Group Lasso estimation of high-dimensional covariance matrices
Bigot, Jérémie; Loubes, Jean-Michel; Alvarez, Lilian Muniz
2010-01-01
In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the process has a sparse representation in a large dictionary of basis functions. Using a matrix regression model, we propose a new methodology for high-dimensional covariance matrix estimation based on empirical contrast regularization by a group Lasso penalty. Using such a penalty, the method selects a sparse set of basis functions in the dictionary used to approximate the process, leading to an approximation of the covariance matrix into a low dimensional space. Consistency of the estimator is studied in Frobenius and operator norms and an application to sparse PCA is proposed.
Zhang, Xuguang; Zhang, Yun; Zhang, Jie; Chen, Shengyong; Chen, Dan; Li, Xiaoli
2012-04-01
Toward the unsupervised clustering for color logo images corrupted by noise, we propose a novel framework in which the logo images are described by a model called singular values based region covariance matrices (SVRCM), and the mean shift algorithm is performed on Lie groups for clustering covariance matrices. To decrease the influence of noise, we choose the larger singular values, which can better represent the original image and discard the smaller singular values. Therefore, the chosen singular values are grouped and fused by a covariance matrix to form a SVRCM model that can represent the correlation and variance between different singular value features to enhance the discriminating ability of the model. In order to cluster covariance matrices, which do not lie on Euclidean space, the mean shift algorithm is performed on manifolds by iteratively transforming points between the Lie group and Lie algebra. Experimental results on 38 categories of logo images demonstrate the superior performance of the proposed method whose clustering rate can be achieved at 88.55%.
Universality of Covariance Matrices
Pillai, Natesh S
2011-01-01
We prove the universality of covariance matrices of the form $H_{N \\times N} = {1 \\over N} \\tp{X}X$ where $[X]_{M \\times N}$ is a rectangular matrix with independent real valued entries $[x_{ij}]$ satisfying $\\E \\,x_{ij} = 0$ and $\\E \\,x^2_{ij} = {1 \\over M}$, $N, M\\to \\infty$. Furthermore it is assumed that these entries have sub-exponential tails. We will study the asymptotics in the regime $N/M = d_N \\in (0,\\infty), \\lim_{N\\to \\infty}d_N \
Eigenvalue variance bounds for covariance matrices
Dallaporta, Sandrine
2013-01-01
This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for Wigner matrices and stated the results for covariance matrices. They are proved in the present paper. Relying on the LUE example, which needs to be investigated first, the main bounds are extended to complex covariance matrices by means of the Tao, Vu and Wan...
Forecasting Covariance Matrices: A Mixed Frequency Approach
DEFF Research Database (Denmark)
Halbleib, Roxana; Voev, Valeri
This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...... matrix dynamics. Our empirical results show that the new mixing approach provides superior forecasts compared to multivariate volatility specifications using single sources of information....
Levy Matrices and Financial Covariances
Burda, Zdzislaw; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, Gabor; Zahed, Ismail
2003-10-01
In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-07
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-05
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Functional CLT for sample covariance matrices
Bai, Zhidong; Zhou, Wang; 10.3150/10-BEJ250
2010-01-01
Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including $[(1-\\sqrt{y})^2,(1+\\sqrt{y})^2]$, the support of the Mar\\u{c}enko--Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-11-30
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
Covariance matrices for use in criticality safety predictability studies
Energy Technology Data Exchange (ETDEWEB)
Derrien, H.; Larson, N.M.; Leal, L.C.
1997-09-01
Criticality predictability applications require as input the best available information on fissile and other nuclides. In recent years important work has been performed in the analysis of neutron transmission and cross-section data for fissile nuclei in the resonance region by using the computer code SAMMY. The code uses Bayes method (a form of generalized least squares) for sequential analyses of several sets of experimental data. Values for Reich-Moore resonance parameters, their covariances, and the derivatives with respect to the adjusted parameters (data sensitivities) are obtained. In general, the parameter file contains several thousand values and the dimension of the covariance matrices is correspondingly large. These matrices are not reported in the current evaluated data files due to their large dimensions and to the inadequacy of the file formats. The present work has two goals: the first is to calculate the covariances of group-averaged cross sections from the covariance files generated by SAMMY, because these can be more readily utilized in criticality predictability calculations. The second goal is to propose a more practical interface between SAMMY and the evaluated files. Examples are given for {sup 235}U in the popular 199- and 238-group structures, using the latest ORNL evaluation of the {sup 235}U resonance parameters.
Linear transformations of variance/covariance matrices.
Parois, Pascal; Lutz, Martin
2011-07-01
Many applications in crystallography require the use of linear transformations on parameters and their standard uncertainties. While the transformation of the parameters is textbook knowledge, the transformation of the standard uncertainties is more complicated and needs the full variance/covariance matrix. For the transformation of second-rank tensors it is suggested that the 3 × 3 matrix is re-written into a 9 × 1 vector. The transformation of the corresponding variance/covariance matrix is then straightforward and easily implemented into computer software. This method is applied in the transformation of anisotropic displacement parameters, the calculation of equivalent isotropic displacement parameters, the comparison of refinements in different space-group settings and the calculation of standard uncertainties of eigenvalues.
Multigroup covariance matrices for fast-reactor studies
Energy Technology Data Exchange (ETDEWEB)
Smith, J.D. III; Broadhead, B.L.
1981-04-01
This report presents the multigroup covariance matrices based on the ENDF/B-V nuclear data evaluations. The materials and reactions have been chosen according to the specifications of ORNL-5517. Several cross section covariances, other than those specified by that report, are included due to the derived nature of the uncertainty files in ENDF/B-V. The materials represented are Ni, Cr, /sup 16/O, /sup 12/C, Fe, Na, /sup 235/U, /sup 238/U, /sup 239/Pu, /sup 240/Pu, /sup 241/Pu, and /sup 10/B (present due to its correlation to /sup 238/U). The data have been originally processed into a 52-group energy structure by PUFF-II and subsequently collapsed to smaller subgroup strutures. The results are illustrated in 52-group correlation matrix plots and tabulated into thirteen groups for convenience.
Parameter inference with estimated covariance matrices
Sellentin, Elena
2015-01-01
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be estimated and thereby becomes a random object with some intrinsic uncertainty itself. We show how to infer parameters in the presence of such an estimated covariance matrix, by marginalising over the true covariance matrix, conditioned on its estimated value. This leads to a likelihood function that is no longer Gaussian, but rather an adapted version of a multivariate $t$-distribution, which has the same numerical complexity as the multivariate Gaussian. As expected, marginalisation over the true covariance matrix improves inference when compared with Hartlap et al.'s method, which uses an unbiased estimate of the inverse covariance matrix but still assumes that the likelihood is Gaussian.
Linear transformations of variance/covariance matrices
Parois, P.J.A.; Lutz, M.
2011-01-01
Many applications in crystallography require the use of linear transformations on parameters and their standard uncertainties. While the transformation of the parameters is textbook knowledge, the transformation of the standard uncertainties is more complicated and needs the full variance/covariance
A simple procedure for the comparison of covariance matrices.
Garcia, Carlos
2012-11-21
Comparing the covariation patterns of populations or species is a basic step in the evolutionary analysis of quantitative traits. Here I propose a new, simple method to make this comparison in two population samples that is based on comparing the variance explained in each sample by the eigenvectors of its own covariance matrix with that explained by the covariance matrix eigenvectors of the other sample. The rationale of this procedure is that the matrix eigenvectors of two similar samples would explain similar amounts of variance in the two samples. I use computer simulation and morphological covariance matrices from the two morphs in a marine snail hybrid zone to show how the proposed procedure can be used to measure the contribution of the matrices orientation and shape to the overall differentiation. I show how this procedure can detect even modest differences between matrices calculated with moderately sized samples, and how it can be used as the basis for more detailed analyses of the nature of these differences. The new procedure constitutes a useful resource for the comparison of covariance matrices. It could fill the gap between procedures resulting in a single, overall measure of differentiation, and analytical methods based on multiple model comparison not providing such a measure.
A simple procedure for the comparison of covariance matrices
2012-01-01
Background Comparing the covariation patterns of populations or species is a basic step in the evolutionary analysis of quantitative traits. Here I propose a new, simple method to make this comparison in two population samples that is based on comparing the variance explained in each sample by the eigenvectors of its own covariance matrix with that explained by the covariance matrix eigenvectors of the other sample. The rationale of this procedure is that the matrix eigenvectors of two similar samples would explain similar amounts of variance in the two samples. I use computer simulation and morphological covariance matrices from the two morphs in a marine snail hybrid zone to show how the proposed procedure can be used to measure the contribution of the matrices orientation and shape to the overall differentiation. Results I show how this procedure can detect even modest differences between matrices calculated with moderately sized samples, and how it can be used as the basis for more detailed analyses of the nature of these differences. Conclusions The new procedure constitutes a useful resource for the comparison of covariance matrices. It could fill the gap between procedures resulting in a single, overall measure of differentiation, and analytical methods based on multiple model comparison not providing such a measure. PMID:23171139
A simple procedure for the comparison of covariance matrices
Directory of Open Access Journals (Sweden)
Garcia Carlos
2012-11-01
Full Text Available Abstract Background Comparing the covariation patterns of populations or species is a basic step in the evolutionary analysis of quantitative traits. Here I propose a new, simple method to make this comparison in two population samples that is based on comparing the variance explained in each sample by the eigenvectors of its own covariance matrix with that explained by the covariance matrix eigenvectors of the other sample. The rationale of this procedure is that the matrix eigenvectors of two similar samples would explain similar amounts of variance in the two samples. I use computer simulation and morphological covariance matrices from the two morphs in a marine snail hybrid zone to show how the proposed procedure can be used to measure the contribution of the matrices orientation and shape to the overall differentiation. Results I show how this procedure can detect even modest differences between matrices calculated with moderately sized samples, and how it can be used as the basis for more detailed analyses of the nature of these differences. Conclusions The new procedure constitutes a useful resource for the comparison of covariance matrices. It could fill the gap between procedures resulting in a single, overall measure of differentiation, and analytical methods based on multiple model comparison not providing such a measure.
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....
Gaussian covariance matrices for anisotropic galaxy clustering measurements
Grieb, Jan Niklas; Sánchez, Ariel G.; Salazar-Albornoz, Salvador; Dalla Vecchia, Claudio
2016-04-01
Measurements of the redshift-space galaxy clustering have been a prolific source of cosmological information in recent years. Accurate covariance estimates are an essential step for the validation of galaxy clustering models of the redshift-space two-point statistics. Usually, only a limited set of accurate N-body simulations is available. Thus, assessing the data covariance is not possible or only leads to a noisy estimate. Further, relying on simulated realizations of the survey data means that tests of the cosmology dependence of the covariance are expensive. With these points in mind, this work presents a simple theoretical model for the linear covariance of anisotropic galaxy clustering observations with synthetic catalogues. Considering the Legendre moments (`multipoles') of the two-point statistics and projections into wide bins of the line-of-sight parameter (`clustering wedges'), we describe the modelling of the covariance for these anisotropic clustering measurements for galaxy samples with a trivial geometry in the case of a Gaussian approximation of the clustering likelihood. As main result of this paper, we give the explicit formulae for Fourier and configuration space covariance matrices. To validate our model, we create synthetic halo occupation distribution galaxy catalogues by populating the haloes of an ensemble of large-volume N-body simulations. Using linear and non-linear input power spectra, we find very good agreement between the model predictions and the measurements on the synthetic catalogues in the quasi-linear regime.
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...... of the problem at hand. We develop a theory for the point process of the normalized eigenvalues of the sample covariance matrix in the case where rows and columns of the data are linearly dependent. Based on the weak convergence of this point process we derive the limit laws of various functionals...... of the eigenvalues. In the second part, we show that the largest and smallest eigenvalues of a highdimensional sample correlation matrix possess almost sure non-random limits if the truncated variance of the entry distribution is “almost slowly varying”, a condition we describe via moment properties of self...
2015-03-01
ALGORITHM—EIGENVALUE ESTIMATION OF HYPERSPECTRAL WISHART COVARIANCE MATRICES FROM A LIMITED NUMBER OF SAMPLES ECBC-TN-067 Avishai Ben-David...Estimation of Hyperspectral Wishart Covariance Matrices from a Limited Number of Samples 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT...covariance matrices and to recompute a revised covariance matrix from the eigenvalues. The MATLAB function is an implementation of the procedure developed
Energy Technology Data Exchange (ETDEWEB)
Bryan, M.F.; Piepel, G.F.; Simpson, D.B.
1996-03-01
The high-level waste (HLW) vitrification plant at the Hanford Site was being designed to transuranic and high-level radioactive waste in borosilicate class. Each batch of plant feed material must meet certain requirements related to plant performance, and the resulting class must meet requirements imposed by the Waste Acceptance Product Specifications. Properties of a process batch and the resultlng glass are largely determined by the composition of the feed material. Empirical models are being developed to estimate some property values from data on feed composition. Methods for checking and documenting compliance with feed and glass requirements must account for various types of uncertainties. This document focuses on the estimation. manipulation, and consequences of composition uncertainty, i.e., the uncertainty inherent in estimates of feed or glass composition. Three components of composition uncertainty will play a role in estimating and checking feed and glass properties: batch-to-batch variability, within-batch uncertainty, and analytical uncertainty. In this document, composition uncertainty and its components are treated in terms of variances and variance components or univariate situations, covariance matrices and covariance components for multivariate situations. The importance of variance and covariance components stems from their crucial role in properly estimating uncertainty In values calculated from a set of observations on a process batch. Two general types of methods for estimating uncertainty are discussed: (1) methods based on data, and (2) methods based on knowledge, assumptions, and opinions about the vitrification process. Data-based methods for estimating variances and covariance matrices are well known. Several types of data-based methods exist for estimation of variance components; those based on the statistical method analysis of variance are discussed, as are the strengths and weaknesses of this approach.
Paraunitary matrices and group rings
Directory of Open Access Journals (Sweden)
Barry Hurley
2014-03-01
Full Text Available Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structuresare presented. These include techniques for designing non-separable multidimensional paraunitary matrices. Properties of the structures are obtained and proofs given. Paraunitary matrices play a central role in signal processing, inparticular in the areas of filterbanks and wavelets.
Chang, Jinyuan; Zhou, Wen; Zhou, Wen-Xin; Wang, Lan
2016-07-05
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.
Compilation of multigroup cross-section covariance matrices for several important reactor materials
Energy Technology Data Exchange (ETDEWEB)
Drischler, J.D.; Weisbin, C.R.
1977-10-01
Multigroup cross-section covariance matrices are presented for fission in /sup 235/U, /sup 238/U, /sup 239/Pu, and /sup 241/Pu; capture in /sup 235/U, /sup 238/U, /sup 239/Pu, /sup 240/Pu, and /sup 241/Pu; fission neutron yield (anti nu) for /sup 235/U, /sup 238/U, /sup 239/Pu, and /sup 240/Pu; elastic scattering for Na and Fe; non-elastic reactions for Na and Fe; first-level inelastic scattering for /sup 238/U; and all reactions provided in the ENDF/B-IV covariance description of N, O, and C. Other data files generated are included for reference but have not yet been tested. The report presents the nultigroup data in six, ten, and fifteen energy group forms corresponding to weighting of the covariance data with fission (GODIVA), LMFBR (ZPR-6/7) and 1/E spectra, respectively.
1998-01-01
In the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \\times d$ matrices, if their traces are known. As a next step $4 \\times 4$ matrices are expressed in terms of Dirac covariants. The third step is the calculation of the corresponding inverse matrices in terms of Dirac covariants.
Pan, Guangming; Zhou, Wang
2010-01-01
A consistent kernel estimator of the limiting spectral distribution of general sample covariance matrices was introduced in Jing, Pan, Shao and Zhou (2010). The central limit theorem of the kernel estimator is proved in this paper.
Universality of sample covariance matrices: CLT of the smoothed empirical spectral distribution
Pan, Guangming; Zhou, Wang
2011-01-01
A central limit theorem (CLT) for the smoothed empirical spectral distribution of sample covariance matrices is established. Moreover, the CLTs for the smoothed quantiles of Marcenko and Pastur's law have been also developed.
Gaussian covariance matrices for anisotropic galaxy clustering measurements
Grieb, Jan Niklas; Salazar-Albornoz, Salvador; Vecchia, Claudio dalla
2015-01-01
Measurements of the redshift-space galaxy clustering have been a prolific source of cosmological information in recent years. In the era of precision cosmology, accurate covariance estimates are an essential step for the validation of galaxy clustering models of the redshift-space two-point statistics. For cases where only a limited set of simulations is available, assessing the data covariance is not possible or only leads to a noisy estimate. Also, relying on simulated realisations of the survey data means that tests of the cosmology dependence of the covariance are expensive. With these two points in mind, this work aims at presenting a simple theoretical model for the linear covariance of anisotropic galaxy clustering observations with synthetic catalogues. Considering the Legendre moments (`multipoles') of the two-point statistics and projections into wide bins of the line-of-sight parameter (`clustering wedges'), we describe the modelling of the covariance for these anisotropic clustering measurements f...
Schur complement inequalities for covariance matrices and monogamy of quantum correlations
Lami, Ludovico; Adesso, Gerardo; Winter, Andreas
2016-01-01
We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This allows us to prove general results on the monogamy of entanglement and steering quantifiers in continuous variable systems with an arbitrary number of modes per party. A powerful hierarchical relation for correlation measures based on the log-determinant of covariance matrices is further established for all Gaussian states, which has no counterpart among quantities based on the conventional von Neumann entropy.
Spectral Density of Sample Covariance Matrices of Colored Noise
Dolezal, Emil
2008-01-01
We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results for some colored noise signals.
Estimation and Forecasting of Large Realized Covariance Matrices and Portfolio Choice
DEFF Research Database (Denmark)
Callot, Laurent; Kock, Anders Bredahl; Medeiros, Marcelo C.
In this paper we consider modeling and forecasting of large realized covariance matrices by penalized vector autoregressive models. We propose using Lasso-type estimators to reduce the dimensionality to a manageable one and provide strong theoretical performance guarantees on the forecast...... capability of our procedure. To be precise, we show that we can forecast future realized covariance matrices almost as precisely as if we had known the true driving dynamics of these in advance. We next investigate the sources of these driving dynamics for the realized covariance matrices of the 30 Dow Jones...... stocks and find that these dynamics are not stable as the data is aggregated from the daily to the weekly and monthly frequency. The theoretical performance guarantees on our forecasts are illustrated on the Dow Jones index. In particular, we can beat our benchmark by a wide margin at the longer forecast...
Peters, Elisabeth; Stuke, Maik
2016-01-01
In this manuscript we study the modeling of experimental data and its impact on the resulting integral experimental covariance and correlation matrices. By investigating a set of three low enriched and water moderated UO2 fuel rod arrays we found that modeling the same set of data with different, yet reasonable assumptions concerning the fuel rod composition and its geometric properties leads to significantly different covariance matrices or correlation coefficients. Following a Monte Carlo sampling approach, we show for nine different modeling assumptions the corresponding correlation coefficients and sensitivity profiles for each pair of the effective neutron multiplication factor keff. Within the 95% confidence interval the correlation coefficients vary from 0 to 1, depending on the modeling assumptions. Our findings show that the choice of modeling can have a huge impact on integral experimental covariance matrices. When the latter are used in a validation procedure to derive a bias, this procedure can be...
Transformation rule for covariance matrices under Bell-like detections
Spedalieri, Gaetana; Pirandola, Stefano
2013-01-01
Starting from the transformation rule of a covariance matrix under homodyne detections, we can easily derive a formula for the transformation of a covariance matrix of (n+2) bosonic modes under Bell-like detections, where the last two modes are combined in an arbitrary beam splitter (i.e., with arbitrary transmissivity) and then homodyned. This formula can be specialized to describe the standard Bell detection and the heterodyne measurement, which are exploited in many contexts, including protocols of quantum teleportation, entanglement swapping and quantum cryptography. Our general formula can be adopted to study these protocols in the presence of experimental imperfections or asymmetric setups, e.g., deriving from the use of unbalanced beam splitters.
On the Estimation of Integrated Covariance Matrices of High Dimensional Diffusion Processes
Zheng, Xinghua
2010-01-01
We consider the estimation of integrated covariance matrices of high dimensional diffusion processes by using high frequency data. We start by studying the most commonly used estimator, the realized covariance matrix (RCV). We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrix Sigma, but also on how the covolatility processes vary in time. In particular, for two high dimensional diffusion processes with the same integrated covariance matrix, the empirical spectral distributions of their RCVs can be very different. Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in general \\emph{not} a good proxy to rely on in the high dimensional case. We then propose an alternative estimator, the time-variation adjusted realized covariance matrix (TVARCV), for ...
Asymptotic behavior of the likelihood function of covariance matrices of spatial Gaussian processes
DEFF Research Database (Denmark)
Zimmermann, Ralf
2010-01-01
The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood......: optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices. The implication of this theorem on Kriging hyperparameter optimization is exposed. A nonartificial example is presented, where maximum likelihood-based Kriging model training...
Gaussian Fluctuations for Sample Covariance Matrices with Dependent Data
Friesen, Olga; Stolz, Michael
2012-01-01
It is known (Hofmann-Credner and Stolz (2008)) that the convergence of the mean empirical spectral distribution of a sample covariance matrix W_n = 1/n Y_n Y_n^t to the Mar\\v{c}enko-Pastur law remains unaffected if the rows and columns of Y_n exhibit some dependence, where only the growth of the number of dependent entries, but not the joint distribution of dependent entries needs to be controlled. In this paper we show that the well-known CLT for traces of powers of W_n also extends to the dependent case.
Eigenvalue distribution of large sample covariance matrices of linear processes
Pfaffel, Oliver
2012-01-01
We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable $i=1,...,p$ is modelled as a linear process $(X_{i,t})_{t=1,...,n}=(\\sum_{j=0}^\\infty c_j Z_{i,t-j})_{t=1,...,n}$, where $\\{Z_{i,t}\\}$ are assumed to be independent random variables with finite fourth moments. If the sample size $n$ and the number of variables $p=p_n$ both converge to infinity such that $y=\\lim_{n\\to\\infty}{n/p_n}>0$, then the empirical spectral distribution of $p^{-1}\\X\\X^T$ converges to a non\\hyp{}random distribution which only depends on $y$ and the spectral density of $(X_{1,t})_{t\\in\\Z}$. In particular, our results apply to (fractionally integrated) ARMA processes, which we illustrate by some examples.
Nonparametric estimate of spectral density functions of sample covariance matrices: A first step
2012-01-01
The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the performance of the estimators.
Variations of cosmic large-scale structure covariance matrices across parameter space
Reischke, Robert; Schäfer, Björn Malte
2016-01-01
The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the nonlinear evolution of the cosmic web. As nonlinear clustering to date has only been described by numerical $N$-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work we describe the change of the matter covariance and of the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from nonlinear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations we find that the method describes...
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.
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.
Energy Technology Data Exchange (ETDEWEB)
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.
MIMO-radar Waveform Covariance Matrices for High SINR and Low Side-lobe Levels
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.
Models with orthogonal block structure, with diagonal blockwise variance-covariance matrices
Carvalho, Francisco; Mexia, João T.; Covas, Ricardo
2017-07-01
We intend to show that in the family of models with orthogonal block structure, OBS, we may single out those with blockwise diagonal variance-covariance matrices, DOBS. Namely we show that for every model with observation vector y with OBS, there is a model y °=P y , with P orthogonal which is DOBS and that the estimation of relevant parameters may be carried out for y ° .
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
An Efficient Algorithm for Maximum-Entropy Extension of Block-Circulant Covariance Matrices
Carli, Francesca P; Pavon, Michele; Picci, Giorgio
2011-01-01
This paper deals with maximum entropy completion of partially specified block-circulant matrices. Since positive definite symmetric circulants happen to be covariance matrices of stationary periodic processes, in particular of stationary reciprocal processes, this problem has applications in signal processing, in particular to image modeling. Maximum entropy completion is strictly related to maximum likelihood estimation subject to certain conditional independence constraints. The maximum entropy completion problem for block-circulant matrices is a nonlinear problem which has recently been solved by the authors, although leaving open the problem of an efficient computation of the solution. The main contribution of this paper is to provide an efficient algorithm for computing the solution. Simulation shows that our iterative scheme outperforms various existing approaches, especially for large dimensional problems. A necessary and sufficient condition for the existence of a positive definite circulant completio...
Variations of cosmic large-scale structure covariance matrices across parameter space
Reischke, Robert; Kiessling, Alina; Schäfer, Björn Malte
2017-03-01
The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the non-linear evolution of the cosmic web. As highly non-linear clustering to date has only been described by numerical N-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work, we describe the change of the matter covariance and the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from non-linear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations, we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to ℓ ≤ 1300. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimizing interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.
Akemann, Gernot; Checinski, Tomasz; Kieburg, Mario
2016-08-01
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.
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.
General Covariance from the Quantum Renormalization Group
Shyam, Vasudev
2016-01-01
The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in the `bulk' of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the $D + 1$ dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the $D$ dimensional boundary. This will be a particular form of the Wess--Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Po...
Universality in the bulk of the spectrum for complex sample covariance matrices
Péché, S
2009-01-01
We consider complex sample covariance matrices $M_N=\\frac{1}{N}YY^*$ where $Y$ is a $N \\times p$ random matrix with i.i.d. entries $Y_{ij}, 1\\leq i\\leq N, 1\\leq j \\leq p$ with distribution $F$. Under some regularity and decay assumption on $F$, we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where $N\\to \\infty$ and $\\lim_{N \\to \\infty}p/N =\\gamma$ for any real number $\\gamma \\in (0, \\infty)$.
Information and Covariance Matrices for Multivariate Burr III and Logistic distributions
Yari, G; Yari, Gholamhossein; Mohammad-Djafari, Ali
2004-01-01
Main result of this paper is to derive the exact analytical expressions of information and covariance matrices for multivariate Burr III and logistic distributions. These distributions arise as tractable parametric models in price and income distributions, reliability, economics, populations growth and survival data. We showed that all the calculations can be obtained from one main moment multi dimensional integral whose expression is obtained through some particular change of variables. Indeed, we consider that this calculus technique for improper integral has its own importance in applied probability calculus.
Directory of Open Access Journals (Sweden)
Gianola Daniel
2007-09-01
Full Text Available Abstract Multivariate linear models are increasingly important in quantitative genetics. In high dimensional specifications, factor analysis (FA may provide an avenue for structuring (covariance matrices, thus reducing the number of parameters needed for describing (codispersion. We describe how FA can be used to model genetic effects in the context of a multivariate linear mixed model. An orthogonal common factor structure is used to model genetic effects under Gaussian assumption, so that the marginal likelihood is multivariate normal with a structured genetic (covariance matrix. Under standard prior assumptions, all fully conditional distributions have closed form, and samples from the joint posterior distribution can be obtained via Gibbs sampling. The model and the algorithm developed for its Bayesian implementation were used to describe five repeated records of milk yield in dairy cattle, and a one common FA model was compared with a standard multiple trait model. The Bayesian Information Criterion favored the FA model.
Totir, Liviu R; Fernando, Rohan L; Dekkers, Jack C M; Fernández, Soledad A; Guldbrandtsen, Bernt
2004-01-01
Under additive inheritance, the Henderson mixed model equations (HMME) provide an efficient approach to obtaining genetic evaluations by marker assisted best linear unbiased prediction (MABLUP) given pedigree relationships, trait and marker data. For large pedigrees with many missing markers, however, it is not feasible to calculate the exact gametic variance covariance matrix required to construct HMME. The objective of this study was to investigate the consequences of using approximate gametic variance covariance matrices on response to selection by MABLUP. Two methods were used to generate approximate variance covariance matrices. The first method (Method A) completely discards the marker information for individuals with an unknown linkage phase between two flanking markers. The second method (Method B) makes use of the marker information at only the most polymorphic marker locus for individuals with an unknown linkage phase. Data sets were simulated with and without missing marker data for flanking markers with 2, 4, 6, 8 or 12 alleles. Several missing marker data patterns were considered. The genetic variability explained by marked quantitative trait loci (MQTL) was modeled with one or two MQTL of equal effect. Response to selection by MABLUP using Method A or Method B were compared with that obtained by MABLUP using the exact genetic variance covariance matrix, which was estimated using 15,000 samples from the conditional distribution of genotypic values given the observed marker data. For the simulated conditions, the superiority of MABLUP over BLUP based only on pedigree relationships and trait data varied between 0.1% and 13.5% for Method A, between 1.7% and 23.8% for Method B, and between 7.6% and 28.9% for the exact method. The relative performance of the methods under investigation was not affected by the number of MQTL in the model.
Bello, Nora M; Steibel, Juan P; Tempelman, Robert J
2010-06-01
Bivariate mixed effects models are often used to jointly infer upon covariance matrices for both random effects (u) and residuals (e) between two different phenotypes in order to investigate the architecture of their relationship. However, these (co)variances themselves may additionally depend upon covariates as well as additional sets of exchangeable random effects that facilitate borrowing of strength across a large number of clusters. We propose a hierarchical Bayesian extension of the classical bivariate mixed effects model by embedding additional levels of mixed effects modeling of reparameterizations of u-level and e-level (co)variances between two traits. These parameters are based upon a recently popularized square-root-free Cholesky decomposition and are readily interpretable, each conveniently facilitating a generalized linear model characterization. Using Markov Chain Monte Carlo methods, we validate our model based on a simulation study and apply it to a joint analysis of milk yield and calving interval phenotypes in Michigan dairy cows. This analysis indicates that the e-level relationship between the two traits is highly heterogeneous across herds and depends upon systematic herd management factors.
Baryon oscillations in galaxy and matter power-spectrum covariance matrices
Neyrinck, Mark C
2007-01-01
We investigate large-amplitude baryon acoustic oscillations (BAO's) in off-diagonal entries of cosmological power-spectrum covariance matrices. These covariance-matrix BAO's describe the increased attenuation of power-spectrum BAO's caused by upward fluctuations in large-scale power. We derive an analytic approximation to covariance-matrix entries in the BAO regime, and check the analytical predictions using N-body simulations. These BAO's look much stronger than the BAO's in the power spectrum, but seem detectable only at about a one-sigma level in gigaparsec-scale galaxy surveys. In estimating cosmological parameters using matter or galaxy power spectra, including the covariance-matrix BAO's can have a several-percent effect on error-bar widths for some parameters directly related to the BAO's, such as the baryon fraction. Also, we find that including the numerous galaxies in small haloes in a survey can reduce error bars in these cosmological parameters more than the simple reduction in shot noise might su...
Energy Technology Data Exchange (ETDEWEB)
Leeb, H., E-mail: leeb@kph.tuwien.ac.at; Schnabel, G.; Srdinko, Th.; Wildpaner, V.
2015-01-15
A new evaluation of neutron-induced reactions on {sup 181}Ta using a consistent procedure based on Bayesian statistics is presented. Starting point of the evaluation is the description of nuclear reactions via nuclear models implemented in TALYS 1.4. A retrieval of experimental data was performed and covariance matrices of the experiments were generated from an extensive study of the corresponding literature. All reaction channels required for a transport file up to 200 MeV have been considered and the covariance matrices of cross section uncertainties for the most important channels are determined. The evaluation has been performed in one step including all available experimental data. A comparison of the evaluated cross sections and spectra with experimental data and available evaluations is performed. In general the evaluated cross section reflect our best knowledge and give a fair description of the observables. However, there are few deviations from expectation which clearly indicate the impact of the prior and the need to account for model defects. Using the results of the evaluation a complete ENDF-file similarly to those of the TENDL library is generated.
Schuurman, N K; Grasman, R P P P; Hamaker, E L
2016-01-01
Multilevel autoregressive models are especially suited for modeling between-person differences in within-person processes. Fitting these models with Bayesian techniques requires the specification of prior distributions for all parameters. Often it is desirable to specify prior distributions that have negligible effects on the resulting parameter estimates. However, the conjugate prior distribution for covariance matrices-the Inverse-Wishart distribution-tends to be informative when variances are close to zero. This is problematic for multilevel autoregressive models, because autoregressive parameters are usually small for each individual, so that the variance of these parameters will be small. We performed a simulation study to compare the performance of three Inverse-Wishart prior specifications suggested in the literature, when one or more variances for the random effects in the multilevel autoregressive model are small. Our results show that the prior specification that uses plug-in ML estimates of the variances performs best. We advise to always include a sensitivity analysis for the prior specification for covariance matrices of random parameters, especially in autoregressive models, and to include a data-based prior specification in this analysis. We illustrate such an analysis by means of an empirical application on repeated measures data on worrying and positive affect.
Universal correlations and power-law tails in financial covariance matrices
Akemann, G.; Fischmann, J.; Vivo, P.
2010-07-01
We investigate whether quantities such as the global spectral density or individual eigenvalues of financial covariance matrices can be best modelled by standard random matrix theory or rather by its generalisations displaying power-law tails. In order to generate individual eigenvalue distributions a chopping procedure is devised, which produces a statistical ensemble of asset-price covariances from a single instance of financial data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay.
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.
Localization in covariance matrices of coupled heterogenous Ornstein-Uhlenbeck processes.
Barucca, Paolo
2014-12-01
We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the presented model formulas are given for the analysis of heterogeneous time series. Furthermore evidence for a localization transition in eigenvectors related to small and large eigenvalues in cross-correlations analysis of this model is found, and a simple explanation of localization phenomena in financial time series is provided. Finally we identify both in our model and in real financial data an inverted-bell effect in correlation between localized components and their local temperature: high- and low-temperature components are the most localized ones.
