litter bag technique was used to study the pattern and rate of litter decomposition and nutrient release of Leucaena leucocephala. Fifty grams of oven-dried ...
Climate history shapes contemporary leaf litter decomposition
Michael S. Strickland; Ashley D. Keiser; Mark A. Bradford
2015-01-01
Litter decomposition is mediated by multiple variables, of which climate is expected to be a dominant factor at global scales. However, like other organisms, traits of decomposers and their communities are shaped not just by the contemporary climate but also their climate history. Whether or not this affects decomposition rates is underexplored. Here we source...
The decomposition of estuarine macrophytes under different ...
African Journals Online (AJOL)
The aim of this study was to determine the decomposition characteristics of the most dominant submerged macrophyte and macroalgal species in the Great Brak Estuary. Laboratory experiments were conducted to determine the effect of different temperature regimes on the rate of decomposition of 3 macrophyte species ...
Decomposition and flame structure of hydrazinium nitroformate
Louwers, J.; Parr, T.; Hanson-Parr, D.
1999-01-01
The decomposition of hydrazinium nitroformate (HNF) was studied in a hot quartz cell and by dropping small amounts of HNF on a hot plate. The species formed during the decomposition were identified by ultraviolet-visible absorption experiments. These experiments reveal that first HONO is formed. The
Multilevel index decomposition analysis: Approaches and application
International Nuclear Information System (INIS)
Xu, X.Y.; Ang, B.W.
2014-01-01
With the growing interest in using the technique of index decomposition analysis (IDA) in energy and energy-related emission studies, such as to analyze the impacts of activity structure change or to track economy-wide energy efficiency trends, the conventional single-level IDA may not be able to meet certain needs in policy analysis. In this paper, some limitations of single-level IDA studies which can be addressed through applying multilevel decomposition analysis are discussed. We then introduce and compare two multilevel decomposition procedures, which are referred to as the multilevel-parallel (M-P) model and the multilevel-hierarchical (M-H) model. The former uses a similar decomposition procedure as in the single-level IDA, while the latter uses a stepwise decomposition procedure. Since the stepwise decomposition procedure is new in the IDA literature, the applicability of the popular IDA methods in the M-H model is discussed and cases where modifications are needed are explained. Numerical examples and application studies using the energy consumption data of the US and China are presented. - Highlights: • We discuss the limitations of single-level decomposition in IDA applied to energy study. • We introduce two multilevel decomposition models, study their features and discuss how they can address the limitations. • To extend from single-level to multilevel analysis, necessary modifications to some popular IDA methods are discussed. • We further discuss the practical significance of the multilevel models and present examples and cases to illustrate
Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method
Directory of Open Access Journals (Sweden)
Shao-Hong Yan
2014-01-01
Full Text Available The local fractional decomposition method is applied to approximate the solutions for Fokker-Planck equations on Cantor sets with local fractional derivative. The obtained results give the present method that is very effective and simple for solving the differential equations on Cantor set.
In situ study of glasses decomposition layer
International Nuclear Information System (INIS)
Zarembowitch-Deruelle, O.
1997-01-01
The aim of this work is to understand the involved mechanisms during the decomposition of glasses by water and the consequences on the morphology of the decomposition layer, in particular in the case of a nuclear glass: the R 7 T 7 . The chemical composition of this glass being very complicated, it is difficult to know the influence of the different elements on the decomposition kinetics and on the resulting morphology because several atoms have a same behaviour. Glasses with simplified composition (only 5 elements) have then been synthesized. The morphological and structural characteristics of these glasses have been given. They have then been decomposed by water. The leaching curves do not reflect the decomposition kinetics but the solubility of the different elements at every moment. The three steps of the leaching are: 1) de-alkalinization 2) lattice rearrangement 3) heavy elements solubilization. Two decomposition layer types have also been revealed according to the glass heavy elements rate. (O.M.)
Cheng, Jiubing; Wu, Zedong; Alkhalifah, Tariq Ali
2014-01-01
decomposition in anisotropic media is costly as the operators involved is dependent on the velocity, and thus not stationary. In this abstract, we propose an efficient approach to directly extrapolate the decomposed elastic waves using lowrank approximate mixed
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
-grams of a tree are all its subtrees of a particular shape. Intuitively, two trees are similar if they have many pq-grams in common. The pq-gram distance is an efficient and effective approximation of the tree edit distance. We analyze the properties of the pq-gram distance and compare it with the tree edit...
Approximation of Surfaces by Cylinders
DEFF Research Database (Denmark)
Randrup, Thomas
1998-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
All-Norm Approximation Algorithms
Azar, Yossi; Epstein, Leah; Richter, Yossi; Woeginger, Gerhard J.; Penttonen, Martti; Meineche Schmidt, Erik
2002-01-01
A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
Approximate reasoning in decision analysis
Energy Technology Data Exchange (ETDEWEB)
Gupta, M M; Sanchez, E
1982-01-01
The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms.
Rational approximation of vertical segments
Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte
2007-08-01
In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.
