Universality for 1d Random Band Matrices: Sigma-Model Approximation

NASA Astrophysics Data System (ADS)

Shcherbina, Mariya; Shcherbina, Tatyana

2018-02-01

The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233-1260, 2016; Commun Math Phys 351:1009-1044, 2017). We consider random Hermitian block band matrices consisting of W× W random Gaussian blocks (parametrized by j,k \\in Λ =[1,n]^d\\cap Z^d ) with a fixed entry's variance J_{jk}=δ _{j,k}W^{-1}+β Δ _{j,k}W^{-2} , β >0 in each block. Taking the limit W→ ∞ with fixed n and β , we derive the sigma-model approximation of the second correlation function similar to Efetov's one. Then, considering the limit β , n→ ∞, we prove that in the dimension d=1 the behaviour of the sigma-model approximation in the bulk of the spectrum, as β ≫ n , is determined by the classical Wigner-Dyson statistics.

A Geometrical Framework for Covariance Matrices of Continuous and Categorical Variables

ERIC Educational Resources Information Center

Vernizzi, Graziano; Nakai, Miki

2015-01-01

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

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

PubMed

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.

Crossover ensembles of random matrices and skew-orthogonal polynomials

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

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

2011-08-15

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

Accuracy of the Parallel Analysis Procedure with Polychoric Correlations

ERIC Educational Resources Information Center

Cho, Sun-Joo; Li, Feiming; Bandalos, Deborah

2009-01-01

The purpose of this study was to investigate the application of the parallel analysis (PA) method for choosing the number of factors in component analysis for situations in which data are dichotomous or ordinal. Although polychoric correlations are sometimes used as input for component analyses, the random data matrices generated for use in PA…

A time-series approach to dynamical systems from classical and quantum worlds

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

Fossion, Ruben

2014-01-08

This contribution discusses some recent applications of time-series analysis in Random Matrix Theory (RMT), and applications of RMT in the statistial analysis of eigenspectra of correlation matrices of multivariate time series.

Virial expansion for almost diagonal random matrices

NASA Astrophysics Data System (ADS)

Yevtushenko, Oleg; Kravtsov, Vladimir E.

2003-08-01

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

The q-dependent detrended cross-correlation analysis of stock market

NASA Astrophysics Data System (ADS)

Zhao, Longfeng; Li, Wei; Fenu, Andrea; Podobnik, Boris; Wang, Yougui; Stanley, H. Eugene

2018-02-01

Properties of the q-dependent cross-correlation matrices of the stock market have been analyzed by using random matrix theory and complex networks. The correlation structures of the fluctuations at different magnitudes have unique properties. The cross-correlations among small fluctuations are much stronger than those among large fluctuations. The large and small fluctuations are dominated by different groups of stocks. We use complex network representation to study these q-dependent matrices and discover some new identities. By utilizing those q-dependent correlation-based networks, we are able to construct some portfolios of those more independent stocks which consistently perform better. The optimal multifractal order for portfolio optimization is around q  =  2 under the mean-variance portfolio framework, and q\\in[2, 6] under the expected shortfall criterion. These results have deepened our understanding regarding the collective behavior of the complex financial system.

CMV matrices in random matrix theory and integrable systems: a survey

NASA Astrophysics Data System (ADS)

Nenciu, Irina

2006-07-01

We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we also emphasize the analogies and connections to Jacobi matrices.

Spectral analysis of finite-time correlation matrices near equilibrium phase transitions

NASA Astrophysics Data System (ADS)

Vinayak; Prosen, T.; Buča, B.; Seligman, T. H.

2014-10-01

We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be derived from the spatial correlations. In practice time series are short in the sense that they are either not stationary over long time intervals or not available over long time intervals. Also we usually do not have time series for all variables available. We shall make numerical simulations on a two-dimensional Ising model with the usual Metropolis algorithm as time evolution. Using all spins on a grid with periodic boundary conditions we find a power law, that is, for large grids, compatible with the analytic result. We still find a power law even if we choose a fairly small subset of grid points at random. The exponents of the power laws will be smaller under such circumstances. For very short time series leading to singular correlation matrices we use a recently developed technique to lift the degeneracy at zero in the spectrum and find a significant signature of critical behavior even in this case as compared to high temperature results which tend to those of random matrix models.

On Fluctuations of Eigenvalues of Random Band Matrices

NASA Astrophysics Data System (ADS)

Shcherbina, M.

2015-10-01

We consider the fluctuations of linear eigenvalue statistics of random band matrices whose entries have the form with i.i.d. possessing the th moment, where the function u has a finite support , so that M has only nonzero diagonals. The parameter b (called the bandwidth) is assumed to grow with n in a way such that . Without any additional assumptions on the growth of b we prove CLT for linear eigenvalue statistics for a rather wide class of test functions. Thus we improve and generalize the results of the previous papers (Jana et al., arXiv:1412.2445; Li et al. Random Matrices 2:04, 2013), where CLT was proven under the assumption . Moreover, we develop a method which allows to prove automatically the CLT for linear eigenvalue statistics of the smooth test functions for almost all classical models of random matrix theory: deformed Wigner and sample covariance matrices, sparse matrices, diluted random matrices, matrices with heavy tales etc.

Comparability of item quality indices from sparse data matrices with random and non-random missing data patterns.

PubMed

Wolfe, Edward W; McGill, Michael T

2011-01-01

This article summarizes a simulation study of the performance of five item quality indicators (the weighted and unweighted versions of the mean square and standardized mean square fit indices and the point-measure correlation) under conditions of relatively high and low amounts of missing data under both random and conditional patterns of missing data for testing contexts such as those encountered in operational administrations of a computerized adaptive certification or licensure examination. The results suggest that weighted fit indices, particularly the standardized mean square index, and the point-measure correlation provide the most consistent information between random and conditional missing data patterns and that these indices perform more comparably for items near the passing score than for items with extreme difficulty values.

Novel image compression-encryption hybrid algorithm based on key-controlled measurement matrix in compressive sensing

NASA Astrophysics Data System (ADS)

Zhou, Nanrun; Zhang, Aidi; Zheng, Fen; Gong, Lihua

2014-10-01

The existing ways to encrypt images based on compressive sensing usually treat the whole measurement matrix as the key, which renders the key too large to distribute and memorize or store. To solve this problem, a new image compression-encryption hybrid algorithm is proposed to realize compression and encryption simultaneously, where the key is easily distributed, stored or memorized. The input image is divided into 4 blocks to compress and encrypt, then the pixels of the two adjacent blocks are exchanged randomly by random matrices. The measurement matrices in compressive sensing are constructed by utilizing the circulant matrices and controlling the original row vectors of the circulant matrices with logistic map. And the random matrices used in random pixel exchanging are bound with the measurement matrices. Simulation results verify the effectiveness, security of the proposed algorithm and the acceptable compression performance.

Localization in covariance matrices of coupled heterogenous Ornstein-Uhlenbeck processes

NASA Astrophysics Data System (ADS)

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.

Spectral density of mixtures of random density matrices for qubits

NASA Astrophysics Data System (ADS)

Zhang, Lin; Wang, Jiamei; Chen, Zhihua

2018-06-01

We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral densities to calculate the average entropy of mixtures of random density matrices, and show that the average entropy of the arithmetic-mean-state of n qubit density matrices randomly chosen from the Hilbert-Schmidt ensemble is never decreasing with the number n. We also get the exact value of the average squared fidelity. Some conjectures and open problems related to von Neumann entropy are also proposed.

Effects of imputation on correlation: implications for analysis of mass spectrometry data from multiple biological matrices.

PubMed

Taylor, Sandra L; Ruhaak, L Renee; Kelly, Karen; Weiss, Robert H; Kim, Kyoungmi

2017-03-01

With expanded access to, and decreased costs of, mass spectrometry, investigators are collecting and analyzing multiple biological matrices from the same subject such as serum, plasma, tissue and urine to enhance biomarker discoveries, understanding of disease processes and identification of therapeutic targets. Commonly, each biological matrix is analyzed separately, but multivariate methods such as MANOVAs that combine information from multiple biological matrices are potentially more powerful. However, mass spectrometric data typically contain large amounts of missing values, and imputation is often used to create complete data sets for analysis. The effects of imputation on multiple biological matrix analyses have not been studied. We investigated the effects of seven imputation methods (half minimum substitution, mean substitution, k-nearest neighbors, local least squares regression, Bayesian principal components analysis, singular value decomposition and random forest), on the within-subject correlation of compounds between biological matrices and its consequences on MANOVA results. Through analysis of three real omics data sets and simulation studies, we found the amount of missing data and imputation method to substantially change the between-matrix correlation structure. The magnitude of the correlations was generally reduced in imputed data sets, and this effect increased with the amount of missing data. Significant results from MANOVA testing also were substantially affected. In particular, the number of false positives increased with the level of missing data for all imputation methods. No one imputation method was universally the best, but the simple substitution methods (Half Minimum and Mean) consistently performed poorly. © The Author 2016. Published by Oxford University Press. For Permissions, please email: journals.permissions@oup.com.

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

PubMed Central

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

2013-01-01

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

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

PubMed

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

2018-02-27

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

Products of random matrices from fixed trace and induced Ginibre ensembles

NASA Astrophysics Data System (ADS)

Akemann, Gernot; Cikovic, Milan

2018-05-01

We investigate the microcanonical version of the complex induced Ginibre ensemble, by introducing a fixed trace constraint for its second moment. Like for the canonical Ginibre ensemble, its complex eigenvalues can be interpreted as a two-dimensional Coulomb gas, which are now subject to a constraint and a modified, collective confining potential. Despite the lack of determinantal structure in this fixed trace ensemble, we compute all its density correlation functions at finite matrix size and compare to a fixed trace ensemble of normal matrices, representing a different Coulomb gas. Our main tool of investigation is the Laplace transform, that maps back the fixed trace to the induced Ginibre ensemble. Products of random matrices have been used to study the Lyapunov and stability exponents for chaotic dynamical systems, where the latter are based on the complex eigenvalues of the product matrix. Because little is known about the universality of the eigenvalue distribution of such product matrices, we then study the product of m induced Ginibre matrices with a fixed trace constraint—which are clearly non-Gaussian—and M  ‑  m such Ginibre matrices without constraint. Using an m-fold inverse Laplace transform, we obtain a concise result for the spectral density of such a mixed product matrix at finite matrix size, for arbitrary fixed m and M. Very recently local and global universality was proven by the authors and their coworker for a more general, single elliptic fixed trace ensemble in the bulk of the spectrum. Here, we argue that the spectral density of mixed products is in the same universality class as the product of M independent induced Ginibre ensembles.

Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices

NASA Astrophysics Data System (ADS)

Passemier, Damien; McKay, Matthew R.; Chen, Yang

2015-07-01

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked correlation), non-central Wishart with rank-one non-centrality, and a related class of non-central matrices. For a generic linear statistic, we derive simple and explicit CLT expressions as the matrix dimensions grow large. For all three ensembles under consideration, we find that the primary effect of the spike is to introduce an correction term to the asymptotic mean of the linear spectral statistic, which we characterize with simple formulas. The utility of our proposed framework is demonstrated through application to three different linear statistics problems: the classical likelihood ratio test for a population covariance, the capacity analysis of multi-antenna wireless communication systems with a line-of-sight transmission path, and a classical multiple sample significance testing problem.

Inference for High-dimensional Differential Correlation Matrices.

PubMed

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.

The price of privately releasing contingency tables, and the spectra of random matrices with correlated rows

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

Kasiviswanathan, Shiva; Rudelson, Mark; Smith, Adam

2009-01-01

Contingency tables are the method of choice of government agencies for releasing statistical summaries of categorical data. In this paper, we consider lower bounds on how much distortion (noise) is necessary in these tables to provide privacy guarantees when the data being summarized is sensitive. We extend a line of recent work on lower bounds on noise for private data analysis [10, 13. 14, 15] to a natural and important class of functionalities. Our investigation also leads to new results on the spectra of random matrices with correlated rows. Consider a database D consisting of n rows (one per individual),more » each row comprising d binary attributes. For any subset of T attributes of size |T| = k, the marginal table for T has 2{sup k} entries; each entry counts how many times in the database a particular setting of these attributes occurs. Imagine an agency that wishes to release all (d/k) contingency tables for a given database. For constant k, previous work showed that distortion {tilde {Omicron}}(min{l_brace}n, (n{sup 2}d){sup 1/3}, {radical}d{sup k}{r_brace}) is sufficient for satisfying differential privacy, a rigorous definition of privacy that has received extensive recent study. Our main contributions are: (1) For {epsilon}- and ({epsilon}, {delta})-differential privacy (with {epsilon} constant and {delta} = 1/poly(n)), we give a lower bound of {tilde {Omega}}(min{l_brace}{radical}n, {radical}d{sup k}{r_brace}), which is tight for n = {tilde {Omega}}(d{sup k}). Moreover, for a natural and popular class of mechanisms based on additive noise, our bound can be strengthened to {Omega}({radical}d{sup k}), which is tight for all n. Our bounds extend even to non-constant k, losing roughly a factor of {radical}2{sup k} compared to the best known upper bounds for large n. (2) We give efficient polynomial time attacks which allow an adversary to reconstruct sensitive infonnation given insufficiently perturbed contingency table releases. For constant k, we obtain a lower bound of {tilde {Omega}}(min{l_brace}{radical}n, {radical}d{sup k}{r_brace}) that applies to a large class of privacy notions, including K-anonymity (along with its variants) and differential privacy. In contrast to our bounds for differential privacy, this bound (a) is shown only for constant k, but (b) is tight for all values of n when k is constant. (3) Our reconstruction-based attacks require a new lower bound on the least singular values of random matrices with correlated rows. For a constant k, consider a matrix M with (d/k) rows which are formed by taking all possible k-way entry-wise products of an underlying set of d random vectors. We show that even for nearly square matrices with d{sup k}/log d columns, the least singular value is {Omega}({radical}d{sup k}) with high probability - asymptotically, the same bound as one gets for a matrix with independent rows. The proof requires several new ideas for analyzing random matrices and could be of independent interest.« less

Random sampling and validation of covariance matrices of resonance parameters

NASA Astrophysics Data System (ADS)

Plevnik, Lucijan; Zerovnik, Gašper

2017-09-01

Analytically exact methods for random sampling of arbitrary correlated parameters are presented. Emphasis is given on one hand on the possible inconsistencies in the covariance data, concentrating on the positive semi-definiteness and consistent sampling of correlated inherently positive parameters, and on the other hand on optimization of the implementation of the methods itself. The methods have been applied in the program ENDSAM, written in the Fortran language, which from a file from a nuclear data library of a chosen isotope in ENDF-6 format produces an arbitrary number of new files in ENDF-6 format which contain values of random samples of resonance parameters (in accordance with corresponding covariance matrices) in places of original values. The source code for the program ENDSAM is available from the OECD/NEA Data Bank. The program works in the following steps: reads resonance parameters and their covariance data from nuclear data library, checks whether the covariance data is consistent, and produces random samples of resonance parameters. The code has been validated with both realistic and artificial data to show that the produced samples are statistically consistent. Additionally, the code was used to validate covariance data in existing nuclear data libraries. A list of inconsistencies, observed in covariance data of resonance parameters in ENDF-VII.1, JEFF-3.2 and JENDL-4.0 is presented. For now, the work has been limited to resonance parameters, however the methods presented are general and can in principle be extended to sampling and validation of any nuclear data.

Fidelity under isospectral perturbations: a random matrix study

NASA Astrophysics Data System (ADS)

Leyvraz, F.; García, A.; Kohler, H.; Seligman, T. H.

2013-07-01

The set of Hamiltonians generated by all unitary transformations from a single Hamiltonian is the largest set of isospectral Hamiltonians we can form. Taking advantage of the fact that the unitary group can be generated from Hermitian matrices we can take the ones generated by the Gaussian unitary ensemble with a small parameter as small perturbations. Similarly, the transformations generated by Hermitian antisymmetric matrices from orthogonal matrices form isospectral transformations among symmetric matrices. Based on this concept we can obtain the fidelity decay of a system that decays under a random isospectral perturbation with well-defined properties regarding time-reversal invariance. If we choose the Hamiltonian itself also from a classical random matrix ensemble, then we obtain solutions in terms of form factors in the limit of large matrices.

User-Friendly Tools for Random Matrices: An Introduction

DTIC Science & Technology

2012-12-03

T 2011 , Oliveira 2010, Mackey et al . 2012, ... Joel A. Tropp, User-Friendly Tools for Random Matrices, NIPS, 3 December 2012 47 To learn more... E...the matrix product Y = AΩ 3. Construct an orthonormal basis Q for the range of Y [Ref] Halko –Martinsson–T, SIAM Rev. 2011 . Joel A. Tropp, User-Friendly...concentration inequalities...” with L. Mackey et al .. Submitted 2012. § “User-Friendly Tools for Random Matrices: An Introduction.” 2012. See also

Inference for High-dimensional Differential Correlation Matrices *

PubMed Central

Cai, T. Tony; Zhang, Anru

2015-01-01

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. PMID:26500380

Analysis of cross-correlations between financial markets after the 2008 crisis

NASA Astrophysics Data System (ADS)

Sensoy, A.; Yuksel, S.; Erturk, M.

2013-10-01

We analyze the cross-correlation matrix C of the index returns of the main financial markets after the 2008 crisis using methods of random matrix theory. We test the eigenvalues of C for universal properties of random matrices and find that the majority of the cross-correlation coefficients arise from randomness. We show that the eigenvector of the largest deviating eigenvalue of C represents a global market itself. We reveal that high volatility of financial markets is observed at the same times with high correlations between them which lowers the risk diversification potential even if one constructs a widely internationally diversified portfolio of stocks. We identify and compare the connection and cluster structure of markets before and after the crisis using minimal spanning and ultrametric hierarchical trees. We find that after the crisis, the co-movement degree of the markets increases. We also highlight the key financial markets of pre and post crisis using main centrality measures and analyze the changes. We repeat the study using rank correlation and compare the differences. Further implications are discussed.

Frequency dispersion of sound propagation in Rouse polymer melts via generalized dynamic random phase approximation.

PubMed

Erukhimovich, I Ya; Kudryavtsev, Ya V

2003-08-01

An extended generalization of the dynamic random phase approximation (DRPA) for L-component polymer systems is presented. Unlike the original version of the DRPA, which relates the (LxL) matrices of the collective density-density time correlation functions and the corresponding susceptibilities of concentrated polymer systems to those of the tracer macromolecules and so-called broken-links system (BLS), our generalized DRPA solves this problem for the (5xL) x (5xL) matrices of the coupled susceptibilities and time correlation functions of the component number, kinetic energy and flux densities. The presented technique is used to study propagation of sound and dynamic form-factor in disentangled (Rouse) monodisperse homopolymer melt. The calculated ultrasonic velocity and absorption coefficient reveal substantial frequency dispersion. The relaxation time tau is proportional to the degree of polymerization N, which is N times less than the Rouse time and evidences strong dynamic screening because of interchain interaction. We discuss also some peculiarities of the Brillouin scattering in polymer melts. Besides, a new convenient expression for the dynamic structure function of the single Rouse chain in (q,p) representation is found.

ESTIMATION OF FUNCTIONALS OF SPARSE COVARIANCE MATRICES.

PubMed

Fan, Jianqing; Rigollet, Philippe; Wang, Weichen

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

ESTIMATION OF FUNCTIONALS OF SPARSE COVARIANCE MATRICES

PubMed Central

Fan, Jianqing; Rigollet, Philippe; Wang, Weichen

2016-01-01

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other ℓr norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are sparsity-adaptive and minimax optimal over a large class of correlation matrices. Akin to previous results on functional estimation, the minimax rates exhibit an elbow phenomenon. Our results are further illustrated in simulated data as well as an empirical study of data arising in financial econometrics. PMID:26806986

Bayes linear covariance matrix adjustment

NASA Astrophysics Data System (ADS)

Wilkinson, Darren J.

1995-12-01

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 amenable to a similar approach. Diagnostics for matrix adjustments are also discussed.

Electron Correlation from the Adiabatic Connection for Multireference Wave Functions

NASA Astrophysics Data System (ADS)

Pernal, Katarzyna

2018-01-01

An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended random phase approximation allows one to find the correlation energy only from reference one- and two-electron reduced density matrices. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approximate AC formula is obtained. This results in the overall M5 scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.

Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance, and out-of-time-ordered correlator

NASA Astrophysics Data System (ADS)

Torres-Herrera, E. J.; García-García, Antonio M.; Santos, Lea F.

2018-02-01

We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival probability, density imbalance, and out-of-time-ordered correlator. They are compared with numerical results for a one-dimensional-disordered model with two-body interactions and shown to bound the decay rate of this realistic system. Power-law decays are seen at intermediate times, and dips below the infinite time averages (correlation holes) occur at long times for all three quantities when the system exhibits level repulsion. The fact that these features are shared by both the random matrix and the realistic disordered model indicates that they are generic to nonintegrable interacting quantum systems out of equilibrium. Assisted by the random matrix analytical results, we propose expressions that describe extremely well the dynamics of the realistic chaotic system at different time scales.

On the extreme value statistics of normal random matrices and 2D Coulomb gases: Universality and finite N corrections

NASA Astrophysics Data System (ADS)

Ebrahimi, R.; Zohren, S.

2018-03-01

In this paper we extend the orthogonal polynomials approach for extreme value calculations of Hermitian random matrices, developed by Nadal and Majumdar (J. Stat. Mech. P04001 arXiv:1102.0738), to normal random matrices and 2D Coulomb gases in general. Firstly, we show that this approach provides an alternative derivation of results in the literature. More precisely, we show convergence of the rescaled eigenvalue with largest modulus of a normal Gaussian ensemble to a Gumbel distribution, as well as universality for an arbitrary radially symmetric potential. Secondly, it is shown that this approach can be generalised to obtain convergence of the eigenvalue with smallest modulus and its universality for ring distributions. Most interestingly, the here presented techniques are used to compute all slowly varying finite N correction of the above distributions, which is important for practical applications, given the slow convergence. Another interesting aspect of this work is the fact that we can use standard techniques from Hermitian random matrices to obtain the extreme value statistics of non-Hermitian random matrices resembling the large N expansion used in context of the double scaling limit of Hermitian matrix models in string theory.

Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials

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

Aptekarev, Alexander I; Lysov, Vladimir G; Tulyakov, Dmitrii N

2011-02-28

Ensembles of random Hermitian matrices with a distribution measure defined by an anharmonic potential perturbed by an external source are considered. The limiting characteristics of the eigenvalue distribution of the matrices in these ensembles are related to the asymptotic behaviour of a certain system of multiple orthogonal polynomials. Strong asymptotic formulae are derived for this system. As a consequence, for matrices in this ensemble the limit mean eigenvalue density is found, and a variational principle is proposed to characterize this density. Bibliography: 35 titles.

ATLAS, an integrated structural analysis and design system. Volume 4: Random access file catalog

NASA Technical Reports Server (NTRS)

Gray, F. P., Jr. (Editor)

1979-01-01

A complete catalog is presented for the random access files used by the ATLAS integrated structural analysis and design system. ATLAS consists of several technical computation modules which output data matrices to corresponding random access file. A description of the matrices written on these files is contained herein.

Community Detection for Correlation Matrices

NASA Astrophysics Data System (ADS)

MacMahon, Mel; Garlaschelli, Diego

2015-04-01

A challenging problem in the study of 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 towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that we show to be intrinsically biased because of 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 appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anticorrelated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested subcommunities with "hard" cores and "soft" peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy; detect "soft stocks" that alternate between communities; and discuss implications for portfolio optimization and risk management.

Correlation Energies from the Two-Component Random Phase Approximation.

PubMed

Kühn, Michael

2014-02-11

The correlation energy within the two-component random phase approximation accounting for spin-orbit effects is derived. The resulting plasmon equation is rewritten-analogously to the scalar relativistic case-in terms of the trace of two Hermitian matrices for (Kramers-restricted) closed-shell systems and then represented as an integral over imaginary frequency using the resolution of the identity approximation. The final expression is implemented in the TURBOMOLE program suite. The code is applied to the computation of equilibrium distances and vibrational frequencies of heavy diatomic molecules. The efficiency is demonstrated by calculation of the relative energies of the Oh-, D4h-, and C5v-symmetric isomers of Pb6. Results within the random phase approximation are obtained based on two-component Kohn-Sham reference-state calculations, using effective-core potentials. These values are finally compared to other two-component and scalar relativistic methods, as well as experimental data.

Analyzing Matrices of Meta-Analytic Correlations: Current Practices and Recommendations

ERIC Educational Resources Information Center

Sheng, Zitong; Kong, Wenmo; Cortina, Jose M.; Hou, Shuofei

2016-01-01

Researchers have become increasingly interested in conducting analyses on meta-analytic correlation matrices. Methodologists have provided guidance and recommended practices for the application of this technique. The purpose of this article is to review current practices regarding analyzing meta-analytic correlation matrices, to identify the gaps…

Properties of networks with partially structured and partially random connectivity

NASA Astrophysics Data System (ADS)

Ahmadian, Yashar; Fumarola, Francesco; Miller, Kenneth D.

2015-01-01

Networks studied in many disciplines, including neuroscience and mathematical biology, have connectivity that may be stochastic about some underlying mean connectivity represented by a non-normal matrix. Furthermore, the stochasticity may not be independent and identically distributed (iid) across elements of the connectivity matrix. More generally, the problem of understanding the behavior of stochastic matrices with nontrivial mean structure and correlations arises in many settings. We address this by characterizing large random N ×N matrices of the form A =M +L J R , where M ,L , and R are arbitrary deterministic matrices and J is a random matrix of zero-mean iid elements. M can be non-normal, and L and R allow correlations that have separable dependence on row and column indices. We first provide a general formula for the eigenvalue density of A . For A non-normal, the eigenvalues do not suffice to specify the dynamics induced by A , so we also provide general formulas for the transient evolution of the magnitude of activity and frequency power spectrum in an N -dimensional linear dynamical system with a coupling matrix given by A . These quantities can also be thought of as characterizing the stability and the magnitude of the linear response of a nonlinear network to small perturbations about a fixed point. We derive these formulas and work them out analytically for some examples of M ,L , and R motivated by neurobiological models. We also argue that the persistence as N →∞ of a finite number of randomly distributed outlying eigenvalues outside the support of the eigenvalue density of A , as previously observed, arises in regions of the complex plane Ω where there are nonzero singular values of L-1(z 1 -M ) R-1 (for z ∈Ω ) that vanish as N →∞ . When such singular values do not exist and L and R are equal to the identity, there is a correspondence in the normalized Frobenius norm (but not in the operator norm) between the support of the spectrum of A for J of norm σ and the σ pseudospectrum of M .

Random Matrix Theory in molecular dynamics analysis.

PubMed

Palese, Luigi Leonardo

2015-01-01

It is well known that, in some situations, principal component analysis (PCA) carried out on molecular dynamics data results in the appearance of cosine-shaped low index projections. Because this is reminiscent of the results obtained by performing PCA on a multidimensional Brownian dynamics, it has been suggested that short-time protein dynamics is essentially nothing more than a noisy signal. Here we use Random Matrix Theory to analyze a series of short-time molecular dynamics experiments which are specifically designed to be simulations with high cosine content. We use as a model system the protein apoCox17, a mitochondrial copper chaperone. Spectral analysis on correlation matrices allows to easily differentiate random correlations, simply deriving from the finite length of the process, from non-random signals reflecting the intrinsic system properties. Our results clearly show that protein dynamics is not really Brownian also in presence of the cosine-shaped low index projections on principal axes. Copyright © 2014 Elsevier B.V. All rights reserved.

Dynamic evolution of cross-correlations in the Chinese stock market.

PubMed

Ren, Fei; Zhou, Wei-Xing

2014-01-01

The analysis of cross-correlations is extensively applied for the understanding of interconnections in stock markets and the portfolio risk estimation. Current studies of correlations in Chinese market mainly focus on the static correlations between return series, and this calls for an urgent need to investigate their dynamic correlations. Our study aims to reveal the dynamic evolution of cross-correlations in the Chinese stock market, and offer an exact interpretation for the evolution behavior. The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different time periods, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes. Our results provide new perspectives for the understanding of the dynamic evolution of cross-correlations in the Chines stock markets, and the result of risk estimation is valuable for the application of risk management.

Dynamic Evolution of Cross-Correlations in the Chinese Stock Market

PubMed Central

Ren, Fei; Zhou, Wei-Xing

2014-01-01

The analysis of cross-correlations is extensively applied for the understanding of interconnections in stock markets and the portfolio risk estimation. Current studies of correlations in Chinese market mainly focus on the static correlations between return series, and this calls for an urgent need to investigate their dynamic correlations. Our study aims to reveal the dynamic evolution of cross-correlations in the Chinese stock market, and offer an exact interpretation for the evolution behavior. The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different time periods, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes. Our results provide new perspectives for the understanding of the dynamic evolution of cross-correlations in the Chines stock markets, and the result of risk estimation is valuable for the application of risk management. PMID:24867071

Long-range correlations in time series generated by time-fractional diffusion: A numerical study

NASA Astrophysics Data System (ADS)

Barbieri, Davide; Vivoli, Alessandro

2005-09-01

Time series models showing power law tails in autocorrelation functions are common in econometrics. A special non-Markovian model for such kind of time series is provided by the random walk introduced by Gorenflo et al. as a discretization of time fractional diffusion. The time series so obtained are analyzed here from a numerical point of view in terms of autocorrelations and covariance matrices.

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

NASA Astrophysics Data System (ADS)

Benaych-Georges, Florent; Guionnet, Alice; Male, Camille

2014-07-01

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.

Synchronous correlation matrices and Connes’ embedding conjecture

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

Dykema, Kenneth J., E-mail: kdykema@math.tamu.edu; Paulsen, Vern, E-mail: vern@math.uh.edu

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 thatmore » 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.« less

Large-deviation theory for diluted Wishart random matrices

NASA Astrophysics Data System (ADS)

Castillo, Isaac Pérez; Metz, Fernando L.

2018-03-01

Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology, and economy. In this work, we develop a theory for the eigenvalue fluctuations of diluted Wishart random matrices based on the replica approach of disordered systems. We derive an analytical expression for the cumulant generating function of the number of eigenvalues IN(x ) smaller than x ∈R+ , from which all cumulants of IN(x ) and the rate function Ψx(k ) controlling its large-deviation probability Prob[IN(x ) =k N ] ≍e-N Ψx(k ) follow. Explicit results for the mean value and the variance of IN(x ) , its rate function, and its third cumulant are discussed and thoroughly compared to numerical diagonalization, showing very good agreement. The present work establishes the theoretical framework put forward in a recent letter [Phys. Rev. Lett. 117, 104101 (2016), 10.1103/PhysRevLett.117.104101] as an exact and compelling approach to deal with eigenvalue fluctuations of sparse random matrices.

Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties

NASA Astrophysics Data System (ADS)

Karp, Jonathan; Torres-Herrera, Jonathan; TáVora, Marco; Santos, Lea

We study the static and dynamical properties of isolated spin 1/2 systems as prototypes of many-body quantum systems and compare the results to those of full random matrices from a Gaussian orthogonal ensemble. Full random matrices do not represent realistic systems, because they imply that all particles interact at the same time, as opposed to realistic Hamiltonians, which are sparse and have only few-body interactions. Nevertheless, with full random matrices we can derive analytical results that can be used as references and bounds for the corresponding properties of realistic systems. In particular, we show that the results for the Shannon information entropy are very similar to those for the von Neumann entanglement entropy, with the former being computationally less expensive. We also discuss the behavior of the survival probability of the initial state at different time scales and show that it contains more information about the system than the entropies. Support from the NSF Grant No. DMR-1147430.

Disentangling giant component and finite cluster contributions in sparse random matrix spectra.

PubMed

Kühn, Reimer

2016-04-01

We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdős-Rényi graphs as an example and test bed. Our methods apply to sparse matrices defined in terms of arbitrary graphs in the configuration model class, as long as they have finite mean degree.

Combining Correlation Matrices: Simulation Analysis of Improved Fixed-Effects Methods

ERIC Educational Resources Information Center

Hafdahl, Adam R.

2007-01-01

The originally proposed multivariate meta-analysis approach for correlation matrices--analyze Pearson correlations, with each study's observed correlations replacing their population counterparts in its conditional-covariance matrix--performs poorly. Two refinements are considered: Analyze Fisher Z-transformed correlations, and substitute better…

Entanglement Measures in Ion-Trap Quantum Simulators without Full Tomography

DTIC Science & Technology

2014-07-21

t). This will allow us to efficiently compute correlations between ψ and ψ∗ in terms of standard expectation values in the enlarged space as follows...measure correlations of the form appearing in Eq. (2), with Θ a linear combination of tensorial products of Pauli matrices and identity operators...matrices will produce the desired correlation . Note that this protocol always results in a correlation of an odd number of Pauli matrices. In order to

Dynamic statistical optimization of GNSS radio occultation bending angles: advanced algorithm and performance analysis

NASA Astrophysics Data System (ADS)

Li, Y.; Kirchengast, G.; Scherllin-Pirscher, B.; Norman, R.; Yuan, Y. B.; Fritzer, J.; Schwaerz, M.; Zhang, K.

2015-08-01

We introduce a new dynamic statistical optimization algorithm to initialize ionosphere-corrected bending angles of Global Navigation Satellite System (GNSS)-based radio occultation (RO) measurements. The new algorithm estimates background and observation error covariance matrices with geographically varying uncertainty profiles and realistic global-mean correlation matrices. The error covariance matrices estimated by the new approach are more accurate and realistic than in simplified existing approaches and can therefore be used in statistical optimization to provide optimal bending angle profiles for high-altitude initialization of the subsequent Abel transform retrieval of refractivity. The new algorithm is evaluated against the existing Wegener Center Occultation Processing System version 5.6 (OPSv5.6) algorithm, using simulated data on two test days from January and July 2008 and real observed CHAllenging Minisatellite Payload (CHAMP) and Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) measurements from the complete months of January and July 2008. The following is achieved for the new method's performance compared to OPSv5.6: (1) significant reduction of random errors (standard deviations) of optimized bending angles down to about half of their size or more; (2) reduction of the systematic differences in optimized bending angles for simulated MetOp data; (3) improved retrieval of refractivity and temperature profiles; and (4) realistically estimated global-mean correlation matrices and realistic uncertainty fields for the background and observations. Overall the results indicate high suitability for employing the new dynamic approach in the processing of long-term RO data into a reference climate record, leading to well-characterized and high-quality atmospheric profiles over the entire stratosphere.

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

DOE PAGES

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry; ...

2016-10-27

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite.more » The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.« less

Single-qubit decoherence under a separable coupling to a random matrix environment

NASA Astrophysics Data System (ADS)

Carrera, M.; Gorin, T.; Seligman, T. H.

2014-08-01

This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude as the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (in the environment Hamiltonian), memory effects, and symmetry-breaking equilibrium states.

Random density matrices versus random evolution of open system

NASA Astrophysics Data System (ADS)

Pineda, Carlos; Seligman, Thomas H.

2015-10-01

We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful convex function. The second, dynamic ensemble, is inspired in random matrix models for decoherence where one evolves a separable pure state with a random Hamiltonian until a given value of purity in the central system is achieved. Several families of Hamiltonians, adequate for different physical situations, are studied. We focus on a two qubit central system, and obtain exact expressions for the static case. The ensemble displays a peak around Werner-like states, modulated by nodes on the degeneracies of the density matrices. For moderate and strong interactions good agreement between the static and the dynamic ensembles is found. Even in a model where one qubit does not interact with the environment excellent agreement is found, but only if there is maximal entanglement with the interacting one. The discussion is started recalling similar considerations for scattering theory. At the end, we comment on the reach of the results for other convex functions of the density matrix, and exemplify the situation with the von Neumann entropy.

A new measure based on degree distribution that links information theory and network graph analysis

PubMed Central

2012-01-01

Background Detailed connection maps of human and nonhuman brains are being generated with new technologies, and graph metrics have been instrumental in understanding the general organizational features of these structures. Neural networks appear to have small world properties: they have clustered regions, while maintaining integrative features such as short average pathlengths. Results We captured the structural characteristics of clustered networks with short average pathlengths through our own variable, System Difference (SD), which is computationally simple and calculable for larger graph systems. SD is a Jaccardian measure generated by averaging all of the differences in the connection patterns between any two nodes of a system. We calculated SD over large random samples of matrices and found that high SD matrices have a low average pathlength and a larger number of clustered structures. SD is a measure of degree distribution with high SD matrices maximizing entropic properties. Phi (Φ), an information theory metric that assesses a system’s capacity to integrate information, correlated well with SD - with SD explaining over 90% of the variance in systems above 11 nodes (tested for 4 to 13 nodes). However, newer versions of Φ do not correlate well with the SD metric. Conclusions The new network measure, SD, provides a link between high entropic structures and degree distributions as related to small world properties. PMID:22726594

Random matrix theory and cross-correlations in global financial indices and local stock market indices

NASA Astrophysics Data System (ADS)

Nobi, Ashadun; Maeng, Seong Eun; Ha, Gyeong Gyun; Lee, Jae Woo

2013-02-01

We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest eigenvectors of the cross-correlation matrix before, during, and after the global financial the crisis in the year 2008. We find that the majority of its eigenvalues fall within the RMT bounds [ λ -, λ +], where λ - and λ + are the lower and the upper bounds of the eigenvalues of random correlation matrices. The components of the eigenvectors for the largest positive eigenvalues indicate the identical financial market mode dominating the global and local indices. On the other hand, the components of the eigenvector corresponding to the second largest eigenvalue are positive and negative values alternatively. The components before the crisis change sign during the crisis, and those during the crisis change sign after the crisis. The largest inverse participation ratio (IPR) corresponding to the smallest eigenvector is higher after the crisis than during any other periods in the global and local indices. During the global financial the crisis, the correlations among the global indices and among the local stock indices are perturbed significantly. However, the correlations between indices quickly recover the trends before the crisis.

Bi-dimensional null model analysis of presence-absence binary matrices.

PubMed

Strona, Giovanni; Ulrich, Werner; Gotelli, Nicholas J

2018-01-01

Comparing the structure of presence/absence (i.e., binary) matrices with those of randomized counterparts is a common practice in ecology. However, differences in the randomization procedures (null models) can affect the results of the comparisons, leading matrix structural patterns to appear either "random" or not. Subjectivity in the choice of one particular null model over another makes it often advisable to compare the results obtained using several different approaches. Yet, available algorithms to randomize binary matrices differ substantially in respect to the constraints they impose on the discrepancy between observed and randomized row and column marginal totals, which complicates the interpretation of contrasting patterns. This calls for new strategies both to explore intermediate scenarios of restrictiveness in-between extreme constraint assumptions, and to properly synthesize the resulting information. Here we introduce a new modeling framework based on a flexible matrix randomization algorithm (named the "Tuning Peg" algorithm) that addresses both issues. The algorithm consists of a modified swap procedure in which the discrepancy between the row and column marginal totals of the target matrix and those of its randomized counterpart can be "tuned" in a continuous way by two parameters (controlling, respectively, row and column discrepancy). We show how combining the Tuning Peg with a wise random walk procedure makes it possible to explore the complete null space embraced by existing algorithms. This exploration allows researchers to visualize matrix structural patterns in an innovative bi-dimensional landscape of significance/effect size. We demonstrate the rational and potential of our approach with a set of simulated and real matrices, showing how the simultaneous investigation of a comprehensive and continuous portion of the null space can be extremely informative, and possibly key to resolving longstanding debates in the analysis of ecological matrices. © 2017 The Authors. Ecology, published by Wiley Periodicals, Inc., on behalf of the Ecological Society of America.

Probabilistic Structures Analysis Methods (PSAM) for select space propulsion system components

NASA Technical Reports Server (NTRS)

1991-01-01

The basic formulation for probabilistic finite element analysis is described and demonstrated on a few sample problems. This formulation is based on iterative perturbation that uses the factorized stiffness on the unperturbed system as the iteration preconditioner for obtaining the solution to the perturbed problem. This approach eliminates the need to compute, store and manipulate explicit partial derivatives of the element matrices and force vector, which not only reduces memory usage considerably, but also greatly simplifies the coding and validation tasks. All aspects for the proposed formulation were combined in a demonstration problem using a simplified model of a curved turbine blade discretized with 48 shell elements, and having random pressure and temperature fields with partial correlation, random uniform thickness, and random stiffness at the root.

Schur Complement Inequalities for Covariance Matrices and Monogamy of Quantum Correlations

NASA Astrophysics Data System (ADS)

Lami, Ludovico; Hirche, Christoph; Adesso, Gerardo; Winter, Andreas

2016-11-01

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.

Schur Complement Inequalities for Covariance Matrices and Monogamy of Quantum Correlations.

PubMed

Lami, Ludovico; Hirche, Christoph; Adesso, Gerardo; Winter, Andreas

2016-11-25

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.

Multiple-image encryption based on double random phase encoding and compressive sensing by using a measurement array preprocessed with orthogonal-basis matrices

NASA Astrophysics Data System (ADS)

Zhang, Luozhi; Zhou, Yuanyuan; Huo, Dongming; Li, Jinxi; Zhou, Xin

2018-09-01

A method is presented for multiple-image encryption by using the combination of orthogonal encoding and compressive sensing based on double random phase encoding. As an original thought in optical encryption, it is demonstrated theoretically and carried out by using the orthogonal-basis matrices to build a modified measurement array, being projected onto the images. In this method, all the images can be compressed in parallel into a stochastic signal and be diffused to be a stationary white noise. Meanwhile, each single-image can be separately reestablished by adopting a proper decryption key combination through the block-reconstruction rather than the entire-rebuilt, for its costs of data and decryption time are greatly decreased, which may be promising both in multi-user multiplexing and huge-image encryption/decryption. Besides, the security of this method is characterized by using the bit-length of key, and the parallelism is investigated as well. The simulations and discussions are also made on the effects of decryption as well as the correlation coefficient by using a series of sampling rates, occlusion attacks, keys with various error rates, etc.

Efficient, massively parallel eigenvalue computation

NASA Technical Reports Server (NTRS)

Huo, Yan; Schreiber, Robert

1993-01-01

In numerical simulations of disordered electronic systems, one of the most common approaches is to diagonalize random Hamiltonian matrices and to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. An effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems, is described. Results of numerical tests and timings are also presented.

Emerging spectra of singular correlation matrices under small power-map deformations

NASA Astrophysics Data System (ADS)

Vinayak; Schäfer, Rudi; Seligman, Thomas H.

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Emerging spectra of singular correlation matrices under small power-map deformations.

PubMed

Vinayak; Schäfer, Rudi; Seligman, Thomas H

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices

NASA Astrophysics Data System (ADS)

Chakhmakhchyan, L.; Cerf, N. J.; Garcia-Patron, R.

2017-08-01

We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithm development.

Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices

PubMed Central

Meyer, Karin; Kirkpatrick, Mark

2005-01-01

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. PMID:15588566

Somatotype and intellectual ability (Raven Progressive Matrices Test) in Chilean school-age children.

PubMed

Tapia, Liliana U; Lizana, Pablo A; Orellana, Yasna Z; Villagrán, Francisca S; Arias, Vanessa F; Almagià, Atilio F; Burrows, Raquel A; Ivanovic, Daniza M

2013-01-01

The aim of this study was to determine the relationship between somatotype and intellectual ability (IA) in 11-12 and 15-16 year-old students (n = 1,015) in the Chile's Metropolitan Region from a representative sample of 33 educational establishments chosen at random. The Heath-Carter somatotype and the IA assessed through the Raven Progressive Matrices Test were measured. The endomorph was observed in 59% of the students; 28% had a mesomorph and 13% ectomorph. The IA was distributed in: 11.2% Grade I, 26.8% Grade II, 41% Grade III, 17.6% Grade IV and 3.2% Grade V. A positive and significant correlation of IA with the endomorphic component (r = 0.074, p = 0.02) was found in the total sample and only in females (r = 0.109, p = 0.02); at the same time, a positive and significant correlation with the ectomorph component was also observed (r = 0.067, p < 0.05). This suggests that other variables would influence more strongly the IA for which further research is needed to quantitate this multifactorial problem. Copyright © AULA MEDICA EDICIONES 2013. Published by AULA MEDICA. All rights reserved.

