Hierarchical matrix approximation of large covariance matrices

KAUST Repository

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

2015-01-01

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

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander

2015-11-30

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

Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures

Directory of Open Access Journals (Sweden)

Nishchal K. Verma

2012-01-01

Full Text Available This paper presents a novel computational approach for estimating fuzzy measures directly from Gaussian mixtures model (GMM. The mixture components of GMM provide the membership functions for the input-output fuzzy sets. By treating consequent part as a function of fuzzy measures, we derived its coefficients from the covariance matrices found directly from GMM and the defuzzified output constructed from both the premise and consequent parts of the nonadditive fuzzy rules that takes the form of Choquet integral. The computational burden involved with the solution of λ-measure is minimized using Q-measure. The fuzzy model whose fuzzy measures were computed using covariance matrices found in GMM has been successfully applied on two benchmark problems and one real-time electric load data of Indian utility. The performance of the resulting model for many experimental studies including the above-mentioned application is found to be better and comparable to recent available fuzzy models. The main contribution of this paper is the estimation of fuzzy measures efficiently and directly from covariance matrices found in GMM, avoiding the computational burden greatly while learning them iteratively and solving polynomial equations of order of the number of input-output variables.

Neutron spectrum adjustment. The role of covariances

International Nuclear Information System (INIS)

Remec, I.

1992-01-01

Neutron spectrum adjustment method is shortly reviewed. Practical example dealing with power reactor pressure vessel exposure rates determination is analysed. Adjusted exposure rates are found only slightly affected by the covariances of measured reaction rates and activation cross sections, while the multigroup spectra covariances were found important. Approximate spectra covariance matrices, as suggested in Astm E944-89, were found useful but care is advised if they are applied in adjustments of spectra at locations without dosimetry. (author) [sl

On spectral distribution of high dimensional covariation matrices

DEFF Research Database (Denmark)

Heinrich, Claudio; Podolskij, Mark

In this paper we present the asymptotic theory for spectral distributions of high dimensional covariation matrices of Brownian diffusions. More specifically, we consider N-dimensional Itô integrals with time varying matrix-valued integrands. We observe n equidistant high frequency data points...... of the underlying Brownian diffusion and we assume that N/n -> c in (0,oo). We show that under a certain mixed spectral moment condition the spectral distribution of the empirical covariation matrix converges in distribution almost surely. Our proof relies on method of moments and applications of graph theory....

Noisy covariance matrices and portfolio optimization II

Science.gov (United States)

Pafka, Szilárd; Kondor, Imre

2003-03-01

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

Status of multigroup sensitivity profiles and covariance matrices available from the radiation shielding information center

International Nuclear Information System (INIS)

Roussin, R.W.; Drischler, J.D.; Marable, J.H.

1980-01-01

In recent years multigroup sensitivity profiles and covariance matrices have been added to the Radiation Shielding Information Center's Data Library Collection (DLC). Sensitivity profiles are available in a single package. DLC-45/SENPRO, and covariance matrices are found in two packages, DLC-44/COVERX and DLC-77/COVERV. The contents of these packages are described and their availability is discussed

Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice

NARCIS (Netherlands)

Callot, Laurent A.F.; Kock, Anders B.; Medeiros, Marcelo C.

2017-01-01

We consider modeling and forecasting large realized covariance matrices by penalized vector autoregressive models. We consider Lasso-type estimators to reduce the dimensionality and provide strong theoretical guarantees on the forecast capability of our procedure. We show that we can forecast

Performance of penalized maximum likelihood in estimation of genetic covariances matrices

Directory of Open Access Journals (Sweden)

Meyer Karin

2011-11-01

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

Covariance matrices and applications to the field of nuclear data

International Nuclear Information System (INIS)

Smith, D.L.

1981-11-01

A student's introduction to covariance error analysis and least-squares evaluation of data is provided. It is shown that the basic formulas used in error propagation can be derived from a consideration of the geometry of curvilinear coordinates. Procedures for deriving covariances for scaler and vector functions of several variables are presented. Proper methods for reporting experimental errors and for deriving covariance matrices from these errors are indicated. The generalized least-squares method for evaluating experimental data is described. Finally, the use of least-squares techniques in data fitting applications is discussed. Specific examples of the various procedures are presented to clarify the concepts

Research Article Comparing covariance matrices: random skewers method compared to the common principal components model

Directory of Open Access Journals (Sweden)

James M. Cheverud

2007-03-01

Full Text Available Comparisons of covariance patterns are becoming more common as interest in the evolution of relationships between traits and in the evolutionary phenotypic diversification of clades have grown. We present parallel analyses of covariance matrix similarity for cranial traits in 14 New World Monkey genera using the Random Skewers (RS, T-statistics, and Common Principal Components (CPC approaches. We find that the CPC approach is very powerful in that with adequate sample sizes, it can be used to detect significant differences in matrix structure, even between matrices that are virtually identical in their evolutionary properties, as indicated by the RS results. We suggest that in many instances the assumption that population covariance matrices are identical be rejected out of hand. The more interesting and relevant question is, How similar are two covariance matrices with respect to their predicted evolutionary responses? This issue is addressed by the random skewers method described here.

Extreme eigenvalues of sample covariance and correlation matrices

DEFF Research Database (Denmark)

Heiny, Johannes

This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance...... matrix of a p-dimensional heavy-tailed time series when p converges to infinity together with the sample size n. We generalize the growth rates of p existing in the literature. Assuming a regular variation condition with tail index ... eigenvalues are essentially determined by the extreme order statistics from an array of iid random variables. The asymptotic behavior of the extreme eigenvalues is then derived routinely from classical extreme value theory. The resulting approximations are strikingly simple considering the high dimension...

Semiparametric estimation of covariance matrices for longitudinal data.

Science.gov (United States)

Fan, Jianqing; Wu, Yichao

2008-12-01

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

Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering.

Science.gov (United States)

Chang, Jinyuan; Zhou, Wen; Zhou, Wen-Xin; Wang, Lan

2017-03-01

Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary between different biological states. We propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of the covariance matrices are much larger than the sample sizes. A distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance matrices. Hence, the test is robust with respect to various complex dependence structures that frequently arise in genomics. We prove that the proposed procedure is asymptotically valid under weak moment conditions. As an interesting application, we derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high-dimensional genomics data. Using an asthma gene expression dataset, we illustrate how the new test helps compare the covariance matrices of the genes across different gene sets/pathways between the disease group and the control group, and how the gene clustering algorithm provides new insights on the way gene clustering patterns differ between the two groups. The proposed methods have been implemented in an R-package HDtest and are available on CRAN. © 2016, The International Biometric Society.

Video based object representation and classification using multiple covariance matrices.

Science.gov (United States)

Zhang, Yurong; Liu, Quan

2017-01-01

Video based object recognition and classification has been widely studied in computer vision and image processing area. One main issue of this task is to develop an effective representation for video. This problem can generally be formulated as image set representation. In this paper, we present a new method called Multiple Covariance Discriminative Learning (MCDL) for image set representation and classification problem. The core idea of MCDL is to represent an image set using multiple covariance matrices with each covariance matrix representing one cluster of images. Firstly, we use the Nonnegative Matrix Factorization (NMF) method to do image clustering within each image set, and then adopt Covariance Discriminative Learning on each cluster (subset) of images. At last, we adopt KLDA and nearest neighborhood classification method for image set classification. Promising experimental results on several datasets show the effectiveness of our MCDL method.

MIMO-radar Waveform Covariance Matrices for High SINR and Low Side-lobe Levels

KAUST Repository

Ahmed, Sajid

2012-12-29

MIMO-radar has better parametric identifiability but compared to phased-array radar it shows loss in signal-to-noise ratio due to non-coherent processing. To exploit the benefits of both MIMO-radar and phased-array two transmit covariance matrices are found. Both of the covariance matrices yield gain in signal-to-interference-plus-noise ratio (SINR) compared to MIMO-radar and have lower side-lobe levels (SLL)\\'s compared to phased-array and MIMO-radar. Moreover, in contrast to recently introduced phased-MIMO scheme, where each antenna transmit different power, our proposed schemes allows same power transmission from each antenna. The SLL\\'s of the proposed first covariance matrix are higher than the phased-MIMO scheme while the SLL\\'s of the second proposed covariance matrix are lower than the phased-MIMO scheme. The first covariance matrix is generated using an auto-regressive process, which allow us to change the SINR and side lobe levels by changing the auto-regressive parameter, while to generate the second covariance matrix the values of sine function between 0 and $\\\\pi$ with the step size of $\\\\pi/n_T$ are used to form a positive-semidefinite Toeplitiz matrix, where $n_T$ is the number of transmit antennas. Simulation results validate our analytical results.

ERRORJ, Multigroup covariance matrices generation from ENDF-6 format

International Nuclear Information System (INIS)

Chiba, Go

2007-01-01

1 - Description of program or function: ERRORJ produces multigroup covariance matrices from ENDF-6 format following mainly the methods of the ERRORR module in NJOY94.105. New version differs from previous version in the following features: Additional features in ERRORJ with respect to the NJOY94.105/ERRORR module: - expands processing for the covariance matrices of resolved and unresolved resonance parameters; - processes average cosine of scattering angle and fission spectrum; - treats cross-correlation between different materials and reactions; - accepts input of multigroup constants with various forms (user input, GENDF, etc.); - outputs files with various formats through utility NJOYCOVX (COVERX format, correlation matrix, relative error and standard deviation); - uses a 1% sensitivity method for processing of resonance parameters; - ERRORJ can process the JENDL-3.2 and 3.3 covariance matrices. Additional features of the version 2 with respect to the previous version of ERRORJ: - Since the release of version 2, ERRORJ has been modified to increase its reliability and stability, - calculation of the correlation coefficients in the resonance region, - Option for high-speed calculation is implemented, - Perturbation amount is optimised in a sensitivity calculation, - Effect of the resonance self-shielding can be considered, - a compact covariance format (LCOMP=2) proposed by N. M. Larson can be read. Additional features of the version 2.2.1 with respect to the previous version of ERRORJ: - Several routines were modified to reduce calculation time. The new one needs shorter calculation time (50-70%) than the old version without changing results. - In the U-233 and Pu-241 files of JENDL-3.3 an inconsistency between resonance parameters in MF=32 and those in MF=2 was corrected. NEA-1676/06: This version differs from the previous one (NEA-1676/05) in the following: ERRORJ2.2.1 was modified to treat the self-shielding effect accurately. NEA-1676/07: This version

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

Science.gov (United States)

Yang, Yang; DeGruttola, Victor

2012-06-22

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

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

KAUST Repository

Litvinenko, Alexander

2017-09-26

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

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

KAUST Repository

Litvinenko, Alexander

2017-09-24

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

Perils of parsimony: properties of reduced-rank estimates of genetic covariance matrices.

Science.gov (United States)

Meyer, Karin; Kirkpatrick, Mark

2008-10-01

Eigenvalues and eigenvectors of covariance matrices are important statistics for multivariate problems in many applications, including quantitative genetics. Estimates of these quantities are subject to different types of bias. This article reviews and extends the existing theory on these biases, considering a balanced one-way classification and restricted maximum-likelihood estimation. Biases are due to the spread of sample roots and arise from ignoring selected principal components when imposing constraints on the parameter space, to ensure positive semidefinite estimates or to estimate covariance matrices of chosen, reduced rank. In addition, it is shown that reduced-rank estimators that consider only the leading eigenvalues and -vectors of the "between-group" covariance matrix may be biased due to selecting the wrong subset of principal components. In a genetic context, with groups representing families, this bias is inverse proportional to the degree of genetic relationship among family members, but is independent of sample size. Theoretical results are supplemented by a simulation study, demonstrating close agreement between predicted and observed bias for large samples. It is emphasized that the rank of the genetic covariance matrix should be chosen sufficiently large to accommodate all important genetic principal components, even though, paradoxically, this may require including a number of components with negligible eigenvalues. A strategy for rank selection in practical analyses is outlined.

MATXTST, Basic Operations for Covariance Matrices

International Nuclear Information System (INIS)

Geraldo, Luiz P.; Smith, Donald

1989-01-01

1 - Description of program or function: MATXTST and MATXTST1 perform the following operations for a covariance matrix: - test for singularity; - test for positive definiteness; - compute the inverse if the matrix is non-singular; - compute the determinant; - determine the number of positive, negative, and zero eigenvalues; - examine all possible 3 X 3 cross correlations within a sub-matrix corresponding to a leading principal minor which is non-positive definite. While the two programs utilize the same input, the calculational procedures employed are somewhat different and their functions are complementary. The available input options include: i) the full covariance matrix, ii) the basic variables plus the relative covariance matrix, or iii) uncertainties in the basic variables plus the correlation matrix. 2 - Method of solution: MATXTST employs LINPACK subroutines SPOFA and SPODI to test for positive definiteness and to perform further optional calculations. Subroutine SPOFA factors a symmetric matrix M using the Cholesky algorithm to determine the elements of a matrix R which satisfies the relation M=R'R, where R' is the transposed matrix of R. Each leading principal minor of M is tested until the first one is found which is not positive definite. MATXTST1 uses LINPACK subroutines SSICO, SSIFA, and SSIDI to estimate whether the matrix is near to singularity or not (SSICO), and to perform the matrix diagonalization process (SSIFA). The algorithm used in SSIFA is generalization of the Method of Lagrange Reduction. SSIDI is used to compute the determinant and inertia of the matrix. 3 - Restrictions on the complexity of the problem: Matrices of sizes up to 50 X 50 elements can be treated by present versions of the programs

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

Science.gov (United States)

Cai, T Tony; Zhang, Anru

2016-09-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data.

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

Science.gov (United States)

Cai, T. Tony; Zhang, Anru

2016-01-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data. PMID:27777471

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

KAUST Repository

Litvinenko, Alexander

2017-01-01

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

Covariance-Based Estimation from Multisensor Delayed Measurements with Random Parameter Matrices and Correlated Noises

Directory of Open Access Journals (Sweden)

R. Caballero-Águila

2014-01-01

Full Text Available The optimal least-squares linear estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems subject to randomly delayed measurements with different delay rates. For each sensor, a different binary sequence is used to model the delay process. The measured outputs are perturbed by both random parameter matrices and one-step autocorrelated and cross correlated noises. Using an innovation approach, computationally simple recursive algorithms are obtained for the prediction, filtering, and smoothing problems, without requiring full knowledge of the state-space model generating the signal process, but only the information provided by the delay probabilities and the mean and covariance functions of the processes (signal, random parameter matrices, and noises involved in the observation model. The accuracy of the estimators is measured by their error covariance matrices, which allow us to analyze the estimator performance in a numerical simulation example that illustrates the feasibility of the proposed algorithms.

MIMO-radar Waveform Covariance Matrices for High SINR and Low Side-lobe Levels

KAUST Repository

Ahmed, Sajid; Alouini, Mohamed-Slim

2012-01-01

MIMO-radar has better parametric identifiability but compared to phased-array radar it shows loss in signal-to-noise ratio due to non-coherent processing. To exploit the benefits of both MIMO-radar and phased-array two transmit covariance matrices

Estimating correlation and covariance matrices by weighting of market similarity

OpenAIRE

Michael C. M\\"unnix; Rudi Sch\\"afer; Oliver Grothe

2010-01-01

We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The resulting estimators are less biased and show lower variance than either unweighted or exponentially weighted estimators. The weighting scheme is based on a similarity measure which compares the current correlation structure of the market to the structures at past ...

Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states

Energy Technology Data Exchange (ETDEWEB)

Guehne, Otfried [Institut fuer Quantenoptik und Quanteninformation, Oesterreichische Akademie der Wissenschaften, A-6020 Innsbruck (Austria); Luetkenhaus, Norbert [Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada)

2007-05-15

Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the set of separable states has no facets. Second, we give a new derivation of nonlinear witnesses based on covariance matrices. Finally, we investigate extensions to the multipartite case.

PUFF-IV, Code System to Generate Multigroup Covariance Matrices from ENDF/B-VI Uncertainty Files

International Nuclear Information System (INIS)

2007-01-01

1 - Description of program or function: The PUFF-IV code system processes ENDF/B-VI formatted nuclear cross section covariance data into multigroup covariance matrices. PUFF-IV is the newest release in this series of codes used to process ENDF uncertainty information and to generate the desired multi-group correlation matrix for the evaluation of interest. This version includes corrections and enhancements over previous versions. It is written in Fortran 90 and allows for a more modular design, thus facilitating future upgrades. PUFF-IV enhances support for resonance parameter covariance formats described in the ENDF standard and now handles almost all resonance parameter covariance information in the resolved region, with the exception of the long range covariance sub-subsections. PUFF-IV is normally used in conjunction with an AMPX master library containing group averaged cross section data. Two utility modules are included in this package to facilitate the data interface. The module SMILER allows one to use NJOY generated GENDF files containing group averaged cross section data in conjunction with PUFF-IV. The module COVCOMP allows one to compare two files written in COVERX format. 2 - Methods: Cross section and flux values on a 'super energy grid,' consisting of the union of the required energy group structure and the energy data points in the ENDF/B-V file, are interpolated from the input cross sections and fluxes. Covariance matrices are calculated for this grid and then collapsed to the required group structure. 3 - Restrictions on the complexity of the problem: PUFF-IV cannot process covariance information for energy and angular distributions of secondary particles. PUFF-IV does not process covariance information in Files 34 and 35; nor does it process covariance information in File 40. These new formats will be addressed in a future version of PUFF

ANGELO-LAMBDA, Covariance matrix interpolation and mathematical verification

International Nuclear Information System (INIS)

Kodeli, Ivo

2007-01-01

1 - Description of program or function: The codes ANGELO-2.3 and LAMBDA-2.3 are used for the interpolation of the cross section covariance data from the original to a user defined energy group structure, and for the mathematical tests of the matrices, respectively. The LAMBDA-2.3 code calculates the eigenvalues of the matrices (both for the original or the converted) and lists them accordingly into positive and negative matrices. This verification is strongly recommended before using any covariance matrices. These versions of the two codes are the extended versions of the previous codes available in the Packages NEA-1264 - ZZ-VITAMIN-J/COVA. They were specifically developed for the purposes of the OECD LWR UAM benchmark, in particular for the processing of the ZZ-SCALE5.1/COVA-44G cross section covariance matrix library retrieved from the SCALE-5.1 package. Either the original SCALE-5.1 libraries or the libraries separated into several files by Nuclides can be (in principle) processed by ANGELO/LAMBDA codes, but the use of the one-nuclide data is strongly recommended. Due to large deviations of the correlation matrix terms from unity observed in some SCALE5.1 covariance matrices, the previous more severe acceptance condition in the ANGELO2.3 code was released. In case the correlation coefficients exceed 1.0, only a warning message is issued, and coefficients are replaced by 1.0. 2 - Methods: ANGELO-2.3 interpolates the covariance matrices to a union grid using flat weighting. LAMBDA-2.3 code includes the mathematical routines to calculate the eigenvalues of the covariance matrices. 3 - Restrictions on the complexity of the problem: The algorithm used in ANGELO is relatively simple, therefore the interpolations involving energy group structure which are very different from the original (e.g. large difference in the number of energy groups) may not be accurate. In particular in the case of the MT=1018 data (fission spectra covariances) the algorithm may not be

Covariance matrices for nuclear cross sections derived from nuclear model calculations

International Nuclear Information System (INIS)

Smith, D. L.

2005-01-01

The growing need for covariance information to accompany the evaluated cross section data libraries utilized in contemporary nuclear applications is spurring the development of new methods to provide this information. Many of the current general purpose libraries of evaluated nuclear data used in applications are derived either almost entirely from nuclear model calculations or from nuclear model calculations benchmarked by available experimental data. Consequently, a consistent method for generating covariance information under these circumstances is required. This report discusses a new approach to producing covariance matrices for cross sections calculated using nuclear models. The present method involves establishing uncertainty information for the underlying parameters of nuclear models used in the calculations and then propagating these uncertainties through to the derived cross sections and related nuclear quantities by means of a Monte Carlo technique rather than the more conventional matrix error propagation approach used in some alternative methods. The formalism to be used in such analyses is discussed in this report along with various issues and caveats that need to be considered in order to proceed with a practical implementation of the methodology

Bayesian estimation of covariance matrices: Application to market risk management at EDF

International Nuclear Information System (INIS)

Jandrzejewski-Bouriga, M.

2012-01-01

In this thesis, we develop new methods of regularized covariance matrix estimation, under the Bayesian setting. The regularization methodology employed is first related to shrinkage. We investigate a new Bayesian modeling of covariance matrix, based on hierarchical inverse-Wishart distribution, and then derive different estimators under standard loss functions. Comparisons between shrunk and empirical estimators are performed in terms of frequentist performance under different losses. It allows us to highlight the critical importance of the definition of cost function and show the persistent effect of the shrinkage-type prior on inference. In a second time, we consider the problem of covariance matrix estimation in Gaussian graphical models. If the issue is well treated for the decomposable case, it is not the case if you also consider non-decomposable graphs. We then describe a Bayesian and operational methodology to carry out the estimation of covariance matrix of Gaussian graphical models, decomposable or not. This procedure is based on a new and objective method of graphical-model selection, combined with a constrained and regularized estimation of the covariance matrix of the model chosen. The procedures studied effectively manage missing data. These estimation techniques were applied to calculate the covariance matrices involved in the market risk management for portfolios of EDF (Electricity of France), in particular for problems of calculating Value-at-Risk or in Asset Liability Management. (author)

Solid-state NMR covariance of homonuclear correlation spectra.

Science.gov (United States)

Hu, Bingwen; Amoureux, Jean-Paul; Trebosc, Julien; Deschamps, Michael; Tricot, Gregory

2008-04-07

Direct covariance NMR spectroscopy, which does not involve a Fourier transformation along the indirect dimension, is demonstrated to obtain homonuclear correlation two-dimensional (2D) spectra in the solid state. In contrast to the usual 2D Fourier transform (2D-FT) NMR, in a 2D covariance (2D-Cov) spectrum the spectral resolution in the indirect dimension is determined by the resolution along the detection dimension, thereby largely reducing the time-consuming indirect sampling requirement. The covariance method does not need any separate phase correction or apodization along the indirect dimension because it uses those applied in the detection dimension. We compare in detail the specifications obtained with 2D-FT and 2D-Cov, for narrow and broad resonances. The efficiency of the covariance data treatment is demonstrated in organic and inorganic samples that are both well crystallized and amorphous, for spin -1/2 nuclei with 13C, 29Si, and 31P through-space or through-bond homonuclear 2D correlation spectra. In all cases, the experimental time has been reduced by at least a factor of 10, without any loss of resolution and signal to noise ratio, with respect to what is necessary with the 2D-FT NMR. According to this method, we have been able to study the silicate network of glasses by 2D NMR within reasonable experimental time despite the very long relaxation time of the 29Si nucleus. The main limitation of the 2D-Cov data treatment is related to the introduction of autocorrelated peaks onto the diagonal, which does not represent any actual connectivity.

Spectral correlation functions of the sum of two independent complex Wishart matrices with unequal covariances

International Nuclear Information System (INIS)

Akemann, Gernot; Checinski, Tomasz; Kieburg, Mario

2016-01-01

We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random matrices. Typically ensembles with correlations among the matrix elements are much more difficult to solve. Using a combination of supersymmetry, superbosonisation and bi-orthogonal functions we are able to determine all spectral k -point density correlation functions of H for arbitrary matrix size N . In the half-degenerate case, when one of the covariance matrices is proportional to the identity, the recent results by Kumar for the joint eigenvalue distribution of H serve as our starting point. In this case the ensemble has a bi-orthogonal structure and we explicitly determine its kernel, providing its exact solution for finite N . The kernel follows from computing the expectation value of a single characteristic polynomial. In the general non-degenerate case the generating function for the k -point resolvent is determined from a supersymmetric evaluation of the expectation value of k ratios of characteristic polynomials. Numerical simulations illustrate our findings for the spectral density at finite N and we also give indications how to do the asymptotic large- N analysis. (paper)

Examination of various roles for covariance matrices in the development, evaluation, and application of nuclear data

International Nuclear Information System (INIS)

Smith, D.L.

1988-01-01

The last decade has been a period of rapid development in the implementation of covariance-matrix methodology in nuclear data research. This paper offers some perspective on the progress which has been made, on some of the unresolved problems, and on the potential yet to be realized. These discussions address a variety of issues related to the development of nuclear data. Topics examined are: the importance of designing and conducting experiments so that error information is conveniently generated; the procedures for identifying error sources and quantifying their magnitudes and correlations; the combination of errors; the importance of consistent and well-characterized measurement standards; the role of covariances in data parameterization (fitting); the estimation of covariances for values calculated from mathematical models; the identification of abnormalities in covariance matrices and the analysis of their consequences; the problems encountered in representing covariance information in evaluated files; the role of covariances in the weighting of diverse data sets; the comparison of various evaluations; the influence of primary-data covariance in the analysis of covariances for derived quantities (sensitivity); and the role of covariances in the merging of the diverse nuclear data information. 226 refs., 2 tabs

PUFF-III: A Code for Processing ENDF Uncertainty Data Into Multigroup Covariance Matrices

International Nuclear Information System (INIS)

Dunn, M.E.

2000-01-01

PUFF-III is an extension of the previous PUFF-II code that was developed in the 1970s and early 1980s. The PUFF codes process the Evaluated Nuclear Data File (ENDF) covariance data and generate multigroup covariance matrices on a user-specified energy grid structure. Unlike its predecessor, PUFF-III can process the new ENDF/B-VI data formats. In particular, PUFF-III has the capability to process the spontaneous fission covariances for fission neutron multiplicity. With regard to the covariance data in File 33 of the ENDF system, PUFF-III has the capability to process short-range variance formats, as well as the lumped reaction covariance data formats that were introduced in ENDF/B-V. In addition to the new ENDF formats, a new directory feature is now available that allows the user to obtain a detailed directory of the uncertainty information in the data files without visually inspecting the ENDF data. Following the correlation matrix calculation, PUFF-III also evaluates the eigenvalues of each correlation matrix and tests each matrix for positive definiteness. Additional new features are discussed in the manual. PUFF-III has been developed for implementation in the AMPX code system, and several modifications were incorporated to improve memory allocation tasks and input/output operations. Consequently, the resulting code has a structure that is similar to other modules in the AMPX code system. With the release of PUFF-III, a new and improved covariance processing code is available to process ENDF covariance formats through Version VI

FoodPro: A Web-Based Tool for Evaluating Covariance and Correlation NMR Spectra Associated with Food Processes

Directory of Open Access Journals (Sweden)

Eisuke Chikayama

2016-10-01

Full Text Available Foods from agriculture and fishery products are processed using various technologies. Molecular mixture analysis during food processing has the potential to help us understand the molecular mechanisms involved, thus enabling better cooking of the analyzed foods. To date, there has been no web-based tool focusing on accumulating Nuclear Magnetic Resonance (NMR spectra from various types of food processing. Therefore, we have developed a novel web-based tool, FoodPro, that includes a food NMR spectrum database and computes covariance and correlation spectra to tasting and hardness. As a result, FoodPro has accumulated 236 aqueous (extracted in D2O and 131 hydrophobic (extracted in CDCl3 experimental bench-top 60-MHz NMR spectra, 1753 tastings scored by volunteers, and 139 hardness measurements recorded by a penetrometer, all placed into a core database. The database content was roughly classified into fish and vegetable groups from the viewpoint of different spectrum patterns. FoodPro can query a user food NMR spectrum, search similar NMR spectra with a specified similarity threshold, and then compute estimated tasting and hardness, covariance, and correlation spectra to tasting and hardness. Querying fish spectra exemplified specific covariance spectra to tasting and hardness, giving positive covariance for tasting at 1.31 ppm for lactate and 3.47 ppm for glucose and a positive covariance for hardness at 3.26 ppm for trimethylamine N-oxide.

FoodPro: A Web-Based Tool for Evaluating Covariance and Correlation NMR Spectra Associated with Food Processes.

Science.gov (United States)

Chikayama, Eisuke; Yamashina, Ryo; Komatsu, Keiko; Tsuboi, Yuuri; Sakata, Kenji; Kikuchi, Jun; Sekiyama, Yasuyo

2016-10-19

Foods from agriculture and fishery products are processed using various technologies. Molecular mixture analysis during food processing has the potential to help us understand the molecular mechanisms involved, thus enabling better cooking of the analyzed foods. To date, there has been no web-based tool focusing on accumulating Nuclear Magnetic Resonance (NMR) spectra from various types of food processing. Therefore, we have developed a novel web-based tool, FoodPro, that includes a food NMR spectrum database and computes covariance and correlation spectra to tasting and hardness. As a result, FoodPro has accumulated 236 aqueous (extracted in D₂O) and 131 hydrophobic (extracted in CDCl₃) experimental bench-top 60-MHz NMR spectra, 1753 tastings scored by volunteers, and 139 hardness measurements recorded by a penetrometer, all placed into a core database. The database content was roughly classified into fish and vegetable groups from the viewpoint of different spectrum patterns. FoodPro can query a user food NMR spectrum, search similar NMR spectra with a specified similarity threshold, and then compute estimated tasting and hardness, covariance, and correlation spectra to tasting and hardness. Querying fish spectra exemplified specific covariance spectra to tasting and hardness, giving positive covariance for tasting at 1.31 ppm for lactate and 3.47 ppm for glucose and a positive covariance for hardness at 3.26 ppm for trimethylamine N -oxide.

ZZ RRDF-98, Cross-sections and covariance matrices for 22 neutron induced dosimetry reactions

International Nuclear Information System (INIS)

Zolotarev, K.I.; Ignatyuk, A.V.; Mahokhin, V.N.; Pashchenko, A.B.

2005-01-01

1 - Description of program or function: Format: ENDF-6 format; Number of groups: Continuous energy; Dosimetry reactions: 6-C-12(n,2n), 8-O-16(n,2n), 9-F-19(n,2n), 12-Mg-24(n,p), 22-Ti-46(n,2n), 22-Ti-46(n,p), 22-Ti-47(n,x), 22-Ti-48(n,p), 22-Ti-48(n,x), 22-Ti-49(n,x), 23-V-51(n,alpha), 26-Fe-54(n,2n), 26-Fe-54(n,alpha), 26-Fe-56(n,p), 27-Co-59(n,alpha), 29-Cu-63(n,alpha), 33-As-75(n,2n), 41-Nb-93(n,2n), 41-Nb-93(n,n'), 45-Rh-103(n,n'), 49-In-115(n,n'), 59-Pr-141(n,2n); Origin: Russian Federation; Weighting spectrum: None. RRDF-98 contains original evaluations of cross section data performed at the Institute of Physics and Power Engineering, Obninsk, for 22 neutron induced dosimetry reactions. The dataset also contains the corresponding covariance matrices. 2 - Methods: The evaluation of excitation functions was performed on the basis of statistical analysis of corrected experimental data in the framework of generalized least squares method and taking into account the results of optical-statistical STAPRE and GNASH calculations. The experimental cross section data including the most recent results were critically reviewed and processed in this study. If necessary, the data were normalized in order to make adjustments in relevant cross sections and decay schemes. The covariance matrices were prepared and the evaluated cross section data are presented in ENDF-6 format (Files 3, 33). For estimation of correlations between experimental data the total uncertainties of measured cross sections have been separated into statistical and systematic parts and correlation coefficients between components of systematic parts were assigned according to information given in the original publications and EXFOR library. Then the correlation matrix of cross sections measured within one experiment was calculated and approximated by matrix with a constant (average) correlation coefficient. The overall correlation matrix was composed of such sub-matrices in the assumption that the cross

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

Science.gov (United States)

Zhu, Lingxue; Lei, Jing; Devlin, Bernie; Roeder, Kathryn

2017-09-01

Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however statistical methods have been limited by the high dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with Sparse Principal Component Analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene "relationship" matrices that are of practical interest, such as the weighted adjacency matrices.

Covariance matrices of experimental data

International Nuclear Information System (INIS)

Perey, F.G.

1978-01-01

A complete statement of the uncertainties in data is given by its covariance matrix. It is shown how the covariance matrix of data can be generated using the information available to obtain their standard deviations. Determination of resonance energies by the time-of-flight method is used as an example. The procedure for combining data when the covariance matrix is non-diagonal is given. The method is illustrated by means of examples taken from the recent literature to obtain an estimate of the energy of the first resonance in carbon and for five resonances of 238 U

Facilitated assignment of large protein NMR signals with covariance sequential spectra using spectral derivatives.

Science.gov (United States)

Harden, Bradley J; Nichols, Scott R; Frueh, Dominique P

2014-09-24

Nuclear magnetic resonance (NMR) studies of larger proteins are hampered by difficulties in assigning NMR resonances. Human intervention is typically required to identify NMR signals in 3D spectra, and subsequent procedures depend on the accuracy of this so-called peak picking. We present a method that provides sequential connectivities through correlation maps constructed with covariance NMR, bypassing the need for preliminary peak picking. We introduce two novel techniques to minimize false correlations and merge the information from all original 3D spectra. First, we take spectral derivatives prior to performing covariance to emphasize coincident peak maxima. Second, we multiply covariance maps calculated with different 3D spectra to destroy erroneous sequential correlations. The maps are easy to use and can readily be generated from conventional triple-resonance experiments. Advantages of the method are demonstrated on a 37 kDa nonribosomal peptide synthetase domain subject to spectral overlap.

Directional variance adjustment: bias reduction in covariance matrices based on factor analysis with an application to portfolio optimization.

Science.gov (United States)

Bartz, Daniel; Hatrick, Kerr; Hesse, Christian W; Müller, Klaus-Robert; Lemm, Steven

2013-01-01

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation.

The Effect of Unequal Samples, Heterogeneity of Covariance Matrices, and Number of Variables on Discriminant Analysis Classification Tables and Related Statistics.

Science.gov (United States)

Spearing, Debra; Woehlke, Paula

To assess the effect on discriminant analysis in terms of correct classification into two groups, the following parameters were systematically altered using Monte Carlo techniques: sample sizes; proportions of one group to the other; number of independent variables; and covariance matrices. The pairing of the off diagonals (or covariances) with…

On estimating cosmology-dependent covariance matrices

International Nuclear Information System (INIS)

Morrison, Christopher B.; Schneider, Michael D.

2013-01-01

We describe a statistical model to estimate the covariance matrix of matter tracer two-point correlation functions with cosmological simulations. Assuming a fixed number of cosmological simulation runs, we describe how to build a 'statistical emulator' of the two-point function covariance over a specified range of input cosmological parameters. Because the simulation runs with different cosmological models help to constrain the form of the covariance, we predict that the cosmology-dependent covariance may be estimated with a comparable number of simulations as would be needed to estimate the covariance for fixed cosmology. Our framework is a necessary first step in planning a simulations campaign for analyzing the next generation of cosmological surveys

Application of unsymmetrical indirect covariance NMR methods to the computation of the (13)C (15)N HSQC-IMPEACH and (13)C (15)N HMBC-IMPEACH correlation spectra.

Science.gov (United States)

Martin, Gary E; Hilton, Bruce D; Irish, Patrick A; Blinov, Kirill A; Williams, Antony J

2007-10-01

Utilization of long-range (1)H--(15)N heteronuclear chemical shift correlation has continually grown in importance since the first applications were reported in 1995. More recently, indirect covariance NMR methods have been introduced followed by the development of unsymmetrical indirect covariance processing methods. The latter technique has been shown to allow the calculation of hyphenated 2D NMR data matrices from more readily acquired nonhyphenated 2D NMR spectra. We recently reported the use of unsymmetrical indirect covariance processing to combine (1)H--(13)C GHSQC and (1)H--(15)N GHMBC long-range spectra to yield a (13)C--(15)N HSQC-HMBC chemical shift correlation spectrum that could not be acquired in a reasonable period of time without resorting to (15)N-labeled molecules. We now report the unsymmetrical indirect covariance processing of (1)H--(13)C GHMBC and (1)H--(15)N IMPEACH spectra to afford a (13)C--(15)N HMBC-IMPEACH spectrum that has the potential to span as many as six to eight bonds. Correlations for carbon resonances long-range coupled to a protonated carbon in the (1)H--(13)C HMBC spectrum are transferred via the long-range (1)H--(15)N coupling pathway in the (1)H--(15)N IMPEACH spectrum to afford a much broader range of correlation possibilities in the (13)C--(15)N HMBC-IMPEACH correlation spectrum. The indole alkaloid vincamine is used as a model compound to illustrate the application of the method. (c) 2007 John Wiley & Sons, Ltd.

Directional Variance Adjustment: Bias Reduction in Covariance Matrices Based on Factor Analysis with an Application to Portfolio Optimization

Science.gov (United States)

Bartz, Daniel; Hatrick, Kerr; Hesse, Christian W.; Müller, Klaus-Robert; Lemm, Steven

2013-01-01

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation. PMID:23844016

Directional variance adjustment: bias reduction in covariance matrices based on factor analysis with an application to portfolio optimization.

Directory of Open Access Journals (Sweden)

Daniel Bartz

Full Text Available Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation.

ESTIMATION OF FUNCTIONALS OF SPARSE COVARIANCE MATRICES.

Science.gov (United States)

Fan, Jianqing; Rigollet, Philippe; Wang, Weichen

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other ℓ r norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are sparsity-adaptive and minimax optimal over a large class of correlation matrices. Akin to previous results on functional estimation, the minimax rates exhibit an elbow phenomenon. Our results are further illustrated in simulated data as well as an empirical study of data arising in financial econometrics.

Dante-unfolding code for energy spectra evaluation

International Nuclear Information System (INIS)

Petilli, M.

1979-01-01

The code DANTE, using the last square method in unfolding for dosimetry purpose, solves the neutron spectra evaluation problem starting by activity measurements. The code DANTE introduced for the first time the correlation between available data by mean of flux and activity variance-covariance matrices and the error propagation. In the present report the solution method is detailed described

High-dimensional covariance estimation with high-dimensional data

CERN Document Server

Pourahmadi, Mohsen

2013-01-01

Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and mac

ANL Critical Assembly Covariance Matrix Generation - Addendum

Energy Technology Data Exchange (ETDEWEB)

McKnight, Richard D. [Argonne National Lab. (ANL), Argonne, IL (United States); Grimm, Karl N. [Argonne National Lab. (ANL), Argonne, IL (United States)

2014-01-13

In March 2012, a report was issued on covariance matrices for Argonne National Laboratory (ANL) critical experiments. That report detailed the theory behind the calculation of covariance matrices and the methodology used to determine the matrices for a set of 33 ANL experimental set-ups. Since that time, three new experiments have been evaluated and approved. This report essentially updates the previous report by adding in these new experiments to the preceding covariance matrix structure.