Houle, D; Meyer, K
2015-08-01
We explore the estimation of uncertainty in evolutionary parameters using a recently devised approach for resampling entire additive genetic variance-covariance matrices (G). Large-sample theory shows that maximum-likelihood estimates (including restricted maximum likelihood, REML) asymptotically have a multivariate normal distribution, with covariance matrix derived from the inverse of the information matrix, and mean equal to the estimated G. This suggests that sampling estimates of G from this distribution can be used to assess the variability of estimates of G, and of functions of G. We refer to this as the REML-MVN method. This has been implemented in the mixed-model program WOMBAT. Estimates of sampling variances from REML-MVN were compared to those from the parametric bootstrap and from a Bayesian Markov chain Monte Carlo (MCMC) approach (implemented in the R package MCMCglmm). We apply each approach to evolvability statistics previously estimated for a large, 20-dimensional data set for Drosophila wings. REML-MVN and MCMC sampling variances are close to those estimated with the parametric bootstrap. Both slightly underestimate the error in the best-estimated aspects of the G matrix. REML analysis supports the previous conclusion that the G matrix for this population is full rank. REML-MVN is computationally very efficient, making it an attractive alternative to both data resampling and MCMC approaches to assessing confidence in parameters of evolutionary interest. © 2015 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2015 European Society For Evolutionary Biology.
Directory of Open Access Journals (Sweden)
Kirkpatrick Mark
2005-01-01
Full Text Available Abstract Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of genetic correlation, a subset of the principal component generally suffices to capture the bulk of genetic variation. Corresponding estimates of genetic covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from k(k + 1/2 to m(2k - m + 1/2 for k effects and m principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the genetic covariance matrix, via restricted maximum likelihood using derivatives of the likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given.
Covariances of the few-group homogenized cross-sections for diffusion calculation
Energy Technology Data Exchange (ETDEWEB)
Sánchez-Cervera, S.; Castro, S.; García-Herranz, N.
2015-07-01
In the context of the NEA/OECD benchmark for Uncertainty Analysis in Modelling (UAM), Exercise I-3 consists of neutronic calculations to propagate uncertainties to core parameters such as k-effective or power distribution. In core simulators, the input uncertainties arise, among others, from few-group lattice-averaged cross-section uncertainties. In this paper, an analysis of those uncertainties due to nuclear data is performed. The core analyzed in Exercise I-3 is the initial loading of the PWR TMI-1, composed by 11 different types of fuel assemblies. By statistically sampling the nuclear data input, the sequence SAMPLER from SCALE system (using its NEWT lattice code) allows to obtain the few-group homogenized cross-sections and with a statistical analysis generates the covariance matrices. The correlations among different reactions and energy groups of the covariance matrices are analyzed. The impact of burnable poisons, control rods or the environment of the assembly is also assessed. It is shown the importance of the correlation between different assembly types. The global covariance matrix will permit to compute the uncertainties in k-eff in a core simulator, once sensitivity coefficients are known. Only if the complete covariance matrix is considered, similar uncertainties to the ones provided by other methodologies are obtained. (Author)
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
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.
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.
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.
Strong subadditivity for log-determinant of covariance matrices and its applications
Adesso, Gerardo
2016-01-01
We prove that the log-determinant of the covariance matrix obeys the strong subadditivity inequality for arbitrary tripartite states of multimode continuous variable quantum systems. This establishes general limitations on the distribution of information encoded in the second moments of canonically conjugate operators. We show that such an inequality implies a strict monogamy-type relation for joint Einstein-Podolsky-Rosen steerability of single modes by Gaussian measurements performed on multiple groups of modes.
Hu, Jiang; Bai, ZhiDong
2016-12-01
In this paper, we will introduce the so called naive tests and give a brief review on the newly development. Naive testing methods are easy to understand and performs robust especially when the dimension is large. In this paper, we mainly focus on reviewing some naive testing methods for the mean vectors and covariance matrices of high dimensional populations and believe this naive test idea can be wildly used in many other testing problems.
Conditioning of the stationary kriging matrices for some well-known covariance models
Energy Technology Data Exchange (ETDEWEB)
Posa, D. (IRMA-CNR, Bari (Italy))
1989-10-01
In this paper, the condition number of the stationary kriging matrix is studied for some well-known covariance models. Indeed, the robustness of the kriging weights is strongly affected by this measure. Such an analysis can justify the choice of a covariance function among other admissible models which could fit a given experimental covariance equally well.
Chen, Junye; Liu, Quanhua; Chattopadhyay, Mohar; Garrett, Kevin L.; Grassotti, Christopher; Liu, Shuyan; Boukabara, Sid
2016-10-01
The NOAA Microwave Integrated Retrieval System (MiRS) retrieves the atmospheric profiles of state variables (temperature, moisture, liquid cloud, hydrometeors, surface emissivity spectrum and skin temperature) simultaneously and coherently with one-dimension Variational (1DVar) method based on passive microwave radiance observation from multiple polar-orbiting operational satellites, including NOAA18, NOAA19, MetOp (A and B), DMSP (F16 and F18) and SNPP. In MiRS, the geophysical consistency between the retrieved state variables is obtained through the constraint from the state variable background covariance matrices, which define the variability of each state variable and the relationship between them. The current atmospheric covariance matrices were mainly built based on the ECMWF 60 layer sample data set (EC60). Because no rain data available in EC60, the MM5 model output rain was used as a substitute. Although MiRS performs well based on current matrices, obviously, there is room for improvement if the matrices could be rebuilt based more representative, higher resolution dataset, and most importantly, all variables are from one datasets, so the cross relationship between parameters could be properly represented. The ECMWF IFS-137 dataset (EC137) is the most recent ECMWF sample data set. Besides several major modifications and improvements in ECMWF forecasting system, comparing with EC60, the profiles in EC137 have more than doubled vertical resolution. The hydrometeor variables are included in EC137, rather than in EC60. With upgraded sampling method, the profiles in EC137 are more evenly distributed in both temporal and spatial domains. And the profile population in EC137 shows significant different statistic characters than its precedents. To generate the new matrices, EC137 data is interpolated from 137 layers to 100 layers. The variable units are transferred to be used for radiation transfer calculation and match with those used in MiRS. For example, the
Energy Technology Data Exchange (ETDEWEB)
Brassart, M. [Ecole Nationale Superieure Ingenieurs de Bourges, 18 - Bourges (France); Mounier, C. [CEA Saclay, Dir. de l' Energie Nucleaire DEN, Service d' Etudes des Reacteurs et de Modelisation Avancee, 91 - Gif sur Yvette (France); Dossantos-Uzarralde, P. [CEA Bruyeres le Chatel, 91 (France). Dept. de Physique Theorique et Appliquee
2004-07-01
Nuclear reaction models play an important role in today's nuclear data evaluations. There are, however, difficulties associated with evaluating data uncertainties, both while performing the experimental measurements as well as constructing them by nuclear models. In this general context, our interest is particularly targeted towards the study of the propagation uncertainties within nuclear models. In this report we discuss two distinct ways of calculating the nuclear cross section variance-covariance matrices and then show these can be applied to the nuclear spherical optical model. (authors)
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 particular...... location, design optimal filters to remove errors from the surfaces, and rigorously assimilate a geoid/MDT into ocean models, or otherwise combine the GOCE gravity field with other data. Here we present an initial investigation into the error characteristics of the GOCE gravity field models...
ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters
Litvinenko, Alexander
2016-10-25
In this work the task is to use the available measurements to estimate unknown hyper-parameters (variance, smoothness parameter and covariance length) of the covariance function. We do it by maximizing the joint log-likelihood function. This is a non-convex and non-linear problem. To overcome cubic complexity in linear algebra, we approximate the discretised covariance function in the hierarchical (ℋ-) matrix format. The ℋ-matrix format has a log-linear computational cost and storage O(knlogn), where rank k is a small integer. On each iteration step of the optimization procedure the covariance matrix itself, its determinant and its Cholesky decomposition are recomputed within ℋ-matrix format. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
Bayesian model selection for a linear model with grouped covariates
National Research Council Canada - National Science Library
Min, Xiaoyi; Sun, Dongchu
2016-01-01
.... The marginal likelihood function is derived under the proposed priors, and a simplified closed-form expression is given assuming the commutativity of the projection matrices from the design matrices...
Least-Squares Data Adjustment with Rank-Deficient Data Covariance Matrices
Energy Technology Data Exchange (ETDEWEB)
Williams, J.G. [The University of Arizona, Tucson, AZ 85721-0119 (United States)
2011-07-01
A derivation of the linear least-squares adjustment formulae is required that avoids the assumption that the covariance matrix of prior parameters can be inverted. Possible proofs are of several kinds, including: (i) extension of standard results for the linear regression formulae, and (ii) minimization by differentiation of a quadratic form of the deviations in parameters and responses. In this paper, the least-squares adjustment equations are derived in both these ways, while explicitly assuming that the covariance matrix of prior parameters is singular. It will be proved that the solutions are unique and that, contrary to statements that have appeared in the literature, the least-squares adjustment problem is not ill-posed. No modification is required to the adjustment formulae that have been used in the past in the case of a singular covariance matrix for the priors. In conclusion: The linear least-squares adjustment formula that has been used in the past is valid in the case of a singular covariance matrix for the covariance matrix of prior parameters. Furthermore, it provides a unique solution. Statements in the literature, to the effect that the problem is ill-posed are wrong. No regularization of the problem is required. This has been proved in the present paper by two methods, while explicitly assuming that the covariance matrix of prior parameters is singular: i) extension of standard results for the linear regression formulae, and (ii) minimization by differentiation of a quadratic form of the deviations in parameters and responses. No modification is needed to the adjustment formulae that have been used in the past. (author)
Riemannian means on special euclidean group and unipotent matrices group.
Duan, Xiaomin; Sun, Huafei; Peng, Linyu
2013-01-01
Among the noncompact matrix Lie groups, the special Euclidean group and the unipotent matrix group play important roles in both theoretic and applied studies. The Riemannian means of a finite set of the given points on the two matrix groups are investigated, respectively. Based on the left invariant metric on the matrix Lie groups, the geodesic between any two points is gotten. And the sum of the geodesic distances is taken as the cost function, whose minimizer is the Riemannian mean. Moreover, a Riemannian gradient algorithm for computing the Riemannian mean on the special Euclidean group and an iterative formula for that on the unipotent matrix group are proposed, respectively. Finally, several numerical simulations in the 3-dimensional case are given to illustrate our results.
Kermarrec, Gaël; Schön, Steffen
2016-12-01
In this contribution, using the example of the Mátern covariance matrices, we study systematically the effect of apriori fully populated variance covariance matrices (VCM) in the Gauss-Markov model, by varying both the smoothness and the correlation length of the covariance function. Based on simulations where we consider a GPS relative positioning scenario with double differences, the true VCM is exactly known. Thus, an accurate study of parameters deviations with respect to the correlation structure is possible. By means of the mean-square error difference of the estimates obtained with the correct and the assumed VCM, the loss of efficiency when the correlation structure is missspecified is considered. The bias of the variance of unit weight is moreover analysed. By acting independently on the correlation length, the smoothness, the batch length, the noise level, or the design matrix, simulations allow to draw conclusions on the influence of these different factors on the least-squares results. Thanks to an adapted version of the Kermarrec-Schön model, fully populated VCM for GPS phase observations are computed where different correlation factors are resumed in a global covariance model with an elevation dependent weighting. Based on the data of the EPN network, two studies for different baseline lengths validate the conclusions of the simulations on the influence of the Mátern covariance parameters. A precise insight into the impact of apriori correlation structures when the VCM is entirely unknown highlights that both the correlation length and the smoothness defined in the Mátern model are important to get a lower loss of efficiency as well as a better estimation of the variance of unit weight. Consecutively, correlations, if present, should not be neglected for accurate test statistics. Therefore, a proposal is made to determine a mean value of the correlation structure based on a rough estimation of the Mátern parameters via maximum likelihood
Kermarrec, Gaël; Schön, Steffen
2017-05-01
In this contribution, using the example of the Mátern covariance matrices, we study systematically the effect of apriori fully populated variance covariance matrices (VCM) in the Gauss-Markov model, by varying both the smoothness and the correlation length of the covariance function. Based on simulations where we consider a GPS relative positioning scenario with double differences, the true VCM is exactly known. Thus, an accurate study of parameters deviations with respect to the correlation structure is possible. By means of the mean-square error difference of the estimates obtained with the correct and the assumed VCM, the loss of efficiency when the correlation structure is missspecified is considered. The bias of the variance of unit weight is moreover analysed. By acting independently on the correlation length, the smoothness, the batch length, the noise level, or the design matrix, simulations allow to draw conclusions on the influence of these different factors on the least-squares results. Thanks to an adapted version of the Kermarrec-Schön model, fully populated VCM for GPS phase observations are computed where different correlation factors are resumed in a global covariance model with an elevation dependent weighting. Based on the data of the EPN network, two studies for different baseline lengths validate the conclusions of the simulations on the influence of the Mátern covariance parameters. A precise insight into the impact of apriori correlation structures when the VCM is entirely unknown highlights that both the correlation length and the smoothness defined in the Mátern model are important to get a lower loss of efficiency as well as a better estimation of the variance of unit weight. Consecutively, correlations, if present, should not be neglected for accurate test statistics. Therefore, a proposal is made to determine a mean value of the correlation structure based on a rough estimation of the Mátern parameters via maximum likelihood
Qubit representations of the braid groups from generalized Yang-Baxter matrices
Vasquez, Jennifer F.; Wang, Zhenghan; Wong, Helen M.
2016-07-01
Generalized Yang-Baxter matrices sometimes give rise to braid group representations. We identify the exact images of some qubit representations of the braid groups from generalized Yang-Baxter matrices obtained from anyons in the metaplectic modular categories.
High-Dimensional Multivariate Repeated Measures Analysis with Unequal Covariance Matrices
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
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.
MULTIPLICATIVE GROUP AUTOMORPHISMS OF INVERTIBLE UPPER TRIANGULAR MATRICES OVER FIELDS
Institute of Scientific and Technical Information of China (English)
2000-01-01
Suppose F is a field of characteristic not 2 and F* its multiplicative group.Let T* n (F) be the multiplicative group of invertible upper triangular n × n matrices over F and ST±n(F) its subgroup {(aij) ∈ T * n(F)｜aii = +1,i}.This paper proves that f:T * n(F) → T * n(F) is a group automorphism if and only if there exist a matrix Q in T * n(F) and a field automorphism σ of F such that either σ -1 f(A) = ψ(A)QAσQ-1,A = (aij) ∈ T * n(F) or f(A) = ψ(A-1)Q[J(Aσ)-TJ]Q-1,A =(aij) ∈ T * n(F),where Aσ = (σ(aij)),A-T is the transpose inverse of A,J = n∑i=1 Ei n+1-i,and ψ :i=1 T * n(F) → F* is a homomorphism which satisfies {ψ(xIn)σ(x)｜x ∈ F*} = F* and {x ∈F*｜ψ(xIn)σ(x) = 1} = {1}.Simultaneously,they also determine the automorphisms of ST±n(F).
Symmetry group and group representations associated with the thermodynamic covariance principle
Sonnino, Giorgio; Evslin, Jarah; Sonnino, Alberto; Steinbrecher, György; Tirapegui, Enrique
2016-10-01
The main objective of this work [previously appeared in literature, the thermodynamical field theory (TFT)] is to determine the nonlinear closure equations (i.e., the flux-force relations) valid for thermodynamic systems out of Onsager's region. The TFT rests upon the concept of equivalence between thermodynamic systems. More precisely, the equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the two sets of thermodynamic forces are linked with each other by the so-called thermodynamic coordinate transformations (TCT). In this work, we describe the Lie group and the group representations associated to the TCT. The TCT guarantee the validity of the so-called thermodynamic covariance principle (TCP): The nonlinear closure equations, i.e., the flux-force relations, everywhere and in particular outside the Onsager region, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces, i.e., under TCT. The TCP ensures the validity of the fundamental theorems for systems far from equilibrium. The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. We derive the conserved (thermodynamic) currents and, as an example of calculation, a system out of equilibrium (tokamak plasmas) where the validity of TCP imposed at the level of the kinetic equations is also analyzed.
Symmetry group and group representations associated with the thermodynamic covariance principle.
Sonnino, Giorgio; Evslin, Jarah; Sonnino, Alberto; Steinbrecher, György; Tirapegui, Enrique
2016-10-01
The main objective of this work [previously appeared in literature, the thermodynamical field theory (TFT)] is to determine the nonlinear closure equations (i.e., the flux-force relations) valid for thermodynamic systems out of Onsager's region. The TFT rests upon the concept of equivalence between thermodynamic systems. More precisely, the equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the two sets of thermodynamic forces are linked with each other by the so-called thermodynamic coordinate transformations (TCT). In this work, we describe the Lie group and the group representations associated to the TCT. The TCT guarantee the validity of the so-called thermodynamic covariance principle (TCP): The nonlinear closure equations, i.e., the flux-force relations, everywhere and in particular outside the Onsager region, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces, i.e., under TCT. The TCP ensures the validity of the fundamental theorems for systems far from equilibrium. The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. We derive the conserved (thermodynamic) currents and, as an example of calculation, a system out of equilibrium (tokamak plasmas) where the validity of TCP imposed at the level of the kinetic equations is also analyzed.
Elementary constituents of the group SL(4,R), and classification of the Mueller matrices
Ovsiyuk, E; Neagu, M; Balan, V; Red'kov, V
2012-01-01
The goal of this paper is to develop a systematic method of locating the Mueller matrices within the class of the matrices of the real group SL(4, R). The main idea is to construct the general transformation of the group SL(4, R) (whose real matrices have unit determinant) is straightforward, but to analyze the adequacy of such a transformation for describing Mueller matrices is highly nontrivial. However, using the technique of Dirac matrices, we can quite easy and explicitly describe all the 16 one-parametric subgroups, from which, using the all possible products, emerges the whole group SL(4, R). As a matter of fact, for these separate 1-parametric subgroups the question of their adequacy of describing Mueller matrices becomes sufficiently simple and thus we obtain in each case a definite answer.
Siren, J; Ovaskainen, O; Merilä, J
2017-07-26
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.
Free Fermionic Elliptic Reflection Matrices and Quantum Group Invariance
Cuerno, R
1993-01-01
Elliptic diagonal solutions for the reflection matrices associated to the elliptic $R$ matrix of the eight vertex free fermion model are presented. They lead through the second derivative of the open chain transfer matrix to an XY hamiltonian in a magnetic field which is invariant under a quantum deformed Clifford--Hopf algebra.
Groups, matrices, and vector spaces a group theoretic approach to linear algebra
Carrell, James B
2017-01-01
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory ...
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…
Selecting groups of covariates in the elastic net
DEFF Research Database (Denmark)
Clemmensen, Line Katrine Harder
. The preservation of relations gives increased interpretability. The method is based on the elastic net and adaptively selects highly correlated groups of variables and does therefore not waste time in grouping irrelevant variables for the problem at hand. The method is illustrated on a simulated data set...
Few Group Collapsing of Covariance Matrix Data Based on a Conservation Principle
Energy Technology Data Exchange (ETDEWEB)
H. Hiruta; G. Palmiotti; M. Salvatores; R. Arcilla, Jr.; R. D. McKnight; G. Aliberti; P. Oblozinsky; W. S. Yang
2008-12-01
A new algorithm for a rigorous collapsing of covariance data is proposed, derived, implemented, and tested. The method is based on a conservation principle that allows the uncertainty calculated in a fine group energy structure for a specific integral parameter, using as weights the associated sensitivity coefficients, to be preserved at a broad energy group structure.
Introduction into Hierarchical Matrices
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.
M-P invertible matrices and unitary groups over Fq2
Institute of Scientific and Technical Information of China (English)
戴宗铎; 万哲先
2002-01-01
The Moor-Penrose generalized inverses (M-P inverses for short) of matrices over a finite field Fq2, which is a generalization of the Moor-Penrose generalized inverses over the complex field, are studied in the present paper. Some necessary and sufficient conditions for an m×n matrix A over Fq2 having an M-P inverse are obtained, which make clear the set of m×n matrices over Fq2 having M-P inverses and reduce the problem of constructing and enumerating the M-P invertible matrices to that of constructing and enumerating the non-isotropic subspaces with respect to the unitary group. Based on this reduction, both the construction problem and the enumeration problem are solved by borrowing the results in geometry of unitary groups over finite fields.
Bayes linear covariance matrix adjustment
Wilkinson, Darren J
1995-01-01
In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of random matrices is motivated and constructed. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability and related specifications to obtain representations allowing analysis. Adjustment is associated with orthogonal projection, and illustrated with examples of adjustments for some common problems. The problem of adjusting the covariance matrices underlying exchangeable random vectors is tackled and discussed. Learning about the covariance matrices associated with multivariate time series dynamic linear models is shown to be a...
Bazzani, Armndop; Cooper, Leon N
2010-01-01
We analyze the effects of noise correlations in the input to, or among, BCM 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 LGN 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.
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.
Secret Message Decryption: Group Consulting Projects Using Matrices and Linear Programming
Gurski, Katharine F.
2009-01-01
We describe two short group projects for finite mathematics students that incorporate matrices and linear programming into fictional consulting requests presented as a letter to the students. The students are required to use mathematics to decrypt secret messages in one project involving matrix multiplication and inversion. The second project…
Area group: an example of style and paste compositional covariation in Maya pottery
Energy Technology Data Exchange (ETDEWEB)
Bishop, R.L.; Reents, D.J.; Harbottle, G.; Sayre, E.V.; van Zelst, L.
1983-06-12
This paper has addressed aspects of ceramic style and iconography as found in Late Classic Maya ceramic art, including the supplemental perspective afforded by the analysis of ceramic paste. The chemical data provide a means to assess the extent of stylistic-paste compositional covariation. Depending upon the strength of that covariation various inferences may be drawn about craft specialization, exchange and information flow within Maya society. At the least, it provides an empirical means of comparing stylistically similar vessels; and when they are members of a chemically homogeneous group, it permits style to be addressed in terms of its variation. Additionally, compositionally defined site or region specific reference units provide a chemical background against which the non-provenienced vessels may be compared, allowing the whole vessels to be related to the archaelogically recovered fragmentary material. Finally, this multidisciplinary approach has been illustrated by preliminary findings concerning a specific group of polychrome vessels, The Area Group.
Bayes linear adjustment for variance matrices
Wilkinson, Darren J
2008-01-01
We examine the problem of covariance belief revision using a geometric approach. We exhibit an inner-product space where covariance matrices live naturally --- a space of random real symmetric matrices. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability specifications.
S-Matrices and Quantum Group Symmetry of q-Deformed Sigma Models
Hollowood, Timothy J; Schmidtt, David M
2015-01-01
Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the q-deformations with q a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
S-matrices and quantum group symmetry of k-deformed sigma models
Hollowood, Timothy J.; Miramontes, J. Luis; Schmidtt, David M.
2016-11-01
Recently, two kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed (Delduc et al 2014 Phys. Rev. Lett. 112 051601; Hollowood et al 2014 J. Phys. A: Math. Theor. 47 495402). One class of these, the k deformations associated to the more general q deformations but with q={{{e}}}{{i}π /k} a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
MODIFIED NEWTON'S ALGORITHM FOR COMPUTING THE GROUP INVERSES OF SINGULAR TOEPLITZ MATRICES
Institute of Scientific and Technical Information of China (English)
Jian-feng Cai; Michael K.Ng; Yi-min Wei
2006-01-01
Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration,the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix,the matrix-vector multiplication involved in Newton's iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.
Institute of Scientific and Technical Information of China (English)
高瑞梅; 吕堂红; 胡江
2016-01-01
Using the method of Stieltjes transform,we gave the explicit expressions of the limiting spectral density functions of the general high dimensional sample covariance matrices,which included:the sample covariance matrix whose elements were independent with zero mean and constant variance;the sum of a sample covariance matrix and a unit matrix;the sample covariance matrix which satisfied that the variance of the elements were different but only had two values;the sum of two different sample covariance matrices.%用 Stieltjes 变换给出一般高维样本协方差矩阵的极限密度函数的显示表达式,包括：样本元素独立且均值为0,方差为常数的样本协方差矩阵；一个样本协方差矩阵与单位阵的和；样本元素方差不等但只取两值的样本协方差矩阵；两个不同的样本协方差矩阵之和。
Directory of Open Access Journals (Sweden)
Privas E.
2016-01-01
Full Text Available A new IAEA Coordinated Research Project (CRP aims to test, validate and improve the IRDF library. Among the isotopes of interest, the modelisation of the 238U capture and fission cross sections represents a challenging task. A new description of the 238U neutrons induced reactions in the fast energy range is within progress in the frame of an IAEA evaluation consortium. The Nuclear Data group of Cadarache participates in this effort utilizing the 238U spectral indices measurements and Post Irradiated Experiments (PIE carried out in the fast reactors MASURCA (CEA Cadarache and PHENIX (CEA Marcoule. Such a collection of experimental results provides reliable integral information on the (n,γ and (n,f cross sections. This paper presents the Integral Data Assimilation (IDA technique of the CONRAD code used to propagate the uncertainties of the integral data on the 238U cross sections of interest for dosimetry applications.
Fischer matrices of Dempwolff group $2^{5}{^{cdot}}GL(5,2$
Directory of Open Access Journals (Sweden)
Ayoub Basheer Mohammed Basheer
2012-12-01
Full Text Available In cite{Demp2} Dempwolff proved the existence of a group of theform $2^{5}{^{cdot}}GL(5,2$ (a non split extension of theelementary abelian group $2^{5}$ by the general linear group$GL(5,2$. This group is the second largest maximal subgroup of thesporadic Thompson simple group $mathrm{Th}.$ In this paper wecalculate the Fischer matrices of Dempwolff group $overline{G} =2^{5}{^{cdot}}GL(5,2.$ The theory of projective characters isinvolved and we have computed the Schur multiplier together with aprojective character table of an inertia factor group. The fullcharacter table of $overline{G}$ is then can be calculated easily.
Bouriga, Mathilde; Féron, Olivier; Marin, Jean-Michel; Robert, Christian
2010-01-01
International audience; Ce papier concerne l'estimation de matrices de covariance dans le cas où le nombre de données utilisées pour l'estimation est faible par rapport à la dimension du problème et où les méthodes d'estimation classiques fondées sur le Maximum de Vraisemblance sont peu robustes. Nous proposons une méthode d'estimation non supervisée fondée sur une modélisation bayésienne hiérarchique du problème d'estimation de matrice de covariance : on pose une loi Inverse Wishart a priori...
Energy Technology Data Exchange (ETDEWEB)
Ren Dongni; Li Zhuo; Gao Yonghua; Feng Qingling, E-mail: biomater@mail.tsinghua.edu.c [State Key Laboratory of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China)
2010-10-01
Calcium carbonate mineralization is significantly influenced by organic matrices in vivo. The effect mainly relies on functional groups in proteins. In order to study the influence of functional groups on calcium carbonate mineralization, -OH, -NH{sub 2} and -COOH groups were grafted onto single crystal silicon chips, and such modified chips were used as substrates in in vitro mineralization experiments. An x-ray photoelectron spectroscopy (XPS) test was conducted to examine the grafting efficiency, and the three groups were successfully grafted. Calcium carbonate mineralization on a modified silicon substrate was examined by a scanning electron microscope (SEM) and x-ray diffraction (XRD), and the results showed that the effects of -OH, -NH{sub 2} and -COOH groups were quite different. Furthermore, a water-soluble protein matrix (WSM) and an acid-soluble protein matrix (ASM) extracted from fish otolith were adsorbed onto the -COOH-modified silicon substrate, and the effects of the protein matrices on calcium carbonate mineralization were studied. The results showed that both WSM and ASM of lapillus could mediate aragonite crystallization, but the size and morphology of the formed crystals were different. The WSM and ASM of asteriscus adsorbed on the silicon substrate had little effect on calcium carbonate mineralization; almost all the crystals were calcite, while both asteriscus WSM and ASM in solution could mediate vaterite crystals, and the morphologies of vaterite crystal aggregates were different.
Biorthonormal transfer-matrix renormalization-group method for non-Hermitian matrices.
Huang, Yu-Kun
2011-03-01
A biorthonormal transfer-matrix renormalization-group (BTMRG) method for non-Hermitian matrices is presented. This BTMRG produces a dual set of biorthonormal bases to construct the renormalized transfer matrix with only half the dimensions of the matrix of a conventional transfer-matrix renormalization group (TMRG). We show that under generic conditions, such biorthonormal bases always exist. Based on a special E·S·E scheme (where S and E represent the system and environment blocks, respectively, and the two dots in between represent two additional physical sites), the BTMRG method can achieve zero truncation of any reduced state in describing both current left and right Perron states so as to reach a high degree of efficiency and accuracy. We believe that the BTMRG constitutes a more powerful and robust tool than conventional TMRG for non-Hermitian matrices and that it would allow us to better understand the collective behaviors and emerging phenomena of strongly correlated many-body systems. We also show that this scheme is particularly adapted to the calculation of the two-site correlation function of a one-dimensional quantum or two-dimensional classical lattice model.
对角方阵的变换群%Transformaion Group of Diagonal Square Matrices
Institute of Scientific and Technical Information of China (English)
张世德; 李程
2011-01-01
In this paper,we show that the transformaion group of diagonal square matrices is a subgroup of direct product Sn × Sn of symetric groups of order n, if the sets of elements of each row, each column and the two diagonals are kept constant, respectively. The diagonal Latin squares, pair of orthogonal daigonal Latin squares, magic squares, magic squares of high dgree, addition multiplacation magic squares are diagonal square matrices. This paper plays an important role in the study of construction and enumeration of the objects above.%在不改变对角方阵各行、各列、主对角线、次对角线的元素之集的条件下,其变换群是n次对称群Sn的直积Sn×Sn的子群,因对角拉丁方、对角拉丁方正交侣、幻方、高次幻方、加乘幻方均属此类方阵,本文对构作这类对象及研究它们的计数有重要意义.
Ludtke, Oliver; Marsh, Herbert W.; Robitzsch, Alexander; Trautwein, Ulrich; Asparouhov, Tihomir; Muthen, Bengt
2008-01-01
In multilevel modeling (MLM), group-level (L2) characteristics are often measured by aggregating individual-level (L1) characteristics within each group so as to assess contextual effects (e.g., group-average effects of socioeconomic status, achievement, climate). Most previous applications have used a multilevel manifest covariate (MMC) approach,…
Adaptive Row-grouped CSR Format for Storing of Sparse Matrices on GPU
Heller, Martin
2012-01-01
We present new adaptive format for storing sparse matrices on GPU. We compare it with several other formats including CUSPARSE which is today probably the best choice for processing of sparse matrices on GPU in CUDA. Contrary to CUSPARSE which works with common CSR format, our new format requires conversion. However, multiplication of sparse-matrix and vector is significantly faster for many atrices. We demonstrate it on set of 1 600 matrices and we show for what types of matrices our format is profitable.
Some Conditions for Matrices over an Incline To Be Invertible and General Linear Group on an Incline
Institute of Scientific and Technical Information of China (English)
Song Chol HAN; Hong Xing LI
2005-01-01
Inclines are the additively idempotent semirings in which products are less than or equal to either factor. In this paper, some necessary and sufficient conditions for a matrix over L to be invertible are given, where L is an incline with 0 and 1. Also it is proved that L is an integral incline if and only if GLn(L) ＝ PLn(L) for any n (n ≥ 2), in which GLn(L) is the group of all n × n invertible matrices over L and PLn (L) is the group of all n × n permutation matrices over L. These results should be regarded as the generalizations and developments of the previous results on the invertible matrices over a distributive lattice.
Rushton, J. Philippe; Bons, Trudy Ann; Vernon, Philip A; Čvorović, Jelena
2007-01-01
We carried out two studies to test the hypothesis that genetic and environmental influences explain population group differences in general mental ability just as they do individual differences within a group. We estimated the heritability and environmentality of scores on the diagrammatic puzzles of the Raven's Coloured and/or Standard Progressive Matrices (CPM/SPM) from two independent twin samples and correlated these estimates with group differences on the same items. In Study 1, 199 pair...
Manifestly covariant electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Hillion, P. [Institut Henri Poincare' , Le Vesinet (France)
1999-03-01
The conventional relativistic formulation of electromagnetism is covariant under the full Lorentz group. But relativity requires covariance only under the proper Lorentz group and the authors present here the formalism covariant under the complex rotation group isomorphic to the proper Lorentz group. The authors discuss successively Maxwell's equations, constitutive relations and potential functions. A comparison is made with the usual formulation.
Institute of Scientific and Technical Information of China (English)
崔先强; 杨元喜; 张晓东
2012-01-01
To use Kalman filtering for kinematic navigation and positioning, we have to deal with function model and stochastic model. The precision and reliability of kinematic Kalman filtering are affected remarkably from the function model and stochastic model errors. Adaptive fitting of both colored noise and covariance matrices by using moving windows are presented based on the assumption that the observation and dynamic model noises mainly include the colored noises with first order self-correlation character. The expressions to calculate the colored noise estimators and covariance matrices of the modified observations and predicted states are obtained. Feasibility and practicability of the model and algorithm are tested by an example. It is shown that the Kalman filtering, based on the adaptive fittings of the colored noises and covariance matrices, can be effectivein resisting the influence of the colored noises on the navigation results.%使用Kalman滤波进行动态导航定位解算需要涉及函数模型和随机模型，而在实际应用中，精确的函数模型和随机模型很难直接给出，因此，动态Kalman滤波的精度和可靠性将会受到函数模型误差和随机模型误差的影响．在假设观测噪声和动力学模型噪声主要是具有一阶自相关特性的有色噪声的基础上，提出了一种基于移动窗口的有色噪声函数模型和随机模型的自适应拟合法．给出了计算有色噪声估值和噪声协方差矩阵的表达式，并利用实测数据验证了模型及算法的可行性和实用性．计算结果表明，该算法能有效抵制有色噪声对导航滤波结果的影响．
Directory of Open Access Journals (Sweden)
Lillian Pascoa
2013-06-01
Full Text Available We used actual and adjusted weights to 120 d and 210 d of age of 72,731 male and female Nellore calves born in 40 PMGRN - Nellore Brazil herds from 1985 to 2005 aiming to compare the effect of different definitions of contemporary groups on estimates of (covariance and genetic parameters. Four models, each one with a different structure of contemporary group (CG, were compared using the Akaike Information Criterion (AIC, the Bayesian Information Criterion (BIC, and the Consistent Akaike Information Criterion (CAIC. (Covariance estimates were obtained using a derivative-free restricted maximum likelihood procedure. Estimates of (covariances and genetic parameters were similar for the four models considered. However, the BIC and CAIC indicated that the most appropriate model for this Nellore population was the one that considered CG to be random, and sex of calf to be fixed and separate from CG, in which CG was defined as the group of calves born in the same herd, year, season of birth (trimester, and undergone the same management.