A matrix contraction process

NASA Astrophysics Data System (ADS)

Wilkinson, Michael; Grant, John

2018-03-01

We consider a stochastic process in which independent identically distributed random matrices are multiplied and where the Lyapunov exponent of the product is positive. We continue multiplying the random matrices as long as the norm, ɛ, of the product is less than unity. If the norm is greater than unity we reset the matrix to a multiple of the identity and then continue the multiplication. We address the problem of determining the probability density function of the norm, \

Derivatives of random matrix characteristic polynomials with applications to elliptic curves

NASA Astrophysics Data System (ADS)

Snaith, N. C.

2005-12-01

The value distribution of derivatives of characteristic polynomials of matrices from SO(N) is calculated at the point 1, the symmetry point on the unit circle of the eigenvalues of these matrices. We consider subsets of matrices from SO(N) that are constrained to have at least n eigenvalues equal to 1 and investigate the first non-zero derivative of the characteristic polynomial at that point. The connection between the values of random matrix characteristic polynomials and values of L-functions in families has been well established. The motivation for this work is the expectation that through this connection with L-functions derived from families of elliptic curves, and using the Birch and Swinnerton-Dyer conjecture to relate values of the L-functions to the rank of elliptic curves, random matrix theory will be useful in probing important questions concerning these ranks.

Computation of transform domain covariance matrices

NASA Technical Reports Server (NTRS)

Fino, B. J.; Algazi, V. R.

1975-01-01

It is often of interest in applications to compute the covariance matrix of a random process transformed by a fast unitary transform. Here, the recursive definition of fast unitary transforms is used to derive recursive relations for the covariance matrices of the transformed process. These relations lead to fast methods of computation of covariance matrices and to substantial reductions of the number of arithmetic operations required.

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

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite.more » The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.« less

Intermittency and random matrices

NASA Astrophysics Data System (ADS)

Sokoloff, Dmitry; Illarionov, E. A.

2015-08-01

A spectacular phenomenon of intermittency, i.e. a progressive growth of higher statistical moments of a physical field excited by an instability in a random medium, attracted the attention of Zeldovich in the last years of his life. At that time, the mathematical aspects underlying the physical description of this phenomenon were still under development and relations between various findings in the field remained obscure. Contemporary results from the theory of the product of independent random matrices (the Furstenberg theory) allowed the elaboration of the phenomenon of intermittency in a systematic way. We consider applications of the Furstenberg theory to some problems in cosmology and dynamo theory.

Pruning a minimum spanning tree

NASA Astrophysics Data System (ADS)

Sandoval, Leonidas

2012-04-01

This work employs various techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis. The first technique establishes a threshold above which connections are considered affected by noise, based on the study of random networks with the same probability density distribution of the original data. The second technique is to judge the strength of a connection by its survival rate, which is the amount of time a connection between two stock market indices endures. The idea is that true connections will survive for longer periods of time, and that random connections will not. That information is then combined with the information obtained from the first technique in order to create a smaller network, in which most of the connections are either strong or enduring in time.

Estimating and Identifying Unspecified Correlation Structure for Longitudinal Data

PubMed Central

Hu, Jianhua; Wang, Peng; Qu, Annie

2014-01-01

Identifying correlation structure is important to achieving estimation efficiency in analyzing longitudinal data, and is also crucial for drawing valid statistical inference for large size clustered data. In this paper, we propose a nonparametric method to estimate the correlation structure, which is applicable for discrete longitudinal data. We utilize eigenvector-based basis matrices to approximate the inverse of the empirical correlation matrix and determine the number of basis matrices via model selection. A penalized objective function based on the difference between the empirical and model approximation of the correlation matrices is adopted to select an informative structure for the correlation matrix. The eigenvector representation of the correlation estimation is capable of reducing the risk of model misspecification, and also provides useful information on the specific within-cluster correlation pattern of the data. We show that the proposed method possesses the oracle property and selects the true correlation structure consistently. The proposed method is illustrated through simulations and two data examples on air pollution and sonar signal studies. PMID:26361433

One-electron reduced density matrices of strongly correlated harmonium atoms.

PubMed

Cioslowski, Jerzy

2015-03-21

Explicit asymptotic expressions are derived for the reduced one-electron density matrices (the 1-matrices) of strongly correlated two- and three-electron harmonium atoms in the ground and first excited states. These expressions, which are valid at the limit of small confinement strength ω, yield electron densities and kinetic energies in agreement with the published values. In addition, they reveal the ω(5/6) asymptotic scaling of the exchange components of the electron-electron repulsion energies that differs from the ω(2/3) scaling of their Coulomb and correlation counterparts. The natural orbitals of the totally symmetric ground state of the two-electron harmonium atom are found to possess collective occupancies that follow a mixed power/Gaussian dependence on the angular momentum in variance with the simple power-law prediction of Hill's asymptotics. Providing rigorous constraints on energies as functionals of 1-matrices, these results are expected to facilitate development of approximate implementations of the density matrix functional theory and ensure their proper description of strongly correlated systems.

Double-scaling limits of random matrices and minimal (2m, 1) models: the merging of two cuts in a degenerate case

NASA Astrophysics Data System (ADS)

Marchal, O.; Cafasso, M.

2011-04-01

In this paper, we show that the double-scaling-limit correlation functions of a random matrix model when two cuts merge with degeneracy 2m (i.e. when y ~ x2m for arbitrary values of the integer m) are the same as the determinantal formulae defined by conformal (2m, 1) models. Our approach follows the one developed by Bergère and Eynard in (2009 arXiv:0909.0854) and uses a Lax pair representation of the conformal (2m, 1) models (giving a Painlevé II integrable hierarchy) as suggested by Bleher and Eynard in (2003 J. Phys. A: Math. Gen. 36 3085). In particular we define Baker-Akhiezer functions associated with the Lax pair in order to construct a kernel which is then used to compute determinantal formulae giving the correlation functions of the double-scaling limit of a matrix model near the merging of two cuts.

Random matrix theory filters in portfolio optimisation: A stability and risk assessment

NASA Astrophysics Data System (ADS)

Daly, J.; Crane, M.; Ruskin, H. J.

2008-07-01

Random matrix theory (RMT) filters, applied to covariance matrices of financial returns, have recently been shown to offer improvements to the optimisation of stock portfolios. This paper studies the effect of three RMT filters on the realised portfolio risk, and on the stability of the filtered covariance matrix, using bootstrap analysis and out-of-sample testing. We propose an extension to an existing RMT filter, (based on Krzanowski stability), which is observed to reduce risk and increase stability, when compared to other RMT filters tested. We also study a scheme for filtering the covariance matrix directly, as opposed to the standard method of filtering correlation, where the latter is found to lower the realised risk, on average, by up to 6.7%. We consider both equally and exponentially weighted covariance matrices in our analysis, and observe that the overall best method out-of-sample was that of the exponentially weighted covariance, with our Krzanowski stability-based filter applied to the correlation matrix. We also find that the optimal out-of-sample decay factors, for both filtered and unfiltered forecasts, were higher than those suggested by Riskmetrics [J.P. Morgan, Reuters, Riskmetrics technical document, Technical Report, 1996. http://www.riskmetrics.com/techdoc.html], with those for the latter approaching a value of α=1. In conclusion, RMT filtering reduced the realised risk, on average, and in the majority of cases when tested out-of-sample, but increased the realised risk on a marked number of individual days-in some cases more than doubling it.

Nuclear data correlation between different isotopes via integral information

NASA Astrophysics Data System (ADS)

Rochman, Dimitri A.; Bauge, Eric; Vasiliev, Alexander; Ferroukhi, Hakim; Perret, Gregory

2018-05-01

This paper presents a Bayesian approach based on integral experiments to create correlations between different isotopes which do not appear with differential data. A simple Bayesian set of equations is presented with random nuclear data, similarly to the usual methods applied with differential data. As a consequence, updated nuclear data (cross sections, ν‾, fission neutron spectra and covariance matrices) are obtained, leading to better integral results. An example for 235U and 238U is proposed taking into account the Bigten criticality benchmark.

Combining Heterogeneous Correlation Matrices: Simulation Analysis of Fixed-Effects Methods

ERIC Educational Resources Information Center

Hafdahl, Adam R.

2008-01-01

Monte Carlo studies of several fixed-effects methods for combining and comparing correlation matrices have shown that two refinements improve estimation and inference substantially. With rare exception, however, these simulations have involved homogeneous data analyzed using conditional meta-analytic procedures. The present study builds on…

Testing Pattern Hypotheses for Correlation Matrices

ERIC Educational Resources Information Center

McDonald, Roderick P.

1975-01-01

The treatment of covariance matrices given by McDonald (1974) can be readily modified to cover hypotheses prescribing zeros and equalities in the correlation matrix rather than the covariance matrix, still with the convenience of the closed-form Least Squares solution and the classical Newton method. (Author/RC)

Matrix Summaries Improve Research Reports: Secondary Analyses Using Published Literature

ERIC Educational Resources Information Center

Zientek, Linda Reichwein; Thompson, Bruce

2009-01-01

Correlation matrices and standard deviations are the building blocks of many of the commonly conducted analyses in published research, and AERA and APA reporting standards recommend their inclusion when reporting research results. The authors argue that the inclusion of correlation/covariance matrices, standard deviations, and means can enhance…

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors

NASA Astrophysics Data System (ADS)

Pandey, Akhilesh; Kumar, Avanish; Puri, Sanjay

2017-11-01

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α , the appropriate FRCG model has the effective range d =b2/N =α2/N , for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors.

PubMed

Pandey, Akhilesh; Kumar, Avanish; Puri, Sanjay

2017-11-01

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has the effective range d=b^{2}/N=α^{2}/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Statistical properties of cross-correlation in the Korean stock market

NASA Astrophysics Data System (ADS)

Oh, G.; Eom, C.; Wang, F.; Jung, W.-S.; Stanley, H. E.; Kim, S.

2011-01-01

We investigate the statistical properties of the cross-correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the cross-correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original cross-correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The β_{473} coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function E(σ) with the portfolio risk σ for the original and filtered cross-correlation matrices are consistent with a power-law function, E( σ) σ^{-γ}, with the exponent γ 2.92 and those for Asian currency crisis decreases significantly.

Spectra of Adjacency Matrices in Networks of Extreme Introverts and Extroverts

NASA Astrophysics Data System (ADS)

Bassler, Kevin E.; Ezzatabadipour, Mohammadmehdi; Zia, R. K. P.

Many interesting properties were discovered in recent studies of preferred degree networks, suitable for describing social behavior of individuals who tend to prefer a certain number of contacts. In an extreme version (coined the XIE model), introverts always cut links while extroverts always add them. While the intra-group links are static, the cross-links are dynamic and lead to an ensemble of bipartite graphs, with extraordinary correlations between elements of the incidence matrix: nij In the steady state, this system can be regarded as one in thermal equilibrium with long-ranged interactions between the nij's, and displays an extreme Thouless effect. Here, we report simulation studies of a different perspective of networks, namely, the spectra associated with this ensemble of adjacency matrices {aij } . As a baseline, we first consider the spectra associated with a simple random (Erdős-Rényi) ensemble of bipartite graphs, where simulation results can be understood analytically. Work supported by the NSF through Grant DMR-1507371.

Simple techniques for improving deep neural network outcomes on commodity hardware

NASA Astrophysics Data System (ADS)

Colina, Nicholas Christopher A.; Perez, Carlos E.; Paraan, Francis N. C.

2017-08-01

We benchmark improvements in the performance of deep neural networks (DNN) on the MNIST data test upon imple-menting two simple modifications to the algorithm that have little overhead computational cost. First is GPU parallelization on a commodity graphics card, and second is initializing the DNN with random orthogonal weight matrices prior to optimization. Eigenspectra analysis of the weight matrices reveal that the initially orthogonal matrices remain nearly orthogonal after training. The probability distributions from which these orthogonal matrices are drawn are also shown to significantly affect the performance of these deep neural networks.

Dissection of genomic correlation matrices using multivariate factor analysis in dairy and dual-purpose cattle breeds

USDA-ARS?s Scientific Manuscript database

SNP effects estimated in genomic selection programs allow for the prediction of direct genomic values (DGV) both at genome-wide and chromosomal level. As a consequence, genome-wide (G_GW) or chromosomal (G_CHR) correlation matrices between genomic predictions for different traits can be calculated. ...

Classifying Correlation Matrices into Relatively Homogeneous Subgroups: A Cluster Analytic Approach

ERIC Educational Resources Information Center

Cheung, Mike W.-L.; Chan, Wai

2005-01-01

Researchers are becoming interested in combining meta-analytic techniques and structural equation modeling to test theoretical models from a pool of studies. Most existing procedures are based on the assumption that all correlation matrices are homogeneous. Few studies have addressed what the next step should be when studies being analyzed are…

Random Matrix Theory and Econophysics

NASA Astrophysics Data System (ADS)

Rosenow, Bernd

2000-03-01

Random Matrix Theory (RMT) [1] is used in many branches of physics as a ``zero information hypothesis''. It describes generic behavior of different classes of systems, while deviations from its universal predictions allow to identify system specific properties. We use methods of RMT to analyze the cross-correlation matrix C of stock price changes [2] of the largest 1000 US companies. In addition to its scientific interest, the study of correlations between the returns of different stocks is also of practical relevance in quantifying the risk of a given stock portfolio. We find [3,4] that the statistics of most of the eigenvalues of the spectrum of C agree with the predictions of RMT, while there are deviations for some of the largest eigenvalues. We interpret these deviations as a system specific property, e.g. containing genuine information about correlations in the stock market. We demonstrate that C shares universal properties with the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of C through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum - a situation reminiscent of localization theory results. This work was done in collaboration with V. Plerou, P. Gopikrishnan, T. Guhr, L.A.N. Amaral, and H.E Stanley and is related to recent work of Laloux et al.. 1. T. Guhr, A. Müller Groeling, and H.A. Weidenmüller, ``Random Matrix Theories in Quantum Physics: Common Concepts'', Phys. Rep. 299, 190 (1998). 2. See, e.g. R.N. Mantegna and H.E. Stanley, Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, England, 1999). 3. V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, and H.E. Stanley, ``Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series'', Phys. Rev. Lett. 83, 1471 (1999). 4. V. Plerou, P. Gopikrishnan, T. Guhr, B. Rosenow, L.A.N. Amaral, and H.E. Stanley, ``Random Matrix Theory Analysis of Diffusion in Stock Price Dynamics, preprint

Small-world bias of correlation networks: From brain to climate

NASA Astrophysics Data System (ADS)

Hlinka, Jaroslav; Hartman, David; Jajcay, Nikola; Tomeček, David; Tintěra, Jaroslav; Paluš, Milan

2017-03-01

Complex systems are commonly characterized by the properties of their graph representation. Dynamical complex systems are then typically represented by a graph of temporal dependencies between time series of state variables of their subunits. It has been shown recently that graphs constructed in this way tend to have relatively clustered structure, potentially leading to spurious detection of small-world properties even in the case of systems with no or randomly distributed true interactions. However, the strength of this bias depends heavily on a range of parameters and its relevance for real-world data has not yet been established. In this work, we assess the relevance of the bias using two examples of multivariate time series recorded in natural complex systems. The first is the time series of local brain activity as measured by functional magnetic resonance imaging in resting healthy human subjects, and the second is the time series of average monthly surface air temperature coming from a large reanalysis of climatological data over the period 1948-2012. In both cases, the clustering in the thresholded correlation graph is substantially higher compared with a realization of a density-matched random graph, while the shortest paths are relatively short, showing thus distinguishing features of small-world structure. However, comparable or even stronger small-world properties were reproduced in correlation graphs of model processes with randomly scrambled interconnections. This suggests that the small-world properties of the correlation matrices of these real-world systems indeed do not reflect genuinely the properties of the underlying interaction structure, but rather result from the inherent properties of correlation matrix.

Small-world bias of correlation networks: From brain to climate.

PubMed

Hlinka, Jaroslav; Hartman, David; Jajcay, Nikola; Tomeček, David; Tintěra, Jaroslav; Paluš, Milan

2017-03-01

Complex systems are commonly characterized by the properties of their graph representation. Dynamical complex systems are then typically represented by a graph of temporal dependencies between time series of state variables of their subunits. It has been shown recently that graphs constructed in this way tend to have relatively clustered structure, potentially leading to spurious detection of small-world properties even in the case of systems with no or randomly distributed true interactions. However, the strength of this bias depends heavily on a range of parameters and its relevance for real-world data has not yet been established. In this work, we assess the relevance of the bias using two examples of multivariate time series recorded in natural complex systems. The first is the time series of local brain activity as measured by functional magnetic resonance imaging in resting healthy human subjects, and the second is the time series of average monthly surface air temperature coming from a large reanalysis of climatological data over the period 1948-2012. In both cases, the clustering in the thresholded correlation graph is substantially higher compared with a realization of a density-matched random graph, while the shortest paths are relatively short, showing thus distinguishing features of small-world structure. However, comparable or even stronger small-world properties were reproduced in correlation graphs of model processes with randomly scrambled interconnections. This suggests that the small-world properties of the correlation matrices of these real-world systems indeed do not reflect genuinely the properties of the underlying interaction structure, but rather result from the inherent properties of correlation matrix.

Levy Matrices and Financial Covariances

NASA Astrophysics Data System (ADS)

Burda, Zdzislaw; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, Gabor; Zahed, Ismail

2003-10-01

In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

Dynamical Analysis of Stock Market Instability by Cross-correlation Matrix

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

2016-08-01

We study stock market instability by using cross-correlations constructed from the return time series of 366 stocks traded on the Tokyo Stock Exchange from January 5, 1998 to December 30, 2013. To investigate the dynamical evolution of the cross-correlations, crosscorrelation matrices are calculated with a rolling window of 400 days. To quantify the volatile market stages where the potential risk is high, we apply the principal components analysis and measure the cumulative risk fraction (CRF), which is the system variance associated with the first few principal components. From the CRF, we detected three volatile market stages corresponding to the bankruptcy of Lehman Brothers, the 2011 Tohoku Region Pacific Coast Earthquake, and the FRB QE3 reduction observation in the study period. We further apply the random matrix theory for the risk analysis and find that the first eigenvector is more equally de-localized when the market is volatile.

The factor structure of the Alcohol Use Disorders Identification Test (AUDIT).

PubMed

Doyle, Suzanne R; Donovan, Dennis M; Kivlahan, Daniel R

2007-05-01

Past research assessing the factor structure of the Alcohol Use Disorders Identification Test (AUDIT) with various exploratory and confirmatory factor analytic techniques has identified one-, two-, and three-factor solutions. Because different factor analytic procedures may result in dissimilar findings, we examined the factor structure of the AUDIT using the same factor analytic technique on two new large clinical samples and on archival data from six samples studied in previous reports. Responses to the AUDIT were obtained from participants who met Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV), criteria for alcohol dependence in two large randomized clinical trials: the COMBINE (Combining Medications and Behavioral Interventions) Study (N = 1,337; 69% men) and Project MATCH (Matching Alcoholism Treatments to Client Heterogeneity; N = 1,711; 76% men). Supplementary analyses involved six correlation matrices of AUDIT data obtained from five previously published articles. Confirmatory factor analyses based on one-, two-, and three-factor models were conducted on the eight correlation matrices to assess the factor structure of the AUDIT. Across samples, analyses supported a correlated, two-factor solution representing alcohol consumption and alcohol-related consequences. The three-factor solution fit the data equally well, but two factors (alcohol dependence and harmful alcohol use) were highly correlated. The one-factor solution did not provide a good fit to the data. These findings support a two-factor solution for the AUDIT (alcohol consumption and alcohol-related consequences). The results contradict the original three-factor design of the AUDIT and the prevalent use of the AUDIT as a one-factor screening instrument with a single cutoff score.

Evaluation of an Approximate Method for Synthesizing Covariance Matrices for Use in Meta-Analytic SEM

ERIC Educational Resources Information Center

Beretvas, S. Natasha; Furlow, Carolyn F.

2006-01-01

Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect…

Calibration and temperature correction of heat dissipation matric potential sensors

USGS Publications Warehouse

Flint, A.L.; Campbell, G.S.; Ellett, K.M.; Calissendorff, C.

2002-01-01

This paper describes how heat dissipation sensors, used to measure soil water matric potential, were analyzed to develop a normalized calibration equation and a temperature correction method. Inference of soil matric potential depends on a correlation between the variable thermal conductance of the sensor's porous ceramic and matric poten-tial. Although this correlation varies among sensors, we demonstrate a normalizing procedure that produces a single calibration relationship. Using sensors from three sources and different calibration methods, the normalized calibration resulted in a mean absolute error of 23% over a matric potential range of -0.01 to -35 MPa. Because the thermal conductivity of variably saturated porous media is temperature dependent, a temperature correction is required for application of heat dissipation sensors in field soils. A temperature correction procedure is outlined that reduces temperature dependent errors by 10 times, which reduces the matric potential measurement errors by more than 30%. The temperature dependence is well described by a thermal conductivity model that allows for the correction of measurements at any temperature to measurements at the calibration temperature.

Dimension from covariance matrices.

PubMed

Carroll, T L; Byers, J M

2017-02-01

We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.

Emergence of a spectral gap in a class of random matrices associated with split graphs

NASA Astrophysics Data System (ADS)

Bassler, Kevin E.; Zia, R. K. P.

2018-01-01

Motivated by the intriguing behavior displayed in a dynamic network that models a population of extreme introverts and extroverts (XIE), we consider the spectral properties of ensembles of random split graph adjacency matrices. We discover that, in general, a gap emerges in the bulk spectrum between -1 and 0 that contains a single eigenvalue. An analytic expression for the bulk distribution is derived and verified with numerical analysis. We also examine their relation to chiral ensembles, which are associated with bipartite graphs.

Communication Optimal Parallel Multiplication of Sparse Random Matrices

DTIC Science & Technology

2013-02-21

Definition 2.1), and (2) the algorithm is sparsity- independent, where the computation is statically partitioned to processors independent of the sparsity...struc- ture of the input matrices (see Definition 2.5). The second assumption applies to nearly all existing al- gorithms for general sparse matrix-matrix...where A and B are n× n ER(d) matrices: Definition 2.1 An ER(d) matrix is an adjacency matrix of an Erdős-Rényi graph with parameters n and d/n. That

Partial transpose of random quantum states: Exact formulas and meanders

NASA Astrophysics Data System (ADS)

Fukuda, Motohisa; Śniady, Piotr

2013-04-01

We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by approximating the matrix of trace 1 by the Wishart matrix of random trace) and shown to be the semicircular distribution or the free difference of two free Poisson distributions, depending on how dimensions of the concerned spaces grow. Our use of Wishart matrices gives exact combinatorial formulas for the moments of the partial transpose of the random state. We find three natural asymptotic regimes in terms of geodesics on the permutation groups. Two of them correspond to the above two cases; the third one turns out to be a new matrix model for the meander polynomials. Moreover, we prove the convergence to the semicircular distribution together with its extreme eigenvalues under weaker assumptions, and show large deviation bound for the latter.

Spectra of random networks in the weak clustering regime

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Improved Estimation and Interpretation of Correlations in Neural Circuits

PubMed Central

Yatsenko, Dimitri; Josić, Krešimir; Ecker, Alexander S.; Froudarakis, Emmanouil; Cotton, R. James; Tolias, Andreas S.

2015-01-01

Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150–350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive ‘excitatory’ interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative ‘inhibitory’ interactions were less selective. Because of its superior performance, this ‘sparse+latent’ estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix. PMID:25826696

RANDOM MATRIX DIAGONALIZATION--A COMPUTER PROGRAM

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

Fuchel, K.; Greibach, R.J.; Porter, C.E.

A computer prograra is described which generates random matrices, diagonalizes them and sorts appropriately the resulting eigenvalues and eigenvector components. FAP and FORTRAN listings for the IBM 7090 computer are included. (auth)

Redistribution of Sr and rare earth elements in the matrices of CV3 carbonaceous chondrites during aqueous alteration in their parent body

NASA Astrophysics Data System (ADS)

Jogo, Kaori; Ito, Motoo; Nakamura, Tomoki; Kobayashi, Sachio; Lee, Jong Ik

2018-03-01

We measured the abundances of Sr and rare earth elements (REEs) in the matrices of five CV3 carbonaceous chondrites: Meteorite Hills (MET) 00430, MET 01070, La Paz ice field (LAP) 02206, Asuka (A) 881317 and Roberts Massif (RBT) 04143. In the MET 00430 and MET 01074 matrices, the Sr/CI and light REE (LREE, La-Nd)/CI ratios positively correlate with the amounts of Ca-rich secondary minerals, which formed during aqueous alteration in the CV3 chondrite parent body. In contrast, in the LAP 02206 and RBT 04143 matrices, although the Sr/CI ratios correlate with the amounts of Ca-rich secondary minerals, the LREE/CI ratios vary independently from the amounts of any secondary minerals. This suggests that the LREE/CI ratios in these matrices were produced prior to the parent body alteration, probably in the solar nebula. The LREE/CI ratios of the LAP 02206 and RBT 04143 matrices reveal the mixing process of matrix minerals prior to the accretion of the CV3 chondrite parent body. The mixing degrees of matrix minerals might be different between these two matrices. Because solid materials would be mixed over time according to the radial diffusion model of a turbulent disk, the matrix minerals consisting of LAP 02206 and RBT 04143 matrices might be incorporated into their parent body with different timing.

The Correlated Jacobi and the Correlated Cauchy-Lorentz Ensembles

NASA Astrophysics Data System (ADS)

Wirtz, Tim; Waltner, Daniel; Kieburg, Mario; Kumar, Santosh

2016-01-01

We calculate the k-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for k=1 to derive a closed-form expression for the eigenvalue density. For real matrices we obtain the density in terms of a twofold integral that we evaluate numerically. For both expressions we find agreement when comparing with Monte Carlo simulations. Relations between these quantities for the Jacobi and the Cauchy-Lorentz ensemble are derived.

Computationally Efficient 2D DOA Estimation with Uniform Rectangular Array in Low-Grazing Angle.

PubMed

Shi, Junpeng; Hu, Guoping; Zhang, Xiaofei; Sun, Fenggang; Xiao, Yu

2017-02-26

In this paper, we propose a computationally efficient spatial differencing matrix set (SDMS) method for two-dimensional direction of arrival (2D DOA) estimation with uniform rectangular arrays (URAs) in a low-grazing angle (LGA) condition. By rearranging the auto-correlation and cross-correlation matrices in turn among different subarrays, the SDMS method can estimate the two parameters independently with one-dimensional (1D) subspace-based estimation techniques, where we only perform difference for auto-correlation matrices and the cross-correlation matrices are kept completely. Then, the pair-matching of two parameters is achieved by extracting the diagonal elements of URA. Thus, the proposed method can decrease the computational complexity, suppress the effect of additive noise and also have little information loss. Simulation results show that, in LGA, compared to other methods, the proposed methods can achieve performance improvement in the white or colored noise conditions.

Computationally Efficient 2D DOA Estimation with Uniform Rectangular Array in Low-Grazing Angle

PubMed Central

Shi, Junpeng; Hu, Guoping; Zhang, Xiaofei; Sun, Fenggang; Xiao, Yu

2017-01-01

In this paper, we propose a computationally efficient spatial differencing matrix set (SDMS) method for two-dimensional direction of arrival (2D DOA) estimation with uniform rectangular arrays (URAs) in a low-grazing angle (LGA) condition. By rearranging the auto-correlation and cross-correlation matrices in turn among different subarrays, the SDMS method can estimate the two parameters independently with one-dimensional (1D) subspace-based estimation techniques, where we only perform difference for auto-correlation matrices and the cross-correlation matrices are kept completely. Then, the pair-matching of two parameters is achieved by extracting the diagonal elements of URA. Thus, the proposed method can decrease the computational complexity, suppress the effect of additive noise and also have little information loss. Simulation results show that, in LGA, compared to other methods, the proposed methods can achieve performance improvement in the white or colored noise conditions. PMID:28245634

On-Chip Neural Data Compression Based On Compressed Sensing With Sparse Sensing Matrices.

PubMed

Zhao, Wenfeng; Sun, Biao; Wu, Tong; Yang, Zhi

2018-02-01

On-chip neural data compression is an enabling technique for wireless neural interfaces that suffer from insufficient bandwidth and power budgets to transmit the raw data. The data compression algorithm and its implementation should be power and area efficient and functionally reliable over different datasets. Compressed sensing is an emerging technique that has been applied to compress various neurophysiological data. However, the state-of-the-art compressed sensing (CS) encoders leverage random but dense binary measurement matrices, which incur substantial implementation costs on both power and area that could offset the benefits from the reduced wireless data rate. In this paper, we propose two CS encoder designs based on sparse measurement matrices that could lead to efficient hardware implementation. Specifically, two different approaches for the construction of sparse measurement matrices, i.e., the deterministic quasi-cyclic array code (QCAC) matrix and -sparse random binary matrix [-SRBM] are exploited. We demonstrate that the proposed CS encoders lead to comparable recovery performance. And efficient VLSI architecture designs are proposed for QCAC-CS and -SRBM encoders with reduced area and total power consumption.

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

PubMed

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

2009-04-01

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

Covariances for the 56Fe radiation damage cross sections

NASA Astrophysics Data System (ADS)

Simakov, Stanislav P.; Koning, Arjan; Konobeyev, Alexander Yu.

2017-09-01

The energy-energy and reaction-reaction covariance matrices were calculated for the n + 56Fe damage cross-sections by Total Monte Carlo method using the TENDL-2013 random files. They were represented in the ENDF-6 format and added to the unperturbed evaluation file. The uncertainties for the spectrum averaged radiation quantities in the representative fission, fusion and spallation facilities were first time assessed as 5-25%. Additional 5 to 20% have to be added to the atom displacement rate uncertainties to account for accuracy of the primary defects simulation in materials. The reaction-reaction correlation were shown to be 1% or less.

Twistor-strings and gravity tree amplitudes

NASA Astrophysics Data System (ADS)

Adamo, Tim; Mason, Lionel

2013-04-01

Recently we discussed how Einstein supergravity tree amplitudes might be obtained from the original Witten and Berkovits twistor-string theory when external conformal gravitons are restricted to be Einstein gravitons. Here we obtain a more systematic understanding of the relationship between conformal and Einstein gravity amplitudes in that twistor-string theory. We show that although it does not in general yield Einstein amplitudes, we can nevertheless obtain some partial twistor-string interpretation of the remarkable formulae recently been found by Hodges and generalized to all tree amplitudes by Cachazo and Skinner. The Hodges matrix and its higher degree generalizations encode the world sheet correlators of the twistor string. These matrices control both Einstein amplitudes and those of the conformal gravity arising from the Witten and Berkovits twistor-string. Amplitudes in the latter case arise from products of the diagonal elements of the generalized Hodges matrices and reduced determinants give the former. The reduced determinants arise if the contractions in the worldsheet correlator are restricted to form connected trees at MHV. The (generalized) Hodges matrices arise as weighted Laplacian matrices for the graph of possible contractions in the correlators and the reduced determinants of these weighted Laplacian matrices give the sum of the connected tree contributions by an extension of the matrix-tree theorem.

Network trending; leadership, followership and neutrality among companies: A random matrix approach

NASA Astrophysics Data System (ADS)

Mobarhan, N. S. Safavi; Saeedi, A.; Roodposhti, F. Rahnamay; Jafari, G. R.

2016-11-01

In this article, we analyze the cross-correlation between returns of different stocks to answer the following important questions. The first one is: If there exists collective behavior in a financial market, how could we detect it? And the second question is: Is there a particular company among the companies of a market as the leader of the collective behavior? Or is there no specified leadership governing the system similar to some complex systems? We use the method of random matrix theory to answer the mentioned questions. Cross-correlation matrix of index returns of four different markets is analyzed. The participation ratio quantity related to each matrices' eigenvectors and the eigenvalue spectrum is calculated. We introduce shuffled-matrix created of cross correlation matrix in such a way that the elements of the later one are displaced randomly. Comparing the participation ratio quantities obtained from a correlation matrix of a market and its related shuffled-one, on the bulk distribution region of the eigenvalues, we detect a meaningful deviation between the mentioned quantities indicating the collective behavior of the companies forming the market. By calculating the relative deviation of participation ratios, we obtain a measure to compare the markets according to their collective behavior. Answering the second question, we show there are three groups of companies: The first group having higher impact on the market trend called leaders, the second group is followers and the third one is the companies who have not a considerable role in the trend. The results can be utilized in portfolio construction.

Quantifying economic fluctuations by adapting methods of statistical physics

NASA Astrophysics Data System (ADS)

Plerou, Vasiliki

2001-09-01

The first focus of this thesis is the investigation of cross-correlations between the price fluctuations of different stocks using the conceptual framework of random matrix theory (RMT), developed in physics to describe the statistical properties of energy-level spectra of complex nuclei. RMT makes predictions for the statistical properties of matrices that are universal, i.e., do not depend on the interactions between the elements comprising the system. In physical systems, deviations from the predictions of RMT provide clues regarding the mechanisms controlling the dynamics of a given system so this framework is of potential value if applied to economic systems. This thesis compares the statistics of cross-correlation matrix C-whose elements Cij are the correlation coefficients of price fluctuations of stock i and j-against the ``null hypothesis'' of a random matrix having the same symmetry properties. It is shown that comparison of the eigenvalue statistics of C with RMT results can be used to distinguish random and non-random parts of C. The non-random part of C which deviates from RMT results, provides information regarding genuine cross-correlations between stocks. The interpretations and potential practical utility of these deviations are also investigated. The second focus is the characterization of the dynamics of stock price fluctuations. The statistical properties of the changes G Δt in price over a time interval Δ t are quantified and the statistical relation between G Δt and the trading activity-measured by the number of transactions NΔ t in the interval Δt is investigated. The statistical properties of the volatility, i.e., the time dependent standard deviation of price fluctuations, is related to two microscopic quantities: NΔt and the variance W2Dt of the price changes for all transactions in the interval Δ t. In addition, the statistical relationship between G Δt and the number of shares QΔt traded in Δ t is investigated.

On the Assessment of Psychometric Adequacy in Correlation Matrices.

ERIC Educational Resources Information Center

Dziuban, Charles D.; Shirkey, Edwin C.

Three techniques for assessing the adequacy of correlation matrices for factor analysis were applied to four examples from the literature. The methods compared were: (1) inspection of the off diagonal elements of the anti-image covariance matrix S(to the 2nd) R(to the -1) and S(to the 2nd); (2) the Measure of Sampling Adequacy (M.S.A.), and (3)…

Optical image encryption using triplet of functions

NASA Astrophysics Data System (ADS)

Yatish; Fatima, Areeba; Nishchal, Naveen Kumar

2018-03-01

We propose an image encryption scheme that brings into play a technique using a triplet of functions to manipulate complex-valued functions. Optical cryptosystems using this method are an easier approach toward the ciphertext generation that avoids the use of holographic setup to record phase. The features of this method were shown in the context of double random phase encoding and phase-truncated Fourier transform-based cryptosystems using gyrator transform. In the first step, the complex function is split into two matrices. These matrices are separated, so they contain the real and imaginary parts. In the next step, these two matrices and a random distribution function are acted upon by one of the functions in the triplet. During decryption, the other two functions in the triplet help us retrieve the complex-valued function. The simulation results demonstrate the effectiveness of the proposed idea. To check the robustness of the proposed scheme, attack analyses were carried out.

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

NASA Astrophysics Data System (ADS)

Stolz, Michael

2018-02-01

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

Quantum Discord for d⊗2 Systems

PubMed Central

Ma, Zhihao; Chen, Zhihua; Fanchini, Felipe Fernandes; Fei, Shao-Ming

2015-01-01

We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary system when the second subsystem is measured. We show that the optimal measurements used in the maximization of the classical correlation in terms of linear entropy, when used to calculate the quantum discord in terms of von Neumann entropy, result in a tight upper bound for arbitrary systems. This bound agrees with all known analytical results about quantum discord in terms of von Neumann entropy and, when comparing it with the numerical results for 106 two-qubit random density matrices, we obtain an average deviation of order 10−4. Furthermore, our results give a way to calculate the quantum discord for arbitrary n-qubit GHZ and W states evolving under the action of the amplitude damping noisy channel. PMID:26036771

Analysis on Vertical Scattering Signatures in Forestry with PolInSAR

NASA Astrophysics Data System (ADS)

Guo, Shenglong; Li, Yang; Zhang, Jingjing; Hong, Wen

2014-11-01

We apply accurate topographic phase to the Freeman-Durden decomposition for polarimetric SAR interferometry (PolInSAR) data. The cross correlation matrix obtained from PolInSAR observations can be decomposed into three scattering mechanisms matrices accounting for the odd-bounce, double-bounce and volume scattering. We estimate the phase based on the Random volume over Ground (RVoG) model, and as the initial input parameter of the numerical method which is used to solve the parameters of decomposition. In addition, the modified volume scattering model introduced by Y. Yamaguchi is applied to the PolInSAR target decomposition in forest areas rather than the pure random volume scattering as proposed by Freeman-Durden to make best fit to the actual measured data. This method can accurately retrieve the magnitude associated with each mechanism and their vertical location along the vertical dimension. We test the algorithms with L- and P- band simulated data.

BCH codes for large IC random-access memory systems

NASA Technical Reports Server (NTRS)

Lin, S.; Costello, D. J., Jr.

1983-01-01

In this report some shortened BCH codes for possible applications to large IC random-access memory systems are presented. These codes are given by their parity-check matrices. Encoding and decoding of these codes are discussed.

Large leptonic Dirac CP phase from broken democracy with random perturbations

NASA Astrophysics Data System (ADS)

Ge, Shao-Feng; Kusenko, Alexander; Yanagida, Tsutomu T.

2018-06-01

A large value of the leptonic Dirac CP phase can arise from broken democracy, where the mass matrices are democratic up to small random perturbations. Such perturbations are a natural consequence of broken residual S3 symmetries that dictate the democratic mass matrices at leading order. With random perturbations, the leptonic Dirac CP phase has a higher probability to attain a value around ± π / 2. Comparing with the anarchy model, broken democracy can benefit from residual S3 symmetries, and it can produce much better, realistic predictions for the mass hierarchy, mixing angles, and Dirac CP phase in both quark and lepton sectors. Our approach provides a general framework for a class of models in which a residual symmetry determines the general features at leading order, and where, in the absence of other fundamental principles, the symmetry breaking appears in the form of random perturbations.

Hurwitz numbers and products of random matrices

NASA Astrophysics Data System (ADS)

Orlov, A. Yu.

2017-09-01

We study multimatrix models, which may be viewed as integrals of products of tau functions depending on the eigenvalues of products of random matrices. We consider tau functions of the two-component Kadomtsev-Petviashvili (KP) hierarchy (semi-infinite relativistic Toda lattice) and of the B-type KP (BKP) hierarchy introduced by Kac and van de Leur. Such integrals are sometimes tau functions themselves. We consider models that generate Hurwitz numbers HE,F, where E is the Euler characteristic of the base surface and F is the number of branch points. We show that in the case where the integrands contain the product of n > 2 matrices, the integral generates Hurwitz numbers with E ≤ 2 and F ≤ n+2. Both the numbers E and F depend both on n and on the order of the factors in the matrix product. The Euler characteristic E can be either an even or an odd number, i.e., it can match both orientable and nonorientable (Klein) base surfaces depending on the presence of the tau function of the BKP hierarchy in the integrand. We study two cases, the products of complex and the products of unitary matrices.

Empirical Bayes method for reducing false discovery rates of correlation matrices with block diagonal structure.

PubMed

Pacini, Clare; Ajioka, James W; Micklem, Gos

2017-04-12

Correlation matrices are important in inferring relationships and networks between regulatory or signalling elements in biological systems. With currently available technology sample sizes for experiments are typically small, meaning that these correlations can be difficult to estimate. At a genome-wide scale estimation of correlation matrices can also be computationally demanding. We develop an empirical Bayes approach to improve covariance estimates for gene expression, where we assume the covariance matrix takes a block diagonal form. Our method shows lower false discovery rates than existing methods on simulated data. Applied to a real data set from Bacillus subtilis we demonstrate it's ability to detecting known regulatory units and interactions between them. We demonstrate that, compared to existing methods, our method is able to find significant covariances and also to control false discovery rates, even when the sample size is small (n=10). The method can be used to find potential regulatory networks, and it may also be used as a pre-processing step for methods that calculate, for example, partial correlations, so enabling the inference of the causal and hierarchical structure of the networks.

Resampling-based Methods in Single and Multiple Testing for Equality of Covariance/Correlation Matrices

PubMed Central

Yang, Yang; DeGruttola, Victor

2016-01-01

Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by group sample means and standardized by group sample covariance matrices. This approach, however, has been observed to inflate type I error when sample size is small or data are generated from heavy-tailed distributions. We propose to improve this approach by using robust estimation for the first and second moments. We discuss two statistics: the Bartlett statistic and a statistic based on eigen-decomposition of sample covariance matrices. Both statistics can be expressed in terms of standardized errors under the null hypothesis. These methods are extended to test homogeneity in correlation matrices. Using simulation studies, we demonstrate that the robust resampling approach provides comparable or superior performance, relative to traditional approaches, for single testing and reasonable performance for multiple testing. The proposed methods are applied to data collected in an HIV vaccine trial to investigate possible determinants, including vaccine status, vaccine-induced immune response level and viral genotype, of unusual correlation pattern between HIV viral load and CD4 count in newly infected patients. PMID:22740584

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

PubMed

Yang, Yang; DeGruttola, Victor

2012-06-22

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

A new phase of disordered phonons modelled by random matrices

NASA Astrophysics Data System (ADS)

Schmittner, Sebastian; Zirnbauer, Martin

2015-03-01

Starting from the clean harmonic crystal and not invoking two-level systems, we propose a model for phonons in a disordered solid. In this model the strength of mass and spring constant disorder can be increased separately. Both types of disorder are modelled by random matrices that couple the degrees of freedom locally. Treated in coherent potential approximation (CPA), the speed of sound decreases with increasing disorder until it reaches zero at finite disorder strength. There, a critical transition to a strong disorder phase occurs. In this novel phase, we find the density of states at zero energy in three dimensions to be finite, leading to a linear temperature dependence of the heat capacity, as observed experimentally for vitreous systems. For any disorder strength, our model is stable, i.e. masses and spring constants are positive, and there are no runaway dynamics. This is ensured by using appropriate probability distributions, inspired by Wishart ensembles, for the random matrices. The CPA self-consistency equations are derived in a very accessible way using planar diagrams. The talk focuses on the model and the results. The first author acknowledges financial support by the Deutsche Telekom Stiftung.

Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

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

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed-trace ensemble fully takes into account the conservation of probability for quantum states. The present paper derives for the first time the exact analytical formula of the one-body distribution function of singular values of random complex matrices in the fixed-trace ensemble. The distribution function of singular values (i.e. Schmidt eigenvalues) of a quantum state ismore » so important since it describes characteristics of the entanglement in the state. The derivation of the exact analytical formula utilizes two recent achievements in mathematics, which appeared in 1990s. The first is the Kaneko theory that extends the famous Selberg integral by inserting a hypergeometric type weight factor into the integrand to obtain an analytical formula for the extended integral. The second is the Petkovsek-Wilf-Zeilberger theory that calculates definite hypergeometric sums in a closed form.« less

Ocean Basin Impact of Ambient Noise on Marine Mammal Detectability, Distribution, and Acoustic Communication

DTIC Science & Technology

2015-09-30

soundscapes , and unit of analysis methodology. The study has culminated in a complex analysis of all environmental factors that could be predictors of...regional soundscapes . To build the correlation matrices from ambient sound recordings, the raw data was first converted into a series of sound...sounds. To compare two different soundscape time periods, the correlation matrices for the two periods were then subtracted from each other

Complexity Characteristics of Currency Networks

NASA Astrophysics Data System (ADS)

Gorski, A. Z.; Drozdz, S.; Kwapien, J.; Oswiecimka, P.

2006-11-01

A large set of daily FOREX time series is analyzed. The corresponding correlation matrices (CM) are constructed for USD, EUR and PLN used as the base currencies. The triangle rule is interpreted as constraints reducing the number of independent returns. The CM spectrum is computed and compared with the cases of shuffled currencies and a fictitious random currency taken as a base currency. The Minimal Spanning Tree (MST) graphs are calculated and the clustering effects for strong currencies are found. It is shown that for MSTs the node rank has power like, scale free behavior. Finally, the scaling exponents are evaluated and found in the range analogous to those identified recently for various complex networks.

Maximizing synchronizability of duplex networks

NASA Astrophysics Data System (ADS)

Wei, Xiang; Emenheiser, Jeffrey; Wu, Xiaoqun; Lu, Jun-an; D'Souza, Raissa M.