Spectra of sparse random matrices

International Nuclear Information System (INIS)

Kuehn, Reimer

2008-01-01

We compute the spectral density for ensembles of sparse symmetric random matrices using replica. Our formulation of the replica-symmetric ansatz shares the symmetries of that suggested in a seminal paper by Rodgers and Bray (symmetry with respect to permutation of replica and rotation symmetry in the space of replica), but uses a different representation in terms of superpositions of Gaussians. It gives rise to a pair of integral equations which can be solved by a stochastic population-dynamics algorithm. Remarkably our representation allows us to identify pure-point contributions to the spectral density related to the existence of normalizable eigenstates. Our approach is not restricted to matrices defined on graphs with Poissonian degree distribution. Matrices defined on regular random graphs or on scale-free graphs, are easily handled. We also look at matrices with row constraints such as discrete graph Laplacians. Our approach naturally allows us to unfold the total density of states into contributions coming from vertices of different local coordinations and an example of such an unfolding is presented. Our results are well corroborated by numerical diagonalization studies of large finite random matrices

Bayesian analysis of finite population sampling in multivariate co-exchangeable structures with separable covariance matric

OpenAIRE

Shaw, Simon C.; Goldstein, Michael

2017-01-01

We explore the effect of finite population sampling in design problems with many variables cross-classified in many ways. In particular, we investigate designs where we wish to sample individuals belonging to different groups for which the underlying covariance matrices are separable between groups and variables. We exploit the generalised conditional independence structure of the model to show how the analysis of the full model can be reduced to an interpretable series of lower dimensional p...

Covariance matrix estimation for stationary time series

OpenAIRE

Xiao, Han; Wu, Wei Biao

2011-01-01

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351–376] idea and relate eigenvalues of covariance matrices to the spectral densities or Fourier transforms...

ROBUST KALMAN FILTERING FOR SYSTEMS UNDER NORM BOUNDED UNCERTAINTIES IN ALL SYSTEM MATRICES AND ERROR COVARIANCE CONSTRAINTS

Institute of Scientific and Technical Information of China (English)

XIA Yuanqing; HAN Jingqing

2005-01-01

This paper concerns robust Kalman filtering for systems under norm bounded uncertainties in all the system matrices and error covariance constraints. Sufficient conditions are given for the existence of such filters in terms of Riccati equations. The solutions to the conditions can be used to design the filters. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed design procedure.

Structural Analysis of Covariance and Correlation Matrices.

Science.gov (United States)

Joreskog, Karl G.

1978-01-01

A general approach to analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.…

An initial investigation of the GOCE error variance-covariance matrices in the context of the GOCE user toolbox project

DEFF Research Database (Denmark)

Bingham, Rory J.; Tscherning, Christian; Knudsen, Per

2011-01-01

The availability of the full error variance-covariance matrices for the GOCE gravity field models is an important feature of the GOCE mission. Potentially, it will allow users to evaluate the accuracy of a geoid or mean dynamic topography (MDT) derived from the gravity field model at any particul...

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

Science.gov (United States)

Siren, J; Ovaskainen, O; Merilä, J

2017-10-01

The genetic variance-covariance matrix (G) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G-matrices is limited for two reasons. First, phenotypes are high-dimensional, whereas traditional statistical methods are tuned to estimate and analyse low-dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high-dimensional G-matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half-sib breeding design of three-spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low-temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability-as well as the similarity among G-matrices-may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G-matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G, they also illustrate that by enabling the estimation of large G-matrices, the BSFG method can improve predicted evolutionary responses to selection. © 2017 John Wiley & Sons Ltd.

Probing dark energy with cluster counts and cosmic shear power spectra: including the full covariance

International Nuclear Information System (INIS)

Takada, Masahiro; Bridle, Sarah

2007-01-01

Several dark energy experiments are available from a single large-area imaging survey and may be combined to improve cosmological parameter constraints and/or test inherent systematics. Two promising experiments are cosmic shear power spectra and counts of galaxy clusters. However, the two experiments probe the same cosmic mass density field in large-scale structure, therefore the combination may be less powerful than first thought. We investigate the cross-covariance between the cosmic shear power spectra and the cluster counts based on the halo model approach, where the cross-covariance arises from the three-point correlations of the underlying mass density field. Fully taking into account the cross-covariance, as well as non-Gaussian errors on the lensing power spectrum covariance, we find a significant cross-correlation between the lensing power spectrum signals at multipoles l∼10 3 and the cluster counts containing halos with masses M∼>10 14 M o-dot . Including the cross-covariance for the combined measurement degrades and in some cases improves the total signal-to-noise (S/N) ratios up to ∼±20% relative to when the two are independent. For cosmological parameter determination, the cross-covariance has a smaller effect as a result of working in a multi-dimensional parameter space, implying that the two observables can be considered independent to a good approximation. We also discuss the fact that cluster count experiments using lensing-selected mass peaks could be more complementary to cosmic shear tomography than mass-selected cluster counts of the corresponding mass threshold. Using lensing selected clusters with a realistic usable detection threshold ((S/N) cluster ∼6 for a ground-based survey), the uncertainty on each dark energy parameter may be roughly halved by the combined experiments, relative to using the power spectra alone

Mass spectra and wave functions of meson systems and the covariant oscillator quark model as an expansion basis

International Nuclear Information System (INIS)

Oda, Ryuichi; Ishida, Shin; Wada, Hiroaki; Yamada, Kenji; Sekiguchi, Motoo

1999-01-01

We examine mass spectra and wave functions of the nn-bar, cc-bar and bb-bar meson systems within the framework of the covariant oscillator quark model with the boosted LS-coupling scheme. We solve nonperturbatively an eigenvalue problem for the squared-mass operator, which incorporates the four-dimensional color-Coulomb-type interaction, by taking a set of covariant oscillator wave functions as an expansion basis. We obtain mass spectra of these meson systems, which reproduce quite well their experimental behavior. The resultant manifestly covariant wave functions, which are applicable to analyses of various reaction phenomena, are given. Our results seem to suggest that the present model may be considered effectively as a covariant version of the nonrelativistic linear-plus-Coulomb potential quark model. (author)

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-01-01

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

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-12-05

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

ACORNS, Covariance and Correlation Matrix Diagonalization

International Nuclear Information System (INIS)

Szondi, E.J.

1990-01-01

1 - Description of program or function: The program allows the user to verify the different types of covariance/correlation matrices used in the activation neutron spectrometry. 2 - Method of solution: The program performs the diagonalization of the input covariance/relative covariance/correlation matrices. The Eigen values are then analyzed to determine the rank of the matrices. If the Eigen vectors of the pertinent correlation matrix have also been calculated, the program can perform a complete factor analysis (generation of the factor matrix and its rotation in Kaiser's 'varimax' sense to select the origin of the correlations). 3 - Restrictions on the complexity of the problem: Matrix size is limited to 60 on PDP and to 100 on IBM PC/AT

Computation of large covariance matrices by SAMMY on graphical processing units and multicore CPUs

International Nuclear Information System (INIS)

Arbanas, G.; Dunn, M.E.; Wiarda, D.

2011-01-01

Computational power of Graphical Processing Units and multicore CPUs was harnessed by the nuclear data evaluation code SAMMY to speed up computations of large Resonance Parameter Covariance Matrices (RPCMs). This was accomplished by linking SAMMY to vendor-optimized implementations of the matrix-matrix multiplication subroutine of the Basic Linear Algebra Library to compute the most time-consuming step. The 235 U RPCM computed previously using a triple-nested loop was re-computed using the NVIDIA implementation of the subroutine on a single Tesla Fermi Graphical Processing Unit, and also using the Intel's Math Kernel Library implementation on two different multicore CPU systems. A multiplication of two matrices of dimensions 16,000×20,000 that had previously taken days, took approximately one minute on the GPU. Comparable performance was achieved on a dual six-core CPU system. The magnitude of the speed-up suggests that these, or similar, combinations of hardware and libraries may be useful for large matrix operations in SAMMY. Uniform interfaces of standard linear algebra libraries make them a promising candidate for a programming framework of a new generation of SAMMY for the emerging heterogeneous computing platforms. (author)

Computation of large covariance matrices by SAMMY on graphical processing units and multicore CPUs

Energy Technology Data Exchange (ETDEWEB)

Arbanas, G.; Dunn, M.E.; Wiarda, D., E-mail: arbanasg@ornl.gov, E-mail: dunnme@ornl.gov, E-mail: wiardada@ornl.gov [Oak Ridge National Laboratory, Oak Ridge, TN (United States)

2011-07-01

Computational power of Graphical Processing Units and multicore CPUs was harnessed by the nuclear data evaluation code SAMMY to speed up computations of large Resonance Parameter Covariance Matrices (RPCMs). This was accomplished by linking SAMMY to vendor-optimized implementations of the matrix-matrix multiplication subroutine of the Basic Linear Algebra Library to compute the most time-consuming step. The {sup 235}U RPCM computed previously using a triple-nested loop was re-computed using the NVIDIA implementation of the subroutine on a single Tesla Fermi Graphical Processing Unit, and also using the Intel's Math Kernel Library implementation on two different multicore CPU systems. A multiplication of two matrices of dimensions 16,000×20,000 that had previously taken days, took approximately one minute on the GPU. Comparable performance was achieved on a dual six-core CPU system. The magnitude of the speed-up suggests that these, or similar, combinations of hardware and libraries may be useful for large matrix operations in SAMMY. Uniform interfaces of standard linear algebra libraries make them a promising candidate for a programming framework of a new generation of SAMMY for the emerging heterogeneous computing platforms. (author)

Position Error Covariance Matrix Validation and Correction

Science.gov (United States)

Frisbee, Joe, Jr.

2016-01-01

In order to calculate operationally accurate collision probabilities, the position error covariance matrices predicted at times of closest approach must be sufficiently accurate representations of the position uncertainties. This presentation will discuss why the Gaussian distribution is a reasonable expectation for the position uncertainty and how this assumed distribution type is used in the validation and correction of position error covariance matrices.

Effect of low-temperature argon matrices on IR spectra and structure of flexible N-acetylglycine molecules

International Nuclear Information System (INIS)

Stepan'yan, S.G.; Ivanov, A.Yu.; Adamowicz, L.

2016-01-01

The influence of the matrix environment on structure and IR spectra of the N-acetylglycine conformers was studied. Based on the FTIR spectra of N-acetyl-glycine isolated in low temperature argon matrices we determined its conformational composition. The spectra bands of main and two minor conformers of N-acetylglycine were identified in the FTIR spectra. The structure of the observed conformers was stabilized by different intramolecular hydrogen bonds. The Gibbs free energies of the conformers (CCSD(T)/CBS method) were performed and population of the con-formers at 360 K were determined. They were 85.3% for the main conformer and 9.6 and 5.1% for the mi-nor N-acetylglycine conformers. We also determined size and shape of the cavities which were formed by embedding of the N-acetylglycine conformers in argon matrices during deposition. It was found that for the planar main conformer the most energetically preferred cavity was formed by substituting of 7 argon atoms. At the same time, bulky minor conformers were embedded in a cavity formed by substituting of 8 argon atoms. Complexation energies as well as the deformation energies of the argon crystal and conformers of N-acetylglycine were calculated. Also we determined values of the matrix shifts of vibrational frequencies of N-acetylglycine conformers.

Covariance Partition Priors: A Bayesian Approach to Simultaneous Covariance Estimation for Longitudinal Data.

Science.gov (United States)

Gaskins, J T; Daniels, M J

2016-01-02

The estimation of the covariance matrix is a key concern in the analysis of longitudinal data. When data consists of multiple groups, it is often assumed the covariance matrices are either equal across groups or are completely distinct. We seek methodology to allow borrowing of strength across potentially similar groups to improve estimation. To that end, we introduce a covariance partition prior which proposes a partition of the groups at each measurement time. Groups in the same set of the partition share dependence parameters for the distribution of the current measurement given the preceding ones, and the sequence of partitions is modeled as a Markov chain to encourage similar structure at nearby measurement times. This approach additionally encourages a lower-dimensional structure of the covariance matrices by shrinking the parameters of the Cholesky decomposition toward zero. We demonstrate the performance of our model through two simulation studies and the analysis of data from a depression study. This article includes Supplementary Material available online.

Massive data compression for parameter-dependent covariance matrices

Science.gov (United States)

Heavens, Alan F.; Sellentin, Elena; de Mijolla, Damien; Vianello, Alvise

2017-12-01

We show how the massive data compression algorithm MOPED can be used to reduce, by orders of magnitude, the number of simulated data sets which are required to estimate the covariance matrix required for the analysis of Gaussian-distributed data. This is relevant when the covariance matrix cannot be calculated directly. The compression is especially valuable when the covariance matrix varies with the model parameters. In this case, it may be prohibitively expensive to run enough simulations to estimate the full covariance matrix throughout the parameter space. This compression may be particularly valuable for the next generation of weak lensing surveys, such as proposed for Euclid and Large Synoptic Survey Telescope, for which the number of summary data (such as band power or shear correlation estimates) is very large, ∼104, due to the large number of tomographic redshift bins which the data will be divided into. In the pessimistic case where the covariance matrix is estimated separately for all points in an Monte Carlo Markov Chain analysis, this may require an unfeasible 109 simulations. We show here that MOPED can reduce this number by a factor of 1000, or a factor of ∼106 if some regularity in the covariance matrix is assumed, reducing the number of simulations required to a manageable 103, making an otherwise intractable analysis feasible.

Covariance as input to and output from resonance analyses

International Nuclear Information System (INIS)

Larson, N.M.

1992-01-01

Accurate data analysis requires understanding of the roles played by both data and parameter covariance matrices. In this paper the entire data reduction/analysis process is examined, for neutron-induced reactions in the resonance region. Interrelationships between data and parameter covariance matrices are examined and alternative reduction/analysis methods discussed

On the covariance matrices in the evaluated nuclear data

International Nuclear Information System (INIS)

Corcuera, R.P.

1983-05-01

The implications of the uncertainties of nuclear data on reactor calculations are shown. The concept of variance, covariance and correlation are expressed first by intuitive definitions and then through statistical theory. The format of the covariance data for ENDF/B is explained and the formulas to obtain the multigroup covariances are given. (Author) [pt

Raman spectra of ruthenium and tantalum trimers in argon matrices

Science.gov (United States)

Fang, Li; Shen, Xiaole; Chen, Xiaoyu; Lombardi, John R.

2000-12-01

The resonance Raman spectra of ruthenium trimers (Ru 3) in argon matrices have been obtained. Three resonance Raman transitions were observed between 570 and 590 nm. Two of them (303.4 and 603.7 cm -1) are assigned to the totally symmetric vibrational progression, giving k e=1.86 mdyne/ Å. The line at 581.5 cm-1 is assigned as the origin of a low-lying electronic state. We also report on the observation of a resonance Raman spectrum of tantalum trimers (Ta 3). Observed lines include 251.2 and 501.9 cm-1 which we assign to the fundamental and the first overtone of the symmetric stretch in Ta 3. This gives k e=2.25 mdyne/ Å.

BASACF, Integral Neutron Spectra Adjustment and Dosimetry

International Nuclear Information System (INIS)

Tichy, Milos

1996-01-01

1 - Description of program or function: Adjustment of a neutron spectrum based on integral detector measurements and calculation of an integral dosimetric quantity (integral flux, d.p.a., dose equivalent) and its variance. The program requires measured data (activities and their covariance matrix) and a priori information (spectrum, dosimetry cross sections, integral quantity conversion factor and their covariance matrices). All a priori covariance matrices can be read in from a file prepared by some other code or can be generated by means of three different methods (by subroutines included in the program). A subroutine which can normalize the a priori flux to measured data is also included. The program provides also adjusted dosimetry cross sections (with covariance matrix) so that it can be used for an adjustment of cross sections (or response functions of e.g. Bonner balls) by measurements in well-known neutron spectra. 2 - Method of solution: Bayesian theorem on conditional probability applied to linearized relation between activities, dosimetry cross sections and flux. All probability distributions are supposed to be normal and this supposition leads to minimizing of the same functional as least squares method (STAY'SL). This task is solved by a covariance filter method which avoids any matrix inversion and is numerically robust and stable. 3 - Restrictions on the complexity of the problem: This version can use 45 energy groups and 5 detectors and occupies 310 kB of main memory. This restriction can be modified according to available memory. The covariance matrix of activities is supposed diagonal. A solution is produced for any set of input data but in the case of non-consistent data, when measured activities do not match the a priori flux, the solution is not very meaningful

Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander

2017-09-03

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

Updated Covariance Processing Capabilities in the AMPX Code System

International Nuclear Information System (INIS)

Wiarda, Dorothea; Dunn, Michael E.

2007-01-01

A concerted effort is in progress within the nuclear data community to provide new cross-section covariance data evaluations to support sensitivity/uncertainty analyses of fissionable systems. The objective of this work is to update processing capabilities of the AMPX library to process the latest Evaluated Nuclear Data File (ENDF)/B formats to generate covariance data libraries for radiation transport software such as SCALE. The module PUFF-IV was updated to allow processing of new ENDF covariance formats in the resolved resonance region. In the resolved resonance region, covariance matrices are given in terms of resonance parameters, which need to be processed into covariance matrices with respect to the group-averaged cross-section data. The parameter covariance matrix can be quite large if the evaluation has many resonances. The PUFF-IV code has recently been used to process an evaluation of 235U, which was prepared in collaboration between Oak Ridge National Laboratory and Los Alamos National Laboratory.

Multilevel maximum likelihood estimation with application to covariance matrices

Czech Academy of Sciences Publication Activity Database

Turčičová, Marie; Mandel, J.; Eben, Kryštof

Published online: 23 January ( 2018 ) ISSN 0361-0926 R&D Projects: GA ČR GA13-34856S Institutional support: RVO:67985807 Keywords : Fisher information * High dimension * Hierarchical maximum likelihood * Nested parameter spaces * Spectral diagonal covariance model * Sparse inverse covariance model Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.311, year: 2016

Recent Advances with the AMPX Covariance Processing Capabilities in PUFF-IV

International Nuclear Information System (INIS)

Wiarda, Dorothea; Arbanas, Goran; Leal, Luiz C.; Dunn, Michael E.

2008-01-01

The program PUFF-IV is used to process resonance parameter covariance information given in ENDF/B File 32 and point-wise covariance matrices given in ENDF/B File 33 into group-averaged covariances matrices on a user-supplied group structure. For large resonance covariance matrices, found for example in 235U, the execution time of PUFF-IV can be quite long. Recently the code was modified to take advandage of Basic Linear Algebra Subprograms (BLAS) routines for the most time-consuming matrix multiplications. This led to a substantial decrease in execution time. This faster processing capability allowed us to investigate the conversion of File 32 data into File 33 data using a larger number of user-defined groups. While conversion substantially reduces the ENDF/B file size requirements for evaluations with a large number of resonances, a trade-off is made between the number of groups used to represent the resonance parameter covariance as a point-wise covariance matrix and the file size. We are also investigating a hybrid version of the conversion, in which the low-energy part of the File 32 resonance parameter covariances matrix is retained and the correlations with higher energies as well as the high energy part are given in File 33.

Covariance NMR Processing and Analysis for Protein Assignment.

Science.gov (United States)

Harden, Bradley J; Frueh, Dominique P

2018-01-01

During NMR resonance assignment it is often necessary to relate nuclei to one another indirectly, through their common correlations to other nuclei. Covariance NMR has emerged as a powerful technique to correlate such nuclei without relying on error-prone peak peaking. However, false-positive artifacts in covariance spectra have impeded a general application to proteins. We recently introduced pre- and postprocessing steps to reduce the prevalence of artifacts in covariance spectra, allowing for the calculation of a variety of 4D covariance maps obtained from diverse combinations of pairs of 3D spectra, and we have employed them to assign backbone and sidechain resonances in two large and challenging proteins. In this chapter, we present a detailed protocol describing how to (1) properly prepare existing 3D spectra for covariance, (2) understand and apply our processing script, and (3) navigate and interpret the resulting 4D spectra. We also provide solutions to a number of errors that may occur when using our script, and we offer practical advice when assigning difficult signals. We believe such 4D spectra, and covariance NMR in general, can play an integral role in the assignment of NMR signals.

An Analysis of Conditional Dependencies of Covariance Matrices for Economic Processes in Selected EU Countries

Directory of Open Access Journals (Sweden)

Janiga-Ćmiel Anna

2016-12-01

Full Text Available The paper looks at the issues related to the research on and assessment of the contagion effect. Based on several examinations of two selected EU countries, Poland paired with one of the EU member states; it presents the interaction between their economic development. A DCC-GARCH model constructed for the purpose of the study was used to generate a covariance matrix Ht, which enabled the calculation of correlation matrices Rt. The resulting variance vectors were used to present a linear correlation model on which a further analysis of the contagion effect was based. The aim of the study was to test a contagion effect among selected EU countries in the years 2000–2014. The transmission channel under study was the GDP of a selected country. The empirical studies confirmed the existence of the contagion effect between the economic development of the Polish and selected EU economies.

More on Estimation of Banded and Banded Toeplitz Covariance Matrices

OpenAIRE

Berntsson, Fredrik; Ohlson, Martin

2017-01-01

In this paper we consider two different linear covariance structures, e.g., banded and bended Toeplitz, and how to estimate them using different methods, e.g., by minimizing different norms. One way to estimate the parameters in a linear covariance structure is to use tapering, which has been shown to be the solution to a universal least squares problem. We know that tapering not always guarantee the positive definite constraints on the estimated covariance matrix and may not be a suitable me...

Undesirable effects of covariance matrix techniques for error analysis

International Nuclear Information System (INIS)

Seibert, D.

1994-01-01

Regression with χ 2 constructed from covariance matrices should not be used for some combinations of covariance matrices and fitting functions. Using the technique for unsuitable combinations can amplify systematic errors. This amplification is uncontrolled, and can produce arbitrarily inaccurate results that might not be ruled out by a χ 2 test. In addition, this technique can give incorrect (artificially small) errors for fit parameters. I give a test for this instability and a more robust (but computationally more intensive) method for fitting correlated data

Consultants' meeting on prompt fission neutron spectra of major actinides. Summary report

International Nuclear Information System (INIS)

Capote Noy, R.; Maslov, V.; Bauge, E.; Ohsawa, T.; Vorobyev, A.; Chadwick, M.B.; Oberstedt, S.

2009-01-01

A Consultants' Meeting on 'Prompt Fission Neutron Spectra of Major Actinides' was held at IAEA Headquarters, Vienna, Austria, to discuss the adequacy and quality of the recommended prompt fission neutron spectra to be found in existing nuclear data applications libraries. These prompt fission neutron spectra were judged to be inadequate, and this problem has proved difficult to resolve by means of theoretical modelling. Major adjustments may be required to ensure the validity of such important data. There is a strong requirement for an international effort to explore and resolve these difficulties and recommend prompt fission neutron spectra and uncertainty covariance matrices for the actinides over the neutron energy range from thermal to 20 MeV. Participants also stressed that there would be a strong need for validation of the resulting data against integral critical assembly and dosimetry data. (author)

A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance.

Science.gov (United States)

Zheng, Binqi; Fu, Pengcheng; Li, Baoqing; Yuan, Xiaobing

2018-03-07

The Unscented Kalman filter (UKF) may suffer from performance degradation and even divergence while mismatch between the noise distribution assumed as a priori by users and the actual ones in a real nonlinear system. To resolve this problem, this paper proposes a robust adaptive UKF (RAUKF) to improve the accuracy and robustness of state estimation with uncertain noise covariance. More specifically, at each timestep, a standard UKF will be implemented first to obtain the state estimations using the new acquired measurement data. Then an online fault-detection mechanism is adopted to judge if it is necessary to update current noise covariance. If necessary, innovation-based method and residual-based method are used to calculate the estimations of current noise covariance of process and measurement, respectively. By utilizing a weighting factor, the filter will combine the last noise covariance matrices with the estimations as the new noise covariance matrices. Finally, the state estimations will be corrected according to the new noise covariance matrices and previous state estimations. Compared with the standard UKF and other adaptive UKF algorithms, RAUKF converges faster to the actual noise covariance and thus achieves a better performance in terms of robustness, accuracy, and computation for nonlinear estimation with uncertain noise covariance, which is demonstrated by the simulation results.

Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

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

2017-01-01

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

Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander

2017-11-01

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

Non-evaluation applications for covariance matrices

Energy Technology Data Exchange (ETDEWEB)

Smith, D.L.

1982-05-01

The possibility for application of covariance matrix techniques to a variety of common research problems other than formal data evaluation are demonstrated by means of several examples. These examples deal with such matters as fitting spectral data, deriving uncertainty estimates for results calculated from experimental data, obtaining the best values for plurally-measured quantities, and methods for analysis of cross section errors based on properties of the experiment. The examples deal with realistic situations encountered in the laboratory, and they are treated in sufficient detail to enable a careful reader to extrapolate the methods to related problems.

Parametric number covariance in quantum chaotic spectra.

Science.gov (United States)

Vinayak; Kumar, Sandeep; Pandey, Akhilesh

2016-03-01

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

Thermally and vibrationally induced conformational isomerizations, infrared spectra, and photochemistry of gallic acid in low-temperature matrices

Energy Technology Data Exchange (ETDEWEB)

Justino, Licínia L. G., E-mail: liciniaj@ci.uc.pt; Reva, Igor; Fausto, Rui [CQC, Department of Chemistry, University of Coimbra, 3004-535 Coimbra (Portugal)

2016-07-07

Near-infrared (near-IR) narrowband selective vibrational excitation and annealing of gallic acid (3,4,5-trihydroxybenzoic acid) isolated in cryogenic matrices were used to induce interconversions between its most stable conformers. The isomerizations were probed by infrared spectroscopy. An extensive set of quantum chemical calculations, carried out at the DFT(B3LYP)/6-311++G(d,p) level of approximation, was used to undertake a detailed analysis of the ground state potential energy surface of the molecule. This investigation of the molecule conformational space allowed extracting mechanistic insights into the observed annealing- or near-IR-induced isomerization processes. The infrared spectra of the two most stable conformers of gallic acid in N{sub 2}, Xe, and Ar matrices were fully assigned. Finally, the UV-induced photochemistry of the matrix isolated compound was investigated.

Thermally and vibrationally induced conformational isomerizations, infrared spectra, and photochemistry of gallic acid in low-temperature matrices

Science.gov (United States)

Justino, Licínia L. G.; Reva, Igor; Fausto, Rui

2016-07-01

Near-infrared (near-IR) narrowband selective vibrational excitation and annealing of gallic acid (3,4,5-trihydroxybenzoic acid) isolated in cryogenic matrices were used to induce interconversions between its most stable conformers. The isomerizations were probed by infrared spectroscopy. An extensive set of quantum chemical calculations, carried out at the DFT(B3LYP)/6-311++G(d,p) level of approximation, was used to undertake a detailed analysis of the ground state potential energy surface of the molecule. This investigation of the molecule conformational space allowed extracting mechanistic insights into the observed annealing- or near-IR-induced isomerization processes. The infrared spectra of the two most stable conformers of gallic acid in N2, Xe, and Ar matrices were fully assigned. Finally, the UV-induced photochemistry of the matrix isolated compound was investigated.

Thermally and vibrationally induced conformational isomerizations, infrared spectra, and photochemistry of gallic acid in low-temperature matrices

International Nuclear Information System (INIS)

Justino, Licínia L. G.; Reva, Igor; Fausto, Rui

2016-01-01

Near-infrared (near-IR) narrowband selective vibrational excitation and annealing of gallic acid (3,4,5-trihydroxybenzoic acid) isolated in cryogenic matrices were used to induce interconversions between its most stable conformers. The isomerizations were probed by infrared spectroscopy. An extensive set of quantum chemical calculations, carried out at the DFT(B3LYP)/6-311++G(d,p) level of approximation, was used to undertake a detailed analysis of the ground state potential energy surface of the molecule. This investigation of the molecule conformational space allowed extracting mechanistic insights into the observed annealing- or near-IR-induced isomerization processes. The infrared spectra of the two most stable conformers of gallic acid in N 2 , Xe, and Ar matrices were fully assigned. Finally, the UV-induced photochemistry of the matrix isolated compound was investigated.

Skew-adjacency matrices of graphs

NARCIS (Netherlands)

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

2012-01-01

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

Relativistic covariant wave equations and acausality in external fields

International Nuclear Information System (INIS)

Pijlgroms, R.B.J.

1980-01-01

The author considers linear, finite dimensional, first order relativistic wave equations: (βsup(μ)ideltasub(μ)-β)PSI(x) = 0 with βsup(μ) and β constant matrices. Firstly , the question of the relativistic covariance conditions on these equations is considered. Then the theory of these equations with β non-singular is summarized. Theories with βsup(μ), β square matrices and β singular are also discussed. Non-square systems of covariant relativistic wave equations for arbitrary spin > 1 are then considered. Finally, the interaction with external fields and the acausality problem are discussed. (G.T.H.)

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

OpenAIRE

Sun, Jiehuan; Zhao, Hongyu

2015-01-01

Background Although Linear Discriminant Analysis (LDA) is commonly used for classification, it may not be directly applied in genomics studies due to the large p, small n problem in these studies. Different versions of sparse LDA have been proposed to address this significant challenge. One implicit assumption of various LDA-based methods is that the covariance matrices are the same across different classes. However, rewiring of genetic networks (therefore different covariance matrices) acros...

Application of Parallel Hierarchical Matrices in Spatial Statistics and Parameter Identification

KAUST Repository

Litvinenko, Alexander

2018-04-20

Parallel H-matrices in spatial statistics 1. Motivation: improve statistical model 2. Tools: Hierarchical matrices [Hackbusch 1999] 3. Matern covariance function and joint Gaussian likelihood 4. Identification of unknown parameters via maximizing Gaussian log-likelihood 5. Implementation with HLIBPro

Transformation of covariant quark Wigner operator to noncovariant one

International Nuclear Information System (INIS)

Selikhov, A.V.

1989-01-01

The gauge in which covariant and noncovariant quark Wigner operators coincide has been found. In this gauge the representations of vector potential via field strength tensor is valid. The system of equations for the coefficients of covariant Wigner operator expansion in the basis γ-matrices algebra is obtained. 12 refs.; 3 figs

Criteria of the validation of experimental and evaluated covariance data

International Nuclear Information System (INIS)

Badikov, S.

2008-01-01

The criteria of the validation of experimental and evaluated covariance data are reviewed. In particular: a) the criterion of the positive definiteness for covariance matrices, b) the relationship between the 'integral' experimental and estimated uncertainties, c) the validity of the statistical invariants, d) the restrictions imposed to correlations between experimental errors, are described. Applying these criteria in nuclear data evaluation was considered and 4 particular points have been examined. First preserving positive definiteness of covariance matrices in case of arbitrary transformation of a random vector was considered, properties of the covariance matrices in operations widely used in neutron and reactor physics (splitting and collapsing energy groups, averaging the physical values over energy groups, estimation parameters on the basis of measurements by means of generalized least squares method) were studied. Secondly, an algorithm for comparison of experimental and estimated 'integral' uncertainties was developed, square root of determinant of a covariance matrix is recommended for use in nuclear data evaluation as a measure of 'integral' uncertainty for vectors of experimental and estimated values. Thirdly, a set of statistical invariants-values which are preserved in statistical processing was presented. And fourthly, the inequality that signals a correlation between experimental errors that leads to unphysical values is given. An application is given concerning the cross-section of the (n,t) reaction on Li 6 with a neutron incident energy comprised between 1 and 100 keV

Progress on Nuclear Data Covariances: AFCI-1.2 Covariance Library

International Nuclear Information System (INIS)

Oblozinsky, P.; Oblozinsky, P.; Mattoon, C.M.; Herman, M.; Mughabghab, S.F.; Pigni, M.T.; Talou, P.; Hale, G.M.; Kahler, A.C.; Kawano, T.; Little, R.C.; Young, P.G

2009-01-01

Improved neutron cross section covariances were produced for 110 materials including 12 light nuclei (coolants and moderators), 78 structural materials and fission products, and 20 actinides. Improved covariances were organized into AFCI-1.2 covariance library in 33-energy groups, from 10 -5 eV to 19.6 MeV. BNL contributed improved covariance data for the following materials: 23 Na and 55 Mn where more detailed evaluation was done; improvements in major structural materials 52 Cr, 56 Fe and 58 Ni; improved estimates for remaining structural materials and fission products; improved covariances for 14 minor actinides, and estimates of mubar covariances for 23 Na and 56 Fe. LANL contributed improved covariance data for 235 U and 239 Pu including prompt neutron fission spectra and completely new evaluation for 240 Pu. New R-matrix evaluation for 16 O including mubar covariances is under completion. BNL assembled the library and performed basic testing using improved procedures including inspection of uncertainty and correlation plots for each material. The AFCI-1.2 library was released to ANL and INL in August 2009.

Uncertainty covariances in robotics applications

International Nuclear Information System (INIS)

Smith, D.L.

1984-01-01

The application of uncertainty covariance matrices in the analysis of robot trajectory errors is explored. First, relevant statistical concepts are reviewed briefly. Then, a simple, hypothetical robot model is considered to illustrate methods for error propagation and performance test data evaluation. The importance of including error correlations is emphasized

Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes

International Nuclear Information System (INIS)

Bachoc, Francois

2014-01-01

Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar regularity parameter. Consistency and asymptotic normality are proved for the Maximum Likelihood and Cross Validation estimators of the covariance parameters. The asymptotic covariance matrices of the covariance parameter estimators are deterministic functions of the regularity parameter. By means of an exhaustive study of the asymptotic covariance matrices, it is shown that the estimation is improved when the regular grid is strongly perturbed. Hence, an asymptotic confirmation is given to the commonly admitted fact that using groups of observation points with small spacing is beneficial to covariance function estimation. Finally, the prediction error, using a consistent estimator of the covariance parameters, is analyzed in detail. (authors)

Impact of the 235U Covariance Data in Benchmark Calculations

International Nuclear Information System (INIS)

Leal, Luiz C.; Mueller, D.; Arbanas, G.; Wiarda, D.; Derrien, H.

2008-01-01

The error estimation for calculated quantities relies on nuclear data uncertainty information available in the basic nuclear data libraries such as the U.S. Evaluated Nuclear Data File (ENDF/B). The uncertainty files (covariance matrices) in the ENDF/B library are generally obtained from analysis of experimental data. In the resonance region, the computer code SAMMY is used for analyses of experimental data and generation of resonance parameters. In addition to resonance parameters evaluation, SAMMY also generates resonance parameter covariance matrices (RPCM). SAMMY uses the generalized least-squares formalism (Bayes method) together with the resonance formalism (R-matrix theory) for analysis of experimental data. Two approaches are available for creation of resonance-parameter covariance data. (1) During the data-evaluation process, SAMMY generates both a set of resonance parameters that fit the experimental data and the associated resonance-parameter covariance matrix. (2) For existing resonance-parameter evaluations for which no resonance-parameter covariance data are available, SAMMY can retroactively create a resonance-parameter covariance matrix. The retroactive method was used to generate covariance data for 235U. The resulting 235U covariance matrix was then used as input to the PUFF-IV code, which processed the covariance data into multigroup form, and to the TSUNAMI code, which calculated the uncertainty in the multiplication factor due to uncertainty in the experimental cross sections. The objective of this work is to demonstrate the use of the 235U covariance data in calculations of critical benchmark systems

Impact of the 235U covariance data in benchmark calculations

International Nuclear Information System (INIS)

Leal, Luiz; Mueller, Don; Arbanas, Goran; Wiarda, Dorothea; Derrien, Herve

2008-01-01

The error estimation for calculated quantities relies on nuclear data uncertainty information available in the basic nuclear data libraries such as the U.S. Evaluated Nuclear Data File (ENDF/B). The uncertainty files (covariance matrices) in the ENDF/B library are generally obtained from analysis of experimental data. In the resonance region, the computer code SAMMY is used for analyses of experimental data and generation of resonance parameters. In addition to resonance parameters evaluation, SAMMY also generates resonance parameter covariance matrices (RPCM). SAMMY uses the generalized least-squares formalism (Bayes' method) together with the resonance formalism (R-matrix theory) for analysis of experimental data. Two approaches are available for creation of resonance-parameter covariance data. (1) During the data-evaluation process, SAMMY generates both a set of resonance parameters that fit the experimental data and the associated resonance-parameter covariance matrix. (2) For existing resonance-parameter evaluations for which no resonance-parameter covariance data are available, SAMMY can retroactively create a resonance-parameter covariance matrix. The retroactive method was used to generate covariance data for 235 U. The resulting 235 U covariance matrix was then used as input to the PUFF-IV code, which processed the covariance data into multigroup form, and to the TSUNAMI code, which calculated the uncertainty in the multiplication factor due to uncertainty in the experimental cross sections. The objective of this work is to demonstrate the use of the 235 U covariance data in calculations of critical benchmark systems. (authors)

Nuclear data and measurements series: Some comments on the effects of long-range correlations in covariance matrices for nuclear data

International Nuclear Information System (INIS)

Smith, D.L.

1987-03-01

Attention is called to the considerable sensitivity of many uncertainty calculations to the magnitude of the long-ranged correlations which appear in covariance matrices. If such correlations do exist, they must be included in order to properly assess the impact of the uncertainties in the data. If, however, certain assumed long-range correlations are unrealistic, then analyses involving such correlation information are almost certain to produce misleading results. The issue is discussed in general terms, and its importance is illustrated by examples based in part on recent work from this laboratory. Some practical suggestions are offered for dealing with the matter of correlations in instances where the available information is incomplete. 23 refs., 2 figs., 1 tab

ERRORJ. Covariance processing code. Version 2.2

International Nuclear Information System (INIS)

Chiba, Go

2004-07-01

ERRORJ is the covariance processing code that can produce covariance data of multi-group cross sections, which are essential for uncertainty analyses of nuclear parameters, such as neutron multiplication factor. The ERRORJ code can process the covariance data of cross sections including resonance parameters, angular and energy distributions of secondary neutrons. Those covariance data cannot be processed by the other covariance processing codes. ERRORJ has been modified and the version 2.2 has been developed. This document describes the modifications and how to use. The main topics of the modifications are as follows. Non-diagonal elements of covariance matrices are calculated in the resonance energy region. Option for high-speed calculation is implemented. Perturbation amount is optimized in a sensitivity calculation. Effect of the resonance self-shielding on covariance of multi-group cross section can be considered. It is possible to read a compact covariance format proposed by N.M. Larson. (author)

Multivariate covariance generalized linear models

DEFF Research Database (Denmark)

Bonat, W. H.; Jørgensen, Bent

2016-01-01

are fitted by using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of types of response variables and covariance structures, including multivariate extensions......We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link...... function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated...