Directory of Open Access Journals (Sweden)
Donald St. P. Richards
2011-08-01
Full Text Available Results from the theory of the generalized hypergeometric functions of matrix argument, and the related zonal polynomials, are used to develop a new approach to study the asymptotic distributions of linear functions of uniformly distributed random matrices from the classical compact matrix groups. In particular, we provide a new approach for proving the following result of D’Aristotile, Diaconis, and Newman: Let the random matrix Hn be uniformly distributed according to Haar measure on the group of n × n orthogonal matrices, and let An be a non-random n × n real matrix such that tr (A'nAn = 1. Then, as n→∞, √n tr AnHn converges in distribution to the standard normal distribution.
Classical r-matrices of real low-dimensional Jacobi-Lie bialgebras and their Jacobi-Lie groups
Rezaei-Aghdam, A.; Sephid, M.
2014-01-01
In this research we obtain the classical r-matrices of real two and three dimensional Jacobi-Lie bialgebras. In this way, we classify all non-isomorphic real two and three dimensional coboundary Jacobi-Lie bialgebras and their types (triangular and quasitriangular). Also, we obtain the generalized Sklyanin bracket formula by use of which, we calculate the Jacobi structures on the related Jacobi-Lie groups. Finally, we present a new method for constructing classical integrable systems using co...
High-dimensional covariance estimation with high-dimensional data
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
Energy Technology Data Exchange (ETDEWEB)
Lepretre, A.; Herault, N. [CEA Saclay, Dept. d' Astrophysique de Physique des Particules, de Physique Nucleaire et de l' Instrumentation Associee, 91- Gif sur Yvette (France); Brusegan, A.; Noguere, G.; Siegler, P. [Institut des Materiaux et des Metrologies - IRMM, Joint Research Centre, Gell (Belgium)
2002-12-01
This report is a follow up of the report CEA DAPNIA/SPHN-99-04T of Vincent Gressier. In the frame of a collaboration between the 'Commissariat a l'Energie Atomique (CEA)' and the Institute for Reference Materials and Measurement (IRMM, Geel, Belgique), the resonance parameters of neptunium 237 have been determined in the energy interval between 0 and 500 eV. These parameters have been obtained by using the Refit code in analysing simultaneously three transmission experiments. The covariance matrix of statistical origin is provided. A new method, based on various sensitivity studies is proposed for determining also the covariance matrix of systematic origin, relating the resonance parameters. From an experimental viewpoint, the study indicated that, with a large probability, the background spectrum has structure. A two dimensional profiler for the neutron density has been proved feasible. Such a profiler could, among others, demonstrate the existence of the structured background. (authors)
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...
Energy Technology Data Exchange (ETDEWEB)
Lorenzen, R.
2007-03-15
Starting from the assumption of modular P{sub 1}CT symmetry in quantum field theory a representation of the universal covering of the Poincar'e group is constructed in terms of pairs of modular conjugations. The modular conjugations are associated with field algebras of unbounded operators localised in wedge regions. It turns out that an essential step consists in characterising the universal covering group of the Lorentz group by pairs of wedge regions, in conjunction with an analysis of its geometrical properties. In this thesis two approaches to this problem are developed in four spacetime dimensions. First a realisation of the universal covering as the quotient space over the set of pairs of wedge regions is presented. In spite of the intuitive definition, the necessary properties of a covering space are not straightforward to prove. But the geometrical properties are easy to handle. The second approach takes advantage of the well-known features of spin groups, given as subgroups of Clifford algebras. Characterising elements of spin groups by pairs of wedge regions is possible in an elegant manner. The geometrical analysis is performed by means of the results achieved in the first approach. These geometrical properties allow for constructing a representation of the universal cover of the Lorentz group in terms of pairs of modular conjugations. For this representation the derivation of the spin-statistics theorem is straightforward, and a PCT operator can be defined. Furthermore, it is possible to transfer the results to nets of field algebras in algebraic quantum field theory with ease. Many of the usual assumptions in quantum field theory like the spectrum condition or the existence of a covariant unitary representation, as well as the assumption on the quantum field to have only finitely many components, are not required. For the standard axioms, the crucial assumption of modular P{sub 1}CT symmetry constitutes no loss of generality because it is a
On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices
Red'Kov, Victor M.; Bogush, Andrei A.; Tokarevskaya, Natalia G.
2008-02-01
Parametrization of 4 × 4-matrices G of the complex linear group GL(4,C) in terms of four complex 4-vector parameters (k,m,n,l) is investigated. Additional restrictions separating some subgroups of GL(4,C) are given explicitly. In the given parametrization, the problem of inverting any 4 × 4 matrix G is solved. Expression for determinant of any matrix G is found: det G = F(k,m,n,l). Unitarity conditions G+ = G-1 have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups G1, G2, G3 - each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consis! ting of a product of a 3-parametric group isomorphic SU(2) and 1-parametric Abelian group. The Dirac basis of generators Λk, being of Gell-Mann type, substantially differs from the basis λi used in the literature on SU(4) group, formulas relating them are found - they permit to separate SU(3) subgroup in SU(4). Special way to list 15 Dirac generators of GL(4,C) can be used {Λk} = {μiÅνjÅ(μiVνj = KÅL ÅM )}, which permit to factorize SU(4) transformations according to S = eiaμ eibνeikKeilLeimM, where two first factors commute with each other and are isomorphic to SU(2) group, the three last ones are 3-parametric groups, each of them consisting of three Abelian commuting unitary subgroups. Besides, the structure of fifteen Dirac matrices Λk permits to separate twenty 3-parametric subgroups in SU(4) isomorphic to SU(2); those subgroups might be used as bigger elementary blocks in constructing of a general transformation SU(4). It is shown how one can specify the present approach for the pseudounitary group SU(2,2) and SU(3,1).
On Parametrization of the Linear GL(4,C and Unitary SU(4 Groups in Terms of Dirac Matrices
Directory of Open Access Journals (Sweden)
Natalia G. Tokarevskaya
2008-02-01
Full Text Available Parametrization of 4 × 4-matrices G of the complex linear group GL(4,C in terms of four complex 4-vector parameters (k,m,n,l is investigated. Additional restrictions separating some subgroups of GL(4,C are given explicitly. In the given parametrization, the problem of inverting any 4 × 4 matrix G is solved. Expression for determinant of any matrix G is found: det G = F(k,m,n,l. Unitarity conditions G+ = G-1 have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups G1, G2, G3 - each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consisting of a product of a 3-parametric group isomorphic SU(2 and 1-parametric Abelian group. The Dirac basis of generators Λk, being of Gell-Mann type, substantially differs from the basis λi used in the literature on SU(4 group, formulas relating them are found - they permit to separate SU(3 subgroup in SU(4. Special way to list 15 Dirac generators of GL(4,C can be used {Λk} = {αiÅβjÅ(αiVβj = KÅL ÅM }, which permit to factorize SU(4 transformations according to S = eiaα eibβeikKeilLeimM, where two first factors commute with each other and are isomorphic to SU(2 group, the three last ones are 3-parametric groups, each of them consisting of three Abelian commuting unitary subgroups. Besides, the structure of fifteen Dirac matrices Λk permits to separate twenty 3-parametric subgroups in SU(4 isomorphic to SU(2; those subgroups might be used as bigger elementary blocks in constructing of a general transformation SU(4. It is shown how one can specify the present approach for the pseudounitary group SU(2,2 and SU(3,1.
Création du groupe FMR (Flux, Matrices, Réseaux
Directory of Open Access Journals (Sweden)
Laurent Beauguitte
2013-06-01
Full Text Available Laurent Beauguitte et César Ducruetont pris l’initiative de créer un groupe de travail sur les réseaux en vue d’intégrer dans l’approche géographique les outils et méthodes issues de l’analyse des réseaux (planaires, sociaux, complexes. Ces derniers paraissent en effet fournir des pistes intéressantes pour l’analyse des flux de toute nature (commerciaux, humains, informationnels, financiers. Ce groupe tient une réunion mensuelle depuis le 26 octobre 2010 à Paris. Trois axes de travail sont...
On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices
Red'kov, Victor M; Tokarevskaya, Natalia G
2008-01-01
Parametrization of $4\\times 4$-matrices $G$ of the complex linear group $GL(4,C)$ in terms of four complex 4-vector parameters $(k,m,n,l)$ is investigated. Additional restrictions separating some subgroups of $GL(4,C)$ are given explicitly. In the given parametrization, the problem of inverting any $4\\times 4$ matrix $G$ is solved. Expression for determinant of any matrix $G$ is found: $\\det G = F(k,m,n,l)$. Unitarity conditions $G^{+} = G^{-1}$ have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups $G_{1}$, $G_{2}$, $G_{3}$ - each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consisting of a product of a 3-parametric group isomorphic SU(2) and 1-parametric Abelian group. The Dirac basis of generators $\\Lambda_{k}$, being of Gell-Mann type, substantially differs from the basis $\\lambda_{i}$ used in the literature o...
Predicting Covariance Matrices with Financial Conditions Indexes
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
Predicting Covariance Matrices with Financial Conditions Indexes
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 conside
Treatment of Nuclear Data Covariance Information in Sample Generation.
Energy Technology Data Exchange (ETDEWEB)
Swiler, Laura Painton; Adams, Brian M.; Wieselquist, William (ORNL)
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.
Rushton, J Philippe; Bons, Trudy Ann; Vernon, Philip A; Cvorović, Jelena
2007-07-22
We carried out two studies to test the hypothesis that genetic and environmental influences explain population group differences in general mental ability just as they do individual differences within a group. We estimated the heritability and environmentality of scores on the diagrammatic puzzles of the Raven's Coloured and/or Standard Progressive Matrices (CPM/SPM) from two independent twin samples and correlated these estimates with group differences on the same items. In Study 1, 199 pairs of 5- to 7-year-old monozygotic (MZ) and dizygotic (DZ) twins reared together provided estimates of heritability and environmentality for 36 puzzles from the CPM. These estimates correlated with the differences between the twins and 94 Serbian Roma (both rs=0.32; Ns=36; psadult MZ and DZ twins reared apart provided estimates of heritability and environmentality for 58 puzzles from the SPM. These estimates correlated with the differences among 11 diverse samples including (i) the reared-apart twins, (ii) another sample of Serbian Roma, and (iii) East Asian, White, South Asian, Coloured and Black high school and university students in South Africa. In 55 comparisons, group differences were more pronounced on the more heritable and on the more environmental items (mean rs=0.40 and 0.47, respectively; Ns=58; ps<0.05). After controlling for measurement reliability and variance in item pass rates, the heritabilities still correlated with the group differences, although the environmentalities did not. Puzzles found relatively difficult (or easy) by the twins were those found relatively difficult (or easy) by the others (mean r=0.87). These results suggest that population group differences are part of the normal variation expected within a universal human cognition.
REFINING GENETICALLY INFERRED RELATIONSHIPS USING TREELET COVARIANCE SMOOTHING1
Crossett, Andrew; Lee, Ann B.; Klei, Lambertus; Devlin, Bernie; Roeder, Kathryn
2013-01-01
Recent technological advances coupled with large sample sets have uncovered many factors underlying the genetic basis of traits and the predisposition to complex disease, but much is left to discover. A common thread to most genetic investigations is familial relationships. Close relatives can be identified from family records, and more distant relatives can be inferred from large panels of genetic markers. Unfortunately these empirical estimates can be noisy, especially regarding distant relatives. We propose a new method for denoising genetically—inferred relationship matrices by exploiting the underlying structure due to hierarchical groupings of correlated individuals. The approach, which we call Treelet Covariance Smoothing, employs a multiscale decomposition of covariance matrices to improve estimates of pairwise relationships. On both simulated and real data, we show that smoothing leads to better estimates of the relatedness amongst distantly related individuals. We illustrate our method with a large genome-wide association study and estimate the “heritability” of body mass index quite accurately. Traditionally heritability, defined as the fraction of the total trait variance attributable to additive genetic effects, is estimated from samples of closely related individuals using random effects models. We show that by using smoothed relationship matrices we can estimate heritability using population-based samples. Finally, while our methods have been developed for refining genetic relationship matrices and improving estimates of heritability, they have much broader potential application in statistics. Most notably, for error-in-variables random effects models and settings that require regularization of matrices with block or hierarchical structure. PMID:24587841
REFINING GENETICALLY INFERRED RELATIONSHIPS USING TREELET COVARIANCE SMOOTHING.
Crossett, Andrew; Lee, Ann B; Klei, Lambertus; Devlin, Bernie; Roeder, Kathryn
2013-06-27
Recent technological advances coupled with large sample sets have uncovered many factors underlying the genetic basis of traits and the predisposition to complex disease, but much is left to discover. A common thread to most genetic investigations is familial relationships. Close relatives can be identified from family records, and more distant relatives can be inferred from large panels of genetic markers. Unfortunately these empirical estimates can be noisy, especially regarding distant relatives. We propose a new method for denoising genetically-inferred relationship matrices by exploiting the underlying structure due to hierarchical groupings of correlated individuals. The approach, which we call Treelet Covariance Smoothing, employs a multiscale decomposition of covariance matrices to improve estimates of pairwise relationships. On both simulated and real data, we show that smoothing leads to better estimates of the relatedness amongst distantly related individuals. We illustrate our method with a large genome-wide association study and estimate the "heritability" of body mass index quite accurately. Traditionally heritability, defined as the fraction of the total trait variance attributable to additive genetic effects, is estimated from samples of closely related individuals using random effects models. We show that by using smoothed relationship matrices we can estimate heritability using population-based samples. Finally, while our methods have been developed for refining genetic relationship matrices and improving estimates of heritability, they have much broader potential application in statistics. Most notably, for error-in-variables random effects models and settings that require regularization of matrices with block or hierarchical structure.
The orbit structure of the Gelfand-Zeitlin group on n x n matrices
Colarusso, Mark
2008-01-01
In recent work ([KW1],[KW2]), Kostant and Wallach construct an action of a simply connected Lie group $A$ isomorphic to \\mathbb{C}^{{n\\choose 2}} on gl(n) using a completely integrable system derived from the Poisson analogue of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In [KW1], the authors show that $A$-orbits of dimension {n\\choose 2} form Lagrangian submanifolds of regular adjoint orbits in gl(n). They describe the orbit structure of $A$ on a certain Zariski open subset of regular semisimple elements. In this paper, we describe all $A$-orbits of dimension {n\\choose 2} and thus all polarizations of regular adjoint orbits obtained using Gelfand-Zeitlin theory.
New Row-grouped CSR format for storing the sparse matrices on GPU with implementation in CUDA
Oberhuber, Tomáš; Vacata, Jan
2010-01-01
In this article we present a new format for storing sparse matrices. The format is designed to perform well mainly on the GPU devices. We present its implementation in CUDA. The performance has been tested on 1,600 different types of matrices and we compare our format with the Hybrid format. We give detailed comparison of both formats and show their strong and weak parts.
Red'kov, V M; Tokarevskaya, N G
2007-01-01
Parametrization of 4x4 - matrices G of the complex linear group GL(4.C) in terms of four complex vector-parameters G=G(k,m,n,l) is investigated. Additional restrictions separating some sub-groups of GL(4.C) are given explicitly. In the given parametrization, the problem of inverting any 4 x 4 - matrix G is solved. Expression for determinant of any matrix G is found: detG =F(k,m,n,l). Unitarity conditions on the base of complex vector parametrization in the theory of the group GL(4.C) is investigated. Unitarity conditions have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Two simplest types of solutions have been constructed: 1-parametric Abelian subgroup G_{0} of 4 x 4 unitary matrices; three 2-parametric subgroups; one 4-parametric unitary sub-group. Curvilinear coordinates to cover these subgroups have been found.
Savage-McGlynn, Emily
2011-01-01
Approved hardbound copy has subtitle "a psychometric investigation of group differences in mean and variability as measured by the Raven's Standard Progressive Matrices Plus" Researchers and the general public alike continue to debate ‘which is the smarter sex?’ Research to date suggests that males outperform females, females outperform males, while others find no differences in mean or variance. These inconsistent results are thought to occur for two reasons. First, studies rely on opport...
Langlois, Michel
2014-01-01
In order to generalize the relativistic notion of boost to the case of non inertial particles and to general relativity, we come back to the definition of Lie group of Lorentz matrices and its Lie algebra and we study how this group acts on the Minskowski space. We thus define the notion of tangent boost along a worldline. This notion very general notion gives a useful tool both in special relativity (for non inertial particles or/and for non rectilinear coordinates) and in general relativity. We also introduce a matrix of the Lie algebra which, together with the tangent boost, gives the whole dynamical description of the considered system (acceleration and Thomas rotation). After studying the properties of Lie algebra matrices and of their reduced forms, we show that the Lie group of special Lorentz matrices has four one-parameter subgroups. These tools lead us to introduce the Thomas rotation in a quite general way. At the end of the paper, we present some examples using these tools and we consider the case...
Mehta, Madan Lal
1990-01-01
Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper on a multiple integral also gave rise to hundreds of recent publications. This book presents a coherent and detailed analytical treatment of random matrices, leading
Energy Technology Data Exchange (ETDEWEB)
Despotopulos, J D; Sudowe, R
2012-02-21
somewhere between Nb and Pa. Much more recent studies have examined the properties of Db from HNO{sub 3}/HF matrices, and suggest Db forms complexes similar to those of Pa. Very little experimental work into the behavior of element 114 has been performed. Thermochromatography experiments of three atoms of element 114 indicate that the element 114 is at least as volatile as Hg, At, and element 112. Lead was shown to deposit on gold at temperatures about 1000 C higher than the atoms of element 114. Results indicate a substantially increased stability of element 114. No liquid phase studies of element 114 or its homologs (Pb, Sn, Ge) or pseudo-homologs (Hg, Cd) have been performed. Theoretical predictions indicate that element 114 is should have a much more stable +2 oxidation state and neutral state than Pb, which would result in element 114 being less reactive and less metallic than Pb. The relativistic effects on the 7p{sub 1/2} electrons are predicted to cause a diagonal relationship to be introduced into the periodic table. Therefore, 114{sup 2+} is expected to behave as if it were somewhere between Hg{sup 2+}, Cd{sup 2+}, and Pb{sup 2+}. In this work two commercially available extraction chromatography resins are evaluated, one for the separation of Db homologs and pseudo?homologs from each other as well as from potential interfering elements such as Group IV Rf homologs and actinides, and the other for separation of element 114 homologs. One resin, Eichrom's DGA resin, contains a N,N,N',N'-tetra-n-octyldiglycolamide extractant, which separates analytes based on both size and charge characteristics of the solvated metal species, coated on an inert support. The DGA resin was examined for Db chemical systems, and shows a high degree of selectivity for tri-, tetra-, and hexavalent metal ions in multiple acid matrices with fast kinetics. The other resin, Eichrom's Pb resin, contains a di-t-butylcyclohexano 18-crown-6 extractant with isodecanol solvent
Earth Observing System Covariance Realism
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.
Multivariate covariance generalized linear models
DEFF Research Database (Denmark)
Bonat, W. H.; Jørgensen, Bent
2016-01-01
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...... 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...
Estimating the power spectrum covariance matrix with fewer mock samples
Pearson, David W
2015-01-01
The covariance matrices of power-spectrum (P(k)) measurements from galaxy surveys are difficult to compute theoretically. The current best practice is to estimate covariance matrices by computing a sample covariance of a large number of mock catalogues. The next generation of galaxy surveys will require thousands of large volume mocks to determine the covariance matrices to desired accuracy. The errors in the inverse covariance matrix are larger and scale with the number of P(k) bins, making the problem even more acute. We develop a method of estimating covariance matrices using a theoretically justified, few-parameter model, calibrated with mock catalogues. Using a set of 600 BOSS DR11 mock catalogues, we show that a seven parameter model is sufficient to fit the covariance matrix of BOSS DR11 P(k) measurements. The covariance computed with this method is better than the sample covariance at any number of mocks and only ~100 mocks are required for it to fully converge and the inverse covariance matrix conver...
Hees, T; Wenclawiak, B; Lustig, S; Schramel, P; Schwarzer, M; Schuster, M; Verstraete, D; Dams, R; Helmers, E
1998-01-01
Trace concentrations of the platinum group elements (PGE; here: Pt, Pd and Rh) play an important role in environmental analysis and assessment. Their importance is based on 1. their increasing use as active compartments in automobile exhaust catalysts, 2. their use as cancer anti-tumor agents in medicine. Due to their allergenic and cytotoxic potential, it is necessary to improve selectivity and sensitivity during analytical investigation of matrices like soil, grass, urine or blood. This paper summarizes the present knowledge of PGE in the fields of analytical chemistry, automobile emission rates, bioavailability, toxicology and medicine.
Stephanov, M A; Wettig, T
2005-01-01
We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper originally appeared as an article in the Wiley Encyclopedia of Electrical and Electronics Engineering.
Covariance Applications with Kiwi
Mattoon, C. M.; Brown, D.; Elliott, J. B.
2012-05-01
The Computational Nuclear Physics group at Lawrence Livermore National Laboratory (LLNL) is developing a new tool, named `Kiwi', that is intended as an interface between the covariance data increasingly available in major nuclear reaction libraries (including ENDF and ENDL) and large-scale Uncertainty Quantification (UQ) studies. Kiwi is designed to integrate smoothly into large UQ studies, using the covariance matrix to generate multiple variations of nuclear data. The code has been tested using critical assemblies as a test case, and is being integrated into LLNL's quality assurance and benchmarking for nuclear data.
Covariance Applications with Kiwi
Directory of Open Access Journals (Sweden)
Elliott J.B.
2012-05-01
Full Text Available The Computational Nuclear Physics group at Lawrence Livermore National Laboratory (LLNL is developing a new tool, named ‘Kiwi’, that is intended as an interface between the covariance data increasingly available in major nuclear reaction libraries (including ENDF and ENDL and large-scale Uncertainty Quantification (UQ studies. Kiwi is designed to integrate smoothly into large UQ studies, using the covariance matrix to generate multiple variations of nuclear data. The code has been tested using critical assemblies as a test case, and is being integrated into LLNL's quality assurance and benchmarking for nuclear data.
Karoui, Noureddine El
2009-01-01
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the asymptotic properties of correlation and covariance matrices, in the setting where $p/n\\to\\rho\\in(0,\\infty),$ for general population covariance. We show that, for a large class of models studied in random matrix theory, spectral properties of large-dimensional correlation matrices are similar to those of large-dimensional covarance matrices. We also derive a Mar\\u{c}enko--Pastur-type system of equations for the limiting spectral distribution of covariance matrices computed from data with elliptical distributions and generalizations of this family. The motivation for this study comes partly from the possible relevance of such distributional assumptions to problems in econometrics and portfolio optimization, as well as robustness questions for certain classical random matrix result...
EQUIVALENT MODELS IN COVARIANCE STRUCTURE-ANALYSIS
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 def
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.
Generalisations of Fisher Matrices
Heavens, Alan
2016-01-01
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.
Courvoisier, E.; Bicaba, Y.; Colin, X.
2016-05-01
The water absorption in two aromatic linear polymers (PEEK and PEI) was studied between 10% and 90% RH at 30, 50 and 70°C. It was found that these polymers display classical Henry and Fick's behaviors. Moreover, they have very close values of equilibrium water concentration C∞ and water diffusivity D presumably because their respective polar groups establish molecular interactions of the same nature with water. This assumption was checked from a literature compilation of values of C∞ and D for a large variety of linear and tridimensional polymers containing a single type of polar group. It was then evidenced that almost all types of carbonyl group (in particular, those belonging to imides, amides and ketones) have the same molar contribution to water absorption, except those belonging to esters which are much less hydrophilic. Furthermore, hydroxyl and sulfone groups are much more hydrophilic than carbonyl groups so that their molar contribution is located on another master curve. On this basis, semi-empirical structure/water transport property relationships were proposed. It was found that C∞ increases exponentially with the concentration of polar groups (presumably because water is doubly bonded), but also with the intensity of their molecular interactions with water. In contrast, D is inversely proportional to C∞, which means that polar group-water interactions slow down the rate of water diffusion.
Estimating Cosmological Parameter Covariance
Taylor, Andy
2014-01-01
We investigate the bias and error in estimates of the cosmological parameter covariance matrix, due to sampling or modelling the data covariance matrix, for likelihood width and peak scatter estimators. We show that these estimators do not coincide unless the data covariance is exactly known. For sampled data covariances, with Gaussian distributed data and parameters, the parameter covariance matrix estimated from the width of the likelihood has a Wishart distribution, from which we derive the mean and covariance. This mean is biased and we propose an unbiased estimator of the parameter covariance matrix. Comparing our analytic results to a numerical Wishart sampler of the data covariance matrix we find excellent agreement. An accurate ansatz for the mean parameter covariance for the peak scatter estimator is found, and we fit its covariance to our numerical analysis. The mean is again biased and we propose an unbiased estimator for the peak parameter covariance. For sampled data covariances the width estimat...
Condition Number Regularized Covariance Estimation.
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.
Condition Number Regularized Covariance Estimation*
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
Representations of Inverse Covariances by Differential Operators
Institute of Scientific and Technical Information of China (English)
Qin XU
2005-01-01
In the cost function of three- or four-dimensional variational data assimilation, each term is weighted by the inverse of its associated error covariance matrix and the background error covariance matrix is usually much larger than the other covariance matrices. Although the background error covariances are traditionally normalized and parameterized by simple smooth homogeneous correlation functions, the covariance matrices constructed from these correlation functions are often too large to be inverted or even manipulated. It is thus desirable to find direct representations of the inverses of background errorcorrelations. This problem is studied in this paper. In particular, it is shown that the background term can be written into ∫ dx|Dv(x)|2, that is, a squared L2 norm of a vector differential operator D, called the D-operator, applied to the field of analysis increment v(x). For autoregressive correlation functions, the Doperators are of finite orders. For Gaussian correlation functions, the D-operators are of infinite order. For practical applications, the Gaussian D-operators must be truncated to finite orders. The truncation errors are found to be small even when the Gaussian D-operators are truncated to low orders. With a truncated D-operator, the background term can be easily constructed with neither inversion nor direct calculation of the covariance matrix. D-operators are also derived for non-Gaussian correlations and transformed into non-isotropic forms.
Processing Neutron Cross Section Covariances using NJOY-99 and PUFF-IV
Energy Technology Data Exchange (ETDEWEB)
Arcilla,R.; Kahler, A.C.; Oblozinsky, P.; Herman, M.
2008-06-24
With the growing demand for multigroup covariances, the National Nuclear Data Center (NNDC) has been experiencing an upsurge in its covariance data processing activities using the two US codes NJOY-99 (LANL) and PUFF-IV (ORNL). The code NJOY-99 was upgraded by incorporating the new module ERRORJ-2.3, while the NNDC served as the active user and provided feedback. The NNDC has been primarily processing neutron cross section covariances on its 64-bit Linux cluster in support of two DOE programs, the Global Nuclear Energy Partnership (GNEP) and the Nuclear Criticality Safety Program (NCSP). For GNEP, the NNDC used NJOY-99.259 to generate multigroup covariance matrices of {sup 56}Fe, {sup 23}Na, {sup 239}Pu, {sup 235}U and {sup 238}U from the JENDL-3.3 library using the 15-, 33-, and 230-energy group structures. These covariance matrices will be used to test a new collapsing algorithm which will subsequently be employed to calculate uncertainties on integral parameters in different fast neutron-based systems. For NCSP, we used PUFF-IV 1.0.4 to verify the processability of new evaluated covariance data of {sup 55}Mn, {sup 239}Pu, {sup 233}U, {sup 235}U and {sup 238}U generated by a collaboration of ORNL and LANL. For the data end-users at large, the NNDC has made available a Web site which provides a static visualization interface for all materials with covariance data in the four major data libraries: ENDF/B-VI.8 (47 materials), ENDF/B-VII.0 (26 materials), JEFF-3.1 (37 materials) and JENDL-3.3 (20 materials).
Bayes linear covariance matrix adjustment for multivariate dynamic linear models
Wilkinson, Darren J
2008-01-01
A methodology is developed for the adjustment of the covariance matrices underlying a multivariate constant time series dynamic linear model. The covariance matrices are embedded in a distribution-free inner-product space of matrix objects which facilitates such adjustment. This approach helps to make the analysis simple, tractable and robust. To illustrate the methods, a simple model is developed for a time series representing sales of certain brands of a product from a cash-and-carry depot. The covariance structure underlying the model is revised, and the benefits of this revision on first order inferences are then examined.
Energy Technology Data Exchange (ETDEWEB)
Roldan-Valadez, Ernesto, E-mail: ernest.roldan@usa.net [Magnetic Resonance Unit, Medica Sur Clinic and Foundation, Mexico City (Mexico); Piña-Jimenez, Carlos [Magnetic Resonance Unit, Medica Sur Clinic and Foundation, Mexico City (Mexico); Favila, Rafael [GE Healthcare, Mexico City (Mexico); Rios, Camilo [Neurochemistry Department, Mexican National Institute of Neurology and Neurosurgery, Mexico City (Mexico)
2013-11-01
Introduction: There is an age-related conversion of red to yellow bone marrow in the axial skeleton, with a gender-related difference less well established. Our purpose was to clarify the variability of bone marrow fat fraction (FF) in the lumbar spine due to the interaction of gender and age groups. Methods: 44 healthy volunteers (20 males, 30–65 years old and 24 females, 30–69 years old) underwent 3T magnetic resonance spectroscopy (MRS) and conventional MRI examination of the lumbar spine; single-voxel spectrum was acquired for each vertebral body (VB). After controlling body mass index (BMI), a two-way between-groups multivariate analysis of covariance (MANCOVA) assessed the gender and age group differences in FF quantification for each lumbar VB. Results: There was a significant interaction between gender and age group, p = .017, with a large effect size (partial η{sup 2} = .330). However the interaction explained only 33% of the observed variance. Main effects were not statistically significant. BMI was non-significantly related to FF quantification. Conclusions: Young males showed a high FF content, which declined in the 4th decade, then increased the next 3 decades to reach a FF content just below the initial FF means. Females’ FF were low in the 3rd decade, depicted an accelerated increase in the 4th decade, then a gradual increase the next 3 decades to reach a FF content similar to males’ values. Our findings suggest that quantification of bone marrow FF using MRS might be used as a surrogate biomarker of bone marrow activity in clinical settings.
On weighted group invertibility for rectangular matrices over an arbitrary ring%关于环上长方矩阵的加权群可逆性
Institute of Scientific and Technical Information of China (English)
章劲鸥
2013-01-01
研究任意环上长方矩阵的加权群逆和加权{1,5}-逆。利用矩阵分解,得到了长方矩阵积的加权群逆存在的一些等价条件和计算方法及任意环上长方矩阵的加权{1,5}-逆的刻画表达式。得到的定理推广了有关方阵群逆和{1,5}-逆的相关结果。结果还可适合应用于加法范畴中的态射。%The weighted group inverses of rectangular matrices and the weighted{1, 5}-inverse of a rectangular matrix over an arbitrary ring are studied. Using Matrix decomposition method,First, the weighted group inverse of a rectangular matrix product P AQ for which there exist P′ and Q′ such that P′P A=A=AQQ′ can be characterized and computed. Moreover, the expressions are given for the weighted{1, 5}-inverse of a rectangular matrix over an arbitrary ring. This generalizes recent results obtained for the group inverse of square matricesand the weighted{1, 5}-inverse of a rectangular matrix over an arbitrary ring . The results also apply to morphisms in (additive) categories.
Moderate deviations for the eigenvalue counting function of Wigner matrices
Doering, Hanna
2011-01-01
We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on fine asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson. The extension to large families of Wigner matrices is based on the Tao and Vu Four Moment Theorem and applies localization results by Erd\\"os, Yau and Yin. Moreover we investigate families of covariance matrices as well.
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.
Covariance NMR spectroscopy by singular value decomposition.
Trbovic, Nikola; Smirnov, Serge; Zhang, Fengli; Brüschweiler, Rafael
2004-12-01
Covariance NMR is demonstrated for homonuclear 2D NMR data collected using the hypercomplex and TPPI methods. Absorption mode 2D spectra are obtained by application of the square-root operation to the covariance matrices. The resulting spectra closely resemble the 2D Fourier transformation spectra, except that they are fully symmetric with the spectral resolution along both dimensions determined by the favorable resolution achievable along omega2. An efficient method is introduced for the calculation of the square root of the covariance spectrum by applying a singular value decomposition (SVD) directly to the mixed time-frequency domain data matrix. Applications are shown for 2D NOESY and 2QF-COSY data sets and computational benchmarks are given for data matrix dimensions typically encountered in practice. The SVD implementation makes covariance NMR amenable to routine applications.
Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander
2017-09-03
We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, since H-matrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.
Group decision-making method with fuzzy comparison matrices%模糊判断矩阵环境下的大型群决策方法
Institute of Scientific and Technical Information of China (English)
兰继斌; 叶新苗; 胡明明
2012-01-01
为解决大型的群决策问题,对传统的模糊C均值算法(FCM)进行了扩展.通过扩展的算法对专家个体模糊判断矩阵聚类,获取模糊划分矩阵和聚类原型,根据模糊划分矩阵确定类权重,进而利用WAA算子对聚类原型进行集结,求取群综合模糊判断矩阵.通过算例验证了该算法的可行性.%Based on the extended Fuzzy c-Means(FCM) algorithm, a group decision-making approach, which is a mass of decision makers, is proposed. The FCM algorithm is extended to the environment of matrices. All the individual fuzzy preference relations are classified by the extended FCM algorithm. The cluster prototypes are aggregated by WAA operator into a collective fuzzy preference relation. The overall group decision-making process is shown, and the numerical example is given.