Pythagorean Approximations and Continued Fractions
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
CP decomposition approach to blind separation for DS-CDMA system using a new performance index
Rouijel, Awatif; Minaoui, Khalid; Comon, Pierre; Aboutajdine, Driss
2014-12-01
In this paper, we present a canonical polyadic (CP) tensor decomposition isolating the scaling matrix. This has two major implications: (i) the problem conditioning shows up explicitly and could be controlled through a constraint on the so-called coherences and (ii) a performance criterion concerning the factor matrices can be exactly calculated and is more realistic than performance metrics used in the literature. Two new algorithms optimizing the CP decomposition based on gradient descent are proposed. This decomposition is illustrated by an application to direct-sequence code division multiplexing access (DS-CDMA) systems; computer simulations are provided and demonstrate the good behavior of these algorithms, compared to others in the literature.
The Effect of Topography on Target Decomposition of Polarimetric SAR Data
Directory of Open Access Journals (Sweden)
Sang-Eun Park
2015-04-01
Full Text Available Polarimetric target decomposition enables the interpretation of radar images more easily, mostly based on physical assumptions, i.e., fitting physically-based scattering models to the polarimetric SAR observations. However, the model-fitting result cannot be always successful. Particularly, the performance of model-fitting in sloping forests is still an open question. In this study, the effect of ground topography on the model-fitting-based polarimetric decomposition techniques is investigated. The estimation accuracy of each scattering component in the decomposition results are evaluated based on the simulated target matrix by using the incoherent vegetation scattering model that accounts for the tilted scattering surface beneath the forest canopy. Experimental results show that the surface and the double-bounce scattering components can be significantly misestimated due to the topographic slope, even when the volume scattering power is successfully estimated.
Three-Component Decomposition Based on Stokes Vector for Compact Polarimetric SAR
Directory of Open Access Journals (Sweden)
Hanning Wang
2015-09-01
Full Text Available In this paper, a three-component decomposition algorithm is proposed for processing compact polarimetric SAR images. By using the correspondence between the covariance matrix and the Stokes vector, three-component scattering models for CTLR and DCP modes are established. The explicit expression of decomposition results is then derived by setting the contribution of volume scattering as a free parameter. The degree of depolarization is taken as the upper bound of the free parameter, for the constraint that the weighting factor of each scattering component should be nonnegative. Several methods are investigated to estimate the free parameter suitable for decomposition. The feasibility of this algorithm is validated by AIRSAR data over San Francisco and RADARSAT-2 data over Flevoland.
Management intensity alters decomposition via biological pathways
Wickings, Kyle; Grandy, A. Stuart; Reed, Sasha; Cleveland, Cory
2011-01-01
Current conceptual models predict that changes in plant litter chemistry during decomposition are primarily regulated by both initial litter chemistry and the stage-or extent-of mass loss. Far less is known about how variations in decomposer community structure (e.g., resulting from different ecosystem management types) could influence litter chemistry during decomposition. Given the recent agricultural intensification occurring globally and the importance of litter chemistry in regulating soil organic matter storage, our objectives were to determine the potential effects of agricultural management on plant litter chemistry and decomposition rates, and to investigate possible links between ecosystem management, litter chemistry and decomposition, and decomposer community composition and activity. We measured decomposition rates, changes in litter chemistry, extracellular enzyme activity, microarthropod communities, and bacterial versus fungal relative abundance in replicated conventional-till, no-till, and old field agricultural sites for both corn and grass litter. After one growing season, litter decomposition under conventional-till was 20% greater than in old field communities. However, decomposition rates in no-till were not significantly different from those in old field or conventional-till sites. After decomposition, grass residue in both conventional- and no-till systems was enriched in total polysaccharides relative to initial litter, while grass litter decomposed in old fields was enriched in nitrogen-bearing compounds and lipids. These differences corresponded with differences in decomposer communities, which also exhibited strong responses to both litter and management type. Overall, our results indicate that agricultural intensification can increase litter decomposition rates, alter decomposer communities, and influence litter chemistry in ways that could have important and long-term effects on soil organic matter dynamics. We suggest that future
Direct application of Padé approximant for solving nonlinear differential equations.
Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario
2014-01-01
This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.
Meuwissen, Theo H E; Indahl, Ulf G; Ødegård, Jørgen
2017-12-27
Non-linear Bayesian genomic prediction models such as BayesA/B/C/R involve iteration and mostly Markov chain Monte Carlo (MCMC) algorithms, which are computationally expensive, especially when whole-genome sequence (WGS) data are analyzed. Singular value decomposition (SVD) of the genotype matrix can facilitate genomic prediction in large datasets, and can be used to estimate marker effects and their prediction error variances (PEV) in a computationally efficient manner. Here, we developed, implemented, and evaluated a direct, non-iterative method for the estimation of marker effects for the BayesC genomic prediction model. The BayesC model assumes a priori that markers have normally distributed effects with probability [Formula: see text] and no effect with probability (1 - [Formula: see text]). Marker effects and their PEV are estimated by using SVD and the posterior probability of the marker having a non-zero effect is calculated. These posterior probabilities are used to obtain marker-specific effect variances, which are subsequently used to approximate BayesC estimates of marker effects in a linear model. A computer simulation study was conducted to compare alternative genomic prediction methods, where a single reference generation was used to estimate marker effects, which were subsequently used for 10 generations of forward prediction, for which accuracies were evaluated. SVD-based posterior probabilities of markers having non-zero effects were generally lower than MCMC-based posterior probabilities, but for some regions the opposite occurred, resulting in clear signals for QTL-rich regions. The accuracies of breeding values estimated using SVD- and MCMC-based BayesC analyses were similar across the 10 generations of forward prediction. For an intermediate number of generations (2 to 5) of forward prediction, accuracies obtained with the BayesC model tended to be slightly higher than accuracies obtained using the best linear unbiased prediction of SNP
Distance matrix-based approach to protein structure prediction.