2018-01-01

We study the synchronizability of duplex networks formed by two randomly generated network layers with different patterns of interlayer node connections. According to the master stability function, we use the smallest nonzero eigenvalue and the eigenratio between the largest and the second smallest eigenvalues of supra-Laplacian matrices to characterize synchronizability on various duplexes. We find that the interlayer linking weight and linking fraction have a profound impact on synchronizability of duplex networks. The increasingly large inter-layer coupling weight is found to cause either decreasing or constant synchronizability for different classes of network dynamics. In addition, negative node degree correlation across interlayer links outperforms positive degree correlation when most interlayer links are present. The reverse is true when a few interlayer links are present. The numerical results and understanding based on these representative duplex networks are illustrative and instructive for building insights into maximizing synchronizability of more realistic multiplex networks.

The performance of the Congruence Among Distance Matrices (CADM) test in phylogenetic analysis

PubMed Central

2011-01-01

Background CADM is a statistical test used to estimate the level of Congruence Among Distance Matrices. It has been shown in previous studies to have a correct rate of type I error and good power when applied to dissimilarity matrices and to ultrametric distance matrices. Contrary to most other tests of incongruence used in phylogenetic analysis, the null hypothesis of the CADM test assumes complete incongruence of the phylogenetic trees instead of congruence. In this study, we performed computer simulations to assess the type I error rate and power of the test. It was applied to additive distance matrices representing phylogenies and to genetic distance matrices obtained from nucleotide sequences of different lengths that were simulated on randomly generated trees of varying sizes, and under different evolutionary conditions. Results Our results showed that the test has an accurate type I error rate and good power. As expected, power increased with the number of objects (i.e., taxa), the number of partially or completely congruent matrices and the level of congruence among distance matrices. Conclusions Based on our results, we suggest that CADM is an excellent candidate to test for congruence and, when present, to estimate its level in phylogenomic studies where numerous genes are analysed simultaneously. PMID:21388552

Mechanical properties and drug release of venlafaxine HCl solid mini matrices prepared by hot-melt extrusion and hot or ambient compression.

PubMed

Avgerinos, Theodoros; Kantiranis, Nikolaos; Panagopoulou, Athanasia; Malamataris, Stavros; Kachrimanis, Kyriakos; Nikolakakis, Ioannis

2018-02-01

Objective/significance: To elucidate the role of plasticizers in different mini matrices and correlate mechanical properties with drug release. Cylindrical pellets were prepared by hot-melt extrusion (HME) and mini tablets by hot (HC) and ambient compression (AC). Venlafaxine HCl was the model drug, Eudragit ® RSPO the matrix former and citric acid or Lutrol ® F127 the plasticizers. The matrices were characterized for morphology, crystallinity, and mechanical properties. The influence of plasticizer's type and content on the extrusion pressure (P e ) during HME and ejection during tableting was examined and the mechanical properties were correlated with drug release parameters. Resistance to extrusion and tablet ejection force were reduced by Lutrol ® F127 which also produced softer and weaker pellets with faster release, but harder and stronger HC tablets with slower release. HME pellets showed greater tensile strength (T) and 100 times slower release than tablets. P e correlated with T and resistance to deformation of the corresponding pellets (r 2  = 0.963 and 0.945). For both HME and HC matrices the decrease of drug release with T followed a single straight line (r 2  = 0.990) and for HME the diffusion coefficient (D e ) and retreat rate constant (k b ) decreased linearly with T (r 2  = 0.934 and 0.972). Lutrol ® F127 and citric acid are efficient plasticizers and Lutrol ® F127 is a thermal binder/lubricant in HC compression. The different bonding mechanisms of the matrices were reflected in the mechanical strength and drug release. Relationships established between T and drug release parameters for HME and HC matrices may be useful during formulation work.

Renormalized Energy Concentration in Random Matrices

NASA Astrophysics Data System (ADS)

Borodin, Alexei; Serfaty, Sylvia

2013-05-01

We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of Sandier and Serfaty (From the Ginzburg-Landau model to vortex lattice problems, 2012; 1D log-gases and the renormalized energy, 2013). Roughly speaking, it is obtained by subtracting two leading terms from the Coulomb potential on a growing number of charges. The functional is expected to be a good measure of disorder of a configuration of points. We give certain formulas for its expectation for general stationary random point processes. For the random matrix β-sine processes on the real line ( β = 1,2,4), and Ginibre point process and zeros of Gaussian analytic functions process in the plane, we compute the expectation explicitly. Moreover, we prove that for these processes the variance of the renormalized energy vanishes, which shows concentration near the expected value. We also prove that the β = 2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels.

Nonlocal torque operators in ab initio theory of the Gilbert damping in random ferromagnetic alloys

NASA Astrophysics Data System (ADS)

Turek, I.; Kudrnovský, J.; Drchal, V.

2015-12-01

We present an ab initio theory of the Gilbert damping in substitutionally disordered ferromagnetic alloys. The theory rests on introduced nonlocal torques which replace traditional local torque operators in the well-known torque-correlation formula and which can be formulated within the atomic-sphere approximation. The formalism is sketched in a simple tight-binding model and worked out in detail in the relativistic tight-binding linear muffin-tin orbital method and the coherent potential approximation (CPA). The resulting nonlocal torques are represented by nonrandom, non-site-diagonal, and spin-independent matrices, which simplifies the configuration averaging. The CPA-vertex corrections play a crucial role for the internal consistency of the theory and for its exact equivalence to other first-principles approaches based on the random local torques. This equivalence is also illustrated by the calculated Gilbert damping parameters for binary NiFe and FeCo random alloys, for pure iron with a model atomic-level disorder, and for stoichiometric FePt alloys with a varying degree of L 10 atomic long-range order.

Noisy covariance matrices and portfolio optimization

NASA Astrophysics Data System (ADS)

Pafka, S.; Kondor, I.

2002-05-01

According to recent findings [#!bouchaud!#,#!stanley!#], empirical covariance matrices deduced from financial return series contain such a high amount of noise that, apart from a few large eigenvalues and the corresponding eigenvectors, their structure can essentially be regarded as random. In [#!bouchaud!#], e.g., it is reported that about 94% of the spectrum of these matrices can be fitted by that of a random matrix drawn from an appropriately chosen ensemble. In view of the fundamental role of covariance matrices in the theory of portfolio optimization as well as in industry-wide risk management practices, we analyze the possible implications of this effect. Simulation experiments with matrices having a structure such as described in [#!bouchaud!#,#!stanley!#] lead us to the conclusion that in the context of the classical portfolio problem (minimizing the portfolio variance under linear constraints) noise has relatively little effect. To leading order the solutions are determined by the stable, large eigenvalues, and the displacement of the solution (measured in variance) due to noise is rather small: depending on the size of the portfolio and on the length of the time series, it is of the order of 5 to 15%. The picture is completely different, however, if we attempt to minimize the variance under non-linear constraints, like those that arise e.g. in the problem of margin accounts or in international capital adequacy regulation. In these problems the presence of noise leads to a serious instability and a high degree of degeneracy of the solutions.

A Generalized Method of Image Analysis from an Intercorrelation Matrix which May Be Singular.

ERIC Educational Resources Information Center

Yanai, Haruo; Mukherjee, Bishwa Nath

1987-01-01

This generalized image analysis method is applicable to singular and non-singular correlation matrices (CMs). Using the orthogonal projector and a weaker generalized inverse matrix, image and anti-image covariance matrices can be derived from a singular CM. (SLD)

Learning in the Machine: Random Backpropagation and the Deep Learning Channel.

PubMed

Baldi, Pierre; Sadowski, Peter; Lu, Zhiqin

2018-07-01

Random backpropagation (RBP) is a variant of the backpropagation algorithm for training neural networks, where the transpose of the forward matrices are replaced by fixed random matrices in the calculation of the weight updates. It is remarkable both because of its effectiveness, in spite of using random matrices to communicate error information, and because it completely removes the taxing requirement of maintaining symmetric weights in a physical neural system. To better understand random backpropagation, we first connect it to the notions of local learning and learning channels. Through this connection, we derive several alternatives to RBP, including skipped RBP (SRPB), adaptive RBP (ARBP), sparse RBP, and their combinations (e.g. ASRBP) and analyze their computational complexity. We then study their behavior through simulations using the MNIST and CIFAR-10 bechnmark datasets. These simulations show that most of these variants work robustly, almost as well as backpropagation, and that multiplication by the derivatives of the activation functions is important. As a follow-up, we study also the low-end of the number of bits required to communicate error information over the learning channel. We then provide partial intuitive explanations for some of the remarkable properties of RBP and its variations. Finally, we prove several mathematical results, including the convergence to fixed points of linear chains of arbitrary length, the convergence to fixed points of linear autoencoders with decorrelated data, the long-term existence of solutions for linear systems with a single hidden layer and convergence in special cases, and the convergence to fixed points of non-linear chains, when the derivative of the activation functions is included.

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

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

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE PAGES

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter; ...

2016-06-30

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

A comparison of SuperLU solvers on the intel MIC architecture

NASA Astrophysics Data System (ADS)

Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.

2016-10-01

In many science and engineering applications, problems may result in solving a sparse linear system AX=B. For example, SuperLU_MCDT, a linear solver, was used for the large penta-diagonal matrices for 2D problems and hepta-diagonal matrices for 3D problems, coming from the incompressible blood flow simulation (see [1]). It is important to test the status and potential improvements of state-of-the-art solvers on new technologies. In this work, sequential, multithreaded and distributed versions of SuperLU solvers (see [2]) are examined on the Intel Xeon Phi coprocessors using offload programming model at the EURORA cluster of CINECA in Italy. We consider a portfolio of test matrices containing patterned matrices from UFMM ([3]) and randomly located matrices. This architecture can benefit from high parallelism and large vectors. We find that the sequential SuperLU benefited up to 45 % performance improvement from the offload programming depending on the sparse matrix type and the size of transferred and processed data.

SMERFS: Stochastic Markov Evaluation of Random Fields on the Sphere

NASA Astrophysics Data System (ADS)

Creasey, Peter; Lang, Annika

2018-04-01

SMERFS (Stochastic Markov Evaluation of Random Fields on the Sphere) creates large realizations of random fields on the sphere. It uses a fast algorithm based on Markov properties and fast Fourier Transforms in 1d that generates samples on an n X n grid in O(n2 log n) and efficiently derives the necessary conditional covariance matrices.

Random matrices and the New York City subway system

NASA Astrophysics Data System (ADS)

Jagannath, Aukosh; Trogdon, Thomas

2017-09-01

We analyze subway arrival times in the New York City subway system. We find regimes where the gaps between trains are well modeled by (unitarily invariant) random matrix statistics and Poisson statistics. The departure from random matrix statistics is captured by the value of the Coulomb potential along the subway route. This departure becomes more pronounced as trains make more stops.

Estimated correlation matrices and portfolio optimization

NASA Astrophysics Data System (ADS)

Pafka, Szilárd; Kondor, Imre

2004-11-01

Correlations of returns on various assets play a central role in financial theory and also in many practical applications. From a theoretical point of view, the main interest lies in the proper description of the structure and dynamics of correlations, whereas for the practitioner the emphasis is on the ability of the models to provide adequate inputs for the numerous portfolio and risk management procedures used in the financial industry. The theory of portfolios, initiated by Markowitz, has suffered from the “curse of dimensions” from the very outset. Over the past decades a large number of different techniques have been developed to tackle this problem and reduce the effective dimension of large bank portfolios, but the efficiency and reliability of these procedures are extremely hard to assess or compare. In this paper, we propose a model (simulation)-based approach which can be used for the systematical testing of all these dimensional reduction techniques. To illustrate the usefulness of our framework, we develop several toy models that display some of the main characteristic features of empirical correlations and generate artificial time series from them. Then, we regard these time series as empirical data and reconstruct the corresponding correlation matrices which will inevitably contain a certain amount of noise, due to the finiteness of the time series. Next, we apply several correlation matrix estimators and dimension reduction techniques introduced in the literature and/or applied in practice. As in our artificial world the only source of error is the finite length of the time series and, in addition, the “true” model, hence also the “true” correlation matrix, are precisely known, therefore in sharp contrast with empirical studies, we can precisely compare the performance of the various noise reduction techniques. One of our recurrent observations is that the recently introduced filtering technique based on random matrix theory performs consistently well in all the investigated cases. Based on this experience, we believe that our simulation-based approach can also be useful for the systematic investigation of several related problems of current interest in finance.

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

Forrester, Peter J., E-mail: p.forrester@ms.unimelb.edu.au; Thompson, Colin J.

The Golden-Thompson inequality, Tr (e{sup A+B}) ⩽ Tr (e{sup A}e{sup B}) for A, B Hermitian matrices, appeared in independent works by Golden and Thompson published in 1965. Both of these were motivated by considerations in statistical mechanics. In recent years the Golden-Thompson inequality has found applications to random matrix theory. In this article, we detail some historical aspects relating to Thompson's work, giving in particular a hitherto unpublished proof due to Dyson, and correspondence with Pólya. We show too how the 2 × 2 case relates to hyperbolic geometry, and how the original inequality holds true with the trace operation replaced bymore » any unitarily invariant norm. In relation to the random matrix applications, we review its use in the derivation of concentration type lemmas for sums of random matrices due to Ahlswede-Winter, and Oliveira, generalizing various classical results.« less

Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions

NASA Astrophysics Data System (ADS)

BoŻek, Piotr

2018-03-01

The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb + Pb collisions at √{sN N}=2760 GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of v22 and v4, of v2v3 and v5, or of v23,v33 , and v6. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.

Using Symbolic-Logic Matrices To Improve Confirmatory Factor Analysis Techniques.

ERIC Educational Resources Information Center

Creighton, Theodore B.; Coleman, Donald G.; Adams, R. C.

A continuing and vexing problem associated with survey instrument development is the creation of items, initially, that correlate favorably a posteriori with constructs being measured. This study tests the use of symbolic-logic matrices developed by D. G. Coleman (1979) in creating factorially "pure" statistically discrete constructs in…

Simulating Non-Fickian Transport across Péclet Regimes by doing Lévy Flights in the Rank Space of Velocity

NASA Astrophysics Data System (ADS)

Most, S.; Dentz, M.; Bolster, D.; Bijeljic, B.; Nowak, W.

2017-12-01

Transport in real porous media shows non-Fickian characteristics. In the Lagrangian perspective this leads to skewed distributions of particle arrival times. The skewness is triggered by particles' memory of velocity that persists over a characteristic length. Capturing process memory is essential to represent non-Fickianity thoroughly. Classical non-Fickian models (e.g., CTRW models) simulate the effects of memory but not the mechanisms leading to process memory. CTRWs have been applied successfully in many studies but nonetheless they have drawbacks. In classical CTRWs each particle makes a spatial transition for which each particle adapts a random transit time. Consecutive transit times are drawn independently from each other, and this is only valid for sufficiently large spatial transitions. If we want to apply a finer numerical resolution than that, we have to implement memory into the simulation. Recent CTRW methods use transitions matrices to simulate correlated transit times. However, deriving such transition matrices require transport data of a fine-scale transport simulation, and the obtained transition matrix is solely valid for this single Péclet regime. The CTRW method we propose overcomes all three drawbacks: 1) We simulate transport without restrictions in transition length. 2) We parameterize our CTRW without requiring a transport simulation. 3) Our parameterization scales across Péclet regimes. We do so by sampling the pore-scale velocity distribution to generate correlated transit times as a Lévy flight on the CDF-axis of velocities with reflection at 0 and 1. The Lévy flight is parametrized only by the correlation length. We explicitly model memory including the evolution and decay of non-Fickianity, so it extends from local via pre-asymptotic to asymptotic scales.

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

Galavis, P; Friedman, K; Chandarana, H

Purpose: Radiomics involves the extraction of texture features from different imaging modalities with the purpose of developing models to predict patient treatment outcomes. The purpose of this study is to investigate texture feature reproducibility across [18F]FDG PET/CT and [18F]FDG PET/MR imaging in patients with primary malignancies. Methods: Twenty five prospective patients with solid tumors underwent clinical [18F]FDG PET/CT scan followed by [18F]FDG PET/MR scans. In all patients the lesions were identified using nuclear medicine reports. The images were co-registered and segmented using an in-house auto-segmentation method. Fifty features, based on the intensity histogram, second and high order matrices, were extractedmore » from the segmented regions from both image data sets. One-way random-effects ANOVA model of the intra-class correlation coefficient (ICC) was used to establish texture feature correlations between both data sets. Results: Fifty features were classified based on their ICC values, which were found in the range from 0.1 to 0.86, in three categories: high, intermediate, and low. Ten features extracted from second and high-order matrices showed large ICC ≥ 0.70. Seventeen features presented intermediate 0.5 ≤ ICC ≤ 0.65 and the remaining twenty three presented low ICC ≤ 0.45. Conclusion: Features with large ICC values could be reliable candidates for quantification as they lead to similar results from both imaging modalities. Features with small ICC indicates a lack of correlation. Therefore, the use of these features as a quantitative measure will lead to different assessments of the same lesion depending on the imaging modality from where they are extracted. This study shows the importance of the need for further investigation and standardization of features across multiple imaging modalities.« less

Separable decompositions of bipartite mixed states

NASA Astrophysics Data System (ADS)

Li, Jun-Li; Qiao, Cong-Feng

2018-04-01

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8:1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then, we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.

Assessing Multivariate Constraints to Evolution across Ten Long-Term Avian Studies

PubMed Central

Teplitsky, Celine; Tarka, Maja; Møller, Anders P.; Nakagawa, Shinichi; Balbontín, Javier; Burke, Terry A.; Doutrelant, Claire; Gregoire, Arnaud; Hansson, Bengt; Hasselquist, Dennis; Gustafsson, Lars; de Lope, Florentino; Marzal, Alfonso; Mills, James A.; Wheelwright, Nathaniel T.; Yarrall, John W.; Charmantier, Anne

2014-01-01

Background In a rapidly changing world, it is of fundamental importance to understand processes constraining or facilitating adaptation through microevolution. As different traits of an organism covary, genetic correlations are expected to affect evolutionary trajectories. However, only limited empirical data are available. Methodology/Principal Findings We investigate the extent to which multivariate constraints affect the rate of adaptation, focusing on four morphological traits often shown to harbour large amounts of genetic variance and considered to be subject to limited evolutionary constraints. Our data set includes unique long-term data for seven bird species and a total of 10 populations. We estimate population-specific matrices of genetic correlations and multivariate selection coefficients to predict evolutionary responses to selection. Using Bayesian methods that facilitate the propagation of errors in estimates, we compare (1) the rate of adaptation based on predicted response to selection when including genetic correlations with predictions from models where these genetic correlations were set to zero and (2) the multivariate evolvability in the direction of current selection to the average evolvability in random directions of the phenotypic space. We show that genetic correlations on average decrease the predicted rate of adaptation by 28%. Multivariate evolvability in the direction of current selection was systematically lower than average evolvability in random directions of space. These significant reductions in the rate of adaptation and reduced evolvability were due to a general nonalignment of selection and genetic variance, notably orthogonality of directional selection with the size axis along which most (60%) of the genetic variance is found. Conclusions These results suggest that genetic correlations can impose significant constraints on the evolution of avian morphology in wild populations. This could have important impacts on evolutionary dynamics and hence population persistence in the face of rapid environmental change. PMID:24608111

Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes.

PubMed

Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Xu, Richard Yi Da; Luo, Xiangfeng

2018-05-01

Sparse nonnegative matrix factorization (SNMF) aims to factorize a data matrix into two optimized nonnegative sparse factor matrices, which could benefit many tasks, such as document-word co-clustering. However, the traditional SNMF typically assumes the number of latent factors (i.e., dimensionality of the factor matrices) to be fixed. This assumption makes it inflexible in practice. In this paper, we propose a doubly sparse nonparametric NMF framework to mitigate this issue by using dependent Indian buffet processes (dIBP). We apply a correlation function for the generation of two stick weights associated with each column pair of factor matrices while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two factor matrices will be columnwise correlated. Under this framework, two classes of correlation function are proposed: 1) using bivariate Beta distribution and 2) using Copula function. Compared with the single IBP-based NMF, this paper jointly makes two factor matrices nonparametric and sparse, which could be applied to broader scenarios, such as co-clustering. This paper is seen to be much more flexible than Gaussian process-based and hierarchial Beta process-based dIBPs in terms of allowing the two corresponding binary matrix columns to have greater variations in their nonzero entries. Our experiments on synthetic data show the merits of this paper compared with the state-of-the-art models in respect of factorization efficiency, sparsity, and flexibility. Experiments on real-world data sets demonstrate the efficiency of this paper in document-word co-clustering tasks.

Measuring multivariate association and beyond

PubMed Central

Josse, Julie; Holmes, Susan

2017-01-01

Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based coefficients are being used by different research communities. Scientists use these coefficients to test whether two random vectors are linked. Once it has been ascertained that there is such association through testing, then a next step, often ignored, is to explore and uncover the association’s underlying patterns. This article provides a survey of various measures of dependence between random vectors and tests of independence and emphasizes the connections and differences between the various approaches. After providing definitions of the coefficients and associated tests, we present the recent improvements that enhance their statistical properties and ease of interpretation. We summarize multi-table approaches and provide scenarii where the indices can provide useful summaries of heterogeneous multi-block data. We illustrate these different strategies on several examples of real data and suggest directions for future research. PMID:29081877

A Note on Parameters of Random Substitutions by γ-Diagonal Matrices

NASA Astrophysics Data System (ADS)

Kang, Ju-Sung

Random substitutions are very useful and practical method for privacy-preserving schemes. In this paper we obtain the exact relationship between the estimation errors and three parameters used in the random substitutions, namely the privacy assurance metric γ, the total number n of data records, and the size N of transition matrix. We also demonstrate some simulations concerning the theoretical result.

Key-Generation Algorithms for Linear Piece In Hand Matrix Method

NASA Astrophysics Data System (ADS)

Tadaki, Kohtaro; Tsujii, Shigeo

The linear Piece In Hand (PH, for short) matrix method with random variables was proposed in our former work. It is a general prescription which can be applicable to any type of multivariate public-key cryptosystems for the purpose of enhancing their security. Actually, we showed, in an experimental manner, that the linear PH matrix method with random variables can certainly enhance the security of HFE against the Gröbner basis attack, where HFE is one of the major variants of multivariate public-key cryptosystems. In 1998 Patarin, Goubin, and Courtois introduced the plus method as a general prescription which aims to enhance the security of any given MPKC, just like the linear PH matrix method with random variables. In this paper we prove the equivalence between the plus method and the primitive linear PH matrix method, which is introduced by our previous work to explain the notion of the PH matrix method in general in an illustrative manner and not for a practical use to enhance the security of any given MPKC. Based on this equivalence, we show that the linear PH matrix method with random variables has the substantial advantage over the plus method with respect to the security enhancement. In the linear PH matrix method with random variables, the three matrices, including the PH matrix, play a central role in the secret-key and public-key. In this paper, we clarify how to generate these matrices and thus present two probabilistic polynomial-time algorithms to generate these matrices. In particular, the second one has a concise form, and is obtained as a byproduct of the proof of the equivalence between the plus method and the primitive linear PH matrix method.

A Comparison of Distribution Free and Non-Distribution Free Factor Analysis Methods

ERIC Educational Resources Information Center

Ritter, Nicola L.

2012-01-01

Many researchers recognize that factor analysis can be conducted on both correlation matrices and variance-covariance matrices. Although most researchers extract factors from non-distribution free or parametric methods, researchers can also extract factors from distribution free or non-parametric methods. The nature of the data dictates the method…

Quantum Crystallography: Density Matrix-Density Functional Theory and the X-Ray Diffraction Experiment

NASA Astrophysics Data System (ADS)

Soirat, Arnaud J. A.

Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine the unknown HK functional, associated with the theorem of Hohenberg and Kohn. The latter is provided by the calculation of helium correlation energy, where we test approximating the second-order density function by the leading term of its McLaurin's series expansion.

Novel value-added uses for sweet potato juice and flour in polyphenol- and protein-enriched functional food ingredients.

PubMed

Grace, Mary H; Truong, An N; Truong, Van-Den; Raskin, Ilya; Lila, Mary Ann

2015-09-01

Blackcurrant, blueberry, and muscadine grape juices were efficiently sorbed, concentrated, and stabilized into dry granular ingredient matrices which combined anti-inflammatory and antioxidant fruit polyphenols with sweet potato functional constituents (carotenoids, vitamins, polyphenols, fibers). Total phenolics were highest in blackcurrant-orange sweet potato ingredient matrices (34.03 mg/g), and lowest in muscadine grape-yellow sweet potato matrices (10.56 mg/g). Similarly, anthocyanins were most concentrated in blackcurrant-fortified orange and yellow sweet potato matrices (5.40 and 6.54 mg/g, respectively). Alternatively, other protein-rich edible matrices (defatted soy flour, light roasted peanut flour, and rice protein concentrate) efficiently captured polyphenols (6.09-9.46 mg/g) and anthocyanins (0.77-1.27 mg/g) from purple-fleshed sweet potato juice, with comparable efficiency. Antioxidant activity correlated well with total phenolic content. All formulated ingredient matrices stabilized and preserved polyphenols for up to 24 weeks, even when stored at 37°C. Complexation with juice-derived polyphenols did not significantly alter protein or carbohydrate profiles of the matrices. Sensory evaluation of the ingredient matrices suggested potential uses for a wide range of functional food products.

State-Space System Realization with Input- and Output-Data Correlation

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan

1997-01-01

This paper introduces a general version of the information matrix consisting of the autocorrelation and cross-correlation matrices of the shifted input and output data. Based on the concept of data correlation, a new system realization algorithm is developed to create a model directly from input and output data. The algorithm starts by computing a special type of correlation matrix derived from the information matrix. The special correlation matrix provides information on the system-observability matrix and the state-vector correlation. A system model is then developed from the observability matrix in conjunction with other algebraic manipulations. This approach leads to several different algorithms for computing system matrices for use in representing the system model. The relationship of the new algorithms with other realization algorithms in the time and frequency domains is established with matrix factorization of the information matrix. Several examples are given to illustrate the validity and usefulness of these new algorithms.

Sector Identification in a Set of Stock Return Time Series Traded at the London Stock Exchange

NASA Astrophysics Data System (ADS)

Coronnello, C.; Tumminello, M.; Lillo, F.; Micciche, S.; Mantegna, R. N.

2005-09-01

We compare some methods recently used in the literature to detect the existence of a certain degree of common behavior of stock returns belonging to the same economic sector. Specifically, we discuss methods based on random matrix theory and hierarchical clustering techniques. We apply these methods to a portfolio of stocks traded at the London Stock Exchange. The investigated time series are recorded both at a daily time horizon and at a 5-minute time horizon. The correlation coefficient matrix is very different at different time horizons confirming that more structured correlation coefficient matrices are observed for long time horizons. All the considered methods are able to detect economic information and the presence of clusters characterized by the economic sector of stocks. However, different methods present a different degree of sensitivity with respect to different sectors. Our comparative analysis suggests that the application of just a single method could not be able to extract all the economic information present in the correlation coefficient matrix of a stock portfolio.

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

PubMed Central

Westgate, Philip M.

2016-01-01

When generalized estimating equations (GEE) incorporate an unstructured working correlation matrix, the variances of regression parameter estimates can inflate due to the estimation of the correlation parameters. In previous work, an approximation for this inflation that results in a corrected version of the sandwich formula for the covariance matrix of regression parameter estimates was derived. Use of this correction for correlation structure selection also reduces the over-selection of the unstructured working correlation matrix. In this manuscript, we conduct a simulation study to demonstrate that an increase in variances of regression parameter estimates can occur when GEE incorporates structured working correlation matrices as well. Correspondingly, we show the ability of the corrected version of the sandwich formula to improve the validity of inference and correlation structure selection. We also study the relative influences of two popular corrections to a different source of bias in the empirical sandwich covariance estimator. PMID:27818539

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

PubMed

Westgate, Philip M

2016-01-01

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

Estimation of regionalized compositions: A comparison of three methods

USGS Publications Warehouse

Pawlowsky, V.; Olea, R.A.; Davis, J.C.

1995-01-01

A regionalized composition is a random vector function whose components are positive and sum to a constant at every point of the sampling region. Consequently, the components of a regionalized composition are necessarily spatially correlated. This spatial dependence-induced by the constant sum constraint-is a spurious spatial correlation and may lead to misinterpretations of statistical analyses. Furthermore, the cross-covariance matrices of the regionalized composition are singular, as is the coefficient matrix of the cokriging system of equations. Three methods of performing estimation or prediction of a regionalized composition at unsampled points are discussed: (1) the direct approach of estimating each variable separately; (2) the basis method, which is applicable only when a random function is available that can he regarded as the size of the regionalized composition under study; (3) the logratio approach, using the additive-log-ratio transformation proposed by J. Aitchison, which allows statistical analysis of compositional data. We present a brief theoretical review of these three methods and compare them using compositional data from the Lyons West Oil Field in Kansas (USA). It is shown that, although there are no important numerical differences, the direct approach leads to invalid results, whereas the basis method and the additive-log-ratio approach are comparable. ?? 1995 International Association for Mathematical Geology.

A 10-minute measure of global cognition: Validation of the Brief Cognitive Assessment Tool for Schizophrenia (B-CATS).

PubMed

Hurford, Irene M; Ventura, Joseph; Marder, Stephen R; Reise, Steven P; Bilder, Robert M

2018-05-01

Schizophrenia is marked by a global cognitive impairment that contributes significantly to chronic disability and unemployment. As new treatments are developed for cognition in schizophrenia, clinicians require easily administered instruments to assess cognition. We previously developed a very brief cognitive battery (Bell et al., 2005). The Brief Cognitive Assessment Tool for Schizophrenia (B-CATS) was developed specifically to provide clinicians with a way to assess cognition in their patients with schizophrenia. Here, we report the results of a validity study comparing B-CATS to a larger neurocognitive battery, the Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) battery. Outpatients with schizophrenia (N=91) were administered the B-CATS and the non-overlapping tests of the MATRICS battery at two time points separated by 1month. They were also administered the UCSD Performance-based Skills Assessment-Brief (UPSA-B), a measure of functional capacity. The B-CATS has an administration time of approximately 10min. It demonstrates good test-retest reliability and internal consistency. It correlates 0.76 (p<0.01) with the MATRICS battery. The shorter B-CATS and the MATRICS battery correlate with the UPSA-B at 0.50 and 0.58 respectively. A 10-minute version of the B-CATS correlates highly with the "gold standard" neurocognitive battery that has an administration time of over 60min. Both measures correlate moderately with a measure of functional capacity. This brief battery was designed to allow clinicians to monitor cognitive change and better inform treatment decisions. Copyright © 2017 Elsevier B.V. All rights reserved.

Improving comprehension in adolescents with severe receptive language impairments: a randomized control trial of intervention for coordinating conjunctions.

PubMed

Ebbels, Susan H; Marić, Nataša; Murphy, Aoife; Turner, Gail

2014-01-01

Little evidence exists for the effectiveness of therapy for children with receptive language difficulties, particularly those whose difficulties are severe and persistent. To establish the effectiveness of explicit speech and language therapy with visual support for secondary school-aged children with language impairments focusing on comprehension of coordinating conjunctions in a randomized control trial with an assessor blind to group status. Fourteen participants (aged 11;3-16;1) with severe RELI (mean standard scores: CELF4 ELS = 48, CELF4 RLS = 53 and TROG-2 = 57), but higher non-verbal (Matrices = 83) and visual perceptual skills (Test of Visual Perceptual Skills (TVPS) = 86) were randomly assigned to two groups: therapy versus waiting controls. In Phase 1, the therapy group received eight 30-min individual sessions of explicit teaching with visual support (Shape Coding) with their usual SLT. In Phase 2, the waiting controls received the same therapy. The participants' comprehension was tested pre-, post-Phase 1 and post-Phase 2 therapy on (1) a specific test of the targeted conjunctions, (2) the TROG-2 and (3) a test of passives. After Phase 1, the therapy group showed significantly more progress than the waiting controls on the targeted conjunctions (d = 1.6) and overall TROG-2 standard score (d = 1.4). The two groups did not differ on the passives test. After Phase 2, the waiting controls made similar progress to those in the original therapy group, who maintained their previous progress. Neither group showed progress on passives. When the two groups were combined, significant progress was found on the specific conjunctions (d = 1.3) and TROG-2 raw (d = 1.1) and standard scores (d = 0.9). Correlations showed no measures taken (including Matrices and TVPS) correlated significantly with progress on the targeted conjunctions or the TROG-2. Four hours of Shape Coding therapy led to significant gains on comprehension of coordinating conjunctions which were maintained after 4 months. Given the significant progress at a group level and the lack of reliable predictors of progress, this approach could be offered to other children with similar difficulties to the participants. However, the intervention was delivered one-to-one by speech and language therapists, thus the effectiveness of this therapy method with other methods of delivery remains to be evaluated. © 2013 Royal College of Speech and Language Therapists.

New Rule Use Drives the Relation between Working Memory Capacity and Raven's Advanced Progressive Matrices

ERIC Educational Resources Information Center

Wiley, Jennifer; Jarosz, Andrew F.; Cushen, Patrick J.; Colflesh, Gregory J. H.

2011-01-01

The correlation between individual differences in working memory capacity and performance on the Raven's Advanced Progressive Matrices (RAPM) is well documented yet poorly understood. The present work proposes a new explanation: that the need to use a new combination of rules on RAPM problems drives the relation between performance and working…

Toward a better determination of dairy powders surface composition through XPS matrices development.

PubMed

Nikolova, Y; Petit, J; Sanders, C; Gianfrancesco, A; Scher, J; Gaiani, C

2015-01-01

The surface composition of dairy powders prepared by mixing various amounts of micellar casein (MC), whey proteins isolate (WPI), lactose, and anhydrous milk fat (AMF) was investigated by XPS measurements. The use of matrices are generally accepted to transform surface atomic composition (i.e., C, O, N contents) into surface component composition (i.e., lactose, proteins, lipids). These atomic-based matrices were revisited and two new matrices based on the surface bond composition were developed. Surface compositions obtained from atomic and bond-based matrices were compared. A successful matrix allowing good correlations between XPS predicted and theoretical surface composition for powders free from fat was identified. Nevertheless, samples containing milk fat were found to present a possible segregation of components owing to the AMF overrepresentation on the surface. Supplementary analyses (FTIR, SEM) were carried out in order to investigate the homogeneity of the mixtures. Copyright © 2014 Elsevier B.V. All rights reserved.

Finding workers, offenders, or students most at-risk for violence: actuarial tests save lives and resources.

PubMed

Zagar, Robert John; Kovach, Joseph W; Basile, Benjamin; Hughes, John Russell; Grove, William M; Busch, Kenneth G; Zablocki, Michael; Osnowitz, William; Neuhengen, Jonas; Liu, Yutong; Zagar, Agata Karolina

2013-12-01

147 adults (107 men, 40 women) and 89 adolescents (61 boys, 28 girls), selected randomly from referrals and volunteers, were given the Ammons Quick Test (QT), the Beck Suicide Scale (BSS), the Minnesota Multiphasic Personality Inventory Second (MMPI-2) or Adolescent Versions (MMPI-A), the Raven's Advanced Progressive Matrices, and the Standard Predictor (SP) of Violence Potential Adult or Adolescent Versions. The goals were to: (a) demonstrate computer and paper-and-pencil tests correlated; (b) validate tests to identify at-risk for violence; (c) show that identifying at-risk saves lives and resources; and (d) find which industries benefited from testing at-risk. Paper-and-pencil vs. computer test correlations (.83-.99), sensitivity (.97-.98), and specificity (.50-.97) were computed. Testing at-risk saves lives and resources. Critical industries for testing at-risk individuals may include airlines, energy generating industries, insurance, military, nonprofit-religious, prisoners, trucking or port workers, and veterans.

Strategy use fully mediates the relationship between working memory capacity and performance on Raven's matrices.

PubMed

Gonthier, Corentin; Thomassin, Noémylle

2015-10-01

Working memory capacity consistently correlates with fluid intelligence. It has been suggested that this relationship is partly attributable to strategy use: Participants with high working memory capacity would use more effective strategies, in turn leading to higher performance on fluid intelligence tasks. However, this idea has never been directly investigated. In 2 experiments, we tested this hypothesis by directly manipulating strategy use in a combined experimental-correlational approach (Experiment 1; N = 250) and by measuring strategy use with a self-report questionnaire (Experiment 2; N = 93). Inducing all participants to use an effective strategy in Raven's matrices decreased the correlation between working memory capacity and performance; the strategy use measure fully mediated the relationship between working memory capacity and performance on the matrices task. These findings indicate that individual differences in strategic behavior drive the predictive utility of working memory. We interpret the results within a theoretical framework integrating the multiple mediators of the relationship between working memory capacity and high-level cognition. (c) 2015 APA, all rights reserved).

Evolutionary Games with Randomly Changing Payoff Matrices

NASA Astrophysics Data System (ADS)

Yakushkina, Tatiana; Saakian, David B.; Bratus, Alexander; Hu, Chin-Kun

2015-06-01

Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff matrices. In this article we assume a possibility of switching the system between two regimes with different sets of payoff matrices. Potentially such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A finite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable at the large population limit. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution using the Hamilton-Jacobi equation formalism.

Generating and using truly random quantum states in Mathematica

NASA Astrophysics Data System (ADS)

Miszczak, Jarosław Adam

2012-01-01

The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states. The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness. It also provides procedures which can be used in simulations not related directly to quantum information processing. Program summaryProgram title: TRQS Catalogue identifier: AEKA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7924 No. of bytes in distributed program, including test data, etc.: 88 651 Distribution format: tar.gz Programming language: Mathematica, C Computer: Requires a Quantis quantum random number generator (QRNG, http://www.idquantique.com/true-random-number-generator/products-overview.html) and supporting a recent version of Mathematica Operating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit) RAM: Case dependent Classification: 4.15 Nature of problem: Generation of random density matrices. Solution method: Use of a physical quantum random number generator. Running time: Generating 100 random numbers takes about 1 second, generating 1000 random density matrices takes more than a minute.

Comparing the structure of an emerging market with a mature one under global perturbation

NASA Astrophysics Data System (ADS)

Namaki, A.; Jafari, G. R.; Raei, R.

2011-09-01

In this paper we investigate the Tehran stock exchange (TSE) and Dow Jones Industrial Average (DJIA) in terms of perturbed correlation matrices. To perturb a stock market, there are two methods, namely local and global perturbation. In the local method, we replace a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series, whereas in the global method, we reconstruct the correlation matrix after replacing the original return series with Gaussian-distributed time series. The local perturbation is just a technical study. We analyze these markets through two statistical approaches, random matrix theory (RMT) and the correlation coefficient distribution. By using RMT, we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks. We find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with Gaussian-distributed time series, the mean values of correlation coefficients, the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the RMT prediction fall sharply in both markets. By comparing these two markets, we can see that the DJIA is more sensitive to global perturbations. These findings are crucial for risk management and portfolio selection.

Structure of a financial cross-correlation matrix under attack

NASA Astrophysics Data System (ADS)

Lim, Gyuchang; Kim, SooYong; Kim, Junghwan; Kim, Pyungsoo; Kang, Yoonjong; Park, Sanghoon; Park, Inho; Park, Sang-Bum; Kim, Kyungsik

2009-09-01

We investigate the structure of a perturbed stock market in terms of correlation matrices. For the purpose of perturbing a stock market, two distinct methods are used, namely local and global perturbation. The former involves replacing a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series while the latter reconstructs the cross-correlation matrix just after replacing the original return series with Gaussian-distributed time series. Concerning the local case, it is a technical study only and there is no attempt to model reality. The term ‘global’ means the overall effect of the replacement on other untouched returns. Through statistical analyses such as random matrix theory (RMT), network theory, and the correlation coefficient distributions, we show that the global structure of a stock market is vulnerable to perturbation. However, apart from in the analysis of inverse participation ratios (IPRs), the vulnerability becomes dull under a small-scale perturbation. This means that these analysis tools are inappropriate for monitoring the whole stock market due to the low sensitivity of a stock market to a small-scale perturbation. In contrast, when going down to the structure of business sectors, we confirm that correlation-based business sectors are regrouped in terms of IPRs. This result gives a clue about monitoring the effect of hidden intentions, which are revealed via portfolios taken mostly by large investors.

Fidelity decay in interacting two-level boson systems: Freezing and revivals

NASA Astrophysics Data System (ADS)

Benet, Luis; Hernández-Quiroz, Saúl; Seligman, Thomas H.

2011-05-01

We study the fidelity decay in the k-body embedded ensembles of random matrices for bosons distributed in two single-particle states, considering the reference or unperturbed Hamiltonian as the one-body terms and the diagonal part of the k-body embedded ensemble of random matrices and the perturbation as the residual off-diagonal part of the interaction. We calculate the ensemble-averaged fidelity with respect to an initial random state within linear response theory to second order on the perturbation strength and demonstrate that it displays the freeze of the fidelity. During the freeze, the average fidelity exhibits periodic revivals at integer values of the Heisenberg time tH. By selecting specific k-body terms of the residual interaction, we find that the periodicity of the revivals during the freeze of fidelity is an integer fraction of tH, thus relating the period of the revivals with the range of the interaction k of the perturbing terms. Numerical calculations confirm the analytical results.

The cognitive cost of anticholinergic burden: decreased response to cognitive training in schizophrenia.

PubMed

Vinogradov, Sophia; Fisher, Melissa; Warm, Heather; Holland, Christine; Kirshner, Margaret A; Pollock, Bruce G

2009-09-01

Schizophrenia is treated with medications that raise serum anticholinergic activity and are known to adversely affect cognition. The authors examined the relationship between serum anticholinergic activity and baseline cognitive performance and response to computerized cognitive training in outpatients with schizophrenia. Fifty-five patients were randomly assigned to either computerized cognitive training or a computer games control condition. A neurocognitive battery based on the Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) initiative was performed at baseline and after the intervention. Serum anticholinergic activity, measured at study entry by radioreceptor assay, was available for 49 patients. Serum anticholinergic activity showed a significant negative correlation with baseline performance in verbal working memory and verbal learning and memory, accounting for 7% of the variance in these measures, independent of age, IQ, or symptom severity. Patients in the cognitive training condition (N=25) showed a significant gain in global cognition compared to those in the control condition, but this improvement was negatively correlated with anticholinergic burden. Serum anticholinergic activity uniquely accounted for 20% of the variance in global cognition change, independent of age, IQ, or symptom severity. Serum anticholinergic activity in schizophrenia patients shows a significant association with impaired performance in MATRICS-based measures of verbal working memory and verbal learning and memory and is significantly associated with a lowered response to an intensive course of computerized cognitive training. These findings underscore the cognitive cost of medications that carry a high anticholinergic burden. The findings also have implications for the design and evaluation of cognitive treatments for schizophrenia.

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

PubMed

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.

Novel value-added uses for sweet potato juice and flour in polyphenol- and protein-enriched functional food ingredients

PubMed Central

Grace, Mary H; Truong, An N; Truong, Van-Den; Raskin, Ilya; Lila, Mary Ann

2015-01-01

Blackcurrant, blueberry, and muscadine grape juices were efficiently sorbed, concentrated, and stabilized into dry granular ingredient matrices which combined anti-inflammatory and antioxidant fruit polyphenols with sweet potato functional constituents (carotenoids, vitamins, polyphenols, fibers). Total phenolics were highest in blackcurrant-orange sweet potato ingredient matrices (34.03 mg/g), and lowest in muscadine grape-yellow sweet potato matrices (10.56 mg/g). Similarly, anthocyanins were most concentrated in blackcurrant-fortified orange and yellow sweet potato matrices (5.40 and 6.54 mg/g, respectively). Alternatively, other protein-rich edible matrices (defatted soy flour, light roasted peanut flour, and rice protein concentrate) efficiently captured polyphenols (6.09–9.46 mg/g) and anthocyanins (0.77–1.27 mg/g) from purple-fleshed sweet potato juice, with comparable efficiency. Antioxidant activity correlated well with total phenolic content. All formulated ingredient matrices stabilized and preserved polyphenols for up to 24 weeks, even when stored at 37°C. Complexation with juice-derived polyphenols did not significantly alter protein or carbohydrate profiles of the matrices. Sensory evaluation of the ingredient matrices suggested potential uses for a wide range of functional food products. PMID:26405527

Chaos and random matrices in supersymmetric SYK

NASA Astrophysics Data System (ADS)

Hunter-Jones, Nicholas; Liu, Junyu

2018-05-01

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

Chitosan-Based Matrices Prepared by Gamma Irradiation for Tissue Regeneration: Structural Properties vs. Preparation Method.