Hadamard Matrices and Their Applications
Horadam, K J
2011-01-01
In Hadamard Matrices and Their Applications, K. J. Horadam provides the first unified account of cocyclic Hadamard matrices and their applications in signal and data processing. This original work is based on the development of an algebraic link between Hadamard matrices and the cohomology of finite groups that was discovered fifteen years ago. The book translates physical applications into terms a pure mathematician will appreciate, and theoretical structures into ones an applied mathematician, computer scientist, or communications engineer can adapt and use. The first half of the book expl
Phenotypic covariance at species’ borders
2013-01-01
Background 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. Results 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. Conclusions 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. PMID:23714580
Inverse m-matrices and ultrametric matrices
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.
Covariant Projective Extensions
Institute of Scientific and Technical Information of China (English)
许天周; 梁洁
2003-01-01
@@ The theory of crossed products of C*-algebras by groups of automorphisms is a well-developed area of the theory of operator algebras. Given the importance and the success ofthat theory, it is natural to attempt to extend it to a more general situation by, for example,developing a theory of crossed products of C*-algebras by semigroups of automorphisms, or evenof endomorphisms. Indeed, in recent years a number of papers have appeared that are concernedwith such non-classicaltheories of covariance algebras, see, for instance [1-3].
A synthetic covariance matrix for monitoring by terrestrial laser scanning
Kauker, Stephanie; Schwieger, Volker
2017-06-01
Modelling correlations within laser scanning point clouds can be achieved by using synthetic covariance matrices. These are based on the elementary error model which contains different groups of correlations: non-correlating, functional correlating and stochastic correlating. By applying the elementary error model on terrestrial laser scanning several groups of error sources should be considered: instrumental, atmospheric and object based. This contribution presents calculations for the Leica HDS 7000. The determined variances and the spatial correlations of the points are estimated and discussed. Hereby, the mean standard deviation of the point cloud is up to 0.6 mm and the mean correlation is about 0.6 with respect to 5 m scanning range. The change of these numerical values compared to previous publications as Kauker and Schwieger [17] is mainly caused by the complete consideration of the object related error sources.
Energy Technology Data Exchange (ETDEWEB)
Zyczkowski, Karol [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/44, 02-668 Warsaw (Poland); Kus, Marek [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/44, 02-668 Warsaw (Poland); Slomczynski, Wojciech [Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Cracow (Poland); Sommers, Hans-Juergen [Fachbereich 7 Physik, Universitaet Essen, 45117 Essen (Germany)
2003-03-28
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N)). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and orthostochastic matrices in the complex plane. We compute averages (entropy, traces) over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices.
Dolan, C.V.; Colom, R.; Abad, F.J.; Wicherts, J.M.; Hessen, D.J.; van de Sluis, S.
2006-01-01
We investigated sex effects and the effects of educational attainment (EA) on the covariance structure of the WAIS-III in a subsample of the Spanish standardization data. We fitted both first order common factor models and second order common factor models. The latter include general intelligence (g
Zyczkowski, K.; Slomczynski, W.; Kus, M.; Sommers, H. -J.
2001-01-01
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and ortostochastic matrices in the complex p...
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
Institute of Scientific and Technical Information of China (English)
Faryad Ali
2007-01-01
The Held group He discovered by Held [10] is a sporadic simple group of order 4030387200 = 210.3a.52.73.17. The group He has 11 conjugacy classes of maximal subgroups as determined by Butler [5] and listed in the ATLAS. Held himself determined much of the local structure of He as well as the conjugacy classes of its elements. Thompson calculated the character table of He. In the present paper, we determine the Fischer Clifford matrices and hence compute the character table of the non-split extension 3.S7,which is a maximal subgroups of He of index 226560 using the technique of Fischer-Clifford matrices. Most of the computations were carried out with the aid of the computer algebra system GAP.
Anderson's absolute objects and constant timelike vector hidden in Dirac matrices
2001-01-01
Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices are the only absolute objects of the Dirac equation. There are two ways of the Dirac matrices transformation: (1) Dirac matrices form a 4-vector and wave function is a scalar, (2) Dirac matrices are scalars and the wave function is a spinor. In the first case the Dirac equation ...
Autism-specific covariation in perceptual performances: "g" or "p" factor?
Directory of Open Access Journals (Sweden)
Andrée-Anne S Meilleur
Full Text Available 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
GENERALIZED NEKRASOV MATRICES AND APPLICATIONS
Institute of Scientific and Technical Information of China (English)
Mingxian Pang; Zhuxiang Li
2003-01-01
In this paper, the concept of generalized Nekrasov matrices is introduced, some properties of these matrices are discussed, obtained equivalent representation of generalized diagonally dominant matrices.
Free probability and random matrices
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.
BLOCK H-MATRICES AND SPECTRUM OF BLOCK MATRICES
Institute of Scientific and Technical Information of China (English)
黄廷祝; 黎稳
2002-01-01
The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations claracterized by Gfunctions for block matrices are got.
Circulant conference matrices for new complex Hadamard matrices
Dita, Petre
2011-01-01
The circulant real and complex matrices are used to find new real and complex conference matrices. With them we construct Sylvester inverse orthogonal matrices by doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the inverse orthogonal matrices transform into complex Hadamard matrices. The method is used for $n=6$ conference matrices and in this way we find new parametrisations of Hadamard matrices for dimension $ n=12$.
Covariant Hamiltonian field theory
Giachetta, G; Sardanashvily, G
1999-01-01
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.
Octonion generalization of Pauli and Dirac matrices
Chanyal, B. C.
2015-10-01
Starting with octonion algebra and its 4 × 4 matrix representation, we have made an attempt to write the extension of Pauli's matrices in terms of division algebra (octonion). The octonion generalization of Pauli's matrices shows the counterpart of Pauli's spin and isospin matrices. In this paper, we also have obtained the relationship between Clifford algebras and the division algebras, i.e. a relation between octonion basis elements with Dirac (gamma), Weyl and Majorana representations. The division algebra structure leads to nice representations of the corresponding Clifford algebras. We have made an attempt to investigate the octonion formulation of Dirac wave equations, conserved current and weak isospin in simple, compact, consistent and manifestly covariant manner.
Wishart distributions for decomposable covariance graph models
Khare, Kshitij; 10.1214/10-AOS841
2011-01-01
Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph $G$. These models are distinctly different from the traditional concentration graph models (often also referred to as Gaussian graphical models or covariance selection models) since the zeros in the parameter are now reflected in the covariance matrix $\\Sigma$, as compared to the concentration matrix $\\Omega =\\Sigma^{-1}$. The parameter space of interest for covariance graph models is the cone $P_G$ of positive definite matrices with fixed zeros corresponding to the missing edges of $G$. As in Letac and Massam [Ann. Statist. 35 (2007) 1278--1323], we consider the case where $G$ is decomposable. In this paper, we construct on the cone $P_G$ a family of Wishart distributions which serve a similar purpose in the covariance graph setting as those constructed by Letac and Massam [Ann. Statist. 35 (2007) 1278--1323] and Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272--1317] do in ...
Energy Technology Data Exchange (ETDEWEB)
Cappellini, Valerio [' Mark Kac' Complex Systems Research Centre, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Krakow (Poland); Sommers, Hans-Juergen [Fachbereich Physik, Universitaet Duisburg-Essen, Campus Duisburg, 47048 Duisburg (Germany); Bruzda, Wojciech; Zyczkowski, Karol [Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Krakow (Poland)], E-mail: valerio@ictp.it, E-mail: h.j.sommers@uni-due.de, E-mail: w.bruzda@uj.edu.pl, E-mail: karol@cft.edu.pl
2009-09-11
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N = 2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary N we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.
Cappellini, V; Bruzda, W; Zyczkowski, K
2009-01-01
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N=2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary $N$ we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.
Multiplicative equations over commuting matrices
Energy Technology Data Exchange (ETDEWEB)
Babai, L. [Univ. of Chicago, IL (United States)]|[Eotvos Univ., Budapest (Hungary); Beals, R. [Rutgers Univ., Piscataway, NJ (United States); Cai, Jin-Yi [SUNY, Buffalo, NY (United States)] [and others
1996-12-31
We consider the solvability of the equation and generalizations, where the A{sub i} and B are given commuting matrices over an algebraic number field F. In the semigroup membership problem, the variables x{sub i} are constrained to be nonnegative integers. While this problem is NP-complete for variable k, we give a polynomial time algorithm if k is fixed. In the group membership problem, the matrices are assumed to be invertible, and the variables x{sub i} may take on negative values. In this case we give a polynomial time algorithm for variable k and give an explicit description of the set of all solutions (as an affine lattice). The special case of 1 x 1 matrices was recently solved by Guoqiang Ge; we heavily rely on his results.
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.
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.
Bickel, Peter J
2010-01-01
In the first part of this paper we give an elementary proof of the fact that if an infinite matrix $A$, which is invertible as a bounded operator on $\\ell^2$, can be uniformly approximated by banded matrices then so can the inverse of $A$. We give explicit formulas for the banded approximations of $A^{-1}$ as well as bounds on their accuracy and speed of convergence in terms of their band-width. In the second part we apply these results to covariance matrices $\\Sigma$ of Gaussian processes and study mixing and beta mixing of processes in terms of properties of $\\Sigma$. Finally, we note some applications of our results to statistics.
HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.
Fan, Jianqing; Liao, Yuan; Mincheva, Martina
2011-01-01
The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.
High-dimensional covariance matrix estimation in approximate factor models
Fan, Jianqing; Mincheva, Martina; 10.1214/11-AOS944
2012-01-01
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 [J. Amer. Statist. Assoc. 106 (2011) 672--684], 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 studi...
Complex Hadamard matrices from Sylvester inverse orthogonal matrices
Dita, Petre
2009-01-01
A novel method to obtain parametrizations of complex inverse orthogonal matrices is provided. These matrices are natural generalizations of complex Hadamard matrices which depend on non zero complex parameters. The method we use is via doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the inverse orthogonal matrices transform into complex Hadamard matrices, and in this way we find new parametrizations of Hadamard matrices for dim...
Matrices and linear transformations
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
Realized mixed-frequency factor models for vast dimensional covariance estimation
K. Bannouh (Karim); M.P.E. Martens (Martin); R.C.A. Oomen (Roel); D.J.C. van Dijk (Dick)
2012-01-01
textabstractWe introduce a Mixed-Frequency Factor Model (MFFM) to estimate vast dimensional covari- ance matrices of asset returns. The MFFM uses high-frequency (intraday) data to estimate factor (co)variances and idiosyncratic risk and low-frequency (daily) data to estimate the factor loadings. We
Earth Observing System Covariance Realism Updates
Ojeda Romero, Juan A.; Miguel, Fred
2017-01-01
This presentation will be given at the International Earth Science Constellation Mission Operations Working Group meetings June 13-15, 2017 to discuss the Earth Observing System Covariance Realism updates.
A Simple Cocyclic Jacket Matrices
Directory of Open Access Journals (Sweden)
Moon Ho Lee
2008-01-01
Full Text Available We present a new class of cocyclic Jacket matrices over complex number field with any size. We also construct cocyclic Jacket matrices over the finite field. Such kind of matrices has close relation with unitary matrices which are a first hand tool in solving many problems in mathematical and theoretical physics. Based on the analysis of the relation between cocyclic Jacket matrices and unitary matrices, the common method for factorizing these two kinds of matrices is presented.
Hamiltonian formalism and symplectic matrices; Formalisme Hamiltonien et Matrices symplectiques
Energy Technology Data Exchange (ETDEWEB)
Bertrand, P. [Project SPIRAL, Grand Accelerateur National d`Ions Lourds, BP 5027, Bd. H. Becquerel, 14076 Caen cedex 5 (France)
1997-12-31
This work consists of five sections. The first one introduces the Lagrangian formalism starting from the fundamental equation of the dynamics. The sections 2 to 4 are devoted to the Hamiltonian formalism and to symplectic matrices. Lie algebra and groups were avoided, although these notions are very useful if higher order effects have to be investigated. The paper is dealing with the properties of the transfer matrices describing different electromagnetic objects like, for instance: dipoles, quadrupoles, cyclotrons, electrostatic deflectors, spiral inflectors, etc. A remarkable property of the first order exact transfer matrices, is the symplecticity which in case of a 3-D object, described in 6-D phase space, provides 15 non-linear equations relating the matrix coefficients. The symplectic matrix ensemble forms an multiplication non-commuting group, consequently the product of n symplectic matrices is still a symplectic matrix. This permits the global description of a system of n objects. Thus, the notion symplecticity is fundamental for the selection of a given electromagnetic object, for its optimization and insertion in a line of beam transfer. The symplectic relations indicate actually that if a given beam characteristic is modified, then another characteristic will be affected and as a result the spurious effects can be limited when a line is to be adjusted. The last section is devoted to the application of the elaborated procedure to describe the drift of non-relativistic and relativistic particles, the dipole and the Muller inflector. Hopefully, this elementary Hamiltonian formalism will help in the familiarization with the symplectic matrices extensively utilized at GANIL 10 refs.
On covariance structure in noisy, big data
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.
Errors on errors - Estimating cosmological parameter covariance
Joachimi, Benjamin
2014-01-01
Current and forthcoming cosmological data analyses share the challenge of huge datasets alongside increasingly tight requirements on the precision and accuracy of extracted cosmological parameters. The community is becoming increasingly aware that these requirements not only apply to the central values of parameters but, equally important, also to the error bars. Due to non-linear effects in the astrophysics, the instrument, and the analysis pipeline, data covariance matrices are usually not well known a priori and need to be estimated from the data itself, or from suites of large simulations. In either case, the finite number of realisations available to determine data covariances introduces significant biases and additional variance in the errors on cosmological parameters in a standard likelihood analysis. Here, we review recent work on quantifying these biases and additional variances and discuss approaches to remedy these effects.
An Irreducible Form of Gamma Matrices for HMDS Coefficients of the Heat Kernel in Higher Dimensions
Fukuda, M.; Yajima, S.; Higashida, Y.; Kubota, S.; Tokuo, S.; Kamo, Y.
2009-05-01
The heat kernel method is used to calculate 1-loop corrections of a fermion interacting with general background fields. To apply the Hadamard-Minakshisundaram-DeWitt-Seeley (HMDS) coefficients a_q(x,x') of the heat kernel to calculate the corrections, it is meaningful to decompose the coefficients into tensorial components with irreducible matrices, which are the totally antisymmetric products of γ matrices. We present formulae for the tensorial forms of the γ-matrix-valued quantities X, tilde{Λ}_{μν} and their product and covariant derivative in terms of the irreducible matrices in higher dimensions. The concrete forms of HMDS coefficients obtained by repeated application of the formulae simplifies the derivation of the loop corrections after the trace calculations, because each term in the coefficients contains one of the irreducible matrices and some of the terms are expressed by commutator and the anticommutator with respect to th e generator of non-abelian gauge groups. The form of the third HMDS coefficient is useful for evaluating some of the fermionic anomalies in 6-dimensional curved space. We show that the new formulae appear in the chiral {U(1)} anomaly when the vector and the third-order tensor gauge fields do not commute.
Developmental plasticity in covariance structure of the skull: effects of prenatal stress.
Gonzalez, Paula N; Hallgrímsson, Benedikt; Oyhenart, Evelia E
2011-02-01
Environmental perturbations of many kinds influence growth and development. Little is known, however, about the influence of environmental factors on the patterns of phenotypic integration observed in complex morphological traits. We analyze the changes in phenotypic variance-covariance structure of the rat skull throughout the early postnatal ontogeny (from birth to weaning) and evaluate the effect of intrauterine growth retardation (IUGR) on this structure. Using 2D coordinates taken from lateral radiographs obtained every 4 days, from birth to 21 days old, we show that the pattern of covariance is temporally dynamic from birth to 21 days. The environmental perturbation provoked during pregnancy altered the skull growth, and reduced the mean size of the IUGR group. These environmental effects persisted throughout lactancy, when the mothers of both groups received a standard diet. More strikingly, the effect grew larger beyond this point. Altering environmental conditions did not affect all traits equally, as revealed by the low correlations between covariance matrices of treatments at the same age. Finally, we found that the IUGR treatment increased morphological integration as measured by the scaled variance of eigenvalues. This increase coincided and is likely related to an increase in morphological variance in this group. This result is expected if somatic growth is a major determinant of covariance structure of the skull. In summary, our findings suggest that environmental perturbations experienced in early ontogeny alter fundamental developmental processes and are an important factor in shaping the variance-covariance structure of complex phenotypic traits. © 2010 The Authors. Journal of Anatomy © 2010 Anatomical Society of Great Britain and Ireland.
Abel-Grassmann's Groupoids of Modulo Matrices
Directory of Open Access Journals (Sweden)
Muhammad Rashad
2016-01-01
Full Text Available The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Z 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 n is transitively commutative AG-groupoid and is a cancellative AG-groupoid ifn is prime. (ii Every AG-groupoid of matrices over Z n of Type-II is a T3-AG-groupoid. (iii An AG-groupoid of matrices over Z n ; G nAG(t,u, is an AG-band, ift+ u=1(mod n.
Daniel Bartz; Kerr Hatrick; Hesse, Christian W.; Klaus-Robert M\\"uller; Steven Lemm
2011-01-01
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, w...
Energy Technology Data Exchange (ETDEWEB)
De Saint Jean, C.; Archier, P.; Noguere, G.; Litaize, O.; Vaglio-Gaudard, C.; Bernard, D.; Leray, O. [CEA, DEN, DER, Cadarache, F-13108 Saint-Paul-lez-Durance (France)
2012-07-01
This paper presents the methodology used to estimate multi-group covariances for some major isotopes used in reactor physics. The starting point of this evaluation is the modelling of the neutron induced reactions based on nuclear reaction models with parameters. These latest are the vectors of uncertainties as they are absorbing uncertainties and correlation arising from the confrontation of nuclear reaction model to microscopic experiment. These uncertainties are then propagated towards multi-group cross sections. As major breakthroughs were then asked by nuclear reactor physicists to assess proper uncertainties to be used in applications, a solution is proposed by the use of integral experiment information at two different stages in the covariance estimation. In this paper, we will explain briefly the treatment of all type of uncertainties, including experimental ones (statistical and systematic) as well as those coming from validation of nuclear data on dedicated integral experiment (nuclear data oriented). We will illustrate the use of this methodology with various isotopes such as {sup 235,238}U, {sup 239}Pu, {sup 241}Am, {sup 56}Fe, {sup 23}Na and {sup 27}Al. (authors)
On greedy and submodular matrices
Faigle, U.; Kern, Walter; Peis, Britta; Marchetti-Spaccamela, Alberto; Segal, Michael
2011-01-01
We characterize non-negative greedy matrices, i.e., 0-1 matrices $A$ such that max $\\{c^Tx|Ax \\le b,\\,x \\ge 0\\}$ can be solved greedily. We identify submodular matrices as a special subclass of greedy matrices. Finally, we extend the notion of greediness to $\\{-1,0,+1\\}$-matrices. We present
Gaussian Fibonacci Circulant Type Matrices
Directory of Open Access Journals (Sweden)
Zhaolin Jiang
2014-01-01
Full Text Available Circulant matrices have become important tools in solving integrable system, Hamiltonian structure, and integral equations. In this paper, we prove that Gaussian Fibonacci circulant type matrices are invertible matrices for n>2 and give the explicit determinants and the inverse matrices. Furthermore, the upper bounds for the spread on Gaussian Fibonacci circulant and left circulant matrices are presented, respectively.
Institute of Scientific and Technical Information of China (English)
姜艳萍; 樊治平
2001-01-01
An aggregated approach is proposed to analize the group decision making problem with multiple fuzzy judgement matrices. Under condition that multiple fuzzy judgement matrices are consistent for the same decision making problem, the theoretic basis of the aggregated approach is presented. Several important properties such as the relationships between the group fuzzy judgement matrix and fuzzy judgement matrix provided by every decision maker are given. The research results lay a solid foundation for studying rankings of alternatives based on the group fuzzy judgement matrix.%对群组模糊判断矩阵的集结方法进行了研究,在对同一决策问题的m个模糊判断矩阵是一致性的情况下,给出了加权集结方法的理论依据,并且进一步分析了关于群的判断矩阵与各决策者给出的判断矩阵之间关系的一些重要性质,从而为基于群的判断矩阵的方案排序问题打下了坚实的基础．
Justino, Júlia
2017-06-01
Matrices with coefficients having uncertainties of type o (.) or O (.), called flexible matrices, are studied from the point of view of nonstandard analysis. The uncertainties of the afore-mentioned kind will be given in the form of the so-called neutrices, for instance the set of all infinitesimals. Since flexible matrices have uncertainties in their coefficients, it is not possible to define the identity matrix in an unique way and so the notion of spectral identity matrix arises. Not all nonsingular flexible matrices can be turned into a spectral identity matrix using Gauss-Jordan elimination method, implying that that not all nonsingular flexible matrices have the inverse matrix. Under certain conditions upon the size of the uncertainties appearing in a nonsingular flexible matrix, a general theorem concerning the boundaries of its minors is presented which guarantees the existence of the inverse matrix of a nonsingular flexible matrix.
On the tensor Permutation Matrices
Rakotonirina, Christian
2011-01-01
A property that tensor permutation matrices permutate tensor product of rectangle matrices is shown. Some examples, in the particular case of tensor commutation matrices, for studying some linear matricial equations are given.
Frasinski, Leszek J.
2016-08-01
Recent technological advances in the generation of intense femtosecond pulses have made covariance mapping an attractive analytical technique. The laser pulses available are so intense that often thousands of ionisation and Coulomb explosion events will occur within each pulse. To understand the physics of these processes the photoelectrons and photoions need to be correlated, and covariance mapping is well suited for operating at the high counting rates of these laser sources. Partial covariance is particularly useful in experiments with x-ray free electron lasers, because it is capable of suppressing pulse fluctuation effects. A variety of covariance mapping methods is described: simple, partial (single- and multi-parameter), sliced, contingent and multi-dimensional. The relationship to coincidence techniques is discussed. Covariance mapping has been used in many areas of science and technology: inner-shell excitation and Auger decay, multiphoton and multielectron ionisation, time-of-flight and angle-resolved spectrometry, infrared spectroscopy, nuclear magnetic resonance imaging, stimulated Raman scattering, directional gamma ray sensing, welding diagnostics and brain connectivity studies (connectomics). This review gives practical advice for implementing the technique and interpreting the results, including its limitations and instrumental constraints. It also summarises recent theoretical studies, highlights unsolved problems and outlines a personal view on the most promising research directions.
Covariant Bardeen perturbation formalism
Vitenti, S. D. P.; Falciano, F. T.; Pinto-Neto, N.
2014-05-01
In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so-called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach, one necessarily introduces an additional hypersurface choice to the problem. Using our mixed and pure tensors approach, we are able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hypersurface dependence inherent to the covariant approach. Finally, through the use of this map, we define full nonlinear tensors that at first order correspond to the three known gauge invariant variables Φ, Ψ and Ξ, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hypersurface invariant variables at any order.
Covariant canonical quantization
Energy Technology Data Exchange (ETDEWEB)
Hippel, G.M. von [University of Regina, Department of Physics, Regina, Saskatchewan (Canada); Wohlfarth, M.N.R. [Universitaet Hamburg, Institut fuer Theoretische Physik, Hamburg (Germany)
2006-09-15
We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. This procedure agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and we apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses. Covariant canonical quantization can thus be understood as a ''first'' or pre-quantization within the framework of conventional QFT. (orig.)
Covariant canonical quantization
Von Hippel, G M; Hippel, Georg M. von; Wohlfarth, Mattias N.R.
2006-01-01
We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. Covariant canonical quantization agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses.
DEFF Research Database (Denmark)
Britz, Thomas
Bipartite graphs and digraphs are used to describe algebraic operations on a free matrix, including Moore-Penrose inversion, finding Schur complements, and normalized LU factorization. A description of the structural properties of a free matrix and its Moore-Penrose inverse is proved, and necessa...... and sufficient conditions are given for the Moore-Penrose inverse of a free matrix to be free. Several of these results are generalized with respect to a family of matrices that contains both the free matrices and the nearly reducible matrices....
DEFF Research Database (Denmark)
Britz, Thomas
Bipartite graphs and digraphs are used to describe algebraic operations on a free matrix, including Moore-Penrose inversion, finding Schur complements, and normalized LU factorization. A description of the structural properties of a free matrix and its Moore-Penrose inverse is proved, and necessa...... and sufficient conditions are given for the Moore-Penrose inverse of a free matrix to be free. Several of these results are generalized with respect to a family of matrices that contains both the free matrices and the nearly reducible matrices....
Remediating Non-Positive Definite State Covariances for Collision Probability Estimation
Hall, Doyle T.; Hejduk, Matthew D.; Johnson, Lauren C.
2017-01-01
The NASA Conjunction Assessment Risk Analysis team estimates the probability of collision (Pc) for a set of Earth-orbiting satellites. The Pc estimation software processes satellite position+velocity states and their associated covariance matri-ces. On occasion, the software encounters non-positive definite (NPD) state co-variances, which can adversely affect or prevent the Pc estimation process. Inter-polation inaccuracies appear to account for the majority of such covariances, alt-hough other mechanisms contribute also. This paper investigates the origin of NPD state covariance matrices, three different methods for remediating these co-variances when and if necessary, and the associated effects on the Pc estimation process.
Indian Academy of Sciences (India)
Narendra Singh
2003-01-01
Assuming a relation between the quark mass matrices of the two sectors a unique solution can be obtained for the CKM ﬂavor mixing matrix. A numerical example is worked out which is in excellent agreement with experimental data.
Generalized Linear Covariance Analysis
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.
Covariance of maximum likelihood evolutionary distances between sequences aligned pairwise.
Dessimoz, Christophe; Gil, Manuel
2008-06-23
The estimation of a distance between two biological sequences is a fundamental process in molecular evolution. It is usually performed by maximum likelihood (ML) on characters aligned either pairwise or jointly in a multiple sequence alignment (MSA). Estimators for the covariance of pairs from an MSA are known, but we are not aware of any solution for cases of pairs aligned independently. In large-scale analyses, it may be too costly to compute MSAs every time distances must be compared, and therefore a covariance estimator for distances estimated from pairs aligned independently is desirable. Knowledge of covariances improves any process that compares or combines distances, such as in generalized least-squares phylogenetic tree building, orthology inference, or lateral gene transfer detection. In this paper, we introduce an estimator for the covariance of distances from sequences aligned pairwise. Its performance is analyzed through extensive Monte Carlo simulations, and compared to the well-known variance estimator of ML distances. Our covariance estimator can be used together with the ML variance estimator to form covariance matrices. The estimator performs similarly to the ML variance estimator. In particular, it shows no sign of bias when sequence divergence is below 150 PAM units (i.e. above ~29% expected sequence identity). Above that distance, the covariances tend to be underestimated, but then ML variances are also underestimated.
Progress on Nuclear Data Covariances: AFCI-1.2 Covariance Library
Energy Technology Data Exchange (ETDEWEB)
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
2009-09-28
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{sup -5} eV to 19.6 MeV. BNL contributed improved covariance data for the following materials: {sup 23}Na and {sup 55}Mn where more detailed evaluation was done; improvements in major structural materials {sup 52}Cr, {sup 56}Fe and {sup 58}Ni; improved estimates for remaining structural materials and fission products; improved covariances for 14 minor actinides, and estimates of mubar covariances for {sup 23}Na and {sup 56}Fe. LANL contributed improved covariance data for {sup 235}U and {sup 239}Pu including prompt neutron fission spectra and completely new evaluation for {sup 240}Pu. New R-matrix evaluation for {sup 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.
Saltas, Ippocratis D
2016-01-01
We derive the 1-loop effective action of the cubic Galileon coupled to quantum-gravitational fluctuations in a background and gauge-independent manner, employing the covariant framework of DeWitt and Vilkovisky. Although the bare action respects shift symmetry, the coupling to gravity induces an effective mass to the scalar, of the order of the cosmological constant, as a direct result of the non-flat field-space metric, the latter ensuring the field-reparametrization invariance of the formalism. Within a gauge-invariant regularization scheme, we discover novel, gravitationally induced non-Galileon higher-derivative interactions in the effective action. These terms, previously unnoticed within standard, non-covariant frameworks, are not Planck suppressed. Unless tuned to be sub-dominant, their presence could have important implications for the classical and quantum phenomenology of the theory.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Using Analysis of Covariance (ANCOVA) with Fallible Covariates
Culpepper, Steven Andrew; Aguinis, Herman
2011-01-01
Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e., measured with error), which is the norm, researchers must choose from among 3 inadequate courses of action: (a) know that the assumption that covariates are perfectly reliable is violated but…
Using Analysis of Covariance (ANCOVA) with Fallible Covariates
Culpepper, Steven Andrew; Aguinis, Herman
2011-01-01
Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e., measured with error), which is the norm, researchers must choose from among 3 inadequate courses of action: (a) know that the assumption that covariates are perfectly reliable is violated but…
Age differences on Raven's Coloured Progressive Matrices.
Panek, P E; Stoner, S B
1980-06-01
Raven's Coloured Progressive Matrices was administered to 150 subjects (75 males, 75 females) ranging in age from 20 to 86 yr. Subjects were placed into one of three age groups: adult (M age = 27.04 yr.), middle-age (M age = 53.36 yr.), old (M age = 73.78 yr.), with 25 males and 25 females in each age group. Significant differences between age groups on the matrices were obtained after partialing out the effects of educational level, while sex of subject was not significant.
Matrices in Engineering Problems
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
Characterizing the evolution of genetic variance using genetic covariance tensors.
Hine, Emma; Chenoweth, Stephen F; Rundle, Howard D; Blows, Mark W
2009-06-12
Determining how genetic variance changes under selection in natural populations has proved to be a very resilient problem in evolutionary genetics. In the same way that understanding the availability of genetic variance within populations requires the simultaneous consideration of genetic variance in sets of functionally related traits, determining how genetic variance changes under selection in natural populations will require ascertaining how genetic variance-covariance (G) matrices evolve. Here, we develop a geometric framework using higher-order tensors, which enables the empirical characterization of how G matrices have diverged among populations. We then show how divergence among populations in genetic covariance structure can then be associated with divergence in selection acting on those traits using key equations from evolutionary theory. Using estimates of G matrices of eight male sexually selected traits from nine geographical populations of Drosophila serrata, we show that much of the divergence in genetic variance occurred in a single trait combination, a conclusion that could not have been reached by examining variation among the individual elements of the nine G matrices. Divergence in G was primarily in the direction of the major axes of genetic variance within populations, suggesting that genetic drift may be a major cause of divergence in genetic variance among these populations.
Infinite matrices and sequence spaces
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
Residual noise covariance for Planck low-resolution data analysis
Keskitalo, R; Cabella, P; Kisner, T; Poutanen, T; Stompor, R; Bartlett, J G; Borrill, J; Cantalupo, C; De Gasperis, G; De Rosa, A; de Troia, G; Eriksen, H K; Finelli, F; Górski, K M; Gruppuso, A; Hivon, E; Jaffe, A; Keihanen, E; Kurki-Suonio, H; Lawrence, C R; Natoli, P; Paci, F; Polenta, G; Rocha, G
2009-01-01
Aims: Develop and validate tools to estimate residual noise covariance in Planck frequency maps. Quantify signal error effects and compare different techniques to produce low-resolution maps. Methods: We derive analytical estimates of covariance of the residual noise contained in low-resolution maps produced using a number of map-making approaches. We test these analytical predictions using Monte Carlo simulations and their impact on angular power spectrum estimation. We use simulations to quantify the level of signal errors incurred in different resolution downgrading schemes considered in this work. Results: We find an excellent agreement between the optimal residual noise covariance matrices and Monte Carlo noise maps. For destriping map-makers, the extent of agreement is dictated by the knee frequency of the correlated noise component and the chosen baseline offset length. The significance of signal striping is shown to be insignificant when properly dealt with. In map resolution downgrading, we find that...
Covariant Magnetic Connection Hypersurfaces
Pegoraro, F
2016-01-01
In the single fluid, nonrelativistic, ideal-Magnetohydrodynamic (MHD) plasma description magnetic field lines play a fundamental role by defining dynamically preserved "magnetic connections" between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MHD description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D {\\it magnetic connection hypersurfaces} in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when ${\\bf E} \\cdot {\\bf B} = 0$.
Accuracy of Pseudo-Inverse Covariance Learning--A Random Matrix Theory Analysis.
Hoyle, David C
2011-07-01
For many learning problems, estimates of the inverse population covariance are required and often obtained by inverting the sample covariance matrix. Increasingly for modern scientific data sets, the number of sample points is less than the number of features and so the sample covariance is not invertible. In such circumstances, the Moore-Penrose pseudo-inverse sample covariance matrix, constructed from the eigenvectors corresponding to nonzero sample covariance eigenvalues, is often used as an approximation to the inverse population covariance matrix. The reconstruction error of the pseudo-inverse sample covariance matrix in estimating the true inverse covariance can be quantified via the Frobenius norm of the difference between the two. The reconstruction error is dominated by the smallest nonzero sample covariance eigenvalues and diverges as the sample size becomes comparable to the number of features. For high-dimensional data, we use random matrix theory techniques and results to study the reconstruction error for a wide class of population covariance matrices. We also show how bagging and random subspace methods can result in a reduction in the reconstruction error and can be combined to improve the accuracy of classifiers that utilize the pseudo-inverse sample covariance matrix. We test our analysis on both simulated and benchmark data sets.
Land, M C
2001-01-01
This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schr\\"odinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the non-relativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is lnear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformat...
Introduction to matrices and vectors
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.
On covariances for fusing laser rangers and vision with sensors onboard a moving robot
Wernersson, Åke; Nygårds, Jonas
1998-01-01
Consider a robot to measure or operate on man made objects randomly located in the workspace. The optronic sensing onboard the robot are a scanning range measuring time-of-flight laser and a CCD camera. The goal of the paper is to give explicit covariance matrices for the extracted geometric primitives in the surrounding workspace. Emphasis is on correlation properties of the stochastic error models during motion. Topics studied include: (i) covariance of Radon/Hough peaks for plane surfaces;...