Kloczkowski, Andrzej; Jernigan, Robert L; Wu, Zhijun; Song, Guang; Yang, Lei; Kolinski, Andrzej; Pokarowski, Piotr
2009-03-01
Much structural information is encoded in the internal distances; a distance matrix-based approach can be used to predict protein structure and dynamics, and for structural refinement. Our approach is based on the square distance matrix D = [r(ij)(2)] containing all square distances between residues in proteins. This distance matrix contains more information than the contact matrix C, that has elements of either 0 or 1 depending on whether the distance r (ij) is greater or less than a cutoff value r (cutoff). We have performed spectral decomposition of the distance matrices D = sigma lambda(k)V(k)V(kT), in terms of eigenvalues lambda kappa and the corresponding eigenvectors v kappa and found that it contains at most five nonzero terms. A dominant eigenvector is proportional to r (2)--the square distance of points from the center of mass, with the next three being the principal components of the system of points. By predicting r (2) from the sequence we can approximate a distance matrix of a protein with an expected RMSD value of about 7.3 A, and by combining it with the prediction of the first principal component we can improve this approximation to 4.0 A. We can also explain the role of hydrophobic interactions for the protein structure, because r is highly correlated with the hydrophobic profile of the sequence. Moreover, r is highly correlated with several sequence profiles which are useful in protein structure prediction, such as contact number, the residue-wise contact order (RWCO) or mean square fluctuations (i.e. crystallographic temperature factors). We have also shown that the next three components are related to spatial directionality of the secondary structure elements, and they may be also predicted from the sequence, improving overall structure prediction. We have also shown that the large number of available HIV-1 protease structures provides a remarkable sampling of conformations, which can be viewed as direct structural information about the
Photogeneration of heptacene in a polymer matrix.
Mondal, Rajib; Shah, Bipin K; Neckers, Douglas C
2006-08-02
Heptacene (1) was generated by the photodecarbonylation of 7,16-dihydro-7,16-ethanoheptacene-19,20-dione (2) in a polymer matrix using a UV-LED lamp (395 +/- 25 nm). Compound 1 showed a long wavelength absorption band extending from 600 to 825 nm (lambdamax approximately 760 nm) and was found to be stable up to 4 h in the polymer matrix. However, irradiation of a solution of 2 in toluene produced only oxygen adducts.
Marais-Werner, Anátulie; Myburgh, J; Becker, P J; Steyn, M
2018-01-01
Several studies have been conducted on decomposition patterns and rates of surface remains; however, much less are known about this process for buried remains. Understanding the process of decomposition in buried remains is extremely important and aids in criminal investigations, especially when attempting to estimate the post mortem interval (PMI). The aim of this study was to compare the rates of decomposition between buried and surface remains. For this purpose, 25 pigs (Sus scrofa; 45-80 kg) were buried and excavated at different post mortem intervals (7, 14, 33, 92, and 183 days). The observed total body scores were then compared to those of surface remains decomposing at the same location. Stages of decomposition were scored according to separate categories for different anatomical regions based on standardised methods. Variation in the degree of decomposition was considerable especially with the buried 7-day interval pigs that displayed different degrees of discolouration in the lower abdomen and trunk. At 14 and 33 days, buried pigs displayed features commonly associated with the early stages of decomposition, but with less variation. A state of advanced decomposition was reached where little change was observed in the next ±90-183 days after interment. Although the patterns of decomposition for buried and surface remains were very similar, the rates differed considerably. Based on the observations made in this study, guidelines for the estimation of PMI are proposed. This pertains to buried remains found at a depth of approximately 0.75 m in the Central Highveld of South Africa.
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...
Hydrogen: Beyond the Classic Approximation
International Nuclear Information System (INIS)
Scivetti, Ivan
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Approximation errors during variance propagation
International Nuclear Information System (INIS)
Dinsmore, Stephen
1986-01-01
Risk and reliability analyses are often performed by constructing and quantifying large fault trees. The inputs to these models are component failure events whose probability of occuring are best represented as random variables. This paper examines the errors inherent in two approximation techniques used to calculate the top event's variance from the inputs' variance. Two sample fault trees are evaluated and several three dimensional plots illustrating the magnitude of the error over a wide range of input means and variances are given
LMDI decomposition approach: A guide for implementation
International Nuclear Information System (INIS)
Ang, B.W.