PubMed

Casimiro, Maria Helena; Lancastre, Joana J H; Rodrigues, Alexandra P; Gomes, Susana R; Rodrigues, Gabriela; Ferreira, Luís M

2017-02-01

In the last decade, new generations of biopolymer-based materials have attracted attention, aiming its application as scaffolds for tissue engineering. These engineered three-dimensional scaffolds are designed to improve or replace damaged, missing, or otherwise compromised tissues or organs. Despite the number of promising methods that can be used to generate 3D cell-instructive matrices, the innovative nature of the present work relies on the application of ionizing radiation technology to form and modify surfaces and matrices with advantage over more conventional technologies (room temperature reaction, absence of harmful initiators or solvents, high penetration through the bulk materials, etc.), and the possibility of preparation and sterilization in one single step. The current chapter summarizes the work done by the authors in the gamma radiation processing of biocompatible and biodegradable chitosan-based matrices for skin regeneration. Particular attention is given to the correlation between the different preparation conditions and the final polymeric matrices' properties. We therefore expect to demonstrate that instructive matrices produced and improved by radiation technology bring to the field of skin regenerative medicine a supplemental advantage over more conservative techniques.

Investigating the role of background and observation error correlations in improving a model forecast of forest carbon balance using four dimensional variational data assimilation.

NASA Astrophysics Data System (ADS)

Pinnington, Ewan; Casella, Eric; Dance, Sarah; Lawless, Amos; Morison, James; Nichols, Nancy; Wilkinson, Matthew; Quaife, Tristan

2016-04-01

Forest ecosystems play an important role in sequestering human emitted carbon-dioxide from the atmosphere and therefore greatly reduce the effect of anthropogenic induced climate change. For that reason understanding their response to climate change is of great importance. Efforts to implement variational data assimilation routines with functional ecology models and land surface models have been limited, with sequential and Markov chain Monte Carlo data assimilation methods being prevalent. When data assimilation has been used with models of carbon balance, background "prior" errors and observation errors have largely been treated as independent and uncorrelated. Correlations between background errors have long been known to be a key aspect of data assimilation in numerical weather prediction. More recently, it has been shown that accounting for correlated observation errors in the assimilation algorithm can considerably improve data assimilation results and forecasts. In this paper we implement a 4D-Var scheme with a simple model of forest carbon balance, for joint parameter and state estimation and assimilate daily observations of Net Ecosystem CO2 Exchange (NEE) taken at the Alice Holt forest CO2 flux site in Hampshire, UK. We then investigate the effect of specifying correlations between parameter and state variables in background error statistics and the effect of specifying correlations in time between observation error statistics. The idea of including these correlations in time is new and has not been previously explored in carbon balance model data assimilation. In data assimilation, background and observation error statistics are often described by the background error covariance matrix and the observation error covariance matrix. We outline novel methods for creating correlated versions of these matrices, using a set of previously postulated dynamical constraints to include correlations in the background error statistics and a Gaussian correlation function to include time correlations in the observation error statistics. The methods used in this paper will allow the inclusion of time correlations between many different observation types in the assimilation algorithm, meaning that previously neglected information can be accounted for. In our experiments we compared the results using our new correlated background and observation error covariance matrices and those using diagonal covariance matrices. We found that using the new correlated matrices reduced the root mean square error in the 14 year forecast of daily NEE by 44 % decreasing from 4.22 g C m-2 day-1 to 2.38 g C m-2 day-1.

Chemiluminescence in cryogenic matrices

NASA Astrophysics Data System (ADS)

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

1989-04-01

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

An efficient parallel-processing method for transposing large matrices in place.

PubMed

Portnoff, M R

1999-01-01

We have developed an efficient algorithm for transposing large matrices in place. The algorithm is efficient because data are accessed either sequentially in blocks or randomly within blocks small enough to fit in cache, and because the same indexing calculations are shared among identical procedures operating on independent subsets of the data. This inherent parallelism makes the method well suited for a multiprocessor computing environment. The algorithm is easy to implement because the same two procedures are applied to the data in various groupings to carry out the complete transpose operation. Using only a single processor, we have demonstrated nearly an order of magnitude increase in speed over the previously published algorithm by Gate and Twigg for transposing a large rectangular matrix in place. With multiple processors operating in parallel, the processing speed increases almost linearly with the number of processors. A simplified version of the algorithm for square matrices is presented as well as an extension for matrices large enough to require virtual memory.

The feasibility and stability of large complex biological networks: a random matrix approach.

PubMed

Stone, Lewi

2018-05-29

In the 70's, Robert May demonstrated that complexity creates instability in generic models of ecological networks having random interaction matrices A. Similar random matrix models have since been applied in many disciplines. Central to assessing stability is the "circular law" since it describes the eigenvalue distribution for an important class of random matrices A. However, despite widespread adoption, the "circular law" does not apply for ecological systems in which density-dependence operates (i.e., where a species growth is determined by its density). Instead one needs to study the far more complicated eigenvalue distribution of the community matrix S = DA, where D is a diagonal matrix of population equilibrium values. Here we obtain this eigenvalue distribution. We show that if the random matrix A is locally stable, the community matrix S = DA will also be locally stable, providing the system is feasible (i.e., all species have positive equilibria D > 0). This helps explain why, unusually, nearly all feasible systems studied here are locally stable. Large complex systems may thus be even more fragile than May predicted, given the difficulty of assembling a feasible system. It was also found that the degree of stability, or resilience of a system, depended on the minimum equilibrium population.

Multiscale Modeling of Thermal Conductivity of Polymer/Carbon Nanocomposites

NASA Technical Reports Server (NTRS)

Clancy, Thomas C.; Frankland, Sarah-Jane V.; Hinkley, Jeffrey A.; Gates, Thomas S.

2010-01-01

Molecular dynamics simulation was used to estimate the interfacial thermal (Kapitza) resistance between nanoparticles and amorphous and crystalline polymer matrices. Bulk thermal conductivities of the nanocomposites were then estimated using an established effective medium approach. To study functionalization, oligomeric ethylene-vinyl alcohol copolymers were chemically bonded to a single wall carbon nanotube. The results, in a poly(ethylene-vinyl acetate) matrix, are similar to those obtained previously for grafted linear hydrocarbon chains. To study the effect of noncovalent functionalization, two types of polyethylene matrices. -- aligned (extended-chain crystalline) vs. amorphous (random coils) were modeled. Both matrices produced the same interfacial thermal resistance values. Finally, functionalization of edges and faces of plate-like graphite nanoparticles was found to be only modestly effective in reducing the interfacial thermal resistance and improving the composite thermal conductivity

Tolcapone-Enhanced Neurocognition in Healthy Adults: Neural Basis and Predictors.

PubMed

Bhakta, Savita G; Light, Gregory A; Talledo, Jo A; Balvaneda, Bryan; Hughes, Erica; Alvarez, Alexis; Rana, Brinda K; Young, Jared W; Swerdlow, Neal R

2017-12-01

Failure of procognitive drug trials in schizophrenia may reflect the clinical heterogeneity of schizophrenia, underscoring the need to identify biomarkers of treatment sensitivity. We used an experimental medicine design to test the procognitive effects of a putative procognitive agent, tolcapone, using an electroencephalogram-based cognitive control task in healthy subjects. Healthy men and women (n=27; ages 18-35 years), homozygous for either the Met/Met or Val/Val rs4680 genotype, received placebo and tolcapone 200 mg orally across 2 test days separated by 1 week in a double-blind, randomized, counterbalanced, within-subject design. On each test day, neurocognitive performance was assessed using the MATRICS Consensus Cognitive Battery and an electroencephalogram-based 5 Choice-Continuous Performance Test. Tolcapone enhanced visual learning in low-baseline MATRICS Consensus Cognitive Battery performers (d=0.35) and had an opposite effect in high performers (d=0.5), and enhanced verbal fluency across all subjects (P=.03) but had no effect on overall MATRICS Consensus Cognitive Battery performance. Tolcapone reduced false alarm rate (d=0.8) and enhanced frontal P200 amplitude during correctly identified nontarget trials (d=0.6) in low-baseline 5 Choice-Continuous Performance Test performers and had opposite effects in high performers (d=0.5 and d=0.25, respectively). Tolcapone's effect on frontal P200 amplitude and false alarm rate was correlated (rs=-0.4, P=.05). All neurocognitive effects of tolcapone were independent of rs4680 genotype. Tolcapone enhanced neurocognition and engaged electroencephalogram measures relevant to cognitive processes in specific subgroups of healthy individuals. These findings support an experimental medicine model for identifying procognitive treatments and provide a strong basis for future biomarker-informed procognitive studies in schizophrenia patients. © The Author 2017. Published by Oxford University Press on behalf of CINP.

Lyapunov exponents for one-dimensional aperiodic photonic bandgap structures

NASA Astrophysics Data System (ADS)

Kissel, Glen J.

2011-10-01

Existing in the "gray area" between perfectly periodic and purely randomized photonic bandgap structures are the socalled aperoidic structures whose layers are chosen according to some deterministic rule. We consider here a onedimensional photonic bandgap structure, a quarter-wave stack, with the layer thickness of one of the bilayers subject to being either thin or thick according to five deterministic sequence rules and binary random selection. To produce these aperiodic structures we examine the following sequences: Fibonacci, Thue-Morse, Period doubling, Rudin-Shapiro, as well as the triadic Cantor sequence. We model these structures numerically with a long chain (approximately 5,000,000) of transfer matrices, and then use the reliable algorithm of Wolf to calculate the (upper) Lyapunov exponent for the long product of matrices. The Lyapunov exponent is the statistically well-behaved variable used to characterize the Anderson localization effect (exponential confinement) when the layers are randomized, so its calculation allows us to more precisely compare the purely randomized structure with its aperiodic counterparts. It is found that the aperiodic photonic systems show much fine structure in their Lyapunov exponents as a function of frequency, and, in a number of cases, the exponents are quite obviously fractal.

Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model

NASA Astrophysics Data System (ADS)

Margarint, Vlad

2018-06-01

We consider Hermitian random band matrices H in d ≥slant 1 dimensions. The matrix elements H_{xy}, indexed by x, y \\in Λ \\subset Z^d, are independent, uniformly distributed random variable if |x-y| is less than the band width W, and zero otherwise. We update the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The result is uniformly in the size |Λ| of the matrix.

Structural Analysis of Covariance and Correlation Matrices.

ERIC Educational Resources Information Center

Joreskog, Karl G.

1978-01-01

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

Exponential smoothing weighted correlations

NASA Astrophysics Data System (ADS)

Pozzi, F.; Di Matteo, T.; Aste, T.

2012-06-01

In many practical applications, correlation matrices might be affected by the "curse of dimensionality" and by an excessive sensitiveness to outliers and remote observations. These shortcomings can cause problems of statistical robustness especially accentuated when a system of dynamic correlations over a running window is concerned. These drawbacks can be partially mitigated by assigning a structure of weights to observational events. In this paper, we discuss Pearson's ρ and Kendall's τ correlation matrices, weighted with an exponential smoothing, computed on moving windows using a data-set of daily returns for 300 NYSE highly capitalized companies in the period between 2001 and 2003. Criteria for jointly determining optimal weights together with the optimal length of the running window are proposed. We find that the exponential smoothing can provide more robust and reliable dynamic measures and we discuss that a careful choice of the parameters can reduce the autocorrelation of dynamic correlations whilst keeping significance and robustness of the measure. Weighted correlations are found to be smoother and recovering faster from market turbulence than their unweighted counterparts, helping also to discriminate more effectively genuine from spurious correlations.

Quantifying fluctuations in economic systems by adapting methods of statistical physics

NASA Astrophysics Data System (ADS)

Stanley, H. E.; Gopikrishnan, P.; Plerou, V.; Amaral, L. A. N.

2000-12-01

The emerging subfield of econophysics explores the degree to which certain concepts and methods from statistical physics can be appropriately modified and adapted to provide new insights into questions that have been the focus of interest in the economics community. Here we give a brief overview of two examples of research topics that are receiving recent attention. A first topic is the characterization of the dynamics of stock price fluctuations. For example, we investigate the relation between trading activity - measured by the number of transactions NΔ t - and the price change GΔ t for a given stock, over a time interval [t, t+ Δt] . We relate the time-dependent standard deviation of price fluctuations - volatility - to two microscopic quantities: the number of transactions NΔ t in Δ t and the variance WΔ t2 of the price changes for all transactions in Δ t. Our work indicates that while the pronounced tails in the distribution of price fluctuations arise from WΔ t, the long-range correlations found in ∣ GΔ t∣ are largely due to NΔ t. We also investigate the relation between price fluctuations and the number of shares QΔ t traded in Δ t. We find that the distribution of QΔ t is consistent with a stable Lévy distribution, suggesting a Lévy scaling relationship between QΔ t and NΔ t, which would provide one explanation for volume-volatility co-movement. A second topic concerns cross-correlations between the price fluctuations of different stocks. We adapt a conceptual framework, random matrix theory (RMT), first used in physics to interpret statistical properties of nuclear energy spectra. RMT makes predictions for the statistical properties of matrices that are universal, that is, do not depend on the interactions between the elements comprising the system. In physics systems, deviations from the predictions of RMT provide clues regarding the mechanisms controlling the dynamics of a given system, so this framework can be of potential value if applied to economic systems. We discuss a systematic comparison between the statistics of the cross-correlation matrix C - whose elements Cij are the correlation-coefficients between the returns of stock i and j - and that of a random matrix having the same symmetry properties. Our work suggests that RMT can be used to distinguish random and non-random parts of C; the non-random part of C, which deviates from RMT results provides information regarding genuine cross-correlations between stocks.

Generalization of Clustering Coefficients to Signed Correlation Networks

PubMed Central

Costantini, Giulio; Perugini, Marco

2014-01-01

The recent interest in network analysis applications in personality psychology and psychopathology has put forward new methodological challenges. Personality and psychopathology networks are typically based on correlation matrices and therefore include both positive and negative edge signs. However, some applications of network analysis disregard negative edges, such as computing clustering coefficients. In this contribution, we illustrate the importance of the distinction between positive and negative edges in networks based on correlation matrices. The clustering coefficient is generalized to signed correlation networks: three new indices are introduced that take edge signs into account, each derived from an existing and widely used formula. The performances of the new indices are illustrated and compared with the performances of the unsigned indices, both on a signed simulated network and on a signed network based on actual personality psychology data. The results show that the new indices are more resistant to sample variations in correlation networks and therefore have higher convergence compared with the unsigned indices both in simulated networks and with real data. PMID:24586367

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

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

Zhou Tao, E-mail: tzhou@lsec.cc.ac.c; Tang Tao, E-mail: ttang@hkbu.edu.h

2010-11-01

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

Monitoring of intrathoracic volemia and cardiac output in critically ill children.

PubMed

Cecchetti, C; Stoppa, F; Vanacore, N; Barbieri, M A; Raucci, U; Pasotti, E; Tomasello, C; Marano, M; Pirozzi, N

2003-12-01

Hemodynamic monitoring is an important step in the management of critically ill children despite the difficulty in measuring preload indices continuously. The aim of the study was to analyze cardiac output parameters and preload indices after acute changes in mean airway pressure and volemia. Twenty-three children treated at our unit were enrolled in a prospective non randomized cohort study. Respiration was supported by controlled mechanical ventilation with positive expiratory-end pressure (PEEP), peak inspiratory pressure <20 cm H(2)O and mean airway pressure <10 cm H(2)O, and hemodynamic monitoring using the PiCCO system. Hemodynamic parameters were measured at T0 (base line), T(1) (after an increase in PEEP of 5 cm H(2)O for 10 min), and T(2) (after fluid challenge). The statistical analysis (BMPD New System software package) comprised comparison of changes at T(0) vs T(1), T(1) vs T(2) and T(0) vs T(2), construction of 3 correlation matrices and multiple linear regression analysis. Sixty-nine hemodynamic parameters were measured in the 23 patients. A comparison between T(0) and T(1) showed no significant changes; differences between T(0) and T(2) were found for cardiac index (CI), (p=0.003); between T(0) and T(2) significant differences were found for CI (p=0.0015), intrathoracic blood volume index (ITBVI) (p=0.04) and stroke volume index (SVI) (p=0.06). The analysis of the correlation matrices yielded ITBVI with CI (p=0.0006), ITBVI with SVI (p=1 x 10(-5)), CI with SVI (p=0.002); a significant correlation between CI and extravascular lung water index (EVLWI) was found only at T(1). Multiple linear regression analysis showed that ITBVI and SVI were predictive for variance of CI at each time point. ITBVI measured by a volumetric monitoring system such as the PiCCO may be considered a sensitive preload indicator also in critically ill children.

Structure-performance relationships of phenyl cinnamic acid derivatives as MALDI-MS matrices for sulfatide detection.

PubMed

Tambe, Suparna; Blott, Henning; Fülöp, Annabelle; Spang, Nils; Flottmann, Dirk; Bräse, Stefan; Hopf, Carsten; Junker, Hans-Dieter

2017-02-01

A key aspect for the further development of matrix-assisted laser desorption ionization (MALDI)-mass spectrometry (MS) is a better understanding of the working principles of MALDI matrices. To address this issue, a chemical compound library of 59 structurally related cinnamic acid derivatives was synthesized. Potential MALDI matrices were evaluated with sulfatides, a class of anionic lipids which are abundant in complex brain lipid mixtures. For each matrix relative mean S/N ratios of sulfatides were determined against 9-aminoacridine as a reference matrix using negative ion mass spectrometry with 355 and 337 nm laser systems. The comparison of matrix features with their corresponding relative mean S/N ratios for sulfatide detection identified correlations between matrix substitution patterns, their chemical functionality, and their MALDI-MS performance. Crystal structures of six selected matrices provided structural insight in hydrogen bond interactions in the solid state. Principal component analysis allowed the additional identification of correlation trends between structural and physical matrix properties like number of exchangeable protons at the head group, MW, logP, UV-Vis, and sulfatide detection sensitivity. Graphical abstract Design, synthesis and mass spectrometric evaluation of MALDI-MS matrix compound libraries allows the identification of matrix structure - MALDI-MS performance relationships using multivariate statistics as a tool.

Singular Behavior of the Leading Lyapunov Exponent of a Product of Random {2 × 2} Matrices

NASA Astrophysics Data System (ADS)

Genovese, Giuseppe; Giacomin, Giambattista; Greenblatt, Rafael Leon

2017-05-01

We consider a certain infinite product of random {2 × 2} matrices appearing in the solution of some 1 and 1 + 1 dimensional disordered models in statistical mechanics, which depends on a parameter ɛ > 0 and on a real random variable with distribution {μ}. For a large class of {μ}, we prove the prediction by Derrida and Hilhorst (J Phys A 16:2641, 1983) that the Lyapunov exponent behaves like {C ɛ^{2 α}} in the limit {ɛ \\searrow 0}, where {α \\in (0,1)} and {C > 0} are determined by {μ}. Derrida and Hilhorst performed a two-scale analysis of the integral equation for the invariant distribution of the Markov chain associated to the matrix product and obtained a probability measure that is expected to be close to the invariant one for small {ɛ}. We introduce suitable norms and exploit contractivity properties to show that such a probability measure is indeed close to the invariant one in a sense that implies a suitable control of the Lyapunov exponent.

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

PubMed

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

2017-11-01

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

Quantum probabilistic logic programming

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan

2015-05-01

We describe a quantum mechanics based logic programming language that supports Horn clauses, random variables, and covariance matrices to express and solve problems in probabilistic logic. The Horn clauses of the language wrap random variables, including infinite valued, to express probability distributions and statistical correlations, a powerful feature to capture relationship between distributions that are not independent. The expressive power of the language is based on a mechanism to implement statistical ensembles and to solve the underlying SAT instances using quantum mechanical machinery. We exploit the fact that classical random variables have quantum decompositions to build the Horn clauses. We establish the semantics of the language in a rigorous fashion by considering an existing probabilistic logic language called PRISM with classical probability measures defined on the Herbrand base and extending it to the quantum context. In the classical case H-interpretations form the sample space and probability measures defined on them lead to consistent definition of probabilities for well formed formulae. In the quantum counterpart, we define probability amplitudes on Hinterpretations facilitating the model generations and verifications via quantum mechanical superpositions and entanglements. We cast the well formed formulae of the language as quantum mechanical observables thus providing an elegant interpretation for their probabilities. We discuss several examples to combine statistical ensembles and predicates of first order logic to reason with situations involving uncertainty.

Derivation of an eigenvalue probability density function relating to the Poincaré disk

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Krishnapur, Manjunath

2009-09-01

A result of Zyczkowski and Sommers (2000 J. Phys. A: Math. Gen. 33 2045-57) gives the eigenvalue probability density function for the top N × N sub-block of a Haar distributed matrix from U(N + n). In the case n >= N, we rederive this result, starting from knowledge of the distribution of the sub-blocks, introducing the Schur decomposition and integrating over all variables except the eigenvalues. The integration is done by identifying a recursive structure which reduces the dimension. This approach is inspired by an analogous approach which has been recently applied to determine the eigenvalue probability density function for random matrices A-1B, where A and B are random matrices with entries standard complex normals. We relate the eigenvalue distribution of the sub-blocks to a many-body quantum state, and to the one-component plasma, on the pseudosphere.

Randomized interpolative decomposition of separated representations

NASA Astrophysics Data System (ADS)

Biagioni, David J.; Beylkin, Daniel; Beylkin, Gregory

2015-01-01

We introduce an algorithm to compute tensor interpolative decomposition (dubbed CTD-ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ɛ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the Alternating Least Squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank.

Meta-Analytic Structural Equation Modeling: A Two-Stage Approach

ERIC Educational Resources Information Center

Cheung, Mike W. L.; Chan, Wai

2005-01-01

To synthesize studies that use structural equation modeling (SEM), researchers usually use Pearson correlations (univariate r), Fisher z scores (univariate z), or generalized least squares (GLS) to combine the correlation matrices. The pooled correlation matrix is then analyzed by the use of SEM. Questionable inferences may occur for these ad hoc…

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables.

ERIC Educational Resources Information Center

Ethington, Corinna A.

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical manifest variables. Two types of correlation matrices were analyzed; one containing Pearson product-moment correlations and one containing tetrachoric,…

Fibronectin alters the rate of formation and structure of the fibrin matrix.

PubMed

Ramanathan, Anand; Karuri, Nancy

2014-01-10

Plasma fibronectin is a vital component of the fibrin clot; however its role on clot structure is not clearly understood. The goal of this study was to examine the influence of fibronectin on the kinetics of formation, structural characteristics and composition of reconstituted fibrin clots or fibrin matrices. Fibrin matrices were formed by adding thrombin to 1, 2 or 4 mg/ml fibrinogen supplemented with 0-0.4 mg/ml fibronectin. The rate of fibrin matrix formation was then monitored by measuring light absorbance properties at different time points. Confocal microscopy of fluorescein conjugated fibrinogen was used to visualize the structural characteristics of fibrin matrices. The amount of fibronectin in fibrin matrices was determined through electrophoresis and immunoblotting of solubilized matrices. Fibronectin concentration positively correlated with the initial rate of fibrin matrix formation and with steady state light absorbance values of fibrin matrices. An increase in fibronectin concentration resulted in thinner and denser fibers in the fibrin matrices. Electrophoresis and immunoblotting showed that fibronectin was covalently and non-covalently bound to fibrin matrices and in the form of high molecular weight multimers. The formation of fibronectin multimers was attributed to cross-linking of fibronectin by trace amounts Factor XIIIa. These findings are novel because they link results from light absorbance studies to microcopy analyses and demonstrate an influence of fibronectin on fibrin matrix structural characteristics. This data is important in developing therapies that destabilize fibrin clots. Copyright © 2014. Published by Elsevier Inc.

Fast method to compute scattering by a buried object under a randomly rough surface: PILE combined with FB-SA.

PubMed

Bourlier, Christophe; Kubické, Gildas; Déchamps, Nicolas

2008-04-01

A fast, exact numerical method based on the method of moments (MM) is developed to calculate the scattering from an object below a randomly rough surface. Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)] have recently developed the PILE (propagation-inside-layer expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. From the inversion of the impedance matrix by block (in which two impedance matrices of each interface and two coupling matrices are involved), this method allows one to calculate separately and exactly the multiple-scattering contributions inside the layer in which the inverses of the impedance matrices of each interface are involved. Our purpose here is to apply this method for an object below a rough surface. In addition, to invert a matrix of large size, the forward-backward spectral acceleration (FB-SA) approach of complexity O(N) (N is the number of unknowns on the interface) proposed by Chou and Johnson [Radio Sci.33, 1277 (1998)] is applied. The new method, PILE combined with FB-SA, is tested on perfectly conducting circular and elliptic cylinders located below a dielectric rough interface obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Uncovering collective listening habits and music genres in bipartite networks.

PubMed

Lambiotte, R; Ausloos, M

2005-12-01

In this paper, we analyze web-downloaded data on people sharing their music library, that we use as their individual musical signatures. The system is represented by a bipartite network, nodes being the music groups and the listeners. Music groups' audience size behaves like a power law, but the individual music library size is an exponential with deviations at small values. In order to extract structures from the network, we focus on correlation matrices, that we filter by removing the least correlated links. This percolation idea-based method reveals the emergence of social communities and music genres, that are visualized by a branching representation. Evidence of collective listening habits that do not fit the neat usual genres defined by the music industry indicates an alternative way of classifying listeners and music groups. The structure of the network is also studied by a more refined method, based upon a random walk exploration of its properties. Finally, a personal identification-community imitation model for growing bipartite networks is outlined, following Potts ingredients. Simulation results do reproduce quite well the empirical data.

Uncovering collective listening habits and music genres in bipartite networks

NASA Astrophysics Data System (ADS)

Lambiotte, R.; Ausloos, M.

2005-12-01

In this paper, we analyze web-downloaded data on people sharing their music library, that we use as their individual musical signatures. The system is represented by a bipartite network, nodes being the music groups and the listeners. Music groups’ audience size behaves like a power law, but the individual music library size is an exponential with deviations at small values. In order to extract structures from the network, we focus on correlation matrices, that we filter by removing the least correlated links. This percolation idea-based method reveals the emergence of social communities and music genres, that are visualized by a branching representation. Evidence of collective listening habits that do not fit the neat usual genres defined by the music industry indicates an alternative way of classifying listeners and music groups. The structure of the network is also studied by a more refined method, based upon a random walk exploration of its properties. Finally, a personal identification-community imitation model for growing bipartite networks is outlined, following Potts ingredients. Simulation results do reproduce quite well the empirical data.

Factor Analysis and Counseling Research

ERIC Educational Resources Information Center

Weiss, David J.

1970-01-01

Topics discussed include factor analysis versus cluster analysis, analysis of Q correlation matrices, ipsativity and factor analysis, and tests for the significance of a correlation matrix prior to application of factor analytic techniques. Techniques for factor extraction discussed include principal components, canonical factor analysis, alpha…

Can nail, hair and urine be used for biomonitoring of human exposure to perfluorooctane sulfonate and perfluorooctanoic acid?

PubMed

Li, Jingguang; Guo, Feifei; Wang, Yuxin; Zhang, Jialing; Zhong, Yuxin; Zhao, Yunfeng; Wu, Yongning

2013-03-01

Because of the disadvantages of invasive sampling, it is desirable to explore non-invasive matrices for human biomonitoring of perfluorooctane sulfonate (PFOS) and perfluorooctanoic acid (PFOA). The aim of this study was to evaluate the application of nail, hair and urine for human biomonitoring of PFOS and PFOA. The concentrations of PFOS and PFOA in matched nail, hair, urine and serum samples collected from 64 donors were measured. The chemicals of interest were detected with high detection frequency in these matrices (90%-100%) except for PFOA in urine samples (56%). Generally, the gender influences on the levels of PFOS and PFOA in these non-invasive matrices were in agreement with that in serum. For PFOS, the coefficients of Spearman correlation between serum samples and nail, hair and urine samples were 0.786 (p<0.001), 0.545 (p<0.001) and 0.302 (p<0.05), respectively. For PFOA, the correlation was only observed between nail samples and serum samples with a correlation coefficient of 0.299 (p<0.05). The results suggested that nail has more potential than hair and urine to be applied in human biomonitoring for PFOS and PFOA in general populations. Copyright © 2013 Elsevier Ltd. All rights reserved.

Meta-Analytic Methods of Pooling Correlation Matrices for Structural Equation Modeling under Different Patterns of Missing Data

ERIC Educational Resources Information Center

Furlow, Carolyn F.; Beretvas, S. Natasha

2005-01-01

Three methods of synthesizing correlations for meta-analytic structural equation modeling (SEM) under different degrees and mechanisms of missingness were compared for the estimation of correlation and SEM parameters and goodness-of-fit indices by using Monte Carlo simulation techniques. A revised generalized least squares (GLS) method for…

Statistical similarity measures for link prediction in heterogeneous complex networks

NASA Astrophysics Data System (ADS)

Shakibian, Hadi; Charkari, Nasrollah Moghadam

2018-07-01

The majority of the link prediction measures in heterogeneous complex networks rely on the nodes connectivities while less attention has been paid to the importance of the nodes and paths. In this paper, we propose some new meta-path based statistical similarity measures to properly perform link prediction task. The main idea in the proposed measures is to drive some co-occurrence events in a number of co-occurrence matrices that are occurred between the visited nodes obeying a meta-path. The extracted co-occurrence matrices are analyzed in terms of the energy, inertia, local homogeneity, correlation, and information measure of correlation to determine various information theoretic measures. We evaluate the proposed measures, denoted as link energy, link inertia, link local homogeneity, link correlation, and link information measure of correlation, using a standard DBLP network data set. The results of the AUC score and Precision rate indicate the validity and accuracy of the proposed measures in comparison to the popular meta-path based similarity measures.

A transfer matrix approach to vibration localization in mistuned blade assemblies

NASA Technical Reports Server (NTRS)

Ottarson, Gisli; Pierre, Chritophe

1993-01-01

A study of mode localization in mistuned bladed disks is performed using transfer matrices. The transfer matrix approach yields the free response of a general, mono-coupled, perfectly cyclic assembly in closed form. A mistuned structure is represented by random transfer matrices, and the expansion of these matrices in terms of the small mistuning parameter leads to the definition of a measure of sensitivity to mistuning. An approximation of the localization factor, the spatially averaged rate of exponential attenuation per blade-disk sector, is obtained through perturbation techniques in the limits of high and low sensitivity. The methodology is applied to a common model of a bladed disk and the results verified by Monte Carlo simulations. The easily calculated sensitivity measure may prove to be a valuable design tool due to its system-independent quantification of mistuning effects such as mode localization.

Medium-induced change of the optical response of metal clusters in rare-gas matrices

NASA Astrophysics Data System (ADS)

Xuan, Fengyuan; Guet, Claude

2017-10-01

Interaction with the surrounding medium modifies the optical response of embedded metal clusters. For clusters from about ten to a few hundreds of silver atoms, embedded in rare-gas matrices, we study the environment effect within the matrix random phase approximation with exact exchange (RPAE) quantum approach, which has proved successful for free silver clusters. The polarizable surrounding medium screens the residual two-body RPAE interaction, adds a polarization term to the one-body potential, and shifts the vacuum energy of the active delocalized valence electrons. Within this model, we calculate the dipole oscillator strength distribution for Ag clusters embedded in helium droplets, neon, argon, krypton, and xenon matrices. The main contribution to the dipole surface plasmon red shift originates from the rare-gas polarization screening of the two-body interaction. The large size limit of the dipole surface plasmon agrees well with the classical prediction.

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

PubMed Central

Cai, T. Tony; Zhang, Anru

2016-01-01

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

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

PubMed

Cai, T Tony; Zhang, Anru

2016-09-01

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

Parallel transmission RF pulse design with strict temperature constraints.

PubMed

Deniz, Cem M; Carluccio, Giuseppe; Collins, Christopher

2017-05-01

RF safety in parallel transmission (pTx) is generally ensured by imposing specific absorption rate (SAR) limits during pTx RF pulse design. There is increasing interest in using temperature to ensure safety in MRI. In this work, we present a local temperature correlation matrix formalism and apply it to impose strict constraints on maximum absolute temperature in pTx RF pulse design for head and hip regions. Electromagnetic field simulations were performed on the head and hip of virtual body models. Temperature correlation matrices were calculated for four different exposure durations ranging between 6 and 24 min using simulated fields and body-specific constants. Parallel transmission RF pulses were designed using either SAR or temperature constraints, and compared with each other and unconstrained RF pulse design in terms of excitation fidelity and safety. The use of temperature correlation matrices resulted in better excitation fidelity compared with the use of SAR in parallel transmission RF pulse design (for the 6 min exposure period, 8.8% versus 21.0% for the head and 28.0% versus 32.2% for the hip region). As RF exposure duration increases (from 6 min to 24 min), the benefit of using temperature correlation matrices on RF pulse design diminishes. However, the safety of the subject is always guaranteed (the maximum temperature was equal to 39°C). This trend was observed in both head and hip regions, where the perfusion rates are very different. Copyright © 2017 John Wiley & Sons, Ltd.

Comparison of Adjacency and Distance-Based Approaches for Spatial Analysis of Multimodal Traffic Crash Data

NASA Astrophysics Data System (ADS)

Gill, G.; Sakrani, T.; Cheng, W.; Zhou, J.

2017-09-01

Many studies have utilized the spatial correlations among traffic crash data to develop crash prediction models with the aim to investigate the influential factors or predict crash counts at different sites. The spatial correlation have been observed to account for heterogeneity in different forms of weight matrices which improves the estimation performance of models. But very rarely have the weight matrices been compared for the prediction accuracy for estimation of crash counts. This study was targeted at the comparison of two different approaches for modelling the spatial correlations among crash data at macro-level (County). Multivariate Full Bayesian crash prediction models were developed using Decay-50 (distance-based) and Queen-1 (adjacency-based) weight matrices for simultaneous estimation crash counts of four different modes: vehicle, motorcycle, bike, and pedestrian. The goodness-of-fit and different criteria for accuracy at prediction of crash count reveled the superiority of Decay-50 over Queen-1. Decay-50 was essentially different from Queen-1 with the selection of neighbors and more robust spatial weight structure which rendered the flexibility to accommodate the spatially correlated crash data. The consistently better performance of Decay-50 at prediction accuracy further bolstered its superiority. Although the data collection efforts to gather centroid distance among counties for Decay-50 may appear to be a downside, but the model has a significant edge to fit the crash data without losing the simplicity of computation of estimated crash count.

The impact of eszopiclone on sleep and cognition in patients with schizophrenia and insomnia: a double-blind, randomized, placebo-controlled trial.

PubMed

Tek, Cenk; Palmese, Laura B; Krystal, Andrew D; Srihari, Vinod H; DeGeorge, Pamela C; Reutenauer, Erin L; Guloksuz, Sinan

2014-12-01

Insomnia is frequent in schizophrenia and may contribute to cognitive impairment as well as overuse of weight inducing sedative antipsychotics. We investigated the effects of eszopiclone on sleep and cognition for patients with schizophrenia-related insomnia in a double-blind placebo controlled study, followed by a two-week, single-blind placebo phase. Thirty-nine clinically stable outpatients with schizophrenia or schizoaffective disorder and insomnia were randomized to either 3mg eszopiclone (n=20) or placebo (n=19). Primary outcome measure was change in Insomnia Severity Index (ISI) over 8 weeks. Secondary outcome measure was change in MATRICS Consensus Cognitive Battery (MATRICS). Sleep diaries, psychiatric symptoms, and quality of life were also monitored. ISI significantly improved more in eszopiclone (mean=-10.7, 95% CI=-13.2; -8.2) than in placebo (mean=-6.9, 95% CI=-9.5; -4.3) with a between-group difference of -3.8 (95% CI=-7.5; -0.2). MATRICS score change did not differ between groups. On further analysis there was a significant improvement in the working memory test, letter-number span component of MATRICS (mean=9.8±9.2, z=-2.00, p=0.045) only for subjects with schizophrenia on eszopiclone. There were improvements in sleep diary items in both groups with no between-group differences. Psychiatric symptoms remained stable. Discontinuation rates were similar. Sleep remained improved during single-blind placebo phase after eszopiclone was stopped, but the working memory improvement in patients with schizophrenia was not durable. Eszopiclone stands as a safe and effective alternative for the treatment of insomnia in patients with schizophrenia. Its effects on cognition require further study. Copyright © 2014 Elsevier B.V. All rights reserved.

Large computer simulations on elastic networks: Small eigenvalues and eigenvalue spectra of the Kirchhoff matrix

NASA Astrophysics Data System (ADS)

Shy, L. Y.; Eichinger, B. E.

1989-05-01

Computer simulations of the formation of trifunctional and tetrafunctional polydimethyl-siloxane networks that are crosslinked by condensation of telechelic chains with multifunctional crosslinking agents have been carried out on systems containing up to 1.05×106 chains. Eigenvalue spectra of Kirchhoff matrices for these networks have been evaluated at two levels of approximation: (1) inclusion of all midchain modes, and (2) suppression of midchain modes. By use of the recursion method of Haydock and Nex, we have been able to effectively diagonalize matrices with 730 498 rows and columns without actually constructing matrices of this size. The small eigenvalues have been computed by use of the Lanczos algorithm. We demonstrate the following results: (1) The smallest eigenvalues (with chain modes suppressed) vary as μ-2/3 for sufficiently large μ, where μ is the number of junctions in the network; (2) the eigenvalue spectra of the Kirchhoff matrices are well described by McKay's theory for random regular graphs in the range of the larger eigenvalues, but there are significant departures in the region of small eigenvalues where computed spectra have many more small eigenvalues than random regular graphs; (3) the smallest eigenvalues vary as n-1.78 where n is the number of Rouse beads in the chains that comprise the network. Computations are done for both monodisperse and polydisperse chain length distributions. Large eigenvalues associated with localized motion of the junctions are found as predicted by theory. The relationship between the small eigenvalues and the equilibrium modulus of elasticity is discussed, as is the relationship between viscoelasticity and the band edge of the spectrum.

A system identification technique based on the random decrement signatures. Part 1: Theory and simulation

NASA Technical Reports Server (NTRS)

Bedewi, Nabih E.; Yang, Jackson C. S.

1987-01-01

Identification of the system parameters of a randomly excited structure may be treated using a variety of statistical techniques. Of all these techniques, the Random Decrement is unique in that it provides the homogeneous component of the system response. Using this quality, a system identification technique was developed based on a least-squares fit of the signatures to estimate the mass, damping, and stiffness matrices of a linear randomly excited system. The mathematics of the technique is presented in addition to the results of computer simulations conducted to demonstrate the prediction of the response of the system and the random forcing function initially introduced to excite the system.

Individual Differences in General Intelligence Correlate with Brain Function during Nonreasoning Tasks.

ERIC Educational Resources Information Center

Haier, Richard J.; White, Nathan S.; Alkire, Michael T.

2003-01-01

Administered Raven's Advanced Progressive Matrices to 22 adults and measured cerebral glucose activity as subjects viewed videos on 2 occasions. Data provide evidence that individual differences in intelligence correlate with brain function even when the brain is engaged in non-reasoning tasks. (SLD)

The Infinitesimal Jackknife with Exploratory Factor Analysis

ERIC Educational Resources Information Center

Zhang, Guangjian; Preacher, Kristopher J.; Jennrich, Robert I.

2012-01-01

The infinitesimal jackknife, a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices. Both…

Meta-Analytic Structural Equation Modeling (MASEM): Comparison of the Multivariate Methods

ERIC Educational Resources Information Center

Zhang, Ying

2011-01-01

Meta-analytic Structural Equation Modeling (MASEM) has drawn interest from many researchers recently. In doing MASEM, researchers usually first synthesize correlation matrices across studies using meta-analysis techniques and then analyze the pooled correlation matrix using structural equation modeling techniques. Several multivariate methods of…

Average fidelity between random quantum states

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

Zyczkowski, Karol; Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Aleja Lotnikow 32/44, 02-668 Warsaw; Perimeter Institute, Waterloo, Ontario, N2L 2Y5

2005-03-01

We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: the Hilbert-Schmidt measure, the Bures (statistical) measure, the measure induced by the partial trace, and the natural measure on the space of pure states. In certain cases explicit probability distributions for the fidelity are derived. The results obtained may be used to gauge the quality of quantum-information-processing schemes.

$n$ -Dimensional Discrete Cat Map Generation Using Laplace Expansions.

PubMed

Wu, Yue; Hua, Zhongyun; Zhou, Yicong

2016-11-01

Different from existing methods that use matrix multiplications and have high computation complexity, this paper proposes an efficient generation method of n -dimensional ( [Formula: see text]) Cat maps using Laplace expansions. New parameters are also introduced to control the spatial configurations of the [Formula: see text] Cat matrix. Thus, the proposed method provides an efficient way to mix dynamics of all dimensions at one time. To investigate its implementations and applications, we further introduce a fast implementation algorithm of the proposed method with time complexity O(n 4 ) and a pseudorandom number generator using the Cat map generated by the proposed method. The experimental results show that, compared with existing generation methods, the proposed method has a larger parameter space and simpler algorithm complexity, generates [Formula: see text] Cat matrices with a lower inner correlation, and thus yields more random and unpredictable outputs of [Formula: see text] Cat maps.

Sparse distributed memory and related models

NASA Technical Reports Server (NTRS)

Kanerva, Pentti

1992-01-01

Described here is sparse distributed memory (SDM) as a neural-net associative memory. It is characterized by two weight matrices and by a large internal dimension - the number of hidden units is much larger than the number of input or output units. The first matrix, A, is fixed and possibly random, and the second matrix, C, is modifiable. The SDM is compared and contrasted to (1) computer memory, (2) correlation-matrix memory, (3) feet-forward artificial neural network, (4) cortex of the cerebellum, (5) Marr and Albus models of the cerebellum, and (6) Albus' cerebellar model arithmetic computer (CMAC). Several variations of the basic SDM design are discussed: the selected-coordinate and hyperplane designs of Jaeckel, the pseudorandom associative neural memory of Hassoun, and SDM with real-valued input variables by Prager and Fallside. SDM research conducted mainly at the Research Institute for Advanced Computer Science (RIACS) in 1986-1991 is highlighted.

Analytical expressions for the evolution of many-body quantum systems quenched far from equilibrium

NASA Astrophysics Data System (ADS)

Santos, Lea F.; Torres-Herrera, E. Jonathan

2017-12-01

Possible strategies to describe analytically the dynamics of many-body quantum systems out of equilibrium include the use of solvable models and of full random matrices. None of the two approaches represent actual realistic systems, but they serve as references for the studies of these ones. We take the second path and obtain analytical expressions for the survival probability, density imbalance, and out-of-time-ordered correlator. Using these findings, we then propose an approximate expression that matches very well numerical results for the evolution of realistic finite quantum systems that are strongly chaotic and quenched far from equilibrium. In the case of the survival probability, the expression proposed covers all different time scales, from the moment the system is taken out of equilibrium to the moment it reaches a new equilibrium. The realistic systems considered are described by one-dimensional spin-1/2 models.

A system identification technique based on the random decrement signatures. Part 2: Experimental results

NASA Technical Reports Server (NTRS)

Bedewi, Nabih E.; Yang, Jackson C. S.

1987-01-01

Identification of the system parameters of a randomly excited structure may be treated using a variety of statistical techniques. Of all these techniques, the Random Decrement is unique in that it provides the homogeneous component of the system response. Using this quality, a system identification technique was developed based on a least-squares fit of the signatures to estimate the mass, damping, and stiffness matrices of a linear randomly excited system. The results of an experiment conducted on an offshore platform scale model to verify the validity of the technique and to demonstrate its application in damage detection are presented.

On the Concept of Random Orientation in Far-Field Electromagnetic Scattering by Nonspherical Particles

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Yurkin, Maxim A.

2017-01-01

Although the model of randomly oriented nonspherical particles has been used in a great variety of applications of far-field electromagnetic scattering, it has never been defined in strict mathematical terms. In this Letter we use the formalism of Euler rigid-body rotations to clarify the concept of statistically random particle orientations and derive its immediate corollaries in the form of most general mathematical properties of the orientation-averaged extinction and scattering matrices. Our results serve to provide a rigorous mathematical foundation for numerous publications in which the notion of randomly oriented particles and its light-scattering implications have been considered intuitively obvious.