Extensive set of low-fidelity cross sections covariances in fast neutron region

International Nuclear Information System (INIS)

Pigni, M.T.; Herman, M.; Oblozinsky, P.

2008-01-01

We produced a large set of neutron cross section covariances in the energy range of 5 keV - 20 MeV. The covariance matrices were calculated for 307 isotopes divided into three major regions: structural materials, fission products, and heavy nuclei. These results have been developed to provide initial, but consistent estimates of covariance data for nuclear criticality safety applications. The methodology for the determination of such covariance matrices is presented. It combines the nuclear reaction model code EMPIRE which calculates sensitivity of cross sections to nuclear reaction model parameters, and the Bayesian code KALMAN that propagates uncertainties of the model parameters to cross sections. Taking into account large number of materials, only marginal reference to experimental data was made. The covariances were derived from the perturbation of several key model parameters selected by the sensitivity analysis. These parameters refer to the optical model potential, the level densities and the strength of the pre-equilibrium emission. This work represents the first try ever to generate nuclear data covariances on such a large scale. (authors)

ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters

KAUST Repository

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

KAUST Repository

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)

New perspective in covariance evaluation for nuclear data

International Nuclear Information System (INIS)

Kanda, Y.

1992-01-01

Methods of nuclear data evaluation have been highly developed during the past decade, especially after introducing the concept of covariance. This makes it utmost important how to evaluate covariance matrices for nuclear data. It can be said that covariance evaluation is just the nuclear data evaluation, because the covariance matrix has quantitatively decisive function in current evaluation methods. The covariance primarily represents experimental uncertainties. However, correlation of individual uncertainties between different data must be taken into account and it can not be conducted without detailed physical considerations on experimental conditions. This procedure depends on the evaluator and the estimated covariance does also. The mathematical properties of the covariance have been intensively discussed. Their physical properties should be studied to apply it to the nuclear data evaluation, and then, in this report, are reviewed to give the base for further development of the covariance application. (orig.)

EQUIVALENT MODELS IN COVARIANCE STRUCTURE-ANALYSIS

NARCIS (Netherlands)

LUIJBEN, TCW

1991-01-01

Defining equivalent models as those that reproduce the same set of covariance matrices, necessary and sufficient conditions are stated for the local equivalence of two expanded identified models M1 and M2 when fitting the more restricted model M0. Assuming several regularity conditions, the rank

Exploiting Data Sparsity In Covariance Matrix Computations on Heterogeneous Systems

KAUST Repository

Charara, Ali M.

2018-05-24

Covariance matrices are ubiquitous in computational sciences, typically describing the correlation of elements of large multivariate spatial data sets. For example, covari- ance matrices are employed in climate/weather modeling for the maximum likelihood estimation to improve prediction, as well as in computational ground-based astronomy to enhance the observed image quality by filtering out noise produced by the adap- tive optics instruments and atmospheric turbulence. The structure of these covariance matrices is dense, symmetric, positive-definite, and often data-sparse, therefore, hier- archically of low-rank. This thesis investigates the performance limit of dense matrix computations (e.g., Cholesky factorization) on covariance matrix problems as the number of unknowns grows, and in the context of the aforementioned applications. We employ recursive formulations of some of the basic linear algebra subroutines (BLAS) to accelerate the covariance matrix computation further, while reducing data traffic across the memory subsystems layers. However, dealing with large data sets (i.e., covariance matrices of billions in size) can rapidly become prohibitive in memory footprint and algorithmic complexity. Most importantly, this thesis investigates the tile low-rank data format (TLR), a new compressed data structure and layout, which is valuable in exploiting data sparsity by approximating the operator. The TLR com- pressed data structure allows approximating the original problem up to user-defined numerical accuracy. This comes at the expense of dealing with tasks with much lower arithmetic intensities than traditional dense computations. In fact, this thesis con- solidates the two trends of dense and data-sparse linear algebra for HPC. Not only does the thesis leverage recursive formulations for dense Cholesky-based matrix al- gorithms, but it also implements a novel TLR-Cholesky factorization using batched linear algebra operations to increase hardware occupancy and

Quality Quantification of Evaluated Cross Section Covariances

International Nuclear Information System (INIS)

Varet, S.; Dossantos-Uzarralde, P.; Vayatis, N.

2015-01-01

Presently, several methods are used to estimate the covariance matrix of evaluated nuclear cross sections. Because the resulting covariance matrices can be different according to the method used and according to the assumptions of the method, we propose a general and objective approach to quantify the quality of the covariance estimation for evaluated cross sections. The first step consists in defining an objective criterion. The second step is computation of the criterion. In this paper the Kullback-Leibler distance is proposed for the quality quantification of a covariance matrix estimation and its inverse. It is based on the distance to the true covariance matrix. A method based on the bootstrap is presented for the estimation of this criterion, which can be applied with most methods for covariance matrix estimation and without the knowledge of the true covariance matrix. The full approach is illustrated on the 85 Rb nucleus evaluations and the results are then used for a discussion on scoring and Monte Carlo approaches for covariance matrix estimation of the cross section evaluations

VITAMIN-J/COVA/EFF-3 cross-section covariance matrix library and its use to analyse benchmark experiments in sinbad database

International Nuclear Information System (INIS)

Kodeli, Ivan-Alexander

2005-01-01

The new cross-section covariance matrix library ZZ-VITAMIN-J/COVA/EFF3 intended to simplify and encourage sensitivity and uncertainty analysis was prepared and is available from the NEA Data Bank. The library is organised in a ready-to-use form including both the covariance matrix data as well as processing tools:-Cross-section covariance matrices from the EFF-3 evaluation for five materials: 9 Be, 28 Si, 56 Fe, 58 Ni and 60 Ni. Other data will be included when available. -FORTRAN program ANGELO-2 to extrapolate/interpolate the covariance matrices to a users' defined energy group structure. -FORTRAN program LAMBDA to verify the mathematical properties of the covariance matrices, like symmetry, positive definiteness, etc. The preparation, testing and use of the covariance matrix library are presented. The uncertainties based on the cross-section covariance data were compared with those based on other evaluations, like ENDF/B-VI. The collapsing procedure used in the ANGELO-2 code was compared and validated with the one used in the NJOY system

Dissecting high-dimensional phenotypes with bayesian sparse factor analysis of genetic covariance matrices.

Science.gov (United States)

Runcie, Daniel E; Mukherjee, Sayan

2013-07-01

Quantitative genetic studies that model complex, multivariate phenotypes are important for both evolutionary prediction and artificial selection. For example, changes in gene expression can provide insight into developmental and physiological mechanisms that link genotype and phenotype. However, classical analytical techniques are poorly suited to quantitative genetic studies of gene expression where the number of traits assayed per individual can reach many thousand. Here, we derive a Bayesian genetic sparse factor model for estimating the genetic covariance matrix (G-matrix) of high-dimensional traits, such as gene expression, in a mixed-effects model. The key idea of our model is that we need consider only G-matrices that are biologically plausible. An organism's entire phenotype is the result of processes that are modular and have limited complexity. This implies that the G-matrix will be highly structured. In particular, we assume that a limited number of intermediate traits (or factors, e.g., variations in development or physiology) control the variation in the high-dimensional phenotype, and that each of these intermediate traits is sparse - affecting only a few observed traits. The advantages of this approach are twofold. First, sparse factors are interpretable and provide biological insight into mechanisms underlying the genetic architecture. Second, enforcing sparsity helps prevent sampling errors from swamping out the true signal in high-dimensional data. We demonstrate the advantages of our model on simulated data and in an analysis of a published Drosophila melanogaster gene expression data set.

How (not) to teach Lorentz covariance of the Dirac equation

International Nuclear Information System (INIS)

Nikolić, Hrvoje

2014-01-01

In the textbook proofs of the Lorentz covariance of the Dirac equation, one treats the wave function as a spinor and gamma matrices as scalars, leading to a quite complicated formalism with several pedagogic drawbacks. As an alternative, I propose to teach the Dirac equation and its Lorentz covariance by using a much simpler, but physically equivalent formalism, in which these drawbacks do not appear. In this alternative formalism, the wave function transforms as a scalar and gamma matrices as components of a vector, such that the standard physically relevant bilinear combinations do not change their transformation properties. The alternative formalism allows also a natural construction of some additional non-standard bilinear combinations with well-defined transformation properties. (paper)

Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold

Directory of Open Access Journals (Sweden)

Xiaoqiang Hua

2018-03-01

Full Text Available This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives.

Inference for High-dimensional Differential Correlation Matrices.

Science.gov (United States)

Cai, T Tony; Zhang, Anru

2016-01-01

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed.

High-Dimensional Multivariate Repeated Measures Analysis with Unequal Covariance Matrices

Science.gov (United States)

Harrar, Solomon W.; Kong, Xiaoli

2015-01-01

In this paper, test statistics for repeated measures design are introduced when the dimension is large. By large dimension is meant the number of repeated measures and the total sample size grow together but either one could be larger than the other. Asymptotic distribution of the statistics are derived for the equal as well as unequal covariance cases in the balanced as well as unbalanced cases. The asymptotic framework considered requires proportional growth of the sample sizes and the dimension of the repeated measures in the unequal covariance case. In the equal covariance case, one can grow at much faster rate than the other. The derivations of the asymptotic distributions mimic that of Central Limit Theorem with some important peculiarities addressed with sufficient rigor. Consistent and unbiased estimators of the asymptotic variances, which make efficient use of all the observations, are also derived. Simulation study provides favorable evidence for the accuracy of the asymptotic approximation under the null hypothesis. Power simulations have shown that the new methods have comparable power with a popular method known to work well in low-dimensional situation but the new methods have shown enormous advantage when the dimension is large. Data from Electroencephalograph (EEG) experiment is analyzed to illustrate the application of the results. PMID:26778861

TRANSPOSABLE REGULARIZED COVARIANCE MODELS WITH AN APPLICATION TO MISSING DATA IMPUTATION.

Science.gov (United States)

Allen, Genevera I; Tibshirani, Robert

2010-06-01

Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable , meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal , in which the rows and columns each have a separate mean vector and covariance matrix. By placing additive penalties on the inverse covariance matrices of the rows and columns, these so called transposable regularized covariance models allow for maximum likelihood estimation of the mean and non-singular covariance matrices. Using these models, we formulate EM-type algorithms for missing data imputation in both the multivariate and transposable frameworks. We present theoretical results exploiting the structure of our transposable models that allow these models and imputation methods to be applied to high-dimensional data. Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility.

Covariance structure in the skull of Catarrhini: a case of pattern stasis and magnitude evolution.

Science.gov (United States)

de Oliveira, Felipe Bandoni; Porto, Arthur; Marroig, Gabriel

2009-04-01

The study of the genetic variance/covariance matrix (G-matrix) is a recent and fruitful approach in evolutionary biology, providing a window of investigating for the evolution of complex characters. Although G-matrix studies were originally conducted for microevolutionary timescales, they could be extrapolated to macroevolution as long as the G-matrix remains relatively constant, or proportional, along the period of interest. A promising approach to investigating the constancy of G-matrices is to compare their phenotypic counterparts (P-matrices) in a large group of related species; if significant similarity is found among several taxa, it is very likely that the underlying G-matrices are also equivalent. Here we study the similarity of covariance and correlation structure in a broad sample of Old World monkeys and apes (Catarrhini). We made phylogenetically structured comparisons of correlation and covariance matrices derived from 39 skull traits, ranging from between species to the superfamily level. We also compared the overall magnitude of integration between skull traits (r2) for all Catarrhini genera. Our results show that P-matrices were not strictly constant among catarrhines, but the amount of divergence observed among taxa was generally low. There was significant and positive correlation between the amount of divergence in correlation and covariance patterns among the 30 genera and their phylogenetic distances derived from a recently proposed phylogenetic hypothesis. Our data demonstrate that the P-matrices remained relatively similar along the evolutionary history of catarrhines, and comparisons with the G-matrix available for a New World monkey genus (Saguinus) suggests that the same holds for all anthropoids. The magnitude of integration, in contrast, varied considerably among genera, indicating that evolution of the magnitude, rather than the pattern of inter-trait correlations, might have played an important role in the diversification of the

On Investigating GMRES Convergence using Unitary Matrices

Czech Academy of Sciences Publication Activity Database

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

2014-01-01

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

A covariance correction that accounts for correlation estimation to improve finite-sample inference with generalized estimating equations: A study on its applicability with structured correlation matrices.

Science.gov (United States)

Westgate, Philip M

2016-01-01

When generalized estimating equations (GEE) incorporate an unstructured working correlation matrix, the variances of regression parameter estimates can inflate due to the estimation of the correlation parameters. In previous work, an approximation for this inflation that results in a corrected version of the sandwich formula for the covariance matrix of regression parameter estimates was derived. Use of this correction for correlation structure selection also reduces the over-selection of the unstructured working correlation matrix. In this manuscript, we conduct a simulation study to demonstrate that an increase in variances of regression parameter estimates can occur when GEE incorporates structured working correlation matrices as well. Correspondingly, we show the ability of the corrected version of the sandwich formula to improve the validity of inference and correlation structure selection. We also study the relative influences of two popular corrections to a different source of bias in the empirical sandwich covariance estimator.

Capture Matrices Handbook

Science.gov (United States)

2014-04-01

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

The utility of covariance of combining ability in plant breeding.

Science.gov (United States)

Arunachalam, V

1976-11-01

The definition of covariances of half- and full sibs, and hence that of variances of general and specific combining ability with regard to a quantitative character, is extended to take into account the respective covariances between a pair of characters. The interpretation of the dispersion and correlation matrices of general and specific combining ability is discussed by considering a set of single, three- and four-way crosses, made using diallel and line × tester mating systems in Pennisetum typhoides. The general implications of the concept of covariance of combining ability in plant breeding are discussed.

Chemiluminescence in cryogenic matrices

Science.gov (United States)

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

1989-04-01

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

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

International Nuclear Information System (INIS)

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

2015-01-01

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

The Production of Polycyclic Aromatic Hydrocarbon Anions in Inert Gas Matrices Doped with Alkali Metals. Electronic Absorption Spectra of the Pentacene Anion (C22H14(-))

Science.gov (United States)

Halasinski, Thomas M.; Hudgins, Douglas M.; Salama, Farid; Allamandola, Louis J.; Mead, Susan (Technical Monitor)

1999-01-01

The absorption spectra of pentacene (C22H14) and its radical cation (C22H14(+)) and anion (C22H14(-)) isolated in inert-gas matrices of Ne, Ar, and Kr are reported from the ultraviolet to the near-infrared. The associated vibronic band systems and their spectroscopic assignments are discussed together with the physical and chemical conditions governing ion (and counterion) production in the solid matrix. In particular, the formation of isolated pentacene anions is found to be optimized in matrices doped with alkali metal (Na and K).

A special form of SPD covariance matrix for interpretation and visualization of data manipulated with Riemannian geometry

Science.gov (United States)

Congedo, Marco; Barachant, Alexandre

2015-01-01

Currently the Riemannian geometry of symmetric positive definite (SPD) matrices is gaining momentum as a powerful tool in a wide range of engineering applications such as image, radar and biomedical data signal processing. If the data is not natively represented in the form of SPD matrices, typically we may summarize them in such form by estimating covariance matrices of the data. However once we manipulate such covariance matrices on the Riemannian manifold we lose the representation in the original data space. For instance, we can evaluate the geometric mean of a set of covariance matrices, but not the geometric mean of the data generating the covariance matrices, the space of interest in which the geometric mean can be interpreted. As a consequence, Riemannian information geometry is often perceived by non-experts as a "black-box" tool and this perception prevents a wider adoption in the scientific community. Hereby we show that we can overcome this limitation by constructing a special form of SPD matrix embedding both the covariance structure of the data and the data itself. Incidentally, whenever the original data can be represented in the form of a generic data matrix (not even square), this special SPD matrix enables an exhaustive and unique description of the data up to second-order statistics. This is achieved embedding the covariance structure of both the rows and columns of the data matrix, allowing naturally a wide range of possible applications and bringing us over and above just an interpretability issue. We demonstrate the method by manipulating satellite images (pansharpening) and event-related potentials (ERPs) of an electroencephalography brain-computer interface (BCI) study. The first example illustrates the effect of moving along geodesics in the original data space and the second provides a novel estimation of ERP average (geometric mean), showing that, in contrast to the usual arithmetic mean, this estimation is robust to outliers. In

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.

Science.gov (United States)

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.

Covariant differential calculus on quantum Minkowski space and the q-analogue of Dirac equation

International Nuclear Information System (INIS)

Song Xingchang; Academia Sinica, Beijing

1992-01-01

The covariant differential calculus on the quantum Minkowski space is presented with the help of the generalized Wess-Zumino method and the quantum Pauli matrices and quantum Dirac matrices are constructed parallel to those in the classical case. Combining these two aspects a q-analogue of Dirac equation follows directly. (orig.)

(13)C-(15)N correlation via unsymmetrical indirect covariance NMR: application to vinblastine.

Science.gov (United States)

Martin, Gary E; Hilton, Bruce D; Blinov, Kirill A; Williams, Antony J

2007-12-01

Unsymmetrical indirect covariance processing methods allow the derivation of hyphenated 2D NMR data from the component 2D spectra, potentially circumventing the acquisition of the much lower sensitivity hyphenated 2D NMR experimental data. Calculation of HSQC-COSY and HSQC-NOESY spectra from GHSQC, COSY, and NOESY spectra, respectively, has been reported. The use of unsymmetrical indirect covariance processing has also been applied to the combination of (1)H- (13)C GHSQC and (1)H- (15)N long-range correlation data (GHMBC, IMPEACH, or CIGAR-HMBC). The application of unsymmetrical indirect covariance processing to spectra of vinblastine is now reported, specifically the algorithmic extraction of (13)C- (15)N correlations via the unsymmetrical indirect covariance processing of the combination of (1)H- (13)C GHSQC and long-range (1)H- (15)N GHMBC to produce the equivalent of a (13)C- (15)N HSQC-HMBC correlation spectrum. The elimination of artifact responses with aromatic solvent-induced shifts (ASIS) is shown in addition to a method of forecasting potential artifact responses through the indirect covariance processing of the GHSQC spectrum used in the unsymmetrical indirect covariance processing.

Paragrassmann analysis and covariant quantum algebras

International Nuclear Information System (INIS)

Filippov, A.T.; Isaev, A.P.; Kurdikov, A.B.; Pyatov, P.N.

1993-01-01

This report is devoted to the consideration from the algebraic point of view the paragrassmann algebras with one and many paragrassmann generators Θ i , Θ p+1 i = 0. We construct the paragrassmann versions of the Heisenberg algebra. For the special case, this algebra is nothing but the algebra for coordinates and derivatives considered in the context of covariant differential calculus on quantum hyperplane. The parameter of deformation q in our case is (p+1)-root of unity. Our construction is nondegenerate only for even p. Taking bilinear combinations of paragrassmann derivatives and coordinates we realize generators for the covariant quantum algebras as tensor products of (p+1) x (p+1) matrices. (orig./HSI)

Application of Parallel Hierarchical Matrices and Low-Rank Tensors in Spatial Statistics and Parameter Identification

KAUST Repository

Litvinenko, Alexander

2018-03-12

Part 1: Parallel H-matrices in spatial statistics 1. Motivation: improve statistical model 2. Tools: Hierarchical matrices 3. Matern covariance function and joint Gaussian likelihood 4. Identification of unknown parameters via maximizing Gaussian log-likelihood 5. Implementation with HLIBPro. Part 2: Low-rank Tucker tensor methods in spatial statistics

A Concise Method for Storing and Communicating the Data Covariance Matrix

Energy Technology Data Exchange (ETDEWEB)

Larson, Nancy M [ORNL

2008-10-01

The covariance matrix associated with experimental cross section or transmission data consists of several components. Statistical uncertainties on the measured quantity (counts) provide a diagonal contribution. Off-diagonal components arise from uncertainties on the parameters (such as normalization or background) that figure into the data reduction process; these are denoted systematic or common uncertainties, since they affect all data points. The full off-diagonal data covariance matrix (DCM) can be extremely large, since the size is the square of the number of data points. Fortunately, it is not necessary to explicitly calculate, store, or invert the DCM. Likewise, it is not necessary to explicitly calculate, store, or use the inverse of the DCM. Instead, it is more efficient to accomplish the same results using only the various component matrices that appear in the definition of the DCM. Those component matrices are either diagonal or small (the number of data points times the number of data-reduction parameters); hence, this implicit data covariance method requires far less array storage and far fewer computations while producing more accurate results.

Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure

NARCIS (Netherlands)

Ros, B.P.; Bijma, F.; de Munck, J.C.; de Gunst, M.C.M.

2016-01-01

This paper deals with multivariate Gaussian models for which the covariance matrix is a Kronecker product of two matrices. We consider maximum likelihood estimation of the model parameters, in particular of the covariance matrix. There is no explicit expression for the maximum likelihood estimator

The error and covariance structures of the mean approach model of pooled cross-section and time series data

International Nuclear Information System (INIS)

Nuamah, N.N.N.N.

1991-01-01

This paper postulates the assumptions underlying the Mean Approach model and recasts the re-expressions of the normal equations of this model in partitioned matrices of covariances. These covariance structures have been analysed. (author). 16 refs

Fission yield covariance generation and uncertainty propagation through fission pulse decay heat calculation

International Nuclear Information System (INIS)

Fiorito, L.; Diez, C.J.; Cabellos, O.; Stankovskiy, A.; Van den Eynde, G.; Labeau, P.E.

2014-01-01

Highlights: • Fission yield data and uncertainty comparison between major nuclear data libraries. • Fission yield covariance generation through Bayesian technique. • Study of the effect of fission yield correlations on decay heat calculations. • Covariance information contribute to reduce fission pulse decay heat uncertainty. - Abstract: Fission product yields are fundamental parameters in burnup/activation calculations and the impact of their uncertainties was widely studied in the past. Evaluations of these uncertainties were released, still without covariance data. Therefore, the nuclear community expressed the need of full fission yield covariance matrices to be able to produce inventory calculation results that take into account the complete uncertainty data. State-of-the-art fission yield data and methodologies for fission yield covariance generation were researched in this work. Covariance matrices were generated and compared to the original data stored in the library. Then, we focused on the effect of fission yield covariance information on fission pulse decay heat results for thermal fission of 235 U. Calculations were carried out using different libraries and codes (ACAB and ALEPH-2) after introducing the new covariance values. Results were compared with those obtained with the uncertainty data currently provided by the libraries. The uncertainty quantification was performed first with Monte Carlo sampling and then compared with linear perturbation. Indeed, correlations between fission yields strongly affect the uncertainty of decay heat. Eventually, a sensitivity analysis of fission product yields to fission pulse decay heat was performed in order to provide a full set of the most sensitive nuclides for such a calculation

The Misspecification of the Covariance Structures in Multilevel Models for Single-Case Data: A Monte Carlo Simulation Study

Science.gov (United States)

Moeyaert, Mariola; Ugille, Maaike; Ferron, John M.; Beretvas, S. Natasha; Van den Noortgate, Wim

2016-01-01

The impact of misspecifying covariance matrices at the second and third levels of the three-level model is evaluated. Results indicate that ignoring existing covariance has no effect on the treatment effect estimate. In addition, the between-case variance estimates are unbiased when covariance is either modeled or ignored. If the research interest…

Estimation of covariance matrix on the experimental data for nuclear data evaluation

International Nuclear Information System (INIS)

Murata, T.

1985-01-01

In order to evaluate fission and capture cross sections of some U and Pu isotopes for JENDL-3, we have a plan for evaluating them simultaneously with a least-squares method. For the simultaneous evaluation, the covariance matrix is required for each experimental data set. In the present work, we have studied the procedures for deriving the covariance matrix from the error data given in the experimental papers. The covariance matrices were obtained using the partial errors and estimated correlation coefficients between the same type partial errors for different neutron energy. Some examples of the covariance matrix estimation are explained and the preliminary results of the simultaneous evaluation are presented. (author)

An Empirical State Error Covariance Matrix Orbit Determination Example

Science.gov (United States)

Frisbee, Joseph H., Jr.

2015-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance

Convex Banding of the Covariance Matrix.

Science.gov (United States)

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Joint Estimation of Multiple Precision Matrices with Common Structures.

Science.gov (United States)

Lee, Wonyul; Liu, Yufeng

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

Condition Number Regularized Covariance Estimation.

Science.gov (United States)

Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala

2013-06-01

Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the "large p small n " setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required.

Homonuclear long-range correlation spectra from HMBC experiments by covariance processing.

Science.gov (United States)

Schoefberger, Wolfgang; Smrecki, Vilko; Vikić-Topić, Drazen; Müller, Norbert

2007-07-01

We present a new application of covariance nuclear magnetic resonance processing based on 1H--13C-HMBC experiments which provides an effective way for establishing indirect 1H--1H and 13C--13C nuclear spin connectivity at natural isotope abundance. The method, which identifies correlated spin networks in terms of covariance between one-dimensional traces from a single decoupled HMBC experiment, derives 13C--13C as well as 1H--1H spin connectivity maps from the two-dimensional frequency domain heteronuclear long-range correlation data matrix. The potential and limitations of this novel covariance NMR application are demonstrated on two compounds: eugenyl-beta-D-glucopyranoside and an emodin-derivative. Copyright (c) 2007 John Wiley & Sons, Ltd.

Photoluminescence of nanocrystals embedded in oxide matrices

International Nuclear Information System (INIS)

Estrada, C.; Gonzalez, J.A.; Kunold, A.; Reyes-Esqueda, J.A.; Pereyra, P.

2006-12-01

We used the theory of finite periodic systems to explain the photoluminescence spectra dependence on the average diameter of nanocrystals embedded in oxide matrices. Because of the broad matrix band gap, the photoluminescence response is basically determined by isolated nanocrystals and sequences of a few of them. With this model we were able to reproduce the shape and displacement of the experimentally observed photoluminescence spectra. (author)

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

KAUST Repository

Boukaram, W.

2015-03-25

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

A Geometrical Framework for Covariance Matrices of Continuous and Categorical Variables

Science.gov (United States)

Vernizzi, Graziano; Nakai, Miki

2015-01-01

It is well known that a categorical random variable can be represented geometrically by a simplex. Accordingly, several measures of association between categorical variables have been proposed and discussed in the literature. Moreover, the standard definitions of covariance and correlation coefficient for continuous random variables have been…

The Bayesian Covariance Lasso.

Science.gov (United States)

Khondker, Zakaria S; Zhu, Hongtu; Chu, Haitao; Lin, Weili; Ibrahim, Joseph G

2013-04-01

Estimation of sparse covariance matrices and their inverse subject to positive definiteness constraints has drawn a lot of attention in recent years. The abundance of high-dimensional data, where the sample size ( n ) is less than the dimension ( d ), requires shrinkage estimation methods since the maximum likelihood estimator is not positive definite in this case. Furthermore, when n is larger than d but not sufficiently larger, shrinkage estimation is more stable than maximum likelihood as it reduces the condition number of the precision matrix. Frequentist methods have utilized penalized likelihood methods, whereas Bayesian approaches rely on matrix decompositions or Wishart priors for shrinkage. In this paper we propose a new method, called the Bayesian Covariance Lasso (BCLASSO), for the shrinkage estimation of a precision (covariance) matrix. We consider a class of priors for the precision matrix that leads to the popular frequentist penalties as special cases, develop a Bayes estimator for the precision matrix, and propose an efficient sampling scheme that does not precalculate boundaries for positive definiteness. The proposed method is permutation invariant and performs shrinkage and estimation simultaneously for non-full rank data. Simulations show that the proposed BCLASSO performs similarly as frequentist methods for non-full rank data.

Novel absorptivity centering method utilizing normalized and factorized spectra for analysis of mixtures with overlapping spectra in different matrices using built-in spectrophotometer software.

Science.gov (United States)

Lotfy, Hayam Mahmoud; Omran, Yasmin Rostom

2018-07-05

A novel, simple, rapid, accurate, and economical spectrophotometric method, namely absorptivity centering (a-Centering) has been developed and validated for the simultaneous determination of mixtures with partially and completely overlapping spectra in different matrices using either normalized or factorized spectrum using built-in spectrophotometer software without a need of special purchased program. Mixture I (Mix I) composed of Simvastatin (SM) and Ezetimibe (EZ) is the one with partial overlapping spectra formulated as tablets, while mixture II (Mix II) formed by Chloramphenicol (CPL) and Prednisolone acetate (PA) is that with complete overlapping spectra formulated as eye drops. These procedures do not require any separation steps. Resolution of spectrally overlapping binary mixtures has been achieved getting recovered zero-order (D 0 ) spectrum of each drug, then absorbance was recorded at their maxima 238, 233.5, 273 and 242.5 nm for SM, EZ, CPL and PA, respectively. Calibration graphs were established with good correlation coefficients. The method shows significant advantages as simplicity, minimal data manipulation besides maximum reproducibility and robustness. Moreover, it was validated according to ICH guidelines. Selectivity was tested using laboratory-prepared mixtures. Accuracy, precision and repeatability were found to be within the acceptable limits. The proposed method is good enough to be applied to an assay of drugs in their combined formulations without any interference from excipients. The obtained results were statistically compared with those of the reported and official methods by applying t-test and F-test at 95% confidence level concluding that there is no significant difference with regard to accuracy and precision. Generally, this method could be used successfully for the routine quality control testing. Copyright © 2018 Elsevier B.V. All rights reserved.

Infrared spectra of complex organic molecules in astronomically relevant ice matrices. I. Acetaldehyde, ethanol, and dimethyl ether

Science.gov (United States)

Terwisscha van Scheltinga, J.; Ligterink, N. F. W.; Boogert, A. C. A.; van Dishoeck, E. F.; Linnartz, H.

2018-03-01

Context. The number of identified complex organic molecules (COMs) in inter- and circumstellar gas-phase environments is steadily increasing. Recent laboratory studies show that many such species form on icy dust grains. At present only smaller molecular species have been directly identified in space in the solid state. Accurate spectroscopic laboratory data of frozen COMs, embedded in ice matrices containing ingredients related to their formation scheme, are still largely lacking. Aim. This work provides infrared reference spectra of acetaldehyde (CH3CHO), ethanol (CH3CH2OH), and dimethyl ether (CH3OCH3) recorded in a variety of ice environments and for astronomically relevant temperatures, as needed to guide or interpret astronomical observations, specifically for upcoming James Webb Space Telescope observations. Methods: Fourier transform transmission spectroscopy (500-4000 cm-1/20-2.5 μm, 1.0 cm-1 resolution) was used to investigate solid acetaldehyde, ethanol and dimethyl ether, pure or mixed with water, CO, methanol, or CO:methanol. These species were deposited on a cryogenically cooled infrared transmissive window at 15 K. A heating ramp was applied, during which IR spectra were recorded until all ice constituents were thermally desorbed. Results: We present a large number of reference spectra that can be compared with astronomical data. Accurate band positions and band widths are provided for the studied ice mixtures and temperatures. Special efforts have been put into those bands of each molecule that are best suited for identification. For acetaldehyde the 7.427 and 5.803 μm bands are recommended, for ethanol the 11.36 and 7.240 μm bands are good candidates, and for dimethyl ether bands at 9.141 and 8.011 μm can be used. All spectra are publicly available in the Leiden Database for Ice.

Condition Number Regularized Covariance Estimation*

Science.gov (United States)

Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala

2012-01-01

Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the “large p small n” setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required. PMID:23730197

On covariance structure in noisy, big data

Science.gov (United States)

Paffenroth, Randy C.; Nong, Ryan; Du Toit, Philip C.

2013-09-01

Herein we describe theory and algorithms for detecting covariance structures in large, noisy data sets. Our work uses ideas from matrix completion and robust principal component analysis to detect the presence of low-rank covariance matrices, even when the data is noisy, distorted by large corruptions, and only partially observed. In fact, the ability to handle partial observations combined with ideas from randomized algorithms for matrix decomposition enables us to produce asymptotically fast algorithms. Herein we will provide numerical demonstrations of the methods and their convergence properties. While such methods have applicability to many problems, including mathematical finance, crime analysis, and other large-scale sensor fusion problems, our inspiration arises from applying these methods in the context of cyber network intrusion detection.

Operator functions and localization of spectra

CERN Document Server

Gil’, Michael I

2003-01-01

"Operator Functions and Localization of Spectra" is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra. In particular bounds for the spectra of integral, differential and integro-differential operators, as well as finite and infinite matrices are established. The volume also presents a systematic exposition of estimates for norms of operator-valued functions and their applications.

Conserved G-matrices of morphological and life-history traits among continental and island blue tit populations.

Science.gov (United States)

Delahaie, B; Charmantier, A; Chantepie, S; Garant, D; Porlier, M; Teplitsky, C

2017-08-01

The genetic variance-covariance matrix (G-matrix) summarizes the genetic architecture of multiple traits. It has a central role in the understanding of phenotypic divergence and the quantification of the evolutionary potential of populations. Laboratory experiments have shown that G-matrices can vary rapidly under divergent selective pressures. However, because of the demanding nature of G-matrix estimation and comparison in wild populations, the extent of its spatial variability remains largely unknown. In this study, we investigate spatial variation in G-matrices for morphological and life-history traits using long-term data sets from one continental and three island populations of blue tit (Cyanistes caeruleus) that have experienced contrasting population history and selective environment. We found no evidence for differences in G-matrices among populations. Interestingly, the phenotypic variance-covariance matrices (P) were divergent across populations, suggesting that using P as a substitute for G may be inadequate. These analyses also provide the first evidence in wild populations for additive genetic variation in the incubation period (that is, the period between last egg laid and hatching) in all four populations. Altogether, our results suggest that G-matrices may be stable across populations inhabiting contrasted environments, therefore challenging the results of previous simulation studies and laboratory experiments.

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

Science.gov (United States)

Sun, Jiehuan; Zhao, Hongyu

2015-02-18

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

Modelling the Covariance Structure in Marginal Multivariate Count Models

DEFF Research Database (Denmark)

Bonat, W. H.; Olivero, J.; Grande-Vega, M.

2017-01-01

The main goal of this article is to present a flexible statistical modelling framework to deal with multivariate count data along with longitudinal and repeated measures structures. The covariance structure for each response variable is defined in terms of a covariance link function combined...... be used to indicate whether there was statistical evidence of a decline in blue duikers and other species hunted during the study period. Determining whether observed drops in the number of animals hunted are indeed true is crucial to assess whether species depletion effects are taking place in exploited...... with a matrix linear predictor involving known matrices. In order to specify the joint covariance matrix for the multivariate response vector, the generalized Kronecker product is employed. We take into account the count nature of the data by means of the power dispersion function associated with the Poisson...

The impact of covariance misspecification in group-based trajectory models for longitudinal data with non-stationary covariance structure.

Science.gov (United States)

Davies, Christopher E; Glonek, Gary Fv; Giles, Lynne C

2017-08-01

One purpose of a longitudinal study is to gain a better understanding of how an outcome of interest changes among a given population over time. In what follows, a trajectory will be taken to mean the series of measurements of the outcome variable for an individual. Group-based trajectory modelling methods seek to identify subgroups of trajectories within a population, such that trajectories that are grouped together are more similar to each other than to trajectories in distinct groups. Group-based trajectory models generally assume a certain structure in the covariances between measurements, for example conditional independence, homogeneous variance between groups or stationary variance over time. Violations of these assumptions could be expected to result in poor model performance. We used simulation to investigate the effect of covariance misspecification on misclassification of trajectories in commonly used models under a range of scenarios. To do this we defined a measure of performance relative to the ideal Bayesian correct classification rate. We found that the more complex models generally performed better over a range of scenarios. In particular, incorrectly specified covariance matrices could significantly bias the results but using models with a correct but more complicated than necessary covariance matrix incurred little cost.

Development of covariance date for fast reactor cores. 3

International Nuclear Information System (INIS)

Shibata, Keiichi; Hasegawa, Akira

1999-03-01

Covariances have been estimated for nuclear data contained in JENDL-3.2. As for Cr and Ni, the physical quantities for which covariances are deduced are cross sections and the first order Legendre-polynomial coefficient for the angular distribution of elastically scattered neutrons. The covariances were estimated by using the same methodology that had been used in the JENDL-3.2 evaluation in order to keep a consistency between mean values and their covariances. In a case where evaluated data were based on experimental data, the covariances were estimated from the same experimental data. For cross section that had been evaluated by nuclear model calculations, the same model was applied to generate the covariances. The covariances obtained were compiled into ENDF-6 format files. The covariances, which had been prepared by the previous fiscal year, were re-examined, and some improvements were performed. Parts of Fe and 235 U covariances were updated. Covariances of nu-p and nu-d for 241 Pu and of fission neutron spectra for 233,235,238 U and 239,240 Pu were newly added to data files. (author)

Construction and use of gene expression covariation matrix

Directory of Open Access Journals (Sweden)

Bellis Michel

2009-07-01

Full Text Available Abstract Background One essential step in the massive analysis of transcriptomic profiles is the calculation of the correlation coefficient, a value used to select pairs of genes with similar or inverse transcriptional profiles across a large fraction of the biological conditions examined. Until now, the choice between the two available methods for calculating the coefficient has been dictated mainly by technological considerations. Specifically, in analyses based on double-channel techniques, researchers have been required to use covariation correlation, i.e. the correlation between gene expression changes measured between several pairs of biological conditions, expressed for example as fold-change. In contrast, in analyses of single-channel techniques scientists have been restricted to the use of coexpression correlation, i.e. correlation between gene expression levels. To our knowledge, nobody has ever examined the possible benefits of using covariation instead of coexpression in massive analyses of single channel microarray results. Results We describe here how single-channel techniques can be treated like double-channel techniques and used to generate both gene expression changes and covariation measures. We also present a new method that allows the calculation of both positive and negative correlation coefficients between genes. First, we perform systematic comparisons between two given biological conditions and classify, for each comparison, genes as increased (I, decreased (D, or not changed (N. As a result, the original series of n gene expression level measures assigned to each gene is replaced by an ordered string of n(n-1/2 symbols, e.g. IDDNNIDID....DNNNNNNID, with the length of the string corresponding to the number of comparisons. In a second step, positive and negative covariation matrices (CVM are constructed by calculating statistically significant positive or negative correlation scores for any pair of genes by comparing their

Treatment of Nuclear Data Covariance Information in Sample Generation

Energy Technology Data Exchange (ETDEWEB)

Swiler, Laura Painton [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Adams, Brian M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Wieselquist, William [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Reactor and Nuclear Systems Division

2017-10-01

This report summarizes a NEAMS (Nuclear Energy Advanced Modeling and Simulation) project focused on developing a sampling capability that can handle the challenges of generating samples from nuclear cross-section data. The covariance information between energy groups tends to be very ill-conditioned and thus poses a problem using traditional methods for generated correlated samples. This report outlines a method that addresses the sample generation from cross-section matrices.