2015-01-01
Since it was first used by researchers to analyze industrial electricity consumption in the early 1980s, index decomposition analysis (IDA) has been widely adopted in energy and emission studies. Lately its use as the analytical component of accounting frameworks for tracking economy-wide energy efficiency trends has attracted considerable attention and interest among policy makers. The last comprehensive literature review of IDA was reported in 2000 which is some years back. After giving an update and presenting the key trends in the last 15 years, this study focuses on the implementation issues of the logarithmic mean Divisia index (LMDI) decomposition methods in view of their dominance in IDA in recent years. Eight LMDI models are presented and their origin, decomposition formulae, and strengths and weaknesses are summarized. Guidelines on the choice among these models are provided to assist users in implementation. - Highlights: • Guidelines for implementing LMDI decomposition approach are provided. • Eight LMDI decomposition models are summarized and compared. • The development of the LMDI decomposition approach is presented. • The latest developments of index decomposition analysis are briefly reviewed.
Thermal decomposition of beryllium perchlorate tetrahydrate
International Nuclear Information System (INIS)
Berezkina, L.G.; Borisova, S.I.; Tamm, N.S.; Novoselova, A.V.
1975-01-01
Thermal decomposition of Be(ClO 4 ) 2 x4H 2 O was studied by the differential flow technique in the helium stream. The kinetics was followed by an exchange reaction of the perchloric acid appearing by the decomposition with potassium carbonate. The rate of CO 2 liberation in this process was recorded by a heat conductivity detector. The exchange reaction yielding CO 2 is quantitative, it is not the limiting one and it does not distort the kinetics of the process of perchlorate decomposition. The solid products of decomposition were studied by infrared and NMR spectroscopy, roentgenography, thermography and chemical analysis. A mechanism suggested for the decomposition involves intermediate formation of hydroxyperchlorate: Be(ClO 4 ) 2 x4H 2 O → Be(OH)ClO 4 +HClO 4 +3H 2 O; Be(OH)ClO 4 → BeO+HClO 4 . Decomposition is accompained by melting of the sample. The mechanism of decomposition is hydrolytic. At room temperature the hydroxyperchlorate is a thick syrup-like compound crystallizing after long storing
WKB approximation in atomic physics
International Nuclear Information System (INIS)
Karnakov, Boris Mikhailovich
2013-01-01
Provides extensive coverage of the Wentzel-Kramers-Brillouin approximation and its applications. Presented as a sequence of problems with highly detailed solutions. Gives a concise introduction for calculating Rydberg states, potential barriers and quasistationary systems. This book has evolved from lectures devoted to applications of the Wentzel-Kramers-Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N -expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.
APPECT: An Approximate Backbone-Based Clustering Algorithm for Tags
DEFF Research Database (Denmark)
Zong, Yu; Xu, Guandong; Jin, Pin
2011-01-01
algorithm for Tags (APPECT). The main steps of APPECT are: (1) we execute the K-means algorithm on a tag similarity matrix for M times and collect a set of tag clustering results Z={C1,C2,…,Cm}; (2) we form the approximate backbone of Z by executing a greedy search; (3) we fix the approximate backbone...... as the initial tag clustering result and then assign the rest tags into the corresponding clusters based on the similarity. Experimental results on three real world datasets namely MedWorm, MovieLens and Dmoz demonstrate the effectiveness and the superiority of the proposed method against the traditional...... Agglomerative Clustering on tagging data, which possess the inherent drawbacks, such as the sensitivity of initialization. In this paper, we instead make use of the approximate backbone of tag clustering results to find out better tag clusters. In particular, we propose an APProximate backbonE-based Clustering...
Efficiency criterion for teleportation via channel matrix, measurement matrix and collapsed matrix
Directory of Open Access Journals (Sweden)
Xin-Wei Zha
Full Text Available In this paper, three kinds of coefficient matrixes (channel matrix, measurement matrix, collapsed matrix associated with the pure state for teleportation are presented, the general relation among channel matrix, measurement matrix and collapsed matrix is obtained. In addition, a criterion for judging whether a state can be teleported successfully is given, depending on the relation between the number of parameter of an unknown state and the rank of the collapsed matrix. Keywords: Channel matrix, Measurement matrix, Collapsed matrix, Teleportation
Variance decomposition-based sensitivity analysis via neural networks
International Nuclear Information System (INIS)
Marseguerra, Marzio; Masini, Riccardo; Zio, Enrico; Cojazzi, Giacomo
2003-01-01
This paper illustrates a method for efficiently performing multiparametric sensitivity analyses of the reliability model of a given system. These analyses are of great importance for the identification of critical components in highly hazardous plants, such as the nuclear or chemical ones, thus providing significant insights for their risk-based design and management. The technique used to quantify the importance of a component parameter with respect to the system model is based on a classical decomposition of the variance. When the model of the system is realistically complicated (e.g. by aging, stand-by, maintenance, etc.), its analytical evaluation soon becomes impractical and one is better off resorting to Monte Carlo simulation techniques which, however, could be computationally burdensome. Therefore, since the variance decomposition method requires a large number of system evaluations, each one to be performed by Monte Carlo, the need arises for possibly substituting the Monte Carlo simulation model with a fast, approximated, algorithm. Here we investigate an approach which makes use of neural networks appropriately trained on the results of a Monte Carlo system reliability/availability evaluation to quickly provide with reasonable approximation, the values of the quantities of interest for the sensitivity analyses. The work was a joint effort between the Department of Nuclear Engineering of the Polytechnic of Milan, Italy, and the Institute for Systems, Informatics and Safety, Nuclear Safety Unit of the Joint Research Centre in Ispra, Italy which sponsored the project
Extended biorthogonal matrix polynomials
Directory of Open Access Journals (Sweden)
Ayman Shehata
2017-01-01
Full Text Available The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Tasdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and certain generating matrix functions, finite series, some matrix recurrence relations, several important properties of matrix differential recurrence relations, biorthogonality relations and matrix differential equation for the pair of biorthogonal matrix polynomials J(A,B n (x, k and K(A,B n (x, k are discussed. For the matrix polynomials J(A,B n (x, k, various families of bilinear and bilateral generating matrix functions are constructed in the sequel.