Revealing the microstructure of the giant component in random graph ensembles

NASA Astrophysics Data System (ADS)

Tishby, Ido; Biham, Ofer; Katzav, Eytan; Kühn, Reimer

2018-04-01

The microstructure of the giant component of the Erdős-Rényi network and other configuration model networks is analyzed using generating function methods. While configuration model networks are uncorrelated, the giant component exhibits a degree distribution which is different from the overall degree distribution of the network and includes degree-degree correlations of all orders. We present exact analytical results for the degree distributions as well as higher-order degree-degree correlations on the giant components of configuration model networks. We show that the degree-degree correlations are essential for the integrity of the giant component, in the sense that the degree distribution alone cannot guarantee that it will consist of a single connected component. To demonstrate the importance and broad applicability of these results, we apply them to the study of the distribution of shortest path lengths on the giant component, percolation on the giant component, and spectra of sparse matrices defined on the giant component. We show that by using the degree distribution on the giant component one obtains high quality results for these properties, which can be further improved by taking the degree-degree correlations into account. This suggests that many existing methods, currently used for the analysis of the whole network, can be adapted in a straightforward fashion to yield results conditioned on the giant component.

Amino Acid Properties Conserved in Molecular Evolution

PubMed Central

Rudnicki, Witold R.; Mroczek, Teresa; Cudek, Paweł

2014-01-01

That amino acid properties are responsible for the way protein molecules evolve is natural and is also reasonably well supported both by the structure of the genetic code and, to a large extent, by the experimental measures of the amino acid similarity. Nevertheless, there remains a significant gap between observed similarity matrices and their reconstructions from amino acid properties. Therefore, we introduce a simple theoretical model of amino acid similarity matrices, which allows splitting the matrix into two parts – one that depends only on mutabilities of amino acids and another that depends on pairwise similarities between them. Then the new synthetic amino acid properties are derived from the pairwise similarities and used to reconstruct similarity matrices covering a wide range of information entropies. Our model allows us to explain up to 94% of the variability in the BLOSUM family of the amino acids similarity matrices in terms of amino acid properties. The new properties derived from amino acid similarity matrices correlate highly with properties known to be important for molecular evolution such as hydrophobicity, size, shape and charge of amino acids. This result closes the gap in our understanding of the influence of amino acids on evolution at the molecular level. The methods were applied to the single family of similarity matrices used often in general sequence homology searches, but it is general and can be used also for more specific matrices. The new synthetic properties can be used in analyzes of protein sequences in various biological applications. PMID:24967708

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

PubMed

Marroig, G; Cheverud, J M

2001-12-01

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

Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing

NASA Astrophysics Data System (ADS)

Zhang, Peng; Gan, Lu; Ling, Cong; Sun, Sumei

2018-04-01

We study the problem of recovering an $s$-sparse signal $\\mathbf{x}^{\\star}\\in\\mathbb{C}^n$ from corrupted measurements $\\mathbf{y} = \\mathbf{A}\\mathbf{x}^{\\star}+\\mathbf{z}^{\\star}+\\mathbf{w}$, where $\\mathbf{z}^{\\star}\\in\\mathbb{C}^m$ is a $k$-sparse corruption vector whose nonzero entries may be arbitrarily large and $\\mathbf{w}\\in\\mathbb{C}^m$ is a dense noise with bounded energy. The aim is to exactly and stably recover the sparse signal with tractable optimization programs. In this paper, we prove the uniform recovery guarantee of this problem for two classes of structured sensing matrices. The first class can be expressed as the product of a unit-norm tight frame (UTF), a random diagonal matrix and a bounded columnwise orthonormal matrix (e.g., partial random circulant matrix). When the UTF is bounded (i.e. $\\mu(\\mathbf{U})\\sim1/\\sqrt{m}$), we prove that with high probability, one can recover an $s$-sparse signal exactly and stably by $l_1$ minimization programs even if the measurements are corrupted by a sparse vector, provided $m = \\mathcal{O}(s \\log^2 s \\log^2 n)$ and the sparsity level $k$ of the corruption is a constant fraction of the total number of measurements. The second class considers randomly sub-sampled orthogonal matrix (e.g., random Fourier matrix). We prove the uniform recovery guarantee provided that the corruption is sparse on certain sparsifying domain. Numerous simulation results are also presented to verify and complement the theoretical results.

Quantum morphogenesis: A variation on Thom's catastrophe theory

NASA Astrophysics Data System (ADS)

Aerts, Dirk; Czachor, Marek; Gabora, Liane; Kuna, Maciej; Posiewnik, Andrzej; Pykacz, Jarosław; Syty, Monika

2003-05-01

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to the phenomenon of morphogenesis that may occur in noncommutative systems. Several explicit exactly solvable models are presented, including “birth and death of an organism” and “development of complementary properties.”

An Assessment of the Dimensionality of SAT-Mathematical.

ERIC Educational Resources Information Center

Lawrence, Ida M.; Dorans, Neil J.

Six editions of Scholastic Aptitude Test-Mathematical (SAT-M) were factor analyzed using confirmatory and exploratory methods. Confirmatory factor analyses (using the LISREL VI program) were conducted on correlation matrices among item parcels--sums of scores on a small subset of items. Item parcels were constructed to yield correlation matrices…

On the number of Bose-selected modes in driven-dissipative ideal Bose gases

NASA Astrophysics Data System (ADS)

Schnell, Alexander; Ketzmerick, Roland; Eckardt, André

2018-03-01

In an ideal Bose gas that is driven into a steady state far from thermal equilibrium, a generalized form of Bose condensation can occur. Namely, the single-particle states unambiguously separate into two groups: the group of Bose-selected states, whose occupations increase linearly with the total particle number, and the group of all other states whose occupations saturate [Phys. Rev. Lett. 111, 240405 (2013), 10.1103/PhysRevLett.111.240405]. However, so far very little is known about how the number of Bose-selected states depends on the properties of the system and its coupling to the environment. The answer to this question is crucial since systems hosting a single, a few, or an extensive number of Bose-selected states will show rather different behavior. While in the former two scenarios each selected mode acquires a macroscopic occupation, corresponding to (fragmented) Bose condensation, the latter case rather bears resemblance to a high-temperature state of matter. In this paper, we systematically investigate the number of Bose-selected states, considering different classes of the rate matrices that characterize the driven-dissipative ideal Bose gases in the limit of weak system-bath coupling. These include rate matrices with continuum limit, rate matrices of chaotic driven systems, random rate matrices, and rate matrices resulting from thermal baths that couple to a few observables only.

On the number of Bose-selected modes in driven-dissipative ideal Bose gases.

PubMed

Schnell, Alexander; Ketzmerick, Roland; Eckardt, André

2018-03-01

In an ideal Bose gas that is driven into a steady state far from thermal equilibrium, a generalized form of Bose condensation can occur. Namely, the single-particle states unambiguously separate into two groups: the group of Bose-selected states, whose occupations increase linearly with the total particle number, and the group of all other states whose occupations saturate [Phys. Rev. Lett. 111, 240405 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.240405]. However, so far very little is known about how the number of Bose-selected states depends on the properties of the system and its coupling to the environment. The answer to this question is crucial since systems hosting a single, a few, or an extensive number of Bose-selected states will show rather different behavior. While in the former two scenarios each selected mode acquires a macroscopic occupation, corresponding to (fragmented) Bose condensation, the latter case rather bears resemblance to a high-temperature state of matter. In this paper, we systematically investigate the number of Bose-selected states, considering different classes of the rate matrices that characterize the driven-dissipative ideal Bose gases in the limit of weak system-bath coupling. These include rate matrices with continuum limit, rate matrices of chaotic driven systems, random rate matrices, and rate matrices resulting from thermal baths that couple to a few observables only.

Methods for Improving Information from ’Undesigned’ Human Factors Experiments.

DTIC Science & Technology

Human factors engineering, Information processing, Regression analysis , Experimental design, Least squares method, Analysis of variance, Correlation techniques, Matrices(Mathematics), Multiple disciplines, Mathematical prediction

Towards rigorous analysis of the Levitov-Mirlin-Evers recursion

NASA Astrophysics Data System (ADS)

Fyodorov, Y. V.; Kupiainen, A.; Webb, C.

2016-12-01

This paper aims to develop a rigorous asymptotic analysis of an approximate renormalization group recursion for inverse participation ratios P q of critical powerlaw random band matrices. The recursion goes back to the work by Mirlin and Evers (2000 Phys. Rev. B 62 7920) and earlier works by Levitov (1990 Phys. Rev. Lett. 64 547, 1999 Ann. Phys. 8 697-706) and is aimed to describe the ensuing multifractality of the eigenvectors of such matrices. We point out both similarities and dissimilarities between the LME recursion and those appearing in the theory of multiplicative cascades and branching random walks and show that the methods developed in those fields can be adapted to the present case. In particular the LME recursion is shown to exhibit a phase transition, which we expect is a freezing transition, where the role of temperature is played by the exponent q. However, the LME recursion has features that make its rigorous analysis considerably harder and we point out several open problems for further study.

Skin Equivalent Tissue-Engineered Construct: Co-Cultured Fibroblasts/ Keratinocytes on 3D Matrices of Sericin Hope Cocoons

PubMed Central

Nayak, Sunita; Dey, Sancharika; Kundu, Subhas C.

2013-01-01

The development of effective and alternative tissue-engineered skin replacements to autografts, allografts and xenografts has became a clinical requirement due to the problems related to source of donor tissue and the perceived risk of disease transmission. In the present study 3D tissue engineered construct of sericin is developed using co-culture of keratinocytes on the upper surface of the fabricated matrices and with fibroblasts on lower surface. Sericin is obtained from “Sericin Hope” silkworm of Bombyx mori mutant and is extracted from cocoons by autoclave. Porous sericin matrices are prepared by freeze dried method using genipin as crosslinker. The matrices are characterized biochemically and biophysically. The cell proliferation and viability of co-cultured fibroblasts and keratinocytes on matrices for at least 28 days are observed by live/dead assay, Alamar blue assay, and by dual fluorescent staining. The growth of the fibroblasts and keratinocytes in co-culture is correlated with the expression level of TGF-β, b-FGF and IL-8 in the cultured supernatants by enzyme-linked immunosorbent assay. The histological analysis further demonstrates a multi-layered stratified epidermal layer of uninhibited keratinocytes in co-cultured constructs. Presence of involucrin, collagen IV and the fibroblast surface protein in immuno-histochemical stained sections of co-cultured matrices indicates the significance of paracrine signaling between keratinocytes and fibroblasts in the expression of extracellular matrix protein for dermal repair. No significant amount of pro inflammatory cytokines (TNF-α, IL-1β and nitric oxide) production are evidenced when macrophages grown on the sericin matrices. The results all together depict the potentiality of sericin 3D matrices as skin equivalent tissue engineered construct in wound repair. PMID:24058626

Skin equivalent tissue-engineered construct: co-cultured fibroblasts/ keratinocytes on 3D matrices of sericin hope cocoons.

PubMed

Nayak, Sunita; Dey, Sancharika; Kundu, Subhas C

2013-01-01

The development of effective and alternative tissue-engineered skin replacements to autografts, allografts and xenografts has became a clinical requirement due to the problems related to source of donor tissue and the perceived risk of disease transmission. In the present study 3D tissue engineered construct of sericin is developed using co-culture of keratinocytes on the upper surface of the fabricated matrices and with fibroblasts on lower surface. Sericin is obtained from "Sericin Hope" silkworm of Bombyx mori mutant and is extracted from cocoons by autoclave. Porous sericin matrices are prepared by freeze dried method using genipin as crosslinker. The matrices are characterized biochemically and biophysically. The cell proliferation and viability of co-cultured fibroblasts and keratinocytes on matrices for at least 28 days are observed by live/dead assay, Alamar blue assay, and by dual fluorescent staining. The growth of the fibroblasts and keratinocytes in co-culture is correlated with the expression level of TGF-β, b-FGF and IL-8 in the cultured supernatants by enzyme-linked immunosorbent assay. The histological analysis further demonstrates a multi-layered stratified epidermal layer of uninhibited keratinocytes in co-cultured constructs. Presence of involucrin, collagen IV and the fibroblast surface protein in immuno-histochemical stained sections of co-cultured matrices indicates the significance of paracrine signaling between keratinocytes and fibroblasts in the expression of extracellular matrix protein for dermal repair. No significant amount of pro inflammatory cytokines (TNF-α, IL-1β and nitric oxide) production are evidenced when macrophages grown on the sericin matrices. The results all together depict the potentiality of sericin 3D matrices as skin equivalent tissue engineered construct in wound repair.

Pascal Statistical Procedures Package (PSPP).

DTIC Science & Technology

1983-12-01

sel4 -correlation matrices and the 4 (a first/second cross-correlation matrix. 4) i s* These partitions are stored in CORRMATRIX (CM). *) *.(*4...8217CR13,YK34 ELfttaSEiac’CH~3) FOR J~a TO N 0D VDE INN N:=P; FOR I:-i TO P DO (e Access sel4 -correlations ) FOR 3:-i TO P DO RYY[I,3:=CMEI,32; FOR i:-i

Study of morphological changes in scattering and optically anisotropic medium through correlation images

NASA Astrophysics Data System (ADS)

Jain, Neha; Shukla, Prashant; Singh, Jai

2018-05-01

Correlation images are very useful in determining the morphological changes. We have investigated the correlation image analysis on depolarization and retardance matrices of polystyrene and gelatine samples respectively. We observed that that correlation images have a potential to show a significant variation with change in the concentration of samples (polystyrene and gelatine). For polystyrene microspheres the correlation value decreases with increasing scattering coefficient. In gelatine samples the correlation also decreases with sample concentration. This variation in correlation for retardance shows the change in a birefringence property of gelatine solution.

Statistical modeling of temperature, humidity and wind fields in the atmospheric boundary layer over the Siberian region

NASA Astrophysics Data System (ADS)

Lomakina, N. Ya.

2017-11-01

The work presents the results of the applied climatic division of the Siberian region into districts based on the methodology of objective classification of the atmospheric boundary layer climates by the "temperature-moisture-wind" complex realized with using the method of principal components and the special similarity criteria of average profiles and the eigen values of correlation matrices. On the territory of Siberia, it was identified 14 homogeneous regions for winter season and 10 regions were revealed for summer. The local statistical models were constructed for each region. These include vertical profiles of mean values, mean square deviations, and matrices of interlevel correlation of temperature, specific humidity, zonal and meridional wind velocity. The advantage of the obtained local statistical models over the regional models is shown.

CORRELATIONS BETWEEN INTELLIGENCE, HEAD CIRCUMFERENCE AND HEIGHT: EVIDENCE FROM TWO SAMPLES IN SAUDI ARABIA.

PubMed

Bakhiet, Salaheldin Farah Attallah; Essa, Yossry Ahmed Sayed; Dwieb, Amira Mahmood Mohsen; Elsayed, Abdelkader Mohamed Abdelkader; Sulman, Afra Sulman Mohammed; Cheng, Helen; Lynn, Richard

2017-03-01

This study was based on two independent studies which in total consisted of 1812 school pupils aged 6-12 years in Saudi Arabia. Study I consisted of 1591 school pupils (609 boys and 982 girls) attending state schools, and Study II consisted of 211 boys with learning disabilities. Intelligence (measured using the Standard Progressive Matrices Plus for Study I and the Standard Progressive Matrices for Study II), head size and height were measured for the two samples. The results showed that intelligence was statistically significantly correlated with head circumference (r=0.350, p<0.001 for Study I and r=0.168, p<0.05 for Study II) and height (r=0.271, p<0.001 for Study I and r=0.178, p<0.05 for Study II).

Computation of canonical correlation and best predictable aspect of future for time series

NASA Technical Reports Server (NTRS)

Pourahmadi, Mohsen; Miamee, A. G.

1989-01-01

The canonical correlation between the (infinite) past and future of a stationary time series is shown to be the limit of the canonical correlation between the (infinite) past and (finite) future, and computation of the latter is reduced to a (generalized) eigenvalue problem involving (finite) matrices. This provides a convenient and essentially, finite-dimensional algorithm for computing canonical correlations and components of a time series. An upper bound is conjectured for the largest canonical correlation.

Matrix density alters zyxin phosphorylation, which limits peripheral process formation and extension in endothelial cells invading 3D collagen matrices.

PubMed

Abbey, Colette A; Bayless, Kayla J

2014-09-01

This study was designed to determine the optimal conditions required for known pro-angiogenic stimuli to elicit successful endothelial sprouting responses. We used an established, quantifiable model of endothelial cell (EC) sprout initiation where ECs were tested for invasion in low (1 mg/mL) and high density (5 mg/mL) 3D collagen matrices. Sphingosine 1-phosphate (S1P) alone, or S1P combined with stromal derived factor-1α (SDF) and phorbol ester (TPA), elicited robust sprouting responses. The ability of these factors to stimulate sprouting was more effective in higher density collagen matrices. S1P stimulation resulted in a significant increase in invasion distance, and with the exception of treatment groups containing phorbol ester, invasion distance was longer in 1mg/mL compared to 5mg/mL collagen matrices. Closer examination of cell morphology revealed that increasing matrix density and supplementing with SDF and TPA enhanced the formation of multicellular structures more closely resembling capillaries. TPA enhanced the frequency and size of lumen formation and correlated with a robust increase in phosphorylation of p42/p44 Erk kinase, while S1P and SDF did not. Also, a higher number of significantly longer extended processes formed in 5mg/mL compared to 1mg/mL collagen matrices. Because collagen matrices at higher density have been reported to be stiffer, we tested for changes in the mechanosensitive protein, zyxin. Interestingly, zyxin phosphorylation levels inversely correlated with matrix density, while levels of total zyxin did not change significantly. Immunofluorescence and localization studies revealed that total zyxin was distributed evenly throughout invading structures, while phosphorylated zyxin was slightly more intense in extended peripheral processes. Silencing zyxin expression increased extended process length and number of processes, while increasing zyxin levels decreased extended process length. Altogether these data indicate that ECs integrate signals from multiple exogenous factors, including changes in matrix density, to accomplish successful sprouting responses. We show here for the first time that zyxin limited the formation and extension of fine peripheral processes used by ECs for matrix interrogation, providing a molecular explanation for altered EC responses to high and low density collagen matrices. Copyright © 2014 International Society of Matrix Biology. Published by Elsevier B.V. All rights reserved.

Intelligence and Creativity: Over the Threshold Together?

ERIC Educational Resources Information Center

Welter, Marisete Maria; Jaarsveld, Saskia; van Leeuwen, Cees; Lachmann, Thomas

2016-01-01

Threshold theory predicts a positive correlation between IQ and creativity scores up to an IQ level of 120 and no correlation above this threshold. Primary school children were tested at beginning (N = 98) and ending (N = 70) of the school year. Participants performed the standard progressive matrices (SPM) and the Test of Creative…

Discrete and morphometric traits reveal contrasting patterns and processes in the macroevolutionary history of a clade of scorpions.

PubMed

Mongiardino Koch, N; Ceccarelli, F S; Ojanguren-Affilastro, A A; Ramírez, M J

2017-04-01

Many palaeontological studies have investigated the evolution of entire body plans, generally relying on discrete character-taxon matrices. In contrast, macroevolutionary studies performed by neontologists have mostly focused on morphometric traits. Although these data types are very different, some studies have suggested that they capture common patterns. Nonetheless, the tests employed to support this claim have not explicitly incorporated a phylogenetic framework and may therefore be susceptible to confounding effects due to the presence of common phylogenetic structure. We address this question using the scorpion genus Brachistosternus Pocock 1893 as case study. We make use of a time-calibrated multilocus molecular phylogeny, and compile discrete and traditional morphometric data sets, both capturing the overall morphology of the organisms. We find that morphospaces derived from these matrices are significantly different, and that the degree of discordance cannot be replicated by simulations of random character evolution. Moreover, we find strong support for contrasting modes of evolution, with discrete characters being congruent with an 'early burst' scenario whereas morphometric traits suggest species-specific adaptations to have driven morphological evolution. The inferred macroevolutionary dynamics are therefore contingent on the choice of character type. Finally, we confirm that metrics of correlation fail to detect these profound differences given common phylogenetic structure in both data sets, and that methods incorporating a phylogenetic framework and accounting for expected covariance should be favoured. © 2017 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2017 European Society For Evolutionary Biology.

Effect of Polydispersity on Diffusion in Random Obstacle Matrices

NASA Astrophysics Data System (ADS)

Cho, Hyun Woo; Kwon, Gyemin; Sung, Bong June; Yethiraj, Arun

2012-10-01

The dynamics of tracers in disordered matrices is of interest in a number of diverse areas of physics such as the biophysics of crowding in cells and cell membranes, and the diffusion of fluids in porous media. To a good approximation the matrices can be modeled as a collection of spatially frozen particles. In this Letter, we consider the effect of polydispersity (in size) of the matrix particles on the dynamics of tracers. We study a two dimensional system of hard disks diffusing in a sea of hard disk obstacles, for different values of the polydispersity of the matrix. We find that for a given average size and area fraction, the diffusion of tracers is very sensitive to the polydispersity. We calculate the pore percolation threshold using Apollonius diagrams. The diffusion constant, D, follows a scaling relation D˜(ϕc-ϕm)μ-β for all values of the polydispersity, where ϕm is the area fraction and ϕc is the value of ϕm at the percolation threshold.

Effect of polydispersity on diffusion in random obstacle matrices.

PubMed

Cho, Hyun Woo; Kwon, Gyemin; Sung, Bong June; Yethiraj, Arun

2012-10-12

The dynamics of tracers in disordered matrices is of interest in a number of diverse areas of physics such as the biophysics of crowding in cells and cell membranes, and the diffusion of fluids in porous media. To a good approximation the matrices can be modeled as a collection of spatially frozen particles. In this Letter, we consider the effect of polydispersity (in size) of the matrix particles on the dynamics of tracers. We study a two dimensional system of hard disks diffusing in a sea of hard disk obstacles, for different values of the polydispersity of the matrix. We find that for a given average size and area fraction, the diffusion of tracers is very sensitive to the polydispersity. We calculate the pore percolation threshold using Apollonius diagrams. The diffusion constant, D, follows a scaling relation D~(φ(c)-φ(m))(μ-β) for all values of the polydispersity, where φ(m) is the area fraction and φ(c) is the value of φ(m) at the percolation threshold.

Random harmonic analysis program, L221 (TEV156). Volume 1: Engineering and usage

NASA Technical Reports Server (NTRS)

Miller, R. D.; Graham, M. L.

1979-01-01

A digital computer program capable of calculating steady state solutions for linear second order differential equations due to sinusoidal forcing functions is described. The field of application of the program, the analysis of airplane response and loads due to continuous random air turbulence, is discussed. Optional capabilities including frequency dependent input matrices, feedback damping, gradual gust penetration, multiple excitation forcing functions, and a static elastic solution are described. Program usage and a description of the analysis used are presented.

Wigner surmises and the two-dimensional homogeneous Poisson point process.

PubMed

Sakhr, Jamal; Nieminen, John M

2006-04-01

We derive a set of identities that relate the higher-order interpoint spacing statistics of the two-dimensional homogeneous Poisson point process to the Wigner surmises for the higher-order spacing distributions of eigenvalues from the three classical random matrix ensembles. We also report a remarkable identity that equates the second-nearest-neighbor spacing statistics of the points of the Poisson process and the nearest-neighbor spacing statistics of complex eigenvalues from Ginibre's ensemble of 2 x 2 complex non-Hermitian random matrices.

Rational decisions, random matrices and spin glasses

NASA Astrophysics Data System (ADS)

Galluccio, Stefano; Bouchaud, Jean-Philippe; Potters, Marc

We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of optimal solutions is generally exponentially large, and each of them is fragile: rationality is in this case of limited use. In addition, this problem is related to spin glasses with Lévy-like (long-ranged) couplings, for which we show that the ground state is not exponentially degenerate.

A dissonant scale: stress recognition in the SAQ.

PubMed

Taylor, Jennifer A; Pandian, Ravi

2013-07-31

Our previous analyses using the Stress Recognition subscale of the Safety Attitudes Questionnaire (SAQ) resulted in significant effect estimates with equally opposing explanations. We suspected construct validity issues and investigated such using our own data and correlation matrices of previous published studies. The correlation matrices for each of the SAQ subscales from two previous studies by Speroff and Taylor were replicated and compared. The SAS Proc Factor procedure and the PRIORS = SMC option were used to perform Common Factor Analysis. The correlation matrices of both studies were very similar. Teamwork, Safety Climate, Job Satisfaction, Perceptions of Management and Working Conditions were well-correlated. The correlations ranged from 0.53 to 0.76. For Stress Recognition correlations ranged from -0.15 to 0.03. Common Factor Analysis confirmed the isolation of Stress Recognition. CFA returned a strong one-factor model that explained virtually all of the communal variance. Stress Recognition loaded poorly on this factor in both instances, and the CFA indicated that 96.4-100.0% of the variance associated with Stress Recognition was unique to that subscale, and not shared with the other 5 subscales. We conclude that the Stress Recognition subscale does not fit into the overall safety climate construct the SAQ intended to reflect. We recommend that this domain be omitted from overall safety climate scale score calculations, and clearly identified as an important yet distinct organizational construct. We suggest that this subscale be investigated for its true meaning, characterized as such, and findings conveyed to SAQ end users. We make no argument against Stress Recognition as an important organizational metric, rather we suggest that as a stand-alone construct its current packaging within the SAQ may be misleading for those intent on intervention development and evaluation in healthcare settings if they interpret Stress Recognition results as emblematic of safety climate.

Vast Portfolio Selection with Gross-exposure Constraints*

PubMed Central

Fan, Jianqing; Zhang, Jingjin; Yu, Ke

2012-01-01

We introduce the large portfolio selection using gross-exposure constraints. We show that with gross-exposure constraint the empirically selected optimal portfolios based on estimated covariance matrices have similar performance to the theoretical optimal ones and there is no error accumulation effect from estimation of vast covariance matrices. This gives theoretical justification to the empirical results in Jagannathan and Ma (2003). We also show that the no-short-sale portfolio can be improved by allowing some short positions. The applications to portfolio selection, tracking, and improvements are also addressed. The utility of our new approach is illustrated by simulation and empirical studies on the 100 Fama-French industrial portfolios and the 600 stocks randomly selected from Russell 3000. PMID:23293404

Bayesian Genomic Prediction with Genotype × Environment Interaction Kernel Models

PubMed Central

Cuevas, Jaime; Crossa, José; Montesinos-López, Osval A.; Burgueño, Juan; Pérez-Rodríguez, Paulino; de los Campos, Gustavo

2016-01-01

The phenomenon of genotype × environment (G × E) interaction in plant breeding decreases selection accuracy, thereby negatively affecting genetic gains. Several genomic prediction models incorporating G × E have been recently developed and used in genomic selection of plant breeding programs. Genomic prediction models for assessing multi-environment G × E interaction are extensions of a single-environment model, and have advantages and limitations. In this study, we propose two multi-environment Bayesian genomic models: the first model considers genetic effects (u) that can be assessed by the Kronecker product of variance–covariance matrices of genetic correlations between environments and genomic kernels through markers under two linear kernel methods, linear (genomic best linear unbiased predictors, GBLUP) and Gaussian (Gaussian kernel, GK). The other model has the same genetic component as the first model (u) plus an extra component, f, that captures random effects between environments that were not captured by the random effects u. We used five CIMMYT data sets (one maize and four wheat) that were previously used in different studies. Results show that models with G × E always have superior prediction ability than single-environment models, and the higher prediction ability of multi-environment models with u and f over the multi-environment model with only u occurred 85% of the time with GBLUP and 45% of the time with GK across the five data sets. The latter result indicated that including the random effect f is still beneficial for increasing prediction ability after adjusting by the random effect u. PMID:27793970

Bayesian Genomic Prediction with Genotype × Environment Interaction Kernel Models.

PubMed

Cuevas, Jaime; Crossa, José; Montesinos-López, Osval A; Burgueño, Juan; Pérez-Rodríguez, Paulino; de Los Campos, Gustavo

2017-01-05

The phenomenon of genotype × environment (G × E) interaction in plant breeding decreases selection accuracy, thereby negatively affecting genetic gains. Several genomic prediction models incorporating G × E have been recently developed and used in genomic selection of plant breeding programs. Genomic prediction models for assessing multi-environment G × E interaction are extensions of a single-environment model, and have advantages and limitations. In this study, we propose two multi-environment Bayesian genomic models: the first model considers genetic effects [Formula: see text] that can be assessed by the Kronecker product of variance-covariance matrices of genetic correlations between environments and genomic kernels through markers under two linear kernel methods, linear (genomic best linear unbiased predictors, GBLUP) and Gaussian (Gaussian kernel, GK). The other model has the same genetic component as the first model [Formula: see text] plus an extra component, F: , that captures random effects between environments that were not captured by the random effects [Formula: see text] We used five CIMMYT data sets (one maize and four wheat) that were previously used in different studies. Results show that models with G × E always have superior prediction ability than single-environment models, and the higher prediction ability of multi-environment models with [Formula: see text] over the multi-environment model with only u occurred 85% of the time with GBLUP and 45% of the time with GK across the five data sets. The latter result indicated that including the random effect f is still beneficial for increasing prediction ability after adjusting by the random effect [Formula: see text]. Copyright © 2017 Cuevas et al.

What Randomized Benchmarking Actually Measures

DOE PAGES

Proctor, Timothy; Rudinger, Kenneth; Young, Kevin; ...

2017-09-28

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r. For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not amore » well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. Here, these theories allow explicit computation of the error rate that RB measures (r), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.« less

Fidelity decay of the two-level bosonic embedded ensembles of random matrices

NASA Astrophysics Data System (ADS)

Benet, Luis; Hernández-Quiroz, Saúl; Seligman, Thomas H.

2010-12-01

We study the fidelity decay of the k-body embedded ensembles of random matrices for bosons distributed over two single-particle states. Fidelity is defined in terms of a reference Hamiltonian, which is a purely diagonal matrix consisting of a fixed one-body term and includes the diagonal of the perturbing k-body embedded ensemble matrix, and the perturbed Hamiltonian which includes the residual off-diagonal elements of the k-body interaction. This choice mimics the typical mean-field basis used in many calculations. We study separately the cases k = 2 and 3. We compute the ensemble-averaged fidelity decay as well as the fidelity of typical members with respect to an initial random state. Average fidelity displays a revival at the Heisenberg time, t = tH = 1, and a freeze in the fidelity decay, during which periodic revivals of period tH are observed. We obtain the relevant scaling properties with respect to the number of bosons and the strength of the perturbation. For certain members of the ensemble, we find that the period of the revivals during the freeze of fidelity occurs at fractional times of tH. These fractional periodic revivals are related to the dominance of specific k-body terms in the perturbation.

Soil salinity and matric potential interaction on water use, water use efficiency and yield response factor of bean and wheat.

PubMed

Khataar, Mahnaz; Mohhamadi, Mohammad Hossien; Shabani, Farzin

2018-02-08

We studied the effects of soil matric potential and salinity on the water use (WU), water use efficiency (WUE) and yield response factor (Ky), for wheat (Triticum aestivum cv. Mahdavi) and bean (Phaseoulus vulgaris cv. COS16) in sandy loam and clay loam soils under greenhouse conditions. Results showed that aeration porosity is the predominant factor controlling WU, WUE, Ky and shoot biomass (Bs) at high soil water potentials. As matric potential was decreased, soil aeration improved, with Bs, WU and Ky reaching maximum value at -6 to -10 kPa, under all salinities. Wheat WUE remained almost unchanged by reduction of matric potential under low salinities (EC ≤ 8 dSm -1 ), but increased under higher salinities (EC ≥ 8 dSm -1 ), as did bean WUE at all salinities, as matric potential decreased to -33 kPa. Wheat WUE exceeds that of bean in both sandy loam and clay loam soils. WUE of both plants increased with higher shoot/root ratio and a high correlation coefficient exists between them. Results showed that salinity decreases all parameters, particularly at high potentials (h = -2 kPa), and amplifies the effects of waterlogging. Further, we observed a strong relationship between transpiration (T) and root respiration (Rr) for all experiments.

Correlation of water vapor adsorption behavior of wood with surface thermodynamic properties

Treesearch

Mandla A. Tshabalala; Agnes R. Denes; R. Sam Williams

1999-01-01

To improve the overall performance of wood-plastic composites, appropriate technologies are needed to control moisture sorption and to improve the interaction of wood fiber with selected hydrophobic matrices. The objective of this study was to determine the surface thermodynamic characteristics of a wood fiber and to correlate those characteristics with the fiberas...

Some physiological responses of wheat and bean to soil salinity at low matric suctions

NASA Astrophysics Data System (ADS)

Khatar, Mahnaz; Mohammadi, Mohammad Hossein; Shekari, Farid

2017-01-01

The effect of soil matric suction (2-33 kPa) and salinity (soil solution electrical conductivity 0.7-8 dS m-1 for bean and 2-20 dS m-1 for wheat) on some physiological characteristics of bean and wheat in a clay loam soil under greenhouse condition was investigated. The results showed that the leaf chlorophyll content index and potassium concentration decrease under salinity stress and increase with matric suction from 2 to 33 kPa suction for both plants. The wheat chlorophyll content index declines during the stress spell but bean chlorophyll content index remains nearly constant. The lowest values of the content of soluble sugars and the highest values of leaf proline content are observed at2 kPa matric suction (highest aeration stress) for bean and wheat. As matric suction increases from 2 to 6 kPa, the soluble sugars increases and proline content decreases significantly and then soluble sugars decreases and proline content increases until 10 kPa suction, and the soluble sugars remains nearly constant at the higher matric suctions for both plants. While the electrical conductivity effect on the soluble sugars is not significant, the values of proline content for both crop increase significantly with electrical conductivity. It was shown that the aeration stress can result in more considerable and rapid physiological responses, in comparison with salinity stress. There is a strong correlation between wheat and bean chlorophyll content index and potassium concentration under salinity and aeration stresses.

Quantitative structure-retention relationships for gas chromatographic retention indices of alkylbenzenes with molecular graph descriptors.

PubMed

Ivanciuc, O; Ivanciuc, T; Klein, D J; Seitz, W A; Balaban, A T

2001-02-01

Quantitative structure-retention relationships (QSRR) represent statistical models that quantify the connection between the molecular structure and the chromatographic retention indices of organic compounds, allowing the prediction of retention indices of novel, not yet synthesized compounds, solely from their structural descriptors. Using multiple linear regression, QSRR models for the gas chromatographic Kováts retention indices of 129 alkylbenzenes are generated using molecular graph descriptors. The correlational ability of structural descriptors computed from 10 molecular matrices is investigated, showing that the novel reciprocal matrices give numerical indices with improved correlational ability. A QSRR equation with 5 graph descriptors gives the best calibration and prediction results, demonstrating the usefulness of the molecular graph descriptors in modeling chromatographic retention parameters. The sequential orthogonalization of descriptors suggests simpler QSRR models by eliminating redundant structural information.

Matrix product representation of the stationary state of the open zero range process

NASA Astrophysics Data System (ADS)

Bertin, Eric; Vanicat, Matthieu

2018-06-01

Many one-dimensional lattice particle models with open boundaries, like the paradigmatic asymmetric simple exclusion process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not explicitly depend on the lattice site. In contrast, the stationary state of the open 1D zero-range process (ZRP) takes an inhomogeneous factorized form, with site-dependent probability weights. We show that in spite of the absence of correlations, the stationary state of the open ZRP can also be represented in a matrix product form, where the matrices are site-independent, non-commuting and determined from algebraic relations resulting from the master equation. We recover the known distribution of the open ZRP in two different ways: first, using an explicit representation of the matrices and boundary vectors; second, from the sole knowledge of the algebraic relations satisfied by these matrices and vectors. Finally, an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden Markov chains.

On Connected Diagrams and Cumulants of Erdős-Rényi Matrix Models

NASA Astrophysics Data System (ADS)

Khorunzhiy, O.

2008-08-01

Regarding the adjacency matrices of n-vertex graphs and related graph Laplacian we introduce two families of discrete matrix models constructed both with the help of the Erdős-Rényi ensemble of random graphs. Corresponding matrix sums represent the characteristic functions of the average number of walks and closed walks over the random graph. These sums can be considered as discrete analogues of the matrix integrals of random matrix theory. We study the diagram structure of the cumulant expansions of logarithms of these matrix sums and analyze the limiting expressions as n → ∞ in the cases of constant and vanishing edge probabilities.

Universality in chaos: Lyapunov spectrum and random matrix theory.

PubMed

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

Universality in chaos: Lyapunov spectrum and random matrix theory

NASA Astrophysics Data System (ADS)

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t =0 , while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

Biodistance analysis of the Moche sacrificial victims from Huaca de la Luna plaza 3C: Matrix method test of their origins.

PubMed

Sutter, Richard C; Verano, John W

2007-02-01

The purpose of this study is to test two competing models regarding the origins of Early Intermediate Period (AD 200-750) sacrificial victims from the Huacas de Moche site using the matrix correlation method. The first model posits the sacrificial victims represent local elites who lost competitions in ritual battles with one another, while the other model suggests the victims were nonlocal warriors captured during warfare with nearby polities. We estimate biodistances for sacrificial victims from Huaca de la Luna Plaza 3C (AD 300-550) with eight previously reported samples from the north coast of Peru using both the mean measure of divergence (MMD) and Mahalanobis' distance (d2). Hypothetical matrices are developed based upon the assumptions of each of the two competing models regarding the origins of Moche sacrificial victims. When the MMD matrix is compared to the two hypothetical matrices using a partial-Mantel test (Smouse et al.: Syst Zool 35 (1986) 627-632), the ritual combat model (i.e. local origins) has a low and nonsignificant correlation (r = 0.134, P = 0.163), while the nonlocal origins model is highly correlated and significant (r = 0.688, P = 0.001). Comparisons of the d2 results and the two hypothetical matrices also produced low and nonsignificant correlation for the ritual combat model (r = 0.210, P = 0.212), while producing a higher and statistically significant result with the nonlocal origins model (r = 0.676, P = 0.002). We suggest that the Moche sacrificial victims represent nonlocal warriors captured in territorial combat with nearby competing polities. Copyright 2006 Wiley-Liss, Inc.

Dose reduction of risperidone and olanzapine can improve cognitive function and negative symptoms in stable schizophrenic patients: A single-blinded, 52-week, randomized controlled study.

PubMed

Zhou, Yanling; Li, Guannan; Li, Dan; Cui, Hongmei; Ning, Yuping

2018-05-01

The long-term effects of dose reduction of atypical antipsychotics on cognitive function and symptomatology in stable patients with schizophrenia remain unclear. We sought to determine the change in cognitive function and symptomatology after reducing risperidone or olanzapine dosage in stable schizophrenic patients. Seventy-five stabilized schizophrenic patients prescribed risperidone (≥4 mg/day) or olanzapine (≥10 mg/day) were randomly divided into a dose-reduction group ( n=37) and a maintenance group ( n=38). For the dose-reduction group, the dose of antipsychotics was reduced by 50%; for the maintenance group, the dose remained unchanged throughout the whole study. The Positive and Negative Syndrome Scale, Negative Symptom Assessment-16, Rating Scale for Extrapyramidal Side Effects, and Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) Consensus Cognitive Battery were measured at baseline, 12, 28, and 52 weeks. Linear mixed models were performed to compare the Positive and Negative Syndrome Scale, Negative Symptom Assessment-16, Rating Scale for Extrapyramidal Side Effects and MATRICS Consensus Cognitive Battery scores between groups. The linear mixed model showed significant time by group interactions on the Positive and Negative Syndrome Scale negative symptoms, Negative Symptom Assessment-16, Rating Scale for Extrapyramidal Side Effects, speed of processing, attention/vigilance, working memory and total score of MATRICS Consensus Cognitive Battery (all p<0.05). Post hoc analyses showed significant improvement in Positive and Negative Syndrome Scale negative subscale, Negative Symptom Assessment-16, Rating Scale for Extrapyramidal Side Effects, speed of processing, working memory and total score of MATRICS Consensus Cognitive Battery for the dose reduction group compared with those for the maintenance group (all p<0.05). This study indicated that a risperidone or olanzapine dose reduction of 50% may not lead to more severe symptomatology but can improve speed of processing, working memory and negative symptoms in patients with stabilized schizophrenia.

Very High Frequency Epr: Instrument and Applications

NASA Astrophysics Data System (ADS)

Wang, Wei

Most Electron Paramagnetic Resonance (EPR, also known as ESR or EMR) experiments are performed at conventional 9 GHz or 35 GHz frequency. But there are numerous situations in which a large increase in the microwave frequency (and/or magnetic field) will result in substantial increase in the information content in EPR spectra. This has motivated us to construct a very high frequency (VHF, 95 GHz) EPR spectrometer at Illinois EPR Research Center. Many advantages of VHF EPR are demonstrated through examples in Chapter 1. The spectrometer and some unique aspects of the instrument are described and documented in Chapter 2. Chapter 3 reports use of the VHF EPR technique to study the structure/spectral relationship of a homologous series of thiophenes, which may be constituents of coal. Two successful methods to generate the cation radicals of these organic sulfur compounds are found. The g matrices (tensors) of the thiophenic radicals are obtained for the first time. The small differences between anisotropic components of the g matrices can be unambiguously resolved. Correlations of the experimentally measured g matrices with the molecular and electronic structures are reported. The g shifts correlate linearly with lambda of their Huckel molecular orbitals; the largest g components are proportional to the pi spin densities on sulfur. In addition, the small proton hyperfine interactions of dibenzothiophene (DBT) are observed for the first time by continuous wave VHF EPR. A multifrequency approach, including auxiliary 2-4 GHz pulsed measurement, has shown that a single set of spin Hamiltonian parameters describes the spin system of DBT over a microwave frequency span of 3 to 95 GHz. These newly available, detailed, and accurate data provide a valuable opportunity to test, and perhaps to improve, the existing theoretical models for predictions on g matrices of organic radicals. Finally, Chapter 4 reports trial calculations of g matrices by several molecular orbital methods.

Powdered activated carbons as effective phases for bar adsorptive micro-extraction (BAμE) to monitor levels of triazinic herbicides in environmental water matrices.

PubMed

Neng, N R; Mestre, A S; Carvalho, A P; Nogueira, J M F

2011-02-15

Bar adsorptive micro-extraction using three powdered activated carbons (ACs) as adsorbent phases followed by liquid desorption and high performance liquid chromatography with diode array detection (BAμE(ACs)-LD/HPLC-DAD), was developed to monitor triazinic herbicides (atrazine, simazine and terbutylazine) in environmental water matrices. ACs used present apparent surface areas around 1000 m(2) g(-1) with an important mesoporous volume and distinct surface chemistry characteristics (pH(PZC) ranging from 6.5 to 10.4). The textural and surface chemistry properties of the ACs adsorbent phases were correlated with the analytical data for a better understanding of the overall enrichment process. Assays performed on 10 mL water samples spiked at the 10.0 μg L(-1) levels under optimized experimental conditions yielded recoveries around 100% for the three herbicides under study. The analytical performance showed good precision (RSD<15.0%), convenient detection limits (≈0.1 μg L(-1)) and suitable linearity (1.0-12.0 μg L(-1)) with good correlation coefficients (r(2)>0.9914). By using the standard addition method, the application of the present method on real water matrices, such as surface water and wastewater, allowed very good performances at the trace level. The proposed methodology proved to be a suitable sorptive extraction alternative for the analysis of priority pollutants with polar characteristics, showing to be easy to implement, reliable, sensitive and requiring a low sample volume to monitor triazinic compounds in water matrices. Copyright © 2010 Elsevier B.V. All rights reserved.

Inter-subject FDG PET Brain Networks Exhibit Multi-scale Community Structure with Different Normalization Techniques.

PubMed

Sperry, Megan M; Kartha, Sonia; Granquist, Eric J; Winkelstein, Beth A

2018-07-01

Inter-subject networks are used to model correlations between brain regions and are particularly useful for metabolic imaging techniques, like 18F-2-deoxy-2-(18F)fluoro-D-glucose (FDG) positron emission tomography (PET). Since FDG PET typically produces a single image, correlations cannot be calculated over time. Little focus has been placed on the basic properties of inter-subject networks and if they are affected by group size and image normalization. FDG PET images were acquired from rats (n = 18), normalized by whole brain, visual cortex, or cerebellar FDG uptake, and used to construct correlation matrices. Group size effects on network stability were investigated by systematically adding rats and evaluating local network connectivity (node strength and clustering coefficient). Modularity and community structure were also evaluated in the differently normalized networks to assess meso-scale network relationships. Local network properties are stable regardless of normalization region for groups of at least 10. Whole brain-normalized networks are more modular than visual cortex- or cerebellum-normalized network (p < 0.00001); however, community structure is similar at network resolutions where modularity differs most between brain and randomized networks. Hierarchical analysis reveals consistent modules at different scales and clustering of spatially-proximate brain regions. Findings suggest inter-subject FDG PET networks are stable for reasonable group sizes and exhibit multi-scale modularity.