Treatment of Nuclear Data Covariance Information in Sample Generation

International Nuclear Information System (INIS)

Swiler, Laura Painton; Adams, Brian M.; Wieselquist, William

2017-01-01

This report summarizes a NEAMS (Nuclear Energy Advanced Modeling and Simulation) project focused on developing a sampling capability that can handle the challenges of generating samples from nuclear cross-section data. The covariance information between energy groups tends to be very ill-conditioned and thus poses a problem using traditional methods for generated correlated samples. This report outlines a method that addresses the sample generation from cross-section matrices.

Beamforming using subspace estimation from a diagonally averaged sample covariance.

Science.gov (United States)

Quijano, Jorge E; Zurk, Lisa M

2017-08-01

The potential benefit of a large-aperture sonar array for high resolution target localization is often challenged by the lack of sufficient data required for adaptive beamforming. This paper introduces a Toeplitz-constrained estimator of the clairvoyant signal covariance matrix corresponding to multiple far-field targets embedded in background isotropic noise. The estimator is obtained by averaging along subdiagonals of the sample covariance matrix, followed by covariance extrapolation using the method of maximum entropy. The sample covariance is computed from limited data snapshots, a situation commonly encountered with large-aperture arrays in environments characterized by short periods of local stationarity. Eigenvectors computed from the Toeplitz-constrained covariance are used to construct signal-subspace projector matrices, which are shown to reduce background noise and improve detection of closely spaced targets when applied to subspace beamforming. Monte Carlo simulations corresponding to increasing array aperture suggest convergence of the proposed projector to the clairvoyant signal projector, thereby outperforming the classic projector obtained from the sample eigenvectors. Beamforming performance of the proposed method is analyzed using simulated data, as well as experimental data from the Shallow Water Array Performance experiment.

The vibrational spectra of some tetrachlorides in rare gas matrices with particular reference to the molecular shapes of ThCl4 and UCl4

International Nuclear Information System (INIS)

Arthers, S.A.; Beattie, I.R.

1984-01-01

Infrared spectra of tin, lead, hafnium, thorium, and uranium tetrachlorides isolated in inert gas matrices are reported. The results obtained for the tin, lead, and hafnium compounds follow the expected isotope patterns for a tetrahedral molecule except for the observation of additional weak features to high frequency of the all- 35 Cl isotopomers. By contrast for thorium tetrachloride the observed spectrum is not characteristic of a Tsub(d) molecule but can be fitted to a species with Csub(2v) symmetry. Similar results (although less detailed) were obtained for uranium tetrachloride. (author)

lme4qtl: linear mixed models with flexible covariance structure for genetic studies of related individuals.

Science.gov (United States)

Ziyatdinov, Andrey; Vázquez-Santiago, Miquel; Brunel, Helena; Martinez-Perez, Angel; Aschard, Hugues; Soria, Jose Manuel

2018-02-27

Quantitative trait locus (QTL) mapping in genetic data often involves analysis of correlated observations, which need to be accounted for to avoid false association signals. This is commonly performed by modeling such correlations as random effects in linear mixed models (LMMs). The R package lme4 is a well-established tool that implements major LMM features using sparse matrix methods; however, it is not fully adapted for QTL mapping association and linkage studies. In particular, two LMM features are lacking in the base version of lme4: the definition of random effects by custom covariance matrices; and parameter constraints, which are essential in advanced QTL models. Apart from applications in linkage studies of related individuals, such functionalities are of high interest for association studies in situations where multiple covariance matrices need to be modeled, a scenario not covered by many genome-wide association study (GWAS) software. To address the aforementioned limitations, we developed a new R package lme4qtl as an extension of lme4. First, lme4qtl contributes new models for genetic studies within a single tool integrated with lme4 and its companion packages. Second, lme4qtl offers a flexible framework for scenarios with multiple levels of relatedness and becomes efficient when covariance matrices are sparse. We showed the value of our package using real family-based data in the Genetic Analysis of Idiopathic Thrombophilia 2 (GAIT2) project. Our software lme4qtl enables QTL mapping models with a versatile structure of random effects and efficient computation for sparse covariances. lme4qtl is available at https://github.com/variani/lme4qtl .

Phenotypic covariance at species' borders.

Science.gov (United States)

Caley, M Julian; Cripps, Edward; Game, Edward T

2013-05-28

Understanding the evolution of species limits is important in ecology, evolution, and conservation biology. Despite its likely importance in the evolution of these limits, little is known about phenotypic covariance in geographically marginal populations, and the degree to which it constrains, or facilitates, responses to selection. We investigated phenotypic covariance in morphological traits at species' borders by comparing phenotypic covariance matrices (P), including the degree of shared structure, the distribution of strengths of pair-wise correlations between traits, the degree of morphological integration of traits, and the ranks of matricies, between central and marginal populations of three species-pairs of coral reef fishes. Greater structural differences in P were observed between populations close to range margins and conspecific populations toward range centres, than between pairs of conspecific populations that were both more centrally located within their ranges. Approximately 80% of all pair-wise trait correlations within populations were greater in the north, but these differences were unrelated to the position of the sampled population with respect to the geographic range of the species. Neither the degree of morphological integration, nor ranks of P, indicated greater evolutionary constraint at range edges. Characteristics of P observed here provide no support for constraint contributing to the formation of these species' borders, but may instead reflect structural change in P caused by selection or drift, and their potential to evolve in the future.

An Adaptive Estimation of Forecast Error Covariance Parameters for Kalman Filtering Data Assimilation

Institute of Scientific and Technical Information of China (English)

Xiaogu ZHENG

2009-01-01

An adaptive estimation of forecast error covariance matrices is proposed for Kalman filtering data assimilation. A forecast error covariance matrix is initially estimated using an ensemble of perturbation forecasts. This initially estimated matrix is then adjusted with scale parameters that are adaptively estimated by minimizing -2log-likelihood of observed-minus-forecast residuals. The proposed approach could be applied to Kalman filtering data assimilation with imperfect models when the model error statistics are not known. A simple nonlinear model (Burgers' equation model) is used to demonstrate the efficacy of the proposed approach.

Phenotypic Covariation and Morphological Diversification in the Ruminant Skull.

Science.gov (United States)

Haber, Annat

2016-05-01

Differences among clades in their diversification patterns result from a combination of extrinsic and intrinsic factors. In this study, I examined the role of intrinsic factors in the morphological diversification of ruminants, in general, and in the differences between bovids and cervids, in particular. Using skull morphology, which embodies many of the adaptations that distinguish bovids and cervids, I examined 132 of the 200 extant ruminant species. As a proxy for intrinsic constraints, I quantified different aspects of the phenotypic covariation structure within species and compared them with the among-species divergence patterns, using phylogenetic comparative methods. My results show that for most species, divergence is well aligned with their phenotypic covariance matrix and that those that are better aligned have diverged further away from their ancestor. Bovids have dispersed into a wider range of directions in morphospace than cervids, and their overall disparity is higher. This difference is best explained by the lower eccentricity of bovids' within-species covariance matrices. These results are consistent with the role of intrinsic constraints in determining amount, range, and direction of dispersion and demonstrate that intrinsic constraints can influence macroevolutionary patterns even as the covariance structure evolves.

Least square methods and covariance matrix applied to the relative efficiency calibration of a Ge(Li) detector

International Nuclear Information System (INIS)

Geraldo, L.P.; Smith, D.L.

1989-01-01

The methodology of covariance matrix and square methods have been applied in the relative efficiency calibration for a Ge(Li) detector apllied in the relative efficiency calibration for a Ge(Li) detector. Procedures employed to generate, manipulate and test covariance matrices which serve to properly represent uncertainties of experimental data are discussed. Calibration data fitting using least square methods has been performed for a particular experimental data set. (author) [pt

Simulations and cosmological inference: A statistical model for power spectra means and covariances

International Nuclear Information System (INIS)

Schneider, Michael D.; Knox, Lloyd; Habib, Salman; Heitmann, Katrin; Higdon, David; Nakhleh, Charles

2008-01-01

We describe an approximate statistical model for the sample variance distribution of the nonlinear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate normal distribution for the power spectrum band powers but takes full account of the (parameter-dependent) power spectrum covariance. The model is calibrated using an extension of the framework in Habib et al. (2007) to train Gaussian processes for the power spectrum mean and covariance given a set of simulation runs over a hypercube in parameter space. We demonstrate the performance of this machinery by estimating the parameters of a power-law model for the power spectrum. Within this framework, our calibrated sample variance distribution is robust to errors in the estimated covariance and shows rapid convergence of the posterior parameter constraints with the number of training simulations.

Inverse m-matrices and ultrametric matrices

CERN Document Server

Dellacherie, Claude; San Martin, Jaime

2014-01-01

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

Treating Sample Covariances for Use in Strongly Coupled Atmosphere-Ocean Data Assimilation

Science.gov (United States)

Smith, Polly J.; Lawless, Amos S.; Nichols, Nancy K.

2018-01-01

Strongly coupled data assimilation requires cross-domain forecast error covariances; information from ensembles can be used, but limited sampling means that ensemble derived error covariances are routinely rank deficient and/or ill-conditioned and marred by noise. Thus, they require modification before they can be incorporated into a standard assimilation framework. Here we compare methods for improving the rank and conditioning of multivariate sample error covariance matrices for coupled atmosphere-ocean data assimilation. The first method, reconditioning, alters the matrix eigenvalues directly; this preserves the correlation structures but does not remove sampling noise. We show that it is better to recondition the correlation matrix rather than the covariance matrix as this prevents small but dynamically important modes from being lost. The second method, model state-space localization via the Schur product, effectively removes sample noise but can dampen small cross-correlation signals. A combination that exploits the merits of each is found to offer an effective alternative.

Testing the equivalence of modern human cranial covariance structure: Implications for bioarchaeological applications.

Science.gov (United States)

von Cramon-Taubadel, Noreen; Schroeder, Lauren

2016-10-01

Estimation of the variance-covariance (V/CV) structure of fragmentary bioarchaeological populations requires the use of proxy extant V/CV parameters. However, it is currently unclear whether extant human populations exhibit equivalent V/CV structures. Random skewers (RS) and hierarchical analyses of common principal components (CPC) were applied to a modern human cranial dataset. Cranial V/CV similarity was assessed globally for samples of individual populations (jackknifed method) and for pairwise population sample contrasts. The results were examined in light of potential explanatory factors for covariance difference, such as geographic region, among-group distance, and sample size. RS analyses showed that population samples exhibited highly correlated multivariate responses to selection, and that differences in RS results were primarily a consequence of differences in sample size. The CPC method yielded mixed results, depending upon the statistical criterion used to evaluate the hierarchy. The hypothesis-testing (step-up) approach was deemed problematic due to sensitivity to low statistical power and elevated Type I errors. In contrast, the model-fitting (lowest AIC) approach suggested that V/CV matrices were proportional and/or shared a large number of CPCs. Pairwise population sample CPC results were correlated with cranial distance, suggesting that population history explains some of the variability in V/CV structure among groups. The results indicate that patterns of covariance in human craniometric samples are broadly similar but not identical. These findings have important implications for choosing extant covariance matrices to use as proxy V/CV parameters in evolutionary analyses of past populations. © 2016 Wiley Periodicals, Inc.

Covariance Inflation in the Ensemble Kalman Filter: A Residual Nudging Perspective and Some Implications

KAUST Repository

Luo, Xiaodong; Hoteit, Ibrahim

2013-01-01

This article examines the influence of covariance inflation on the distance between the measured observation and the simulated (or predicted) observation with respect to the state estimate. In order for the aforementioned distance to be bounded in a certain interval, some sufficient conditions are derived, indicating that the covariance inflation factor should be bounded in a certain interval, and that the inflation bounds are related to the maximum and minimum eigenvalues of certain matrices. Implications of these analytic results are discussed, and a numerical experiment is presented to verify the validity of the analysis conducted.

Covariance Inflation in the Ensemble Kalman Filter: A Residual Nudging Perspective and Some Implications

KAUST Repository

Luo, Xiaodong

2013-10-01

This article examines the influence of covariance inflation on the distance between the measured observation and the simulated (or predicted) observation with respect to the state estimate. In order for the aforementioned distance to be bounded in a certain interval, some sufficient conditions are derived, indicating that the covariance inflation factor should be bounded in a certain interval, and that the inflation bounds are related to the maximum and minimum eigenvalues of certain matrices. Implications of these analytic results are discussed, and a numerical experiment is presented to verify the validity of the analysis conducted.

Flavonoids as matrices for MALDI-TOF mass spectrometric analysis of transition metal complexes

Science.gov (United States)

Petkovic, Marijana; Petrovic, Biljana; Savic, Jasmina; Bugarcic, Zivadin D.; Dimitric-Markovic, Jasmina; Momic, Tatjana; Vasic, Vesna

2010-02-01

Matrix-assisted laser desorption and ionization time-of-flight mass spectrometry (MALDI-TOF MS) is a suitable method for the analysis of inorganic and organic compounds and biomolecules. This makes MALDI-TOF MS convenient for monitoring the interaction of metallo-drugs with biomolecules. Results presented in this manuscript demonstrate that flavonoids such as apigenin, kaempferol and luteolin are suitable for MALDI-TOF MS analysis of Pt(II), Pd(II), Pt(IV) and Ru(III) complexes, giving different signal-to-noise ratios of the analyte peak. The MALDI-TOF mass spectra of inorganic complexes acquired with these flavonoid matrices are easy to interpret and have some advantages over the application of other commonly used matrices: a low number of matrix peaks are detectable and the coordinative metal-ligand bond is, in most cases, preserved. On the other hand, flavonoids do not act as typical matrices, as their excess is not required for the acquisition of MALDI-TOF mass spectra of inorganic complexes.

Generalisations of Fisher Matrices

Directory of Open Access Journals (Sweden)

Alan Heavens

2016-06-01

Full Text Available Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters—both their errors and covariances. In this short review, I outline a number of extensions to the simple Fisher matrix formalism, covering a number of recent developments in the field. These are: (a situations where the data (in the form of ( x , y pairs have errors in both x and y; (b modifications to parameter inference in the presence of systematic errors, or through fixing the values of some model parameters; (c Derivative Approximation for LIkelihoods (DALI - higher-order expansions of the likelihood surface, going beyond the Gaussian shape approximation; (d extensions of the Fisher-like formalism, to treat model selection problems with Bayesian evidence.

Fine structure of spectral properties for random correlation matrices: an application to financial markets.

Science.gov (United States)

Livan, Giacomo; Alfarano, Simone; Scalas, Enrico

2011-07-01

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross correlations between stocks. We interpret and corroborate these findings in terms of factor models, and we compare empirical spectra to those predicted by random matrix theory for such models.

Fine structure of spectral properties for random correlation matrices: An application to financial markets

Science.gov (United States)

Livan, Giacomo; Alfarano, Simone; Scalas, Enrico

2011-07-01

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross correlations between stocks. We interpret and corroborate these findings in terms of factor models, and we compare empirical spectra to those predicted by random matrix theory for such models.

Analytical Derivation of the Inverse Moments of One-Sided Correlated Gram Matrices With Applications

KAUST Repository

Elkhalil, Khalil

2016-02-03

This paper addresses the development of analytical tools for the computation of the inverse moments of random Gram matrices with one side correlation. Such a question is mainly driven by applications in signal processing and wireless communications wherein such matrices naturally arise. In particular, we derive closed-form expressions for the inverse moments and show that the obtained results can help approximate several performance metrics such as the average estimation error corresponding to the Best Linear Unbiased Estimator (BLUE) and the Linear Minimum Mean Square Error (LMMSE) estimator or also other loss functions used to measure the accuracy of covariance matrix estimates.

An Empirical State Error Covariance Matrix for Batch State Estimation

Science.gov (United States)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the

The influence of inorganic matrices on the decomposition of Eucalyptus litter

International Nuclear Information System (INIS)

Skene, T.M.; Oades, J.M.; Clarke, P.J.; Skjemstad, J.O.; Oades, J.M.; Skjemstad, J.O.

1997-01-01

The decomposition of Eucalyptus litter (EL) in the presence and absence of inorganic matrices [sad (S), sand+kaolin (S+K), loamy sand (LS)] with and without added N (urea) was followed over 48 weeks using chemical and spectroscopic means. At the end of the incubation, the residual organic matter in different density and particle size fractions was examined. Urea addition inhibited the mineralisation of C from the litter in all treatments except EL+S+N, whereas the inorganic matrices had little influence on mineralisation. Solid state 13 C CP/MAS NMR spectra of the whole samples suggested there were no differences in the treatments, despite significant differences in the amount of C mineralized. The NMR spectra of the whole samples suggest that a reaction between aromatic-C and urea occurred during thr first week of the incubation which may have rendered the N unavailable to microorganisms. The results were quite different from a similar study on the decomposition of straw. these differences suggest that, for high quality substrates, physical protection by inorganic matrices is the limiting factor to decomposition, whereas for low quality substrates, chemical protection is the limiting factor. 13 refs., 2 tabs., 6 figs

A Phylogenetic Analysis of Shape Covariance Structure in the Anthropoid Skull

OpenAIRE

De Oliveira, Felipe; Marroig, Gabriel; Garcia, Guilherme

2016-01-01

Phenotypic traits evolve in a coordinated manner due to developmental and functional interactions, mediated by the dynamics of natural selection; the dependence between traits arising from these three factors is captured by genetic ( G ) and phenotypic ( P ) covariance matrices. Mammalian skull development produces an intricate pattern of tissue organization and mutual signaling that integrates this structure, although the set of functions it performs is quite disparate. Therefore, the interp...

Are Low-order Covariance Estimates Useful in Error Analyses?

Science.gov (United States)

Baker, D. F.; Schimel, D.

2005-12-01

Atmospheric trace gas inversions, using modeled atmospheric transport to infer surface sources and sinks from measured concentrations, are most commonly done using least-squares techniques that return not only an estimate of the state (the surface fluxes) but also the covariance matrix describing the uncertainty in that estimate. Besides allowing one to place error bars around the estimate, the covariance matrix may be used in simulation studies to learn what uncertainties would be expected from various hypothetical observing strategies. This error analysis capability is routinely used in designing instrumentation, measurement campaigns, and satellite observing strategies. For example, Rayner, et al (2002) examined the ability of satellite-based column-integrated CO2 measurements to constrain monthly-average CO2 fluxes for about 100 emission regions using this approach. Exact solutions for both state vector and covariance matrix become computationally infeasible, however, when the surface fluxes are solved at finer resolution (e.g., daily in time, under 500 km in space). It is precisely at these finer scales, however, that one would hope to be able to estimate fluxes using high-density satellite measurements. Non-exact estimation methods such as variational data assimilation or the ensemble Kalman filter could be used, but they achieve their computational savings by obtaining an only approximate state estimate and a low-order approximation of the true covariance. One would like to be able to use this covariance matrix to do the same sort of error analyses as are done with the full-rank covariance, but is it correct to do so? Here we compare uncertainties and `information content' derived from full-rank covariance matrices obtained from a direct, batch least squares inversion to those from the incomplete-rank covariance matrices given by a variational data assimilation approach solved with a variable metric minimization technique (the Broyden-Fletcher- Goldfarb

Covariances for measured activation and fission ratios data

International Nuclear Information System (INIS)

Smith, D.L.; Meadows, J.W.; Watanabe, Y.

1986-01-01

Methods which are routinely used in the determination of covariance matrices for both integral and differential activation and fission-ratios data acquired at the Argonne National Laboratory Fast-Neutron Generator Facility (FNG) are discussed. Special consideration is given to problems associated with the estimation of correlations between various identified sources of experimental error. Approximation methods which are commonly used to reduce the labor involved in this analysis to manageable levels are described. Results from some experiments which have been recently carried out in this laboratory are presented to illustrate these procedures. 13 refs., 1 fig., 5 tabs

Generation of integral experiment covariance data and their impact on criticality safety validation

Energy Technology Data Exchange (ETDEWEB)

Stuke, Maik; Peters, Elisabeth; Sommer, Fabian

2016-11-15

The quantification of statistical dependencies in data of critical experiments and how to account for them properly in validation procedures has been discussed in the literature by various groups. However, these subjects are still an active topic in the Expert Group on Uncertainty Analysis for Criticality Safety Assessment (UACSA) of the OECDNEA Nuclear Science Committee. The latter compiles and publishes the freely available experimental data collection, the International Handbook of Evaluated Criticality Safety Benchmark Experiments, ICSBEP. Most of the experiments were performed as series and share parts of experimental setups, consequently leading to correlation effects in the results. The correct consideration of correlated data seems to be inevitable if the experimental data in a validation procedure is limited or one cannot rely on a sufficient number of uncorrelated data sets, e.g. from different laboratories using different setups. The general determination of correlations and the underlying covariance data as well as the consideration of them in a validation procedure is the focus of the following work. We discuss and demonstrate possible effects on calculated k{sub eff}'s, their uncertainties, and the corresponding covariance matrices due to interpretation of evaluated experimental data and its translation into calculation models. The work shows effects of various modeling approaches, varying distribution functions of parameters and compares and discusses results from the applied Monte-Carlo sampling method with available data on correlations. Our findings indicate that for the reliable determination of integral experimental covariance matrices or the correlation coefficients a detailed study of the underlying experimental data, the modeling approach and assumptions made, and the resulting sensitivity analysis seems to be inevitable. Further, a Bayesian method is discussed to include integral experimental covariance data when estimating an

Generation of integral experiment covariance data and their impact on criticality safety validation

International Nuclear Information System (INIS)

Stuke, Maik; Peters, Elisabeth; Sommer, Fabian

2016-11-01

The quantification of statistical dependencies in data of critical experiments and how to account for them properly in validation procedures has been discussed in the literature by various groups. However, these subjects are still an active topic in the Expert Group on Uncertainty Analysis for Criticality Safety Assessment (UACSA) of the OECDNEA Nuclear Science Committee. The latter compiles and publishes the freely available experimental data collection, the International Handbook of Evaluated Criticality Safety Benchmark Experiments, ICSBEP. Most of the experiments were performed as series and share parts of experimental setups, consequently leading to correlation effects in the results. The correct consideration of correlated data seems to be inevitable if the experimental data in a validation procedure is limited or one cannot rely on a sufficient number of uncorrelated data sets, e.g. from different laboratories using different setups. The general determination of correlations and the underlying covariance data as well as the consideration of them in a validation procedure is the focus of the following work. We discuss and demonstrate possible effects on calculated k eff 's, their uncertainties, and the corresponding covariance matrices due to interpretation of evaluated experimental data and its translation into calculation models. The work shows effects of various modeling approaches, varying distribution functions of parameters and compares and discusses results from the applied Monte-Carlo sampling method with available data on correlations. Our findings indicate that for the reliable determination of integral experimental covariance matrices or the correlation coefficients a detailed study of the underlying experimental data, the modeling approach and assumptions made, and the resulting sensitivity analysis seems to be inevitable. Further, a Bayesian method is discussed to include integral experimental covariance data when estimating an application

No-go theorems for functorial localic spectra of noncommutative rings

NARCIS (Netherlands)

van den Berg, B.; Heunen, C.

2011-01-01

Any functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices for n at least 3. The same obstruction applies to the Zariski, Stone, and Pierce spectra. The possibility of spectra in

On the Two Spectra Inverse Problem for Semi-infinite Jacobi Matrices

International Nuclear Information System (INIS)

Silva, Luis O.; Weder, Ricardo

2006-01-01

We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg-Marchenko theorem for Schroedinger operators on the half-line. Furthermore, we give necessary and sufficient conditions for two real sequences to be the spectra of a Jacobi operator with different boundary conditions

QCD's Partner Needed for Mass Spectra and Parton Structure Functions

International Nuclear Information System (INIS)

Kim, Y.S.

2009-01-01

as in the case of the hydrogen atom, bound-state wave functions are needed to generate hadronic spectra. For this purpose, in 1971, Feynman and his students wrote down a Lorentz-invariant harmonic oscillator equation. This differential equation has one set of solutions satisfying the Lorentz-covariant boundary condition. This covariant set generates Lorentz-invariant mass spectra with their degeneracies. Furthermore, the Lorentz-covariant wave functions allow us to calculate the valence parton distribution by Lorentz-boosting the quark-model wave function from the hadronic rest frame. However, this boosted wave function does not give an accurate parton distribution. The wave function needs QCD corrections to make a contact with the real world. Likewise, QCD needs the wave function as a starting point for calculating the parton structure function. (author)

Autism-specific covariation in perceptual performances: "g" or "p" factor?

Science.gov (United States)

Meilleur, Andrée-Anne S; Berthiaume, Claude; Bertone, Armando; Mottron, Laurent

2014-01-01

Autistic perception is characterized by atypical and sometimes exceptional performance in several low- (e.g., discrimination) and mid-level (e.g., pattern matching) tasks in both visual and auditory domains. A factor that specifically affects perceptive abilities in autistic individuals should manifest as an autism-specific association between perceptual tasks. The first purpose of this study was to explore how perceptual performances are associated within or across processing levels and/or modalities. The second purpose was to determine if general intelligence, the major factor that accounts for covariation in task performances in non-autistic individuals, equally controls perceptual abilities in autistic individuals. We asked 46 autistic individuals and 46 typically developing controls to perform four tasks measuring low- or mid-level visual or auditory processing. Intelligence was measured with the Wechsler's Intelligence Scale (FSIQ) and Raven Progressive Matrices (RPM). We conducted linear regression models to compare task performances between groups and patterns of covariation between tasks. The addition of either Wechsler's FSIQ or RPM in the regression models controlled for the effects of intelligence. In typically developing individuals, most perceptual tasks were associated with intelligence measured either by RPM or Wechsler FSIQ. The residual covariation between unimodal tasks, i.e. covariation not explained by intelligence, could be explained by a modality-specific factor. In the autistic group, residual covariation revealed the presence of a plurimodal factor specific to autism. Autistic individuals show exceptional performance in some perceptual tasks. Here, we demonstrate the existence of specific, plurimodal covariation that does not dependent on general intelligence (or "g" factor). Instead, this residual covariation is accounted for by a common perceptual process (or "p" factor), which may drive perceptual abilities differently in autistic and

Autism-specific covariation in perceptual performances: "g" or "p" factor?

Directory of Open Access Journals (Sweden)

Andrée-Anne S Meilleur

Full Text Available Autistic perception is characterized by atypical and sometimes exceptional performance in several low- (e.g., discrimination and mid-level (e.g., pattern matching tasks in both visual and auditory domains. A factor that specifically affects perceptive abilities in autistic individuals should manifest as an autism-specific association between perceptual tasks. The first purpose of this study was to explore how perceptual performances are associated within or across processing levels and/or modalities. The second purpose was to determine if general intelligence, the major factor that accounts for covariation in task performances in non-autistic individuals, equally controls perceptual abilities in autistic individuals.We asked 46 autistic individuals and 46 typically developing controls to perform four tasks measuring low- or mid-level visual or auditory processing. Intelligence was measured with the Wechsler's Intelligence Scale (FSIQ and Raven Progressive Matrices (RPM. We conducted linear regression models to compare task performances between groups and patterns of covariation between tasks. The addition of either Wechsler's FSIQ or RPM in the regression models controlled for the effects of intelligence.In typically developing individuals, most perceptual tasks were associated with intelligence measured either by RPM or Wechsler FSIQ. The residual covariation between unimodal tasks, i.e. covariation not explained by intelligence, could be explained by a modality-specific factor. In the autistic group, residual covariation revealed the presence of a plurimodal factor specific to autism.Autistic individuals show exceptional performance in some perceptual tasks. Here, we demonstrate the existence of specific, plurimodal covariation that does not dependent on general intelligence (or "g" factor. Instead, this residual covariation is accounted for by a common perceptual process (or "p" factor, which may drive perceptual abilities differently in

Covariance specification and estimation to improve top-down Green House Gas emission estimates

Science.gov (United States)

Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Whetstone, J. R.

2015-12-01

The National Institute of Standards and Technology (NIST) operates the North-East Corridor (NEC) project and the Indianapolis Flux Experiment (INFLUX) in order to develop measurement methods to quantify sources of Greenhouse Gas (GHG) emissions as well as their uncertainties in urban domains using a top down inversion method. Top down inversion updates prior knowledge using observations in a Bayesian way. One primary consideration in a Bayesian inversion framework is the covariance structure of (1) the emission prior residuals and (2) the observation residuals (i.e. the difference between observations and model predicted observations). These covariance matrices are respectively referred to as the prior covariance matrix and the model-data mismatch covariance matrix. It is known that the choice of these covariances can have large effect on estimates. The main objective of this work is to determine the impact of different covariance models on inversion estimates and their associated uncertainties in urban domains. We use a pseudo-data Bayesian inversion framework using footprints (i.e. sensitivities of tower measurements of GHGs to surface emissions) and emission priors (based on Hestia project to quantify fossil-fuel emissions) to estimate posterior emissions using different covariance schemes. The posterior emission estimates and uncertainties are compared to the hypothetical truth. We find that, if we correctly specify spatial variability and spatio-temporal variability in prior and model-data mismatch covariances respectively, then we can compute more accurate posterior estimates. We discuss few covariance models to introduce space-time interacting mismatches along with estimation of the involved parameters. We then compare several candidate prior spatial covariance models from the Matern covariance class and estimate their parameters with specified mismatches. We find that best-fitted prior covariances are not always best in recovering the truth. To achieve

MIMO Radar Transmit Beampattern Design Without Synthesising the Covariance Matrix

KAUST Repository

Ahmed, Sajid

2013-10-28

Compared to phased-array, multiple-input multiple-output (MIMO) radars provide more degrees-offreedom (DOF) that can be exploited for improved spatial resolution, better parametric identifiability, lower side-lobe levels at the transmitter/receiver, and design variety of transmit beampatterns. The design of the transmit beampattern generally requires the waveforms to have arbitrary auto- and crosscorrelation properties. The generation of such waveforms is a two step complicated process. In the first step a waveform covariance matrix is synthesised, which is a constrained optimisation problem. In the second step, to realise this covariance matrix actual waveforms are designed, which is also a constrained optimisation problem. Our proposed scheme converts this two step constrained optimisation problem into a one step unconstrained optimisation problem. In the proposed scheme, in contrast to synthesising the covariance matrix for the desired beampattern, nT independent finite-alphabet constantenvelope waveforms are generated and pre-processed, with weight matrix W, before transmitting from the antennas. In this work, two weight matrices are proposed that can be easily optimised for the desired symmetric and non-symmetric beampatterns and guarantee equal average power transmission from each antenna. Simulation results validate our claims.

Tensor Dictionary Learning for Positive Definite Matrices.

Science.gov (United States)

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

2015-11-01

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

Generalised Wigner surmise for (2 X 2) random matrices

International Nuclear Information System (INIS)

Chau Huu-Tai, P.; Van Isacker, P.; Smirnova, N.A.

2001-01-01

We present new analytical results concerning the spectral distributions for (2 x 2) random real symmetric matrices which generalize the Wigner surmise. The study of the statistical properties of spectra of realistic many-body Hamiltonians requires consideration of a random matrix ensemble whose elements are not independent or whose distribution is not invariant under orthogonal transformation of a chosen basis. In this letter we have concentrated on the properties of (2 x 2) real symmetric matrices whose elements are independent Gaussian variables with zero means but do not belong to the GOE. We have derived the distribution of eigenvalues for such a matrix, the nearest-neighbour spacing distribution which generalizes the Wigner surmise and we have calculated some important moments. (authors)

Numerical Differentiation Methods for Computing Error Covariance Matrices in Item Response Theory Modeling: An Evaluation and a New Proposal

Science.gov (United States)

Tian, Wei; Cai, Li; Thissen, David; Xin, Tao

2013-01-01

In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…

Separation of Correlated Astrophysical Sources Using Multiple-Lag Data Covariance Matrices

Directory of Open Access Journals (Sweden)

Baccigalupi C

2005-01-01

Full Text Available This paper proposes a new strategy to separate astrophysical sources that are mutually correlated. This strategy is based on second-order statistics and exploits prior information about the possible structure of the mixing matrix. Unlike ICA blind separation approaches, where the sources are assumed mutually independent and no prior knowledge is assumed about the mixing matrix, our strategy allows the independence assumption to be relaxed and performs the separation of even significantly correlated sources. Besides the mixing matrix, our strategy is also capable to evaluate the source covariance functions at several lags. Moreover, once the mixing parameters have been identified, a simple deconvolution can be used to estimate the probability density functions of the source processes. To benchmark our algorithm, we used a database that simulates the one expected from the instruments that will operate onboard ESA's Planck Surveyor Satellite to measure the CMB anisotropies all over the celestial sphere.

Covariance J-resolved spectroscopy: Theory and application in vivo.

Science.gov (United States)

Iqbal, Zohaib; Verma, Gaurav; Kumar, Anand; Thomas, M Albert

2017-08-01

Magnetic resonance spectroscopy (MRS) is a powerful tool capable of investigating the metabolic status of several tissues in vivo. In particular, single-voxel-based 1 H spectroscopy provides invaluable biochemical information from a volume of interest (VOI) and has therefore been used in a variety of studies. Unfortunately, typical one-dimensional MRS data suffer from severe signal overlap and thus important metabolites are difficult to distinguish. One method that is used to disentangle overlapping resonances is the two-dimensional J-resolved spectroscopy (JPRESS) experiment. Due to the long acquisition duration of the JPRESS experiment, a limited number of points are acquired in the indirect dimension, leading to poor spectral resolution along this dimension. Poor spectral resolution is problematic because proper peak assignment may be hindered, which is why the zero-filling method is often used to improve resolution as a post-processing step. However, zero-filling leads to spectral artifacts, which may affect visualization and quantitation of spectra. A novel method utilizing a covariance transformation, called covariance J-resolved spectroscopy (CovJ), was developed in order to improve spectral resolution along the indirect dimension (F 1 ). Comparison of simulated data demonstrates that peak structures remain qualitatively similar between JPRESS and the novel method along the diagonal region (F 1 = 0 Hz), whereas differences arise in the cross-peak (F 1 ≠0 Hz) regions. In addition, quantitative results of in vivo JPRESS data acquired on a 3T scanner show significant correlations (r 2 >0.86, pCOVariance Spectral Evaluation of 1 H Acquisitions using Representative prior knowledge' (Cov-SEHAR), was developed in order to quantify γ-aminobutyric acid and glutamate from the CovJ spectra. These preliminary findings indicate that the CovJ method may be used to improve spectral resolution without hindering metabolite quantitation for J-resolved spectra

Covariance expressions for eigenvalue and eigenvector problems

Science.gov (United States)

Liounis, Andrew J.

There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.

Nonlinear consider covariance analysis using a sigma-point filter formulation

Science.gov (United States)

Lisano, Michael E.

2006-01-01

The research reported here extends the mathematical formulation of nonlinear, sigma-point estimators to enable consider covariance analysis for dynamical systems. This paper presents a novel sigma-point consider filter algorithm, for consider-parameterized nonlinear estimation, following the unscented Kalman filter (UKF) variation on the sigma-point filter formulation, which requires no partial derivatives of dynamics models or measurement models with respect to the parameter list. It is shown that, consistent with the attributes of sigma-point estimators, a consider-parameterized sigma-point estimator can be developed entirely without requiring the derivation of any partial-derivative matrices related to the dynamical system, the measurements, or the considered parameters, which appears to be an advantage over the formulation of a linear-theory sequential consider estimator. It is also demonstrated that a consider covariance analysis performed with this 'partial-derivative-free' formulation yields equivalent results to the linear-theory consider filter, for purely linear problems.

New distributed fusion filtering algorithm based on covariances over sensor networks with random packet dropouts

Science.gov (United States)

Caballero-Águila, R.; Hermoso-Carazo, A.; Linares-Pérez, J.

2017-07-01

This paper studies the distributed fusion estimation problem from multisensor measured outputs perturbed by correlated noises and uncertainties modelled by random parameter matrices. Each sensor transmits its outputs to a local processor over a packet-erasure channel and, consequently, random losses may occur during transmission. Different white sequences of Bernoulli variables are introduced to model the transmission losses. For the estimation, each lost output is replaced by its estimator based on the information received previously, and only the covariances of the processes involved are used, without requiring the signal evolution model. First, a recursive algorithm for the local least-squares filters is derived by using an innovation approach. Then, the cross-correlation matrices between any two local filters is obtained. Finally, the distributed fusion filter weighted by matrices is obtained from the local filters by applying the least-squares criterion. The performance of the estimators and the influence of both sensor uncertainties and transmission losses on the estimation accuracy are analysed in a numerical example.

The donor OH stretching–libration dynamics of hydrogen-bonded methanol dimers in cryogenic matrices

DEFF Research Database (Denmark)

Heger, M.; Andersen, J.; Suhm, M. A.

2016-01-01

FTIR spectra of the methanol dimer trapped in neon matrices are presented. The fundamental, overtone and combination bands involving the donor OH libration and stretching motions were observed in order to extract relevant anharmonicity constants. We find a stretching–libration coupling constant...