Inference for High-dimensional Differential Correlation Matrices.
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.
Covariance of the selfdual vector model
2004-01-01
The Poisson algebra between the fields involved in the vectorial selfdual action is obtained by means of the reduced action. The conserved charges associated with the invariance under the inhomogeneous Lorentz group are obtained and its action on the fields. The covariance of the theory is proved using the Schwinger-Dirac algebra. The spin of the excitations is discussed.
Domcke, Valerie
2016-01-01
We study natural lepton mass matrices, obtained assuming the stability of physical flavour observables with respect to the variations of individual matrix elements. We identify all four possible stable neutrino textures from algebraic conditions on their entries. Two of them turn out to be uniquely associated to specific neutrino mass patterns. We then concentrate on the semi-degenerate pattern, corresponding to an overall neutrino mass scale within the reach of future experiments. In this context we show that i) the neutrino and charged lepton mixings and mass matrices are largely constrained by the requirement of stability, ii) naturalness considerations give a mild preference for the Majorana phase most relevant for neutrinoless double-beta decay, $\\alpha \\sim \\pi/2$, and iii) SU(5) unification allows to extend the implications of stability to the down quark sector. The above considerations would benefit from an experimental determination of the PMNS ratio $|U_{32}/U_{31}|$, i.e. of the Dirac phase $\\delta...
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...
Gil, José J; José, Ignacio San
2015-01-01
Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance, or because its associated canonical depolarizer has the property of fully randomizing, the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, of potential usefulness to experimentalists dealing with such media.
Nanoceramic Matrices: Biomedical Applications
Directory of Open Access Journals (Sweden)
Willi Paul
2006-01-01
Full Text Available Natural bone consisted of calcium phosphate with nanometer-sized needle-like crystals of approximately 5-20 nm width by 60 nm length. Synthetic calcium phosphates and Bioglass are biocompatible and bioactive as they bond to bone and enhance bone tissue formation. This property is attributed to their similarity with the mineral phase of natural bone except its constituent particle size. Calcium phosphate ceramics have been used in dentistry and orthopedics for over 30 years because of these properties. Several studies indicated that incorporation of growth hormones into these ceramic matrices facilitated increased tissue regeneration. Nanophase calcium phosphates can mimic the dimensions of constituent components of natural tissues; can modulate enhanced osteoblast adhesion and resorption with long-term functionality of tissue engineered implants. This mini review discusses some of the recent developments in nanophase ceramic matrices utilized for bone tissue engineering.
Hubeny, Veronika E
2014-01-01
A recently explored interesting quantity in AdS/CFT, dubbed 'residual entropy', characterizes the amount of collective ignorance associated with either boundary observers restricted to finite time duration, or bulk observers who lack access to a certain spacetime region. However, the previously-proposed expression for this quantity involving variation of boundary entanglement entropy (subsequently renamed to 'differential entropy') works only in a severely restrictive context. We explain the key limitations, arguing that in general, differential entropy does not correspond to residual entropy. Given that the concept of residual entropy as collective ignorance transcends these limitations, we identify two correspondingly robust, covariantly-defined constructs: a 'strip wedge' associated with boundary observers and a 'rim wedge' associated with bulk observers. These causal sets are well-defined in arbitrary time-dependent asymptotically AdS spacetimes in any number of dimensions. We discuss their relation, spec...
Deriving covariant holographic entanglement
Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund
2016-11-01
We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Rényi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.
Deriving covariant holographic entanglement
Dong, Xi; Rangamani, Mukund
2016-01-01
We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Renyi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.
Covariant Macroscopic Quantum Geometry
Hogan, Craig J
2012-01-01
A covariant noncommutative algebra of position operators is presented, and interpreted as the macroscopic limit of a geometry that describes a collective quantum behavior of the positions of massive bodies in a flat emergent space-time. The commutator defines a quantum-geometrical relationship between world lines that depends on their separation and relative velocity, but on no other property of the bodies, and leads to a transverse uncertainty of the geometrical wave function that increases with separation. The number of geometrical degrees of freedom in a space-time volume scales holographically, as the surface area in Planck units. Ongoing branching of the wave function causes fluctuations in transverse position, shared coherently among bodies with similar trajectories. The theory can be tested using appropriately configured Michelson interferometers.
Saltas, Ippocratis D.; Vitagliano, Vincenzo
2017-05-01
We derive the 1-loop effective action of the cubic Galileon coupled to quantum-gravitational fluctuations in a background and gauge-independent manner, employing the covariant framework of DeWitt and Vilkovisky. Although the bare action respects shift symmetry, the coupling to gravity induces an effective mass to the scalar, of the order of the cosmological constant, as a direct result of the nonflat field-space metric, the latter ensuring the field-reparametrization invariance of the formalism. Within a gauge-invariant regularization scheme, we discover novel, gravitationally induced non-Galileon higher-derivative interactions in the effective action. These terms, previously unnoticed within standard, noncovariant frameworks, are not Planck suppressed. Unless tuned to be subdominant, their presence could have important implications for the classical and quantum phenomenology of the theory.
Covariant holographic entanglement negativity
Chaturvedi, Pankaj; Sengupta, Gautam
2016-01-01
We conjecture a holographic prescription for the covariant entanglement negativity of $d$-dimensional conformal field theories dual to non static bulk $AdS_{d+1}$ gravitational configurations in the framework of the $AdS/CFT$ correspondence. Application of our conjecture to a $AdS_3/CFT_2$ scenario involving bulk rotating BTZ black holes exactly reproduces the entanglement negativity of the corresponding $(1+1)$ dimensional conformal field theories and precisely captures the distillable quantum entanglement. Interestingly our conjecture for the scenario involving dual bulk extremal rotating BTZ black holes also accurately leads to the entanglement negativity for the chiral half of the corresponding $(1+1)$ dimensional conformal field theory at zero temperature.
On Random Correlation Matrices
1988-10-28
the spectral features of the resulting matrices are unknown. Method 2: Perturbation about a Mean This method is discussed by Marsaglia and Okin,10...complete regressor set. Finally, Marsaglia and Olkin (1984, Reference 10) give a rigorous mathematical description of Methods 2 through 4 described in the...short paper by Marsaglia 46 has a review of these early contributions, along with an improved method. More recent references are the pragmatic paper
Concentration for noncommutative polynomials in random matrices
2011-01-01
We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries and unitary or orthogonal matrices.
A comparison of covariance structure in wild and laboratory muroid crania.
Jamniczky, Heather A; Hallgrímsson, Benedikt
2009-06-01
Mutations have the ability to produce dramatic changes to covariance structure by altering the variance of covariance-generating developmental processes. Several evolutionary mechanisms exist that may be acting interdependently to stabilize covariance structure, despite this developmental potential for variation within species. We explore covariance structure in the crania of laboratory mouse mutants exhibiting mild-to-significant developmental perturbations of the cranium, and contrast it with covariance structure in related wild muroid taxa. Phenotypic covariance structure is conserved among wild muroidea, but highly variable and mutation-dependent within the laboratory group. We show that covariance structures in natural populations of related species occupy a more restricted portion of covariance structure space than do the covariance structures resulting from single mutations of significant effect or the almost nonexistent genetic differences that separate inbred mouse strains. Our results suggest that developmental constraint is not the primary mechanism acting to stabilize covariance structure, and imply a more important role for other mechanisms.
Covariant Quantum Gravity with Continuous Quantum Geometry I: Covariant Hamiltonian Framework
Pilc, Marián
2016-01-01
The first part of the series is devoted to the formulation of the Einstein-Cartan Theory within the covariant hamiltonian framework. In the first section the general multisymplectic approach is revised and the notion of the d-jet bundles is introduced. Since the whole Standard Model Lagrangian (including gravity) can be written as the functional of the forms, the structure of the d-jet bundles is more appropriate for the covariant hamiltonian analysis than the standard jet bundle approach. The definition of the local covariant Poisson bracket on the space of covariant observables is recalled. The main goal of the work is to show that the gauge group of the Einstein-Cartan theory is given by the semidirect product of the local Lorentz group and the group of spacetime diffeomorphisms. Vanishing of the integral generators of the gauge group is equivalent to equations of motion of the Einstein-Cartan theory and the local covariant algebra generated by Noether's currents is closed Lie algebra.
Mirror-Symmetric Matrices and Their Application
Institute of Scientific and Technical Information of China (English)
李国林; 冯正和
2002-01-01
The well-known centrosymmetric matrices correctly reflect mirror-symmetry with no component or only one component on the mirror plane. Mirror-symmetric matrices defined in this paper can represent mirror-symmetric structures with various components on the mirror plane. Some basic properties of mirror-symmetric matrices were studied and applied to interconnection analysis. A generalized odd/even-mode decomposition scheme was developed based on the mirror reflection relationship for mirror-symmetric multiconductor transmission lines (MTLs). The per-unit-length (PUL) impedance matrix Z and admittance matrix Y can be divided into odd-mode and even-mode PUL matrices. Thus the order of the MTL system is reduced from n to k and k+p, where p(≥0)is the conductor number on the mirror plane. The analysis of mirror-symmetric matrices is related to the theory of symmetric group, which is the most effective tool for the study of symmetry.
Accelerating Matrix-Vector Multiplication on Hierarchical Matrices Using Graphical Processing Units
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.
Yang, Chunwei; Yao, Junping; Sun, Dawei; Wang, Shicheng; Liu, Huaping
2016-05-01
Automatic target recognition in infrared imagery is a challenging problem. In this paper, a kernel sparse coding method for infrared target recognition using covariance descriptor is proposed. First, covariance descriptor combining gray intensity and gradient information of the infrared target is extracted as a feature representation. Then, due to the reason that covariance descriptor lies in non-Euclidean manifold, kernel sparse coding theory is used to solve this problem. We verify the efficacy of the proposed algorithm in terms of the confusion matrices on the real images consisting of seven categories of infrared vehicle targets.
Residual noise covariance for Planck low-resolution data analysis
Keskitalo, R.; Ashdown, M. A. J.; Cabella, P.; Kisner, T.; Poutanen, T.; Stompor, R.; Bartlett, J. G.; Borrill, J.; Cantalupo, C.; de Gasperis, G.; de Rosa, A.; de Troia, G.; Eriksen, H. K.; Finelli, F.; Górski, K. M.; Gruppuso, A.; Hivon, E.; Jaffe, A.; Keihänen, E.; Kurki-Suonio, H.; Lawrence, C. R.; Natoli, P.; Paci, F.; Polenta, G.; Rocha, G.
2010-11-01
Aims: We develop and validate tools for estimating residual noise covariance in Planck frequency maps, we also quantify signal error effects and compare different techniques to produce low-resolution maps. Methods: We derived analytical estimates of covariance of the residual noise contained in low-resolution maps produced using a number of mapmaking approaches. We tested these analytical predictions using both Monte Carlo simulations and by applying them to angular power spectrum estimation. We used simulations to quantify the level of signal errors incurred in the different resolution downgrading schemes considered in this work. Results: We find excellent agreement between the optimal residual noise covariance matrices and Monte Carlo noise maps. For destriping mapmakers, the extent of agreement is dictated by the knee frequency of the correlated noise component and the chosen baseline offset length. Signal striping is shown to be insignificant when properly dealt with. In map resolution downgrading, we find that a carefully selected window function is required to reduce aliasing to the subpercent level at multipoles, ℓ > 2Nside, where Nside is the HEALPix resolution parameter. We show that, for a polarization measurement, reliable characterization of the residual noise is required to draw reliable constraints on large-scale anisotropy. Conclusions: Methods presented and tested in this paper allow for production of low-resolution maps with both controlled sky signal error level and a reliable estimate of covariance of the residual noise. We have also presented a method for smoothing the residual noise covariance matrices to describe the noise correlations in smoothed, bandwidth-limited maps.
Covariant electromagnetic field lines
Hadad, Y.; Cohen, E.; Kaminer, I.; Elitzur, A. C.
2017-08-01
Faraday introduced electric field lines as a powerful tool for understanding the electric force, and these field lines are still used today in classrooms and textbooks teaching the basics of electromagnetism within the electrostatic limit. However, despite attempts at generalizing this concept beyond the electrostatic limit, such a fully relativistic field line theory still appears to be missing. In this work, we propose such a theory and define covariant electromagnetic field lines that naturally extend electric field lines to relativistic systems and general electromagnetic fields. We derive a closed-form formula for the field lines curvature in the vicinity of a charge, and show that it is related to the world line of the charge. This demonstrates how the kinematics of a charge can be derived from the geometry of the electromagnetic field lines. Such a theory may also provide new tools in modeling and analyzing electromagnetic phenomena, and may entail new insights regarding long-standing problems such as radiation-reaction and self-force. In particular, the electromagnetic field lines curvature has the attractive property of being non-singular everywhere, thus eliminating all self-field singularities without using renormalization techniques.
Schneider, Hans
1989-01-01
Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t
M Wedderburn, J H
1934-01-01
It is the organization and presentation of the material, however, which make the peculiar appeal of the book. This is no mere compendium of results-the subject has been completely reworked and the proofs recast with the skill and elegance which come only from years of devotion. -Bulletin of the American Mathematical Society The very clear and simple presentation gives the reader easy access to the more difficult parts of the theory. -Jahrbuch über die Fortschritte der Mathematik In 1937, the theory of matrices was seventy-five years old. However, many results had only recently evolved from sp
An Empirical State Error Covariance Matrix Orbit Determination Example
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
An Empirical State Error Covariance Matrix for Batch State Estimation
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
Tensor Dictionary Learning for Positive Definite Matrices.
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.
Truncations of random unitary matrices
Zyczkowski, K; Zyczkowski, Karol; Sommers, Hans-Juergen
1999-01-01
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ratio M/N. For the truncated CUE we derive analytically the joint density of eigenvalues from which easily all correlation functions are obtained. For N-M fixed and N--> infinity the universal resonance-width distribution with N-M open channels is recovered.
Criteria of the Nonsingular H-Matrices
Institute of Scientific and Technical Information of China (English)
GAO jian; LIU Futi; HUANG Tingzhu
2004-01-01
The nonsingular H-matrices play an important role in the study of the matrix theory and the iterative method of systems of linear equations,etc.It has always been searched how to verify nonsingular H-matrices.In this paper,nonsingular H-matrices is studies by applying diagonally dominant matrices,irreducible diagonally dominant matrices and comparison matrices and several practical criteria for identifying nonsingular H-matrices are obtained.
Block-diagonal representations for covariance-based anomalous change detectors
Energy Technology Data Exchange (ETDEWEB)
Matsekh, Anna M [Los Alamos National Laboratory; Theiler, James P [Los Alamos National Laboratory
2010-01-01
We use singular vectors of the whitened cross-covariance matrix of two hyper-spectral images and the Golub-Kahan permutations in order to obtain equivalent tridiagonal representations of the coefficient matrices for a family of covariance-based quadratic Anomalous Change Detection (ACD) algorithms. Due to the nature of the problem these tridiagonal matrices have block-diagonal structure, which we exploit to derive analytical expressions for the eigenvalues of the coefficient matrices in terms of the singular values of the whitened cross-covariance matrix. The block-diagonal structure of the matrices of the RX, Chronochrome, symmetrized Chronochrome, Whitened Total Least Squares, Hyperbolic and Subpixel Hyperbolic Anomalous Change Detectors are revealed by the white singular value decomposition and Golub-Kahan transformations. Similarities and differences in the properties of these change detectors are illuminated by their eigenvalue spectra. We presented a methodology that provides the eigenvalue spectrum for a wide range of quadratic anomalous change detectors. Table I summarizes these results, and Fig. I illustrates them. Although their eigenvalues differ, we find that RX, HACD, Subpixel HACD, symmetrized Chronochrome, and WTLSQ share the same eigenvectors. The eigen vectors for the two variants of Chronochrome defined in (18) are different, and are different from each other, even though they share many (but not all, unless d{sub x} = d{sub y}) eigenvalues. We demonstrated that it is sufficient to compute SVD of the whitened cross covariance matrix of the data in order to almost immediately obtain highly structured sparse matrices (and their eigenvalue spectra) of the coefficient matrices of these ACD algorithms in the white SVD-transformed coordinates. Converting to the original non-white coordinates, these eigenvalues will be modified in magnitude but not in sign. That is, the number of positive, zero-valued, and negative eigenvalues will be conserved.
Covariant representations of subproduct systems
Viselter, Ami
2010-01-01
A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with finding conditions for a covariant representation of a \\emph{subproduct system} to extend to a $C^*$-representation of the Toeplitz algebra. This framework is much more general than the former. We are able to find sufficient conditions, and show that in important special cases, they are also necessary. Further results include the universality of the tensor algebra, dilations of completely contractive covariant representations, Wold decompositions and von Neumann inequalities.
矩阵逆半群%Inverse Semigroups of Matrices
Institute of Scientific and Technical Information of China (English)
朱用文
2008-01-01
We discuss some fundamental properties of inverse semigroups of matrices, and prove that the idempotents of such a semigroup constitute a subsemilattice of a finite Boolean lattice,and that the inverse semigroups of some matrices with the same rank are groups. At last, we determine completely the construction of the inverse semigroups of some 2 x 2 matrices: such a semigroup is isomorphic to a linear group of dimension 2 or a null-adjoined group, or is afinite semilattice of Abelian linear groups of finite dimension, or satisfies some other properties.The necessary and sufficient conditions are given that the sets consisting of some 2 × 2 matrices become inverse semigroups.
VanderLaan Circulant Type Matrices
Directory of Open Access Journals (Sweden)
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.
General covariance in computational electrodynamics
DEFF Research Database (Denmark)
Shyroki, Dzmitry; Lægsgaard, Jesper; Bang, Ole;
2007-01-01
We advocate the generally covariant formulation of Maxwell equations as underpinning some recent advances in computational electrodynamics—in the dimensionality reduction for separable structures; in mesh truncation for finite-difference computations; and in adaptive coordinate mapping as opposed...
Polynomial Fibonacci-Hessenberg matrices
Energy Technology Data Exchange (ETDEWEB)
Esmaeili, Morteza [Dept. of Mathematical Sciences, Isfahan University of Technology, 84156-83111 Isfahan (Iran, Islamic Republic of)], E-mail: emorteza@cc.iut.ac.ir; Esmaeili, Mostafa [Dept. of Electrical and Computer Engineering, Isfahan University of Technology, 84156-83111 Isfahan (Iran, Islamic Republic of)
2009-09-15
A Fibonacci-Hessenberg matrix with Fibonacci polynomial determinant is referred to as a polynomial Fibonacci-Hessenberg matrix. Several classes of polynomial Fibonacci-Hessenberg matrices are introduced. The notion of two-dimensional Fibonacci polynomial array is introduced and three classes of polynomial Fibonacci-Hessenberg matrices satisfying this property are given.
Enhancing Understanding of Transformation Matrices
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…
Enhancing Understanding of Transformation Matrices
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…
Hierarchical matrices algorithms and analysis
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 ...
A trade-off solution between model resolution and covariance in surface-wave inversion
Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.
2010-01-01
Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.
On the use of fully populated matrices in GPS least-squares adjustment
Kermarrec, Gael; Schön, Steffen
2016-04-01
The mathematical model for GNSS positioning is well described. However, the stochastic model is said to remain improvable. Indeed, heteroscedastic is mainly assumed, i.e. the variance of the observations is having an elevation dependency, typically based on 1/sin elevation models, on SNR or CN0 based values as well as elevation-based exponential models. However, correlations between satellites observations remain ignored. Over the last years, covariance functions that try to model GNSS correlations have been proposed and tested, such as the empirical exponential model or double integration of turbulence based functions. In this contribution, we will present a way to take atmospheric correlations into account based on the turbulence theory, which is a simplification of the Schön and Brunner model (2008). As a result, fully populated covariance matrices based on physically plausible results can be easily computed and integrated in least-squares adjustment. Moreover, the use of the flexible Matern covariance family allow put both to model other kind of correlations (stronger or lower) by adapting the smoothness and the correlation length factor of the covariance function. Thus the influence of fully populated matrices versus diagonal matrices on the parameter domain can be tested. By means of simulations where the covariance matrices are exactly known, it is shown that the rms-improvement of the parameters to estimate by taking correlations into account is mainly limited to submm domain, particularly for double-differenced data. The dependency of the estimates differences with the sample length and the correlation structure will be investigated. Finally, we will show that the fully populated matrices can be approximated by an equivalent diagonal kernel that facilitates taking correlations into account.
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
Random matrices as models for the statistics of quantum mechanics
Casati, Giulio; Guarneri, Italo; Mantica, Giorgio
1986-05-01
Random matrices from the Gaussian unitary ensemble generate in a natural way unitary groups of evolution in finite-dimensional spaces. The statistical properties of this time evolution can be investigated by studying the time autocorrelation functions of dynamical variables. We prove general results on the decay properties of such autocorrelation functions in the limit of infinite-dimensional matrices. We discuss the relevance of random matrices as models for the dynamics of quantum systems that are chaotic in the classical limit. Permanent address: Dipartimento di Fisica, Via Celoria 16, 20133 Milano, Italy.
Estimating sparse precision matrices
Padmanabhan, Nikhil; White, Martin; Zhou, Harrison H.; O'Connell, Ross
2016-08-01
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological precision matrices are often approximately sparse, the method allows one to exploit this sparsity of the precision matrix to more quickly converge to an asymptotic 1/sqrt{N_sim} rate while simultaneously providing an error model for all of the terms. Such an estimate can be used as the starting point for further regularization efforts which can improve upon the 1/sqrt{N_sim} limit above, and incorporating such additional steps is straightforward within this framework. We demonstrate the technique with toy models and with an example motivated by large-scale structure two-point analysis, showing significant improvements in the rate of convergence. For the large-scale structure example, we find errors on the precision matrix which are factors of 5 smaller than for the sample precision matrix for thousands of simulations or, alternatively, convergence to the same error level with more than an order of magnitude fewer simulations.
Generating random density matrices
Zyczkowski, Karol; Nechita, Ion; Collins, Benoit
2010-01-01
We study various methods to generate ensembles of quantum density matrices of a fixed size N and analyze the corresponding probability distributions P(x), where x denotes the rescaled eigenvalue, x=N\\lambda. Taking a random pure state of a two-partite system and performing the partial trace over one subsystem one obtains a mixed state represented by a Wishart--like matrix W=GG^{\\dagger}, distributed according to the induced measure and characterized asymptotically, as N -> \\infty, by the Marchenko-Pastur distribution. Superposition of k random maximally entangled states leads to another family of explicitly derived distributions, describing singular values of the sum of k independent random unitaries. Taking a larger system composed of 2s particles, constructing $s$ random bi-partite states, performing the measurement into a product of s-1 maximally entangled states and performing the partial trace over the remaining subsystem we arrive at a random state characterized by the Fuss-Catalan distribution of order...
Calcul Stochastique Covariant à Sauts & Calcul Stochastique à Sauts Covariants
Maillard-Teyssier, Laurence
2003-01-01
We propose a stochastic covariant calculus forcàdlàg semimartingales in the tangent bundle $TM$ over a manifold $M$. A connection on $M$ allows us to define an intrinsic derivative ofa $C^1$ curve $(Y_t)$ in $TM$, the covariantderivative. More precisely, it is the derivative of$(Y_t)$ seen in a frame moving parallelly along its projection curve$(x_t)$ on $M$. With the transfer principle, Norris defined thestochastic covariant integration along a continuous semimartingale in$TM$. We describe t...
Covariate-free and Covariate-dependent Reliability.
Bentler, Peter M
2016-12-01
Classical test theory reliability coefficients are said to be population specific. Reliability generalization, a meta-analysis method, is the main procedure for evaluating the stability of reliability coefficients across populations. A new approach is developed to evaluate the degree of invariance of reliability coefficients to population characteristics. Factor or common variance of a reliability measure is partitioned into parts that are, and are not, influenced by control variables, resulting in a partition of reliability into a covariate-dependent and a covariate-free part. The approach can be implemented in a single sample and can be applied to a variety of reliability coefficients.
Graph-theoretical matrices in chemistry
Janezic, Dusanka; Nikolic, Sonja; Trinajstic, Nenad
2015-01-01
Graph-Theoretical Matrices in Chemistry presents a systematic survey of graph-theoretical matrices and highlights their potential uses. This comprehensive volume is an updated, extended version of a former bestseller featuring a series of mathematical chemistry monographs. In this edition, nearly 200 graph-theoretical matrices are included.This second edition is organized like the previous one-after an introduction, graph-theoretical matrices are presented in five chapters: The Adjacency Matrix and Related Matrices, Incidence Matrices, The Distance Matrix and Related Matrices, Special Matrices
Cleaning large correlation matrices: Tools from Random Matrix Theory
Bun, Joël; Bouchaud, Jean-Philippe; Potters, Marc
2017-01-01
This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marčenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.
Hopf monoids from class functions on unitriangular matrices
Aguiar, Marcelo; Thiem, Nathaniel
2012-01-01
We build, from the collection of all groups of unitriangular matrices, Hopf monoids in Joyal's category of species. Such structure is carried by the collection of class function spaces on those groups, and also by the collection of superclass function spaces, in the sense of Diaconis and Isaacs. Superclasses of unitriangular matrices admit a simple description from which we deduce a combinatorial model for the Hopf monoid of superclass functions, in terms of the Hadamard product of the Hopf monoids of linear orders and of set partitions. This implies a recent result relating the Hopf algebra of superclass functions on unitriangular matrices to symmetric functions in noncommuting variables. We determine the algebraic structure of the Hopf monoid: it is a free monoid in species, with the canonical Hopf structure. As an application, we derive certain estimates on the number of conjugacy classes of unitriangular matrices.
Szekeres models: a covariant approach
Apostolopoulos, Pantelis S
2016-01-01
We exploit the 1+1+2 formalism to covariantly describe the inhomogeneous and anisotropic Szekeres models. It is shown that an \\emph{average scale length} can be defined \\emph{covariantly} which satisfies a 2d equation of motion driven from the \\emph{effective gravitational mass} (EGM) contained in the dust cloud. The contributions to the EGM are encoded to the energy density of the dust fluid and the free gravitational field $E_{ab}$. In addition the notions of the Apparent and Absolute Apparent Horizons are briefly discussed and we give an alternative gauge-invariant form to define them in terms of the kinematical variables of the spacelike congruences. We argue that the proposed program can be used in order to express the Sachs optical equations in a covariant form and analyze the confrontation of a spatially inhomogeneous irrotational overdense fluid model with the observational data.
Covariance evaluation work at LANL
Energy Technology Data Exchange (ETDEWEB)
Kawano, Toshihiko [Los Alamos National Laboratory; Talou, Patrick [Los Alamos National Laboratory; Young, Phillip [Los Alamos National Laboratory; Hale, Gerald [Los Alamos National Laboratory; Chadwick, M B [Los Alamos National Laboratory; Little, R C [Los Alamos National Laboratory
2008-01-01
Los Alamos evaluates covariances for nuclear data library, mainly for actinides above the resonance regions and light elements in the enUre energy range. We also develop techniques to evaluate the covariance data, like Bayesian and least-squares fitting methods, which are important to explore the uncertainty information on different types of physical quantities such as elastic scattering angular distribution, or prompt neutron fission spectra. This paper summarizes our current activities of the covariance evaluation work at LANL, including the actinide and light element data mainly for the criticality safety study and transmutation technology. The Bayesian method based on the Kalman filter technique, which combines uncertainties in the theoretical model and experimental data, is discussed.
An introduction to the theory of canonical matrices
Turnbull, H W
2004-01-01
Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory's principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations. 1952 edition. Index. Appendix. Historical notes. Bibliographies. 275 problems.
Generalized linear models with coarsened covariates: a practical Bayesian approach.
Johnson, Timothy R; Wiest, Michelle M
2014-06-01
Coarsened covariates are a common and sometimes unavoidable phenomenon encountered in statistical modeling. Covariates are coarsened when their values or categories have been grouped. This may be done to protect privacy or to simplify data collection or analysis when researchers are not aware of their drawbacks. Analyses with coarsened covariates based on ad hoc methods can compromise the validity of inferences. One valid method for accounting for a coarsened covariate is to use a marginal likelihood derived by summing or integrating over the unknown realizations of the covariate. However, algorithms for estimation based on this approach can be tedious to program and can be computationally expensive. These are significant obstacles to their use in practice. To overcome these limitations, we show that when expressed as a Bayesian probability model, a generalized linear model with a coarsened covariate can be posed as a tractable missing data problem where the missing data are due to censoring. We also show that this model is amenable to widely available general-purpose software for simulation-based inference for Bayesian probability models, providing researchers a very practical approach for dealing with coarsened covariates.
Cosmic Censorship Conjecture revisited: Covariantly
Hamid, Aymen I M; Maharaj, Sunil D
2014-01-01
In this paper we study the dynamics of the trapped region using a frame independent semi-tetrad covariant formalism for general Locally Rotationally Symmetric (LRS) class II spacetimes. We covariantly prove some important geometrical results for the apparent horizon, and state the necessary and sufficient conditions for a singularity to be locally naked. These conditions bring out, for the first time in a quantitative and transparent manner, the importance of the Weyl curvature in deforming and delaying the trapped region during continual gravitational collapse, making the central singularity locally visible.
Spinorial Reduction of the Superdimensional Dual-covariant Field Theory
Derbenev, Yaroslav
2015-01-01
In this paper we produce further specification of the geometric and algebraic properties of the earlier introduced superdimensional dual-covariant field theory (SFT) in a N-dimensional manifold [1] as an approach to a unified field theory (UFT). Considerations in the present paper are directed by a requirement of transformational invariance of connections of derivatives of dual state vector (DSV) and unified gauge field (UGF matrices) to these objects themselves established by mean of N split metric matrices of a rank {\\mu} (SM, an extended analog of Dirac matrices) in frame of the related Euler-Lagrange equations for DSV, UGF and SM derived in [1]. This requirement is posed on SFT as one of the aspects of the general demand of irreducibility claimed to UFT; it leads to rotational invariance of SM and grand metric tensor (GM) as being structured on SM. Study in this work has led to explication of geometrical nature of SM and DSV as spin-affinors (variable in space of the unified manifold) and dual spin-field,...
Anderson's absolute objects and constant timelike vector hidden in Dirac matrices
Rylov, Yu A
2001-01-01
Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices are the only absolute objects of the Dirac equation. There are two ways of the Dirac matrices transformation: (1) Dirac matrices form a 4-vector and wave function is a scalar, (2) Dirac matrices are scalars and the wave function is a spinor. In the first case the Dirac equation is nonrelativistic, in the second one it is relativistic. Transforming Dirac equation to another scalar-vector variables, one shows that the first way of transformation is valid, and the Dirac equation is not relativistic
Covariant description of isothermic surfaces
Tafel, Jacek
2014-01-01
We present a covariant formulation of the Gauss-Weingarten equations and the Gauss-Mainardi-Codazzi equations for surfaces in 3-dimensional curved spaces. We derive a coordinate invariant condition on the first and second fundamental form which is necessary and sufficient for the surface to be isothermic.
Covariation Neglect among Novice Investors
Hedesstrom, Ted Martin; Svedsater, Henrik; Garling, Tommy
2006-01-01
In 4 experiments, undergraduates made hypothetical investment choices. In Experiment 1, participants paid more attention to the volatility of individual assets than to the volatility of aggregated portfolios. The results of Experiment 2 show that most participants diversified even when this increased risk because of covariation between the returns…
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.
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.
Covariant Formulations of Superstring Theories.
Mikovic, Aleksandar Radomir
1990-01-01
Chapter 1 contains a brief introduction to the subject of string theory, and tries to motivate the study of superstrings and covariant formulations. Chapter 2 describes the Green-Schwarz formulation of the superstrings. The Hamiltonian and BRST structure of the theory is analysed in the case of the superparticle. Implications for the superstring case are discussed. Chapter 3 describes the Siegel's formulation of the superstring, which contains only the first class constraints. It is shown that the physical spectrum coincides with that of the Green-Schwarz formulation. In chapter 4 we analyse the BRST structure of the Siegel's formulation. We show that the BRST charge has the wrong cohomology, and propose a modification, called first ilk, which gives the right cohomology. We also propose another superparticle model, called second ilk, which has infinitely many coordinates and constraints. We construct the complete BRST charge for it, and show that it gives the correct cohomology. In chapter 5 we analyse the properties of the covariant vertex operators and the corresponding S-matrix elements by using the Siegel's formulation. We conclude that the knowledge of the ghosts is necessary, even at the tree level, in order to obtain the correct S-matrix. In chapter 6 we attempt to calculate the superstring loops, in a covariant gauge. We calculate the vacuum-to -vacuum amplitude, which is also the cosmological constant. We show that it vanishes to all loop orders, under the assumption that the free covariant gauge-fixed action exists. In chapter 7 we present our conclusions, and briefly discuss the random lattice approach to the string theory, as a possible way of resolving the problem of the covariant quantization and the nonperturbative definition of the superstrings.
MIMO Radar Transmit Beampattern Design Without Synthesising the Covariance Matrix
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.
Extending a scatterplot for displaying group structure in multivariate ...
African Journals Online (AJOL)
covariance matrices. ... In risk management, for example, a financial institution ... biplot is related to a multivariate analysis of variance (MANOVA) performed for ..... plants by using biplots, American Institute for Chemical Engineering Journal, ...