Matrix completion by deep matrix factorization.
Fan, Jicong; Cheng, Jieyu
2018-02-01
Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations. In this paper, a novel method called deep matrix factorization (DMF) is proposed for nonlinear matrix completion. Different from conventional matrix completion methods that are based on linear latent variable models, DMF is on the basis of a nonlinear latent variable model. DMF is formulated as a deep-structure neural network, in which the inputs are the low-dimensional unknown latent variables and the outputs are the partially observed variables. In DMF, the inputs and the parameters of the multilayer neural network are simultaneously optimized to minimize the reconstruction errors for the observed entries. Then the missing entries can be readily recovered by propagating the latent variables to the output layer. DMF is compared with state-of-the-art methods of linear and nonlinear matrix completion in the tasks of toy matrix completion, image inpainting and collaborative filtering. The experimental results verify that DMF is able to provide higher matrix completion accuracy than existing methods do and DMF is applicable to large matrices. Copyright © 2017 Elsevier Ltd. All rights reserved.
Thermal decomposition of lanthanide and actinide tetrafluorides
International Nuclear Information System (INIS)
Gibson, J.K.; Haire, R.G.
1988-01-01
The thermal stabilities of several lanthanide/actinide tetrafluorides have been studied using mass spectrometry to monitor the gaseous decomposition products, and powder X-ray diffraction (XRD) to identify solid products. The tetrafluorides, TbF 4 , CmF 4 , and AmF 4 , have been found to thermally decompose to their respective solid trifluorides with accompanying release of fluorine, while cerium tetrafluoride has been found to be significantly more thermally stable and to congruently sublime as CeF 4 prior to appreciable decomposition. The results of these studies are discussed in relation to other relevant experimental studies and the thermodynamics of the decomposition processes. 9 refs., 3 figs
Decomposition of orthogonal polygons in a set of rectanglеs
Shestakov, E.; Voronov, A.
2009-01-01
Algorithm for covering orthogonal integrated circuit layout objects is considered. Objects of the research are special single-connected orthogonal polygons which are generated during decomposition of any multiply connected polygon in a set of single-connected orthogonal polygons. Developed algorithm for covering polygons based on the mathematical techinque of logic matrix transformation. Results described in this paper, can be applied in computer geometry and image analysis.
Pade approximants in field theory: pion and kaon systems
International Nuclear Information System (INIS)
Zinn-Justin, J.
1969-01-01
We construct the Pade approximants of the S-matrix, starting from the perturbation series, in the case of two body pion and kaon systems. We have three parameters. The seven lowest lying two body resonances (ρ, K * (890), φ, K * (1420), f 0 , f', A 2 ) are obtained within a few per cent of their actual masses. The Regge trajectories are rising, the intercepts of the ρ and f 0 agree well with the experimental values. In the appendices we give some properties and applications of the Pade approximants. (author) [fr
Pade approximants and the calculation of effective interactions
International Nuclear Information System (INIS)
Schucan, T.H.
1975-01-01
It is known that the series expansion of the effective interaction in nuclei diverges in practical applications due to the occurrence of low lying collective states. An approximation scheme which can be used to overcome the difficulties connected with this divergence is reviewed and it is shown that a continued fraction expansion can be used to calculate the eigenstate that has the larger overlap with the model space. An extension of this method is obtained by using Pade approximants (P.A.) which are then applied to the effective interaction, and to related matrices and matrix elements. Mathematical properties of the P.A. are discussed in light of these applications. 7 figures
Decomposition of lake phytoplankton. 1
International Nuclear Information System (INIS)
Hansen, L.; Krog, G.F.; Soendergaard, M.
1986-01-01
Short-time (24 h) and long-time (4-6 d) decomposition of phytoplankton cells were investigasted under in situ conditions in four Danish lakes. Carbon-14-labelled, dead algae were exposed to sterile or natural lake water and the dynamics of cell lysis and bacterial utilization of the leached products were followed. The lysis process was dominated by an initial fast water extraction. Within 2 to 4 h from 4 to 34% of the labelled carbon leached from the algal cells. After 24 h from 11 to 43% of the initial particulate carbon was found as dissolved carbon in the experiments with sterile lake water; after 4 to 6 d the leaching was from 67 to 78% of the initial 14 C. The leached compounds were utilized by bacteria. A comparison of the incubations using sterile and natural water showed that a mean of 71% of the lysis products was metabolized by microorganisms within 24 h. In two experiments the uptake rate equalled the leaching rate. (author)
Decomposition of lake phytoplankton. 2
International Nuclear Information System (INIS)
Hansen, L.; Krog, G.F.; Soendergaard, M.