Averaging operations on matrices

Indian Academy of Sciences (India)

2014-07-03

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

Autism-Specific Covariation in Perceptual Performances: “g” or “p” Factor?

Science.gov (United States)

Meilleur, Andrée-Anne S.; Berthiaume, Claude; Bertone, Armando; Mottron, Laurent

2014-01-01

Background Autistic perception is characterized by atypical and sometimes exceptional performance in several low- (e.g., discrimination) and mid-level (e.g., pattern matching) tasks in both visual and auditory domains. A factor that specifically affects perceptive abilities in autistic individuals should manifest as an autism-specific association between perceptual tasks. The first purpose of this study was to explore how perceptual performances are associated within or across processing levels and/or modalities. The second purpose was to determine if general intelligence, the major factor that accounts for covariation in task performances in non-autistic individuals, equally controls perceptual abilities in autistic individuals. Methods We asked 46 autistic individuals and 46 typically developing controls to perform four tasks measuring low- or mid-level visual or auditory processing. Intelligence was measured with the Wechsler's Intelligence Scale (FSIQ) and Raven Progressive Matrices (RPM). We conducted linear regression models to compare task performances between groups and patterns of covariation between tasks. The addition of either Wechsler's FSIQ or RPM in the regression models controlled for the effects of intelligence. Results In typically developing individuals, most perceptual tasks were associated with intelligence measured either by RPM or Wechsler FSIQ. The residual covariation between unimodal tasks, i.e. covariation not explained by intelligence, could be explained by a modality-specific factor. In the autistic group, residual covariation revealed the presence of a plurimodal factor specific to autism. Conclusions Autistic individuals show exceptional performance in some perceptual tasks. Here, we demonstrate the existence of specific, plurimodal covariation that does not dependent on general intelligence (or “g” factor). Instead, this residual covariation is accounted for by a common perceptual process (or “p” factor), which may drive

Evaluation of covariance data for chromium, iron and nickel contained in JENDL-3.2

International Nuclear Information System (INIS)

Oh, Soo-Youl; Shibata, Keiichi.

1998-01-01

An evaluation has been made for the covariances of neutron cross sections of 52 Cr, 56 Fe, 58 Ni and 60 Ni contained in JENDL-3.2. Reactions considered were the threshold reactions such as (n, 2n), (n, nα), (n, np), (n, p), (n, d), (n, t) and (n, α), the radiative capture reaction above the resonance region, and the inelastic scattering to discrete and continuum levels. Evaluation guidelines and procedures were established during the work. A generalized least-squares fitting code GMA was used in estimating covariances for reactions of which JENDL-3.2 cross sections had been evaluated by taking account of many measured data. For cross sections that had been evaluated by nuclear reaction model calculations, the KALMAN code, which yields covariances of cross sections and of associated model parameters on the basis of the Bayesian statistics, was used in conjunction with reaction model codes EGNASH and CASTHY. The evaluated uncertainties of a few percent to 30% in the cross sections look reasonable, and the correlation matrices show understandable trends. Even though there is no strict way to confirm the validity of the evaluated covariances, tools and procedures adopted in the present work are appropriate for producing covariance files based on JENDL-3.2. The covariances obtained will be compiled into JENDL in the near future. Meanwhile, new sets of optical model and level density parameters were proposed as one of byproducts obtained from the KALMAN calculations. (author)

Four-Component Scattering Power Decomposition Algorithm with Rotation of Covariance Matrix Using ALOS-PALSAR Polarimetric Data

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.

Filler size effects on the conductivity of polymer nanocomposites: semiconductive phthalocyanine nanoparticles in epoxy matrices

NARCIS (Netherlands)

Yuan, M.; Brokken-Zijp, J.C.M.; Huijbregts, L.J.; With, de G.

2008-01-01

Three Cobalt(III) phthalocyanine (Phthalcon) powders with different particle sizes and chemical compositions, but almost equal XRD spectra and powder conductivity were synthesized and used as conductive fillers in crosslinked epoxy matrices. Two of these Phthalcons are new compounds. The relation

Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity.

Science.gov (United States)

Chang, Jinyuan; Zheng, Chao; Zhou, Wen-Xin; Zhou, Wen

2017-12-01

In this article, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two-step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic data sets and an human acute lymphoblastic leukemia gene expression data set, we illustrate the performance of the new tests and how they may provide assistance on detecting disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN. © 2017, The International Biometric Society.

On the Kalman Filter error covariance collapse into the unstable subspace

Directory of Open Access Journals (Sweden)

A. Trevisan

2011-03-01

Full Text Available When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N⁺ + N⁰ where N⁺ and N⁰ are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.

VanderLaan Circulant Type Matrices

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Hongyan Pan

2015-01-01

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

Power law deformation of Wishart–Laguerre ensembles of random matrices

International Nuclear Information System (INIS)

Akemann, Gernot; Vivo, Pierpaolo

2008-01-01

We introduce a one-parameter deformation of the Wishart–Laguerre or chiral ensembles of positive definite random matrices with Dyson index β = 1,2 and 4. Our generalized model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size N × M for all three values of β, in terms of the orthogonal polynomials of the standard Wishart–Laguerre ensembles. For large N in a certain double-scaling limit we obtain a generalized Marčenko–Pastur distribution on the macroscopic scale, and a generalized Bessel law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power law tails, where the microscopic limit depends on β and the difference M−N. In the limit where our parameter governing the power law goes to infinity we recover the correlations of the Wishart–Laguerre ensembles. To illustrate these findings, the generalized Marčenko–Pastur distribution is shown to be in very good agreement with empirical data from financial covariance matrices

Colloquium: Random matrices and chaos in nuclear spectra

International Nuclear Information System (INIS)

Papenbrock, T.; Weidenmueller, H. A.

2007-01-01

Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. The question is answered using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification

Approximate joint diagonalization and geometric mean of symmetric positive definite matrices.

Science.gov (United States)

Congedo, Marco; Afsari, Bijan; Barachant, Alexandre; Moakher, Maher

2014-01-01

We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of covariance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations.

Approximate joint diagonalization and geometric mean of symmetric positive definite matrices.

Directory of Open Access Journals (Sweden)

Marco Congedo

Full Text Available We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD matrices and their approximate joint diagonalization (AJD. Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of covariance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations.

Generation of covariance files for the isotopes of Cr, Fe, Ni, Cu, and Pb in ENDF/B-VI

International Nuclear Information System (INIS)

Hetrick, D.M.; Larson, D.C.; Fu, C.Y.

1991-02-01

The considerations that governed the development of the uncertainty files for the isotopes of Cr, Fe, Ni, Cu, and Pb in ENDF/B-VI are summarized. Four different approaches were used in providing the covariance information. Some examples are given which show the standard deviations as a function of incident energy and the corresponding correlation matrices. 11 refs., 5 tabs

Evaluating the effect of neighbourhood weight matrices on smoothing properties of Conditional Autoregressive (CAR models

Directory of Open Access Journals (Sweden)

Ryan Louise

2007-11-01

Full Text Available Abstract Background The Conditional Autoregressive (CAR model is widely used in many small-area ecological studies to analyse outcomes measured at an areal level. There has been little evaluation of the influence of different neighbourhood weight matrix structures on the amount of smoothing performed by the CAR model. We examined this issue in detail. Methods We created several neighbourhood weight matrices and applied them to a large dataset of births and birth defects in New South Wales (NSW, Australia within 198 Statistical Local Areas. Between the years 1995–2003, there were 17,595 geocoded birth defects and 770,638 geocoded birth records with available data. Spatio-temporal models were developed with data from 1995–2000 and their fit evaluated within the following time period: 2001–2003. Results We were able to create four adjacency-based weight matrices, seven distance-based weight matrices and one matrix based on similarity in terms of a key covariate (i.e. maternal age. In terms of agreement between observed and predicted relative risks, categorised in epidemiologically relevant groups, generally the distance-based matrices performed better than the adjacency-based neighbourhoods. In terms of recovering the underlying risk structure, the weight-7 model (smoothing by maternal-age 'Covariate model' was able to correctly classify 35/47 high-risk areas (sensitivity 74% with a specificity of 47%, and the 'Gravity' model had sensitivity and specificity values of 74% and 39% respectively. Conclusion We found considerable differences in the smoothing properties of the CAR model, depending on the type of neighbours specified. This in turn had an effect on the models' ability to recover the observed risk in an area. Prior to risk mapping or ecological modelling, an exploratory analysis of the neighbourhood weight matrix to guide the choice of a suitable weight matrix is recommended. Alternatively, the weight matrix can be chosen a priori

On the regularity of the covariance matrix of a discretized scalar field on the sphere

Energy Technology Data Exchange (ETDEWEB)

Bilbao-Ahedo, J.D. [Departamento de Física Moderna, Universidad de Cantabria, Av. los Castros s/n, 39005 Santander (Spain); Barreiro, R.B.; Herranz, D.; Vielva, P.; Martínez-González, E., E-mail: bilbao@ifca.unican.es, E-mail: barreiro@ifca.unican.es, E-mail: herranz@ifca.unican.es, E-mail: vielva@ifca.unican.es, E-mail: martinez@ifca.unican.es [Instituto de Física de Cantabria (CSIC-UC), Av. los Castros s/n, 39005 Santander (Spain)

2017-02-01

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.

Estimation of genetic connectedness diagnostics based on prediction errors without the prediction error variance-covariance matrix.

Science.gov (United States)

Holmes, John B; Dodds, Ken G; Lee, Michael A

2017-03-02

An important issue in genetic evaluation is the comparability of random effects (breeding values), particularly between pairs of animals in different contemporary groups. This is usually referred to as genetic connectedness. While various measures of connectedness have been proposed in the literature, there is general agreement that the most appropriate measure is some function of the prediction error variance-covariance matrix. However, obtaining the prediction error variance-covariance matrix is computationally demanding for large-scale genetic evaluations. Many alternative statistics have been proposed that avoid the computational cost of obtaining the prediction error variance-covariance matrix, such as counts of genetic links between contemporary groups, gene flow matrices, and functions of the variance-covariance matrix of estimated contemporary group fixed effects. In this paper, we show that a correction to the variance-covariance matrix of estimated contemporary group fixed effects will produce the exact prediction error variance-covariance matrix averaged by contemporary group for univariate models in the presence of single or multiple fixed effects and one random effect. We demonstrate the correction for a series of models and show that approximations to the prediction error matrix based solely on the variance-covariance matrix of estimated contemporary group fixed effects are inappropriate in certain circumstances. Our method allows for the calculation of a connectedness measure based on the prediction error variance-covariance matrix by calculating only the variance-covariance matrix of estimated fixed effects. Since the number of fixed effects in genetic evaluation is usually orders of magnitudes smaller than the number of random effect levels, the computational requirements for our method should be reduced.

AFCI-2.0 Neutron Cross Section Covariance Library

Energy Technology Data Exchange (ETDEWEB)

Herman, M.; Herman, M; Oblozinsky, P.; Mattoon, C.M.; Pigni, M.; Hoblit, S.; Mughabghab, S.F.; Sonzogni, A.; Talou, P.; Chadwick, M.B.; Hale, G.M.; Kahler, A.C.; Kawano, T.; Little, R.C.; Yount, P.G.

2011-03-01

materials and fission products, and 20 actinides. Covariances are given in 33-energy groups, from 10?5 eV to 19.6 MeV, obtained by processing with LANL processing code NJOY using 1/E flux. In addition to these 110 files, the library contains 20 files with nu-bar covariances, 3 files with covariances of prompt fission neutron spectra (238,239,240-Pu), and 2 files with mu-bar covariances (23-Na, 56-Fe). Over the period of three years several working versions of the library have been released and tested by ANL and INL reactor analysts. Useful feedback has been collected allowing gradual improvements of the library. In addition, QA system was developed to check basic properties and features of the whole library, allowing visual inspection of uncertainty and correlations plots, inspection of uncertainties of integral quantities with independent databases, and dispersion of cross sections between major evaluated libraries. The COMMARA-2.0 beta version of the library was released to ANL and INL reactor analysts in October 2010. The final version, described in the present report, was released in March 2011.

AFCI-2.0 Neutron Cross Section Covariance Library

International Nuclear Information System (INIS)

Herman, M.; Oblozinsky, P.; Mattoon, C.M.; Pigni, M.; Hoblit, S.; Mughabghab, S.F.; Sonzogni, A.; Talou, P.; Chadwick, M.B.; Hale, G.M.; Kahler, A.C.; Kawano, T.; Little, R.C.; Yount, P.G.

2011-01-01

structural materials and fission products, and 20 actinides. Covariances are given in 33-energy groups, from 10?5 eV to 19.6 MeV, obtained by processing with LANL processing code NJOY using 1/E flux. In addition to these 110 files, the library contains 20 files with nu-bar covariances, 3 files with covariances of prompt fission neutron spectra (238,239,240-Pu), and 2 files with mu-bar covariances (23-Na, 56-Fe). Over the period of three years several working versions of the library have been released and tested by ANL and INL reactor analysts. Useful feedback has been collected allowing gradual improvements of the library. In addition, QA system was developed to check basic properties and features of the whole library, allowing visual inspection of uncertainty and correlations plots, inspection of uncertainties of integral quantities with independent databases, and dispersion of cross sections between major evaluated libraries. The COMMARA-2.0 beta version of the library was released to ANL and INL reactor analysts in October 2010. The final version, described in the present report, was released in March 2011.

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

Science.gov (United States)

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

2016-10-01

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

COLORED DISSOLVED ORGANIC MATTER (CDOM) CHARACTERIZATION BY ABSORPTION AND FLUORESCENCE SPECTRA

OpenAIRE

Goncalves Araujo, Rafael; Ramirez-Perez, Marta; Kraberg, Alexandra; Piera, Jaume; Bracher, Astrid

2014-01-01

Colored dissolved organic matter (CDOM) absorption and fluorescence spectra were analyzed from samples collected in the Lena River Delta region (Siberia, Russia; summer-2013) and in the Alfacs Bay (Ebro River Delta, Spain; summer-2013/winter-2014) in order to use optical measurements to infer loading and origin of CDOM. Absorbance spectra and Excitation-Emission matrices (EEMs) were obtained with a HORIBA Aqualog® spectrofluorometer. CDOM absorption at 443nm (a443) and terrestrial absorption ...

Estimated 55Mn and 90Zr cross section covariances in the fast neutron energy region

International Nuclear Information System (INIS)

Pigni, M.T.; Herman, M.; Oblozinsky, P.

2008-01-01

We completed estimates of neutron cross section covariances for 55 Mn and 90 Zr, from keV range to 25 MeV, considering the most important reaction channels, total, elastic, inelastic, capture, and (n,2n). The nuclear reaction model code EMPIRE was used to calculate sensitivity to model parameters by perturbation of parameters that define the optical model potential, nuclear level densities and strength of the pre-equilibrium emission. The sensitivity analysis was performed with the set of parameters which reproduces the ENDF/B-VII.0 cross sections. The experimental data were analyzed and both statistical and systematic uncertainties were extracted from almost 30 selected experiments. Then, the Bayesian code KALMAN was used to combine the sensitivity analysis and the experiments to obtain the evaluated covariance matrices

Estimated 55Mn and 90Zr cross section covariances in the fast neutron energy region

Energy Technology Data Exchange (ETDEWEB)

Pigni,M.T.; Herman, M.; Oblozinsky, P.

2008-06-24

We completed estimates of neutron cross section covariances for {sup 55}Mn and {sup 90}Zr, from keV range to 25 MeV, considering the most important reaction channels, total, elastic, inelastic, capture, and (n,2n). The nuclear reaction model code EMPIRE was used to calculate sensitivity to model parameters by perturbation of parameters that define the optical model potential, nuclear level densities and strength of the pre-equilibrium emission. The sensitivity analysis was performed with the set of parameters which reproduces the ENDF/B-VII.0 cross sections. The experimental data were analyzed and both statistical and systematic uncertainties were extracted from almost 30 selected experiments. Then, the Bayesian code KALMAN was used to combine the sensitivity analysis and the experiments to obtain the evaluated covariance matrices.

A heteroskedastic error covariance matrix estimator using a first-order conditional autoregressive Markov simulation for deriving asympotical efficient estimates from ecological sampled Anopheles arabiensis aquatic habitat covariates

Directory of Open Access Journals (Sweden)

Githure John I

2009-09-01

Full Text Available Abstract Background Autoregressive regression coefficients for Anopheles arabiensis aquatic habitat models are usually assessed using global error techniques and are reported as error covariance matrices. A global statistic, however, will summarize error estimates from multiple habitat locations. This makes it difficult to identify where there are clusters of An. arabiensis aquatic habitats of acceptable prediction. It is therefore useful to conduct some form of spatial error analysis to detect clusters of An. arabiensis aquatic habitats based on uncertainty residuals from individual sampled habitats. In this research, a method of error estimation for spatial simulation models was demonstrated using autocorrelation indices and eigenfunction spatial filters to distinguish among the effects of parameter uncertainty on a stochastic simulation of ecological sampled Anopheles aquatic habitat covariates. A test for diagnostic checking error residuals in an An. arabiensis aquatic habitat model may enable intervention efforts targeting productive habitats clusters, based on larval/pupal productivity, by using the asymptotic distribution of parameter estimates from a residual autocovariance matrix. The models considered in this research extends a normal regression analysis previously considered in the literature. Methods Field and remote-sampled data were collected during July 2006 to December 2007 in Karima rice-village complex in Mwea, Kenya. SAS 9.1.4® was used to explore univariate statistics, correlations, distributions, and to generate global autocorrelation statistics from the ecological sampled datasets. A local autocorrelation index was also generated using spatial covariance parameters (i.e., Moran's Indices in a SAS/GIS® database. The Moran's statistic was decomposed into orthogonal and uncorrelated synthetic map pattern components using a Poisson model with a gamma-distributed mean (i.e. negative binomial regression. The eigenfunction

Bayesian source term determination with unknown covariance of measurements

Science.gov (United States)

Belal, Alkomiet; Tichý, Ondřej; Šmídl, Václav

2017-04-01

Determination of a source term of release of a hazardous material into the atmosphere is a very important task for emergency response. We are concerned with the problem of estimation of the source term in the conventional linear inverse problem, y = Mx, where the relationship between the vector of observations y is described using the source-receptor-sensitivity (SRS) matrix M and the unknown source term x. Since the system is typically ill-conditioned, the problem is recast as an optimization problem minR,B(y - Mx)TR-1(y - Mx) + xTB-1x. The first term minimizes the error of the measurements with covariance matrix R, and the second term is a regularization of the source term. There are different types of regularization arising for different choices of matrices R and B, for example, Tikhonov regularization assumes covariance matrix B as the identity matrix multiplied by scalar parameter. In this contribution, we adopt a Bayesian approach to make inference on the unknown source term x as well as unknown R and B. We assume prior on x to be a Gaussian with zero mean and unknown diagonal covariance matrix B. The covariance matrix of the likelihood R is also unknown. We consider two potential choices of the structure of the matrix R. First is the diagonal matrix and the second is a locally correlated structure using information on topology of the measuring network. Since the inference of the model is intractable, iterative variational Bayes algorithm is used for simultaneous estimation of all model parameters. The practical usefulness of our contribution is demonstrated on an application of the resulting algorithm to real data from the European Tracer Experiment (ETEX). This research is supported by EEA/Norwegian Financial Mechanism under project MSMT-28477/2014 Source-Term Determination of Radionuclide Releases by Inverse Atmospheric Dispersion Modelling (STRADI).

A method to construct covariance files in ENDF/B format for criticality safety applications

International Nuclear Information System (INIS)

Naberejnev, D.G.; Smith, D.L.

1999-01-01

Argonne National Laboratory is providing support for a criticality safety analysis project that is being performed at Oak Ridge National Laboratory. The ANL role is to provide the covariance information needed by ORNL for this project. The ENDF/B-V evaluation is being used for this particular criticality analysis. In this evaluation, covariance information for several isotopes or elements of interest to this analysis is either not given or needs to be reconsidered. For some required materials, covariance information does not exist in ENDF/B-V: 233 U, 236 U, Zr, Mg, Gd, and Hf. For others, existing covariance information may need to be re-examined in light of the newer ENDF/B-V evaluation and recent experimental data. In this category are the following materials: 235 U, 238 U, 239 Pu, 240 Pu, 241 Pu, Fe, H, C, N, O, Al, Si, and B. A reasonable estimation of the fractional errors for various evaluated neutron cross sections from ENDF/B-V can be based on the comparisons between the major more recent evaluations including ENDF/B-VI, JENDL3.2, BROND2.2, and JEF2.2, as well as a careful examination of experimental data. A reasonable method to construct correlation matrices is proposed here. Coupling both of these considerations suggests a method to construct covariances files in ENDF/B format that can be used to express uncertainties for specific ENDF/B-V cross sections

Reducing System Artifacts in Hyperspectral Image Data Analysis with the Use of Estimates of the Error Covariance in the Data; TOPICAL

International Nuclear Information System (INIS)

HAALAND, DAVID M.; VAN BENTHEM, MARK H.; WEHLBURG, CHRISTINE M.; KOEHLER, IV FREDERICK W.

2002-01-01

Hyperspectral Fourier transform infrared images have been obtained from a neoprene sample aged in air at elevated temperatures. The massive amount of spectra available from this heterogeneous sample provides the opportunity to perform quantitative analysis of the spectral data without the need for calibration standards. Multivariate curve resolution (MCR) methods with non-negativity constraints applied to the iterative alternating least squares analysis of the spectral data has been shown to achieve the goal of quantitative image analysis without the use of standards. However, the pure-component spectra and the relative concentration maps were heavily contaminated by the presence of system artifacts in the spectral data. We have demonstrated that the detrimental effects of these artifacts can be minimized by adding an estimate of the error covariance structure of the spectral image data to the MCR algorithm. The estimate is added by augmenting the concentration and pure-component spectra matrices with scores and eigenvectors obtained from the mean-centered repeat image differences of the sample. The implementation of augmentation is accomplished by employing efficient equality constraints on the MCR analysis. Augmentation with the scores from the repeat images is found to primarily improve the pure-component spectral estimates while augmentation with the corresponding eigenvectors primarily improves the concentration maps. Augmentation with both scores and eigenvectors yielded the best result by generating less noisy pure-component spectral estimates and relative concentration maps that were largely free from a striping artifact that is present due to system errors in the FT-IR images. The MCR methods presented are general and can also be applied productively to non-image spectral data

Fluctuations of Wigner-type random matrices associated with symmetric spaces of class DIII and CI

Science.gov (United States)

Stolz, Michael

2018-02-01

Wigner-type randomizations of the tangent spaces of classical symmetric spaces can be thought of as ordinary Wigner matrices on which additional symmetries have been imposed. In particular, they fall within the scope of a framework, due to Schenker and Schulz-Baldes, for the study of fluctuations of Wigner matrices with additional dependencies among their entries. In this contribution, we complement the results of these authors by explicit calculations of the asymptotic covariances for symmetry classes DIII and CI and thus obtain explicit CLTs for these classes. On the technical level, the present work is an exercise in controlling the cumulative effect of systematically occurring sign factors in an involved sum of products by setting up a suitable combinatorial model for the summands. This aspect may be of independent interest. Research supported by Deutsche Forschungsgemeinschaft (DFG) via SFB 878.

HSQC-1,n-ADEQUATE: a new approach to long-range 13C-13C correlation by covariance processing.

Science.gov (United States)

Martin, Gary E; Hilton, Bruce D; Willcott, M Robert; Blinov, Kirill A

2011-10-01

Long-range, two-dimensional heteronuclear shift correlation NMR methods play a pivotal role in the assembly of novel molecular structures. The well-established GHMBC method is a high-sensitivity mainstay technique, affording connectivity information via (n)J(CH) coupling pathways. Unfortunately, there is no simple way of determining the value of n and hence no way of differentiating two-bond from three- and occasionally four-bond correlations. Three-bond correlations, however, generally predominate. Recent work has shown that the unsymmetrical indirect covariance or generalized indirect covariance processing of multiplicity edited GHSQC and 1,1-ADEQUATE spectra provides high-sensitivity access to a (13)C-(13) C connectivity map in the form of an HSQC-1,1-ADEQUATE spectrum. Covariance processing of these data allows the 1,1-ADEQUATE connectivity information to be exploited with the inherent sensitivity of the GHSQC spectrum rather than the intrinsically lower sensitivity of the 1,1-ADEQUATE spectrum itself. Data acquisition times and/or sample size can be substantially reduced when covariance processing is to be employed. In an extension of that work, 1,n-ADEQUATE spectra can likewise be subjected to covariance processing to afford high-sensitivity access to the equivalent of (4)J(CH) GHMBC connectivity information. The method is illustrated using strychnine as a model compound. Copyright © 2011 John Wiley & Sons, Ltd.

Infinite matrices and sequence spaces

CERN Document Server

Cooke, Richard G

2014-01-01

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

High PEC conversion efficiencies from CuSe film electrodes modified with metalloporphyrin/polyethylene matrices

International Nuclear Information System (INIS)

Zyoud, Ahed; Al-Kerm, Rola S.; Al-Kerm, Rana S.; Waseem, Mansur; Mohammed, H.S. Helal; Park, DaeHoon; Campet, Guy; Sabli, Nordin; Hilal, Hikmat S.

2015-01-01

Enhancement of hole-transfer across CuSe electrode/liquid junction can be facilitated by coating with metalloporphyrin complexes embedded inside polyethylene matrices. - Highlights: • CuSe films were electrochemically deposited onto FTO/Glass • Annealing CuSe film electrodes enhanced PEC characteristics • PEC characteristics were further enhanced by metalloporphyrin/polyethylene matrices, yielding ∼15% efficiency • Matrix behavior as charge transfer mediator enhanced electrode conversion efficiency and stability - Abstract: Electrodeposited CuSe film electrodes have been prepared onto FTO/glass by a facile method based on earlier methods described for other systems. The films were characterized, modified by annealing and further characterized. The films were then modified by coating with tetra(-4-pyridyl) pophyrinato-manganese (MnTPyP) complexes embedded inside commercial polyethylene (PE) matrices. The effects of modifications on different film properties, such as X-ray diffraction (XRD) patterns, surface morphology, photoluminescence (PL) spectra and electronic absorption spectra were investigated. Compared with other thin film electrode systems, very high photoelectrochemical (PEC) conversion efficiency values have been observed here. Pre-annealing the CuSe films at 150°C for 2 h, followed by attaching the MnTPyP/PE matrices remarkably enhanced their PEC characteristics. The conversion efficiency was significantly enhanced, from less than 1.0% to more than 15%. Fill factor (FF) was also enhanced from ∼30% to ∼80%. Values of open-circuit potential (V OC ) and short-circuit current (J SC ) were significantly enhanced. While annealing affects uniformity, particle inter-connection and surface texture of the CuSe films, the MnTPyP complex species behaves as an additional charge-transfer mediator across the film/electrolyte junction. Optimization of PEC characteristics, using different deposition times, different annealing temperatures, different

Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices

Czech Academy of Sciences Publication Activity Database

Hnětynková, Iveta; Plešinger, M.

2015-01-01

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

Interstellar matrices: the chemical composition and evolution of interstellar ices as observed by ISO.

Science.gov (United States)

d'Hendecourt, L; Dartois, E

2001-03-15

Matrix isolation techniques have been developed in the early sixties as a tool for studying the spectroscopic properties of out of equilibrium species (atoms, radicals, ions, reactive molecules), embedded in rare gas inert matrices at low temperatures. Cold interstellar grains surfaces are able to condense out gas phase molecules, routinely observed by radioastronomy. These grain 'mantles' can be considered as 'interstellar matrices'. However, these matrices are not clean and unreactive. They are made principally of dirty ices whose composition must be determined carefully to assess the importance of the solid state chemistry that takes place in the Interstellar Medium. Infrared spectroscopy, both in astronomy and in the laboratory, is the unique tool to determine the chemical composition of these ices. Astronomical spectra can directly be compared with laboratory ones obtained using classical matrix isolation techniques. Furthermore, dedicated experiments may be undertaken to further improve the understanding of the basic physico-chemical processes that take place in cosmic ices.

Composite glycerol/graphite/aromatic acid matrices for thin-layer chromatography/matrix-assisted laser desorption/ionization mass spectrometry of heterocyclic compounds.

Science.gov (United States)

Esparza, Cesar; Borisov, R S; Varlamov, A V; Zaikin, V G

2016-10-28

New composite matrices have been suggested for the analysis of mixtures of different synthetic organic compounds (N-containing heterocycles and erectile dysfunction drugs) by thin layer chromatography/matrix-assisted laser desorption ionization time-of-flight mass spectrometry (TLC/MALDI-TOF). Different mixtures of classical MALDI matrices and graphite particles dispersed in glycerol were used for the registration of MALDI mass spectra directly from TLC plates after analytes separation. In most of cases, the mass spectra possessed [M+H] + ions; however, for some analytes only [M+Na] + and [M+K] + ions were observed. These ions have been used to generate visualized TLC chromatograms. The described approach increases the desorption/ionization efficiencies of analytes separated by TLC, prevent spot blurring, simplifies and decrease time for sample preparation. Copyright © 2016 Elsevier B.V. All rights reserved.

Evaluation of an on-line methodology for measuring volatile organic compounds (VOC) fluxes by eddy-covariance with a PTR-TOF-Qi-MS

Science.gov (United States)

Loubet, Benjamin; Buysse, Pauline; Lafouge, Florence; Ciuraru, Raluca; Decuq, Céline; Zurfluh, Olivier

2017-04-01

Field scale flux measurements of volatile organic compounds (VOC) are essential for improving our knowledge of VOC emissions from ecosystems. Many VOCs are emitted from and deposited to ecosystems. Especially less known, are crops which represent more than 50% of French terrestrial surfaces. In this study, we evaluate a new on-line methodology for measuring VOC fluxes by Eddy Covariance with a PTR-Qi-TOF-MS. Measurements were performed at the ICOS FR-GRI site over a crop using a 30 m long high flow rate sampling line and an ultrasonic anemometer. A Labview program was specially designed for acquisition and on-line covariance calculation: Whole mass spectra ( 240000 channels) were acquired on-line at 10 Hz and stored in a temporary memory. Every 5 minutes, the spectra were mass-calibrated and normalized by the primary ion peak integral at 10 Hz. The mass spectra peaks were then retrieved from the 5-min averaged spectra by withdrawing the baseline, determining the resolution and using a multiple-peak detection algorithm. In order to optimize the peak detection algorithm for the covariance, we determined the covariances as the integrals of the peaks of the vertical-air-velocity-fluctuation weighed-averaged-spectra. In other terms, we calculate , were w is the vertical component of the air velocity, Sp is the spectra, t is time, lag is the decorrelation lag time and denotes an average. The lag time was determined as the decorrelation time between w and the primary ion (at mass 21.022) which integrates the contribution of all reactions of VOC and water with the primary ion. Our algorithm was evaluated by comparing the exchange velocity of water vapor measured by an open path absorption spectroscopy instrument and the water cluster measured with the PTRQi-TOF-MS. The influence of the algorithm parameters and lag determination is discussed. This study was supported by the ADEME-CORTEA COV3ER project (http://www6.inra.fr/cov3er).

A Small Guide to Generating Covariances of Experimental Data

International Nuclear Information System (INIS)

Mannhart, Wolf

2011-05-01

A complete description of the uncertainties of an experiment can only be realized by a detailed list of all the uncertainty components, their value and a specification of existing correlations between the data. Based on such information the covariance matrix can be generated, which is necessary for any further proceeding with the experimental data. It is not necessary, and not recommended, that an experimenter evaluates this covariance matrix. The reason for this is that a incorrectly evaluated final covariance matrix can never be corrected if the details are not given. (Such obviously wrong covariance matrices have recently occasionally been found in the literature). Hence quotation of a covariance matrix is an additional step which should not occur without quoting a detailed list of the various uncertainty components and their correlations as well. It must be hoped that editors of journals will understand these necessary requirements. The generalized least squares procedure shown permits an easy way of interchanging data D 0 with parameter estimates P. This means new data can easily be combined with an earlier evaluation. However, it must be mentioned that this is only valid as long as the new data have no correlation with any of the older data of the prior evaluation. Otherwise the old data which show correlation with new data have to be extracted from the evaluation and then, together with the new data and taking account of the correlation, have again to be added to the reduced evaluation. In most cases this step cannot be performed and the evaluation has to be completely redone. A partial way out is given if the evaluation is performed step by step and the results of each step are stored. Then the evaluation need only be repeated from the step which contains correlated data for the first time while all earlier steps remain unchanged. Finally it should be noted that the addition of a small set of new data to a prior evaluation consisting of a large number of

On reflectionless equi-transmitting matrices

Directory of Open Access Journals (Sweden)

Pavel Kurasov

2014-01-01

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

Dispersion curve estimation via a spatial covariance method with ultrasonic wavefield imaging.

Science.gov (United States)

Chong, See Yenn; Todd, Michael D

2018-05-01

Numerous Lamb wave dispersion curve estimation methods have been developed to support damage detection and localization strategies in non-destructive evaluation/structural health monitoring (NDE/SHM) applications. In this paper, the covariance matrix is used to extract features from an ultrasonic wavefield imaging (UWI) scan in order to estimate the phase and group velocities of S0 and A0 modes. A laser ultrasonic interrogation method based on a Q-switched laser scanning system was used to interrogate full-field ultrasonic signals in a 2-mm aluminum plate at five different frequencies. These full-field ultrasonic signals were processed in three-dimensional space-time domain. Then, the time-dependent covariance matrices of the UWI were obtained based on the vector variables in Cartesian and polar coordinate spaces for all time samples. A spatial covariance map was constructed to show spatial correlations within the full wavefield. It was observed that the variances may be used as a feature for S0 and A0 mode properties. The phase velocity and the group velocity were found using a variance map and an enveloped variance map, respectively, at five different frequencies. This facilitated the estimation of Lamb wave dispersion curves. The estimated dispersion curves of the S0 and A0 modes showed good agreement with the theoretical dispersion curves. Copyright © 2018 Elsevier B.V. All rights reserved.

Covariant Transform

OpenAIRE

Kisil, Vladimir V.

2010-01-01

The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. Covariant transform extends an applicability of the popular wavelets construction to classic examples like the Hardy space H_2, Banach spaces, covariant functional calculus and many others. Keywords: Wavelets, cohe...

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

Are your covariates under control? How normalization can re-introduce covariate effects.

Science.gov (United States)

Pain, Oliver; Dudbridge, Frank; Ronald, Angelica

2018-04-30

Many statistical tests rely on the assumption that the residuals of a model are normally distributed. Rank-based inverse normal transformation (INT) of the dependent variable is one of the most popular approaches to satisfy the normality assumption. When covariates are included in the analysis, a common approach is to first adjust for the covariates and then normalize the residuals. This study investigated the effect of regressing covariates against the dependent variable and then applying rank-based INT to the residuals. The correlation between the dependent variable and covariates at each stage of processing was assessed. An alternative approach was tested in which rank-based INT was applied to the dependent variable before regressing covariates. Analyses based on both simulated and real data examples demonstrated that applying rank-based INT to the dependent variable residuals after regressing out covariates re-introduces a linear correlation between the dependent variable and covariates, increasing type-I errors and reducing power. On the other hand, when rank-based INT was applied prior to controlling for covariate effects, residuals were normally distributed and linearly uncorrelated with covariates. This latter approach is therefore recommended in situations were normality of the dependent variable is required.

Computer code ENDSAM for random sampling and validation of the resonance parameters covariance matrices of some major nuclear data libraries

International Nuclear Information System (INIS)

Plevnik, Lucijan; Žerovnik, Gašper

2016-01-01

Highlights: • Methods for random sampling of correlated parameters. • Link to open-source code for sampling of resonance parameters in ENDF-6 format. • Validation of the code on realistic and artificial data. • Validation of covariances in three major contemporary nuclear data libraries. - Abstract: Methods for random sampling of correlated parameters are presented. The methods are implemented for sampling of resonance parameters in ENDF-6 format and a link to the open-source code ENDSAM is given. The code has been validated on realistic data. Additionally, consistency of covariances of resonance parameters of three major contemporary nuclear data libraries (JEFF-3.2, ENDF/B-VII.1 and JENDL-4.0u2) has been checked.

Structural and Thermal Studies of ZnS and CdS Nanoparticles in Polymer Matrices

OpenAIRE

Osuntokun, Jejenija; Ajibade, Peter A.

2016-01-01

We report the synthesis and structural studies of ZnS and CdS nanoparticles in polyvinylpyrrolidone (PVP), poly(vinyl alcohol) (PVA), and poly(methyl methacrylate) (PMMA) matrices. The metal sulfides/polymer nanocomposites were characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy, electronic spectroscopy (UV-Vis), transmission electron microscopy (TEM), and thermogravimetric analysis (TGA). The particle sizes as calculated from the absorption spectra were in agree...

Covariance evaluation system

International Nuclear Information System (INIS)

Kawano, Toshihiko; Shibata, Keiichi.

1997-09-01

A covariance evaluation system for the evaluated nuclear data library was established. The parameter estimation method and the least squares method with a spline function are used to generate the covariance data. Uncertainties of nuclear reaction model parameters are estimated from experimental data uncertainties, then the covariance of the evaluated cross sections is calculated by means of error propagation. Computer programs ELIESE-3, EGNASH4, ECIS, and CASTHY are used. Covariances of 238 U reaction cross sections were calculated with this system. (author)

Structure of radicals produced by γ radiolysis. Part 4. Adamantane matrices doped with various 5-membered heterocyclic molecules

International Nuclear Information System (INIS)

Winters, D.L.; Ling, A.C.