Covariance specification and estimation to improve top-down Green House Gas emission estimates
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
Houle, David; Fierst, Janna
2013-04-01
We estimated mutational variance-covariance matrices, M, for wing shape and size in two genotypes of Drosophila melanogaster after 192 generations of mutation accumulation. We characterized 21 potentially independent aspects of wing shape and size using geometric morphometrics, and analyzed the data using a likelihood-based factor-analytic approach. We implement a previously unused analysis that describes those directions with the greatest difference in evolvability between pairs of matrices. There are significant mutational effects on 19 of 21 possible aspects of wing form, consistent with the high dimensionality of standing genetic variation for wing shape previously identified in D. melanogaster. Mutations have partially recessive effects, consistent with average dominance around 0.25. Sex-specific matrices are relatively similar, although male-specific matrices are slightly larger, as expected due to dosage compensation on the X chromosome. Genotype-specific matrices are quite different. Matrices may differ both because of sampling error based on small samples of mutations with large phenotypic effects, and because of the mutational properties of the genotypes. Genotypic differences are likely to be involved, as the two genotypes have different molecular mutation rates and properties. © 2012 The Author(s). Evolution© 2012 The Society for the Study of Evolution.
Unification of SU(2)xU(1) Using a Generalized Covariant Derivative and U(3)
Chaves, M
1998-01-01
A generalization of the Yang-Mills covariant derivative, that uses both vector and scalar fields and transforms as a 4-vector contracted with Dirac matrices, is used to simplify and unify the Glashow-Weinberg-Salam model. Since SU(3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U(3) to obtain all the correct quantum numbers. A surplus gauge scalar boson emerges in the process, but it uncouples from all other particles.
Dirac Matrices and Feynman's Rest of the Universe
Kim, Young S
2012-01-01
There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four $\\gamma$ matrices. These fifteen matrices can also serve as the generators of the group $SL(4,r)$. The second set consists of ten generators of the $Sp(4)$ group which he derived from two coupled harmonic oscillators. In classical mechanics, it is possible to extend the symmetry of the coupled oscillators to the SL(4,r) regime with fifteen Majorana matrices, while quantum mechanics allows only ten generators. This difference can serve as an illustrative example of Feynman's rest of the universe. The universe of the coupled oscillators consists of fifteen generators, and the ten generators are for the world where quantum mechanics is valid. The remaining five generators belong to the rest of the universe. It is noted that the groups $SL(4,r)$ and $Sp(4)$ are locally isomorphic to the Lorentz groups O(3,3) and O(3,2) respectively. This allows us to interpret Feynman's rest...
Discrete Symmetries in Covariant LQG
Rovelli, Carlo
2012-01-01
We study time-reversal and parity ---on the physical manifold and in internal space--- in covariant loop gravity. We consider a minor modification of the Holst action which makes it transform coherently under such transformations. The classical theory is not affected but the quantum theory is slightly different. In particular, the simplicity constraints are slightly modified and this restricts orientation flips in a spinfoam to occur only across degenerate regions, thus reducing the sources of potential divergences.
Analytical Derivation of the Inverse Moments of One-Sided Correlated Gram Matrices With Applications
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.
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.
Iterative methods for Toeplitz-like matrices
Energy Technology Data Exchange (ETDEWEB)
Huckle, T. [Universitaet Wurzburg (Germany)
1994-12-31
In this paper the author will give a survey on iterative methods for solving linear equations with Toeplitz matrices, Block Toeplitz matrices, Toeplitz plus Hankel matrices, and matrices with low displacement rank. He will treat the following subjects: (1) optimal (w)-circulant preconditioners is a generalization of circulant preconditioners; (2) Optimal implementation of circulant-like preconditioners in the complex and real case; (3) preconditioning of near-singular matrices; what kind of preconditioners can be used in this case; (4) circulant preconditioning for more general classes of Toeplitz matrices; what can be said about matrices with coefficients that are not l{sub 1}-sequences; (5) preconditioners for Toeplitz least squares problems, for block Toeplitz matrices, and for Toeplitz plus Hankel matrices.
Sign pattern matrices that admit M-, N-, P- or inverse M-matrices
Araújo, C. Mendes; Torregrosa, Juan R.
2009-01-01
In this paper we identify the sign pattern matrices that occur among the N–matrices, the P–matrices and the M–matrices. We also address to the class of inverse M–matrices and the related admissibility of sign pattern matrices problem. Fundação para a Ciência e a Tecnologia (FCT) Spanish DGI grant number MTM2007-64477
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
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.
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...
Lahti, P J; Scheffold, E; Ylinen, K; Lahti, Pekka; Maczynski, Maciej J.; Scheffold, Egon; Ylinen, Kari
2006-01-01
Noise sequences of infinite matrices associated with covariant phase and box localization observables are defined and determined. The canonical observables are characterized within the relevant classes of observables as those with asymptotically minimal or minimal noise, i.e., the noise tending to 0 or having the value 0.
Fractal Structure of Random Matrices
Hussein, M S
2000-01-01
A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the transition between the universality ensembles of random matrix theory and Poisson .
Open string fields as matrices
Kishimoto, Isao; Masuda, Toru; Takahashi, Tomohiko; Takemoto, Shoko
2015-03-01
We show that the action expanded around Erler-Maccaferri's N D-brane solution describes the N+1 D-brane system where one D-brane disappears due to tachyon condensation. String fields on multi-branes can be regarded as block matrices of a string field on a single D-brane in the same way as matrix theories.
Open String Fields as Matrices
Kishimoto, Isao; Takahashi, Tomohiko; Takemoto, Shoko
2014-01-01
We show that the action expanded around Erler-Maccaferri's N D-branes solution describes the N+1 D-branes system where one D-brane disappears due to tachyon condensation. String fields on the multi-branes can be regarded as block matrices of a string field on a single D-brane in the same way as matrix theories.
Arnold's Projective Plane and -Matrices
Directory of Open Access Journals (Sweden)
K. Uchino
2010-01-01
Full Text Available We will explain Arnold's 2-dimensional (shortly, 2D projective geometry (Arnold, 2005 by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular -matrices is the pencil of tangent lines of a quadratic curve on Arnold's projective plane.
Fibonacci Identities, Matrices, and Graphs
Huang, Danrun
2005-01-01
General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others…
Scattering matrices with block symmetries
Życzkowski, Karol
1997-01-01
Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a system with or without the time reversal invariance. An interpolating formula for the case of gradual time reversal symmetry breaking is proposed.
Making almost commuting matrices commute
Energy Technology Data Exchange (ETDEWEB)
Hastings, Matthew B [Los Alamos National Laboratory
2008-01-01
Suppose two Hermitian matrices A, B almost commute ({parallel}[A,B]{parallel} {<=} {delta}). Are they close to a commuting pair of Hermitian matrices, A', B', with {parallel}A-A'{parallel},{parallel}B-B'{parallel} {<=} {epsilon}? A theorem of H. Lin shows that this is uniformly true, in that for every {epsilon} > 0 there exists a {delta} > 0, independent of the size N of the matrices, for which almost commuting implies being close to a commuting pair. However, this theorem does not specifiy how {delta} depends on {epsilon}. We give uniform bounds relating {delta} and {epsilon}. The proof is constructive, giving an explicit algorithm to construct A' and B'. We provide tighter bounds in the case of block tridiagonal and tridiagnonal matrices. Within the context of quantum measurement, this implies an algorithm to construct a basis in which we can make a projective measurement that approximately measures two approximately commuting operators simultaneously. Finally, we comment briefly on the case of approximately measuring three or more approximately commuting operators using POVMs (positive operator-valued measures) instead of projective measurements.
Skills Underlying Coloured Progressive Matrices
Kirby, J. R.; Das, J. P.
1978-01-01
Raven's Coloured Progressive Matrices and a battery of ability tests were administered to a sample of 104 male fourth graders for purposes of investigating the relationships between 2 previously identified subscales of the Raven and the ability tests. Results indicated use of a spatial strategy and to a lesser extent, use of reasoning, indicating…
The diagonalization of cubic matrices
Cocolicchio, D.; Viggiano, M.
2000-08-01
This paper is devoted to analysing the problem of the diagonalization of cubic matrices. We extend the familiar algebraic approach which is based on the Cardano formulae. We rewrite the complex roots of the associated resolvent secular equation in terms of transcendental functions and we derive the diagonalizing matrix.
Spectral problems for operator matrices
Bátkai, A.; Binding, P.; Dijksma, A.; Hryniv, R.; Langer, H.
2005-01-01
We study spectral properties of 2 × 2 block operator matrices whose entries are unbounded operators between Banach spaces and with domains consisting of vectors satisfying certain relations between their components. We investigate closability in the product space, essential spectra and generation of
On the regularity of the covariance matrix of a discretized scalar field on the sphere
Bilbao-Ahedo, J. D.; Barreiro, R. B.; Herranz, D.; Vielva, P.; Martínez-González, E.
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.
TRANSPOSABLE REGULARIZED COVARIANCE MODELS WITH AN APPLICATION TO MISSING DATA IMPUTATION.
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.
Source Coding in Networks with Covariance Distortion Constraints
DEFF Research Database (Denmark)
Zahedi, Adel; Østergaard, Jan; Jensen, Søren Holdt
2016-01-01
-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our......We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate...... results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design...
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.
Needs of reliable nuclear data and covariance matrices for Burnup Credit in JEFF-3 library
Directory of Open Access Journals (Sweden)
Lecarpentier D.
2013-03-01
Full Text Available Burnup Credit (BUC is the concept which consists in taking into account credit for the reduction of nuclear spent fuel reactivity due to its burnup. In the case of PWR-MOx spent fuel, studies pointed out that the contribution of the 15 most absorbing, stable and non-volatile fission products selected to the credit is as important as the one of the actinides. In order to get a “best estimate” value of the keff, biases of their inventory calculation and individual reactivity worth should be considered in criticality safety studies. This paper enhances the most penalizing bias towards criticality and highlights possible improvements of nuclear data for the 15 FPs of PWRMOx BUC. Concerning the fuel inventory, trends in function of the burnup can be derived from experimental validation of the DARWIN-2.3 package (using the JEFF-3.1.1/SHEM library. Thanks to the BUC oscillation programme of separated FPs in the MINERVE reactor and fully validated scheme PIMS, calculation over experiment ratios can be accurately transposed to tendencies on the FPs integral cross sections.
Cheung, Mike W. L.; Chan, Wai
2009-01-01
Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation…
Otermann, Bente; Berg, van den Stephanie M.
2016-01-01
An abundance of research shows significant resemblance in standardized IQ scores in children and their biological parents. Twin and family studies based on such standardized scores suggest that a large proportion of the resemblance is due to genetic transmission, rather than cultural transmission. H
Schuurman, N.K.; Grasman, R.P.P.P.; Hamaker, E.L.
2016-01-01
Multilevel autoregressive models are especially suited for modeling between-person differences in within-person processes. Fitting these models with Bayesian techniques requires the specification of prior distributions for all parameters. Often it is desirable to specify prior distributions that
Otermann, Bente; van den Berg, Stéphanie Martine
2016-01-01
An abundance of research shows significant resemblance in standardized IQ scores in children and their biological parents. Twin and family studies based on such standardized scores suggest that a large proportion of the resemblance is due to genetic transmission, rather than cultural transmission.
MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices
Directory of Open Access Journals (Sweden)
Li-Wen Xu
2014-01-01
satisfactorily for various cell sizes and parameter configurations and generally outperforms the AHT test in terms of controlling the nominal size. For the heteroscedastic cases, the PB test outperforms the AHT test in terms of power. In addition, the PB test does not lose too much power when the homogeneity assumption is actually valid.
Cheung, Mike W. L.; Chan, Wai
2009-01-01
Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation…
Non-linear shrinkage estimation of large-scale structure covariance
Joachimi, Benjamin
2017-03-01
In many astrophysical settings, covariance matrices of large data sets have to be determined empirically from a finite number of mock realizations. The resulting noise degrades inference and precludes it completely if there are fewer realizations than data points. This work applies a recently proposed non-linear shrinkage estimator of covariance to a realistic example from large-scale structure cosmology. After optimizing its performance for the usage in likelihood expressions, the shrinkage estimator yields subdominant bias and variance comparable to that of the standard estimator with a factor of ∼50 less realizations. This is achieved without any prior information on the properties of the data or the structure of the covariance matrix, at a negligible computational cost.
Covariant and quasi-covariant quantum dynamics in Robertson-Walker space-times
Buchholz, D; Summers, S J; Buchholz, Detlev; Mund, Jens; Summers, Stephen J.
2002-01-01
We propose a canonical description of the dynamics of quantum systems on a class of Robertson-Walker space-times. We show that the worldline of an observer in such space-times determines a unique orbit in the local conformal group SO(4,1) of the space-time and that this orbit determines a unique transport on the space-time. For a quantum system on the space-time modeled by a net of local algebras, the associated dynamics is expressed via a suitable family of ``propagators''. In the best of situations, this dynamics is covariant, but more typically the dynamics will be ``quasi-covariant'' in a sense we make precise. We then show by using our technique of ``transplanting'' states and nets of local algebras from de Sitter space to Robertson-Walker space that there exist quantum systems on Robertson-Walker spaces with quasi-covariant dynamics. The transplanted state is locally passive, in an appropriate sense, with respect to this dynamics.
Shrinkage covariance matrix approach for microarray data
Karjanto, Suryaefiza; Aripin, Rasimah
2013-04-01
Microarray technology was developed for the purpose of monitoring the expression levels of thousands of genes. A microarray data set typically consists of tens of thousands of genes (variables) from just dozens of samples due to various constraints including the high cost of producing microarray chips. As a result, the widely used standard covariance estimator is not appropriate for this purpose. One such technique is the Hotelling's T2 statistic which is a multivariate test statistic for comparing means between two groups. It requires that the number of observations (n) exceeds the number of genes (p) in the set but in microarray studies it is common that n Hotelling's T2 statistic with the shrinkage approach is proposed to estimate the covariance matrix for testing differential gene expression. The performance of this approach is then compared with other commonly used multivariate tests using a widely analysed diabetes data set as illustrations. The results across the methods are consistent, implying that this approach provides an alternative to existing techniques.
Hierarchical multivariate covariance analysis of metabolic connectivity.
Carbonell, Felix; Charil, Arnaud; Zijdenbos, Alex P; Evans, Alan C; Bedell, Barry J
2014-12-01
Conventional brain connectivity analysis is typically based on the assessment of interregional correlations. Given that correlation coefficients are derived from both covariance and variance, group differences in covariance may be obscured by differences in the variance terms. To facilitate a comprehensive assessment of connectivity, we propose a unified statistical framework that interrogates the individual terms of the correlation coefficient. We have evaluated the utility of this method for metabolic connectivity analysis using [18F]2-fluoro-2-deoxyglucose (FDG) positron emission tomography (PET) data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. As an illustrative example of the utility of this approach, we examined metabolic connectivity in angular gyrus and precuneus seed regions of mild cognitive impairment (MCI) subjects with low and high β-amyloid burdens. This new multivariate method allowed us to identify alterations in the metabolic connectome, which would not have been detected using classic seed-based correlation analysis. Ultimately, this novel approach should be extensible to brain network analysis and broadly applicable to other imaging modalities, such as functional magnetic resonance imaging (MRI).
The MATRICS Consensus Cognitive Battery (MCCB): performance and functional correlates.
Lystad, June Ullevoldsæter; Falkum, Erik; Mohn, Christine; Haaland, Vegard Øksendal; Bull, Helen; Evensen, Stig; Rund, Bjørn Rishovd; Ueland, Torill
2014-12-30
Neurocognitive impairment is a core feature in psychotic disorders and the MATRICS Consensus Cognitive Battery (MCCB) is now widely used to assess neurocognition in this group. The MATRICS has been translated into several languages, including Norwegian; although this version has yet to be investigated in an adult clinical population. Further, the relationship between the MATRICS and different measures of functioning needs examination. The purpose of this study was to describe neurocognition assessed with the Norwegian version of the MATRICS battery in a sample of patients with psychotic disorders compared to age and gender matched healthy controls and to examine the association with educational-, occupational- and social-functioning in the patient group. One hundred and thirty one patients and 137 healthy controls completed the battery. The Norwegian version of the MATRICS was sensitive to the magnitude of neurocognitive impairments in patients with psychotic disorders, with patients displaying significant impairments on all domains relative to healthy controls. Neurocognition was also related to both self-rated and objective functional measures such as social functioning, educational- and employment-history.
Institute of Scientific and Technical Information of China (English)
张晓东; 杨尚骏
2001-01-01
本文探讨矩阵的一个重要子类（F-矩阵）的性质.F-矩阵包含以下在理论及应用中都很重要的三个矩阵类：对称正半定矩阵，M-矩阵和完全非负矩阵.我们首先证明F-矩阵的一些有趣性，特别是给出n-阶F-矩阵A满足detA=an…ann的充分必要条件.接着研究逆F-矩阵的性质，特别是证明逆M-矩阵和逆完全非负矩阵都是F-矩阵，从而满足Fischer不等式.最后我们引入F-矩阵一个子类:W-矩阵并证明逆W-矩阵也是F-矩阵.%We investigate a class of P0-matrices, called F-matrices, whichcontains well known three important classes of matrices satisfying Hadamard's inequality and Fischer's inequality-positive semidefinite symmetric matrices, M-matrices and totally nonnegative matrices. Firstly we prove some interesting properties of F-matrices and give the necessary and sufficient condition for an n×n F-matrix to satisfy det A=a11…ann. Then we investigate inverse F-matrices and prove both inverse M-matrices and inverse totally nonnegative matrices are F-matrices. Finally we introduce a new class of F-matrices, i.e. W-matrices and prove both W-matrices and inverse W-matrices are also F-matrices.
STABILITY FOR SEVERAL TYPES OF INTERVAL MATRICES
Institute of Scientific and Technical Information of China (English)
NianXiaohong; GaoJintai
1999-01-01
The robust stability for some types of tlme-varying interval raatrices and nonlineartime-varying interval matrices is considered and some sufficient conditions for robust stability of such interval matrices are given, The main results of this paper are only related to the verticesset of a interval matrices, and therefore, can be easily applied to test robust stability of interval matrices. Finally, some examples are given to illustrate the results.
The Bessel Numbers and Bessel Matrices
Institute of Scientific and Technical Information of China (English)
Sheng Liang YANG; Zhan Ke QIAO
2011-01-01
In this paper,using exponential Riordan arrays,we investigate the Bessel numbers and Bessel matrices.By exploring links between the Bessel matrices,the Stirling matrices and the degenerate Stirling matrices,we show that the Bessel numbers are special case of the degenerate Stirling numbers,and derive explicit formulas for the Bessel numbers in terms of the Stirling numbers and binomial coefficients.
Exact Distributions of Finite Random Matrices and Their Applications to Spectrum Sensing.
Zhang, Wensheng; Wang, Cheng-Xiang; Tao, Xiaofeng; Patcharamaneepakorn, Piya
2016-07-29
The exact and simple distributions of finite random matrix theory (FRMT) are critically important for cognitive radio networks (CRNs). In this paper, we unify some existing distributions of the FRMT with the proposed coefficient matrices (vectors) and represent the distributions with the coefficient-based formulations. A coefficient reuse mechanism is studied, i.e., the same coefficient matrices (vectors) can be exploited to formulate different distributions. For instance, the same coefficient matrices can be used by the largest eigenvalue (LE) and the scaled largest eigenvalue (SLE); the same coefficient vectors can be used by the smallest eigenvalue (SE) and the Demmel condition number (DCN). A new and simple cumulative distribution function (CDF) of the DCN is also deduced. In particular, the dimension boundary between the infinite random matrix theory (IRMT) and the FRMT is initially defined. The dimension boundary provides a theoretical way to divide random matrices into infinite random matrices and finite random matrices. The FRMT-based spectrum sensing (SS) schemes are studied for CRNs. The SLE-based scheme can be considered as an asymptotically-optimal SS scheme when the dimension K is larger than two. Moreover, the standard condition number (SCN)-based scheme achieves the same sensing performance as the SLE-based scheme for dual covariance matrix K = 2 . The simulation results verify that the coefficient-based distributions can fit the empirical results very well, and the FRMT-based schemes outperform the IRMT-based schemes and the conventional SS schemes.
Transfer Matrix Approach to 1d Random Band Matrices: Density of States
Shcherbina, Mariya; Shcherbina, Tatyana
2016-09-01
We study the special case of n× n 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix J=(-W^2triangle +1)^{-1}. Assuming that n≥ CW log W≫ 1, we prove that the averaged density of states coincides with the Wigner semicircle law up to the correction of order W^{-1}.
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|matrices...... of reciprocal Fibonacci numbers called Filbert matrices. We find a formula for the entries of the inverse quantum Hilbert matrix....
Simultaneous diagonalization of two quaternion matrices
Institute of Scientific and Technical Information of China (English)
ZhouJianhua
2003-01-01
The simultaneous diagonalization by congruence of pairs of Hermitian quatemion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quatemion matrix. It is proved that any two semi-positive definite Hermitian quatemion matrices can be simultaneously diagonalized by congruence.
USING COVARIANCE INTERSECTION FOR CHANGE DETECTION IN REMOTE SENSING IMAGES
Institute of Scientific and Technical Information of China (English)
Yang Meng; Zhang Gong
2011-01-01
In this paper,an unsupervised change detection technique for remote sensing images acquired on the same geographical area but at different time instances is proposed by conducting Covariance Intersection (CI) to perform unsupervised fusion of the final fuzzy partition matrices from the Fuzzy C-Means (FCM) clustering for the feature space by applying compressed sampling to the given remote sensing images.The proposed approach exploits a CI-based data fusion of the membership function matrices,which are obtained by taking the Fuzzy C-Means (FCM) clustering of the frequency-domain feature vectors and spatial-domain feature vectors,aimed at enhancing the unsupervised change detection performance.Compressed sampling is performed to realize the image local feature sampling,which is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery.The experimental results demonstrate that the proposed algorithm has a good change detection results and also performs quite well on denoising purpose.
Bombardelli, Diego
2016-08-01
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. In loving memory of Lilia Grandi.
Eigenvectors of some large sample covariance matrix ensembles
Ledoit, Olivier
2009-01-01
We consider sample covariance matrices $S_N=\\frac{1}{p}\\Sigma_N^{1/2}X_NX_N^* \\Sigma_N^{1/2}$ where $X_N$ is a $N \\times p$ real or complex matrix with i.i.d. entries with finite $12^{\\rm th}$ moment and $\\Sigma_N$ is a $N \\times N$ positive definite matrix. In addition we assume that the spectral measure of $\\Sigma_N$ almost surely converges to some limiting probability distribution as $N \\to \\infty$ and $p/N \\to \\gamma >0.$ We quantify the relationship between sample and population eigenvectors by studying the asymptotics of functionals of the type $\\frac{1}{N} \\text{Tr} (g(\\Sigma_N) (S_N-zI)^{-1})),$ where $I$ is the identity matrix, $g$ is a bounded function and $z$ is a complex number. This is then used to compute the asymptotically optimal bias correction for sample eigenvalues, paving the way for a new generation of improved estimators of the covariance matrix and its inverse.
Adaptive error covariances estimation methods for ensemble Kalman filters
Energy Technology Data Exchange (ETDEWEB)
Zhen, Yicun, E-mail: zhen@math.psu.edu [Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 (United States); Harlim, John, E-mail: jharlim@psu.edu [Department of Mathematics and Department of Meteorology, The Pennsylvania State University, University Park, PA 16802 (United States)
2015-08-01
This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of Belanger's recursive method, to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large. When we use only product of innovation processes up to one-lag, the computational cost is indeed comparable to a recently proposed method by Berry–Sauer's. However, our method is more flexible since it allows for using information from product of innovation processes of more than one-lag. Extensive numerical comparisons between the proposed method and both the original Belanger's and Berry–Sauer's schemes are shown in various examples, ranging from low-dimensional linear and nonlinear systems of SDEs and 40-dimensional stochastically forced Lorenz-96 model. Our numerical results suggest that the proposed scheme is as accurate as the original Belanger's scheme on low-dimensional problems and has a wider range of more accurate estimates compared to Berry–Sauer's method on L-96 example.
USING COVARIANCE MATRIX FOR CHANGE DETECTION OF POLARIMETRIC SAR DATA
Directory of Open Access Journals (Sweden)
M. Esmaeilzade
2017-09-01
Full Text Available Nowadays change detection is an important role in civil and military fields. The Synthetic Aperture Radar (SAR images due to its independent of atmospheric conditions and cloud cover, have attracted much attention in the change detection applications. When the SAR data are used, one of the appropriate ways to display the backscattered signal is using covariance matrix that follows the Wishart distribution. Based on this distribution a statistical test for equality of two complex variance-covariance matrices can be used. In this study, two full polarization data in band L from UAVSAR are used for change detection in agricultural fields and urban areas in the region of United States which the first image belong to 2014 and the second one is from 2017. To investigate the effect of polarization on the rate of change, full polarization data and dual polarization data were used and the results were compared. According to the results, full polarization shows more changes than dual polarization.
Covariance and correlation estimation in electron-density maps.
Altomare, Angela; Cuocci, Corrado; Giacovazzo, Carmelo; Moliterni, Anna; Rizzi, Rosanna
2012-03-01
Quite recently two papers have been published [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218; Giacovazzo et al. (2011). Acta Cryst. A67, 368-382] which calculate the variance in any point of an electron-density map at any stage of the phasing process. The main aim of the papers was to associate a standard deviation to each pixel of the map, in order to obtain a better estimate of the map reliability. This paper deals with the covariance estimate between points of an electron-density map in any space group, centrosymmetric or non-centrosymmetric, no matter the correlation between the model and target structures. The aim is as follows: to verify if the electron density in one point of the map is amplified or depressed as an effect of the electron density in one or more other points of the map. High values of the covariances are usually connected with undesired features of the map. The phases are the primitive random variables of our probabilistic model; the covariance changes with the quality of the model and therefore with the quality of the phases. The conclusive formulas show that the covariance is also influenced by the Patterson map. Uncertainty on measurements may influence the covariance, particularly in the final stages of the structure refinement; a general formula is obtained taking into account both phase and measurement uncertainty, valid at any stage of the crystal structure solution.
Dirac Matrices and Feynman’s Rest of the Universe
Directory of Open Access Journals (Sweden)
Young S. Kim
2012-10-01
Full Text Available There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four γ matrices. These fifteen matrices can also serve as the generators of the group SL(4, r. The second set consists of ten generators of the Sp(4 group which Dirac derived from two coupled harmonic oscillators. It is shown possible to extend the symmetry of Sp(4 to that of SL(4, r if the area of the phase space of one of the oscillators is allowed to become smaller without a lower limit. While there are no restrictions on the size of phase space in classical mechanics, Feynman’s rest of the universe makes this Sp(4-to-SL(4, r transition possible. The ten generators are for the world where quantum mechanics is valid. The remaining five generators belong to the rest of the universe. It is noted that the groups SL(4, r and Sp(4 are locally isomorphic to the Lorentz groups O(3, 3 and O(3, 2 respectively. This allows us to interpret Feynman’s rest of the universe in terms of space-time symmetry.
Wigner law for matrices with dependent entries - a perturbative approach
Krajewski, T; Vu, D L
2016-01-01
We show that Wigner semi-circle law holds for Hermitian matrices with dependent entries, provided the deviation of the cumulants from the normalised Gaussian case obeys a simple power law bound in the size of the matrix. To establish this result, we use replicas interpreted as a zero-dimensional quantum field theoretical model whose effective potential obey a renormalisation group equation.
Raven's Matrices Performance in Down Syndrome: Evidence of Unusual Errors
Gunn, Deborah M.; Jarrold, Christopher
2004-01-01
The aim of this study was to investigate the types of errors produced by three participant groups (individuals with Down syndrome, with moderate learning disability, and typically developing children) whilst completing the Raven's Coloured Progressive Matrices task. An analysis of error categories revealed that individuals with Down syndrome…
About limit matrices of finite-state Markov chains
Nieuwenhuis, J.W.
1997-01-01
By means of the concept of group inverse of a matrix we study limiting properties of a collection of stochastic matrices {P-epsilon, epsilon is an element of [0, 1]}, where For All epsilon is an element of [0, 1], P-epsilon is an element of R(nxn) and where P-0 = lim(epsilon-->0)P(epsilon). (C) Else
Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations
Directory of Open Access Journals (Sweden)
Han Guo
2012-01-01
Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.
Rotationally invariant ensembles of integrable matrices.
Yuzbashyan, Emil A; Shastry, B Sriram; Scaramazza, Jasen A
2016-05-01
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)-a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N-M independent commuting N×N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.
Rotationally invariant ensembles of integrable matrices
Yuzbashyan, Emil A.; Shastry, B. Sriram; Scaramazza, Jasen A.
2016-05-01
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)—a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N -M independent commuting N ×N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.
Covariant diagrams for one-loop matching
Zhang, Zhengkang
2016-01-01
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.
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.
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.
Treatment Effects with Many Covariates and Heteroskedasticity
DEFF Research Database (Denmark)
Cattaneo, Matias D.; Jansson, Michael; Newey, Whitney K.
The linear regression model is widely used in empirical work in Economics. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtai......The linear regression model is widely used in empirical work in Economics. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results...... then propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: (i) parametric linear models with many covariates, (ii...
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
DEFF Research Database (Denmark)
Hukkerikar, Amol; Sarup, Bent; Ten Kate, Antoon
2012-01-01
The aim of this work is to present revised and improved model parameters for group-contribution+ (GC+) models (combined group-contribution (GC) method and atom connectivity index (CI) method) employed for the estimation of pure component properties, together with covariance matrices to quantify.......g. prediction errors in terms of 95% confidence intervals) in the estimated property values. This feature allows one to evaluate the effects of these uncertainties on product-process design, simulation and optimization calculations, contributing to better-informed and more reliable engineering solutions. (C...
Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
Yanai, Haruo; Takane, Yoshio
2011-01-01
Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because
Random matrices and Riemann hypothesis
Pierre, Christian
2011-01-01
The curious connection between the spacings of the eigenvalues of random matrices and the corresponding spacings of the non trivial zeros of the Riemann zeta function is analyzed on the basis of the geometric dynamical global program of Langlands whose fundamental structures are shifted quantized conjugacy class representatives of bilinear algebraic semigroups.The considered symmetry behind this phenomenology is the differential bilinear Galois semigroup shifting the product,right by left,of automorphism semigroups of cofunctions and functions on compact transcendental quanta.
Sparse Matrices in Frame Theory
DEFF Research Database (Denmark)
Lemvig, Jakob; Krahmer, Felix; Kutyniok, Gitta
2014-01-01
Frame theory is closely intertwined with signal processing through a canon of methodologies for the analysis of signals using (redundant) linear measurements. The canonical dual frame associated with a frame provides a means for reconstruction by a least squares approach, but other dual frames...... yield alternative reconstruction procedures. The novel paradigm of sparsity has recently entered the area of frame theory in various ways. Of those different sparsity perspectives, we will focus on the situations where frames and (not necessarily canonical) dual frames can be written as sparse matrices...
Cosmetic crossings and Seifert matrices
Balm, Cheryl; Kalfagianni, Efstratia; Powell, Mark
2011-01-01
We study cosmetic crossings in knots of genus one and obtain obstructions to such crossings in terms of knot invariants determined by Seifert matrices. In particular, we prove that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove the nugatory crossing conjecture for twisted Whitehead doubles of non-cable knots. We also verify the conjecture for several families of pretzel knots and all genus one knots with up to 12 crossings.
Superalgebraic representation of Dirac matrices
Monakhov, V. V.
2016-01-01
We consider a Clifford extension of the Grassmann algebra in which operators are constructed from products of Grassmann variables and derivatives with respect to them. We show that this algebra contains a subalgebra isomorphic to a matrix algebra and that it additionally contains operators of a generalized matrix algebra that mix states with different numbers of Grassmann variables. We show that these operators are extensions of spin-tensors to the case of superspace. We construct a representation of Dirac matrices in the form of operators of a generalized matrix algebra.
Orthogonal polynomials and random matrices
Deift, Percy
2000-01-01
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
Assessing spatial covariance among time series of abundance.
Jorgensen, Jeffrey C; Ward, Eric J; Scheuerell, Mark D; Zabel, Richard W
2016-04-01
For species of conservation concern, an essential part of the recovery planning process is identifying discrete population units and their location with respect to one another. A common feature among geographically proximate populations is that the number of organisms tends to covary through time as a consequence of similar responses to exogenous influences. In turn, high covariation among populations can threaten the persistence of the larger metapopulation. Historically, explorations of the covariance in population size of species with many (>10) time series have been computationally difficult. Here, we illustrate how dynamic factor analysis (DFA) can be used to characterize diversity among time series of population abundances and the degree to which all populations can be represented by a few common signals. Our application focuses on anadromous Chinook salmon (Oncorhynchus tshawytscha), a species listed under the US Endangered Species Act, that is impacted by a variety of natural and anthropogenic factors. Specifically, we fit DFA models to 24 time series of population abundance and used model selection to identify the minimum number of latent variables that explained the most temporal variation after accounting for the effects of environmental covariates. We found support for grouping the time series according to 5 common latent variables. The top model included two covariates: the Pacific Decadal Oscillation in spring and summer. The assignment of populations to the latent variables matched the currently established population structure at a broad spatial scale. At a finer scale, there was more population grouping complexity. Some relatively distant populations were grouped together, and some relatively close populations - considered to be more aligned with each other - were more associated with populations further away. These coarse- and fine-grained examinations of spatial structure are important because they reveal different structural patterns not evident
Unbiased community detection for correlation matrices
MacMahon, Mel
2013-01-01
A challenging problem in the study of large complex systems is that of resolving, without prior information, the emergent mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented at identifying such modules and suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, the attempts made so far have merely replaced network data with correlation matrices, a procedure that we show to be fundamentally biased due to its inconsistency with the null hypotheses underlying the existing algorithms. Here we introduce, via a consistent redefinition of null models based on Random Matrix Theory, the unbiased correlation-based counterparts of the most popular community detection techniques. After successfully benchmarking our methods, we apply them to s...
Covariance structure models of expectancy.