Short-Term Memory in Orthogonal Neural Networks

NASA Astrophysics Data System (ADS)

White, Olivia L.; Lee, Daniel D.; Sompolinsky, Haim

2004-04-01

We study the ability of linear recurrent networks obeying discrete time dynamics to store long temporal sequences that are retrievable from the instantaneous state of the network. We calculate this temporal memory capacity for both distributed shift register and random orthogonal connectivity matrices. We show that the memory capacity of these networks scales with system size.

Computation of mean and variance of the radiotherapy dose for PCA-modeled random shape and position variations of the target.

PubMed

Budiarto, E; Keijzer, M; Storchi, P R M; Heemink, A W; Breedveld, S; Heijmen, B J M

2014-01-20

Radiotherapy dose delivery in the tumor and surrounding healthy tissues is affected by movements and deformations of the corresponding organs between fractions. The random variations may be characterized by non-rigid, anisotropic principal component analysis (PCA) modes. In this article new dynamic dose deposition matrices, based on established PCA modes, are introduced as a tool to evaluate the mean and the variance of the dose at each target point resulting from any given set of fluence profiles. The method is tested for a simple cubic geometry and for a prostate case. The movements spread out the distributions of the mean dose and cause the variance of the dose to be highest near the edges of the beams. The non-rigidity and anisotropy of the movements are reflected in both quantities. The dynamic dose deposition matrices facilitate the inclusion of the mean and the variance of the dose in the existing fluence-profile optimizer for radiotherapy planning, to ensure robust plans with respect to the movements.

Measurement Matrix Design for Phase Retrieval Based on Mutual Information

NASA Astrophysics Data System (ADS)

Shlezinger, Nir; Dabora, Ron; Eldar, Yonina C.

2018-01-01

In phase retrieval problems, a signal of interest (SOI) is reconstructed based on the magnitude of a linear transformation of the SOI observed with additive noise. The linear transform is typically referred to as a measurement matrix. Many works on phase retrieval assume that the measurement matrix is a random Gaussian matrix, which, in the noiseless scenario with sufficiently many measurements, guarantees invertability of the transformation between the SOI and the observations, up to an inherent phase ambiguity. However, in many practical applications, the measurement matrix corresponds to an underlying physical setup, and is therefore deterministic, possibly with structural constraints. In this work we study the design of deterministic measurement matrices, based on maximizing the mutual information between the SOI and the observations. We characterize necessary conditions for the optimality of a measurement matrix, and analytically obtain the optimal matrix in the low signal-to-noise ratio regime. Practical methods for designing general measurement matrices and masked Fourier measurements are proposed. Simulation tests demonstrate the performance gain achieved by the proposed techniques compared to random Gaussian measurements for various phase recovery algorithms.

Raney Distributions and Random Matrix Theory

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Liu, Dang-Zheng

2015-03-01

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

Non-continuum, anisotropic nanomechanics of random and aligned electrospun nanofiber matrices

NASA Astrophysics Data System (ADS)

Chery, Daphney; Han, Biao; Mauck, Robert; Shenoy, Vivek; Han, Lin

Polymer nanofiber assemblies are widely used in cell culture and tissue engineering, while their nanomechanical characteristics have received little attention. In this study, to understand their nanoscale structure-mechanics relations, nanofibers of polycaprolactone (PCL) and poly(vinyl alcohol) (PVA) were fabricated via electrospinning, and tested via AFM-nanoindentation with a microspherical tip (R ~10 μm) in PBS. For the hydrophobic, less-swollen PCL, a novel, non-continuum linear F-D dependence was observed, instead of the typical Hertzian F-D3/2 behavior, which is usually expected for continuum materials. This linear trend is likely resulted from the tensile stretch of a few individual nanofibers as they were indented in the normal plane. In contrast, for the hydrophilic, highly swollen PVA, the observed typical Hertzian response indicates the dominance of localized deformation within each nanofiber, which had swollen to become hydrogels. Furthermore, for both matrices, aligned fibers showed significantly higher stiffness than random fibers. These results provide a fundamental basis on the nanomechanics of biomaterials for specialized applications in cell phenotype and tissue repair.

Abnormal functional connectivity of EEG gamma band in patients with depression during emotional face processing.

PubMed

Li, Yingjie; Cao, Dan; Wei, Ling; Tang, Yingying; Wang, Jijun

2015-11-01

This paper evaluates the large-scale structure of functional brain networks using graph theoretical concepts and investigates the difference in brain functional networks between patients with depression and healthy controls while they were processing emotional stimuli. Electroencephalography (EEG) activities were recorded from 16 patients with depression and 14 healthy controls when they performed a spatial search task for facial expressions. Correlations between all possible pairs of 59 electrodes were determined by coherence, and the coherence matrices were calculated in delta, theta, alpha, beta, and gamma bands (low gamma: 30-50Hz and high gamma: 50-80Hz, respectively). Graph theoretical analysis was applied to these matrices by using two indexes: the clustering coefficient and the characteristic path length. The global EEG coherence of patients with depression was significantly higher than that of healthy controls in both gamma bands, especially in the high gamma band. The global coherence in both gamma bands from healthy controls appeared higher in negative conditions than in positive conditions. All the brain networks were found to hold a regular and ordered topology during emotion processing. However, the brain network of patients with depression appeared randomized compared with the normal one. The abnormal network topology of patients with depression was detected in both the prefrontal and occipital regions. The negative bias from healthy controls occurred in both gamma bands during emotion processing, while it disappeared in patients with depression. The proposed work studied abnormally increased connectivity of brain functional networks in patients with depression. By combing the clustering coefficient and the characteristic path length, we found that the brain networks of patients with depression and healthy controls had regular networks during emotion processing. Yet the brain networks of the depressed group presented randomization trends. Moreover, negative bias was detected in the healthy controls during emotion processing, while it was not detected in patients with depression, which might be related to the types of negative stimuli used in this study. The brain networks from both patients with depression and healthy controls were found to hold a regular and ordered topology. Yet the brain networks of patients with depression had randomization trends. Copyright © 2015 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Analysis of stock prices of mining business

NASA Astrophysics Data System (ADS)

Ahn, Sanghyun; Lim, G. C.; Kim, S. H.; Kim, Soo Yong; Yoon, Kwon Youb; Stanfield, Joseph Lee; Kim, Kyungsik

2011-06-01

Stock exchanges have a diversity of so-called business groups and much evidence has been presented by covariance matrix analysis (Laloux et al. (1999) [6], Plerou et al. (2002) [7], Plerou et al. (1999) [8], Mantegna (1999) [9], Utsugi et al. (2004) [21] and Lim et al. (2009) [26]). A market-wide effect plays a crucial role in shifting the correlation structure from random to non-random. In this work, we study the structural properties of stocks related to the mining industry, especially rare earth minerals, listed on two exchanges, namely the TSX (Toronto stock exchange) and the TSX-V (Toronto stock exchange-ventures). In general, raw-material businesses are sensitively affected by the global economy while each firm has its own cycle. We prove that the global crisis during 2006-2009 affected the mineral market considerably. These two aspects compete to control price fluctuations. We show that the internal cycle overwhelms the global economic environment in terms of random matrix theory and overlapping matrices. However, during the period of 2006-2009, the effect of the global economic environment emerges. This result is well explained by the recent global financial/economic crisis. For comparison, we analyze the time stability of business clusters of the KOSPI, that is, the electric/electronic business, using an overlapping matrix. A clear difference in behavior is confirmed. Consequently, rare earth minerals in the raw-material business should be classified not by standard business classifications but by the internal cycle of business.

HBTprogs Version 1.0

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

Brown, D; Danielewicz, P

2002-03-15

This is the manual for a collection of programs that can be used to invert angled-averaged (i.e. one dimensional) two-particle correlation functions. This package consists of several programs that generate kernel matrices (basically the relative wavefunction of the pair, squared), programs that generate test correlation functions from test sources of various types and the program that actually inverts the data using the kernel matrix.

Distinct neural substrates of visuospatial and verbal-analytic reasoning as assessed by Raven's Advanced Progressive Matrices.

PubMed

Chen, Zhencai; De Beuckelaer, Alain; Wang, Xu; Liu, Jia

2017-11-24

Recent studies revealed spontaneous neural activity to be associated with fluid intelligence (gF) which is commonly assessed by Raven's Advanced Progressive Matrices, and embeds two types of reasoning: visuospatial and verbal-analytic reasoning. With resting-state fMRI data, using global brain connectivity (GBC) analysis which averages functional connectivity of a voxel in relation to all other voxels in the brain, distinct neural correlates of these two reasoning types were found. For visuospatial reasoning, negative correlations were observed in both the primary visual cortex (PVC) and the precuneus, and positive correlations were observed in the temporal lobe. For verbal-analytic reasoning, negative correlations were observed in the right inferior frontal gyrus (rIFG), dorsal anterior cingulate cortex and temporoparietal junction, and positive correlations were observed in the angular gyrus. Furthermore, an interaction between GBC value and type of reasoning was found in the PVC, rIFG and the temporal lobe. These findings suggest that visuospatial reasoning benefits more from elaborate perception to stimulus features, whereas verbal-analytic reasoning benefits more from feature integration and hypothesis testing. In sum, the present study offers, for different types of reasoning in gF, first empirical evidence of separate neural substrates in the resting brain.

Targeting functional motifs of a protein family

NASA Astrophysics Data System (ADS)

Bhadola, Pradeep; Deo, Nivedita

2016-10-01

The structural organization of a protein family is investigated by devising a method based on the random matrix theory (RMT), which uses the physiochemical properties of the amino acid with multiple sequence alignment. A graphical method to represent protein sequences using physiochemical properties is devised that gives a fast, easy, and informative way of comparing the evolutionary distances between protein sequences. A correlation matrix associated with each property is calculated, where the noise reduction and information filtering is done using RMT involving an ensemble of Wishart matrices. The analysis of the eigenvalue statistics of the correlation matrix for the β -lactamase family shows the universal features as observed in the Gaussian orthogonal ensemble (GOE). The property-based approach captures the short- as well as the long-range correlation (approximately following GOE) between the eigenvalues, whereas the previous approach (treating amino acids as characters) gives the usual short-range correlations, while the long-range correlations are the same as that of an uncorrelated series. The distribution of the eigenvector components for the eigenvalues outside the bulk (RMT bound) deviates significantly from RMT observations and contains important information about the system. The information content of each eigenvector of the correlation matrix is quantified by introducing an entropic estimate, which shows that for the β -lactamase family the smallest eigenvectors (low eigenmodes) are highly localized as well as informative. These small eigenvectors when processed gives clusters involving positions that have well-defined biological and structural importance matching with experiments. The approach is crucial for the recognition of structural motifs as shown in β -lactamase (and other families) and selectively identifies the important positions for targets to deactivate (activate) the enzymatic actions.

Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

NASA Astrophysics Data System (ADS)

van Wonderen, A. J.; Suttorp, L. G.

2018-04-01

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

Systemic risk and spatiotemporal dynamics of the US housing market.

PubMed

Meng, Hao; Xie, Wen-Jie; Jiang, Zhi-Qiang; Podobnik, Boris; Zhou, Wei-Xing; Stanley, H Eugene

2014-01-13

Housing markets play a crucial role in economies and the collapse of a real-estate bubble usually destabilizes the financial system and causes economic recessions. We investigate the systemic risk and spatiotemporal dynamics of the US housing market (1975-2011) at the state level based on the Random Matrix Theory (RMT). We identify richer economic information in the largest eigenvalues deviating from RMT predictions for the housing market than for stock markets and find that the component signs of the eigenvectors contain either geographical information or the extent of differences in house price growth rates or both. By looking at the evolution of different quantities such as eigenvalues and eigenvectors, we find that the US housing market experienced six different regimes, which is consistent with the evolution of state clusters identified by the box clustering algorithm and the consensus clustering algorithm on the partial correlation matrices. We find that dramatic increases in the systemic risk are usually accompanied by regime shifts, which provide a means of early detection of housing bubbles.

Non-equilibrium many-body dynamics following a quantum quench

NASA Astrophysics Data System (ADS)

Vyas, Manan

2017-12-01

We study analytically and numerically the non-equilibrium dynamics of an isolated interacting many-body quantum system following a random quench. We model the system Hamiltonian by Embedded Gaussian Orthogonal Ensemble (EGOE) of random matrices with one plus few-body interactions for fermions. EGOE are paradigmatic models to study the crossover from integrability to chaos in interacting many-body quantum systems. We obtain a generic formulation, based on spectral variances, for describing relaxation dynamics of survival probabilities as a function of rank of interactions. Our analytical results are in good agreement with numerics.

Optimal neighborhood indexing for protein similarity search.

PubMed

Peterlongo, Pierre; Noé, Laurent; Lavenier, Dominique; Nguyen, Van Hoa; Kucherov, Gregory; Giraud, Mathieu

2008-12-16

Similarity inference, one of the main bioinformatics tasks, has to face an exponential growth of the biological data. A classical approach used to cope with this data flow involves heuristics with large seed indexes. In order to speed up this technique, the index can be enhanced by storing additional information to limit the number of random memory accesses. However, this improvement leads to a larger index that may become a bottleneck. In the case of protein similarity search, we propose to decrease the index size by reducing the amino acid alphabet. The paper presents two main contributions. First, we show that an optimal neighborhood indexing combining an alphabet reduction and a longer neighborhood leads to a reduction of 35% of memory involved into the process, without sacrificing the quality of results nor the computational time. Second, our approach led us to develop a new kind of substitution score matrices and their associated e-value parameters. In contrast to usual matrices, these matrices are rectangular since they compare amino acid groups from different alphabets. We describe the method used for computing those matrices and we provide some typical examples that can be used in such comparisons. Supplementary data can be found on the website http://bioinfo.lifl.fr/reblosum. We propose a practical index size reduction of the neighborhood data, that does not negatively affect the performance of large-scale search in protein sequences. Such an index can be used in any study involving large protein data. Moreover, rectangular substitution score matrices and their associated statistical parameters can have applications in any study involving an alphabet reduction.

Optimal neighborhood indexing for protein similarity search

PubMed Central

Peterlongo, Pierre; Noé, Laurent; Lavenier, Dominique; Nguyen, Van Hoa; Kucherov, Gregory; Giraud, Mathieu

2008-01-01

Background Similarity inference, one of the main bioinformatics tasks, has to face an exponential growth of the biological data. A classical approach used to cope with this data flow involves heuristics with large seed indexes. In order to speed up this technique, the index can be enhanced by storing additional information to limit the number of random memory accesses. However, this improvement leads to a larger index that may become a bottleneck. In the case of protein similarity search, we propose to decrease the index size by reducing the amino acid alphabet. Results The paper presents two main contributions. First, we show that an optimal neighborhood indexing combining an alphabet reduction and a longer neighborhood leads to a reduction of 35% of memory involved into the process, without sacrificing the quality of results nor the computational time. Second, our approach led us to develop a new kind of substitution score matrices and their associated e-value parameters. In contrast to usual matrices, these matrices are rectangular since they compare amino acid groups from different alphabets. We describe the method used for computing those matrices and we provide some typical examples that can be used in such comparisons. Supplementary data can be found on the website . Conclusion We propose a practical index size reduction of the neighborhood data, that does not negatively affect the performance of large-scale search in protein sequences. Such an index can be used in any study involving large protein data. Moreover, rectangular substitution score matrices and their associated statistical parameters can have applications in any study involving an alphabet reduction. PMID:19087280

Non-Hermitian localization in biological networks.

PubMed

Amir, Ariel; Hatano, Naomichi; Nelson, David R

2016-04-01

We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N, the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to 90^{∘} rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias-dependent shape of this hole tracks the bias-independent contours of constant localization length. We treat the large-N limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's law" (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

Non-Hermitian localization in biological networks

NASA Astrophysics Data System (ADS)

Amir, Ariel; Hatano, Naomichi; Nelson, David R.

2016-04-01

We explore the spectra and localization properties of the N -site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N , the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to 90∘ rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias-dependent shape of this hole tracks the bias-independent contours of constant localization length. We treat the large-N limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's law" (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

Work distributions for random sudden quantum quenches

NASA Astrophysics Data System (ADS)

Łobejko, Marcin; Łuczka, Jerzy; Talkner, Peter

2017-05-01

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.

Tensor Dictionary Learning for Positive Definite Matrices.

PubMed

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.

Number statistics for β-ensembles of random matrices: Applications to trapped fermions at zero temperature.

PubMed

Marino, Ricardo; Majumdar, Satya N; Schehr, Grégory; Vivo, Pierpaolo

2016-09-01

Let P_{β}^{(V)}(N_{I}) be the probability that a N×Nβ-ensemble of random matrices with confining potential V(x) has N_{I} eigenvalues inside an interval I=[a,b] on the real line. We introduce a general formalism, based on the Coulomb gas technique and the resolvent method, to compute analytically P_{β}^{(V)}(N_{I}) for large N. We show that this probability scales for large N as P_{β}^{(V)}(N_{I})≈exp[-βN^{2}ψ^{(V)}(N_{I}/N)], where β is the Dyson index of the ensemble. The rate function ψ^{(V)}(k_{I}), independent of β, is computed in terms of single integrals that can be easily evaluated numerically. The general formalism is then applied to the classical β-Gaussian (I=[-L,L]), β-Wishart (I=[1,L]), and β-Cauchy (I=[-L,L]) ensembles. Expanding the rate function around its minimum, we find that generically the number variance var(N_{I}) exhibits a nonmonotonic behavior as a function of the size of the interval, with a maximum that can be precisely characterized. These analytical results, corroborated by numerical simulations, provide the full counting statistics of many systems where random matrix models apply. In particular, we present results for the full counting statistics of zero-temperature one-dimensional spinless fermions in a harmonic trap.

Multi-population Genomic Relationships for Estimating Current Genetic Variances Within and Genetic Correlations Between Populations.

PubMed

Wientjes, Yvonne C J; Bijma, Piter; Vandenplas, Jérémie; Calus, Mario P L

2017-10-01

Different methods are available to calculate multi-population genomic relationship matrices. Since those matrices differ in base population, it is anticipated that the method used to calculate genomic relationships affects the estimate of genetic variances, covariances, and correlations. The aim of this article is to define the multi-population genomic relationship matrix to estimate current genetic variances within and genetic correlations between populations. The genomic relationship matrix containing two populations consists of four blocks, one block for population 1, one block for population 2, and two blocks for relationships between the populations. It is known, based on literature, that by using current allele frequencies to calculate genomic relationships within a population, current genetic variances are estimated. In this article, we theoretically derived the properties of the genomic relationship matrix to estimate genetic correlations between populations and validated it using simulations. When the scaling factor of across-population genomic relationships is equal to the product of the square roots of the scaling factors for within-population genomic relationships, the genetic correlation is estimated unbiasedly even though estimated genetic variances do not necessarily refer to the current population. When this property is not met, the correlation based on estimated variances should be multiplied by a correction factor based on the scaling factors. In this study, we present a genomic relationship matrix which directly estimates current genetic variances as well as genetic correlations between populations. Copyright © 2017 by the Genetics Society of America.

Green electrospun pantothenic acid/silk fibroin composite nanofibers: fabrication, characterization and biological activity.

PubMed

Fan, Linpeng; Cai, Zengxiao; Zhang, Kuihua; Han, Feng; Li, Jingliang; He, Chuanglong; Mo, Xiumei; Wang, Xungai; Wang, Hongsheng

2014-05-01

Silk fibroin (SF) from Bombyx mori has many established excellent properties and has found various applications in the biomedical field. However, some abilities or capacities of SF still need improving to meet the need for using practically. Indeed, diverse SF-based composite biomaterials have been developed. Here we report the feasibility of fabricating pantothenic acid (vitamin B5, VB5)-reinforcing SF nanofibrous matrices for biomedical applications through green electrospinning. Results demonstrated the successful loading of D-pantothenic acid hemicalcium salt (VB5-hs) into resulting composite nanofibers. The introduction of VB5-hs did not alter the smooth ribbon-like morphology and the silk I structure of SF, but significantly decreased the mean width of SF fibers. SF conformation transformed into β-sheet from random coil when composite nanofibrous matrices were exposed to 75% (v/v) ethanol vapor. Furthermore, nanofibers still remained good morphology after being soaked in water environment for five days. Interestingly, as-prepared composite nanofibrous matrices supported a higher level of cell viability, especially in a long culture period and significantly assisted skin cells to survive under oxidative stress compared with pure SF nanofibrous matrices. These findings provide a basis for further extending the application of SF in the biomedical field, especially in the personal skin-care field. Copyright © 2013 Elsevier B.V. All rights reserved.

From deep TLS validation to ensembles of atomic models built from elemental motions

DOE PAGES

Urzhumtsev, Alexandre; Afonine, Pavel V.; Van Benschoten, Andrew H.; ...

2015-07-28

The translation–libration–screw model first introduced by Cruickshank, Schomaker and Trueblood describes the concerted motions of atomic groups. Using TLS models can improve the agreement between calculated and experimental diffraction data. Because the T, L and S matrices describe a combination of atomic vibrations and librations, TLS models can also potentially shed light on molecular mechanisms involving correlated motions. However, this use of TLS models in mechanistic studies is hampered by the difficulties in translating the results of refinement into molecular movement or a structural ensemble. To convert the matrices into a constituent molecular movement, the matrix elements must satisfy severalmore » conditions. Refining the T, L and S matrix elements as independent parameters without taking these conditions into account may result in matrices that do not represent concerted molecular movements. Here, a mathematical framework and the computational tools to analyze TLS matrices, resulting in either explicit decomposition into descriptions of the underlying motions or a report of broken conditions, are described. The description of valid underlying motions can then be output as a structural ensemble. All methods are implemented as part of the PHENIX project.« less

Atom and Bond Fukui Functions and Matrices: A Hirshfeld-I Atoms-in-Molecule Approach.

PubMed

Oña, Ofelia B; De Clercq, Olivier; Alcoba, Diego R; Torre, Alicia; Lain, Luis; Van Neck, Dimitri; Bultinck, Patrick

2016-09-19

The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Electronic polarization effect on low-frequency infrared and Raman spectra of aprotic solvent: Molecular dynamics simulation study with charge response kernel by second order Møller-Plesset perturbation method

NASA Astrophysics Data System (ADS)

Isegawa, Miho; Kato, Shigeki

2007-12-01

Low-frequency infrared (IR) and depolarized Raman scattering (DRS) spectra of acetonitrile, methylene chloride, and acetone liquids are simulated via molecular dynamics calculations with the charge response kernel (CRK) model obtained at the second order Møller-Plesset perturbation (MP2) level. For this purpose, the analytical second derivative technique for the MP2 energy is employed to evaluate the CRK matrices. The calculated IR spectra reasonably agree with the experiments. In particular, the agreement is excellent for acetone because the present CRK model well reproduces the experimental polarizability in the gas phase. The importance of interaction induced dipole moments in characterizing the spectral shapes is stressed. The DRS spectrum of acetone is mainly discussed because the experimental spectrum is available only for this molecule. The calculated spectrum is close to the experiment. The comparison of the present results with those by the multiple random telegraph model is also made. By decomposing the polarizability anisotropy time correlation function to the contributions from the permanent, induced polarizability and their cross term, a discrepancy from the previous calculations is observed in the sign of permanent-induce cross term contribution. The origin of this discrepancy is discussed by analyzing the correlation functions for acetonitrile.

Scale free effects in world currency exchange network

NASA Astrophysics Data System (ADS)

Górski, A. Z.; Drożdż, S.; Kwapień, J.

2008-11-01

A large collection of daily time series for 60 world currencies' exchange rates is considered. The correlation matrices are calculated and the corresponding Minimal Spanning Tree (MST) graphs are constructed for each of those currencies used as reference for the remaining ones. It is shown that multiplicity of the MST graphs' nodes to a good approximation develops a power like, scale free distribution with the scaling exponent similar as for several other complex systems studied so far. Furthermore, quantitative arguments in favor of the hierarchical organization of the world currency exchange network are provided by relating the structure of the above MST graphs and their scaling exponents to those that are derived from an exactly solvable hierarchical network model. A special status of the USD during the period considered can be attributed to some departures of the MST features, when this currency (or some other tied to it) is used as reference, from characteristics typical to such a hierarchical clustering of nodes towards those that correspond to the random graphs. Even though in general the basic structure of the MST is robust with respect to changing the reference currency some trace of a systematic transition from somewhat dispersed - like the USD case - towards more compact MST topology can be observed when correlations increase.

A Random Algorithm for Low-Rank Decomposition of Large-Scale Matrices With Missing Entries.

PubMed

Liu, Yiguang; Lei, Yinjie; Li, Chunguang; Xu, Wenzheng; Pu, Yifei

2015-11-01

A random submatrix method (RSM) is proposed to calculate the low-rank decomposition U(m×r)V(n×r)(T) (r < m, n) of the matrix Y∈R(m×n) (assuming m > n generally) with known entry percentage 0 < ρ ≤ 1. RSM is very fast as only O(mr(2)ρ(r)) or O(n(3)ρ(3r)) floating-point operations (flops) are required, compared favorably with O(mnr+r(2)(m+n)) flops required by the state-of-the-art algorithms. Meanwhile, RSM has the advantage of a small memory requirement as only max(n(2),mr+nr) real values need to be saved. With the assumption that known entries are uniformly distributed in Y, submatrices formed by known entries are randomly selected from Y with statistical size k×nρ(k) or mρ(l)×l , where k or l takes r+1 usually. We propose and prove a theorem, under random noises the probability that the subspace associated with a smaller singular value will turn into the space associated to anyone of the r largest singular values is smaller. Based on the theorem, the nρ(k)-k null vectors or the l-r right singular vectors associated with the minor singular values are calculated for each submatrix. The vectors ought to be the null vectors of the submatrix formed by the chosen nρ(k) or l columns of the ground truth of V(T). If enough submatrices are randomly chosen, V and U can be estimated accordingly. The experimental results on random synthetic matrices with sizes such as 13 1072 ×10(24) and on real data sets such as dinosaur indicate that RSM is 4.30 ∼ 197.95 times faster than the state-of-the-art algorithms. It, meanwhile, has considerable high precision achieving or approximating to the best.

MicroRNA Biomarkers of Toxicity in Biological Matrices

EPA Science Inventory

Biomarker measurements that reliably correlate with tissue injury and can be measured from sampling accessible biofluids offer enormous benefits in terms of cost, time, and convenience when assessing environmental and drug-induced toxicity in model systems or human cohorts. Micro...

Inflation with a graceful exit in a random landscape

NASA Astrophysics Data System (ADS)

Pedro, F. G.; Westphal, A.

2017-03-01

We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N ≪ 10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.

Low-temperature methyl group dynamics of hexamethylbenzene in crystalline and glassy matrices as studied by 2H NMR

NASA Astrophysics Data System (ADS)

Börner, K.; Diezemann, G.; Rössler, E.; Vieth, H. M.

1991-07-01

2H NMR spectra of hexamethylbenzene (HMB) in protonated crystalline and amorphous matrices at low temperatures are presented. All spectra reveal lineshape changes which can be attributed to methyl group tunnelling. Compared to neat HMB, a drastic increase of the tunnelling frequency is found for all systems. This indicates that the hindering potential originates predominantly from intermolecular forces. We studied the temperature dependence of these spectra and the spin-lattice relaxation in order to exclude a distribution of motional correlation times describing a thermally activated process. In addition, we find a distortion of the methyl tetrahedron.

Solvent-induced dimensional changes in EDTA-demineralized dentin matrix.

PubMed

Pashley, D H; Agee, K A; Nakajima, M; Tay, F R; Carvalho, R M; Terada, R S; Harmon, F J; Lee, W K; Rueggeberg, F A

2001-08-01

The purpose of this study was to test the null hypothesis that the re-expansion of dried matrix and the shrinkage of moist, demineralized dentin is not influenced by polar solvents. Dentin disks were prepared from midcoronal dentin of extracted human third molars. After complete demineralization in 0.5M of EDTA (pH 7), the specimens were placed in the well of a device that measures changes in matrix height in real time. Dry, collapsed matrices were created by blowing dry N(2) on the specimens until they shrank to a stable plateau. Polar solvents [water, methanol, ethanol, n-propanol, n-butanol, formamide, ethylene glycol, hydroxyethyl methacrylate (HEMA), or mixtures of water-HEMA] as model primers then were added and the degree of re-expansion measured. These same solvents also were applied to moist, expanded matrices and the solvent-induced shrinkages measured. Regression analysis was used to test the correlations between matrix height and Hansen's dispersive, polar, hydrogen bonding, and total solubility parameters (delta(d), delta(p), delta(h), delta(t)). The results indicate that water-free polar solvents of low hydrogen bonding (H-bond) ability (e.g., neat HEMA) do not re-expand dried matrices and that they shrink moist matrices. When HEMA was mixed with progressively higher water concentrations, the model water-HEMA primers expanded the dried matrix in proportion to their water concentrations and they produced less shrinkage of moist matrices. Solvents with higher H-bonding capacities (methanol, ethanol, ethylene glycol, formamide, and water) re-expanded the dried matrix in proportion to their solubility parameters for H-bonding (delta(h)). They also induced small transient shrinkages of moist matrices, which slowly re-expanded. The results require rejection of the null hypothesis. Copyright 2001 John Wiley & Sons, Inc. J Biomed Mater Res 56: 273-281, 2001

Crack Modelling for Radiography

NASA Astrophysics Data System (ADS)

Chady, T.; Napierała, L.

2010-02-01

In this paper, possibility of creation of three-dimensional crack models, both random type and based on real-life radiographic images is discussed. Method for storing cracks in a number of two-dimensional matrices, as well algorithm for their reconstruction into three-dimensional objects is presented. Also the possibility of using iterative algorithm for matching simulated images of cracks to real-life radiographic images is discussed.

Interaction between moving tandem wheels and an infinite rail with periodic supports - Green's matrices of the track method in stationary reference frame

NASA Astrophysics Data System (ADS)

Mazilu, Traian

2017-08-01

This paper approaches the issue of the interaction between moving tandem wheels and an infinite periodically supported rail and points out at the basic characteristics in the steady-state interaction behaviour and in the interaction in the presence of the rail random irregularity. The rail is modelled as an infinite Timoshenko beam resting on supports which are discretely modelling the inertia of the sleepers and ballast and also the viscoelastic features of the rail pads, the ballast and the subgrade. Green‧s matrices of the track method in stationary reference frame were applied so as to conduct the time-domain analysis. This method allows to consider the nonlinearities of the wheel/rail contact and the Doppler effect. The study highlights certain aspects regarding the influence of the wheel base on the wheels/rail contact forces, particularly at the parametric resonance, due to the coincidence between the wheel/rail natural frequency and the passing frequency and also when the rail surface exhibits random irregularity. It has been shown that the wheel/rail dynamic behaviour is less intense when the wheel base equals integer multiple of the sleeper bay.

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

Proctor, Timothy; Rudinger, Kenneth; Young, Kevin

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r. For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not amore » well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. Here, these theories allow explicit computation of the error rate that RB measures (r), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.« less

Multiscale Anomaly Detection and Image Registration Algorithms for Airborne Landmine Detection

DTIC Science & Technology

2008-05-01

with the sensed image. The two- dimensional correlation coefficient r for two matrices A and B both of size M ×N is given by r = ∑ m ∑ n (Amn...correlation based method by matching features in a high- dimensional feature- space . The current implementation of the SIFT algorithm uses a brute-force...by repeatedly convolving the image with a Guassian kernel. Each plane of the scale

Fourier-Legendre expansion of the one-electron density matrix of ground-state two-electron atoms.

PubMed

Ragot, Sébastien; Ruiz, María Belén

2008-09-28

The density matrix rho(r,r(')) of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials P(l)(cos theta=rr(')rr(')). Application is here made to harmonically trapped electron pairs (i.e., Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of rho(r,r(')). The series expansions are shown to converge rapidly in each case, with respect to both the electron number and the kinetic energy. In practice, a two-term expansion accounts for most of the correlation effects, so that the correlated density matrices of the atoms at issue are essentially a linear functions of P(l)(cos theta)=cos theta. For example, in the case of Hooke's atom, a two-term expansion takes in 99.9% of the electrons and 99.6% of the kinetic energy. The correlated density matrices obtained are finally compared to their determinantal counterparts, using a simplified representation of the density matrix rho(r,r(')), suggested by the Legendre expansion. Interestingly, two-particle correlation is shown to impact the angular delocalization of each electron, in the one-particle space spanned by the r and r(') variables.

Measuring Brain Connectivity: Diffusion Tensor Imaging Validates Resting State Temporal Correlations

PubMed Central

Skudlarski, Pawel; Jagannathan, Kanchana; Calhoun, Vince D.; Hampson, Michelle; Skudlarska, Beata A.; Pearlson, Godfrey

2015-01-01

Diffusion tensor imaging (DTI) and resting state temporal correlations (RSTC) are two leading techniques for investigating the connectivity of the human brain. They have been widely used to investigate the strength of anatomical and functional connections between distant brain regions in healthy subjects, and in clinical populations. Though they are both based on magnetic resonance imaging (MRI) they have not yet been compared directly. In this work both techniques were employed to create global connectivity matrices covering the whole brain gray matter. This allowed for direct comparisons between functional connectivity measured by RSTC with anatomical connectivity quantified using DTI tractography. We found that connectivity matrices obtained using both techniques showed significant agreement. Connectivity maps created for a priori defined anatomical regions showed significant correlation, and furthermore agreement was especially high in regions showing strong overall connectivity, such as those belonging to the default mode network. Direct comparison between functional RSTC and anatomical DTI connectivity, presented here for the first time, links two powerful approaches for investigating brain connectivity and shows their strong agreement. It provides a crucial multi-modal validation for resting state correlations as representing neuronal connectivity. The combination of both techniques presented here allows for further combining them to provide richer representation of brain connectivity both in the healthy brain and in clinical conditions. PMID:18771736

Measuring brain connectivity: diffusion tensor imaging validates resting state temporal correlations.

PubMed

Skudlarski, Pawel; Jagannathan, Kanchana; Calhoun, Vince D; Hampson, Michelle; Skudlarska, Beata A; Pearlson, Godfrey

2008-11-15

Diffusion tensor imaging (DTI) and resting state temporal correlations (RSTC) are two leading techniques for investigating the connectivity of the human brain. They have been widely used to investigate the strength of anatomical and functional connections between distant brain regions in healthy subjects, and in clinical populations. Though they are both based on magnetic resonance imaging (MRI) they have not yet been compared directly. In this work both techniques were employed to create global connectivity matrices covering the whole brain gray matter. This allowed for direct comparisons between functional connectivity measured by RSTC with anatomical connectivity quantified using DTI tractography. We found that connectivity matrices obtained using both techniques showed significant agreement. Connectivity maps created for a priori defined anatomical regions showed significant correlation, and furthermore agreement was especially high in regions showing strong overall connectivity, such as those belonging to the default mode network. Direct comparison between functional RSTC and anatomical DTI connectivity, presented here for the first time, links two powerful approaches for investigating brain connectivity and shows their strong agreement. It provides a crucial multi-modal validation for resting state correlations as representing neuronal connectivity. The combination of both techniques presented here allows for further combining them to provide richer representation of brain connectivity both in the healthy brain and in clinical conditions.

On the role of covariance information for GRACE K-band observations in the Celestial Mechanics Approach

NASA Astrophysics Data System (ADS)

Bentel, Katrin; Meyer, Ulrich; Arnold, Daniel; Jean, Yoomin; Jäggi, Adrian

2017-04-01

The Astronomical Institute at the University of Bern (AIUB) derives static and time-variable gravity fields by means of the Celestial Mechanics Approach (CMA) from GRACE (level 1B) data. This approach makes use of the close link between orbit and gravity field determination. GPS-derived kinematic GRACE orbit positions, inter-satellite K-band observations, which are the core observations of GRACE, and accelerometer data are combined to rigorously estimate orbit and spherical harmonic gravity field coefficients in one adjustment step. Pseudo-stochastic orbit parameters are set up to absorb unmodeled noise. The K-band range measurements in along-track direction lead to a much higher correlation of the observations in this direction compared to the other directions and thus, to north-south stripes in the unconstrained gravity field solutions, so-called correlated errors. By using a full covariance matrix for the K-band observations the correlation can be taken into account. One possibility is to derive correlation information from post-processing K-band residuals. This is then used in a second iteration step to derive an improved gravity field solution. We study the effects of pre-defined covariance matrices and residual-derived covariance matrices on the final gravity field product with the CMA.

Absorption and scattering of light by nonspherical particles. [in atmosphere

NASA Technical Reports Server (NTRS)

Bohren, C. F.

1986-01-01

Using the example of the polarization of scattered light, it is shown that the scattering matrices for identical, randomly ordered particles and for spherical particles are unequal. The spherical assumptions of Mie theory are therefore inconsistent with the random shapes and sizes of atmospheric particulates. The implications for corrections made to extinction measurements of forward scattering light are discussed. Several analytical methods are examined as potential bases for developing more accurate models, including Rayleigh theory, Fraunhoffer Diffraction theory, anomalous diffraction theory, Rayleigh-Gans theory, the separation of variables technique, the Purcell-Pennypacker method, the T-matrix method, and finite difference calculations.

A comparative study between melt granulation/compression and hot melt extrusion/injection molding for the manufacturing of oral sustained release thermoplastic polyurethane matrices.

PubMed

Verstraete, G; Mertens, P; Grymonpré, W; Van Bockstal, P J; De Beer, T; Boone, M N; Van Hoorebeke, L; Remon, J P; Vervaet, C

2016-11-20

During this project 3 techniques (twin screw melt granulation/compression (TSMG), hot melt extrusion (HME) and injection molding (IM)) were evaluated for the manufacturing of thermoplastic polyurethane (TPU)-based oral sustained release matrices, containing a high dose of the highly soluble metformin hydrochloride. Whereas formulations with a drug load between 0 and 70% (w/w) could be processed via HME/(IM), the drug content of granules prepared via melt granulation could only be varied between 85 and 90% (w/w) as these formulations contained the proper concentration of binder (i.e. TPU) to obtain a good size distribution of the granules. While release from HME matrices and IM tablets could be sustained over 24h, release from the TPU-based TSMG tablets was too fast (complete release within about 6h) linked to their higher drug load and porosity. By mixing hydrophilic and hydrophobic TPUs the in vitro release kinetics of both formulations could be adjusted: a higher content of hydrophobic TPU was correlated with a slower release rate. Although mini-matrices showed faster release kinetics than IM tablets, this observation was successfully countered by changing the hydrophobic/hydrophilic TPU ratio. In vivo experiments via oral administration to dogs confirmed the versatile potential of the TPU platform as intermediate-strong and low-intermediate sustained characteristics were obtained for the IM tablets and HME mini-matrices, respectively. Copyright © 2016 Elsevier B.V. All rights reserved.

Simulating Multivariate Nonnormal Data Using an Iterative Algorithm

ERIC Educational Resources Information Center

Ruscio, John; Kaczetow, Walter

2008-01-01

Simulating multivariate nonnormal data with specified correlation matrices is difficult. One especially popular method is Vale and Maurelli's (1983) extension of Fleishman's (1978) polynomial transformation technique to multivariate applications. This requires the specification of distributional moments and the calculation of an intermediate…

Noisy covariance matrices and portfolio optimization II

NASA Astrophysics Data System (ADS)

Pafka, Szilárd; Kondor, Imre

2003-03-01

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

Subjective randomness as statistical inference.

PubMed

Griffiths, Thomas L; Daniels, Dylan; Austerweil, Joseph L; Tenenbaum, Joshua B

2018-06-01

Some events seem more random than others. For example, when tossing a coin, a sequence of eight heads in a row does not seem very random. Where do these intuitions about randomness come from? We argue that subjective randomness can be understood as the result of a statistical inference assessing the evidence that an event provides for having been produced by a random generating process. We show how this account provides a link to previous work relating randomness to algorithmic complexity, in which random events are those that cannot be described by short computer programs. Algorithmic complexity is both incomputable and too general to capture the regularities that people can recognize, but viewing randomness as statistical inference provides two paths to addressing these problems: considering regularities generated by simpler computing machines, and restricting the set of probability distributions that characterize regularity. Building on previous work exploring these different routes to a more restricted notion of randomness, we define strong quantitative models of human randomness judgments that apply not just to binary sequences - which have been the focus of much of the previous work on subjective randomness - but also to binary matrices and spatial clustering. Copyright © 2018 Elsevier Inc. All rights reserved.

Cadmium Concentration in Mother's Blood, Milk, and Newborn's Blood and Its Correlation with Fatty Acids, Anthropometric Characteristics, and Mother's Smoking Status.

PubMed

Olszowski, Tomasz; Baranowska-Bosiacka, Irena; Rębacz-Maron, Ewa; Gutowska, Izabela; Jamioł, Dominika; Prokopowicz, Adam; Goschorska, Marta; Chlubek, Dariusz

2016-11-01

The aim of this study was to determine cadmium concentration in mothers' blood, milk, and newborns' blood from Szczecin (Poland) as a result of environmental cadmium exposure and evaluate the correlation (1) between cadmium levels in analyzed matrices, (2) between cadmium and fatty acids in those matrices, and (3) between cadmium and some selected personal variables, such as anthropometric characteristics, mothers' smoking status, and fruit and fish consumption by mothers. The concentration of cadmium in whole blood and milk of mothers and in the umbilical cord blood of newborns was determined by atomic absorption spectrometry with graphite furnace atomization and Zeeman correction. The fatty acid concentrations were determined by gas chromatography in our previous study. The mean concentrations of cadmium in maternal blood, newborn's blood, and breast milk were 0.61 ± 0.62 μg/L, 0.05 ± 0.04 μg/L, and 0.11 ± 0.07 μg/L, respectively, and differed significantly between analyzed matrices. Cadmium concentrations in the umbilical cord blood were 15 % (range 0-83 %) of the concentration in maternal blood, whereas cadmium concentrations in breast milk constituted 35 % (range 3-142 %) of the concentration in mothers' blood. No correlation was found between cadmium levels in three analyzed matrices. The correlation analysis revealed significant low positive correlation between maternal blood cadmium concentrations and concentrations of elaidic, oleic, and cis-vaccenic acids in mothers' milk (correlation coefficients 0.30, 0.32, and 0.31, respectively). Mothers' blood cadmium correlated with mothers' age (r = -0.26, p = 0.03), maternal smoking before pregnancy (r = 0.55, p < 0.000), maternal smoking during pregnancy (r = 0.58, p < 0.000), and fruit consumption by mothers after delivery (r = -0.44, p = 0.003). Mothers' height was the only variable that correlated significantly with breast milk cadmium levels. Newborns' blood cadmium concentrations correlated significantly with mothers' height (r = 0.28, p = 0.02), newborns' birth weight (r = 0.26, p = 0.03), maternal smoking during pregnancy (r = 0.24, p = 0.048), and fish consumption by mothers after delivery (r = 0.37, p = 0.02). The concentrations of cadmium in Polish mother-newborn pairs are among the lowest in Europe and within the norms established by different institutions. The results of our study confirm the existence of effective partial barriers (such as the placenta and mammary gland) restricting cadmium passage from mother to newborn. The significant positive correlations between maternal blood Cd and concentrations of oleic, elaidic, and cis-vaccenic acids in breast milk might suggest the increased cadmium toxicity to infant, taking into consideration even low cadmium passage to milk. Maternal smoking during pregnancy increases both maternal and newborn's blood cadmium level. Promotion of nonsmoking among pregnant women could substantially reduce prenatal and neonatal exposure to cadmium. Moreover, the results of our study point to the need of establishing complex biomonitoring of cadmium in mother-infant pairs in order to better protect children from this toxic and carcinogenic metal exposure.

Evaluation of indirect impedance for measuring microbial growth in complex food matrices.