1986-01-01
The lysis process of phytoplankton was followed in 24 h incubations in three Danish lakes. By means of gel-chromatography it was shown that the dissolved carbon leaching from different algal groups differed in molecular weight composition. Three distinct molecular weight classes (>10,000; 700 to 10,000 and < 700 Daltons) leached from blue-green algae in almost equal proportion. The lysis products of spring-bloom diatoms included only the two smaller size classes, and the molecules between 700 and 10,000 Daltons dominated. Measurements of cell content during decomposition of the diatoms revealed polysaccharides and low molecular weight compounds to dominate the lysis products. No proteins were leached during the first 24 h after cell death. By incubating the dead algae in natural lake water, it was possible to detect a high bacterial affinity towards molecules between 700 and 10,000 Daltons, although the other size classes were also utilized. Bacterial transformation of small molecules to larger molecules could be demonstrated. (author)
Thermal Decomposition Mechanisms of Lignin Model Compounds: From Phenol to Vanillin
Scheer, Adam Michael
Lignin is a complex, aromatic polymer abundant in cellulosic biomass (trees, switchgrass etc.). Thermochemical breakdown of lignin for liquid fuel production results in undesirable polycyclic aromatic hydrocarbons that lead to tar and soot byproducts. The fundamental chemistry governing these processes is not well understood. We have studied the unimolecular thermal decomposition mechanisms of aromatic lignin model compounds using a miniature SiC tubular reactor. Products are detected and characterized using time-of-flight mass spectrometry with both single photon (118.2 nm; 10.487 eV) and 1 + 1 resonance-enhanced multiphoton ionization (REMPI) as well as matrix isolation infrared spectroscopy. Gas exiting the heated reactor (300 K--1600 K) is subject to a free expansion after a residence time of approximately 100 micros. The expansion into vacuum rapidly cools the gas mixture and allows the detection of radicals and other highly reactive intermediates. By understanding the unimolecular fragmentation patterns of phenol (C6H5OH), anisole (C6H 5OCH3) and benzaldehyde (C6H5CHO), the more complicated thermocracking processes of the catechols (HO-C 6H4-OH), methoxyphenols (HO-C6H4-OCH 3) and hydroxybenzaldehydes (HO-C6H4-CHO) can be interpreted. These studies have resulted in a predictive model that allows the interpretation of vanillin, a complex phenolic ether containing methoxy, hydroxy and aldehyde functional groups. This model will serve as a guide for the pyrolyses of larger systems including lignin monomers such as coniferyl alcohol. The pyrolysis mechanisms of the dimethoxybenzenes (H3C-C 6H4-OCH3) and syringol, a hydroxydimethoxybenzene have also been studied. These results will aid in the understanding of the thermal fragmentation of sinapyl alcohol, the most complex lignin monomer. In addition to the model compound work, pyrolyisis of biomass has been studied via the pulsed laser ablation of poplar wood. With the REMPI scheme, aromatic lignin decomposition
Surface spinodal decomposition in coherent metal-hydrogen and other alloys
International Nuclear Information System (INIS)
Kappus, W.; Horner, H.
1977-01-01
Spinodal decomposition in metal hydrides and alloys near a surface under the influence of elastic interactions is investigated. As long as the crystals remain coherent this process sets in prior to spinodal decomposition in the bulk. A statistical theory containing thermal fluctuations and nonlinear effects is developed and solutions are found in a mean field approximation. The theory is applied to niobium-hydride and a possible explanation for the appearance of quasiperiodic β-phase precipitates in quenched probes is given. (orig.) [de
Ab initio study of spinodal decomposition in (Zn,Cr)Te
International Nuclear Information System (INIS)
Fukushima, T.; Sato, K.; Katayama-Yoshida, H.; Dederichs, P.H.
2006-01-01
The spinodal decomposition in (Zn,Cr)Te is simulated by using first principles calculations and Monte Carlo simulation. It is found that the chemical pair interaction between Cr atoms in (Zn,Cr)Te is attractive interaction and leads to spinodal decomposition. Curie temperatures in decomposed situation are estimated by the random phase approximation with taking the magnetic percolation effect into account. This decomposed phase makes the random pattern of high concentration regions which connect each other and have possibility to realize high Curie temperature. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Directory of Open Access Journals (Sweden)
Mishra Vinod
2016-01-01
Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.
The Wigner transform and the semi-classical approximations
International Nuclear Information System (INIS)
Shlomo, S.
1985-01-01
The Wigner transform provides a reformulation of quantum mechanics in terms of classical concepts. Some properties of the Wigner transform of the density matrix which justify its interpretation as the quantum-mechanical analog of the classical phase-space distribution function are presented. Considering some applications, it is demonstrated that the Wigner distribution function serves as a good starting point for semi-classical approximations to properties of the (nuclear) many-body system
Pade approximants for the Saxon-Woods potential
International Nuclear Information System (INIS)
Niculescu, V.I.R.; Catana, D.