Henderson, M J; Goldman, M S; Coovert, M D; Carnevalla, N
1994-05-01
Antecedent variables under the broad categories of genetic, environmental and cultural influences have been linked to the risk for alcohol abuse. Such risk factors have not been shown to result in high correlations with alcohol consumption and leave unclear an understanding of the mechanism by which these variables lead to increased risk. This study employed covariance structure modeling to examine the mediational influence of stored information in memory about alcohol, alcohol expectancies in relation to two biologically and environmentally driven antecedent variables, family history of alcohol abuse and a sensation-seeking temperament in a college population. We also examined the effect of criterion contamination on the relationship between sensation-seeking and alcohol consumption. Results indicated that alcohol expectancy acts as a significant, partial mediator of the relationship between sensation-seeking and consumption, that family history of alcohol abuse is not related to drinking outcome and that overlap in items on sensation-seeking and alcohol consumption measures may falsely inflate their relationship.
Terranova, Nicholas; Serot, Olivier; Archier, Pascal; De Saint Jean, Cyrille; Sumini, Marco
2017-09-01
Fission product yields (FY) are fundamental nuclear data for several applications, including decay heat, shielding, dosimetry, burn-up calculations. To be safe and sustainable, modern and future nuclear systems require accurate knowledge on reactor parameters, with reduced margins of uncertainty. Present nuclear data libraries for FY do not provide consistent and complete uncertainty information which are limited, in many cases, to only variances. In the present work we propose a methodology to evaluate covariance matrices for thermal and fast neutron induced fission yields. The semi-empirical models adopted to evaluate the JEFF-3.1.1 FY library have been used in the Generalized Least Square Method available in CONRAD (COde for Nuclear Reaction Analysis and Data assimilation) to generate covariance matrices for several fissioning systems such as the thermal fission of U235, Pu239 and Pu241 and the fast fission of U238, Pu239 and Pu240. The impact of such covariances on nuclear applications has been estimated using deterministic and Monte Carlo uncertainty propagation techniques. We studied the effects on decay heat and reactivity loss uncertainty estimation for simplified test case geometries, such as PWR and SFR pin-cells. The impact on existing nuclear reactors, such as the Jules Horowitz Reactor under construction at CEA-Cadarache, has also been considered.
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.
On the Origin of Gravitational Lorentz Covariance
Khoury, Justin; Tolley, Andrew J
2013-01-01
We provide evidence that general relativity is the unique spatially covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of general relativity, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector.
COVARIATION BIAS AND THE RETURN OF FEAR
de Jong, Peter; VANDENHOUT, MA; MERCKELBACH, H
1995-01-01
Several studies have indicated that phobic fear is accompanied by a covariation bias, i.e. that phobic Ss tend to overassociate fear relevant stimuli and aversive outcomes. Such a covariation bias seems to be a fairly direct and powerful way to confirm danger expectations and enhance fear. Therefore
Covariant derivative of fermions and all that
Shapiro, Ilya L
2016-01-01
We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. The text represents a part of the initial chapter of a one-semester course on semiclassical gravity.
Superstatistical generalizations of Wishart-Laguerre ensembles of random matrices
Energy Technology Data Exchange (ETDEWEB)
Abul-Magd, A Y [Faculty of Engineering Sciences, Sinai University, El-Arish (Egypt); Akemann, G [Department of Mathematical Sciences and BURSt Research Centre, Brunel University West London, UB8 3PH Uxbridge (United Kingdom); Vivo, P [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste (Italy)
2009-05-01
Using Beck and Cohen's superstatistics, we introduce in a systematic way a family of generalized Wishart-Laguerre ensembles of random matrices with Dyson index {beta} = 1, 2 and 4. The entries of the data matrix are Gaussian random variables whose variances {eta} fluctuate from one sample to another according to a certain probability density f({eta}) and a single deformation parameter {gamma}. Three superstatistical classes for f({eta}) are usually considered: {chi}{sup 2}-, inverse {chi}{sup 2}- and log-normal distributions. While the first class, already considered by two of the authors, leads to a power-law decay of the spectral density, we here introduce and solve exactly a superposition of Wishart-Laguerre ensembles with inverse {chi}{sup 2}-distribution. The corresponding macroscopic spectral density is given by a {gamma}-deformation of the semi-circle and Marcenko-Pastur laws, on a non-compact support with exponential tails. After discussing in detail the validity of Wigner's surmise in the Wishart-Laguerre class, we introduce a generalized {gamma}-dependent surmise with stretched-exponential tails, which well approximates the individual level spacing distribution in the bulk. The analytical results are in excellent agreement with numerical simulations. To illustrate our findings we compare the {chi}{sup 2}- and inverse {chi}{sup 2}-classes to empirical data from financial covariance matrices.
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.
Searching for partial Hadamard matrices
Álvarez, Víctor; Frau, María-Dolores; Gudiel, Félix; Güemes, María-Belén; Martín, Elena; Osuna, Amparo
2012-01-01
Three algorithms looking for pretty large partial Hadamard matrices are described. Here "large" means that hopefully about a third of a Hadamard matrix (which is the best asymptotic result known so far, [dLa00]) is achieved. The first one performs some kind of local exhaustive search, and consequently is expensive from the time consuming point of view. The second one comes from the adaptation of the best genetic algorithm known so far searching for cliques in a graph, due to Singh and Gupta [SG06]. The last one consists in another heuristic search, which prioritizes the required processing time better than the final size of the partial Hadamard matrix to be obtained. In all cases, the key idea is characterizing the adjacency properties of vertices in a particular subgraph G_t of Ito's Hadamard Graph Delta (4t) [Ito85], since cliques of order m in G_t can be seen as (m+3)*4t partial Hadamard matrices.
A concise guide to complex Hadamard matrices
Tadej, W; Tadej, Wojciech; Zyczkowski, Karol
2005-01-01
Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for dimension N=2,...,16. In particular, we explicitly write down some families of complex Hadamard matrices for N=12,14 and 16, which we could not find in the existing literature.
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.
Xie, Yong; Liu, Pan; Cai, Guo-Ping
2016-08-01
In this paper, the on-orbit identification of modal parameters for a spacecraft is investigated. Firstly, the coupled dynamic equation of the system is established with the Lagrange method and the stochastic state-space model of the system is obtained. Then, the covariance-driven stochastic subspace identification (SSI-COV) algorithm is adopted to identify the modal parameters of the system. In this algorithm, it just needs the covariance of output data of the system under ambient excitation to construct a Toeplitz matrix, thus the system matrices are obtained by the singular value decomposition on the Toeplitz matrix and the modal parameters of the system can be found from the system matrices. Finally, numerical simulations are carried out to demonstrate the validity of the SSI-COV algorithm. Simulation results indicate that the SSI-COV algorithm is effective in identifying the modal parameters of the spacecraft only using the output data of the system under ambient excitation.
Lambda-matrices and vibrating systems
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
Matrices with totally positive powers and their generalizations
Kushel, Olga Y.
2013-01-01
In this paper, eventually totally positive matrices (i.e. matrices all whose powers starting with some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of eventually positive matrices. We mainly focus on the spectral properties of such matrices. We also study eventually J-sign-symmetric matrices and matrices, whose powers are P-matrices.
A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES
Institute of Scientific and Technical Information of China (English)
Qi-Ming HE; Eldon GUNN
2003-01-01
In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2×2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3×3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical methods for computing stochastic root matrices of stochastic matrices.
FINITE RIODAN MATRIX AND RIODAN GROUP
Institute of Scientific and Technical Information of China (English)
2000-01-01
Riodan Matrix is a lower triangular matrix of in finite order with certainly restricted conditions.In this paper,the author defines two kinds of finite Riodan matrices which are not limited to lower triangular.Properties of group theory of the two kinds matrices are considered.Applications of the finite Riodan matrices are researched.
Institute of Scientific and Technical Information of China (English)
YANG Lizhen; CHEN Kefei
2004-01-01
In this paper, we analyze the structure of the orders of matrices (mod n), and present the relation between the orders of matrices over finite fields and their Jordan normal forms. Then we generalize 2-dimensional Arnold transformation matrix to two types of n-dimensional Arnold transformation matrices: A-type Arnold transformation matrix and B-type transformation matrix, and analyze their orders and other properties based on our earlier results about the orders of matrices.
The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices.
Wang, Dafei; Zhang, Xumei
2017-01-01
The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequality theory, the new and more accurate estimations for the lower bounds for the rank are deduced. Furthermore, based on the estimation for the rank, some sufficient conditions for nonsingular matrices are obtained.
Dow, M M; Cheverud, J M
1985-11-01
Questions concerning the relative effects of various evolutionary forces in molding the genetic variability exhibited by groups of human populations have typically been investigated by comparing a variety of genetic and cultural/historical "distance" matrices. A major methodological difficulty has been the lack of formal testing procedures with which to assess the degree of confirmation or disconfirmation of an estimated measure of relationship between such matrices. In this paper, we examine a very flexible matrix combinatorial procedure which generates statistical significance levels for correlational measures of pattern similarity between distance matrices. A recent generalization of the basic procedure to the three-matrix case allows questions concerning which of two matrices best fits a third matrix to be formally tested. Applications of these hypothesis testing and inference procedures to two separate sets of genetic, geographic, and cultural distance matrices illustrates their potential for finally solving a long-standing problem in anthropological genetics.
Some families of density matrices for which separability is easily tested
Braunstein, S L; Mansour, T; Severini, S; Wilson, R C; Braunstein, Samuel L.; Ghosh, Sibasish; Mansour, Toufik; Severini, Simone; Wilson, Richard C.
2005-01-01
We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree condition") to test separability of density matrices of graphs. The condition is directly related to the PPT-criterion. We prove that the degree condition is necessary for separability and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest point graphs and perfect matchings. We observe that the degree condition appears to have value beyond density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. The paper isolates a number of problems and delineates further generalizations.
Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
Levin, A; Smirnov, A; Zotov, A
2012-01-01
We discuss quantum dynamical elliptic R-matrices related to arbitrary complex simple Lie group G. They generalize the known vertex and dynamical R-matrices and play an intermediate role between these two types. The R-matrices are defined by the corresponding characteristic classes describing the underlying vector bundles. The latter are related to elements of the center Z(G) of G. While the known dynamical R-matrices are related to the bundles with trivial characteristic classes, the Baxter-Belavin-Drinfeld-Sklyanin vertex R-matrix corresponds to the generator of the center Z_N of SL(N). We construct the R-matrices related to SL(N)- bundles with an arbitrary characteristic class explicitly and discuss the corresponding IRF models.
The covariate-adjusted frequency plot.
Holling, Heinz; Böhning, Walailuck; Böhning, Dankmar; Formann, Anton K
2016-04-01
Count data arise in numerous fields of interest. Analysis of these data frequently require distributional assumptions. Although the graphical display of a fitted model is straightforward in the univariate scenario, this becomes more complex if covariate information needs to be included into the model. Stratification is one way to proceed, but has its limitations if the covariate has many levels or the number of covariates is large. The article suggests a marginal method which works even in the case that all possible covariate combinations are different (i.e. no covariate combination occurs more than once). For each covariate combination the fitted model value is computed and then summed over the entire data set. The technique is quite general and works with all count distributional models as well as with all forms of covariate modelling. The article provides illustrations of the method for various situations and also shows that the proposed estimator as well as the empirical count frequency are consistent with respect to the same parameter.
A note on "Block H-matrices and spectrum of block matrices"
Institute of Scientific and Technical Information of China (English)
LIU Jian-zhou; HUANG Ze-jun
2008-01-01
In this paper, we make further discussions and improvements on the results presented in the previously published work "Block H-matrices and spectrum of block matrices". Furthermore, a new bound for eigenvalues of block matrices is given with examples to show advantages of the new result.
A partial classification of primes in the positive matrices and in the doubly stochastic matrices
G. Picci; J.M. van den Hof; J.H. van Schuppen (Jan)
1995-01-01
textabstractThe algebraic structure of the set of square positive matrices is that of a semi-ring. The concept of a prime in the positive matrices has been introduced. A few examples of primes in the positive matrices are known but there is no general classification. In this paper a partial
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
Dynamical invariance for random matrices
Unterberger, Jeremie
2016-01-01
We consider a general Langevin dynamics for the one-dimensional N-particle Coulomb gas with confining potential $V$ at temperature $\\beta$. These dynamics describe for $\\beta=2$ the time evolution of the eigenvalues of $N\\times N$ random Hermitian matrices. The equilibrium partition function -- equal to the normalization constant of the Laughlin wave function in fractional quantum Hall effect -- is known to satisfy an infinite number of constraints called Virasoro or loop constraints. We introduce here a dynamical generating function on the space of random trajectories which satisfies a large class of constraints of geometric origin. We focus in this article on a subclass induced by the invariance under the Schr\\"odinger-Virasoro algebra.
A review of inversion techniques related to the use of relationship matrices in animal breeding
Directory of Open Access Journals (Sweden)
Faux, P.
2014-01-01
Full Text Available Synthèse bibliographique des techniques d'inversion impliquées dans l'utilisation de matrices de parenté en amélioration animale. En amélioration animale, les effets génétiques sont habituellement prédits par l'utilisation de modèles mixtes. Pour n'importe quel effet génétique, les modèles mixtes nécessitent l'inversion de la matrice de covariance associée à cet effet. Cette matrice est égale à la matrice de parenté associée, multipliée par le composant de la variance génétique également associé à cet effet. Etant donné la taille de nombreux systèmes d'évaluations génétiques, établir l'inverse de ces matrices de parenté peut s'avérer couteux d'un point de vue computationnel. Dans cette synthèse bibliographique, notre objectif est de passer en revue les techniques qui facilitent l'inversion de matrices de parenté utilisée en amélioration animale pour la prédiction des types d'effets génétiques suivants : effet additif, effet gamétique, effet dû à la présence de loci marqués de caractères quantitatifs, effet de dominance et différent effet d'épistasie. Les règles de construction de la matrice et les algorithmes d'inversion sont détaillés pour chaque matrice de parenté. Dans la discussion finale, nous esquissons un cadre théorique commun à la plupart des techniques d'inversion passées en revue. Deux contraintes computationnelles ressortent de ce cadre théorique : l'établissement de la matrice de dépendances entre niveaux de l'effet et celui de certaines parties (diagonales ou bloc-diagonales de la matrice de parenté à inverser.
Estimation of Low-Rank Covariance Function
Koltchinskii, Vladimir; Lounici, Karim; Tsybakov, Alexander B.
2015-01-01
We consider the problem of estimating a low rank covariance function $K(t,u)$ of a Gaussian process $S(t), t\\in [0,1]$ based on $n$ i.i.d. copies of $S$ observed in a white noise. We suggest a new estimation procedure adapting simultaneously to the low rank structure and the smoothness of the covariance function. The new procedure is based on nuclear norm penalization and exhibits superior performances as compared to the sample covariance function by a polynomial factor in the sample size $n$...
Tensor Products of Random Unitary Matrices
Tkocz, Tomasz; Kus, Marek; Zeitouni, Ofer; Zyczkowski, Karol
2012-01-01
Tensor products of M random unitary matrices of size N from the circular unitary ensemble are investigated. We show that the spectral statistics of the tensor product of random matrices becomes Poissonian if M=2, N become large or M become large and N=2.
Products of Generalized Stochastic Sarymsakov Matrices
Xia, Weiguo; Liu, Ji; Cao, Ming; Johansson, Karl; Basar, Tamer
2015-01-01
In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of stochastic Sarymsakov matrices is the largest known subset (i) that is closed under matrix multiplication and (ii) the inﬁnitely long left-product of the elements from a compact subset converges to a rank-one matrix. In
Calculation of Covariance Matrix for Multi-mode Gaussian States in Decoherence Processes
Institute of Scientific and Technical Information of China (English)
XIANG Shao-Hua; SHAO Bin; SONG Ke-Hui
2009-01-01
We investigate the dynamics of n single-mode continuous variable systems in a generic Gaussian state under the influence of the independent and correlated noises making use of the characteristic function method.In two models the bath is assumed to be a squeezed thermal one.We derive an explicit input-output expression between the initial and final covariance matrices.As an example,we study the evolution of entanglement of three-mode Gaussian state embedded in two noisy models.
A Fast Algorithm for the Computation of HAC Covariance Matrix Estimators
Directory of Open Access Journals (Sweden)
Jochen Heberle
2017-01-01
Full Text Available This paper considers the algorithmic implementation of the heteroskedasticity and autocorrelation consistent (HAC estimation problem for covariance matrices of parameter estimators. We introduce a new algorithm, mainly based on the fast Fourier transform, and show via computer simulation that our algorithm is up to 20 times faster than well-established alternative algorithms. The cumulative effect is substantial if the HAC estimation problem has to be solved repeatedly. Moreover, the bandwidth parameter has no impact on this performance. We provide a general description of the new algorithm as well as code for a reference implementation in R.
Ponçot, Angélique; Bouriquet, Bertrand; Erhard, Patrick; Gratton, Serge; Thual, Olivier
2013-01-01
Data assimilation method consists in combining all available pieces of information about a system to obtain optimal estimates of initial states. The different sources of information are weighted according to their accuracy by the means of error covariance matrices. Our purpose here is to evaluate the efficiency of variational data assimilation for the xenon induced oscillations forecasts in nuclear cores. In this paper we focus on the comparison between 3DVAR schemes with optimised background error covariance matrix B and a 4DVAR scheme. Tests were made in twin experiments using a simulation code which implements a mono-dimensional coupled model of xenon dynamics, thermal, and thermal-hydraulic processes. We enlighten the very good efficiency of the 4DVAR scheme as well as good results with the 3DVAR one using a careful multivariate modelling of B.
On the Kalman Filter error covariance collapse into the unstable subspace
Trevisan, A.; Palatella, L.
2011-03-01
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.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Micho Đurđevich; Stephen Bruce Sontz
2011-01-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space $E$, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators amo...
Generalized graph states based on Hadamard matrices
Energy Technology Data Exchange (ETDEWEB)
Cui, Shawn X. [Department of Mathematics, University of California, Santa Barbara, California 93106 (United States); Yu, Nengkun [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China); Zeng, Bei [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8 (Canada)
2015-07-15
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a stabilizer group or an encoding circuit, both can be directly given by the graph. To generalize graph states, whose stabilizer groups are abelian subgroups of the Pauli group, one approach taken is to study non-abelian stabilizers. In this work, we propose to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix. We study the entanglement structures of these generalized graph states and show that they are all maximally mixed locally. We also explore the relationship between the equivalence of Hadamard matrices and local equivalence of the corresponding generalized graph states. This leads to a natural generalization of the Pauli (X, Z) pairs, which characterizes the local symmetries of these generalized graph states. Our approach is also naturally generalized to construct graph quantum codes which are beyond stabilizer codes.
Covariant Quantization with Extended BRST Symmetry
Geyer, B; Lavrov, P M
1999-01-01
A short rewiev of covariant quantization methods based on BRST-antiBRST symmetry is given. In particular problems of correct definition of Sp(2) symmetric quantization scheme known as triplectic quantization are considered.
Conformally covariant parametrizations for relativistic initial data
Delay, Erwann
2017-01-01
We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems. This type of parametrization is certainly more natural for non constant mean curvature initial data.
Information content of weak lensing bispectrum: including the non-Gaussian error covariance matrix
Kayo, Issha; Jain, Bhuvnesh
2013-01-01
We address a long-standing problem, how can we extract information in the non-Gaussian regime of weak lensing surveys, by accurate modeling of all relevant covariances between the power spectra and bispectra. We use 1000 ray-tracing simulation realizations for a Lambda-CDM model and an analytical halo model. We develop a formalism to describe the covariance matrices of power spectra and bispectra of all triangle configurations, which extend to 6-point correlation functions. We include a new contribution arising from coupling of the lensing Fourier modes with large-scale mass fluctuations on scales comparable with the survey region via halo bias theory, which we call the halo sample variance (HSV) effect. We show that the model predictions are in excellent agreement with the simulation results for the power spectrum and bispectrum covariances. The HSV effect gives a dominant contribution to the covariances at multipoles l > 10^3, which arise from massive halos with masses of about 10^14 solar masses and at rel...
Quantifying lost information due to covariance matrix estimation in parameter inference
Sellentin, Elena; Heavens, Alan F.
2017-02-01
Parameter inference with an estimated covariance matrix systematically loses information due to the remaining uncertainty of the covariance matrix. Here, we quantify this loss of precision and develop a framework to hypothetically restore it, which allows to judge how far away a given analysis is from the ideal case of a known covariance matrix. We point out that it is insufficient to estimate this loss by debiasing the Fisher matrix as previously done, due to a fundamental inequality that describes how biases arise in non-linear functions. We therefore develop direct estimators for parameter credibility contours and the figure of merit, finding that significantly fewer simulations than previously thought are sufficient to reach satisfactory precisions. We apply our results to DES Science Verification weak lensing data, detecting a 10 per cent loss of information that increases their credibility contours. No significant loss of information is found for KiDS. For a Euclid-like survey, with about 10 nuisance parameters we find that 2900 simulations are sufficient to limit the systematically lost information to 1 per cent, with an additional uncertainty of about 2 per cent. Without any nuisance parameters, 1900 simulations are sufficient to only lose 1 per cent of information. We further derive estimators for all quantities needed for forecasting with estimated covariance matrices. Our formalism allows to determine the sweetspot between running sophisticated simulations to reduce the number of nuisance parameters, and running as many fast simulations as possible.
Lee, Wonyul; Liu, Yufeng
2012-10-01
Multivariate regression is a common statistical tool for practical problems. Many multivariate regression techniques are designed for univariate response cases. For problems with multiple response variables available, one common approach is to apply the univariate response regression technique separately on each response variable. Although it is simple and popular, the univariate response approach ignores the joint information among response variables. In this paper, we propose three new methods for utilizing joint information among response variables. All methods are in a penalized likelihood framework with weighted L(1) regularization. The proposed methods provide sparse estimators of conditional inverse co-variance matrix of response vector given explanatory variables as well as sparse estimators of regression parameters. Our first approach is to estimate the regression coefficients with plug-in estimated inverse covariance matrices, and our second approach is to estimate the inverse covariance matrix with plug-in estimated regression parameters. Our third approach is to estimate both simultaneously. Asymptotic properties of these methods are explored. Our numerical examples demonstrate that the proposed methods perform competitively in terms of prediction, variable selection, as well as inverse covariance matrix estimation.
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 action for type IIB supergravity
Sen, Ashoke
2016-07-01
Taking clues from the recent construction of the covariant action for type II and heterotic string field theories, we construct a manifestly Lorentz covariant action for type IIB supergravity, and discuss its gauge fixing maintaining manifest Lorentz invariance. The action contains a (non-gravitating) free 4-form field besides the usual fields of type IIB supergravity. This free field, being completely decoupled from the interacting sector, has no physical consequence.
On the covariance of residual lives
Directory of Open Access Journals (Sweden)
N. Unnikrishnan Nair
2007-10-01
Full Text Available Various properties of residual life such as mean, median, percentiles, variance etc have been discussed in literature on reliability and survival analysis. However a detailed study on covariance between residual lives in a two component system does not seem to have been undertaken. The present paper discusses various properties of product moment and covariance of residual lives. Relationships the product moment has with mean residual life and failure rate are studied and some characterizations are established.
Covariant Hamilton equations for field theory
Energy Technology Data Exchange (ETDEWEB)
Giachetta, Giovanni [Department of Mathematics and Physics, University of Camerino, Camerino (Italy); Mangiarotti, Luigi [Department of Mathematics and Physics, University of Camerino, Camerino (Italy)]. E-mail: mangiaro@camserv.unicam.it; Sardanashvily, Gennadi [Department of Theoretical Physics, Physics Faculty, Moscow State University, Moscow (Russian Federation)]. E-mail: sard@grav.phys.msu.su
1999-09-24
We study the relations between the equations of first-order Lagrangian field theory on fibre bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. If a Lagrangian is hyperregular, these equations are equivalent. A degenerate Lagrangian requires a set of associated Hamiltonian forms in order to exhaust all solutions of the Euler-Lagrange equations. The case of quadratic degenerate Lagrangians is studied in detail. (author)
Economical Phase-Covariant Cloning of Qudits
Buscemi, F; Macchiavello, C; Buscemi, Francesco; Ariano, Giacomo Mauro D'; Macchiavello, Chiara
2004-01-01
We derive the optimal $N\\to M$ phase-covariant quantum cloning for equatorial states in dimension $d$ with $M=kd+N$, $k$ integer. The cloning maps are optimal for both global and single-qudit fidelity. The map is achieved by an ``economical'' cloning machine, which works without ancilla. The connection between optimal phase-covariant cloning and optimal multi-phase estimation is finally established.
Directory of Open Access Journals (Sweden)
Berge Léonie
2016-01-01
Full Text Available As the need for precise handling of nuclear data covariances grows ever stronger, no information about covariances of prompt fission neutron spectra (PFNS are available in the evaluated library JEFF-3.2, although present in ENDF/B-VII.1 and JENDL-4.0 libraries for the main fissile isotopes. The aim of this work is to provide an estimation of covariance matrices related to PFNS, in the frame of some commonly used models for the evaluated files, such as the Maxwellian spectrum, the Watt spectrum, or the Madland-Nix spectrum. The evaluation of PFNS through these models involves an adjustment of model parameters to available experimental data, and the calculation of the spectrum variance-covariance matrix arising from experimental uncertainties. We present the results for thermal neutron induced fission of 235U. The systematic experimental uncertainties are propagated via the marginalization technique available in the CONRAD code. They are of great influence on the final covariance matrix, and therefore, on the spectrum uncertainty band width. In addition to this covariance estimation work, we have also investigated the importance on a reactor calculation of the fission spectrum model choice. A study of the vessel fluence depending on the PFNS model is presented. This is done through the propagation of neutrons emitted from a fission source in a simplified PWR using the TRIPOLI-4® code. This last study includes thermal fission spectra from the FIFRELIN Monte-Carlo code dedicated to the simulation of prompt particles emission during fission.
Berge, Léonie; Litaize, Olivier; Serot, Olivier; Archier, Pascal; De Saint Jean, Cyrille; Pénéliau, Yannick; Regnier, David
2016-02-01
As the need for precise handling of nuclear data covariances grows ever stronger, no information about covariances of prompt fission neutron spectra (PFNS) are available in the evaluated library JEFF-3.2, although present in ENDF/B-VII.1 and JENDL-4.0 libraries for the main fissile isotopes. The aim of this work is to provide an estimation of covariance matrices related to PFNS, in the frame of some commonly used models for the evaluated files, such as the Maxwellian spectrum, the Watt spectrum, or the Madland-Nix spectrum. The evaluation of PFNS through these models involves an adjustment of model parameters to available experimental data, and the calculation of the spectrum variance-covariance matrix arising from experimental uncertainties. We present the results for thermal neutron induced fission of 235U. The systematic experimental uncertainties are propagated via the marginalization technique available in the CONRAD code. They are of great influence on the final covariance matrix, and therefore, on the spectrum uncertainty band width. In addition to this covariance estimation work, we have also investigated the importance on a reactor calculation of the fission spectrum model choice. A study of the vessel fluence depending on the PFNS model is presented. This is done through the propagation of neutrons emitted from a fission source in a simplified PWR using the TRIPOLI-4® code. This last study includes thermal fission spectra from the FIFRELIN Monte-Carlo code dedicated to the simulation of prompt particles emission during fission.
On Decompositions of Matrices over Distributive Lattices
Directory of Open Access Journals (Sweden)
Yizhi Chen
2014-01-01
Full Text Available Let L be a distributive lattice and Mn,q (L(Mn(L, resp. the semigroup (semiring, resp. of n × q (n × n, resp. matrices over L. In this paper, we show that if there is a subdirect embedding from distributive lattice L to the direct product ∏i=1mLi of distributive lattices L1,L2, …,Lm, then there will be a corresponding subdirect embedding from the matrix semigroup Mn,q(L (semiring Mn(L, resp. to semigroup ∏i=1mMn,q(Li (semiring ∏i=1mMn(Li, resp.. Further, it is proved that a matrix over a distributive lattice can be decomposed into the sum of matrices over some of its special subchains. This generalizes and extends the decomposition theorems of matrices over finite distributive lattices, chain semirings, fuzzy semirings, and so forth. Finally, as some applications, we present a method to calculate the indices and periods of the matrices over a distributive lattice and characterize the structures of idempotent and nilpotent matrices over it. We translate the characterizations of idempotent and nilpotent matrices over a distributive lattice into the corresponding ones of the binary Boolean cases, which also generalize the corresponding structures of idempotent and nilpotent matrices over general Boolean algebras, chain semirings, fuzzy semirings, and so forth.
Compressed Adjacency Matrices: Untangling Gene Regulatory Networks.
Dinkla, K; Westenberg, M A; van Wijk, J J
2012-12-01
We present a novel technique-Compressed Adjacency Matrices-for visualizing gene regulatory networks. These directed networks have strong structural characteristics: out-degrees with a scale-free distribution, in-degrees bound by a low maximum, and few and small cycles. Standard visualization techniques, such as node-link diagrams and adjacency matrices, are impeded by these network characteristics. The scale-free distribution of out-degrees causes a high number of intersecting edges in node-link diagrams. Adjacency matrices become space-inefficient due to the low in-degrees and the resulting sparse network. Compressed adjacency matrices, however, exploit these structural characteristics. By cutting open and rearranging an adjacency matrix, we achieve a compact and neatly-arranged visualization. Compressed adjacency matrices allow for easy detection of subnetworks with a specific structure, so-called motifs, which provide important knowledge about gene regulatory networks to domain experts. We summarize motifs commonly referred to in the literature, and relate them to network analysis tasks common to the visualization domain. We show that a user can easily find the important motifs in compressed adjacency matrices, and that this is hard in standard adjacency matrix and node-link diagrams. We also demonstrate that interaction techniques for standard adjacency matrices can be used for our compressed variant. These techniques include rearrangement clustering, highlighting, and filtering.
Typical kernel size and number of sparse random matrices over GF(q) - a statistical physics approach
Alamino, Roberto C.; Saad, David
2008-01-01
Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of $GF(q)$ matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the re...
Directory of Open Access Journals (Sweden)
Marina Arav
2009-01-01
Full Text Available Let H be an m×n real matrix and let Zi be the set of column indices of the zero entries of row i of H. Then the conditions |Zk∩(∪i=1k−1Zi|≤1 for all k (2≤k≤m are called the (row Zero Position Conditions (ZPCs. If H satisfies the ZPC, then H is said to be a (row ZPC matrix. If HT satisfies the ZPC, then H is said to be a column ZPC matrix. The real matrix H is said to have a zero cycle if H has a sequence of at least four zero entries of the form hi1j1,hi1j2,hi2j2,hi2j3,…,hikjk,hikj1 in which the consecutive entries alternatively share the same row or column index (but not both, and the last entry has one common index with the first entry. Several connections between the ZPC and the nonexistence of zero cycles are established. In particular, it is proved that a matrix H has no zero cycle if and only if there are permutation matrices P and Q such that PHQ is a row ZPC matrix and a column ZPC matrix.
Random Matrices and Lyapunov Coefficients Regularity
Gallavotti, Giovanni
2017-02-01
Analyticity and other properties of the largest or smallest Lyapunov exponent of a product of real matrices with a "cone property" are studied as functions of the matrices entries, as long as they vary without destroying the cone property. The result is applied to stability directions, Lyapunov coefficients and Lyapunov exponents of a class of products of random matrices and to dynamical systems. The results are not new and the method is the main point of this work: it is is based on the classical theory of the Mayer series in Statistical Mechanics of rarefied gases.
Statistical properties of random density matrices
Sommers, H J; Sommers, Hans-Juergen; Zyczkowski, Karol
2004-01-01
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of the random density matrices are analyzed: we derive the eigenvalue distribution for the Bures ensemble which is shown to be broader then the quarter--circle distribution characteristic of the Hilbert--Schmidt ensemble. For measures induced by partial tracing over the environment we compute exactly the two-point eigenvalue correlation function.
Statistical properties of random density matrices
Energy Technology Data Exchange (ETDEWEB)
Sommers, Hans-Juergen [Fachbereich Physik, Universitaet Duisburg-Essen, Campus Essen, 45117 Essen (Germany); Zyczkowski, Karol [Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Cracow (Poland)
2004-09-03
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of the random density matrices are analysed: we derive the eigenvalue distribution for the Bures ensemble which is shown to be broader then the quarter-circle distribution characteristic of the Hilbert-Schmidt ensemble. For measures induced by partial tracing over the environment we compute exactly the two-point eigenvalue correlation function.
Direct dialling of Haar random unitary matrices
Russell, Nicholas J.; Chakhmakhchyan, Levon; O’Brien, Jeremy L.; Laing, Anthony
2017-03-01
Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly implement Haar random unitary matrices in optical circuits, with no requirement for prior or explicit matrix calculations. Our physically motivated and compact representation directly maps independent probability density functions for parameters in Haar random unitary matrices, to optical circuit components. We go on to extend the results to the case of random unitaries for qubits.
A method for generating realistic correlation matrices
Garcia, Stephan Ramon
2011-01-01
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating normal data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating normal data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Finally, using our results with an existing clustering algorithm, we show that simulating correlation matrices can help assess statistical methodology.
The Antitriangular Factorization of Saddle Point Matrices
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.
Problems and Progress in Covariant High Spin Description
Kirchbach, Mariana
2016-01-01
A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant bases such as Lorentz tensors for bosons, Lorentz-tensors with Dirac spinor components for fermions, or, within the basis of the more fundamental Weyl-Van-der-Waerden sl(2,C) spinor-tensors. At the root of the method, which is free from the pathologies suffered by the traditional approaches, are projectors constructed from the Casimir invariants of the spin-Lorentz group, and the group of translations in the Minkowski space time.
Problems and Progress in Covariant High Spin Description
Kirchbach, Mariana; Banda Guzmán, Víctor Miguel
2016-10-01
A universal description of particles with spins j > 1, transforming in (j, 0) ⊕ (0, j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant bases such as Lorentz tensors for bosons, Lorentz-tensors with Dirac spinor components for fermions, or, within the basis of the more fundamental Weyl- Van-der-Waerden sl(2,C) spinor-tensors. At the root of the method, which is free from the pathologies suffered by the traditional approaches, are projectors constructed from the Casimir invariants of the spin-Lorentz group, and the group of translations in the Minkowski space time.