PubMed

Johnson, N; Chang, Z; Bravo Almeida, C; Michel, M; Iversen, C; Callanan, M

2014-09-01

The suitability of indirect impedance to accurately measure microbial growth in real food matrices was investigated. A variety of semi-solid and liquid food products were inoculated with Bacillus cereus, Listeria monocytogenes, Staphylococcus aureus, Lactobacillus plantarum, Pseudomonas aeruginosa, Escherichia coli, Salmonella enteriditis, Candida tropicalis or Zygosaccharomyces rouxii and CO2 production was monitored using a conductimetric (Don Whitely R.A.B.I.T.) system. The majority (80%) of food and microbe combinations produced a detectable growth signal. The linearity of conductance responses in selected food products was investigated and a good correlation (R(2) ≥ 0.84) was observed between inoculum levels and times to detection. Specific growth rate estimations from the data were sufficiently accurate for predictive modeling in some cases. This initial evaluation of the suitability of indirect impedance to generate microbial growth data in complex food matrices indicates significant potential for the technology as an alternative to plating methods. Copyright © 2014 Elsevier Ltd. All rights reserved.

Clustering Coefficients for Correlation Networks.

PubMed

Masuda, Naoki; Sakaki, Michiko; Ezaki, Takahiro; Watanabe, Takamitsu

2018-01-01

Graph theory is a useful tool for deciphering structural and functional networks of the brain on various spatial and temporal scales. The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is affected by attentional and cognitive conditions, age, psychiatric disorders and so forth. However, it remains unclear how the clustering coefficient should be measured in a correlation-based network, which is among major representations of brain networks. In the present article, we propose clustering coefficients tailored to correlation matrices. The key idea is to use three-way partial correlation or partial mutual information to measure the strength of the association between the two neighboring nodes of a focal node relative to the amount of pseudo-correlation expected from indirect paths between the nodes. Our method avoids the difficulties of previous applications of clustering coefficient (and other) measures in defining correlational networks, i.e., thresholding on the correlation value, discarding of negative correlation values, the pseudo-correlation problem and full partial correlation matrices whose estimation is computationally difficult. For proof of concept, we apply the proposed clustering coefficient measures to functional magnetic resonance imaging data obtained from healthy participants of various ages and compare them with conventional clustering coefficients. We show that the clustering coefficients decline with the age. The proposed clustering coefficients are more strongly correlated with age than the conventional ones are. We also show that the local variants of the proposed clustering coefficients (i.e., abundance of triangles around a focal node) are useful in characterizing individual nodes. In contrast, the conventional local clustering coefficients were strongly correlated with and therefore may be confounded by the node's connectivity. The proposed methods are expected to help us to understand clustering and lack thereof in correlational brain networks, such as those derived from functional time series and across-participant correlation in neuroanatomical properties.

Clustering Coefficients for Correlation Networks

PubMed Central

Masuda, Naoki; Sakaki, Michiko; Ezaki, Takahiro; Watanabe, Takamitsu

2018-01-01

Graph theory is a useful tool for deciphering structural and functional networks of the brain on various spatial and temporal scales. The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is affected by attentional and cognitive conditions, age, psychiatric disorders and so forth. However, it remains unclear how the clustering coefficient should be measured in a correlation-based network, which is among major representations of brain networks. In the present article, we propose clustering coefficients tailored to correlation matrices. The key idea is to use three-way partial correlation or partial mutual information to measure the strength of the association between the two neighboring nodes of a focal node relative to the amount of pseudo-correlation expected from indirect paths between the nodes. Our method avoids the difficulties of previous applications of clustering coefficient (and other) measures in defining correlational networks, i.e., thresholding on the correlation value, discarding of negative correlation values, the pseudo-correlation problem and full partial correlation matrices whose estimation is computationally difficult. For proof of concept, we apply the proposed clustering coefficient measures to functional magnetic resonance imaging data obtained from healthy participants of various ages and compare them with conventional clustering coefficients. We show that the clustering coefficients decline with the age. The proposed clustering coefficients are more strongly correlated with age than the conventional ones are. We also show that the local variants of the proposed clustering coefficients (i.e., abundance of triangles around a focal node) are useful in characterizing individual nodes. In contrast, the conventional local clustering coefficients were strongly correlated with and therefore may be confounded by the node's connectivity. The proposed methods are expected to help us to understand clustering and lack thereof in correlational brain networks, such as those derived from functional time series and across-participant correlation in neuroanatomical properties. PMID:29599714

What is the effect of matrices on cartilage repair? A systematic review.

PubMed

Wylie, James D; Hartley, Melissa K; Kapron, Ashley L; Aoki, Stephen K; Maak, Travis G

2015-05-01

Articular cartilage has minimal endogenous ability to undergo repair. Multiple chondral restoration strategies have been attempted with varied results. The purpose of our review was to determine: (1) Does articular chondrocyte transplantation or matrix-assisted articular chondrocyte transplantation provide better patient-reported outcomes scores, MRI morphologic measurements, or histologic quality of repair tissue compared with microfracture in prospective comparative studies of articular cartilage repair; and (2) which available matrices for matrix-assisted articular chondrocyte transplantation show the best patient-reported outcomes scores, MRI morphologic measurements, or histologic quality of repair tissue? We conducted a systematic review of PubMed, CINAHL, and MEDLINE from March 2004 to February 2014 using keywords determined to be important for articular cartilage repair, including "cartilage", "chondral", "cell source", "chondrocyte", "matrix", "augment", "articular", "joint", "repair", "treatment", "regeneration", and "restoration" to find articles related to cell-based articular cartilage repair of the knee. The articles were reviewed by two authors (JDW, MKH), our study exclusion criteria were applied, and articles were determined to be relevant (or not) to the research questions. The Methodological Index for Nonrandomized Studies (MINORS) scale was used to judge the quality of nonrandomized manuscripts used in this review and the Jadad score was used to judge the quality of randomized trials. Seventeen articles were reviewed for the first research question and 83 articles were reviewed in the second research question from 301 articles identified in the original systematic search. The average MINORS score was 9.9 (62%) for noncomparative studies and 16.1 (67%) for comparative studies. The average Jadad score was 2.3 for the randomized studies. Articular chondrocyte transplantation shows better patient-reported outcomes at 5 years in patients without chronic symptoms preoperatively compared with microfracture (p = 0.026). Matrix-assisted articular chondrocyte transplantation consistently showed improved patient-reported functional outcomes compared with microfracture (p values ranging from < 0.001 to 0.029). Hyalograft C(®) (Anika Therapeutics Inc, Bedford, MA, USA) and Chondro-gide(®) (Genzyme Biosurgery, Kastrup, Denmark) are the matrices with the most published evidence in the literature, but no studies comparing different matrices met our inclusion criteria, because the literature consists only of uncontrolled case series. Matrix-assisted articular chondrocyte transplantation leads to better patient-reported outcomes in cartilage repair compared with microfracture; however, future prospective research is needed comparing different matrices to determine which products optimize cartilage repair. Level IV, therapeutic study.

Tandem sulfur chemiluminescence and flame ionization detection with planar microfluidic devices for the characterization of sulfur compounds in hydrocarbon matrices.

PubMed

Luong, J; Gras, R; Shellie, R A; Cortes, H J

2013-07-05

The detection of sulfur compounds in different hydrocarbon matrices, from light hydrocarbon feedstocks to medium synthetic crude oil feeds provides meaningful information for optimization of refining processes as well as demonstration of compliance with petroleum product specifications. With the incorporation of planar microfluidic devices in a novel chromatographic configuration, sulfur compounds from hydrogen sulfide to alkyl dibenzothiophenes and heavier distributions of sulfur compounds over a wide range of matrices spanning across a boiling point range of more than 650°C can be characterized, using one single analytical configuration in less than 25min. In tandem with a sulfur chemiluminescence detector for sulfur analysis is a flame ionization detector. The flame ionization detector can be used to establish the boiling point range of the sulfur compounds in various hydrocarbon fractions for elemental specific simulated distillation analysis as well as profiling the hydrocarbon matrices for process optimization. Repeatability of less than 3% RSD (n=20) over a range of 0.5-1000 parts per million (v/v) was obtained with a limit of detection of 50 parts per billion and a linear range of 0.5-1000 parts per million with a correlation co-efficient of 0.998. Copyright © 2013 Elsevier B.V. All rights reserved.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

PubMed

Chen, Xin; Wu, Yinghua; Batista, Victor S

2005-02-08

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

Multiple image encryption scheme based on pixel exchange operation and vector decomposition

NASA Astrophysics Data System (ADS)

Xiong, Y.; Quan, C.; Tay, C. J.

2018-02-01

We propose a new multiple image encryption scheme based on a pixel exchange operation and a basic vector decomposition in Fourier domain. In this algorithm, original images are imported via a pixel exchange operator, from which scrambled images and pixel position matrices are obtained. Scrambled images encrypted into phase information are imported using the proposed algorithm and phase keys are obtained from the difference between scrambled images and synthesized vectors in a charge-coupled device (CCD) plane. The final synthesized vector is used as an input in a random phase encoding (DRPE) scheme. In the proposed encryption scheme, pixel position matrices and phase keys serve as additional private keys to enhance the security of the cryptosystem which is based on a 4-f system. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed encryption scheme.

Product of Ginibre matrices: Fuss-Catalan and Raney distributions

NASA Astrophysics Data System (ADS)

Penson, Karol A.; Życzkowski, Karol

2011-06-01

Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions Ps(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions Ps(x) in terms of a combination of s hypergeometric functions of the type sFs-1. The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

Product of Ginibre matrices: Fuss-Catalan and Raney distributions.

PubMed

Penson, Karol A; Zyczkowski, Karol

2011-06-01

Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions P(s)(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions P(s)(x) in terms of a combination of s hypergeometric functions of the type (s)F(s-1). The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

Probabilistic Signal Recovery and Random Matrices

DTIC Science & Technology

2016-12-08

applications in statistics , biomedical data analysis, quantization, dimen- sion reduction, and networks science. 1. High-dimensional inference and geometry Our...low-rank approxima- tion, with applications to community detection in networks, Annals of Statistics 44 (2016), 373–400. [7] C. Le, E. Levina, R...approximation, with applications to community detection in networks, Annals of Statistics 44 (2016), 373–400. C. Le, E. Levina, R. Vershynin, Concentration

Learning Circulant Sensing Kernels

DTIC Science & Technology

2014-03-01

Furthermore, we test learning the circulant sensing matrix/operator and the nonparametric dictionary altogether and obtain even better performance. We...scale. Furthermore, we test learning the circulant sensing matrix/operator and the nonparametric dictionary altogether and obtain even better performance...matrices, Tropp et al.[28] de - scribes a random filter for acquiring a signal x̄; Haupt et al.[12] describes a channel estimation problem to identify a

Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory

NASA Astrophysics Data System (ADS)

Torquato, Salvatore; Scardicchio, A.; Zachary, Chase E.

2008-11-01

It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line \\mathbb {R} . Here we analytically provide exact generalizations of such a point process in d-dimensional Euclidean space \\mathbb {R}^d for any d, which are special cases of determinantal processes. In particular, we obtain the n-particle correlation functions for any n, which completely specify the point processes in \\mathbb {R}^d . We also demonstrate that spin-polarized fermionic systems in \\mathbb {R}^d have these same n-particle correlation functions in each dimension. The point processes for any d are shown to be hyperuniform, i.e., infinite wavelength density fluctuations vanish, and the structure factor (or power spectrum) S(k) has a non-analytic behavior at the origin given by S(k)~|k| (k \\rightarrow 0 ). The latter result implies that the pair correlation function g2(r) tends to unity for large pair distances with a decay rate that is controlled by the power law 1/rd+1, which is a well-known property of bosonic ground states and more recently has been shown to characterize maximally random jammed sphere packings. We graphically display one-and two-dimensional realizations of the point processes in order to vividly reveal their 'repulsive' nature. Indeed, we show that the point processes can be characterized by an effective 'hard core' diameter that grows like the square root of d. The nearest-neighbor distribution functions for these point processes are also evaluated and rigorously bounded. Among other results, this analysis reveals that the probability of finding a large spherical cavity of radius r in dimension d behaves like a Poisson point process but in dimension d+1, i.e., this probability is given by exp[-κ(d)rd+1] for large r and finite d, where κ(d) is a positive d-dependent constant. We also show that as d increases, the point process behaves effectively like a sphere packing with a coverage fraction of space that is no denser than 1/2d. This coverage fraction has a special significance in the study of sphere packings in high-dimensional Euclidean spaces.

From micro-correlations to macro-correlations

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

Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

2016-11-15

Random vectors with a symmetric correlation structure share a common value of pair-wise correlation between their different components. The symmetric correlation structure appears in a multitude of settings, e.g. mixture models. In a mixture model the components of the random vector are drawn independently from a general probability distribution that is determined by an underlying parameter, and the parameter itself is randomized. In this paper we study the overall correlation of high-dimensional random vectors with a symmetric correlation structure. Considering such a random vector, and terming its pair-wise correlation “micro-correlation”, we use an asymptotic analysis to derive the random vector’smore » “macro-correlation” : a score that takes values in the unit interval, and that quantifies the random vector’s overall correlation. The method of obtaining macro-correlations from micro-correlations is then applied to a diverse collection of frameworks that demonstrate the method’s wide applicability.« less

A sensitive LC-MS/MS method for measurement of organophosphorus pesticides and their oxygen analogs in air sampling matrices

PubMed Central

ARMSTRONG, JENNA L.; DILLS, RUSSELL L.; YU, JIANBO; YOST, MICHAEL G.; FENSKE, RICHARD A.

2018-01-01

A rapid liquid chromatography tandem mass spectrometry (LC-MS/MS) method has been developed for determination of levels of the organophosphorus (OP) pesticides chlorpyrifos (CPF), azinphos methyl (AZM), and their oxygen analogs chlorpyrifos-oxon (CPF-O) and azinphos methyl-oxon (AZM-O) on common active air sampling matrices. XAD-2 resin and polyurethane foam (PUF) matrices were extracted with acetonitrile containing stable-isotope labeled internal standards (ISTD). Analysis was accomplished in Multiple Reaction Monitoring (MRM) mode, and analytes in unknown samples were identified by retention time (±0.1 min) and qualifier ratio (±30% absolute) as compared to the mean of calibrants. For all compounds, calibration linearity correlation coefficients were ≥0.996. Limits of detection (LOD) ranged from 0.15–1.1 ng/sample for CPF, CPF-O, AZM, and AZM-O on active sampling matrices. Spiked fortification recoveries were 78–113% from XAD-2 active air sampling tubes and 71–108% from PUF active air sampling tubes. Storage stability tests also yielded recoveries ranging from 74–94% after time periods ranging from 2–10 months. The results demonstrate that LC-MS/MS is a sensitive method for determining these compounds from two different matrices at the low concentrations that can result from spray drift and long range transport in non-target areas following agricultural applications. In an inter-laboratory comparison, the limit of quantification (LOQ) for LC-MS/MS was 100 times lower than a typical gas chromatography-mass spectrometry (GC-MS) method. PMID:24328542

A sensitive LC-MS/MS method for measurement of organophosphorus pesticides and their oxygen analogs in air sampling matrices.

PubMed

Armstrong, Jenna L; Dills, Russell L; Yu, Jianbo; Yost, Michael G; Fenske, Richard A

2014-01-01

A rapid liquid chromatography tandem mass spectrometry (LC-MS/MS) method has been developed for determination of levels of the organophosphorus (OP) pesticides chlorpyrifos (CPF), azinphos methyl (AZM), and their oxygen analogs chlorpyrifos-oxon (CPF-O) and azinphos methyl-oxon (AZM-O) on common active air sampling matrices. XAD-2 resin and polyurethane foam (PUF) matrices were extracted with acetonitrile containing stable-isotope labeled internal standards (ISTD). Analysis was accomplished in Multiple Reaction Monitoring (MRM) mode, and analytes in unknown samples were identified by retention time (±0.1 min) and qualifier ratio (±30% absolute) as compared to the mean of calibrants. For all compounds, calibration linearity correlation coefficients were ≥0.996. Limits of detection (LOD) ranged from 0.15-1.1 ng/sample for CPF, CPF-O, AZM, and AZM-O on active sampling matrices. Spiked fortification recoveries were 78-113% from XAD-2 active air sampling tubes and 71-108% from PUF active air sampling tubes. Storage stability tests also yielded recoveries ranging from 74-94% after time periods ranging from 2-10 months. The results demonstrate that LC-MS/MS is a sensitive method for determining these compounds from two different matrices at the low concentrations that can result from spray drift and long range transport in non-target areas following agricultural applications. In an inter-laboratory comparison, the limit of quantification (LOQ) for LC-MS/MS was 100 times lower than a typical gas chromatography-mass spectrometry (GC-MS) method.

Fluorescence spectroscopy of UV-MALDI matrices and implications of ionization mechanisms

NASA Astrophysics Data System (ADS)

Lin, Hou-Yu; Hsu, Hsu Chen; Lu, I.-Chung; Hsu, Kuo-Tung; Liao, Chih-Yu; Lee, Yin-Yu; Tseng, Chien-Ming; Lee, Yuan-Tseh; Ni, Chi-Kung

2014-10-01

Matrix-assisted laser desorption ionization (MALDI) has been widely used in the mass analysis of biomolecules; however, there are a lot of debates about the ionization mechanisms. Previous studies have indicated that S1-S1 annihilation might be a key process in the generation of primary ions. This study investigates S1-S1 annihilation by examining the time-resolved fluorescence spectra of 12 matrices. No S1-S1 annihilation was observed in six of these matrices (3-hydroxy-picolinic acid, 6-aza-2-thiothymine, 2,4-dihydroxy-acetophenone, 2,6-dihydroxy-acetophenone, 2,4,6-trihydroxy-acetophenone, and ferulic acid). We observed two matrix molecules reacting in an electronically excited state (S1) in five of these matrices (2,5-dihydroxybenzoic acid, α-cyano-4-hydroxycinnamic acid, 2,5-dihydroxy-acetophenone, 2,3-dihydroxybenzoic acid, and 2,6-dihydroxybenzoic acid), and S1-S1 annihilation was a possible reaction. Among these five matrices, no S1-S1 annihilation was observed for 2,3-dihydroxybenzoic acid in typical peak power region of nanosecond laser pulses in MALDI, but a very small value of reaction rate constant was observed only in the high peak power region. The excited-state lifetime of sinapinic acid was too short to determine whether the molecules reacted in an electronically excited state. No correlation was observed between the ion generation efficiency of MALDI and S1-S1 annihilation. The results indicate that the proposal of S1-S1 annihilation is unnecessary in MALDI and energy pooling model for MALDI ionization mechanism has to be modified.

Systemic risk and spatiotemporal dynamics of the US housing market

PubMed Central

Meng, Hao; Xie, Wen-Jie; Jiang, Zhi-Qiang; Podobnik, Boris; Zhou, Wei-Xing; Stanley, H. Eugene

2014-01-01

Housing markets play a crucial role in economies and the collapse of a real-estate bubble usually destabilizes the financial system and causes economic recessions. We investigate the systemic risk and spatiotemporal dynamics of the US housing market (1975–2011) at the state level based on the Random Matrix Theory (RMT). We identify richer economic information in the largest eigenvalues deviating from RMT predictions for the housing market than for stock markets and find that the component signs of the eigenvectors contain either geographical information or the extent of differences in house price growth rates or both. By looking at the evolution of different quantities such as eigenvalues and eigenvectors, we find that the US housing market experienced six different regimes, which is consistent with the evolution of state clusters identified by the box clustering algorithm and the consensus clustering algorithm on the partial correlation matrices. We find that dramatic increases in the systemic risk are usually accompanied by regime shifts, which provide a means of early detection of housing bubbles. PMID:24413626

Comparison of Mediterranean Pistacia lentiscus genotypes by random amplified polymorphic DNA, chemical, and morphological analyses.

PubMed

Barazani, Oz; Dudai, Nativ; Golan-Goldhirsh, Avi

2003-08-01

Characterization of the genetic variability of Mediterranean Pistacia lentiscus genotypes by RAPD, composition of essential oils, and morphology is presented. High polymorphism in morphological parameters was found among accessions, with no significant differences in relation to geographical origin, or to gender. GC-MS analysis of leaves extracted by t-butyl methyl ether, showed 12 monoterpenes, seven sesquiterpenes, and one linear nonterpenic compound. Cluster analysis divided the accessions into two main groups according to the relative content of the major compounds, with no relation to their geographical origin. In contrast, a dendrogram based on RAPD analysis gave two main clusters according to their geographical origins. Low correlation was found between genetic and essential oil content matrices. High morphological and chemical variability on one hand, and genotypic polymorphism on the other, provide ecological advantages that might explain the distribution of Pistacia lentiscus over a wide range of habitats. The plants under study were grown together in the same climatic and environmental conditions, thus pointing to the plausible genetic basis of the observed phenotypic differences.

A probabilistic model of a porous heat exchanger

NASA Technical Reports Server (NTRS)

Agrawal, O. P.; Lin, X. A.

1995-01-01

This paper presents a probabilistic one-dimensional finite element model for heat transfer processes in porous heat exchangers. The Galerkin approach is used to develop the finite element matrices. Some of the submatrices are asymmetric due to the presence of the flow term. The Neumann expansion is used to write the temperature distribution as a series of random variables, and the expectation operator is applied to obtain the mean and deviation statistics. To demonstrate the feasibility of the formulation, a one-dimensional model of heat transfer phenomenon in superfluid flow through a porous media is considered. Results of this formulation agree well with the Monte-Carlo simulations and the analytical solutions. Although the numerical experiments are confined to parametric random variables, a formulation is presented to account for the random spatial variations.

Altered brain structural networks in attention deficit/hyperactivity disorder children revealed by cortical thickness.

PubMed

Liu, Tian; Chen, Yanni; Li, Chenxi; Li, Youjun; Wang, Jue

2017-07-04

This study investigated the cortical thickness and topological features of human brain anatomical networks related to attention deficit/hyperactivity disorder. Data were collected from 40 attention deficit/hyperactivity disorder children and 40 normal control children. Interregional correlation matrices were established by calculating the correlations of cortical thickness between all pairs of cortical regions (68 regions) of the whole brain. Further thresholds were applied to create binary matrices to construct a series of undirected and unweighted graphs, and global, local, and nodal efficiencies were computed as a function of the network cost. These experimental results revealed abnormal cortical thickness and correlations in attention deficit/hyperactivity disorder, and showed that the brain structural networks of attention deficit/hyperactivity disorder subjects had inefficient small-world topological features. Furthermore, their topological properties were altered abnormally. In particular, decreased global efficiency combined with increased local efficiency in attention deficit/hyperactivity disorder children led to a disorder-related shift of the network topological structure toward regular networks. In addition, nodal efficiency, cortical thickness, and correlation analyses revealed that several brain regions were altered in attention deficit/hyperactivity disorder patients. These findings are in accordance with a hypothesis of dysfunctional integration and segregation of the brain in patients with attention deficit/hyperactivity disorder and provide further evidence of brain dysfunction in attention deficit/hyperactivity disorder patients by observing cortical thickness on magnetic resonance imaging.

Making Brains run Faster: are they Becoming Smarter?

PubMed

Pahor, Anja; Jaušovec, Norbert

2016-12-05

A brief overview of structural and functional brain characteristics related to g is presented in the light of major neurobiological theories of intelligence: Neural Efficiency, P-FIT and Multiple-Demand system. These theories provide a framework to discuss the main objective of the paper: what is the relationship between individual alpha frequency (IAF) and g? Three studies were conducted in order to investigate this relationship: two correlational studies and a third study in which we experimentally induced changes in IAF by means of transcranial alternating current stimulation (tACS). (1) In a large scale study (n = 417), no significant correlations between IAF and IQ were observed. However, in males IAF positively correlated with mental rotation and shape manipulation and with an attentional focus on detail. (2) The second study showed sex-specific correlations between IAF (obtained during task performance) and scope of attention in males and between IAF and reaction time in females. (3) In the third study, individuals' IAF was increased with tACS. The induced changes in IAF had a disrupting effect on male performance on Raven's matrices, whereas a mild positive effect was observed for females. Neuro-electric activity after verum tACS showed increased desynchronization in the upper alpha band and dissociation between fronto-parietal and right temporal brain areas during performance on Raven's matrices. The results are discussed in the light of gender differences in brain structure and activity.

An Exploring Model of Intelligence and Personality in Different Culture

ERIC Educational Resources Information Center

Wu, Yufeng; Qian, Guoying

2005-01-01

Middle school subjects of 13-21 years (from 4 nationalities) were used for studying the relationship between progressive cognition and personality characteristics by Raven's Standard Progressive Matrices and Eysenk's Personality Questionnaire. The results showed: (1) the correlation and stepwise regression were completely identical: P score was…

A non-verbal technique for the assessment of general intellectual ability in selection of aviation personnel.

DOT National Transportation Integrated Search

1971-06-01

A study was conducted in which performance on a non-verbal problem- solving task was correlated with the Otis Quick Scoring Mental Ability Test and the Raven Progressive Matrices Test. The problem-solving task, called 'code- lock' required the subjec...

Parameter Accuracy in Meta-Analyses of Factor Structures

ERIC Educational Resources Information Center

Gnambs, Timo; Staufenbiel, Thomas

2016-01-01

Two new methods for the meta-analysis of factor loadings are introduced and evaluated by Monte Carlo simulations. The direct method pools each factor loading individually, whereas the indirect method synthesizes correlation matrices reproduced from factor loadings. The results of the two simulations demonstrated that the accuracy of…

Inference on the Ranks of the Canonical Correlation Matrices for Elliptically Symmetric Populations.

DTIC Science & Technology

1985-05-01

robust estimates of the covariance matrix, the reader is referred to Devlin, Gnanadesikan and Kettenring (1975) and Maronna (1976). Murihead and...contoured distributions. J. Multivariate Anal. 11, 368-385. 6. DEVLIN, S.J. GNANADESIKAN , R. and KETTENRING, J. (1975). Robust estima- tion and outlier

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables.

ERIC Educational Resources Information Center

Ethington, Corinna A.

1987-01-01

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical variables. The analysis of mixed matrices produced estimates that closely approximated the model parameters except where dichotomous variables were…

Investigating the Structure of the WJ-III Cognitive at School Age

ERIC Educational Resources Information Center

Dombrowski, Stefan C.

2013-01-01

During its development, the Woodcock-Johnson, Third Edition Cognitive (WJ-III Cognitive; McGrew & Woodcock, 2001) was never subjected to structural analysis using exploratory and higher order factor analyses. Instead, confirmatory factor analyses were conducted on separate sets of WJ-III correlation matrices, yielding a seven-factor model…

Orbit Determination Using Vinti’s Solution

DTIC Science & Technology

2016-09-15

Surveillance Network STK Systems Tool Kit TBP Two Body Problem TLE Two-line Element Set xv Acronym Definition UKF Unscented Kalman Filter WPAFB Wright...simplicity, stability, and speed. On the other hand, Kalman filters would be best suited for sequential estimation of stochastic or random components of a...be likened to how an Unscented Kalman Filter samples a system’s nonlinearities directly, avoiding linearizing the dynamics in the partials matrices

Spiked Models of Large Dimensional Random Matrices Applied to Wireless Communications and Array Signal Processing

DTIC Science & Technology

2013-12-14

population covariance matrix with application to array signal processing; and 5) a sample covariance matrix for which a CLT is studied on linear...Applications , (01 2012): 1150004. doi: Walid Hachem, Malika Kharouf, Jamal Najim, Jack W. Silverstein. A CLT FOR INFORMATION- THEORETIC STATISTICS...for Multi-source Power Estimation, (04 2010) Malika Kharouf, Jamal Najim, Jack W. Silverstein, Walid Hachem. A CLT FOR INFORMATION- THEORETIC

Event-Based Variance-Constrained ${\\mathcal {H}}_{\\infty }$ Filtering for Stochastic Parameter Systems Over Sensor Networks With Successive Missing Measurements.

PubMed

Wang, Licheng; Wang, Zidong; Han, Qing-Long; Wei, Guoliang

2018-03-01

This paper is concerned with the distributed filtering problem for a class of discrete time-varying stochastic parameter systems with error variance constraints over a sensor network where the sensor outputs are subject to successive missing measurements. The phenomenon of the successive missing measurements for each sensor is modeled via a sequence of mutually independent random variables obeying the Bernoulli binary distribution law. To reduce the frequency of unnecessary data transmission and alleviate the communication burden, an event-triggered mechanism is introduced for the sensor node such that only some vitally important data is transmitted to its neighboring sensors when specific events occur. The objective of the problem addressed is to design a time-varying filter such that both the requirements and the variance constraints are guaranteed over a given finite-horizon against the random parameter matrices, successive missing measurements, and stochastic noises. By recurring to stochastic analysis techniques, sufficient conditions are established to ensure the existence of the time-varying filters whose gain matrices are then explicitly characterized in term of the solutions to a series of recursive matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of the developed event-triggered distributed filter design strategy.

Multi-dimensional Fokker-Planck equation analysis using the modified finite element method

NASA Astrophysics Data System (ADS)

Náprstek, J.; Král, R.

2016-09-01

The Fokker-Planck equation (FPE) is a frequently used tool for the solution of cross probability density function (PDF) of a dynamic system response excited by a vector of random processes. FEM represents a very effective solution possibility, particularly when transition processes are investigated or a more detailed solution is needed. Actual papers deal with single degree of freedom (SDOF) systems only. So the respective FPE includes two independent space variables only. Stepping over this limit into MDOF systems a number of specific problems related to a true multi-dimensionality must be overcome. Unlike earlier studies, multi-dimensional simplex elements in any arbitrary dimension should be deployed and rectangular (multi-brick) elements abandoned. Simple closed formulae of integration in multi-dimension domain have been derived. Another specific problem represents the generation of multi-dimensional finite element mesh. Assembling of system global matrices should be subjected to newly composed algorithms due to multi-dimensionality. The system matrices are quite full and no advantages following from their sparse character can be profited from, as is commonly used in conventional FEM applications in 2D/3D problems. After verification of partial algorithms, an illustrative example dealing with a 2DOF non-linear aeroelastic system in combination with random and deterministic excitations is discussed.

Cryptosystem for Securing Image Encryption Using Structured Phase Masks in Fresnel Wavelet Transform Domain

NASA Astrophysics Data System (ADS)

Singh, Hukum

2016-12-01

A cryptosystem for securing image encryption is considered by using double random phase encoding in Fresnel wavelet transform (FWT) domain. Random phase masks (RPMs) and structured phase masks (SPMs) based on devil's vortex toroidal lens (DVTL) are used in spatial as well as in Fourier planes. The images to be encrypted are first Fresnel transformed and then single-level discrete wavelet transform (DWT) is apply to decompose LL,HL, LH and HH matrices. The resulting matrices from the DWT are multiplied by additional RPMs and the resultants are subjected to inverse DWT for the encrypted images. The scheme is more secure because of many parameters used in the construction of SPM. The original images are recovered by using the correct parameters of FWT and SPM. Phase mask SPM based on DVTL increases security that enlarges the key space for encryption and decryption. The proposed encryption scheme is a lens-less optical system and its digital implementation has been performed using MATLAB 7.6.0 (R2008a). The computed value of mean-squared-error between the retrieved and the input images shows the efficacy of scheme. The sensitivity to encryption parameters, robustness against occlusion, entropy and multiplicative Gaussian noise attacks have been analysed.

Uncovering the spatial structure of mobility networks

NASA Astrophysics Data System (ADS)

Louail, Thomas; Lenormand, Maxime; Picornell, Miguel; García Cantú, Oliva; Herranz, Ricardo; Frias-Martinez, Enrique; Ramasco, José J.; Barthelemy, Marc

2015-01-01

The extraction of a clear and simple footprint of the structure of large, weighted and directed networks is a general problem that has relevance for many applications. An important example is seen in origin-destination matrices, which contain the complete information on commuting flows, but are difficult to analyze and compare. We propose here a versatile method, which extracts a coarse-grained signature of mobility networks, under the form of a 2 × 2 matrix that separates the flows into four categories. We apply this method to origin-destination matrices extracted from mobile phone data recorded in 31 Spanish cities. We show that these cities essentially differ by their proportion of two types of flows: integrated (between residential and employment hotspots) and random flows, whose importance increases with city size. Finally, the method allows the determination of categories of networks, and in the mobility case, the classification of cities according to their commuting structure.

Correlation of financial markets in times of crisis

NASA Astrophysics Data System (ADS)

Sandoval, Leonidas; Franca, Italo De Paula

2012-01-01

Using the eigenvalues and eigenvectors of correlations matrices of some of the main financial market indices in the world, we show that high volatility of markets is directly linked with strong correlations between them. This means that markets tend to behave as one during great crashes. In order to do so, we investigate financial market crises that occurred in the years 1987 (Black Monday), 1998 (Russian crisis), 2001 (Burst of the dot-com bubble and September 11), and 2008 (Subprime Mortgage Crisis), which mark some of the largest downturns of financial markets in the last three decades.

Joint genome-wide prediction in several populations accounting for randomness of genotypes: A hierarchical Bayes approach. II: Multivariate spike and slab priors for marker effects and derivation of approximate Bayes and fractional Bayes factors for the complete family of models.

PubMed

Martínez, Carlos Alberto; Khare, Kshitij; Banerjee, Arunava; Elzo, Mauricio A

2017-03-21

This study corresponds to the second part of a companion paper devoted to the development of Bayesian multiple regression models accounting for randomness of genotypes in across population genome-wide prediction. This family of models considers heterogeneous and correlated marker effects and allelic frequencies across populations, and has the ability of considering records from non-genotyped individuals and individuals with missing genotypes in any subset of loci without the need for previous imputation, taking into account uncertainty about imputed genotypes. This paper extends this family of models by considering multivariate spike and slab conditional priors for marker allele substitution effects and contains derivations of approximate Bayes factors and fractional Bayes factors to compare models from part I and those developed here with their null versions. These null versions correspond to simpler models ignoring heterogeneity of populations, but still accounting for randomness of genotypes. For each marker loci, the spike component of priors corresponded to point mass at 0 in R S , where S is the number of populations, and the slab component was a S-variate Gaussian distribution, independent conditional priors were assumed. For the Gaussian components, covariance matrices were assumed to be either the same for all markers or different for each marker. For null models, the priors were simply univariate versions of these finite mixture distributions. Approximate algebraic expressions for Bayes factors and fractional Bayes factors were found using the Laplace approximation. Using the simulated datasets described in part I, these models were implemented and compared with models derived in part I using measures of predictive performance based on squared Pearson correlations, Deviance Information Criterion, Bayes factors, and fractional Bayes factors. The extensions presented here enlarge our family of genome-wide prediction models making it more flexible in the sense that it now offers more modeling options. Copyright © 2017 Elsevier Ltd. All rights reserved.

Inverse eigenproblem for R-symmetric matrices and their approximation

NASA Astrophysics Data System (ADS)

Yuan, Yongxin

2009-11-01

Let be a nontrivial involution, i.e., R=R-1[not equal to]±In. We say that is R-symmetric if RGR=G. The set of all -symmetric matrices is denoted by . In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors in and a set of complex numbers , find a matrix such that and are, respectively, the eigenvalues and eigenvectors of A. We then consider the following approximation problem: Given an n×n matrix , find such that , where is the solution set of IEP and ||[dot operator]|| is the Frobenius norm. We provide an explicit formula for the best approximation solution by means of the canonical correlation decomposition.

Real time evolution at finite temperatures with operator space matrix product states

NASA Astrophysics Data System (ADS)

Pižorn, Iztok; Eisler, Viktor; Andergassen, Sabine; Troyer, Matthias

2014-07-01

We propose a method to simulate the real time evolution of one-dimensional quantum many-body systems at finite temperature by expressing both the density matrices and the observables as matrix product states. This allows the calculation of expectation values and correlation functions as scalar products in operator space. The simulations of density matrices in inverse temperature and the local operators in the Heisenberg picture are independent and result in a grid of expectation values for all intermediate temperatures and times. Simulations can be performed using real arithmetics with only polynomial growth of computational resources in inverse temperature and time for integrable systems. The method is illustrated for the XXZ model and the single impurity Anderson model.

Extractive Atmospheric Pressure Photoionization (EAPPI) Mass Spectrometry: Rapid Analysis of Chemicals in Complex Matrices.

PubMed

Liu, Chengyuan; Yang, Jiuzhong; Wang, Jian; Hu, Yonghua; Zhao, Wan; Zhou, Zhongyue; Qi, Fei; Pan, Yang

2016-10-01

Extractive atmospheric pressure photoionization (EAPPI) mass spectrometry was designed for rapid qualitative and quantitative analysis of chemicals in complex matrices. In this method, an ultrasonic nebulization system was applied to sample extraction, nebulization, and vaporization. Mixed with a gaseous dopant, vaporized analytes were ionized through ambient photon-induced ion-molecule reactions, and were mass-analyzed by a high resolution time-of-flight mass spectrometer (TOF-MS). After careful optimization and testing with pure sample solution, EAPPI was successfully applied to the fast screening of capsules, soil, natural products, and viscous compounds. Analysis was completed within a few seconds without the need for preseparation. Moreover, the quantification capability of EAPPI for matrices was evaluated by analyzing six polycyclic aromatic hydrocarbons (PAHs) in soil. The correlation coefficients (R (2) ) for standard curves of all six PAHs were above 0.99, and the detection limits were in the range of 0.16-0.34 ng/mg. In addition, EAPPI could also be used to monitor organic chemical reactions in real time. Graphical Abstract ᅟ.

Riemannian multi-manifold modeling and clustering in brain networks

NASA Astrophysics Data System (ADS)

Slavakis, Konstantinos; Salsabilian, Shiva; Wack, David S.; Muldoon, Sarah F.; Baidoo-Williams, Henry E.; Vettel, Jean M.; Cieslak, Matthew; Grafton, Scott T.

2017-08-01

This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.

The effect of stochiastic technique on estimates of population viability from transition matrix models

USGS Publications Warehouse

Kaye, T.N.; Pyke, David A.

2003-01-01

Population viability analysis is an important tool for conservation biologists, and matrix models that incorporate stochasticity are commonly used for this purpose. However, stochastic simulations may require assumptions about the distribution of matrix parameters, and modelers often select a statistical distribution that seems reasonable without sufficient data to test its fit. We used data from long-term (5a??10 year) studies with 27 populations of five perennial plant species to compare seven methods of incorporating environmental stochasticity. We estimated stochastic population growth rate (a measure of viability) using a matrix-selection method, in which whole observed matrices were selected at random at each time step of the model. In addition, we drew matrix elements (transition probabilities) at random using various statistical distributions: beta, truncated-gamma, truncated-normal, triangular, uniform, or discontinuous/observed. Recruitment rates were held constant at their observed mean values. Two methods of constraining stage-specific survival to a??100% were also compared. Different methods of incorporating stochasticity and constraining matrix column sums interacted in their effects and resulted in different estimates of stochastic growth rate (differing by up to 16%). Modelers should be aware that when constraining stage-specific survival to 100%, different methods may introduce different levels of bias in transition element means, and when this happens, different distributions for generating random transition elements may result in different viability estimates. There was no species effect on the results and the growth rates derived from all methods were highly correlated with one another. We conclude that the absolute value of population viability estimates is sensitive to model assumptions, but the relative ranking of populations (and management treatments) is robust. Furthermore, these results are applicable to a range of perennial plants and possibly other life histories.

Proteolytic and non-proteolytic regulation of collective cell invasion: tuning by ECM density and organization

PubMed Central

Kumar, Sandeep; Kapoor, Aastha; Desai, Sejal; Inamdar, Mandar M.; Sen, Shamik

2016-01-01

Cancer cells manoeuvre through extracellular matrices (ECMs) using different invasion modes, including single cell and collective cell invasion. These modes rely on MMP-driven ECM proteolysis to make space for cells to move. How cancer-associated alterations in ECM influence the mode of invasion remains unclear. Further, the sensitivity of the two invasion modes to MMP dynamics remains unexplored. In this paper, we address these open questions using a multiscale hybrid computational model combining ECM density-dependent MMP secretion, MMP diffusion, ECM degradation by MMP and active cell motility. Our results demonstrate that in randomly aligned matrices, collective cell invasion is more efficient than single cell invasion. Although increase in MMP secretion rate enhances invasiveness independent of cell–cell adhesion, sustenance of collective invasion in dense matrices requires high MMP secretion rates. However, matrix alignment can sustain both single cell and collective cell invasion even without ECM proteolysis. Similar to our in-silico observations, increase in ECM density and MMP inhibition reduced migration of MCF-7 cells embedded in sandwich gels. Together, our results indicate that apart from cell intrinsic factors (i.e., high cell–cell adhesion and MMP secretion rates), ECM density and organization represent two important extrinsic parameters that govern collective cell invasion and invasion plasticity. PMID:26832069

Easy way to determine quantitative spatial resolution distribution for a general inverse problem

NASA Astrophysics Data System (ADS)

An, M.; Feng, M.

2013-12-01

The spatial resolution computation of a solution was nontrivial and more difficult than solving an inverse problem. Most geophysical studies, except for tomographic studies, almost uniformly neglect the calculation of a practical spatial resolution. In seismic tomography studies, a qualitative resolution length can be indicatively given via visual inspection of the restoration of a synthetic structure (e.g., checkerboard tests). An effective strategy for obtaining quantitative resolution length is to calculate Backus-Gilbert resolution kernels (also referred to as a resolution matrix) by matrix operation. However, not all resolution matrices can provide resolution length information, and the computation of resolution matrix is often a difficult problem for very large inverse problems. A new class of resolution matrices, called the statistical resolution matrices (An, 2012, GJI), can be directly determined via a simple one-parameter nonlinear inversion performed based on limited pairs of random synthetic models and their inverse solutions. The total procedure were restricted to forward/inversion processes used in the real inverse problem and were independent of the degree of inverse skill used in the solution inversion. Spatial resolution lengths can be directly given during the inversion. Tests on 1D/2D/3D model inversion demonstrated that this simple method can be at least valid for a general linear inverse problem.

Limited Rationality and Its Quantification Through the Interval Number Judgments With Permutations.

PubMed

Liu, Fang; Pedrycz, Witold; Zhang, Wei-Guo

2017-12-01

The relative importance of alternatives expressed in terms of interval numbers in the fuzzy analytic hierarchy process aims to capture the uncertainty experienced by decision makers (DMs) when making a series of comparisons. Under the assumption of full rationality, the judgements of DMs in the typical analytic hierarchy process could be consistent. However, since the uncertainty in articulating the opinions of DMs is unavoidable, the interval number judgements are associated with the limited rationality. In this paper, we investigate the concept of limited rationality by introducing interval multiplicative reciprocal comparison matrices. By analyzing the consistency of interval multiplicative reciprocal comparison matrices, it is observed that the interval number judgements are inconsistent. By considering the permutations of alternatives, the concepts of approximation-consistency and acceptable approximation-consistency of interval multiplicative reciprocal comparison matrices are proposed. The exchange method is designed to generate all the permutations. A novel method of determining the interval weight vector is proposed under the consideration of randomness in comparing alternatives, and a vector of interval weights is determined. A new algorithm of solving decision making problems with interval multiplicative reciprocal preference relations is provided. Two numerical examples are carried out to illustrate the proposed approach and offer a comparison with the methods available in the literature.

Advances in stir bar sorptive extraction for the determination of acidic pharmaceuticals in environmental water matrices Comparison between polyurethane and polydimethylsiloxane polymeric phases.

PubMed

Silva, Ana Rita M; Portugal, Fátima C M; Nogueira, J M F

2008-10-31

Stir bar sorptive extraction with polyurethane (PU) and polydimethylsiloxane (PDMS) polymeric phases followed by high-performance liquid chromatography with diode array detection [SBSE(PU or PDMS)/HPLC-DAD] was studied for the determination of six acidic pharmaceuticals [o-acetylsalicylic acid (ACA), ibuprofen (IBU), diclofenac sodium (DIC), naproxen (NAP), mefenamic acid (MEF) and gemfibrozil (GEM)], selected as non-steroidal acidic anti-inflammatory drugs and lipid regulators model compounds in environmental water matrices. The main parameters affecting the efficiency of the proposed methodology are fully discussed. Assays performed on 25 mL of water samples spiked at the 10 microg L(-1) level under optimized experimental conditions, yielded recoveries ranging from 45.3+/-9.0% (ACA) to 90.6+/-7.2% (IBU) by SBSE(PU) and 9.8+/-1.6% (NAP) to 73.4+/-5.0% (GEM) by SBSE(PDMS), where the former polymeric phase presented a better affinity to extract these target analytes from water matrices at the trace level. The methodology showed also excellent linear dynamic ranges for the six acidic pharmaceuticals studied, with correlation coefficients higher than 0.9976, limits of detection and quantification between 0.40-1.7 microg L(-1) and 1.5-5.8 microg L(-1), respectively, and suitable precision (RSD <15%). Moreover, the developed methodology was applied for the determination of these target analytes in several environmental matrices, including river, sea and wastewater samples, having achieved good performance and moderate matrix effects. In short, the PU foams demonstrated to be an excellent alternative for the enrichment of the more polar metabolites from water matrices by SBSE, overcoming the limitations of the conventional PDMS phase.