1976-01-01

The effects of γ-radiolysis at room temperature on adamantane and adamantane-d 16 matrices doped with 5-membered heterocyclic molecules has been examined by X-band electron spin resonance (esr) spectrometry. Radical structures formed from heterocyclic solute molecules are discussed and tentative assignments made. Discussion of possible radical structures derived from selected heterocyclic compounds is included, but unambiguous assignmens of structure cannot be made for these compounds from the esr data obtained. It was noted that perdeuterated adamantane matrices provided superior resolution for esr spectra derived from radicals with a delocalized spin center such as allyl or allenyl species. (author)

Quarkonia and heavy-light mesons in a covariant quark model

Directory of Open Access Journals (Sweden)

Leitão Sofia

2016-01-01

Full Text Available Preliminary calculations using the Covariant Spectator Theory (CST employed a scalar linear confining interaction and an additional constant vector potential to compute the mesonic mass spectra. In this work we generalize the confining interaction to include more general structures, in particular a vector and also a pseudoscalar part, as suggested by a recent study [1]. A one-gluon-exchange kernel is also implemented to describe the short-range part of the interaction. We solve the simplest CST approximation to the complete Bethe-Salpeter equation, the one-channel spectator equation, using a numerical technique that eliminates all singularities from the kernel. The parameters of the model are determined through a fit to the experimental pseudoscalar meson spectra, with a good agreement for both quarkonia and heavy-light states.

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

Science.gov (United States)

Waller, Niels G

2016-01-01

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

On the algebraic structure of covariant anomalies and covariant Schwinger terms

International Nuclear Information System (INIS)

Kelnhofer, G.

1992-01-01

A cohomological characterization of covariant anomalies and covariant Schwinger terms in an anomalous Yang-Mills theory is formulated and w ill be geometrically interpreted. The BRS and anti-BRS transformations are defined as purely differential geometric objects. Finally the covariant descent equations are formulated within this context. (author)

Adjustment of the 235U Fission Spectrum

International Nuclear Information System (INIS)

GRIFFIN, PATRICK J.; WILLIAMS, J.G.

1999-01-01

The latest nuclear data are used to examine the sensitivity of the least squares adjustment of the 235 U fission spectrum to the measured reaction rates, dosimetry cross sections, and prior spectrum covariance matrix. All of these parameters were found to be very important in the spectrum adjustment. The most significant deficiency in the nuclear data is the absence of a good prior covariance matrix. Covariance matrices generated from analytic models of the fission spectra have been used in the past. This analysis reveals some unusual features in the covariance matrix produced with this approach. Specific needs are identified for improved nuclear data to better determine the 235 U spectrum. An improved 235 U covariance matrix and adjusted spectrum are recommended for use in radiation transport sensitivity analyses

A class of covariate-dependent spatiotemporal covariance functions

Science.gov (United States)

Reich, Brian J; Eidsvik, Jo; Guindani, Michele; Nail, Amy J; Schmidt, Alexandra M.

2014-01-01

In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in the correlation structure. Therefore, it has been of prolonged interest in the literature to provide flexible and effective ways to model non-stationarity in the spatial effects. Arguably, due to the local nature of the problem, we might envision that the correlation structure would be highly dependent on local characteristics of the domain of study, namely the latitude, longitude and altitude of the observation sites, as well as other locally defined covariate information. In this work, we provide a flexible and computationally feasible way for allowing the correlation structure of the underlying processes to depend on local covariate information. We discuss the properties of the induced covariance functions and discuss methods to assess its dependence on local covariate information by means of a simulation study and the analysis of data observed at ozone-monitoring stations in the Southeast United States. PMID:24772199

Double stochastic matrices in quantum mechanics

International Nuclear Information System (INIS)

Louck, J.D.

1997-01-01

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

ENDF-6 File 30: Data covariances obtained from parameter covariances and sensitivities

International Nuclear Information System (INIS)

Muir, D.W.

1989-01-01

File 30 is provided as a means of describing the covariances of tabulated cross sections, multiplicities, and energy-angle distributions that result from propagating the covariances of a set of underlying parameters (for example, the input parameters of a nuclear-model code), using an evaluator-supplied set of parameter covariances and sensitivities. Whenever nuclear data are evaluated primarily through the application of nuclear models, the covariances of the resulting data can be described very adequately, and compactly, by specifying the covariance matrix for the underlying nuclear parameters, along with a set of sensitivity coefficients giving the rate of change of each nuclear datum of interest with respect to each of the model parameters. Although motivated primarily by these applications of nuclear theory, use of File 30 is not restricted to any one particular evaluation methodology. It can be used to describe data covariances of any origin, so long as they can be formally separated into a set of parameters with specified covariances and a set of data sensitivities

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

Science.gov (United States)

Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen

2013-01-01

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588

Matrices and linear transformations

CERN Document Server

Cullen, Charles G

1990-01-01

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

Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization.

Science.gov (United States)

Brier, Matthew R; Mitra, Anish; McCarthy, John E; Ances, Beau M; Snyder, Abraham Z

2015-11-01

Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a complicated covariance structure. Partial covariance assesses the unique variance shared between two brain regions excluding any widely shared variance, hence is appropriate for the analysis of multivariate fMRI datasets. However, calculation of partial covariance requires inversion of the covariance matrix, which, in most functional connectivity studies, is not invertible owing to rank deficiency. Here we apply Ledoit-Wolf shrinkage (L2 regularization) to invert the high dimensional BOLD covariance matrix. We investigate the network organization and brain-state dependence of partial covariance-based functional connectivity. Although RSNs are conventionally defined in terms of shared variance, removal of widely shared variance, surprisingly, improved the separation of RSNs in a spring embedded graphical model. This result suggests that pair-wise unique shared variance plays a heretofore unrecognized role in RSN covariance organization. In addition, application of partial correlation to fMRI data acquired in the eyes open vs. eyes closed states revealed focal changes in uniquely shared variance between the thalamus and visual cortices. This result suggests that partial correlation of resting state BOLD time series reflect functional processes in addition to structural connectivity. Copyright © 2015 Elsevier Inc. All rights reserved.

Brownian distance covariance

OpenAIRE

Székely, Gábor J.; Rizzo, Maria L.

2010-01-01

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero if and only if the random vectors are independent. The notion of covariance with...

A random matrix approach to VARMA processes

International Nuclear Information System (INIS)

Burda, Zdzislaw; Jarosz, Andrzej; Nowak, Maciej A; Snarska, Malgorzata

2010-01-01

We apply random matrix theory to derive the spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q 1 , q 2 ) processes. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N/T is fixed. In this regime, the underlying random matrices are asymptotically equivalent to free random variables (FRV). We apply the FRV calculus to calculate the eigenvalue density of the sample covariance for several VARMA-type processes. We explicitly solve the VARMA(1, 1) case and demonstrate perfect agreement between the analytical result and the spectra obtained by Monte Carlo simulations. The proposed method is purely algebraic and can be easily generalized to q 1 >1 and q 2 >1.

Lambda-matrices and vibrating systems

CERN Document Server

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

1966-01-01

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

Manin matrices and Talalaev's formula

International Nuclear Information System (INIS)

Chervov, A; Falqui, G

2008-01-01

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

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

Science.gov (United States)

Zhang, Ying-Ying; Yang, Cai; Zhang, Ping

2017-05-01

In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.

Covariant representations of nuclear *-algebras

International Nuclear Information System (INIS)

Moore, S.M.

1978-01-01

Extensions of the Csup(*)-algebra theory for covariant representations to nuclear *-algebra are considered. Irreducible covariant representations are essentially unique, an invariant state produces a covariant representation with stable vacuum, and the usual relation between ergodic states and covariant representations holds. There exist construction and decomposition theorems and a possible relation between derivations and covariant representations

MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD

Directory of Open Access Journals (Sweden)

N. A. Balonin

2014-05-01

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

Earth Observing System Covariance Realism

Science.gov (United States)

Zaidi, Waqar H.; Hejduk, Matthew D.

2016-01-01

The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.

Structural and Thermal Studies of ZnS and CdS Nanoparticles in Polymer Matrices

Directory of Open Access Journals (Sweden)

Jejenija Osuntokun

2016-01-01

Full Text Available We report the synthesis and structural studies of ZnS and CdS nanoparticles in polyvinylpyrrolidone (PVP, poly(vinyl alcohol (PVA, and poly(methyl methacrylate (PMMA matrices. The metal sulfides/polymer nanocomposites were characterized by X-ray diffraction (XRD, Fourier transform infrared spectroscopy, electronic spectroscopy (UV-Vis, transmission electron microscopy (TEM, and thermogravimetric analysis (TGA. The particle sizes as calculated from the absorption spectra were in agreement with the results obtained from TEM and XRD data. They showed metal sulfides nanoparticles in the polymers matrices with average crystallite sizes of 1.5–6.9 nm. The TGA results indicate that incorporation of the nanoparticles significantly altered the thermal properties of the respective polymers with ZnS/PVA and CdS/PVA nanocomposites displaying higher thermal stability than the other polymer nanocomposites.

Intrinsic character of Stokes matrices

Science.gov (United States)

Gagnon, Jean-François; Rousseau, Christiane

2017-02-01

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

Hierarchical matrices algorithms and analysis

CERN Document Server

Hackbusch, Wolfgang

2015-01-01

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

Special matrices of mathematical physics stochastic, circulant and Bell matrices

CERN Document Server

Aldrovandi, R

2001-01-01

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

Covariant field equations in supergravity

Energy Technology Data Exchange (ETDEWEB)

Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)

2017-12-15

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Covariant field equations in supergravity

International Nuclear Information System (INIS)

Vanhecke, Bram; Proeyen, Antoine van

2017-01-01

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Complete super-sample lensing covariance in the response approach

Science.gov (United States)

Barreira, Alexandre; Krause, Elisabeth; Schmidt, Fabian

2018-06-01

We derive the complete super-sample covariance (SSC) of the matter and weak lensing convergence power spectra using the power spectrum response formalism to accurately describe the coupling of super- to sub-survey modes. The SSC term is completely characterized by the survey window function, the nonlinear matter power spectrum and the full first-order nonlinear power spectrum response function, which describes the response to super-survey density and tidal field perturbations. Generalized separate universe simulations can efficiently measure these responses in the nonlinear regime of structure formation, which is necessary for lensing applications. We derive the lensing SSC formulae for two cases: one under the Limber and flat-sky approximations, and a more general one that goes beyond the Limber approximation in the super-survey mode and is valid for curved sky applications. Quantitatively, we find that for sky fractions fsky ≈ 0.3 and a single source redshift at zS=1, the use of the flat-sky and Limber approximation underestimates the total SSC contribution by ≈ 10%. The contribution from super-survey tidal fields to the lensing SSC, which has not been included in cosmological analyses so far, is shown to represent about 5% of the total lensing covariance on multipoles l1,l2 gtrsim 300. The SSC is the dominant off-diagonal contribution to the total lensing covariance, making it appropriate to include these tidal terms and beyond flat-sky/Limber corrections in cosmic shear analyses.

A special covariance structure for random coefficient models with both between and within covariates

International Nuclear Information System (INIS)

Riedel, K.S.

1990-07-01

We review random coefficient (RC) models in linear regression and propose a bias correction to the maximum likelihood (ML) estimator. Asymmptotic expansion of the ML equations are given when the between individual variance is much larger or smaller than the variance from within individual fluctuations. The standard model assumes all but one covariate varies within each individual, (we denote the within covariates by vector χ 1 ). We consider random coefficient models where some of the covariates do not vary in any single individual (we denote the between covariates by vector χ 0 ). The regression coefficients, vector β k , can only be estimated in the subspace X k of X. Thus the number of individuals necessary to estimate vector β and the covariance matrix Δ of vector β increases significantly in the presence of more than one between covariate. When the number of individuals is sufficient to estimate vector β but not the entire matrix Δ , additional assumptions must be imposed on the structure of Δ. A simple reduced model is that the between component of vector β is fixed and only the within component varies randomly. This model fails because it is not invariant under linear coordinate transformations and it can significantly overestimate the variance of new observations. We propose a covariance structure for Δ without these difficulties by first projecting the within covariates onto the space perpendicular to be between covariates. (orig.)

Media effects on the optical absorption spectra of silver clusters embedded in rara gas matrices

International Nuclear Information System (INIS)

Fedrigo, S.; Harbich, W.; Buttet, J.

1993-01-01

The optical absorption of small mass selected Ag n -clusters (n=7, 11, 15, 21) embedded in solid Ar, Kr and Xe has been measured. The absorption spectra show 1 to 3 major peaks between 3 and 4.5 eV, depending on the cluster size. Changing the matrix gas Ar→Kr→Xe induces a redshift which is comparable for all sizes studied and does not affect the main structure of the absorption spectra. We propose a scheme to estimate the gas phase value of the absorption energies which is in fair agreement with an estimation obtained by a simple model based on a Drude metal. (author). 10 refs, 2 figs

Covariant w∞ gravity

NARCIS (Netherlands)

Bergshoeff, E.; Pope, C.N.; Stelle, K.S.

1990-01-01

We discuss the notion of higher-spin covariance in w∞ gravity. We show how a recently proposed covariant w∞ gravity action can be obtained from non-chiral w∞ gravity by making field redefinitions that introduce new gauge-field components with corresponding new gauge transformations.

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

Energy Technology Data Exchange (ETDEWEB)

Wagner, C.

1996-12-31

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

The nature of trapping sites and recombination centres in PVK and PVK-PBD electroluminescent matrices seen by spectrally resolved thermoluminescence

International Nuclear Information System (INIS)

Glowacki, Ireneusz; Szamel, Zbigniew

2010-01-01

Two electroluminescent polymer matrices poly(N-vinylcarbazole) (PVK) and PVK with 40 wt% of 2-tert-butylphenyl-5-biphenyl-1,3,4-oxadiazole (PBD) were studied using spectrally resolved thermoluminescence (SRTL) in the temperature range 15-325 K. The comparison of the SRTL results with the electroluminescence (EL) spectra has allowed identification of the localized (trapping) sites and the radiative recombination centres present in the investigated matrices. In the neat PVK films deep traps with a depth about 200 meV, related to triplet excimers dominate, while in the PVK-PBD (40 wt%) blend films the traps that are related to triplet exciplexes formed by the carbazole groups and the PBD molecules dominate. Depth of the traps in the PVK-PBD blend is somewhat lower than that in the neat PVK. An analysis of the EL spectra shows that in the PVK and in the PVK-PBD blend the dominant radiative centres are singlet excimers and singlet exciplexes, respectively. However, in the neat PVK some contributions of the triplet monomer and the triplet excimer states in the EL were also detected.

Thinking outside the box: effects of modes larger than the survey on matter power spectrum covariance

International Nuclear Information System (INIS)

Putter, Roland de; Wagner, Christian; Verde, Licia; Mena, Olga; Percival, Will J.

2012-01-01

Accurate power spectrum (or correlation function) covariance matrices are a crucial requirement for cosmological parameter estimation from large scale structure surveys. In order to minimize reliance on computationally expensive mock catalogs, it is important to have a solid analytic understanding of the different components that make up a covariance matrix. Considering the matter power spectrum covariance matrix, it has recently been found that there is a potentially dominant effect on mildly non-linear scales due to power in modes of size equal to and larger than the survey volume. This beat coupling effect has been derived analytically in perturbation theory and while it has been tested with simulations, some questions remain unanswered. Moreover, there is an additional effect of these large modes, which has so far not been included in analytic studies, namely the effect on the estimated average density which enters the power spectrum estimate. In this article, we work out analytic, perturbation theory based expressions including both the beat coupling and this local average effect and we show that while, when isolated, beat coupling indeed causes large excess covariance in agreement with the literature, in a realistic scenario this is compensated almost entirely by the local average effect, leaving only ∼ 10% of the excess. We test our analytic expressions by comparison to a suite of large N-body simulations, using both full simulation boxes and subboxes thereof to study cases without beat coupling, with beat coupling and with both beat coupling and the local average effect. For the variances, we find excellent agreement with the analytic expressions for k −1 at z = 0.5, while the correlation coefficients agree to beyond k = 0.4 hMpc −1 . As expected, the range of agreement increases towards higher redshift and decreases slightly towards z = 0. We finish by including the large-mode effects in a full covariance matrix description for arbitrary survey

Introduction to matrices and vectors

CERN Document Server

Schwartz, Jacob T

2001-01-01

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

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

Science.gov (United States)

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

2015-03-19

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

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

Science.gov (United States)

Zhang, Ying-Ying; Yang, Cai; Zhang, Ping

2017-08-01

In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.

Evaluation and processing of covariance data

International Nuclear Information System (INIS)

Wagner, M.

1993-01-01

These proceedings of a specialists'meeting on evaluation and processing of covariance data is divided into 4 parts bearing on: part 1- Needs for evaluated covariance data (2 Papers), part 2- generation of covariance data (15 Papers), part 3- Processing of covariance files (2 Papers), part 4-Experience in the use of evaluated covariance data (2 Papers)

Effortless assignment with 4D covariance sequential correlation maps.

Science.gov (United States)

Harden, Bradley J; Mishra, Subrata H; Frueh, Dominique P

2015-11-01

Traditional Nuclear Magnetic Resonance (NMR) assignment procedures for proteins rely on preliminary peak-picking to identify and label NMR signals. However, such an approach has severe limitations when signals are erroneously labeled or completely neglected. The consequences are especially grave for proteins with substantial peak overlap, and mistakes can often thwart entire projects. To overcome these limitations, we previously introduced an assignment technique that bypasses traditional pick peaking altogether. Covariance Sequential Correlation Maps (COSCOMs) transform the indirect connectivity information provided by multiple 3D backbone spectra into direct (H, N) to (H, N) correlations. Here, we present an updated method that utilizes a single four-dimensional spectrum rather than a suite of three-dimensional spectra. We demonstrate the advantages of 4D-COSCOMs relative to their 3D counterparts. We introduce improvements accelerating their calculation. We discuss practical considerations affecting their quality. And finally we showcase their utility in the context of a 52 kDa cyclization domain from a non-ribosomal peptide synthetase. Copyright © 2015 Elsevier Inc. All rights reserved.

Covariance data processing code. ERRORJ

International Nuclear Information System (INIS)

Kosako, Kazuaki

2001-01-01

The covariance data processing code, ERRORJ, was developed to process the covariance data of JENDL-3.2. ERRORJ has the processing functions of covariance data for cross sections including resonance parameters, angular distribution and energy distribution. (author)

Pathological rate matrices: from primates to pathogens

Directory of Open Access Journals (Sweden)

Knight Rob

2008-12-01

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

Configuration of organic dye excimers in nanoporous SiO2 matrices

International Nuclear Information System (INIS)

Sorokin, A.V.; Gnap, B.A.; Bespalova, I.I.; Yefimova, S.L.; Malyukin, Yu.V.

2016-01-01

The effect of cyanine dye 3,3′-dioctadecyloxacarbocyanine perchlorate (DiO) and benzimidazole dye 4-dimethylamino-1,8-naphthoylene-1′,2′-benzimidazole (DNBI) accumulation in nanoporous silica matrices on the dyes luminescence properties has been studied. For both dyes, ground state dimer formation with perpendicular transition dipoles at high dye concentrations has been considered as a result of restricted geometry of the nanoscale pores. The dimer excitation leads to excimer formation revealing by appearance of new long-wavelength luminescence band and shortening the dye luminescence lifetime. In the excimer luminescence excitation spectra two additional bands have been observed, one of which is bathochromically shifted relatively to the absorption band and another one is hypsocromically shifted. Using the Kasha exciton model it was shown that the excimers possess oblique transition dipoles configuration. - Highlights: • Organic dye molecules are efficiently accumulated in nanoporous silica matrices. • Restricted geometry of SiO 2 nanopores provokes excimerization of both cyanine and benzimidazole dyes. • The excimers reveal configuration of oblique dimers. • The excimers are originated from ground state dimers with a perpendicular arrangement of transition dipoles.

NOTES ON OPTIMAL ALLOCATION FOR FIXED SIZE CONFIDENCE REGIONS OF THE DIFFERENCE OF TWO MULTINORMAL MEANS

OpenAIRE

Hyakutake, Hiroto; Kawasaki, Hidefumi

2004-01-01

We consider the problem of constructing a fixed-size confidence region of the difference of two multinormal means when the covariance matrices have intraclass correlation structure. When the covariance matrices are known, we derive an optimal allocation. A two-stage procedure is given for the problem with unknown covariance matrices.

Determination of neutron spectra using the programs GNSR and SPECTRIX

International Nuclear Information System (INIS)

Weyrauch, M.; Dietz, E.; Matzke, M.

2002-01-01

We describe the capabilities and the application of two computer programs, which have been developed in order to facilitate common tasks in neutron spectrometry: GNSR (calculation of response matrices) and SPECTRIX (unfolding). Gas-filled Neutron Spectrometer Response calculates response functions and response matrices of various gas-filled neutron detectors. It can be configured to accommodate the appropriate gas-fillings and supports a number of different neutron beam configurations with a possibility to input calculated or measured neutron beam spectra. The program includes graphical capabilities as well as a context-sensitive help system. SPECTRIX implements several unfolding algorithms as well as support algorithms for unfolding and includes graphics capabilities and context-sensitive help. We apply both programs to a specific example: calculation of the response matrix of a 3 He detector and unfolding of the neutron spectrum of a thick accelerator target using the calculated response matrix

Covariance Bell inequalities

Science.gov (United States)

Pozsgay, Victor; Hirsch, Flavien; Branciard, Cyril; Brunner, Nicolas

2017-12-01

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities is their nonlinearity; this has nontrivial consequences for the derivation of their local bound, which is not reached by deterministic local correlations. For our simplest inequality, we derive analytically tight bounds for both local and quantum correlations. An interesting application of covariance Bell inequalities is that they can act as "shared randomness witnesses": specifically, the value of the Bell expression gives device-independent lower bounds on both the dimension and the entropy of the shared random variable in a local model.

Eigenvalue distributions for a class of covariance matrices with application to Bienenstock-Cooper-Munro neurons under noisy conditions.

Science.gov (United States)

Bazzani, Armando; Castellani, Gastone C; Cooper, Leon N

2010-05-01

We analyze the effects of noise correlations in the input to, or among, Bienenstock-Cooper-Munro neurons using the Wigner semicircular law to construct random, positive-definite symmetric correlation matrices and compute their eigenvalue distributions. In the finite dimensional case, we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments. These correlations can be due either to correlations in the noise from the input lateral geniculate nucleus neurons, or correlations in the variability of lateral connections in a network of neurons. In particular, we find that for fixed dimensionality, a large noise variance can give rise to long lifetimes of synaptic strengths. This may be of physiological significance.

Distance covariance for stochastic processes

DEFF Research Database (Denmark)

Matsui, Muneya; Mikosch, Thomas Valentin; Samorodnitsky, Gennady

2017-01-01

The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analog of the distance covariance for two stochastic processes...

Solid-state surface luminescence of polycyclic aromatic hydrocarbons adsorbed on cellulose diacetate matrices

Science.gov (United States)

Rogacheva, Svetlana M.; Shipovskaya, Anna B.; Volkova, Elena V.; Khurshudyan, Grachia N.; Suska-Malawska, Malgorzata; Gubina, Tamara I.

2018-04-01

The spectral-kinetic characteristics of luminescence of 17 polycyclic aromatic hydrocarbons (PAH) sorbed from a "water-organic solvent" medium on cellulose diacetate (CDA) matrices were studied. A significant increase in the fluorescence signal on the CDA matrix was observed for 13 PAHs in comparison with aqueous solutions. The highest detection sensitivity was found for pyrene, benzo(a)pyrene, and benzo(k)fluoranthene. The fluorescence spectra of two PAH indicator pairs (anthracene-phenanthrene and pyrene-fluoranthene) used to control toxicant emission sources were studied with the simultaneous presence of isomers in the analyte, depending on the excitation wavelength. For both isomer pairs, it has been found that the spectra of their solid-state luminescence overlap insignificantly, the characteristic peaks do not coincide and do not overlap, the sensitivities of detection are close to each other, which makes it possible to consider this technique as promising to control PAH contamination sources.

Exciton Scattering approach for conjugated macromolecules: from electronic spectra to electron-phonon coupling

Science.gov (United States)

Tretiak, Sergei

2014-03-01

The exciton scattering (ES) technique is a multiscale approach developed for efficient calculations of excited-state electronic structure and optical spectra in low-dimensional conjugated macromolecules. Within the ES method, the electronic excitations in the molecular structure are attributed to standing waves representing quantum quasi-particles (excitons), which reside on the graph. The exciton propagation on the linear segments is characterized by the exciton dispersion, whereas the exciton scattering on the branching centers is determined by the energy-dependent scattering matrices. Using these ES energetic parameters, the excitation energies are then found by solving a set of generalized ``particle in a box'' problems on the graph that represents the molecule. All parameters can be extracted from quantum-chemical computations of small molecular fragments and tabulated in the ES library for further applications. Subsequently, spectroscopic modeling for any macrostructure within considered molecular family could be performed with negligible numerical effort. The exciton scattering properties of molecular vertices can be further described by tight-binding or equivalently lattice models. The on-site energies and hopping constants are obtained from the exciton dispersion and scattering matrices. Such tight-binding model approach is particularly useful to describe the exciton-phonon coupling, energetic disorder and incoherent energy transfer in large branched conjugated molecules. Overall the ES applications accurately reproduce the optical spectra compared to the reference quantum chemistry results, and make possible to predict spectra of complex macromolecules, where conventional electronic structure calculations are unfeasible.

Covariance Manipulation for Conjunction Assessment

Science.gov (United States)

Hejduk, M. D.

2016-01-01

The manipulation of space object covariances to try to provide additional or improved information to conjunction risk assessment is not an uncommon practice. Types of manipulation include fabricating a covariance when it is missing or unreliable to force the probability of collision (Pc) to a maximum value ('PcMax'), scaling a covariance to try to improve its realism or see the effect of covariance volatility on the calculated Pc, and constructing the equivalent of an epoch covariance at a convenient future point in the event ('covariance forecasting'). In bringing these methods to bear for Conjunction Assessment (CA) operations, however, some do not remain fully consistent with best practices for conducting risk management, some seem to be of relatively low utility, and some require additional information before they can contribute fully to risk analysis. This study describes some basic principles of modern risk management (following the Kaplan construct) and then examines the PcMax and covariance forecasting paradigms for alignment with these principles; it then further examines the expected utility of these methods in the modern CA framework. Both paradigms are found to be not without utility, but only in situations that are somewhat carefully circumscribed.

Spectra of random networks in the weak clustering regime

Science.gov (United States)

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

2018-03-01

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

Evaluation of cross-section data from threshold to 40-60 MeV for specific neutron reactions important for neutron dosimetry applications. Part 1: Evaluation of the excitation functions for the 27Al(n,α)24Na, 55Mn(n,2n)54Mn, 59Co(n,p)59Fe, 59Co(n,2n)58m+gCo and 90Zr(n,2n)89m+gZr reactions

International Nuclear Information System (INIS)

Zolotarev, K.I.

2009-04-01

Evaluations of cross sections and their associated covariance matrices have been carried out for five dosimetry reactions: - excitation functions were re-evaluated for the 27 Al(n,α) 24 Na, 55 Mn(n,2n) 54 Mn and 90 Zr(n,2n) 89m+g Zr reactions over the neutron energy range from threshold to 40 MeV; - excitation functions were re-evaluated for the 59 Co(n,p) 59 Fe and 59 Co(n,2n) 58m+g Co reactions over the neutron energy range from threshold to 60 MeV. Uncertainties in the cross sections for all of those reactions were also derived in the form of relative covariance matrices. Benchmark calculations performed for 235 U thermal fission and 252 Cf spontaneous fission neutron spectra show that the integral cross sections calculated from the newly evaluated excitation functions exhibit improved agreement with related experimental data when compared with the equivalent data from the IRDF-2002 library. (author)

Evaluation of Cross-Section Data from Threshold to 40 MeV for some Neutron Reactions Important for Fusion Dosimetry Applications. Part 2 Evaluation of the Excitation Functions for the 59Co(n,3n)57Co, 89Y(n,2n)88Y, 93Nb(n,2n)92mNb, 169Tm(n,2n)168Tm and 209Bi(n,3n)207Bi Reactions

International Nuclear Information System (INIS)

Zolotarev, K.I.

2010-11-01

Evaluations of cross sections and their associated covariance matrices have been carried out for five dosimetry reactions: excitation functions were re-evaluated for the 89 Y(n,2n) 88 Y, 93 Nb(n,2n) 92 mNb and 169 Tm(n,2n) 168 Tm reactions over the neutron energy range from threshold up to 40 MeV; excitation functions were re-evaluated for the 59 Co(n,3n) 57 Co and 209 Bi(n,3n) 207 Bi reactions over the neutron energy range from threshold to 85 and 45 MeV, respectively. Uncertainties in the cross sections for all of those reactions were also derived in the form of relative covariance matrices. Benchmark calculations performed for 235 U thermal fission and 252 Cf spontaneous fission neutron spectra show that the integral cross sections calculated from the newly evaluated excitation functions exhibit improved agreement with related experimental data when compared with the equivalent data from the IRDF-2002 library. (author)

Characterizing protein conformations by correlation analysis of coarse-grained contact matrices

Science.gov (United States)

Lindsay, Richard J.; Siess, Jan; Lohry, David P.; McGee, Trevor S.; Ritchie, Jordan S.; Johnson, Quentin R.; Shen, Tongye

2018-01-01

We have developed a method to capture the essential conformational dynamics of folded biopolymers using statistical analysis of coarse-grained segment-segment contacts. Previously, the residue-residue contact analysis of simulation trajectories was successfully applied to the detection of conformational switching motions in biomolecular complexes. However, the application to large protein systems (larger than 1000 amino acid residues) is challenging using the description of residue contacts. Also, the residue-based method cannot be used to compare proteins with different sequences. To expand the scope of the method, we have tested several coarse-graining schemes that group a collection of consecutive residues into a segment. The definition of these segments may be derived from structural and sequence information, while the interaction strength of the coarse-grained segment-segment contacts is a function of the residue-residue contacts. We then perform covariance calculations on these coarse-grained contact matrices. We monitored how well the principal components of the contact matrices is preserved using various rendering functions. The new method was demonstrated to assist the reduction of the degrees of freedom for describing the conformation space, and it potentially allows for the analysis of a system that is approximately tenfold larger compared with the corresponding residue contact-based method. This method can also render a family of similar proteins into the same conformational space, and thus can be used to compare the structures of proteins with different sequences.

ACCELERATED FITTING OF STELLAR SPECTRA

Energy Technology Data Exchange (ETDEWEB)

Ting, Yuan-Sen; Conroy, Charlie [Harvard–Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Rix, Hans-Walter [Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg (Germany)

2016-07-20

Stellar spectra are often modeled and fitted by interpolating within a rectilinear grid of synthetic spectra to derive the stars’ labels: stellar parameters and elemental abundances. However, the number of synthetic spectra needed for a rectilinear grid grows exponentially with the label space dimensions, precluding the simultaneous and self-consistent fitting of more than a few elemental abundances. Shortcuts such as fitting subsets of labels separately can introduce unknown systematics and do not produce correct error covariances in the derived labels. In this paper we present a new approach—Convex Hull Adaptive Tessellation (chat)—which includes several new ideas for inexpensively generating a sufficient stellar synthetic library, using linear algebra and the concept of an adaptive, data-driven grid. A convex hull approximates the region where the data lie in the label space. A variety of tests with mock data sets demonstrate that chat can reduce the number of required synthetic model calculations by three orders of magnitude in an eight-dimensional label space. The reduction will be even larger for higher dimensional label spaces. In chat the computational effort increases only linearly with the number of labels that are fit simultaneously. Around each of these grid points in the label space an approximate synthetic spectrum can be generated through linear expansion using a set of “gradient spectra” that represent flux derivatives at every wavelength point with respect to all labels. These techniques provide new opportunities to fit the full stellar spectra from large surveys with 15–30 labels simultaneously.

Eddy covariance measurements of sea spray particles over the Atlantic Ocean

Directory of Open Access Journals (Sweden)

S. J. Norris

2008-02-01

Full Text Available Most estimates of sea spray aerosol source functions have used indirect means to infer the rate of production as a function of wind speed. Only recently has the technology become available to make high frequency measurements of aerosol spectra suitable for direct eddy correlation determination of the sea spray particle flux. This was accomplished in this study by combining a newly developed fast aerosol particle counter with an ultrasonic anemometer which allowed for eddy covariance measurements of size-segregated particle fluxes. The aerosol instrument is the Compact Lightweight Aerosol Spectrometer Probe (CLASP – capable of measuring 8-channel size spectra for mean radii between 0.15 and 3.5 µm at 10 Hz. The first successful measurements were made during the Waves, Air Sea Fluxes, Aerosol and Bubbles (WASFAB field campaign in October 2005 in Duck (NC, USA. The method and initial results are presented and comparisons are made with recent sea spray source functions from the literature.

The invariant theory of matrices

CERN Document Server

Concini, Corrado De

2017-01-01

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

Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix

Directory of Open Access Journals (Sweden)

Yanpeng Zheng

2015-01-01

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

Enhancing Understanding of Transformation Matrices

Science.gov (United States)

Dick, Jonathan; Childrey, Maria

2012-01-01

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

Group inverses of M-matrices and their applications

CERN Document Server

Kirkland, Stephen J

2013-01-01

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

Poincare covariance and κ-Minkowski spacetime

International Nuclear Information System (INIS)

Dabrowski, Ludwik; Piacitelli, Gherardo

2011-01-01

A fully Poincare covariant model is constructed as an extension of the κ-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincare group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincare covariance is realised a la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of 'Poincare covariance'. -- Highlights: → We construct a 4d model of noncommuting coordinates (quantum spacetime). → The coordinates are fully covariant under the undeformed Poincare group. → Covariance a la Wigner holds in presence of two dimensionful parameters. → Hence we are not forced to deform covariance (e.g. as quantum groups). → The underlying κ-Minkowski model is unphysical; covariantisation does not cure this.

Phenomenological mass matrices with a democratic warp

International Nuclear Information System (INIS)

Kleppe, A.

2018-01-01

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

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

International Nuclear Information System (INIS)

Feldman, V.I.

1998-01-01

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

Raman spectra of thiolated arsenicals with biological importance.

Science.gov (United States)

Yang, Mingwei; Sun, Yuzhen; Zhang, Xiaobin; McCord, Bruce; McGoron, Anthony J; Mebel, Alexander; Cai, Yong

2018-03-01

Surface enhanced Raman scattering (SERS) has great potential as an alternative tool for arsenic speciation in biological matrices. SERS measurements have advantages over other techniques due to its ability to maintain the integrity of arsenic species and its minimal requirements for sample preparation. Up to now, very few Raman spectra of arsenic compounds have been reported. This is particularly true for thiolated arsenicals, which have recently been found to be widely present in humans. The lack of data for Raman spectra in arsenic speciation hampers the development of new tools using SERS. Herein, we report the results of a study combining the analysis of experimental Raman spectra with that obtained from density functional calculations for some important arsenic metabolites. The results were obtained with a hybrid functional B3LYP approach using different basis sets to calculate Raman spectra of the selected arsenicals. By comparing experimental and calculated spectra of dimethylarsinic acid (DMA V ), the basis set 6-311++G** was found to provide computational efficiency and precision in vibrational frequency prediction. The Raman frequencies for the rest of organoarsenicals were studied using this basis set, including monomethylarsonous acid (MMA III ), dimethylarsinous acid (DMA III ), dimethylmonothioarinic acid (DMMTA V ), dimethyldithioarsinic acid (DMDTA V ), S-(Dimethylarsenic) cysteine (DMA III (Cys)) and dimethylarsinous glutathione (DMA III GS). The results were compared with fingerprint Raman frequencies from As─O, As─C, and As─S obtained under different chemical environments. These fingerprint vibrational frequencies should prove useful in future measurements of different species of arsenic using SERS. Copyright © 2017 Elsevier B.V. All rights reserved.

Modeling Covariance Breakdowns in Multivariate GARCH

OpenAIRE

Jin, Xin; Maheu, John M

2014-01-01

This paper proposes a flexible way of modeling dynamic heterogeneous covariance breakdowns in multivariate GARCH (MGARCH) models. During periods of normal market activity, volatility dynamics are governed by an MGARCH specification. A covariance breakdown is any significant temporary deviation of the conditional covariance matrix from its implied MGARCH dynamics. This is captured through a flexible stochastic component that allows for changes in the conditional variances, covariances and impl...

Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics

OpenAIRE

Ole E. Barndorff-Nielsen; Neil Shephard

2002-01-01

This paper analyses multivariate high frequency financial data using realised covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis and covariance. It will be based on a fixed interval of time (e.g. a day or week), allowing the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions and covariances change through time. In particular w...

Fluorescence lifetime selectivity in excitation-emission matrices for qualitative analysis of a two-component system

International Nuclear Information System (INIS)

Millican, D.W.; McGown, L.B.

1989-01-01

Steady-state fluorescence excitation-emission matrices (EEMs), and phase-resolved EEMs (PREEMs) collected at modulation frequencies of 6, 18, and 30 MHz, were used for qualitative analysis of mixtures of benzo[k]fluoranthene (τ = 8 ns) and benzo[b]fluoranthene (τ = 29 ns) in ethanol. The EEMs of the individual components were extracted from mixture EEMs by means of wavelength component vector-gram (WCV) analysis. Phase resolution was found to be superior to steady-state measurements for extraction of the component spectra, for mixtures in which the intensity contributions from the two components are unequal

Diagonalization of the mass matrices

International Nuclear Information System (INIS)

Rhee, S.S.

1984-01-01

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

Energy spectra of primary knock-on atoms under neutron irradiation

International Nuclear Information System (INIS)

Gilbert, M.R.; Marian, J.; Sublet, J.-Ch.

2015-01-01

Materials subjected to neutron irradiation will suffer from a build-up of damage caused by the displacement cascades initiated by nuclear reactions. Previously, the main “measure” of this damage accumulation has been through the displacements per atom (dpa) index, which has known limitations. This paper describes a rigorous methodology to calculate the primary atomic recoil events (often called the primary knock-on atoms or PKAs) that lead to cascade damage events as a function of energy and recoiling species. A new processing code SPECTRA-PKA combines a neutron irradiation spectrum with nuclear recoil data obtained from the latest nuclear data libraries to produce PKA spectra for any material composition. Via examples of fusion relevant materials, it is shown that these PKA spectra can be complex, involving many different recoiling species, potentially differing in both proton and neutron number from the original target nuclei, including high energy recoils of light emitted particles such as α-particles and protons. The variations in PKA spectra as a function of time, neutron field, and material are explored. The application of PKA spectra to the quantification of radiation damage is exemplified using two approaches: the binary collision approximation and stochastic cluster dynamics, and the results from these different models are discussed and compared. - Highlights: • Recoil cross-section matrices under neutron irradiation are generated. • Primary knock-on atoms (PKA) spectra are calculated for fusion relevant materials. • Variation in PKA spectra due to changes in geometry are considered. • Inventory simulations to consider time-evolution in PKA spectra. • Damage quantification using damage functions from different approximations.