Skuy, Mervyn; Gewer, Anthony; Osrin, Yael; Khunou, David; Fridjhon, Peter; Rushton, J. Philippe
2002-01-01
Studied whether mediated learning experience would improve the scores of African students on Raven's Standard Progressive Matrices. Seventy African and 28 non-African college students in South Africa were given the Raven's Progressive Matrices on 2 occasions, and some subjects were exposed to the mediated learning experience. Both groups improved…
Cross-covariance functions for multivariate geostatistics
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.
Lorentz covariance of loop quantum gravity
Rovelli, Carlo
2010-01-01
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the "projected" spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleuler formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This c...
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 EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES
Institute of Scientific and Technical Information of China (English)
Wen Li; Jian-xin Chen
2006-01-01
In this paper we present some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices, which improves some recent results. The eigenvalue inclusion region is also discussed.
Sufficient Conditions of Nonsingular H-matrices
Institute of Scientific and Technical Information of China (English)
王广彬; 洪振杰; 高中喜
2004-01-01
From the concept of a diagonally dominant matrix, two sufficient conditions of nonsingular H-matrices were obtained in this paper. An example was given to show that these results improve the known results.
Optimizing the Evaluation of Finite Element Matrices
Kirby, Robert C; Logg, Anders; Scott, L Ridgway; 10.1137/040607824
2012-01-01
Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce the cost of building local stiffness matrices for the Laplace operator and for the trilinear form for Navier-Stokes. For the Laplace operator in two space dimensions, we have developed a heuristic graph algorithm that searches for such redundancies and generates code for computing the local stiffness matrices. Up to cubics, we are able to build the stiffness matrix on any triangle in less than one multiply-add pair per entry. Up to sixth degree, we can do it in less than about two. Preliminary low-degree results for Poisson and Navier-Stokes operators in three dimensions are also promising.
Orthogonal Polynomials from Hermitian Matrices II
Odake, Satoru
2016-01-01
This is the second part of the project `unified theory of classical orthogonal polynomials of a discrete variable derived from the eigenvalue problems of hermitian matrices.' In a previous paper, orthogonal polynomials having Jackson integral measures were not included, since such measures cannot be obtained from single infinite dimensional hermitian matrices. Here we show that Jackson integral measures for the polynomials of the big $q$-Jacobi family are the consequence of the recovery of self-adjointness of the unbounded Jacobi matrices governing the difference equations of these polynomials. The recovery of self-adjointness is achieved in an extended $\\ell^2$ Hilbert space on which a direct sum of two unbounded Jacobi matrices acts as a Hamiltonian or a difference Schr\\"odinger operator for an infinite dimensional eigenvalue problem. The polynomial appearing in the upper/lower end of Jackson integral constitutes the eigenvector of each of the two unbounded Jacobi matrix of the direct sum. We also point out...
A Few Applications of Imprecise Matrices
Directory of Open Access Journals (Sweden)
Sahalad Borgoyary
2015-07-01
Full Text Available This article introduces generalized form of extension definition of the Fuzzy set and its complement in the sense of reference function namely in imprecise set and its complement. Discuss Partial presence of element, Membership value of an imprecise number in the normal and subnormal imprecise numbers. Further on the basis of reference function define usual matrix into imprecise form with new notation. And with the help of maximum and minimum operators, obtain some new matrices like reducing imprecise matrices, complement of reducing imprecise matrix etc. Along with discuss some of the classical matrix properties which are hold good in the imprecise matrix also. Further bring out examples of application of the addition of imprecise matrices, subtraction of imprecise matrices etc. in the field of transportation problems.
Balanced random Toeplitz and Hankel Matrices
Basak, Anirban
2010-01-01
Except the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist, share a common property--the number of times each random variable appears in the matrix is (more or less) same across the variables. Thus it seems natural to ask what happens to the spectrum of the Toeplitz and Hankel matrices when each entry is scaled by the square root of the number of times that entry appears in the matrix instead of the uniform scaling by $n^{-1/2}$. We show that the LSD of these balanced matrices exist and derive integral formulae for the moments of the limit distribution. Curiously, it is not clear if these moments define a unique distribution.
Directory of Open Access Journals (Sweden)
Emre DEMIR
2016-10-01
Full Text Available Objective: Markers which are used for classification into two groups, such as patient / healthy, benign/malignant or prediction of optimal cut off value for diagnostic test and evaluating the performance of diagnostic tests is evaluated by Receiver Operating Characteristic (ROC curve in the diagnostic test researches. In classification accuracy research, some variables such as gender and age, commonly is not similar in groups. In these cases, covariates should be considered to estimate in the area under ROC and covariate adjustment for ROC should be performed. This study aims to introduce methods in the literature for the effect of covariate adjustment and to present an application with sample from the health field. Material and Methods: In the study, we introduced methods used in the literatüre for covariate adjustment and prediction of the area under ROC curves as well as an application with data from the field of urology. In this study, 105 PSA (prostate specific antigen measurements were taken in order to examine the covariate effect for the age variable and to assess the diagnostic performance of PSA measurements with regard to pathologic methods. Results: Covariate effect were found statistically significant with 0.733 parameter estimation of the age in ROC curves analysis with PSA data (p<0.001. According to the methods (Non-parametric (empirical, non-parametric (normal, semi-parametric (empirical, parametric (normal that estimates of the area under ROC curves which is obtained without covariate effect were found 0.708, 0.629, 0.709 and 0.628, respectively, by using PSA measurements. Area under the curve that obtained by covariate adjustment were significantly lower as compared to the traditional ROC with estimation 0.580, 0.577, 0.582 and 0.579. Conclusion: Area under the ROC curves should be estimated with adjustment according to the covariates that could affect the markers value of diagnostic tests performed in concert with matching
Accurate covariance estimation of galaxy-galaxy weak lensing: limitations of jackknife covariance
Shirasaki, Masato; Miyatake, Hironao; Takahashi, Ryuichi; Hamana, Takashi; Nishimichi, Takahiro; Murata, Ryoma
2016-01-01
We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations. We populate a real catalog of source galaxies into a light-cone simulation realization, simulate the lensing effect on each galaxy, and then identify lensing halos that are considered to host galaxies or clusters of interest. We use the mock catalog to study the error covariance matrix of galaxy-galaxy weak lensing and find that the super-sample covariance (SSC), which arises from density fluctuations with length scales comparable with or greater than a size of survey area, gives a dominant source of the sample variance. We then compare the full covariance with the jackknife (JK) covariance, the method that estimates the covariance from the resamples of the data itself. We show that, although the JK method gives an unbiased estimator of the covariance in the shot noise or Gaussian regime, it always over-estimates the true covariance in the sample variance regime, because the JK covariance turns out to be a...
Voxel-wise comparisons of the morphology of diffusion tensors across groups of experimental subjects
DEFF Research Database (Denmark)
Bansal, Ravi; Staib, Lawrence H; Plessen, Kerstin J;
2007-01-01
and eigenvectors that create the 3D morphologies of DTs. We present a mathematical framework that permits the direct comparison across groups of mean eigenvalues and eigenvectors of individual DTs. We show that group-mean eigenvalues and eigenvectors are multivariate Gaussian distributed, and we use the Delta...... method to compute their approximate covariance matrices. Our results show that the theoretically computed mean tensor (MT) eigenvectors and eigenvalues match well with their respective true values. Furthermore, a comparison of synthetically generated groups of DTs highlights the limitations of using FA...... neuropsychiatric illnesses. Comparisons of tensor morphology across groups have typically been performed on scalar measures of diffusivity, such as Fractional Anisotropy (FA) rather than directly on the complex 3D morphologies of DTs. Scalar measures, however, are related in nonlinear ways to the eigenvalues...
Boolean Inner product Spaces and Boolean Matrices
Gudder, Stan; Latremoliere, Frederic
2009-01-01
This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and stochastic and unitary Boolean matrices are studied. A dimension theorem for orthonormal bases of a Boolean space is proven. We characterize the invariant stochastic Boolean vectors for a Boolean stochastic matrix and show that they can be used to reduce a unitary m...
Generalized Inverses of Matrices over Rings
Institute of Scientific and Technical Information of China (English)
韩瑞珠; 陈建龙
1992-01-01
Let R be a ring,*be an involutory function of the set of all finite matrices over R. In this pa-per,necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse,(1,4)-inverse,or Morre-Penrose inverse,relative to *.Some results about generalized inverses of matrices over division rings are generalized and improved.
A Euclidean algorithm for integer matrices
DEFF Research Database (Denmark)
Lauritzen, Niels; Thomsen, Jesper Funch
2015-01-01
We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers.......We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers....
Infinite Products of Random Isotropically Distributed Matrices
Il'yn, A S; Zybin, K P
2016-01-01
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
A Wegner estimate for Wigner matrices
Maltsev, Anna
2011-01-01
In the first part of these notes, we review some of the recent developments in the study of the spectral properties of Wigner matrices. In the second part, we present a new proof of a Wegner estimate for the eigenvalues of a large class of Wigner matrices. The Wegner estimate gives an upper bound for the probability to find an eigenvalue in an interval $I$, proportional to the size $|I|$ of the interval.
Matrices related to some Fock space operators
Directory of Open Access Journals (Sweden)
Krzysztof Rudol
2011-01-01
Full Text Available Matrices of operators with respect to frames are sometimes more natural and easier to compute than the ones related to bases. The present work investigates such operators on the Segal-Bargmann space, known also as the Fock space. We consider in particular some properties of matrices related to Toeplitz and Hankel operators. The underlying frame is provided by normalised reproducing kernel functions at some lattice points.
Linear algebra for skew-polynomial matrices
Abramov, Sergei; Bronstein, Manuel
2002-01-01
We describe an algorithm for transforming skew-polynomial matrices over an Ore domain in row-reduced form, and show that this algorithm can be used to perform the standard calculations of linear algebra on such matrices (ranks, kernels, linear dependences, inhomogeneous solving). The main application of our algorithm is to desingularize recurrences and to compute the rational solutions of a large class of linear functional systems. It also turns out to be efficient when applied to ordinary co...
Moment matrices, border bases and radical computation
Mourrain, B.; J. B. Lasserre; Laurent, Monique; Rostalski, P.; Trebuchet, Philippe
2013-01-01
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-denite programming. While the border basis algorithms of [17] are ecient and numerically stable for computing complex roots, algorithms based on moment matrices [12] allow the incorporation of additional polynomials, ...
Infinite Products of Random Isotropically Distributed Matrices
Il'yn, A. S.; Sirota, V. A.; Zybin, K. P.
2017-01-01
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
Energy Technology Data Exchange (ETDEWEB)
McEwan, C.; Ball, M.; Novog, D., E-mail: mcewac2@mcmaster.ca [McMaster Univ., Hamilton, Ontario (Canada)
2013-07-01
Simulation results are of little use if nothing is known about the uncertainty in the results. In order to assess the uncertainty in a set of output parameters due to uncertainty in a set of input parameters, knowledge of the covariance between input parameters is required. Current practice is to apply the covariance between multigroup cross sections at infinite dilution to all cross sections including those at non-infinite dilutions. In this work, the effect of dilution on multigroup cross section covariance is investigated as well as the effect on the covariance between the few group homogenized cross sections produced by lattice code DRAGON. (author)
Covariant Lyapunov vectors for rigid disk systems.
Bosetti, Hadrien; Posch, Harald A
2010-10-05
We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard-disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes parallel to the x-axis of the box. The Oseledec splitting into covariant subspaces of the tangent space is considered by computing the full set of covariant perturbation vectors co-moving with the flow in tangent space. These vectors are shown to be transversal, but generally not orthogonal to each other. Only the angle between covariant vectors associated with immediate adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the probability of this angle to vanish approaches zero. The stable and unstable manifolds are transverse to each other and the system is hyperbolic.
Manifest Covariant Hamiltonian Theory of General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.
Hui, Yi; Law, Siu Seong; Ku, Chiu Jen
2017-02-01
Covariance of the auto/cross-covariance matrix based method is studied for the damage identification of a structure with illustrations on its advantages and limitations. The original method is extended for structures under direct white noise excitations. The auto/cross-covariance function of the measured acceleration and its corresponding derivatives are formulated analytically, and the method is modified in two new strategies to enable successful identification with much fewer sensors. Numerical examples are adopted to illustrate the improved method, and the effects of sampling frequency and sampling duration are discussed. Results show that the covariance of covariance calculated from responses of higher order modes of a structure play an important role to the accurate identification of local damage in a structure.
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)
Spatial implications of covariate adjustment on patterns of risk
DEFF Research Database (Denmark)
Sabel, Clive Eric; Wilson, Jeff Gaines; Kingham, Simon
2007-01-01
Epidemiological studies that examine the relationship between environmental exposures and health often address other determinants of health that may influence the relationship being studied by adjusting for these factors as covariates. While disease surveillance methods routinely control for cova......Epidemiological studies that examine the relationship between environmental exposures and health often address other determinants of health that may influence the relationship being studied by adjusting for these factors as covariates. While disease surveillance methods routinely control......), then for a deprivation index, and finally for both PM10 and deprivation. Spatial patterns of risk, disease clusters and cold and hot spots were generated using a spatial scan statistic and a Getis-Ord Gi* statistic. In all disease groups tested (except the control disease), adjustment for chronic PM10 exposure...... area to a mixed residential/industrial area, possibly introducing new environmental exposures. Researchers should be aware of the potential spatial effects inherent in adjusting for covariates when considering study design and interpreting results. © 2007 Elsevier Ltd. All rights reserved....
Abnormalities in Structural Covariance of Cortical Gyrification in Parkinson's Disease
Xu, Jinping; Zhang, Jiuquan; Zhang, Jinlei; Wang, Yue; Zhang, Yanling; Wang, Jian; Li, Guanglin; Hu, Qingmao; Zhang, Yuanchao
2017-01-01
Although abnormal cortical morphology and connectivity between brain regions (structural covariance) have been reported in Parkinson's disease (PD), the topological organizations of large-scale structural brain networks are still poorly understood. In this study, we investigated large-scale structural brain networks in a sample of 37 PD patients and 34 healthy controls (HC) by assessing the structural covariance of cortical gyrification with local gyrification index (lGI). We demonstrated prominent small-world properties of the structural brain networks for both groups. Compared with the HC group, PD patients showed significantly increased integrated characteristic path length and integrated clustering coefficient, as well as decreased integrated global efficiency in structural brain networks. Distinct distributions of hub regions were identified between the two groups, showing more hub regions in the frontal cortex in PD patients. Moreover, the modular analyses revealed significantly decreased integrated regional efficiency in lateral Fronto-Insula-Temporal module, and increased integrated regional efficiency in Parieto-Temporal module in the PD group as compared to the HC group. In summary, our study demonstrated altered topological properties of structural networks at a global, regional and modular level in PD patients. These findings suggests that the structural networks of PD patients have a suboptimal topological organization, resulting in less effective integration of information between brain regions.
Notes on Cosmic Censorship Conjecture revisited: Covariantly
Hamid, Aymen I M; Maharaj, Sunil D
2016-01-01
In this paper we study the dynamics of the trapped region using a frame independent semi-tetrad covariant formalism for general Locally Rotationally Symmetric (LRS) class II spacetimes. We covariantly prove some important geometrical results for the apparent horizon, and state the necessary and sufficient conditions for a singularity to be locally naked. These conditions bring out, for the first time in a quantitative and transparent manner, the importance of the Weyl curvature in deforming and delaying the trapped region during continual gravitational collapse, making the central singularity locally visible.
A covariant formulation of classical spinning particle
Cho, J H; Kim, J K; Jin-Ho Cho; Seungjoon Hyun; Jae-Kwan Kim
1994-01-01
Covariantly we reformulate the description of a spinning particle in terms of the which entails all possible constraints explicitly; all constraints can be obtained just from the Lagrangian. Furthermore, in this covariant reformulation, the Lorentz element is to be considered to evolve the momentum or spin component from an arbitrary fixed frame and not just from the particle rest frame. In distinction with the usual formulation, our system is directly comparable with the pseudo-classical formulation. We get a peculiar symmetry which resembles the supersymmetry of the pseudo-classical formulation.
A violation of the covariant entropy bound?
Masoumi, Ali
2014-01-01
Several arguments suggest that the entropy density at high energy density $\\rho$ should be given by the expression $s=K\\sqrt{\\rho/G}$, where $K$ is a constant of order unity. On the other hand the covariant entropy bound requires that the entropy on a light sheet be bounded by $A/4G$, where $A$ is the area of the boundary of the sheet. We find that in a suitably chosen cosmological geometry, the above expression for $s$ violates the covariant entropy bound. We consider different possible explanations for this fact; in particular the possibility that entropy bounds should be defined in terms of volumes of regions rather than areas of surfaces.
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
A Brief Historical Introduction to Matrices and Their Applications
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…
A Brief Historical Introduction to Matrices and Their Applications
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…
Representation-independent manipulations with Dirac matrices and spinors
2007-01-01
Dirac matrices, also known as gamma matrices, are defined only up to a similarity transformation. Usually, some explicit representation of these matrices is assumed in order to deal with them. In this article, we show how it is possible to proceed without any such assumption. Various important identities involving Dirac matrices and spinors have been derived without assuming any representation at any stage.
Quantum Racah matrices and 3-strand braids in irreps R with |R|=4
Mironov, A; Morozov, An; Sleptsov, A
2016-01-01
We describe the inclusive Racah matrices for the first non-(anti)symmetric rectangular representation R=[2,2] for quantum groups U_q(sl_N). Most of them have sizes 2, 3, and 4 and are fully described by the eigenvalue hypothesis. Of two 6x6 matrices, one is also described in this way, but the other one corresponds to the case of degenerate eigenvalues and is evaluated by the highest weight method. Together with the much harder calculation for R=[3,1] in arXiv:1605.02313 and with the new method to extract exclusive matrices S and \\bar S from the inclusive ones, this completes the story of Racah matrices for |R|\\leq 4 and allows one to calculate and investigate the corresponding colored HOMFLY polynomials for arbitrary 3-strand and arborescent knots.
Condition number estimation of preconditioned matrices.
Kushida, Noriyuki
2015-01-01
The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.
Condition number estimation of preconditioned matrices.
Directory of Open Access Journals (Sweden)
Noriyuki Kushida
Full Text Available The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.
The Massless Spectrum of Covariant Superstrings
Grassi, P A; van Nieuwenhuizen, P
2002-01-01
We obtain the correct cohomology at any ghost number for the open and closed covariant superstring, quantized by an approach which we recently developed. We define physical states by the usual condition of BRST invariance and a new condition involving a new current which is related to a grading of the underlying affine Lie algebra.
Optimal covariate designs theory and applications
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...
Covariant formulation of pion-nucleon scattering
Lahiff, A. D.; Afnan, I. R.
A covariant model of elastic pion-nucleon scattering based on the Bethe-Salpeter equation is presented. The kernel consists of s- and u-channel nucleon and delta poles, along with rho and sigma exchange in the t-channel. A good fit is obtained to the s- and p-wave phase shifts up to the two-pion production threshold.
Approximate methods for derivation of covariance data
Energy Technology Data Exchange (ETDEWEB)
Tagesen, S. [Vienna Univ. (Austria). Inst. fuer Radiumforschung und Kernphysik; Larson, D.C. [Oak Ridge National Lab., TN (United States)
1992-12-31
Several approaches for the derivation of covariance information for evaluated nuclear data files (EFF2 and ENDF/B-VI) have been developed and used at IRK and ORNL respectively. Considerations, governing the choice of a distinct method depending on the quantity and quality of available data are presented, advantages/disadvantages are discussed and examples of results are given.
Covariance of noncommutative Grassmann star product
Daoud, M.
2004-01-01
Using the Coherent states of many fermionic degrees of freedom labeled by Gra\\ss mann variables, we introduce the noncommutative (precisely non anticommutative) Gra\\ss mann star product. The covariance of star product under unitary transformations, particularly canonical ones, is studied. The super star product, based on supercoherent states of supersymmetric harmonic oscillator, is also considered.
Covariant Photon Quantization in the SME
Colladay, Don
2013-01-01
The Gupta Bleuler quantization procedure is applied to the SME photon sector. A direct application of the method to the massless case fails due to an unavoidable incompleteness in the polarization states. A mass term can be included into the photon lagrangian to rescue the quantization procedure and maintain covariance.
Covariant derivative expansion of the heat kernel
Energy Technology Data Exchange (ETDEWEB)
Salcedo, L.L. [Universidad de Granada, Departamento de Fisica Moderna, Granada (Spain)
2004-11-01
Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four derivatives. The results apply to boundaryless flat space-times and arbitrary non-Abelian scalar and gauge background fields. (orig.)
Gelatin Nanofiber Matrices Derived from Schiff Base Derivative for Tissue Engineering Applications.
Jaiswal, Devina; James, Roshan; Shelke, Namdev B; Harmon, Matthew D; Brown, Justin L; Hussain, Fazle; Kumbar, Sangamesh G
2015-11-01
Electrospinning of water-soluble polymers and retaining their mechanical strength and bioactivity remain challenging. Volatile organic solvent soluble polymers and their derivatives are preferred for fabricating electrospun nanofibers. We report the synthesis and characterization of 2-nitrobenzyl-gelatin (N-Gelatin)--a novel gelatin Schiff base derivative--and the resulting electrospun nanofiber matrices. The 2-nitrobenzyl group is a photoactivatable-caged compound and can be cleaved from the gelatin nanofiber matrices following UV exposure. Such hydrophobic modification allowed the fabrication of gelatin and blend nanofibers with poly(caprolactone) (PCL) having significantly improved tensile properties. Neat gelatin and their PCL blend nanofiber matrices showed a modulus of 9.08 ± 1.5 MPa and 27.61 ± 4.3 MPa, respectively while the modified gelatin and their blends showed 15.63 ± 2.8 MPa and 24.47 ± 8.7 MPa, respectively. The characteristic infrared spectroscopy band for gelatin Schiff base derivative at 1560 cm(-1) disappeared following exposure to UV light indicating the regeneration of free NH2 group and gelatin. These nanofiber matrices supported cell attachment and proliferation with a well spread morphology as evidenced through cell proliferation assay and microscopic techniques. Modified gelatin fiber matrices showed a 73% enhanced cell attachment and proliferation rate compared to pure gelatin. This polymer modification methodology may offer a promising way to fabricate electrospun nanofiber matrices using a variety of proteins and peptides without loss of bioactivity and mechanical strength.
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....
Approximate joint diagonalization and geometric mean of symmetric positive definite matrices.
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
Congedo, Marco; Afsari, Bijan; Barachant, Alexandre; Moakher, Maher
2015-01-01
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. PMID:25919667
Spatially Covariant Theories of a Transverse, Traceless Graviton, Part I: Formalism
Khoury, Justin; Tolley, Andrew J
2011-01-01
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of general covariance. In this paper, we explore modifications of general relativity that retain the same number of gravitational degrees of freedom, and therefore explicitly break general covariance. Motivated by cosmology, the modifications of interest maintain spatial covariance. Demanding consistency of the theory forces the physical Hamiltonian density to obey an analogue of the renormalization group equation. In this context, the equation encodes the invariance of the theory under flow through the space of conformally equivalent spatial metrics. This paper is dedicated to setting up the formalism of our approach and applying it to a realistic class of theories. Forthcoming work will apply the formalism more generally.
Unravelling Lorentz Covariance and the Spacetime Formalism
Directory of Open Access Journals (Sweden)
Cahill R. T.
2008-10-01
Full Text Available We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the space-time construct are consistent with the existence of a dynamical 3-space, and absolute motion. We illustrate this mapping first with the standard theory of sound, as vibrations of a medium, which itself may be undergoing fluid motion, and which is covariant under Galilean coordinate transformations. By introducing a different non-physical class of space and time coordinates it may be cast into a form that is covariant under Lorentz transformations wherein the speed of sound is now the invariant speed. If this latter formalism were taken as fundamental and complete we would be lead to the introduction of a pseudo-Riemannian spacetime description of sound, with a metric characterised by an invariant speed of sound. This analysis is an allegory for the development of 20th century physics, but where the Lorentz covariant Maxwell equations were constructed first, and the Galilean form was later constructed by Hertz, but ignored. It is shown that the Lorentz covariance of the Maxwell equations only occurs because of the use of non-physical space and time coordinates. The use of this class of coordinates has confounded 20th century physics, and resulted in the existence of a allowing dynamical 3-space being overlooked. The discovery of the dynamics of this 3-space has lead to the derivation of an extended gravity theory as a quantum effect, and confirmed by numerous experiments and observations
Unravelling Lorentz Covariance and the Spacetime Formalism
Directory of Open Access Journals (Sweden)
Cahill R. T.
2008-10-01
Full Text Available We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the space- time construct are consistent with the existence of a dynamical 3-space, and “absolute motion”. We illustrate this mapping first with the standard theory of sound, as vibra- tions of a medium, which itself may be undergoing fluid motion, and which is covari- ant under Galilean coordinate transformations. By introducing a different non-physical class of space and time coordinates it may be cast into a form that is covariant under “Lorentz transformations” wherein the speed of sound is now the “invariant speed”. If this latter formalism were taken as fundamental and complete we would be lead to the introduction of a pseudo-Riemannian “spacetime” description of sound, with a metric characterised by an “invariant speed of sound”. This analysis is an allegory for the development of 20th century physics, but where the Lorentz covariant Maxwell equa- tions were constructed first, and the Galilean form was later constructed by Hertz, but ignored. It is shown that the Lorentz covariance of the Maxwell equations only occurs because of the use of non-physical space and time coordinates. The use of this class of coordinates has confounded 20th century physics, and resulted in the existence of a “flowing” dynamical 3-space being overlooked. The discovery of the dynamics of this 3-space has lead to the derivation of an extended gravity theory as a quantum effect, and confirmed by numerous experiments and observations
Error analysis of quadratic power spectrum estimates for CMB polarization: sampling covariance
Challinor, A; Challinor, Anthony; Chon, Gayoung
2004-01-01
Quadratic methods with heuristic weighting (e.g. pseudo-C_l or correlation function methods) represent an efficient way to estimate power spectra of the cosmic microwave background (CMB) anisotropies and their polarization. We construct the sample covariance properties of such estimators for CMB polarization, and develop semi-analytic techniques to approximate the pseudo-C_l sample covariance matrices at high Legendre multipoles, taking account of the geometric effects of mode coupling and the mixing between the electric (E) and magnetic (B) polarization that arise for observations covering only part of the sky. The E-B mixing ultimately limits the applicability of heuristically-weighted quadratic methods to searches for the gravitational-wave signal in the large-angle B-mode polarization, even for methods that can recover (exactly) unbiased estimates of the B-mode power. We show that for surveys covering one or two per cent of the sky, the contribution of E-mode power to the covariance of the recovered B-mod...
Analysis of the covariance structure of digital ridge counts in the offspring of monozygotic twins.
Cantor, R M; Nance, W E; Eaves, L J; Winter, P M; Blanchard, M M
1983-03-01
Improved methods for analysis of covariance structures now permit the rigorous testing of multivariate genetic hypotheses. Using Jöreskog's Lisrel IV computer program we have conducted a confirmatory factor analysis of dermal ridge counts on the individual fingers of 509 offspring of 107 monozygotic twin pairs. Prior to the initiation of the model-fitting procedure, the sex-adjusted ridge counts for the offspring of male and female twins were partitioned by a multivariate nested analysis of variance yielding five 10 X 10 variance-covariance matrices containing a total of 275 distinctly observed parameters with which to estimate latent sources of genetic and environmental variation and test hypotheses about the factor structure of those latent causes. To provide an adequate explanation for the observed patterns of covariation, it was necessary to include additive genetic, random environmental, epistatic and maternal effects in the model and a structure for the additive genetic effects which included a general factor and allowed for hand asymmetry and finger symmetry. The results illustrate the value of these methods for the analysis of interrelated metric traits.
Second central extension in Galilean covariant field theory
Hagen, C R
2002-01-01
The second central extension of the planar Galilei group has been alleged to have its origin in the spin variable. This idea is explored here by considering local Galilean covariant field theory for free fields of arbitrary spin. It is shown that such systems generally display only a trivial realization of the second central extension. While it is possible to realize any desired value of the extension parameter by suitable redefinition of the boost operator, such an approach has no necessary connection to the spin of the basic underlying field.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Durdevich, Micho; Sontz, Stephen Bruce
2013-05-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Directory of Open Access Journals (Sweden)
Micho Đurđevich
2013-05-01
Full Text Available A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
evich, Micho Đurđ
2011-01-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutivity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Bayesian Nonparametric Clustering for Positive Definite Matrices.
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.
Using Elimination Theory to construct Rigid Matrices
Kumar, Abhinav; Patankar, Vijay M; N, Jayalal Sarma M
2009-01-01
The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r=Omega(n). In this paper, we construct an infinite family of complex matrices with the largest possible, i.e., (n-r)^2, rigidity. The entries of an nxn matrix in this family are distinct primitive roots of unity of orders roughly exp(n^4 log n). To the best of our knowledge, this is the first family of concrete (but not entirely explicit) matrices having maximal rigidity and a succinct algebraic description. Our construction is based on elimination...
Improved Rosetta Pedotransfer Estimation of Hydraulic Properties and Their Covariance
Zhang, Y.; Schaap, M. G.
2014-12-01
Quantitative knowledge of the soil hydraulic properties is necessary for most studies involving water flow and solute transport in the vadose zone. However, it is always expensive, difficult, and time consuming to measure hydraulic properties directly. Pedotransfer functions (PTFs) have been widely used to forecast soil hydraulic parameters. Rosetta is is one of many PTFs and based on artificial neural network analysis coupled with the bootstrap sampling method. The model provides hierarchical PTFs for different levels of input data for Rosetta (H1-H5 models, with higher order models requiring more input variables). The original Rosetta model consists of separate PTFs for the four "van Genuchten" (VG) water retention parameters and saturated hydraulic conductivity (Ks) because different numbers of samples were available for these characteristics. In this study, we present an improved Rosetta pedotransfer function that uses a single model for all five parameters combined; these parameters are weighed for each sample individually using the covariance matrix obtained from the curve-fit of the VG parameters to the primary data. The optimal number of hidden nodes, weights for saturated hydraulic conductivity and water retention parameters in the neural network and bootstrap realization were selected. Results show that root mean square error (RMSE) for water retention decreased from 0.076 to 0.072 cm3/cm3 for the H2 model and decreased from 0.044 to 0.039 cm3/cm3 for the H5 model. Mean errors which indicate variable matric potential-dependent bias were also reduced significantly in the new model. The RMSE for Ks increased slightly (H2: 0.717 to 0.722; H5: 0.581 to 0.594); this increase is minimal and a result of using a single model for water retention and Ks. Despite this small increase the new model is recommended because of its improved estimation of water retention, and because it is now possible to calculate the full covariance matrix of soil water retention
Janes, Holly; Pepe, Margaret S
2009-06-01
Recent scientific and technological innovations have produced an abundance of potential markers that are being investigated for their use in disease screening and diagnosis. In evaluating these markers, it is often necessary to account for covariates associated with the marker of interest. Covariates may include subject characteristics, expertise of the test operator, test procedures or aspects of specimen handling. In this paper, we propose the covariate-adjusted receiver operating characteristic curve, a measure of covariate-adjusted classification accuracy. Nonparametric and semiparametric estimators are proposed, asymptotic distribution theory is provided and finite sample performance is investigated. For illustration we characterize the age-adjusted discriminatory accuracy of prostate-specific antigen as a biomarker for prostate cancer.
Geometry of 2×2 hermitian matrices
Institute of Scientific and Technical Information of China (English)
HUANG; Liping(黄礼平); WAN; Zhexian(万哲先)
2002-01-01
Let D be a division ring which possesses an involution a→ā. Assume that F = {a∈D|a=ā} is a proper subfield of D and is contained in the center of D. It is pointed out that if D is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two, D is a separable quadratic extension of F. Thus the trace map Tr: D→F,hermitian matrices over D when n≥3 and now can be deleted. When D is a field, the fundamental theorem of 2×2 hermitian matrices over D has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two.
INERTIA SETS OF SYMMETRIC SIGN PATTERN MATRICES
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A sign pattern matrix is a matrixwhose entries are from the set {+ ,- ,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative fri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.
Generalized Inverse Eigenvalue Problem for Centrohermitian Matrices
Institute of Scientific and Technical Information of China (English)
刘仲云; 谭艳祥; 田兆录
2004-01-01
In this paper we first consider the existence and the general form of solution to the following generalized inverse eigenvalue problem(GIEP) : given a set of n-dimension complex vectors { xj }jm = 1 and a set of complex numbers { λj} jm = 1, find two n × n centrohermitian matrices A, B such that { xj }jm = 1 and { λj }jm= 1 are the generalized eigenvectors and generalized eigenvalues of Ax = λBx, respectively. We then discuss the optimal approximation problem for the GIEP. More concretely, given two arbitrary matrices, A-, B- ∈Cn×n , we find two matrices A* and B* such that the matrix (A* ,B* ) is closest to (A- ,B-) in the Frobenius norm, where the matrix (A*, B* ) is the solution to the GIEP. We show that the expression of the solution of the optimal approximation is unique and derive the expression for it.
PRM: A database of planetary reflection matrices
Stam, D. M.; Batista, S. F. A.
2014-04-01
We present the PRM database with reflection matrices of various types of planets. With the matrices, users can calculate the total, and the linearly and circularly polarized fluxes of incident unpolarized light that is reflected by a planet for arbitrary illumination and viewing geometries. To allow for flexibility in these geometries, the database does not contain the elements of reflection matrices, but the coefficients of their Fourier series expansion. We describe how to sum these coefficients for given illumination and viewing geometries to obtain the local reflection matrix. The coefficients in the database can also be used to calculate flux and polarization signals of exoplanets, by integrating, for a given planetary phase angle, locally reflected fluxes across the visible part of the planetary disk. Algorithms for evaluating the summation for locally reflected fluxes, as applicable to spatially resolved observations of planets, and the subsequent integration for the disk-integrated fluxes, as applicable to spatially unresolved exoplanets are also in the database