1995-01-01
In the present work central Saxon-Woods (SW) potential and a uniform sphere Coulomb potential for protons are replaced with a Pade approximants. In this way expressions of the matrix elements of this potential form can be evaluated by the theory of complex functions. The methods assures satisfactory precision in a shorter computational time. (M.I.C) 1 fig., 2 tabs., 5 refs
Finite-rank potential that reproduces the Pade approximant
International Nuclear Information System (INIS)
Tani, S.
1979-01-01
If a scattering potential is of a finite rank, say N, the exact solution of the problem can be obtained from the Born series, if the potential strength is within the radius of convergence; the exact solution can be obtained from the analytical continuation of the formal Born series outside the radius of convergence. Beyond the first 2N terms of the Born series, an individual term of the Born series depends on the first 2N terms, and the [N/N] Pade approximant and the exact solution agree with each other. The above-mentioned features of a finite-rank problem are relevant to scattering theory in general, because most scattering problems may be handled as an extension of the rank-N problem, in which the rank N tends to infinity. The foregoing aspects of scattering theory will be studied in depth in the present paper, and in so doing we proceed in the opposite direction. Namely, given a potential, we calculate the first 2N terms of the Born series for the K matrix and the first N terms of the Born series for the wave function. Using these data, a special rank-N potential is constructed in such a way that it reproduces the [N/N] Pade approximant of the K matrix of the original scattering problem. One great advantage of obtaining such a rank-N potential is that the wave function of the system may be approximated in the same spirit as done for the K matrix; hence, we can introduce a new approximation method for dealing with an off-shell T matrix. A part of the mathematical work is incomplete, but the physical aspects are thoroughly discussed
Structure and decomposition of the silver formate Ag(HCO{sub 2})
Energy Technology Data Exchange (ETDEWEB)
Puzan, Anna N., E-mail: anna_puzan@mail.ru; Baumer, Vyacheslav N.; Mateychenko, Pavel V.
2017-02-15
Crystal structure of the silver formate Ag(HCO{sub 2}) has been determined (orthorhombic, sp.gr. Pccn, a=7.1199(5), b=10.3737(4), c=6.4701(3)Å, V=477.88(4) Å{sup 3}, Z=8). The structure contains isolated formate ions and the pairs Ag{sub 2}{sup 2+} which form the layers in (001) planes (the shortest Ag–Ag distances is 2.919 in the pair and 3.421 and 3.716 Å between the nearest Ag atoms of adjacent pairs). Silver formate is unstable compound which decompose spontaneously vs time. Decomposition was studied using Rietveld analysis of the powder diffraction patterns. It was concluded that the diffusion of Ag atoms leads to the formation of plate-like metal particles as nuclei in the (100) planes which settle parallel to (001) planes of the silver formate matrix. - Highlights: • Silver formate Ag(HCO{sub 2}) was synthesized and characterized. • Layered packing of Ag-Ag pairs in the structure was found. • Decomposition of Ag(HCO{sub 2}) and formation of metal phase were studied. • Rietveld-refined micro-structural characteristics during decomposition reveal the space relationship between the matrix structure and forming Ag phase REPLACE with: Space relationship between the matrix structure and forming Ag phase.
Structure and decomposition of the silver formate Ag(HCO2)
International Nuclear Information System (INIS)
Puzan, Anna N.; Baumer, Vyacheslav N.; Mateychenko, Pavel V.
2017-01-01
Crystal structure of the silver formate Ag(HCO 2 ) has been determined (orthorhombic, sp.gr. Pccn, a=7.1199(5), b=10.3737(4), c=6.4701(3)Å, V=477.88(4) Å 3 , Z=8). The structure contains isolated formate ions and the pairs Ag 2 2+ which form the layers in (001) planes (the shortest Ag–Ag distances is 2.919 in the pair and 3.421 and 3.716 Å between the nearest Ag atoms of adjacent pairs). Silver formate is unstable compound which decompose spontaneously vs time. Decomposition was studied using Rietveld analysis of the powder diffraction patterns. It was concluded that the diffusion of Ag atoms leads to the formation of plate-like metal particles as nuclei in the (100) planes which settle parallel to (001) planes of the silver formate matrix. - Highlights: • Silver formate Ag(HCO 2 ) was synthesized and characterized. • Layered packing of Ag-Ag pairs in the structure was found. • Decomposition of Ag(HCO 2 ) and formation of metal phase were studied. • Rietveld-refined micro-structural characteristics during decomposition reveal the space relationship between the matrix structure and forming Ag phase REPLACE with: Space relationship between the matrix structure and forming Ag phase.