ISSUES IN NEUTRON CROSS SECTION COVARIANCES

Energy Technology Data Exchange (ETDEWEB)

Mattoon, C.M.; Oblozinsky,P.

2010-04-30

We review neutron cross section covariances in both the resonance and fast neutron regions with the goal to identify existing issues in evaluation methods and their impact on covariances. We also outline ideas for suitable covariance quality assurance procedures.We show that the topic of covariance data remains controversial, the evaluation methodologies are not fully established and covariances produced by different approaches have unacceptable spread. The main controversy is in very low uncertainties generated by rigorous evaluation methods and much larger uncertainties based on simple estimates from experimental data. Since the evaluators tend to trust the former, while the users tend to trust the latter, this controversy has considerable practical implications. Dedicated effort is needed to arrive at covariance evaluation methods that would resolve this issue and produce results accepted internationally both by evaluators and users.

Infrared Spectra of the n-PROPYL and i-PROPYL Radicals in Solid Para-Hydrogen

Science.gov (United States)

Pullen, Gregory T.; Franke, Peter R.; Douberly, Gary E.; Lee, Yuan-Pern

2017-06-01

We report the infrared spectra of the n-propyl and i-propyl radicals measured in solid para-hydrogen (p-H_2) matrices at 3.2 K. n-Propyl and i-propyl radicals were produced via the 248 nm irradiation of matrices formed by co-depositing p-H_2 and either 1-Iodopropane (n-propyl) or 2-Iodopropane (i-propyl). Secondary photolysis was used to group spectral lines all due to the same species. Lines in the C-H stretching region were compared to previous work using the Helium Nanodroplet Isolation (HENDI) technique, and are in excellent agreement. In addition to a few lines previously measured in Ar matrices, we observe many previously unreported bands below 2000 \\wn, which we attribute to the n-propyl and i-propyl radicals. The assignment of features below 2000 \\wn are made via comparisons to anharmonic VPT2+K frequency computations. Peter R. Franke, Daniel P. Tabor, Christopher P. Moradi, Gary E. Douberly, Jay Agarwal, Henry F. Schaefer III, and Edwin L. Sibert III, Journal of Chemical Physics 145, 224304 (2016).

The construction of factorized S-matrices

International Nuclear Information System (INIS)

Chudnovsky, D.V.

1981-01-01

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

Configuration interaction in LTE spectra of heavy elements

International Nuclear Information System (INIS)

Bar-Shalom, A.; Oreg, J.; Goldstein, W.

1992-11-01

We present a method for including the effects of configuration interaction (CI) between relativistic subconfigurations of an electron configuration in the calculation of emission and absorption spectra of plasmas in local thermodynamic equilibrium (LTE). Analytical expressions for the correction to the intensities, owing to Cl, of an unresolved transition array (UTA) and of a supertransition array (STA) are obtained when the correction is small compared to the spin-orbit splitting, bypassing the need to diagonalize energy matrices. These expressions serve as working formulas in the STA model and, in addition, reveal a priori the conditions under which CI effects are significant. Examples of the effect are presented

Matrices in Engineering Problems

CERN Document Server

Tobias, Marvin

2011-01-01

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

Covariant diagrams for one-loop matching

Energy Technology Data Exchange (ETDEWEB)

Zhang, Zhengkang [Michigan Center for Theoretical Physics (MCTP), University of Michigan,450 Church Street, Ann Arbor, MI 48109 (United States); Deutsches Elektronen-Synchrotron (DESY),Notkestraße 85, 22607 Hamburg (Germany)

2017-05-30

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Covariant diagrams for one-loop matching

International Nuclear Information System (INIS)

Zhang, Zhengkang

2017-01-01

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

A Brief Historical Introduction to Matrices and Their Applications

Science.gov (United States)

Debnath, L.

2014-01-01

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

Fast Computing for Distance Covariance

OpenAIRE

Huo, Xiaoming; Szekely, Gabor J.

2014-01-01

Distance covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors. If the computation of distance covariance and distance correlation is implemented directly accordingly to its definition then its computational complexity is O($n^2$) which is a disadvantage compared to other faster methods. In this paper we show that the computation of distance covariance and distance correlation of real valued random variables can be...

Hypercyclic Abelian Semigroups of Matrices on Cn

International Nuclear Information System (INIS)

Ayadi, Adlene; Marzougui, Habib

2010-07-01

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

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

OpenAIRE

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

2013-01-01

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

General Galilei Covariant Gaussian Maps

Science.gov (United States)

Gasbarri, Giulio; Toroš, Marko; Bassi, Angelo

2017-09-01

We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we consider translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined by Nimmrichter and Hornberger [Phys. Rev. Lett. 110, 16 (2013)].

Formal matrices

CERN Document Server

Krylov, Piotr

2017-01-01

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

Competing risks and time-dependent covariates

DEFF Research Database (Denmark)

Cortese, Giuliana; Andersen, Per K

2010-01-01

Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates......, as classified by Kalbfleisch and Prentice [The Statistical Analysis of Failure Time Data, Wiley, New York, 2002] with the intent of clarifying their role and emphasizing the limitations in standard survival models and in the competing risks setting. If random (internal) time-dependent covariates...

Activities of covariance utilization working group

International Nuclear Information System (INIS)

Tsujimoto, Kazufumi

2013-01-01

During the past decade, there has been a interest in the calculational uncertainties induced by nuclear data uncertainties in the neutronics design of advanced nuclear system. The covariance nuclear data is absolutely essential for the uncertainty analysis. In the latest version of JENDL, JENDL-4.0, the covariance data for many nuclides, especially actinide nuclides, was substantialy enhanced. The growing interest in the uncertainty analysis and the covariance data has led to the organisation of the working group for covariance utilization under the JENDL committee. (author)

THE ALGORITHM AND PROGRAM OF M-MATRICES SEARCH AND STUDY

Directory of Open Access Journals (Sweden)

Y. N. Balonin

2013-05-01

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

Improvement of covariance data for fast reactors

International Nuclear Information System (INIS)

Shibata, Keiichi; Hasegawa, Akira

2000-02-01

We estimated covariances of the JENDL-3.2 data on the nuclides and reactions needed to analyze fast-reactor cores for the past three years, and produced covariance files. The present work was undertaken to re-examine the covariance files and to make some improvements. The covariances improved are the ones for the inelastic scattering cross section of 16 O, the total cross section of 23 Na, the fission cross section of 235 U, the capture cross section of 238 U, and the resolved resonance parameters for 238 U. Moreover, the covariances of 233 U data were newly estimated by the present work. The covariances obtained were compiled in the ENDF-6 format. (author)

Lorentz Covariance of Langevin Equation

International Nuclear Information System (INIS)

Koide, T.; Denicol, G.S.; Kodama, T.

2008-01-01

Relativistic covariance of a Langevin type equation is discussed. The requirement of Lorentz invariance generates an entanglement between the force and noise terms so that the noise itself should not be a covariant quantity. (author)

The modified Gauss diagonalization of polynomial matrices

International Nuclear Information System (INIS)

Saeed, K.

1982-10-01

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

Quantum Hilbert matrices and orthogonal polynomials

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Berg, Christian

2009-01-01

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

Discrete canonical transforms that are Hadamard matrices

International Nuclear Information System (INIS)

Healy, John J; Wolf, Kurt Bernardo

2011-01-01

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

Abel-grassmann's groupoids of modulo matrices

International Nuclear Information System (INIS)

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

2016-01-01

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

Cross-section covariance propagation for LWR fuel cells in one and two dimensions - 308

International Nuclear Information System (INIS)

Ball, M.; Novog, D.R.; Parisi, C.; D'Auria, F.

2010-01-01

Within the framework of the Uncertainty Analysis in Modeling (UAM) for Design, Operation and Safety Analysis of LWRs Benchmark sponsored by the OECD/NEA, a tool has been developed for the propagation of covariance uncertainty through resonance self-shielding and other neutron kinetics calculations using a direct, cross-section generation and substitution approach. The motivation behind the work described in this paper was to develop a portable uncertainty propagation tool that could be easily implemented with several neutron kinetics codes, without relying on detailed knowledge of the internal workings of those codes or access to adjoint solutions. Implemented initially with the SCALE code package, 'self-shielded' covariance matrices for common LWR fuel cells have been calculated, as well as contributions to K eff uncertainty by selected neutron cross-sections and processes in both one and two dimensions. The one dimensional results generated by the tool are compared against those obtained using the TSUNAMI-1D module of SCALE in order to verify the efficacy of the methodology. One-dimensional results show good agreement with TSUNAMI-1D, but there is also an indication that the loss of dimensionality corresponding to one-dimensional equivalent geometries of two-dimensional fuel cells may lead to significant changes in the calculated uncertainty on K eff arising from particular neutron-nuclide reactions. (authors)

Photolysis of allene-ozone mixtures at 647 nm in cryogenic matrices. Part 1. Formation of allene oxide

Science.gov (United States)

Singmaster, Karen A.; Pimentel, George C.

1989-03-01

Matrix studies of the photolytic reaction at 647 nm between allene and ozone were carried out at 12 K. Primary photoproducts include carbon monoxide, acrolein ( cis and trans), cyclopropanone, ketene, ethylene, allene oxide and formaldehyde. In Ar and Kr matrices both acrolein and cyclopropanone are produced in high yields, whereas in Xe matrices cyclopropanone is the major product. Infrared spectra for cyclopropanone and its oxygen-18 and deuterium substitutes are reported. The carbonyl stretch for cyclopropanone is observed at 1815 cm -1 in an Ar matrix. Also reported is the first synthesis of allene oxide. The carbon—carbon double bond stretch is observed at 1823.4 cm -1 and it exhibits a small oxygen-18 shift. The change in product distribution is discussed in terms of heavy atom spin—orbit enhancement of singlet—triplet excitation, so that in xenon reaction takes place on a triplet surface, whereas in argon it occurs on a singlet surface.

Free probability and random matrices

CERN Document Server

Mingo, James A

2017-01-01

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

Quantum matrices in two dimensions

International Nuclear Information System (INIS)

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

1991-01-01

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

Covariance descriptor fusion for target detection

Science.gov (United States)

Cukur, Huseyin; Binol, Hamidullah; Bal, Abdullah; Yavuz, Fatih

2016-05-01

Target detection is one of the most important topics for military or civilian applications. In order to address such detection tasks, hyperspectral imaging sensors provide useful images data containing both spatial and spectral information. Target detection has various challenging scenarios for hyperspectral images. To overcome these challenges, covariance descriptor presents many advantages. Detection capability of the conventional covariance descriptor technique can be improved by fusion methods. In this paper, hyperspectral bands are clustered according to inter-bands correlation. Target detection is then realized by fusion of covariance descriptor results based on the band clusters. The proposed combination technique is denoted Covariance Descriptor Fusion (CDF). The efficiency of the CDF is evaluated by applying to hyperspectral imagery to detect man-made objects. The obtained results show that the CDF presents better performance than the conventional covariance descriptor.

Generalized Linear Covariance Analysis

Science.gov (United States)

Carpenter, James R.; Markley, F. Landis

2014-01-01

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Econometric analysis of realized covariation: high frequency based covariance, regression, and correlation in financial economics

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Shephard, N.

2004-01-01

This paper analyses multivariate high frequency financial data using realized covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis, and covariance. It will be based on a fixed interval of time (e.g., a day or week), allowing...... the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions, and covariances change through time. In particular we provide confidence intervals for each of these quantities....

Spectroscopic studies of the size effects in the absorption spectra of (NH2(C2H5)2)2CuCl4 nanocrystals incorporated into the PMMA photopolymer matrix

International Nuclear Information System (INIS)

Kapustianyk, V.; Partyka, M.; Rudyk, V.; Piasecki, M.; Brik, M.G.; Tkaczyk, S.; Ozga, K.; Plucinski, K.; Romanyshyn, S.; Kityk, I.V.

2010-01-01

The absorption spectra of (NH 2 (C 2 H 5 ) 2 ) 2 CuCl 4 (DEACC) single crystals and nanocrystals (NC) incorporated into the polymethyl methacrylate (PMMA) polymer matrices were investigated both experimentally and theoretically. It was established that the crystal field spectra of Cu 2+ ion detect clearly the quantum size effects. The observed spectra were analyzed using first principle crystal field quantum chemical calculations. It was shown that incorporation of NCs into the polymer matrix allows to identify the charge-transfer (CT) bands in the spectra of DEACC crystals.

Covariant canonical quantization of fields and Bohmian mechanics

International Nuclear Information System (INIS)

Nikolic, H.

2005-01-01

We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space and time arguments of fields are treated on an equal footing. To achieve both covariance and consistency with standard non-covariant canonical quantization of fields in Minkowski spacetime, it is necessary to adopt a covariant Bohmian formulation of quantum field theory. A preferred foliation of spacetime emerges dynamically owing to a purely quantum effect. The application to a simple time-reparametrization invariant system and quantum gravity is discussed and compared with the conventional non-covariant Wheeler-DeWitt approach. (orig.)

Consistency between data from the ENDF/B-V dosimetry file and corresponding experimental data for some fast neutron reference spectra

International Nuclear Information System (INIS)

Nolthenius, H.J.; Zijp, W.L.

1981-11-01

Results are given of a study on the consistency between 'integral' and 'differential' cross sections data for four benchmark neutron spectra and 36 neutron reactions of importance for reactor neutron metrology. The energy dependent cross section data and their uncertainty data are obtained from the ENDF/B-V dosimetry file. The reactions have been considered with respect to the following quantities: 1. the precision of the averaged cross sections, for a specified spectrum; 2. the discrepancy between the measured and the calculated average cross section values; 3. the consistency between the measured and calculated average cross section values, described by the chi 2 -parameter. It was possible to take into account the available cross section covariance information present in the ENDF/B-V dosimetry file. Covariance information on the benchmark flux density spectra was not taken into account in this study

Synchronous correlation matrices and Connes’ embedding conjecture

Energy Technology Data Exchange (ETDEWEB)

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

2016-01-15

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

The Effects of Moisture Conditions—From Wet to Hyper dry—On Visible Near-Infrared Spectra of Danish Reference Soils

DEFF Research Database (Denmark)

Knadel, Maria; Deng, Fan; Alinejadian, Afsaneh

2014-01-01

Changes in soil water content are known to affect soil reflectance. Even though it was suggested some time ago that the phenomenon of increased forward scattering due to the presence of water in the soil is related to water film thickness and matric potential, there has been no detailed...... investigation of this in any studies. The effects of moisture conditions on visible nearinfrared (vis-NIR) spectra of four representative soils in Denmark have been assessed as a function of both water film thickness (expressed as the number of molecular layers) and matric potential. Complete water retention...... curves, from wet (pF 0.3, pF = log(|j|), where j is the matric potential in cm) to hyper dry end (oven-dried and freeze-dried soil), were obtained by initial wetting followed by successive draining and drying of soil samples, performing NIR measurements at each step. Soil reflectance was found...

Proofs of Contracted Length Non-covariance

International Nuclear Information System (INIS)

Strel'tsov, V.N.

1994-01-01

Different proofs of contracted length non covariance are discussed. The way based on the establishment of interval inconstancy (dependence on velocity) seems to be the most convincing one. It is stressed that the known non covariance of the electromagnetic field energy and momentum of a moving charge ('the problem 4/3') is a direct consequence of contracted length non covariance. 8 refs

Realm of Matrices

Indian Academy of Sciences (India)

IAS Admin

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

Virial expansion for almost diagonal random matrices

Science.gov (United States)

Yevtushenko, Oleg; Kravtsov, Vladimir E.

2003-08-01

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

Covariate analysis of bivariate survival data

Energy Technology Data Exchange (ETDEWEB)

Bennett, L.E.

1992-01-01

The methods developed are used to analyze the effects of covariates on bivariate survival data when censoring and ties are present. The proposed method provides models for bivariate survival data that include differential covariate effects and censored observations. The proposed models are based on an extension of the univariate Buckley-James estimators which replace censored data points by their expected values, conditional on the censoring time and the covariates. For the bivariate situation, it is necessary to determine the expectation of the failure times for one component conditional on the failure or censoring time of the other component. Two different methods have been developed to estimate these expectations. In the semiparametric approach these expectations are determined from a modification of Burke's estimate of the bivariate empirical survival function. In the parametric approach censored data points are also replaced by their conditional expected values where the expected values are determined from a specified parametric distribution. The model estimation will be based on the revised data set, comprised of uncensored components and expected values for the censored components. The variance-covariance matrix for the estimated covariate parameters has also been derived for both the semiparametric and parametric methods. Data from the Demographic and Health Survey was analyzed by these methods. The two outcome variables are post-partum amenorrhea and breastfeeding; education and parity were used as the covariates. Both the covariate parameter estimates and the variance-covariance estimates for the semiparametric and parametric models will be compared. In addition, a multivariate test statistic was used in the semiparametric model to examine contrasts. The significance of the statistic was determined from a bootstrap distribution of the test statistic.

Covariant diagrams for one-loop matching

International Nuclear Information System (INIS)

Zhang, Zhengkang

2016-10-01

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Covariant diagrams for one-loop matching

Energy Technology Data Exchange (ETDEWEB)

Zhang, Zhengkang [Michigan Univ., Ann Arbor, MI (United States). Michigan Center for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2016-10-15

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Chequered surfaces and complex matrices

International Nuclear Information System (INIS)

Morris, T.R.; Southampton Univ.

1991-01-01

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

Interrelating meteorite and asteroid spectra at UV-Vis-NIR wavelengths using novel multiple-scattering methods

Science.gov (United States)

Martikainen, Julia; Penttilä, Antti; Gritsevich, Maria; Muinonen, Karri

2017-10-01

Asteroids have remained mostly the same for the past 4.5 billion years, and provide us information on the origin, evolution and current state of the Solar System. Asteroids and meteorites can be linked by matching their respective reflectance spectra. This is difficult, because spectral features depend strongly on the surface properties, and meteorite surfaces are free of regolith dust present in asteroids. Furthermore, asteroid surfaces experience space weathering which affects their spectral features.We present a novel simulation framework for assessing the spectral properties of meteorites and asteroids and matching their reflectance spectra. The simulations are carried out by utilizing a light-scattering code that takes inhomogeneous waves into account and simulates light scattering by Gaussian-random-sphere particles large compared to the wavelength of the incident light. The code uses incoherent input and computes phase matrices by utilizing incoherent scattering matrices. Reflectance spectra are modeled by combining olivine, pyroxene, and iron, the most common materials that dominate the spectral features of asteroids and meteorites. Space weathering is taken into account by adding nanoiron into the modeled asteroid spectrum. The complex refractive indices needed for the simulations are obtained from existing databases, or derived using an optimization that utilizes our ray-optics code and the measured spectrum of the material.We demonstrate our approach by applying it to the reflectance spectrum of (4) Vesta and the reflectance spectrum of the Johnstown meteorite measured with the University of Helsinki integrating-sphere UV-Vis-NIR spectrometer.Acknowledgments. The research is funded by the ERC Advanced Grant No. 320773 (SAEMPL).

Covariance and sensitivity data generation at ORNL

International Nuclear Information System (INIS)

Leal, L. C.; Derrien, H.; Larson, N. M.; Alpan, A.

2005-01-01

Covariance data are required to assess uncertainties in design parameters in several nuclear applications. The error estimation of calculated quantities relies on the nuclear data uncertainty information available in the basic nuclear data libraries, such as the US Evaluated Nuclear Data Library, ENDF/B. The uncertainty files in the ENDF/B library are obtained from the analysis of experimental data and are stored as variance and covariance data. In this paper we address the generation of covariance data in the resonance region done with the computer code SAMMY. SAMMY is used in the evaluation of the experimental data in the resolved and unresolved resonance energy regions. The data fitting of cross sections is based on the generalised least-squares formalism (Bayesian theory) together with the resonance formalism described by R-matrix theory. Two approaches are used in SAMMY for the generation of resonance parameter covariance data. In the evaluation process SAMMY generates a set of resonance parameters that fit the data, and, it provides the resonance parameter covariances. For resonance parameter evaluations where there are no resonance parameter covariance data available, the alternative is to use an approach called the 'retroactive' resonance parameter covariance generation. In this paper, we describe the application of the retroactive covariance generation approach for the gadolinium isotopes. (authors)

Covariance Evaluation Methodology for Neutron Cross Sections

Energy Technology Data Exchange (ETDEWEB)

Herman,M.; Arcilla, R.; Mattoon, C.M.; Mughabghab, S.F.; Oblozinsky, P.; Pigni, M.; Pritychenko, b.; Songzoni, A.A.

2008-09-01

We present the NNDC-BNL methodology for estimating neutron cross section covariances in thermal, resolved resonance, unresolved resonance and fast neutron regions. The three key elements of the methodology are Atlas of Neutron Resonances, nuclear reaction code EMPIRE, and the Bayesian code implementing Kalman filter concept. The covariance data processing, visualization and distribution capabilities are integral components of the NNDC methodology. We illustrate its application on examples including relatively detailed evaluation of covariances for two individual nuclei and massive production of simple covariance estimates for 307 materials. Certain peculiarities regarding evaluation of covariances for resolved resonances and the consistency between resonance parameter uncertainties and thermal cross section uncertainties are also discussed.

Intrinsic Density Matrices of the Nuclear Shell Model

International Nuclear Information System (INIS)

Deveikis, A.; Kamuntavichius, G.

1996-01-01

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

Covariant perturbations of Schwarzschild black holes

International Nuclear Information System (INIS)

Clarkson, Chris A; Barrett, Richard K

2003-01-01

We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation in a Schwarzschild black-hole spacetime. The 1 + 3 covariant approach is extended to a '1 + 1 + 2 covariant sheet' formalism by introducing a radial unit vector in addition to the timelike congruence, and decomposing all covariant quantities with respect to this. The background Schwarzschild solution is discussed and a covariant characterization is given. We give the full first-order system of linearized 1 + 1 + 2 covariant equations, and we show how, by introducing (time and spherical) harmonic functions, these may be reduced to a system of first-order ordinary differential equations and algebraic constraints for the 1 + 1 + 2 variables which may be solved straightforwardly. We show how both odd- and even-parity perturbations may be unified by the discovery of a covariant, frame- and gauge-invariant, transverse-traceless tensor describing gravitational waves, which satisfies a covariant wave equation equivalent to the Regge-Wheeler equation for both even- and odd-parity perturbations. We show how the Zerilli equation may be derived from this tensor, and derive a similar transverse-traceless tensor equation equivalent to this equation. The so-called special quasinormal modes with purely imaginary frequency emerge naturally. The significance of the degrees of freedom in the choice of the two frame vectors is discussed, and we demonstrate that, for a certain frame choice, the underlying dynamics is governed purely by the Regge-Wheeler tensor. The two transverse-traceless Weyl tensors which carry the curvature of gravitational waves are discussed, and we give the closed system of four first-order ordinary differential equations describing their propagation. Finally, we consider the extension of this work to the study of

Spatial-temporal-covariance-based modeling, analysis, and simulation of aero-optics wavefront aberrations.

Science.gov (United States)

Vogel, Curtis R; Tyler, Glenn A; Wittich, Donald J

2014-07-01

We introduce a framework for modeling, analysis, and simulation of aero-optics wavefront aberrations that is based on spatial-temporal covariance matrices extracted from wavefront sensor measurements. Within this framework, we present a quasi-homogeneous structure function to analyze nonhomogeneous, mildly anisotropic spatial random processes, and we use this structure function to show that phase aberrations arising in aero-optics are, for an important range of operating parameters, locally Kolmogorov. This strongly suggests that the d5/3 power law for adaptive optics (AO) deformable mirror fitting error, where d denotes actuator separation, holds for certain important aero-optics scenarios. This framework also allows us to compute bounds on AO servo lag error and predictive control error. In addition, it provides us with the means to accurately simulate AO systems for the mitigation of aero-effects, and it may provide insight into underlying physical processes associated with turbulent flow. The techniques introduced here are demonstrated using data obtained from the Airborne Aero-Optics Laboratory.

Random matrices and random difference equations

International Nuclear Information System (INIS)

Uppuluri, V.R.R.

1975-01-01

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

Quantum Entanglement and Reduced Density Matrices

Science.gov (United States)

Purwanto, Agus; Sukamto, Heru; Yuwana, Lila

2018-05-01

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

Covariation in Natural Causal Induction.

Science.gov (United States)

Cheng, Patricia W.; Novick, Laura R.

1991-01-01

Biases and models usually offered by cognitive and social psychology and by philosophy to explain causal induction are evaluated with respect to focal sets (contextually determined sets of events over which covariation is computed). A probabilistic contrast model is proposed as underlying covariation computation in natural causal induction. (SLD)

Malware analysis using visualized image matrices.

Science.gov (United States)

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

2014-01-01

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

Malware Analysis Using Visualized Image Matrices

Directory of Open Access Journals (Sweden)

KyoungSoo Han

2014-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-11-01

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

Polynomial sequences generated by infinite Hessenberg matrices

Directory of Open Access Journals (Sweden)

Verde-Star Luis

2017-01-01

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

Do all roads lead to Rome? A comparison of brain networks derived from inter-subject volumetric and metabolic covariance and moment-to-moment hemodynamic correlations in old individuals.

Science.gov (United States)

Di, Xin; Gohel, Suril; Thielcke, Andre; Wehrl, Hans F; Biswal, Bharat B

2017-11-01

Relationships between spatially remote brain regions in human have typically been estimated by moment-to-moment correlations of blood-oxygen-level dependent signals in resting-state using functional MRI (fMRI). Recently, studies using subject-to-subject covariance of anatomical volumes, cortical thickness, and metabolic activity are becoming increasingly popular. However, question remains on whether these measures reflect the same inter-region connectivity and brain network organizations. In the current study, we systematically analyzed inter-subject volumetric covariance from anatomical MRI images, metabolic covariance from fluorodeoxyglucose positron emission tomography images from 193 healthy subjects, and resting-state moment-to-moment correlations from fMRI images of a subset of 44 subjects. The correlation matrices calculated from the three methods were found to be minimally correlated, with higher correlation in the range of 0.31, as well as limited proportion of overlapping connections. The volumetric network showed the highest global efficiency and lowest mean clustering coefficient, leaning toward random-like network, while the metabolic and resting-state networks conveyed properties more resembling small-world networks. Community structures of the volumetric and metabolic networks did not reflect known functional organizations, which could be observed in resting-state network. The current results suggested that inter-subject volumetric and metabolic covariance do not necessarily reflect the inter-regional relationships and network organizations as resting-state correlations, thus calling for cautions on interpreting results of inter-subject covariance networks.

Spatiotemporal noise covariance estimation from limited empirical magnetoencephalographic data

International Nuclear Information System (INIS)

Jun, Sung C; Plis, Sergey M; Ranken, Doug M; Schmidt, David M

2006-01-01

The performance of parametric magnetoencephalography (MEG) and electroencephalography (EEG) source localization approaches can be degraded by the use of poor background noise covariance estimates. In general, estimation of the noise covariance for spatiotemporal analysis is difficult mainly due to the limited noise information available. Furthermore, its estimation requires a large amount of storage and a one-time but very large (and sometimes intractable) calculation or its inverse. To overcome these difficulties, noise covariance models consisting of one pair or a sum of multi-pairs of Kronecker products of spatial covariance and temporal covariance have been proposed. However, these approaches cannot be applied when the noise information is very limited, i.e., the amount of noise information is less than the degrees of freedom of the noise covariance models. A common example of this is when only averaged noise data are available for a limited prestimulus region (typically at most a few hundred milliseconds duration). For such cases, a diagonal spatiotemporal noise covariance model consisting of sensor variances with no spatial or temporal correlation has been the common choice for spatiotemporal analysis. In this work, we propose a different noise covariance model which consists of diagonal spatial noise covariance and Toeplitz temporal noise covariance. It can easily be estimated from limited noise information, and no time-consuming optimization and data-processing are required. Thus, it can be used as an alternative choice when one-pair or multi-pair noise covariance models cannot be estimated due to lack of noise information. To verify its capability we used Bayesian inference dipole analysis and a number of simulated and empirical datasets. We compared this covariance model with other existing covariance models such as conventional diagonal covariance, one-pair and multi-pair noise covariance models, when noise information is sufficient to estimate them. We

S-matrices and integrability

International Nuclear Information System (INIS)

Bombardelli, Diego

2016-01-01

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

Matrices Aléatoires Tri-diagonales et Par Blocs.

OpenAIRE

MEKKI, Slimane

2014-01-01

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

Hierarchical quark mass matrices

International Nuclear Information System (INIS)

Rasin, A.

1998-02-01

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

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

Science.gov (United States)

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

2012-06-01

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

Modifications of Sp(2) covariant superfield quantization

Energy Technology Data Exchange (ETDEWEB)

Gitman, D.M.; Moshin, P.Yu

2003-12-04

We propose a modification of the Sp(2) covariant superfield quantization to realize a superalgebra of generating operators isomorphic to the massless limit of the corresponding superalgebra of the osp(1,2) covariant formalism. The modified scheme ensures the compatibility of the superalgebra of generating operators with extended BRST symmetry without imposing restrictions eliminating superfield components from the quantum action. The formalism coincides with the Sp(2) covariant superfield scheme and with the massless limit of the osp(1,2) covariant quantization in particular cases of gauge-fixing and solutions of the quantum master equations.

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Science.gov (United States)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to

Covariant quantizations in plane and curved spaces

International Nuclear Information System (INIS)

Assirati, J.L.M.; Gitman, D.M.

2017-01-01

We present covariant quantization rules for nonsingular finite-dimensional classical theories with flat and curved configuration spaces. In the beginning, we construct a family of covariant quantizations in flat spaces and Cartesian coordinates. This family is parametrized by a function ω(θ), θ element of (1,0), which describes an ambiguity of the quantization. We generalize this construction presenting covariant quantizations of theories with flat configuration spaces but already with arbitrary curvilinear coordinates. Then we construct a so-called minimal family of covariant quantizations for theories with curved configuration spaces. This family of quantizations is parametrized by the same function ω(θ). Finally, we describe a more wide family of covariant quantizations in curved spaces. This family is already parametrized by two functions, the previous one ω(θ) and by an additional function Θ(x,ξ). The above mentioned minimal family is a part at Θ = 1 of the wide family of quantizations. We study constructed quantizations in detail, proving their consistency and covariance. As a physical application, we consider a quantization of a non-relativistic particle moving in a curved space, discussing the problem of a quantum potential. Applying the covariant quantizations in flat spaces to an old problem of constructing quantum Hamiltonian in polar coordinates, we directly obtain a correct result. (orig.)

Covariant quantizations in plane and curved spaces

Energy Technology Data Exchange (ETDEWEB)

Assirati, J.L.M. [University of Sao Paulo, Institute of Physics, Sao Paulo (Brazil); Gitman, D.M. [Tomsk State University, Department of Physics, Tomsk (Russian Federation); P.N. Lebedev Physical Institute, Moscow (Russian Federation); University of Sao Paulo, Institute of Physics, Sao Paulo (Brazil)

2017-07-15

We present covariant quantization rules for nonsingular finite-dimensional classical theories with flat and curved configuration spaces. In the beginning, we construct a family of covariant quantizations in flat spaces and Cartesian coordinates. This family is parametrized by a function ω(θ), θ element of (1,0), which describes an ambiguity of the quantization. We generalize this construction presenting covariant quantizations of theories with flat configuration spaces but already with arbitrary curvilinear coordinates. Then we construct a so-called minimal family of covariant quantizations for theories with curved configuration spaces. This family of quantizations is parametrized by the same function ω(θ). Finally, we describe a more wide family of covariant quantizations in curved spaces. This family is already parametrized by two functions, the previous one ω(θ) and by an additional function Θ(x,ξ). The above mentioned minimal family is a part at Θ = 1 of the wide family of quantizations. We study constructed quantizations in detail, proving their consistency and covariance. As a physical application, we consider a quantization of a non-relativistic particle moving in a curved space, discussing the problem of a quantum potential. Applying the covariant quantizations in flat spaces to an old problem of constructing quantum Hamiltonian in polar coordinates, we directly obtain a correct result. (orig.)

Construction of covariance matrix for experimental data

International Nuclear Information System (INIS)

Liu Tingjin; Zhang Jianhua

1992-01-01

For evaluators and experimenters, the information is complete only in the case when the covariance matrix is given. The covariance matrix of the indirectly measured data has been constructed and discussed. As an example, the covariance matrix of 23 Na(n, 2n) cross section is constructed. A reasonable result is obtained

Smooth individual level covariates adjustment in disease mapping.

Science.gov (United States)

Huque, Md Hamidul; Anderson, Craig; Walton, Richard; Woolford, Samuel; Ryan, Louise

2018-05-01

Spatial models for disease mapping should ideally account for covariates measured both at individual and area levels. The newly available "indiCAR" model fits the popular conditional autoregresssive (CAR) model by accommodating both individual and group level covariates while adjusting for spatial correlation in the disease rates. This algorithm has been shown to be effective but assumes log-linear associations between individual level covariates and outcome. In many studies, the relationship between individual level covariates and the outcome may be non-log-linear, and methods to track such nonlinearity between individual level covariate and outcome in spatial regression modeling are not well developed. In this paper, we propose a new algorithm, smooth-indiCAR, to fit an extension to the popular conditional autoregresssive model that can accommodate both linear and nonlinear individual level covariate effects while adjusting for group level covariates and spatial correlation in the disease rates. In this formulation, the effect of a continuous individual level covariate is accommodated via penalized splines. We describe a two-step estimation procedure to obtain reliable estimates of individual and group level covariate effects where both individual and group level covariate effects are estimated separately. This distributed computing framework enhances its application in the Big Data domain with a large number of individual/group level covariates. We evaluate the performance of smooth-indiCAR through simulation. Our results indicate that the smooth-indiCAR method provides reliable estimates of all regression and random effect parameters. We illustrate our proposed methodology with an analysis of data on neutropenia admissions in New South Wales (NSW), Australia. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The Antitriangular Factorization of Saddle Point Matrices

KAUST Repository

Pestana, J.

2014-01-01

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

Precomputing Process Noise Covariance for Onboard Sequential Filters

Science.gov (United States)

Olson, Corwin G.; Russell, Ryan P.; Carpenter, J. Russell

2017-01-01

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis studies is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

Graphs and matrices

CERN Document Server

Bapat, Ravindra B

2014-01-01

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

Bayesian Nonparametric Clustering for Positive Definite Matrices.

Science.gov (United States)

Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2016-05-01

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

The covariant chiral ring

Energy Technology Data Exchange (ETDEWEB)

Bourget, Antoine; Troost, Jan [Laboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond, 75005 Paris (France)

2016-03-23

We construct a covariant generating function for the spectrum of chiral primaries of symmetric orbifold conformal field theories with N=(4,4) supersymmetry in two dimensions. For seed target spaces K3 and T{sup 4}, the generating functions capture the SO(21) and SO(5) representation theoretic content of the chiral ring respectively. Via string dualities, we relate the transformation properties of the chiral ring under these isometries of the moduli space to the Lorentz covariance of perturbative string partition functions in flat space.

Basic hypergeometric functions and covariant spaces for even-dimensional representations of Uq[osp(1/2)

International Nuclear Information System (INIS)

Aizawa, N; Chakrabarti, R; Mohammed, S S Naina; Segar, J

2007-01-01

Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and is observed that they may be expressed in terms of the Q-Hahn polynomials. We next investigate representations of the quantum supergroup OSp q (1/2) which are not well defined in the classical limit. Employing the universal T-matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in all cases. Using the Clebsch-Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even-dimensional representations of the quantum supergroup OSp q (1/2)

GLq(N)-covariant quantum algebras and covariant differential calculus

International Nuclear Information System (INIS)

Isaev, A.P.; Pyatov, P.N.

1992-01-01

GL q (N)-covariant quantum algebras with generators satisfying quadratic polynomial relations are considered. It is that, up to some innessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. 25 refs

Introduction to covariant formulation of superstring (field) theory

International Nuclear Information System (INIS)

Anon.

1987-01-01

The author discusses covariant formulation of superstring theories based on BRS invariance. New formulation of superstring was constructed by Green and Schwarz in the light-cone gauge first and then a covariant action was discovered. The covariant action has some interesting geometrical interpretation, however, covariant quantizations are difficult to perform because of existence of local supersymmetries. Introducing extra variables into the action, a modified action has been proposed. However, it would be difficult to prescribe constraints to define a physical subspace, or to reproduce the correct physical spectrum. Hence the old formulation, i.e., the Neveu-Schwarz-Ramond (NSR) model for covariant quantization is used. The author begins by quantizing the NSR model in a covariant way using BRS charges. Then the author discusses the field theory of (free) superstring

Synthesis, structural modelling and luminescence of a novel erbium(III) complex with 2,4-nonanedione and 2,2‧-bipyridine ligands for chitosan matrices doping

Science.gov (United States)

Martín-Ramos, P.; Chamorro-Posada, P.; Ramos Silva, M.; Pereira da Silva, P. S.; Martín, I. R.; Lahoz, F.; Lavín, V.; Martín-Gil, J.

2015-03-01

We report the synthesis, the Sparkle/PM7 semi-empirical quantum model for the ground state geometry and the absorption/luminescent properties of the Er3+ ternary complex [Er(nd)3(bipy)] (where Hnd is 2,4-nonanedione and bipy is 2,2‧-bipyridine). The solid-state electronic absorption spectra and the photoluminescent spectra show long-wavelength 4f-4f transitions which provide a potential use of the compound as a NIR-emitting material for the doping of polymer-based matrices for waveguides or for bio-analytical applications. The dispersion of the novel complex in a biocompatible chitosan film has been assessed.

Graphical representation of covariant-contravariant modal formulae

Directory of Open Access Journals (Sweden)

Miguel Palomino

2011-08-01

Full Text Available Covariant-contravariant simulation is a combination of standard (covariant simulation, its contravariant counterpart and bisimulation. We have previously studied its logical characterization by means of the covariant-contravariant modal logic. Moreover, we have investigated the relationships between this model and that of modal transition systems, where two kinds of transitions (the so-called may and must transitions were combined in order to obtain a simple framework to express a notion of refinement over state-transition models. In a classic paper, Boudol and Larsen established a precise connection between the graphical approach, by means of modal transition systems, and the logical approach, based on Hennessy-Milner logic without negation, to system specification. They obtained a (graphical representation theorem proving that a formula can be represented by a term if, and only if, it is consistent and prime. We show in this paper that the formulae from the covariant-contravariant modal logic that admit a "graphical" representation by means of processes, modulo the covariant-contravariant simulation preorder, are also the consistent and prime ones. In order to obtain the desired graphical representation result, we first restrict ourselves to the case of covariant-contravariant systems without bivariant actions. Bivariant actions can be incorporated later by means of an encoding that splits each bivariant action into its covariant and its contravariant parts.

Catalogue of response spectra for unfolding in situ gamma-ray pulse-height distributions

International Nuclear Information System (INIS)

Dymke, N.

1982-01-01

To unfold in situ gamma-ray pulse-height distributions by means of a response matrix technique, the matrix must be in keeping with the measurement geometry, detector size, and energy range to be covered by the measurements. A methodology has been described for determination of standard gamma-ray spectra needed in deriving response matrices and a spectrum catalogue compiled containing graphs and data for the 0-3 MeV (4 x 4 in. NaI(Tl)) and 0-8 MeV (1.5 x 1.5 in. NaI(Tl)) ranges. (author)

Mahalanobis Distance Based Iterative Closest Point

DEFF Research Database (Denmark)

Hansen, Mads Fogtmann; Blas, Morten Rufus; Larsen, Rasmus

2007-01-01

the notion of a mahalanobis distance map upon a point set with associated covariance matrices which in addition to providing correlation weighted distance implicitly provides a method for assigning correspondence during alignment. This distance map provides an easy formulation of the ICP problem that permits...... a fast optimization. Initially, the covariance matrices are set to the identity matrix, and all shapes are aligned to a randomly selected shape (equivalent to standard ICP). From this point the algorithm iterates between the steps: (a) obtain mean shape and new estimates of the covariance matrices from...... the aligned shapes, (b) align shapes to the mean shape. Three different methods for estimating the mean shape with associated covariance matrices are explored in the paper. The proposed methods are validated experimentally on two separate datasets (IMM face dataset and femur-bones). The superiority of ICP...

On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers

Directory of Open Access Journals (Sweden)

Zhaolin Jiang

2014-01-01

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

Immanant Conversion on Symmetric Matrices

Directory of Open Access Journals (Sweden)

Purificação Coelho M.

2014-01-01

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

Covariant single-hole optical potential

International Nuclear Information System (INIS)

Kam, J. de

1982-01-01

In this investigation a covariant optical potential model is constructed for scattering processes of mesons from nuclei in which the meson interacts repeatedly with one of the target nucleons. The nuclear binding interactions in the intermediate scattering state are consistently taken into account. In particular for pions and K - projectiles this is important in view of the strong energy dependence of the elementary projectile-nucleon amplitude. Furthermore, this optical potential satisfies unitarity and relativistic covariance. The starting point in our discussion is the three-body model for the optical potential. To obtain a practical covariant theory I formulate the three-body model as a relativistic quasi two-body problem. Expressions for the transition interactions and propagators in the quasi two-body equations are found by imposing the correct s-channel unitarity relations and by using dispersion integrals. This is done in such a way that the correct non-relativistic limit is obtained, avoiding clustering problems. Corrections to the quasi two-body treatment from the Pauli principle and the required ground-state exclusion are taken into account. The covariant equations that we arrive at are amenable to practical calculations. (orig.)

The 'golden' matrices and a new kind of cryptography

International Nuclear Information System (INIS)

Stakhov, A.P.

2007-01-01

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

Advanced incomplete factorization algorithms for Stiltijes matrices

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

A comparison of phenotypic variation and covariation patterns and the role of phylogeny, ecology, and ontogeny during cranial evolution of new world monkeys.

Science.gov (United States)

Marroig, G; Cheverud, J M

2001-12-01

Similarity of genetic and phenotypic variation patterns among populations is important for making quantitative inferences about past evolutionary forces acting to differentiate populations and for evaluating the evolution of relationships among traits in response to new functional and developmental relationships. Here, phenotypic co variance and correlation structure is compared among Platyrrhine Neotropical primates. Comparisons range from among species within a genus to the superfamily level. Matrix correlation followed by Mantel's test and vector correlation among responses to random natural selection vectors (random skewers) were used to compare correlation and variance/covariance matrices of 39 skull traits. Sampling errors involved in matrix estimates were taken into account in comparisons using matrix repeatability to set upper limits for each pairwise comparison. Results indicate that covariance structure is not strictly constant but that the amount of variance pattern divergence observed among taxa is generally low and not associated with taxonomic distance. Specific instances of divergence are identified. There is no correlation between the amount of divergence in covariance patterns among the 16 genera and their phylogenetic distance derived from a conjoint analysis of four already published nuclear gene datasets. In contrast, there is a significant correlation between phylogenetic distance and morphological distance (Mahalanobis distance among genus centroids). This result indicates that while the phenotypic means were evolving during the last 30 millions years of New World monkey evolution, phenotypic covariance structures of Neotropical primate skulls have remained relatively consistent. Neotropical primates can be divided into four major groups based on their feeding habits (fruit-leaves, seed-fruits, insect-fruits, and gum-insect-fruits). Differences in phenotypic covariance structure are correlated with differences in feeding habits, indicating

On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices

KAUST Repository

Pestana, Jennifer

2014-01-01

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

A compact and stable eddy covariance set-up for methane measurements using off-axis integrated cavity output spectroscopy

Directory of Open Access Journals (Sweden)

D. M. D. Hendriks

2008-01-01

Full Text Available A Fast Methane Analyzer (FMA is assessed for its applicability in a closed path eddy covariance field set-up in a peat meadow. The FMA uses off-axis integrated cavity output spectroscopy combined with a highly specific narrow band laser for the detection of CH₄ and strongly reflective mirrors to obtain a laser path length of 2–20×10³ m. Statistical testing and a calibration experiment showed high precision (7.8×10⁻³ ppb and accuracy (<0.30% of the instrument, while no drift was observed. The instrument response time was determined to be 0.10 s. In the field set-up, the FMA is attached to a scroll pump and combined with a 3-axis ultrasonic anemometer and an open path infrared gas analyzer for measurements of carbon dioxide and water vapour. The power-spectra and co-spectra of the instruments were satisfactory for 10 Hz sampling rates.

Due to erroneous measurements, spikes and periods of low turbulence the data series consisted for 26% of gaps. Observed CH₄ fluxes consisted mainly of emission, showed a diurnal cycle, but were rather variable over. The average CH₄ emission was 29.7 nmol m⁻² s⁻¹, while the typical maximum CH₄ emission was approximately 80.0 nmol m⁻² s⁻¹ and the typical minimum flux was approximately 0.0 nmol m⁻² s⁻¹. The correspondence of the measurements with flux chamber measurements in the footprint was good and the observed CH₄ emission rates were comparable with eddy covariance CH₄ measurements in other peat areas.

Additionally, three measurement techniques with lower sampling frequencies were simulated, which might give the possibility to measure CH₄ fluxes without an external pump and save energy. Disjunct eddy covariance appeared to be the most reliable substitute for 10 Hz eddy covariance, while relaxed eddy accumulation gave

Field intercomparison of four methane gas analyzers suitable for eddy covariance flux measurements

Science.gov (United States)

Peltola, O.; Mammarella, I.; Haapanala, S.; Burba, G.; Vesala, T.

2013-06-01

Performances of four methane gas analyzers suitable for eddy covariance measurements are assessed. The assessment and comparison was performed by analyzing eddy covariance data obtained during summer 2010 (1 April to 26 October) at a pristine fen, Siikaneva, Southern Finland. High methane fluxes with pronounced seasonality have been measured at this fen. The four participating methane gas analyzers are commercially available closed-path units TGA-100A (Campbell Scientific Inc., USA), RMT-200 (Los Gatos Research, USA), G1301-f (Picarro Inc., USA) and an early prototype open-path unit Prototype-7700 (LI-COR Biosciences, USA). The RMT-200 functioned most reliably throughout the measurement campaign, during low and high flux periods. Methane fluxes from RMT-200 and G1301-f had the smallest random errors and the fluxes agree remarkably well throughout the measurement campaign. Cospectra and power spectra calculated from RMT-200 and G1301-f data agree well with corresponding temperature spectra during a high flux period. None of the gas analyzers showed statistically significant diurnal variation for methane flux. Prototype-7700 functioned only for a short period of time, over one month, in the beginning of the measurement campaign during low flux period, and thus, its overall accuracy and season-long performance were not assessed. The open-path gas analyzer is a practical choice for measurement sites in remote locations due to its low power demand, whereas for G1301-f methane measurements interference from water vapor is straightforward to correct since the instrument measures both gases simultaneously. In any case, if only the performance in this intercomparison is considered, RMT-200 performed the best and is the recommended choice if a new fast response methane gas analyzer is needed.

Nuclear data covariances in the Indian context

International Nuclear Information System (INIS)

Ganesan, S.

2014-01-01

The topic of covariances is recognized as an important part of several ongoing nuclear data science activities, since 2007, in the Nuclear Data Physics Centre of India (NDPCI). A Phase-1 project in collaboration with the Statistics department in Manipal University, Karnataka (Prof. K.M. Prasad and Prof. S. Nair) on nuclear data covariances was executed successfully during 2007-2011 period. In Phase-I, the NDPCI has conducted three national Theme meetings sponsored by the DAE-BRNS in 2008, 2010 and 2013 on nuclear data covariances. In Phase-1, the emphasis was on a thorough basic understanding of the concept of covariances including assigning uncertainties to experimental data in terms of partial errors and micro correlations, through a study and a detailed discussion of open literature. Towards the end of Phase-1, measurements and a first time covariance analysis of cross-sections for 58 Ni (n, p) 58 Co reaction measured in Mumbai Pelletron accelerator using 7 Li (p,n) reactions as neutron source in the MeV energy region were performed under a PhD programme on nuclear data covariances in which enrolled are two students, Shri B.S. Shivashankar and Ms. Shanti Sheela. India is also successfully evolving a team of young researchers to code nuclear data of uncertainties, with the perspectives on covariances, in the IAEA-EXFOR format. A Phase-II DAE-BRNS-NDPCI proposal of project at Manipal has been submitted and the proposal is undergoing a peer-review at this time. In Phase-2, modern nuclear data evaluation techniques that including covariances will be further studied as a research and development effort, as a first time effort. These efforts include the use of techniques such as that of the Kalman filter. Presently, a 48 hours lecture series on treatment of errors and their propagation is being formulated under auspices of the Homi Bhabha National Institute. The talk describes the progress achieved thus far in the learning curve of the above-mentioned and exciting

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

Science.gov (United States)

Lee, Ken Voon

2013-04-01

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

Predicting Covariance Matrices with Financial Conditions Indexes

NARCIS (Netherlands)

A. Opschoor (Anne); D.J.C. van Dijk (Dick); M. van der Wel (Michel)

2013-01-01

textabstractWe model the impact of financial conditions on asset market volatility and correlation. We propose extensions of (factor-)GARCH models for volatility and DCC models for correlation that allow for including indexes that measure financial conditions. In our empirical application we

Experience in using the covariances of some ENDF/B-V dosimetry cross sections: proposed improvements and addition of cross-reaction covariances

International Nuclear Information System (INIS)

Fu, C.Y.; Hetrick, D.M.

1982-01-01

Recent ratio data, with carefully evaluated covariances, were combined with eleven of the ENDF/B-V dosimetry cross sections using the generalized least-squares method. The purpose was to improve these evaluated cross sections and covariances, as well as to generate values for the cross-reaction covariances. The results represent improved cross sections as well as realistic and usable covariances. The latter are necessary for meaningful intergral-differential comparisons and for spectrum unfolding

SIGMA WEB INTERFACE FOR REACTOR DATA APPLICATIONS

Energy Technology Data Exchange (ETDEWEB)

Pritychenko,B.; Sonzogni, A.A.

2010-05-09

We present Sigma Web interface which provides user-friendly access for online analysis and plotting of the evaluated and experimental nuclear reaction data stored in the ENDF-6 and EXFOR formats. The interface includes advanced browsing and search capabilities, interactive plots of cross sections, angular distributions and spectra, nubars, comparisons between evaluated and experimental data, computations for cross section data sets, pre-calculated integral quantities, neutron cross section uncertainties plots and visualization of covariance matrices. Sigma is publicly available at the National Nuclear Data Center website at http://www.nndc.bnl.gov/sigma.

Sigma Web Interface For Reactor Data Applications

International Nuclear Information System (INIS)

Pritychenko, B.; Sonzogni, A.A.

2010-01-01

We present Sigma Web interface which provides user-friendly access for online analysis and plotting of the evaluated and experimental nuclear reaction data stored in the ENDF-6 and EXFOR formats. The interface includes advanced browsing and search capabilities, interactive plots of cross sections, angular distributions and spectra, nubars, comparisons between evaluated and experimental data, computations for cross section data sets, pre-calculated integral quantities, neutron cross section uncertainties plots and visualization of covariance matrices. Sigma is publicly available at the National Nuclear Data Center website at http://www.nndc.bnl.gov/sigma.

Covariance problem in two-dimensional quantum chromodynamics

International Nuclear Information System (INIS)

Hagen, C.R.

1979-01-01

The problem of covariance in the field theory of a two-dimensional non-Abelian gauge field is considered. Since earlier work has shown that covariance fails (in charged sectors) for the Schwinger model, particular attention is given to an evaluation of the role played by the non-Abelian nature of the fields. In contrast to all earlier attempts at this problem, it is found that the potential covariance-breaking terms are identical to those found in the Abelian theory provided that one expresses them in terms of the total (i.e., conserved) current operator. The question of covariance is thus seen to reduce in all cases to a determination as to whether there exists a conserved global charge in the theory. Since the charge operator in the Schwinger model is conserved only in neutral sectors, one is thereby led to infer a probable failure of covariance in the non-Abelian theory, but one which is identical to that found for the U(1) case

Schroedinger covariance states in anisotropic waveguides

International Nuclear Information System (INIS)

Angelow, A.; Trifonov, D.

1995-03-01

In this paper Squeezed and Covariance States based on Schroedinger inequality and their connection with other nonclassical states are considered for particular case of anisotropic waveguide in LiNiO 3 . Here, the problem of photon creation and generation of squeezed and Schroedinger covariance states in optical waveguides is solved in two steps: 1. Quantization of electromagnetic field is provided in the presence of dielectric waveguide using normal-mode expansion. The photon creation and annihilation operators are introduced, expanding the solution A-vector(r-vector,t) in a series in terms of the Sturm - Liouville mode-functions. 2. In terms of these operators the Hamiltonian of the field in a nonlinear waveguide is derived. For such Hamiltonian we construct the covariance states as stable (with nonzero covariance), which minimize the Schroedinger uncertainty relation. The evolutions of the three second momenta of q-circumflex j and p-circumflex j are calculated. For this Hamiltonian all three momenta are expressed in terms of one real parameters s only. It is found out how covariance, via this parameter s, depends on the waveguide profile n(x,y), on the mode-distributions u-vector j (x,y), and on the waveguide phase mismatching Δβ. (author). 37 refs

Form of the manifestly covariant Lagrangian

Science.gov (United States)

Johns, Oliver Davis

1985-10-01

The preferred form for the manifestly covariant Lagrangian function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' Lagrangian and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant Lagrangian theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' Lagrangian, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives Lagrangian theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' Lagrangian is a completely adequate basis for covariant Lagrangian theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the Lagrangian and other four-vector equations.

Determination of covariant Schwinger terms in anomalous gauge theories

International Nuclear Information System (INIS)

Kelnhofer, G.

1991-01-01

A functional integral method is used to determine equal time commutators between the covariant currents and the covariant Gauss-law operators in theories which are affected by an anomaly. By using a differential geometrical setup we show how the derivation of consistent- and covariant Schwinger terms can be understood on an equal footing. We find a modified consistency condition for the covariant anomaly. As a by-product the Bardeen-Zumino functional, which relates consistent and covariant anomalies, can be interpreted as connection on a certain line bundle over all gauge potentials. Finally the covariant commutator anomalies are calculated for the two- and four dimensional case. (orig.)

Cross-population myelination covariance of human cerebral cortex.

Science.gov (United States)

Ma, Zhiwei; Zhang, Nanyin

2017-09-01

Cross-population covariance of brain morphometric quantities provides a measure of interareal connectivity, as it is believed to be determined by the coordinated neurodevelopment of connected brain regions. Although useful, structural covariance analysis predominantly employed bulky morphological measures with mixed compartments, whereas studies of the structural covariance of any specific subdivisions such as myelin are rare. Characterizing myelination covariance is of interest, as it will reveal connectivity patterns determined by coordinated development of myeloarchitecture between brain regions. Using myelin content MRI maps from the Human Connectome Project, here we showed that the cortical myelination covariance was highly reproducible, and exhibited a brain organization similar to that previously revealed by other connectivity measures. Additionally, the myelination covariance network shared common topological features of human brain networks such as small-worldness. Furthermore, we found that the correlation between myelination covariance and resting-state functional connectivity (RSFC) was uniform within each resting-state network (RSN), but could considerably vary across RSNs. Interestingly, this myelination covariance-RSFC correlation was appreciably stronger in sensory and motor networks than cognitive and polymodal association networks, possibly due to their different circuitry structures. This study has established a new brain connectivity measure specifically related to axons, and this measure can be valuable to investigating coordinated myeloarchitecture development. Hum Brain Mapp 38:4730-4743, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

CONVERGENCE OF POWERS OF CONTROLLABLE INTUITIONISTIC FUZZY MATRICES

OpenAIRE

Riyaz Ahmad Padder; P. Murugadas

2016-01-01

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

Covariant extensions and the nonsymmetric unified field

International Nuclear Information System (INIS)

Borchsenius, K.

1976-01-01

The problem of generally covariant extension of Lorentz invariant field equations, by means of covariant derivatives extracted from the nonsymmetric unified field, is considered. It is shown that the contracted curvature tensor can be expressed in terms of a covariant gauge derivative which contains the gauge derivative corresponding to minimal coupling, if the universal constant p, characterizing the nonsymmetric theory, is fixed in terms of Planck's constant and the elementary quantum of charge. By this choice the spinor representation of the linear connection becomes closely related to the spinor affinity used by Infeld and Van Der Waerden (Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl.; 9:380 (1933)) in their generally covariant formulation of Dirac's equation. (author)

Computing more proper covariances of energy dependent nuclear data

International Nuclear Information System (INIS)

Vanhanen, R.

2016-01-01

Highlights: • We present conditions for covariances of energy dependent nuclear data to be proper. • We provide methods to detect non-positive and inconsistent covariances in ENDF-6 format. • We propose methods to find nearby more proper covariances. • The methods can be used as a part of a quality assurance program. - Abstract: We present conditions for covariances of energy dependent nuclear data to be proper in the sense that the covariances are positive, i.e., its eigenvalues are non-negative, and consistent with respect to the sum rules of nuclear data. For the ENDF-6 format covariances we present methods to detect non-positive and inconsistent covariances. These methods would be useful as a part of a quality assurance program. We also propose methods that can be used to find nearby more proper energy dependent covariances. These methods can be used to remove unphysical components, while preserving most of the physical components. We consider several different senses in which the nearness can be measured. These methods could be useful if a re-evaluation of improper covariances is not feasible. Two practical examples are processed and analyzed. These demonstrate some of the properties of the methods. We also demonstrate that the ENDF-6 format covariances of linearly dependent nuclear data should usually be encoded with the derivation rules.

Loop diagrams without γ matrices

International Nuclear Information System (INIS)

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

1993-01-01

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

Covariance Spectroscopy for Fissile Material Detection

International Nuclear Information System (INIS)

Trainham, Rusty; Tinsley, Jim; Hurley, Paul; Keegan, Ray

2009-01-01

Nuclear fission produces multiple prompt neutrons and gammas at each fission event. The resulting daughter nuclei continue to emit delayed radiation as neutrons boil off, beta decay occurs, etc. All of the radiations are causally connected, and therefore correlated. The correlations are generally positive, but when different decay channels compete, so that some radiations tend to exclude others, negative correlations could also be observed. A similar problem of reduced complexity is that of cascades radiation, whereby a simple radioactive decay produces two or more correlated gamma rays at each decay. Covariance is the usual means for measuring correlation, and techniques of covariance mapping may be useful to produce distinct signatures of special nuclear materials (SNM). A covariance measurement can also be used to filter data streams because uncorrelated signals are largely rejected. The technique is generally more effective than a coincidence measurement. In this poster, we concentrate on cascades and the covariance filtering problem

Optimal covariate designs theory and applications

CERN Document Server

Das, Premadhis; Mandal, Nripes Kumar; Sinha, Bikas Kumar

2015-01-01

This book primarily addresses the optimality aspects of covariate designs. A covariate model is a combination of ANOVA and regression models. Optimal estimation of the parameters of the model using a suitable choice of designs is of great importance; as such choices allow experimenters to extract maximum information for the unknown model parameters. The main emphasis of this monograph is to start with an assumed covariate model in combination with some standard ANOVA set-ups such as CRD, RBD, BIBD, GDD, BTIBD, BPEBD, cross-over, multi-factor, split-plot and strip-plot designs, treatment control designs, etc. and discuss the nature and availability of optimal covariate designs. In some situations, optimal estimations of both ANOVA and the regression parameters are provided. Global optimality and D-optimality criteria are mainly used in selecting the design. The standard optimality results of both discrete and continuous set-ups have been adapted, and several novel combinatorial techniques have been applied for...

Covariate Imbalance and Precision in Measuring Treatment Effects

Science.gov (United States)

Liu, Xiaofeng Steven

2011-01-01

Covariate adjustment can increase the precision of estimates by removing unexplained variance from the error in randomized experiments, although chance covariate imbalance tends to counteract the improvement in precision. The author develops an easy measure to examine chance covariate imbalance in randomization by standardizing the average…

Covariant description of Hamiltonian form for field dynamics

International Nuclear Information System (INIS)

Ozaki, Hiroshi

2005-01-01

Hamiltonian form of field dynamics is developed on a space-like hypersurface in space-time. A covariant Poisson bracket on the space-like hypersurface is defined and it plays a key role to describe every algebraic relation into a covariant form. It is shown that the Poisson bracket has the same symplectic structure that was brought in the covariant symplectic approach. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density generates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory. By converting the covariant Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to quantum field theory in the Heisenberg picture without spoiling the explicit relativistic covariance. As an example the canonical QCD is displayed in a covariant way on a space-like hypersurface

Classification en référence à une matrice stochastique

OpenAIRE

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

2009-01-01

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

Biomimetic mineralization of recombinant collagen type I derived protein to obtain hybrid matrices for bone regeneration.

Science.gov (United States)

Ramírez-Rodríguez, Gloria Belén; Delgado-López, José Manuel; Iafisco, Michele; Montesi, Monica; Sandri, Monica; Sprio, Simone; Tampieri, Anna

2016-11-01

Understanding the mineralization mechanism of synthetic protein has recently aroused great interest especially in the development of advanced materials for bone regeneration. Herein, we propose the synthesis of composite materials through the mineralization of a recombinant collagen type I derived protein (RCP) enriched with RGD sequences in the presence of magnesium ions (Mg) to closer mimic bone composition. The role of both RCP and Mg ions in controlling the precipitation of the mineral phase is in depth evaluated. TEM and X-ray powder diffraction reveal the crystallization of nanocrystalline apatite (Ap) in all the evaluated conditions. However, Raman spectra point out also the precipitation of amorphous calcium phosphate (ACP). This amorphous phase is more evident when RCP and Mg are at work, indicating the synergistic role of both in stabilizing the amorphous precursor. In addition, hybrid matrices are prepared to tentatively address their effectiveness as scaffolds for bone tissue engineering. SEM and AFM imaging show an homogeneous mineral distribution on the RCP matrix mineralized in presence of Mg, which provides a surface roughness similar to that found in bone. Preliminary in vitro tests with pre-osteoblast cell line show good cell-material interaction on the matrices prepared in the presence of Mg. To the best of our knowledge this work represents the first attempt to mineralize recombinant collagen type I derived protein proving the simultaneous effect of the organic phase (RCP) and Mg on ACP stabilization. This study opens the possibility to engineer, through biomineralization process, advanced hybrid matrices for bone regeneration. Copyright © 2016 Elsevier Inc. All rights reserved.

Binary Positive Semidefinite Matrices and Associated Integer Polytopes

DEFF Research Database (Denmark)

Letchford, Adam N.; Sørensen, Michael Malmros

2012-01-01

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

UV-Visible Spectra of PAHs and Derivatives Seeded in Supersonic Jet. Astrophysical Implications

Science.gov (United States)

Salma, Bejaoui; Salama, Farid

2018-06-01

Laboratory absorption spectra of Polycyclic Aromatic Hydrocarbons (PAHs) and PAH derivatives measured under astrophysical relevant conditions are crucial to test the PAHs-DIBs hypothesis as well as the PAH model for the IR emission bands. Our dedicated experimental setup on the COsmic SImulation Chamber (COSmIC) provides an excellent platform to study neutral and ionized PAHs under the low temperature and pressure conditions that are representative of interstellar environments [1]. In this work, we study the effect of the substitution of CH bond(s) by a nitrogen atom(s) on the electronic spectra of phenanthrene. The electronic transitions associated with the lower excited states of neutral phenanthrene (C14H10) and phenanthridine (C13H9N) are measured in gas phase in the 315-345 nm region. Molecules are seeded in a supersonic expansion of argon gas and the absorption spectra are measured using the Cavity Ring Down Spectroscopy (CRDS) technique. Additional measurements of the absorption spectra of phenanthrene, phenantridine and 1,10-phenanthroline (C12H8N2) isolated in 10 K argon matrices are also performed. The comparison between the CRDS spectra with the absorption of the matrix-isolated molecules highlight the matrix-induced perturbations in band position, profiles and broadening and illustrates the need of gas phase measurements for more accurate comparisons with astronomical spectra.[1] Salama, F., Galazutdinov, G., Krelowski, et al. ApJ 728, 154[FS1] (2011).[2] A. Tielens, ApJ 526 Pt 1265–273 (2008),Acknowledgements: This research is supported by the APRA Program of NASA SMD

Sparsity-Based Space-Time Adaptive Processing Using OFDM Radar

Energy Technology Data Exchange (ETDEWEB)

Sen, Satyabrata [ORNL

2012-01-01

We propose a sparsity-based space-time adaptive processing (STAP) algorithm to detect a slowly-moving target using an orthogonal frequency division multiplexing (OFDM) radar. We observe that the target and interference spectra are inherently sparse in the spatio-temporal domain, and hence we exploit that sparsity to develop an efficient STAP technique. In addition, the use of an OFDM signal increases the frequency diversity of our system, as different scattering centers of a target resonate at different frequencies, and thus improves the target detectability. First, we formulate a realistic sparse-measurement model for an OFDM radar considering both the clutter and jammer as the interfering sources. Then, we show that the optimal STAP-filter weight-vector is equal to the generalized eigenvector corresponding to the minimum generalized eigenvalue of the interference and target covariance matrices. To estimate the target and interference covariance matrices, we apply a residual sparse-recovery technique that enables us to incorporate the partially known support of the sparse vector. Our numerical results demonstrate that the sparsity-based STAP algorithm, with considerably lesser number of secondary data, produces an equivalent performance as the other existing STAP techniques.

Chain of matrices, loop equations and topological recursion

CERN Document Server

Orantin, Nicolas

2009-01-01

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

The problem of channel dependence in foil-absorption X-ray spectroscopy

International Nuclear Information System (INIS)

Rodriguez-Trelles, F.; Caputo, M.C.

1986-01-01

We analyze the interdependence among measurements of X-ray spectra in the energy range 4-60 keV by a multi-channel instrument. Two methods of estimating it are described. One gives the error magnification expected in spectrum deconvolution resulting from the covariance matrix of the products of filter transmission times detector sensitivity, evaluated over the whole accessible range of photon energies. The other is an extension of the former evaluating the covariance matrices over consecutive energy bands. This extension allows one to analyze channel dependence for each band, thus improving the prospects of filter and detector selection in the design of an experiment. We present tables showing the expected behaviors of several combinations of filters (homogeneous, heterogeneous, doublets, Ross) and detectors (flat, film, diodes). The advantages of heterogeneous filters are emphasized. (orig.)

THE MEASUREMENT, TREATMENT, AND IMPACT OF SPECTRAL COVARIANCE AND BAYESIAN PRIORS IN INTEGRAL -FIELD SPECTROSCOPY OF EXOPLANETS

Energy Technology Data Exchange (ETDEWEB)

Greco, Johnny P. [Department of Astrophysical Sciences, Princeton University, Princeton, NJ (United States); Brandt, Timothy D. [Institute for Advanced Study, Princeton, NJ (United States)

2016-12-20

The recovery of an exoplanet’s atmospheric parameters from its spectrum requires accurate knowledge of the spectral errors and covariances. Unfortunately, the complex image processing used in high-contrast integral-field spectrograph (IFS) observations generally produces spectral covariances that are poorly understood and often ignored. In this work, we show how to measure the spectral errors and covariances and include them self-consistently in parameter retrievals. By combining model exoplanet spectra with a realistic noise model generated from the Gemini Planet Imager (GPI) early science data, we show that ignoring spectral covariance in high-contrast IFS data can both bias inferred parameters and lead to unreliable confidence regions on those parameters. This problem is made worse by the common practice of scaling the χ {sup 2} per degree of freedom to unity; the input parameters then fall outside the 95% confidence regions in as many as ∼80% of noise realizations. The biases we observe can approach the typical levels of precision achieved in high-contrast spectroscopy. Accounting for realistic priors in fully Bayesian retrievals can also have a significant impact on the inferred parameters. Plausible priors on effective temperature and surface gravity can vary by an order of magnitude across the confidence regions appropriate for objects with weak age constraints; priors for objects with good age constraints are dominated by modeling uncertainties. Our methods are directly applicable to existing high-contrast IFSs including GPI and SPHERE, as well as upcoming instruments like CHARIS and, ultimately, WFIRST-AFTA.

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

OpenAIRE

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

2017-01-01

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

Parametric Covariance Model for Horizon-Based Optical Navigation

Science.gov (United States)

Hikes, Jacob; Liounis, Andrew J.; Christian, John A.

2016-01-01

This Note presents an entirely parametric version of the covariance for horizon-based optical navigation measurements. The covariance can be written as a function of only the spacecraft position, two sensor design parameters, the illumination direction, the size of the observed planet, the size of the lit arc to be used, and the total number of observed horizon points. As a result, one may now more clearly understand the sensitivity of horizon-based optical navigation performance as a function of these key design parameters, which is insight that was obscured in previous (and nonparametric) versions of the covariance. Finally, the new parametric covariance is shown to agree with both the nonparametric analytic covariance and results from a Monte Carlo analysis.

Structure and properties of hydrocarbon radical cations in low-temperature matrices as studied by a combination of EPR and IR spectroscopy

International Nuclear Information System (INIS)

Feldman, V.I.

1997-01-01

Use of IR spectroscopy (as a supplement to EPR) may provide new insight into the problem of analysis of structure and properties of organic radical cations. In this work, the results of combined EPR/IR studies of the formation, structure and properties of hydrocarbon radical cations in halocarbon and solid rare gas matrices are discussed. Both IR and EPR studies were carried out with matrix deposited samples irradiated with fast electrons at 15 or 77 K. IR spectroscopic data were found to be helpful in three aspects: (i) characterization of the conformation and association and molecule-matrix interactions of the parent molecules; (ii) identification of diamagnetic products of the reactions of radical cations in ground and excited states; (iii) determining the characteristics of vibrational spectra of the radical cations, which are of primary interest for analysis of chemical bonding and reactivity of the radical cations. The applications of the combined approach are illustrated with examples of studies of several alkenes in Freon matrices and alkanes in solid rare gas matrices. The matrix effects on trapping and degradation of radical cations were interpreted as the result of variations in matrix electronic characteristics (IP, polarizability) and molecule-matrix interactions. (au) 48 refs

Activities on covariance estimation in Japanese Nuclear Data Committee

Energy Technology Data Exchange (ETDEWEB)

Shibata, Keiichi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

1997-03-01

Described are activities on covariance estimation in the Japanese Nuclear Data Committee. Covariances are obtained from measurements by using the least-squares methods. A simultaneous evaluation was performed to deduce covariances of fission cross sections of U and Pu isotopes. A code system, KALMAN, is used to estimate covariances of nuclear model calculations from uncertainties in model parameters. (author)

The Modern Origin of Matrices and Their Applications

Science.gov (United States)

Debnath, L.

2014-01-01

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

Flux Jacobian Matrices For Equilibrium Real Gases

Science.gov (United States)

Vinokur, Marcel

1990-01-01

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

Cross-covariance functions for multivariate geostatistics

KAUST Repository

Genton, Marc G.

2015-05-01

Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Matérn and nonstationary and space-time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems. © Institute of Mathematical Statistics, 2015.

Cross-covariance functions for multivariate geostatistics

KAUST Repository

Genton, Marc G.; Kleiber, William

2015-01-01

Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Matérn and nonstationary and space-time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems. © Institute of Mathematical Statistics, 2015.

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

Science.gov (United States)

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

2016-08-01

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

The method of covariant symbols in curved space-time

International Nuclear Information System (INIS)

Salcedo, L.L.

2007-01-01

Diagonal matrix elements of pseudodifferential operators are needed in order to compute effective Lagrangians and currents. For this purpose the method of symbols is often used, which however lacks manifest covariance. In this work the method of covariant symbols, introduced by Pletnev and Banin, is extended to curved space-time with arbitrary gauge and coordinate connections. For the Riemannian connection we compute the covariant symbols corresponding to external fields, the covariant derivative and the Laplacian, to fourth order in a covariant derivative expansion. This allows one to obtain the covariant symbol of general operators to the same order. The procedure is illustrated by computing the diagonal matrix element of a nontrivial operator to second order. Applications of the method are discussed. (orig.)

Propositional matrices as alternative representation of truth values ...

African Journals Online (AJOL)

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

Conformally covariant massless spin-two field equations

International Nuclear Information System (INIS)

Drew, M.S.; Gegenberg, J.D.

1980-01-01

An explicit proof is constructed to show that the field equations for a symmetric tensor field hsub(ab) describing massless spin-2 particles in Minkowski space-time are not covariant under the 15-parameter group SOsub(4,2); this group is usually associated with conformal transformations on flat space, and here it will be considered as a global gauge group which acts upon matter fields defined on space-time. Notwithstanding the above noncovariance, the equations governing the rank-4 tensor Ssub(abcd) constructed from hsub(ab) are shown to be covariant provided the contraction Ssub(ab) vanishes. Conformal covariance is proved by demonstrating the covariance of the equations for the equivalent 5-component complex field; in fact, covariance is proved for a general field equation applicable to massless particles of any spin >0. It is shown that the noncovariance of the hsub(ab) equations may be ascribed to the fact that the transformation behaviour of hsub(ab) is not the same as that of a field consisting of a gauge only. Since this is in contradistinction to the situation for the electromagnetic-field equations, the vector form of the electromagnetic equations is cast into a form which can be duplicated for the hsub(ab)-field. This procedure results in an alternative, covariant, field equation for hsub(ab). (author)

Measurement and analysis of neutron flux spectra in a neutronics mock-up of the HCLL test blanket module

International Nuclear Information System (INIS)

Klix, A.; Batistoni, P.; Boettger, R.; Lebrun-Grandie, D.; Fischer, U.; Henniger, J.; Leichtle, D.; Villari, R.

2010-01-01

Fast neutron and gamma-ray flux spectra and time-of-arrival spectra of slow neutrons have been measured in a neutronics mock-up of the European Helium-Cooled Lithium-Lead Test Blanket Module with the aim to validate nuclear cross-section data. The mock-up was irradiated with fusion peak neutrons from the DT neutron generator of the Technical University of Dresden. A well characterized cylindrical NE-213 scintillator was inserted into two positions in the LiPb/EUROFER assembly. Pulse height spectra from neutrons and gamma-rays were recorded from the NE-213 output. The spectra were then unfolded with experimentally obtained response matrices of the NE-213 detector. Time-of-arrival spectra of slow neutrons were measured with a 3 He counter placed in the mock-up, and the neutron generator was operated in pulsed mode. Monte Carlo calculations using the MCNP code and nuclear cross-section data from the JEFF-3.1.1 and FENDL-2.1 libraries were performed and the results are compared with the experimental results. A good agreement of measurement and calculation was found with some deviations in certain energy intervals.

Evaluation of covariance for 238U cross sections

International Nuclear Information System (INIS)

Kawano, Toshihiko; Nakamura, Masahiro; Matsuda, Nobuyuki; Kanda, Yukinori

1995-01-01

Covariances of 238 U are generated using analytic functions for representation of the cross sections. The covariances of the (n,2n) and (n,3n) reactions are derived with a spline function, while the covariances of the total and the inelastic scattering cross section are estimated with a linearized nuclear model calculation. (author)

GLq(N)-covariant quantum algebras and covariant differential calculus

International Nuclear Information System (INIS)

Isaev, A.P.; Pyatov, P.N.

1993-01-01

We consider GL q (N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. The connection with the bicovariant differential calculus on the linear quantum groups is discussed. (orig.)

Asset allocation with different covariance/correlation estimators

OpenAIRE

Μανταφούνη, Σοφία

2007-01-01

The subject of the study is to test whether the use of different covariance – correlation estimators than the historical covariance matrix that is widely used, would help in portfolio optimization through the mean-variance analysis. In other words, if an investor would like to use the mean-variance analysis in order to invest in assets like stocks or indices, would it be of some help to use more sophisticated estimators for the covariance matrix of the returns of his portfolio? The procedure ...

Wishart and anti-Wishart random matrices

International Nuclear Information System (INIS)

Janik, Romuald A; Nowak, Maciej A

2003-01-01

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

Information geometry of density matrices and state estimation

International Nuclear Information System (INIS)

Brody, Dorje C

2011-01-01

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

Methods and Issues for the Combined Use of Integral Experiments and Covariance Data