Energy Technology Data Exchange (ETDEWEB)
Jemcov, A.; Matovic, M.D. [Queen`s Univ., Kingston, Ontario (Canada)
1996-12-31
This paper examines the sparse representation and preconditioning of a discrete Steklov-Poincare operator which arises in domain decomposition methods. A non-overlapping domain decomposition method is applied to a second order self-adjoint elliptic operator (Poisson equation), with homogeneous boundary conditions, as a model problem. It is shown that the discrete Steklov-Poincare operator allows sparse representation with a bounded condition number in wavelet basis if the transformation is followed by thresholding and resealing. These two steps combined enable the effective use of Krylov subspace methods as an iterative solution procedure for the system of linear equations. Finding the solution of an interface problem in domain decomposition methods, known as a Schur complement problem, has been shown to be equivalent to the discrete form of Steklov-Poincare operator. A common way to obtain Schur complement matrix is by ordering the matrix of discrete differential operator in subdomain node groups then block eliminating interface nodes. The result is a dense matrix which corresponds to the interface problem. This is equivalent to reducing the original problem to several smaller differential problems and one boundary integral equation problem for the subdomain interface.
Approximate solutions to Mathieu's equation
Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.
2018-06-01
Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.
Quantum tunneling beyond semiclassical approximation
International Nuclear Information System (INIS)
Banerjee, Rabin; Majhi, Bibhas Ranjan
2008-01-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.
Generalized Gradient Approximation Made Simple
International Nuclear Information System (INIS)
Perdew, J.P.; Burke, K.; Ernzerhof, M.
1996-01-01
Generalized gradient approximations (GGA close-quote s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. copyright 1996 The American Physical Society
Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames
Directory of Open Access Journals (Sweden)
Martin Ehler
2015-01-01
Full Text Available We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks, all filters have equal norm, and the essential features of the original filter bank are preserved. Unitary filter banks providing perfect reconstruction are induced by tight generalized frames, which enable signal decomposition using a set of linear operators. If, in addition, frame elements have equal norm, then the signal energy is spread through the various filter bank channels in some uniform fashion, which is often more suitable for further signal processing. We start with a given generalized frame whose elements allow for fast matrix vector multiplication, as, for instance, convolution operators, and compute a normalized tight frame, for which signal analysis and synthesis still preserve those fast algorithmic schemes.
Single-particle density matrix of liquid 4He
International Nuclear Information System (INIS)
Vakarchuk, I.A.
2008-01-01
The density single-particle matrix in the coordinate notation was calculated based on the expression for the interacting Bose-particle N system density matrix. Under the low temperatures the mentioned matrix in the first approximation enables to reproduce the Bogoliubov theory results. In the classical terms the mentioned theory enables to reproduce the results of the theory of the classical fluids in the approximation of the chaotic phases. On the basis of the density single-particle matrix one managed to obtain the function of the pulse distribution of the particles, the Bose-liquid average kinetic energy, and to study the Bose-Einstein condensation phenomenon [ru
Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander
2017-11-01
The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\H$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.
Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander; Sun, Ying; Genton, Marc G.; Keyes, David E.
2017-01-01
The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\H$-) matrix format with computational cost $\\mathcal{O}(k^2n \\log^2 n/p)$ and storage $\\mathcal{O}(kn \\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.
A Decomposition Theorem for Finite Automata.
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Spatial domain decomposition for neutron transport problems
International Nuclear Information System (INIS)
Yavuz, M.; Larsen, E.W.
1989-01-01
A spatial Domain Decomposition method is proposed for modifying the Source Iteration (SI) and Diffusion Synthetic Acceleration (DSA) algorithms for solving discrete ordinates problems. The method, which consists of subdividing the spatial domain of the problem and performing the transport sweeps independently on each subdomain, has the advantage of being parallelizable because the calculations in each subdomain can be performed on separate processors. In this paper we describe the details of this spatial decomposition and study, by numerical experimentation, the effect of this decomposition on the SI and DSA algorithms. Our results show that the spatial decomposition has little effect on the convergence rates until the subdomains become optically thin (less than about a mean free path in thickness)
Big geo data surface approximation using radial basis functions: A comparative study
Majdisova, Zuzana; Skala, Vaclav
2017-12-01
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in n-dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.
Impulse approximation in solid helium
International Nuclear Information System (INIS)
Glyde, H.R.
1985-01-01
The incoherent dynamic form factor S/sub i/(Q, ω) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine the Q values for which the IA is valid for systems such a helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For 3 He, S/sub i/(Q, ω) is evaluated from first principles, beginning with the pair potential. The density of states g(ω) is evaluated using the self-consistent phonon theory and S/sub i/(Q,ω) is expressed in terms of g(ω). For solid 4 He resonable models of g(ω) using observed input parameters are used to evaluate S/sub i/(Q,ω). In both cases S/sub i/(Q, ω) is found to approach the impulse approximation S/sub IA/(Q, ω) closely for wave vector transfers Q> or approx. =20 A -1 . The difference between S/sub i/ and S/sub IA/, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (ω-ω/sub R/), where ω/sub R/ is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium
Finite approximations in fluid mechanics
International Nuclear Information System (INIS)
Hirschel, E.H.
1986-01-01
This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems
Plasma Physics Approximations in Ares
International Nuclear Information System (INIS)
Managan, R. A.
2015-01-01
Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, Fn( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζ ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ )F 1/2 (μ/θ), F 1/2 '/F 1/2 , F c α , and F c β . In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.