Fluorescence spectroscopy of UV-MALDI matrices and implications of ionization mechanisms

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

Lin, Hou-Yu; Hsu, Hsu Chen; Lu, I-Chung

2014-10-28

Matrix-assisted laser desorption ionization (MALDI) has been widely used in the mass analysis of biomolecules; however, there are a lot of debates about the ionization mechanisms. Previous studies have indicated that S{sub 1}-S{sub 1} annihilation might be a key process in the generation of primary ions. This study investigates S{sub 1}-S{sub 1} annihilation by examining the time-resolved fluorescence spectra of 12 matrices. No S{sub 1}-S{sub 1} annihilation was observed in six of these matrices (3-hydroxy-picolinic acid, 6-aza-2-thiothymine, 2,4-dihydroxy-acetophenone, 2,6-dihydroxy-acetophenone, 2,4,6-trihydroxy-acetophenone, and ferulic acid). We observed two matrix molecules reacting in an electronically excited state (S{sub 1}) in five of thesemore » matrices (2,5-dihydroxybenzoic acid, α-cyano-4-hydroxycinnamic acid, 2,5-dihydroxy-acetophenone, 2,3-dihydroxybenzoic acid, and 2,6-dihydroxybenzoic acid), and S{sub 1}-S{sub 1} annihilation was a possible reaction. Among these five matrices, no S{sub 1}-S{sub 1} annihilation was observed for 2,3-dihydroxybenzoic acid in typical peak power region of nanosecond laser pulses in MALDI, but a very small value of reaction rate constant was observed only in the high peak power region. The excited-state lifetime of sinapinic acid was too short to determine whether the molecules reacted in an electronically excited state. No correlation was observed between the ion generation efficiency of MALDI and S{sub 1}-S{sub 1} annihilation. The results indicate that the proposal of S{sub 1}-S{sub 1} annihilation is unnecessary in MALDI and energy pooling model for MALDI ionization mechanism has to be modified.« less

Dimensionality Assessment for Dichotomously Scored Items Using Multidimensional Scaling.

ERIC Educational Resources Information Center

Jones, Patricia B.; And Others

In order to determine the effectiveness of multidimensional scaling (MDS) in recovering the dimensionality of a set of dichotomously-scored items, data were simulated in one, two, and three dimensions for a variety of correlations with the underlying latent trait. Similarity matrices were constructed from these data using three margin-sensitive…

Seeking the Cause of Correlations among Mental Abilities: Large Twin Analysis in a National Testing Program.

ERIC Educational Resources Information Center

Page, Ellis B.; Jarjoura, David

1979-01-01

A computer scan of ACT Assessment records identified 3,427 sets of twins. The Hardy-Weinberg rule was used to estimate the proportion of monozygotic twins in the sample. Matrices of genetic and environmental influences were produced. The heaviest loadings were clearly in the genetic matrix. (SJL)

Dysgenic Fertility, Intelligence and Family Size in Libya

ERIC Educational Resources Information Center

Al-Shahomee, Alsedig Abdalgadr; Lynn, Richard; Abdalla, Saleh El-ghmary

2013-01-01

The Standard Progressive Matrices (SPM) was administered to a sample of 592 16 year old school students in Libya. There was a small negative correlation of -0.14 between SPM scores and the number of siblings, indicating only marginal dysgenic fertility. Supplementary material giving the data is given online. (Contains 1 table.)

Factor Covariance Analysis in Subgroups.

ERIC Educational Resources Information Center

Pennell, Roger

The problem considered is that of an investigator sampling two or more correlation matrices and desiring to fit a model where a factor pattern matrix is assumed to be identical across samples and we need to estimate only the factor covariance matrix and the unique variance for each sample. A flexible, least squares solution is worked out and…

HiCRep: assessing the reproducibility of Hi-C data using a stratum-adjusted correlation coefficient

PubMed Central

Yang, Tao; Zhang, Feipeng; Yardımcı, Galip Gürkan; Song, Fan; Hardison, Ross C.; Noble, William Stafford; Yue, Feng; Li, Qunhua

2017-01-01

Hi-C is a powerful technology for studying genome-wide chromatin interactions. However, current methods for assessing Hi-C data reproducibility can produce misleading results because they ignore spatial features in Hi-C data, such as domain structure and distance dependence. We present HiCRep, a framework for assessing the reproducibility of Hi-C data that systematically accounts for these features. In particular, we introduce a novel similarity measure, the stratum adjusted correlation coefficient (SCC), for quantifying the similarity between Hi-C interaction matrices. Not only does it provide a statistically sound and reliable evaluation of reproducibility, SCC can also be used to quantify differences between Hi-C contact matrices and to determine the optimal sequencing depth for a desired resolution. The measure consistently shows higher accuracy than existing approaches in distinguishing subtle differences in reproducibility and depicting interrelationships of cell lineages. The proposed measure is straightforward to interpret and easy to compute, making it well-suited for providing standardized, interpretable, automatable, and scalable quality control. The freely available R package HiCRep implements our approach. PMID:28855260

Hexamethylbenzene as a sensitive nuclear magnetic resonance probe for studying organic crystals and glasses

NASA Astrophysics Data System (ADS)

Jansen-Glaw, B.; Rössler, E.; Taupitz, M.; Vieth, H. M.

1989-06-01

Deuterated hexamethylbenzene (HMB) is used as a probe molecule for 2H NMR studies of the crystalline state of hexachlorobenzene and of several organic glasses. By measuring the spin-lattice relaxation and the line shape in the temperature range of 4-300 K the dynamical parameters of the molecular reorientation are investigated. For the system HMB/hexachlorobenzene, we find exponential relaxation and for the corresponding T1 an increase of its activation energy by a factor of 2 in comparison to the neat HMB. A homogeneous mixing of the guest and host molecules is found at least for guest concentrations up to 7%. In contrast, nonexponential spin-lattice relaxation is characteristic for all glass matrices, indicating motional heterogeneities. A log-Gauss distribution for the corresponding motional correlation times gives a good fit of the data. Its width parameter decreases linearly with temperature, while the mean correlation times are described by an Arrhenius law. The mean activation energy is reduced by a factor of about 3.5 as compared to neat HMB, demonstrating a loose packing of the molecules in the glass matrices.

Follicular fluid and urinary concentrations of phthalate metabolites among infertile women and associations with in vitro fertilization parameters.

PubMed

Du, Yao-Yao; Fang, Yue-Li; Wang, Yi-Xin; Zeng, Qiang; Guo, Na; Zhao, Hua; Li, Yu-Feng

2016-06-01

Evidence from toxicological studies has demonstrated that phthalates can lead to reduced fertility through effects on folliculogenesis, oocyte maturation and embryonic development, but human data are limited. Concentrations of eight phthalate metabolites in 110 follicular fluid (FF) and urine samples collected from 112 women attending an infertility clinic in Wuhan, China were quantified, and correlations between paired matrices were explored. Associations between metabolite concentrations and in vitro fertilization (IVF) parameters were evaluated with multivariable models. Six metabolites were detected in >72.73% of the FF samples. MEHP and MBP were the dominant metabolites with a median level of 2.80 and 2.05ng/mL, respectively. Significant correlations between the two matrices, urine and FF, were found for MEP (rs=0.44), and MBP (rs=0.22). FF and urinary metabolite concentrations were not associated with any IVF parameters. However, given the prevalence of phthalates exposure, further work is needed to elucidate the potential hazard on female reproduction. Copyright © 2016 Elsevier Inc. All rights reserved.

Low-temperature matrix effects on orientational motion of Methyl radical trapped in gas solids: Angular tunneling vs. libration

NASA Astrophysics Data System (ADS)

Dmitriev, Yurij A.; Zelenetckii, Ilia A.; Benetis, Nikolas P.

2018-05-01

EPR investigation of the lineshape of matrix -isolated methyl radical, CH3, spectra recorded in solid N2O and CO2 was carried out. Reversible temperature-dependent line width anisotropy was observed in both matrices. This effect is a fingerprint of the extra-slow radical rotation about the in-plane C2 axes. The rotation was found to be anisotropic and closely correlated to the orientational dynamics of the matrix molecules. It was suggested that a recently discovered "hoping precession" effect of matrix molecules in solid CO2 is a common feature of matrices of the linear molecules CO, N2O, and CO2. A new low-temperature matrix effect, referred to as "libration trap", was proposed which accounts for the changing CH3 reorientational motion about the radical C3-axis from rotation to libration. Temperature dependence of the intensity of the EPR satellites produced by these nonrotating-but librating methyls was presented. This allowed for a rough estimation of the rotation hindering potential due to correlation mismatch between the radical and the nearest matrix molecules' librations.

Scalable randomized benchmarking of non-Clifford gates

NASA Astrophysics Data System (ADS)

Cross, Andrew; Magesan, Easwar; Bishop, Lev; Smolin, John; Gambetta, Jay

Randomized benchmarking is a widely used experimental technique to characterize the average error of quantum operations. Benchmarking procedures that scale to enable characterization of n-qubit circuits rely on efficient procedures for manipulating those circuits and, as such, have been limited to subgroups of the Clifford group. However, universal quantum computers require additional, non-Clifford gates to approximate arbitrary unitary transformations. We define a scalable randomized benchmarking procedure over n-qubit unitary matrices that correspond to protected non-Clifford gates for a class of stabilizer codes. We present efficient methods for representing and composing group elements, sampling them uniformly, and synthesizing corresponding poly (n) -sized circuits. The procedure provides experimental access to two independent parameters that together characterize the average gate fidelity of a group element. We acknowledge support from ARO under Contract W911NF-14-1-0124.

The Restricted Isometry Property for Time-Frequency Structured Random Matrices

DTIC Science & Technology

2011-06-16

tests illustrating the use of Ψg for compressive sensing are presented in [41]. They illustrate that empirically Ψg performs very similarly to a...E.J., J., Tao, T., Romberg , J.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans...Inform. Theory 52(2), 489–509 (2006) [12] Candès, E.J., Romberg , J., Tao, T.: Stable signal recovery from incomplete and inaccurate mea- surements. Comm

Asymptotic analysis of the density of states in random matrix models associated with a slowly decaying weight

NASA Astrophysics Data System (ADS)

Kuijlaars, A. B. J.

2001-08-01

The asymptotic behavior of polynomials that are orthogonal with respect to a slowly decaying weight is very different from the asymptotic behavior of polynomials that are orthogonal with respect to a Freud-type weight. While the latter has been extensively studied, much less is known about the former. Following an earlier investigation into the zero behavior, we study here the asymptotics of the density of states in a unitary ensemble of random matrices with a slowly decaying weight. This measure is also naturally connected with the orthogonal polynomials. It is shown that, after suitable rescaling, the weak limit is the same as the weak limit of the rescaled zeros.

Electromagnetic Scattering by Spheroidal Volumes of Discrete Random Medium

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

We use the superposition T-matrix method to compare the far-field scattering matrices generated by spheroidal and spherical volumes of discrete random medium having the same volume and populated by identical spherical particles. Our results fully confirm the robustness of the previously identified coherent and diffuse scattering regimes and associated optical phenomena exhibited by spherical particulate volumes and support their explanation in terms of the interference phenomenon coupled with the order-of-scattering expansion of the far-field Foldy equations. We also show that increasing non-sphericity of particulate volumes causes discernible (albeit less pronounced) optical effects in forward and backscattering directions and explain them in terms of the same interference/multiple-scattering phenomenon.

Computer access security code system

NASA Technical Reports Server (NTRS)

Collins, Earl R., Jr. (Inventor)

1990-01-01

A security code system for controlling access to computer and computer-controlled entry situations comprises a plurality of subsets of alpha-numeric characters disposed in random order in matrices of at least two dimensions forming theoretical rectangles, cubes, etc., such that when access is desired, at least one pair of previously unused character subsets not found in the same row or column of the matrix is chosen at random and transmitted by the computer. The proper response to gain access is transmittal of subsets which complete the rectangle, and/or a parallelepiped whose opposite corners were defined by first groups of code. Once used, subsets are not used again to absolutely defeat unauthorized access by eavesdropping, and the like.

Tests of Hypotheses Arising In the Correlated Random Coefficient Model*

PubMed Central

Heckman, James J.; Schmierer, Daniel

2010-01-01

This paper examines the correlated random coefficient model. It extends the analysis of Swamy (1971), who pioneered the uncorrelated random coefficient model in economics. We develop the properties of the correlated random coefficient model and derive a new representation of the variance of the instrumental variable estimator for that model. We develop tests of the validity of the correlated random coefficient model against the null hypothesis of the uncorrelated random coefficient model. PMID:21170148

Reparametrization-based estimation of genetic parameters in multi-trait animal model using Integrated Nested Laplace Approximation.

PubMed

Mathew, Boby; Holand, Anna Marie; Koistinen, Petri; Léon, Jens; Sillanpää, Mikko J

2016-02-01

A novel reparametrization-based INLA approach as a fast alternative to MCMC for the Bayesian estimation of genetic parameters in multivariate animal model is presented. Multi-trait genetic parameter estimation is a relevant topic in animal and plant breeding programs because multi-trait analysis can take into account the genetic correlation between different traits and that significantly improves the accuracy of the genetic parameter estimates. Generally, multi-trait analysis is computationally demanding and requires initial estimates of genetic and residual correlations among the traits, while those are difficult to obtain. In this study, we illustrate how to reparametrize covariance matrices of a multivariate animal model/animal models using modified Cholesky decompositions. This reparametrization-based approach is used in the Integrated Nested Laplace Approximation (INLA) methodology to estimate genetic parameters of multivariate animal model. Immediate benefits are: (1) to avoid difficulties of finding good starting values for analysis which can be a problem, for example in Restricted Maximum Likelihood (REML); (2) Bayesian estimation of (co)variance components using INLA is faster to execute than using Markov Chain Monte Carlo (MCMC) especially when realized relationship matrices are dense. The slight drawback is that priors for covariance matrices are assigned for elements of the Cholesky factor but not directly to the covariance matrix elements as in MCMC. Additionally, we illustrate the concordance of the INLA results with the traditional methods like MCMC and REML approaches. We also present results obtained from simulated data sets with replicates and field data in rice.

Improvement of geomagnetic core field modeling with a priori information about Gauss coefficient correlations

NASA Astrophysics Data System (ADS)

Schachtschneider, R.; Rother, M.; Lesur, V.

2013-12-01

We introduce a method that enables us to account for existing correlations between Gauss coefficients in core field modelling. The information about the correlations are obtained from a highly accurate field model based on CHAMP data, e.g. the GRIMM-3 model. We compute the covariance matrices of the geomagnetic field, the secular variation, and acceleration up to degree 18 and use these in the regularization scheme of the core field inversion. For testing our method we followed two different approaches by applying it to two different synthetic satellite data sets. The first is a short data set with a time span of only three months. Here we test how the information about correlations help to obtain an accurate model when only very little information are available. The second data set is a large one covering several years. In this case, besides reducing the residuals in general, we focus on the improvement of the model near the boundaries of the data set where the accerelation is generally more difficult to handle. In both cases the obtained covariance matrices are included in the damping scheme of the regularization. That way information from scales that could otherwise not be resolved by the data can be extracted. We show that by using this technique we are able to improve the models of the field and the secular variation for both, the short and the long term data set, compared to approaches using more conventional regularization techniques.

Tolerant compressed sensing with partially coherent sensing matrices

NASA Astrophysics Data System (ADS)

Birnbaum, Tobias; Eldar, Yonina C.; Needell, Deanna

2017-08-01

Most of compressed sensing (CS) theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications, such as signal detection, motion detection and radar. Moreover, in these applications it is often not necessary to know the support of the signal exactly, but instead small errors in the support and signal are tolerable. Despite the abundance of work utilizing incoherent sensing matrices, for this type of tolerant recovery we suggest that coherence is actually beneficial . We promote the use of coherent sampling when tolerant support recovery is acceptable, and demonstrate its advantages empirically. In addition, we provide a first step towards theoretical analysis by considering a specific reconstruction method for selected signal classes.

Projected quasiparticle theory for molecular electronic structure

NASA Astrophysics Data System (ADS)

Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Samanta, Kousik; Ellis, Jason K.

2011-09-01

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.

Nuisance Caused by Light Aviation: Enquiry Conducted Around Four Aerodromes of the Parisian District. Appendix to the Report

NASA Technical Reports Server (NTRS)

1981-01-01

Maps of the four aerodromes and the results of polls taken in those areas are presented. The Guttman scale and the Green and Loevinger criteria were reviewed. The weighting factors and matrices of correlation are described. Extracts of the talks in one district and the questionnaire used are presented.

Developing Multidimensional Likert Scales Using Item Factor Analysis: The Case of Four-Point Items

ERIC Educational Resources Information Center

Asún, Rodrigo A.; Rdz-Navarro, Karina; Alvarado, Jesús M.

2016-01-01

This study compares the performance of two approaches in analysing four-point Likert rating scales with a factorial model: the classical factor analysis (FA) and the item factor analysis (IFA). For FA, maximum likelihood and weighted least squares estimations using Pearson correlation matrices among items are compared. For IFA, diagonally weighted…

W 4 toda example as hidden Liouville CFT

NASA Astrophysics Data System (ADS)

Furlan, P.; Petkova, V. B.

2017-03-01

We construct correlators in the W 4 Toda 2d conformal field theory for a particular class of representations and demonstrate a relation to a W 2 (Virasoro) theory with different central charge. The relevance of the classical limits of the constructed 3-point functions and braiding matrices to problems in 4d conformal theories is discussed.

Spatio-temporal Hotelling observer for signal detection from image sequences

PubMed Central

Caucci, Luca; Barrett, Harrison H.; Rodríguez, Jeffrey J.

2010-01-01

Detection of signals in noisy images is necessary in many applications, including astronomy and medical imaging. The optimal linear observer for performing a detection task, called the Hotelling observer in the medical literature, can be regarded as a generalization of the familiar prewhitening matched filter. Performance on the detection task is limited by randomness in the image data, which stems from randomness in the object, randomness in the imaging system, and randomness in the detector outputs due to photon and readout noise, and the Hotelling observer accounts for all of these effects in an optimal way. If multiple temporal frames of images are acquired, the resulting data set is a spatio-temporal random process, and the Hotelling observer becomes a spatio-temporal linear operator. This paper discusses the theory of the spatio-temporal Hotelling observer and estimation of the required spatio-temporal covariance matrices. It also presents a parallel implementation of the observer on a cluster of Sony PLAYSTATION 3 gaming consoles. As an example, we consider the use of the spatio-temporal Hotelling observer for exoplanet detection. PMID:19550494

Spatio-temporal Hotelling observer for signal detection from image sequences.

PubMed

Caucci, Luca; Barrett, Harrison H; Rodriguez, Jeffrey J

2009-06-22

Detection of signals in noisy images is necessary in many applications, including astronomy and medical imaging. The optimal linear observer for performing a detection task, called the Hotelling observer in the medical literature, can be regarded as a generalization of the familiar prewhitening matched filter. Performance on the detection task is limited by randomness in the image data, which stems from randomness in the object, randomness in the imaging system, and randomness in the detector outputs due to photon and readout noise, and the Hotelling observer accounts for all of these effects in an optimal way. If multiple temporal frames of images are acquired, the resulting data set is a spatio-temporal random process, and the Hotelling observer becomes a spatio-temporal linear operator. This paper discusses the theory of the spatio-temporal Hotelling observer and estimation of the required spatio-temporal covariance matrices. It also presents a parallel implementation of the observer on a cluster of Sony PLAYSTATION 3 gaming consoles. As an example, we consider the use of the spatio-temporal Hotelling observer for exoplanet detection.

Gossip and Distributed Kalman Filtering: Weak Consensus Under Weak Detectability

NASA Astrophysics Data System (ADS)

Kar, Soummya; Moura, José M. F.

2011-04-01

The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1. the GIKF error process remains stochastically bounded, irrespective of the instability properties of the random process dynamics; and 2. the network achieves \\emph{weak consensus}, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semi-definite matrices (independent of the initial state.) To prove these results, we interpret the filtered states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a non-stationary Markov chain on the network graph.

Preliminary Evaluation of an Algorithm for Analysis of Stationary Random Data from a Multiple-Input Linear System.

DTIC Science & Technology

1979-07-01

nel for low-frequency filters with Lg92/Lgl = 4.4 for S/N1 = 1. 71. CASE 1, S/NF= 1, S/I1 1 M=5 M1=10 M1=20 C! a ip a a a a 00 2 3Ma a0 0 M𔃺 M 3...Gantmacher, The Theory of Matrices, VoZ . 1, Chelsea Publishing Co., New York, NJ.Y., 1959. 163

Mechanical environmental test program for the Communications Technology Satellite

NASA Technical Reports Server (NTRS)

Buckingham, R.; Sharp, G. R.

1974-01-01

This paper describes the spacecraft and subsystem level mechanical environmental test program which was developed for the Communications Technology Satellite (CTS). At the spacecraft level it includes sine and random vibration, static loading, centrifuge loading, pyrotechnic and separation shock simulation and (tentatively) acoustics. At the subsystem level it entails the same type of environmental exposure as applicable. Matrices of system and subsystem tests are presented showing type, level and hardware status for each major test.

Cork-based activated carbons as supported adsorbent materials for trace level analysis of ibuprofen and clofibric acid in environmental and biological matrices.

PubMed

Neng, N R; Mestre, A S; Carvalho, A P; Nogueira, J M F

2011-09-16

In this contribution, powdered activated carbons (ACs) from cork waste were supported for bar adsorptive micro-extraction (BAμE), as novel adsorbent phases for the analysis of polar compounds. By combining this approach with liquid desorption followed by high performance liquid chromatography with diode array detection (BAμE(AC)-LD/HPLC-DAD), good analytical performance was achieved using clofibric acid (CLOF) and ibuprofen (IBU) model compounds in environmental and biological matrices. Assays performed on 30 mL water samples spiked at the 25.0 μg L(-1) level yielded recoveries around 80% for CLOF and 95% for IBU, under optimized experimental conditions. The ACs textural and surface chemistry properties were correlated with the results obtained. The analytical performance showed good precision (<15%), suitable detection limits (0.24 and 0.78 μg L(-1) for CLOF and IBU, respectively) and good linear dynamic ranges (r(2)>0.9922) from 1.0 to 600.0 μg L(-1). By using the standard addition methodology, the application of the present approach to environmental water and urine matrices allowed remarkable performance at the trace level. The proposed methodology proved to be a viable alternative for acidic pharmaceuticals analysis, showing to be easy to implement, reliable, sensitive and requiring low sample volume to monitor these priority compounds in environmental and biological matrices. Copyright © 2011 Elsevier B.V. All rights reserved.

Impact of an autologous oxygenating matrix culture system on rat islet transplantation outcome.

PubMed

Schaschkow, A; Mura, C; Bietiger, W; Peronet, C; Langlois, A; Bodin, F; Dissaux, C; Bruant-Rodier, C; Pinget, M; Jeandidier, N; Juszczak, M T; Sigrist, S; Maillard, E

2015-06-01

Disruption of the pancreatic islet environment combined with the decrease in oxygen supply that occurs during isolation leads to poor islet survival. The aim of this study was to validate the benefit of using a plasma-based scaffold supplemented with perfluorodecalin to improve islet transplantation outcome. Rat islets were cultured in three conditions: i) control group, ii) plasma based-matrix (P-matrix), and iii) P-matrix supplemented with emulsified perfluorodecalin. After 24 h culture, matrix/cell contacts (Integrinβ1, p-FAK/FAK, p-Akt/Akt), survival (caspase 3, TUNEL, FDA/PI), function, and HIF-1α translocation were assessed. Afterwards, P-matrices were dissolved and the islets were intraportally transplanted. Graft function was monitored for 31 days with glycaemia and C-peptide follow up. Inflammation was assessed by histology (macrophage and granulocyte staining) and thrombin/anti-thrombin complex measurement. Islet survival correlated with an increase in integrin, FAK, and Akt activation in P-matrices and function was maintained. Perfluorodecalin supplementation decreased translocation of HIF-1α in the nucleus and post-transplantation islet structure was better preserved in P-matrices, but a quicker activation of IBMIR resulted in early loss of graft function. "Oxygenating" P-matrices provided a real benefit to islet survival and resistance in vivo. However, intraportal transplantation is not suitable for this kind of culture due to IBMIR; thus, alternative sites must be explored. Copyright © 2015 Elsevier Ltd. All rights reserved.

A Global Overview of Exposure Levels and Biological Effects of Trace Elements in Penguins.

PubMed

Espejo, Winfred; Celis, José E; GonzÃlez-Acuña, Daniel; Banegas, Andiranel; Barra, Ricardo; Chiang, Gustavo

2018-01-01

Trace elements are chemical contaminants that can be present almost anywhere on the planet. The study of trace elements in biotic matrices is a topic of great relevance for the implications that it can have on wildlife and human health. Penguins are very useful, since they live exclusively in the Southern Hemisphere and represent about 90% of the biomass of birds of the Southern Ocean. The levels of trace elements (dry weight) in different biotic matrices of penguins were reviewed here. Maps of trace element records in penguins were included. Data on exposure and effects of trace elements in penguins were collected from the literature. The most reported trace elements in penguins are aluminum, arsenic, cadmium, lead, mercury, copper, zinc, and manganese. Trace elements have been measured in 11 of the 18 species of penguins. The most studied biotic matrices are feathers and excreta. Most of the studies have been performed in Antarctica and subantarctic Islands. Little is known about the interaction among metals, which could provide better knowledge about certain mechanisms of detoxification in penguins. Future studies of trace elements in penguins must incorporate other metals such as vanadium, cobalt, nickel, and chromium. Data of metals in the species such as Eudyptes pachyrhynchus, Eudyptes moseleyi, Eudyptes sclateri, Eudyptes robustus, Eudyptes schlegeli, Spheniscus demersus, Spheniscus mendiculus, and Megadyptes antipodes are urged. It is important to correlate levels of metals in different biotic matrices with the effects on different species and in different geographic locations.

A computational proposal for designing structured RNA pools for in vitro selection of RNAs.

PubMed

Kim, Namhee; Gan, Hin Hark; Schlick, Tamar

2007-04-01

Although in vitro selection technology is a versatile experimental tool for discovering novel synthetic RNA molecules, finding complex RNA molecules is difficult because most RNAs identified from random sequence pools are simple motifs, consistent with recent computational analysis of such sequence pools. Thus, enriching in vitro selection pools with complex structures could increase the probability of discovering novel RNAs. Here we develop an approach for engineering sequence pools that links RNA sequence space regions with corresponding structural distributions via a "mixing matrix" approach combined with a graph theory analysis. We define five classes of mixing matrices motivated by covariance mutations in RNA; these constructs define nucleotide transition rates and are applied to chosen starting sequences to yield specific nonrandom pools. We examine the coverage of sequence space as a function of the mixing matrix and starting sequence via clustering analysis. We show that, in contrast to random sequences, which are associated only with a local region of sequence space, our designed pools, including a structured pool for GTP aptamers, can target specific motifs. It follows that experimental synthesis of designed pools can benefit from using optimized starting sequences, mixing matrices, and pool fractions associated with each of our constructed pools as a guide. Automation of our approach could provide practical tools for pool design applications for in vitro selection of RNAs and related problems.

Comprehensive Metabolomic Analysis in Blood, Urine, Fat, and Muscle in Men with Metabolic Syndrome: A Randomized, Placebo-Controlled Clinical Trial on the Effects of Resveratrol after Four Months' Treatment.

PubMed

Korsholm, Anne Sofie; Kjær, Thomas Nordstrøm; Ornstrup, Marie Juul; Pedersen, Steen Bønløkke

2017-03-04

Resveratrol possesses several beneficial metabolic effects in rodents, while the effects of resveratrol in humans remain unclear. Therefore, we performed a non-targeted comprehensive metabolomic analysis on blood, urine, adipose tissue, and skeletal muscle tissue in middle-aged men with metabolic syndrome randomized to either resveratrol or placebo treatment for four months. Changes in steroid hormones across all four matrices were the most pronounced changes observed. Resveratrol treatment reduced sulfated androgen precursors in blood, adipose tissue, and muscle tissue, and increased these metabolites in urine. Furthermore, markers of muscle turnover were increased and lipid metabolism was affected, with increased intracellular glycerol and accumulation of long-chain saturated, monounsaturated, and polyunsaturated (n3 and n6) free fatty acids in resveratrol-treated men. Finally, urinary derivatives of aromatic amino acids, which mainly reflect the composition of the gut microbiota, were altered upon resveratrol treatment. In conclusion, the non-targeted metabolomics approach applied to four different matrices provided evidence of subtle but robust effects on several metabolic pathways following resveratrol treatment for four months in men with metabolic syndrome-effects that, for the most part, would not have been detected by routine analyses. The affected pathways should be the focus of future clinical trials on resveratrol's effects, and perhaps particularly the areas of steroid metabolism and the gut microbiome.

Correlations of multiscale entropy in the FX market

NASA Astrophysics Data System (ADS)

Stosic, Darko; Stosic, Dusan; Ludermir, Teresa; Stosic, Tatijana

2016-09-01

The regularity of price fluctuations in exchange rates plays a crucial role in FX market dynamics. Distinct variations in regularity arise from economic, social and political events, such as interday trading and financial crisis. This paper applies a multiscale time-dependent entropy method on thirty-three exchange rates to analyze price fluctuations in the FX. Correlation matrices of entropy values, termed entropic correlations, are in turn used to describe global behavior of the market. Empirical results suggest a weakly correlated market with pronounced collective behavior at bi-weekly trends. Correlations arise from cycles of low and high regularity in long-term trends. Eigenvalues of the correlation matrix also indicate a dominant European market, followed by shifting American, Asian, African, and Pacific influences. As a result, we find that entropy is a powerful tool for extracting important information from the FX market.

A stochastic Markov chain model to describe lung cancer growth and metastasis.

PubMed

Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila A; Nieva, Jorge; Kuhn, Peter

2012-01-01

A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.

Right unilateral electroconvulsive therapy does not cause more cognitive impairment than pharmacologic treatment in treatment-resistant bipolar depression: A 6-month randomized controlled trial follow-up study.

PubMed

Bjoerke-Bertheussen, Jeanette; Schoeyen, Helle; Andreassen, Ole A; Malt, Ulrik F; Oedegaard, Ketil J; Morken, Gunnar; Sundet, Kjetil; Vaaler, Arne E; Auestad, Bjoern; Kessler, Ute

2017-12-21

Electroconvulsive therapy is an effective treatment for bipolar depression, but there are concerns about whether it causes long-term neurocognitive impairment. In this multicenter randomized controlled trial, in-patients with treatment-resistant bipolar depression were randomized to either algorithm-based pharmacologic treatment or right unilateral electroconvulsive therapy. After the 6-week treatment period, all of the patients received maintenance pharmacotherapy as recommended by their clinician guided by a relevant treatment algorithm. Patients were assessed at baseline and at 6 months. Neurocognitive functions were assessed using the Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) Consensus Cognitive Battery, and autobiographical memory consistency was assessed using the Autobiographical Memory Interview-Short Form. Seventy-three patients entered the trial, of whom 51 and 26 completed neurocognitive assessments at baseline and 6 months, respectively. The MATRICS Consensus Cognitive Battery composite score improved by 4.1 points in both groups (P = .042) from baseline to 6 months (from 40.8 to 44.9 and from 41.9 to 46.0 in the algorithm-based pharmacologic treatment and electroconvulsive therapy groups, respectively). The Autobiographical Memory Interview-Short Form consistency scores were reduced in both groups (72.3% vs 64.3% in the algorithm-based pharmacologic treatment and electroconvulsive therapy groups, respectively; P = .085). This study did not find that right unilateral electroconvulsive therapy caused long-term impairment in neurocognitive functions compared to algorithm-based pharmacologic treatment in bipolar depression as measured using standard neuropsychological tests, but due to the low number of patients in the study the results should be interpreted with caution. ClinicalTrials.gov: NCT00664976. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

In vivo time-gated diffuse correlation spectroscopy at quasi-null source-detector separation.

PubMed

Pagliazzi, M; Sekar, S Konugolu Venkata; Di Sieno, L; Colombo, L; Durduran, T; Contini, D; Torricelli, A; Pifferi, A; Mora, A Dalla

2018-06-01

We demonstrate time domain diffuse correlation spectroscopy at quasi-null source-detector separation by using a fast time-gated single-photon avalanche diode without the need of time-tagging electronics. This approach allows for increased photon collection, simplified real-time instrumentation, and reduced probe dimensions. Depth discriminating, quasi-null distance measurement of blood flow in a human subject is presented. We envision the miniaturization and integration of matrices of optical sensors of increased spatial resolution and the enhancement of the contrast of local blood flow changes.

Expanding the Bethe/Gauge dictionary

NASA Astrophysics Data System (ADS)

Bullimore, Mathew; Kim, Hee-Cheol; Lukowski, Tomasz

2017-11-01

We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2, 2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe states as orbifold defects in the A-twisted supersymmetric gauge theory and study their correlation functions. We also present an alternative description of off-shell Bethe states as boundary conditions in an effective N = 4 supersymmetric quantum mechanics. Finally, we interpret spin chain R-matrices as correlation functions of Janus interfaces for mass parameters in the supersymmetric quantum mechanics.

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

NASA Astrophysics Data System (ADS)

Mejía, José; Zapata, Camilo; Botero, Alonso

2017-01-01

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

H∞ control for uncertain linear system over networks with Bernoulli data dropout and actuator saturation.

PubMed

Yu, Jimin; Yang, Chenchen; Tang, Xiaoming; Wang, Ping

2018-03-01

This paper investigates the H ∞ control problems for uncertain linear system over networks with random communication data dropout and actuator saturation. The random data dropout process is modeled by a Bernoulli distributed white sequence with a known conditional probability distribution and the actuator saturation is confined in a convex hull by introducing a group of auxiliary matrices. By constructing a quadratic Lyapunov function, effective conditions for the state feedback-based H ∞ controller and the observer-based H ∞ controller are proposed in the form of non-convex matrix inequalities to take the random data dropout and actuator saturation into consideration simultaneously, and the problem of non-convex feasibility is solved by applying cone complementarity linearization (CCL) procedure. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed new design techniques. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Partitioning dynamic electron correlation energy: Viewing Møller-Plesset correlation energies through Interacting Quantum Atom (IQA) energy partitioning

NASA Astrophysics Data System (ADS)

McDonagh, James L.; Vincent, Mark A.; Popelier, Paul L. A.

2016-10-01

Here MP2, MP3 and MP4(SDQ) are energy-partitioned for the first time within the Interacting Quantum Atoms (IQA) context, as proof-of-concept for H2, He2 and HF. Energies are decomposed into four primary energy contributions: (i) atomic self-energies, and atomic interaction energies comprising of (ii) Coulomb, (iii) exchange and (iv) dynamic election correlation terms. We generate and partition one- and two-particle density-matrices to obtain all atomic energy components. This work suggests that, in terms of Van der Waals dispersion, the correlation energies represent an atomic stabilisation, by proximity to other atoms, as opposed to direct interactions with other nearby atoms.

Quasi-Likelihood Techniques in a Logistic Regression Equation for Identifying Simulium damnosum s.l. Larval Habitats Intra-cluster Covariates in Togo.

PubMed

Jacob, Benjamin G; Novak, Robert J; Toe, Laurent; Sanfo, Moussa S; Afriyie, Abena N; Ibrahim, Mohammed A; Griffith, Daniel A; Unnasch, Thomas R

2012-01-01

The standard methods for regression analyses of clustered riverine larval habitat data of Simulium damnosum s.l. a major black-fly vector of Onchoceriasis, postulate models relating observational ecological-sampled parameter estimators to prolific habitats without accounting for residual intra-cluster error correlation effects. Generally, this correlation comes from two sources: (1) the design of the random effects and their assumed covariance from the multiple levels within the regression model; and, (2) the correlation structure of the residuals. Unfortunately, inconspicuous errors in residual intra-cluster correlation estimates can overstate precision in forecasted S.damnosum s.l. riverine larval habitat explanatory attributes regardless how they are treated (e.g., independent, autoregressive, Toeplitz, etc). In this research, the geographical locations for multiple riverine-based S. damnosum s.l. larval ecosystem habitats sampled from 2 pre-established epidemiological sites in Togo were identified and recorded from July 2009 to June 2010. Initially the data was aggregated into proc genmod. An agglomerative hierarchical residual cluster-based analysis was then performed. The sampled clustered study site data was then analyzed for statistical correlations using Monthly Biting Rates (MBR). Euclidean distance measurements and terrain-related geomorphological statistics were then generated in ArcGIS. A digital overlay was then performed also in ArcGIS using the georeferenced ground coordinates of high and low density clusters stratified by Annual Biting Rates (ABR). This data was overlain onto multitemporal sub-meter pixel resolution satellite data (i.e., QuickBird 0.61m wavbands ). Orthogonal spatial filter eigenvectors were then generated in SAS/GIS. Univariate and non-linear regression-based models (i.e., Logistic, Poisson and Negative Binomial) were also employed to determine probability distributions and to identify statistically significant parameter estimators from the sampled data. Thereafter, Durbin-Watson test statistics were used to test the null hypothesis that the regression residuals were not autocorrelated against the alternative that the residuals followed an autoregressive process in AUTOREG. Bayesian uncertainty matrices were also constructed employing normal priors for each of the sampled estimators in PROC MCMC. The residuals revealed both spatially structured and unstructured error effects in the high and low ABR-stratified clusters. The analyses also revealed that the estimators, levels of turbidity and presence of rocks were statistically significant for the high-ABR-stratified clusters, while the estimators distance between habitats and floating vegetation were important for the low-ABR-stratified cluster. Varying and constant coefficient regression models, ABR- stratified GIS-generated clusters, sub-meter resolution satellite imagery, a robust residual intra-cluster diagnostic test, MBR-based histograms, eigendecomposition spatial filter algorithms and Bayesian matrices can enable accurate autoregressive estimation of latent uncertainity affects and other residual error probabilities (i.e., heteroskedasticity) for testing correlations between georeferenced S. damnosum s.l. riverine larval habitat estimators. The asymptotic distribution of the resulting residual adjusted intra-cluster predictor error autocovariate coefficients can thereafter be established while estimates of the asymptotic variance can lead to the construction of approximate confidence intervals for accurately targeting productive S. damnosum s.l habitats based on spatiotemporal field-sampled count data.

Using the MATRICS to guide development of a preclinical cognitive test battery for research in schizophrenia

PubMed Central

YOUNG, Jared W; POWELL, Susan; RISBROUGH, Victoria; MARSTON, Hugh M; GEYER, Mark A

2009-01-01

Cognitive deficits in schizophrenia are among the core symptoms of the disease, correlate with functional outcome, and are not well treated with current antipsychotic therapies. In order to bring together academic, industrial, and governmental bodies to address this great ‘unmet therapeutic need’, the NIMH sponsored the Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) initiative. Through careful factor analysis and consensus of expert opinion, MATRICS identified seven domains of cognition that are deficient in schizophrenia (attention/vigilance, working memory, reasoning and problem solving, processing speed, visual learning and memory, verbal learning and memory, and social cognition) and recommended a specific neuropsychological test battery to probe these domains. In order to move the field forward and outline an approach for translational research, there is a need for a “preclinical MATRICS” to develop a rodent test battery that is appropriate for drug development. In this review, we outline such an approach and review current rodent tasks that target these seven domains of cognition. The rodent tasks are discussed in terms of their validity for probing each cognitive domain as well as a brief overview of the pharmacology and manipulations relevant to schizophrenia for each task. PMID:19269307

Effect of diisocyanate linkers on the degradation characteristics of copolyester urethanes as potential drug carrier matrices.

PubMed

Mathew, Simi; Baudis, Stefan; Neffe, Axel T; Behl, Marc; Wischke, Christian; Lendlein, Andreas

2015-09-01

In this study, the effect of three aliphatic diisocyanate linkers, L-lysine diisocyanate ethyl ester (LDI), hexamethylene diisocyanate (HDI), and racemic 2,2,4-/2,4,4-trimethyl hexamethylene diisocyanate (TMDI), on the degradation of oligo[(rac-lactide)-co-glycolide] (64:36 mol%) based polyester urethanes (PEU) was examined. Samples were characterized for their molecular weight, mass loss, water uptake, sequence structure, and thermal and mechanical properties. Compared to non-segmented PLGA, the PEU showed higher water uptake and generally degraded faster. Interestingly, the rate of degradation was not directly correlating with the hydrophilicity of the diisocyanate moieties; instead, competing intra-/intermolecular hydrogen bonds in between urethane moieties appear to substantially decrease the rate of degradation for LDI-derived PEU. By comparing microparticles (μm) and films (mm) as matrices of different dimensions, it was shown that autocatalysis remains a contributor to degradation of the larger-sized PEU matrices as it is typical for non-segmented lactide/glycolide copolymers. The shown capacity of lactide/glycolide-based multiblock copolymers to degrade faster than PLGA and exhibit improved elastic properties could be of interest for medical implants and drug release systems. Copyright © 2015 Elsevier B.V. All rights reserved.

Eigenpairs of Toeplitz and Disordered Toeplitz Matrices with a Fisher-Hartwig Symbol

NASA Astrophysics Data System (ADS)

Movassagh, Ramis; Kadanoff, Leo P.

2017-05-01

Toeplitz matrices have entries that are constant along diagonals. They model directed transport, are at the heart of correlation function calculations of the two-dimensional Ising model, and have applications in quantum information science. We derive their eigenvalues and eigenvectors when the symbol is singular Fisher-Hartwig. We then add diagonal disorder and study the resulting eigenpairs. We find that there is a "bulk" behavior that is well captured by second order perturbation theory of non-Hermitian matrices. The non-perturbative behavior is classified into two classes: Runaways type I leave the complex-valued spectrum and become completely real because of eigenvalue attraction. Runaways type II leave the bulk and move very rapidly in response to perturbations. These have high condition numbers and can be predicted. Localization of the eigenvectors are then quantified using entropies and inverse participation ratios. Eigenvectors corresponding to Runaways type II are most localized (i.e., super-exponential), whereas Runaways type I are less localized than the unperturbed counterparts and have most of their probability mass in the interior with algebraic decays. The results are corroborated by applying free probability theory and various other supporting numerical studies.

Composite electrochemical biosensors: a comparison of three different electrode matrices for the construction of amperometric tyrosinase biosensors.

PubMed

Serra, B; Jiménez, S; Mena, M L; Reviejo, A J; Pingarrón, J M

2002-03-01

A comparison of the behaviour of three different rigid composite matrices for the construction of amperometric tyrosinase biosensors, which are widely used for the detection of phenolic compounds, is reported. The composite electrode matrices were, graphite-Teflon; reticulated vitreous carbon (RVC)-epoxy resin; and graphite-ethylene/propylene/diene (EPD) terpolymer. After optimization of the experimental conditions, different aspects regarding the stability of the three composite tyrosinase electrode designs were considered and compared. A better reproducibility of the amperometric responses was found with the graphite-EPD electrodes, whereas a longer useful lifetime was observed for the graphite-Teflon electrodes. The kinetic parameters of the tyrosinase reaction were calculated for eight different phenolic compounds, as well as their corresponding calibration plots. The general trend in sensitivity was graphite-EPD>graphite-Teflon>RVC-epoxy resin. A correlation between sensitivity and the catalytic efficiency of the enzyme reaction for each phenolic substrate was found. Furthermore, differences in the sensitivity order for the phenolic compounds were observed among the three biocomposite electrodes, which suggests that the nature of the electrode matrix influences the interactions in the tyrosinase catalytic cycle.

Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition

PubMed Central

Ong, Frank; Lustig, Michael

2016-01-01

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information. PMID:28450978

Optimal portfolio strategy with cross-correlation matrix composed by DCCA coefficients: Evidence from the Chinese stock market

NASA Astrophysics Data System (ADS)

Sun, Xuelian; Liu, Zixian

2016-02-01

In this paper, a new estimator of correlation matrix is proposed, which is composed of the detrended cross-correlation coefficients (DCCA coefficients), to improve portfolio optimization. In contrast to Pearson's correlation coefficients (PCC), DCCA coefficients acquired by the detrended cross-correlation analysis (DCCA) method can describe the nonlinear correlation between assets, and can be decomposed in different time scales. These properties of DCCA make it possible to improve the investment effect and more valuable to investigate the scale behaviors of portfolios. The minimum variance portfolio (MVP) model and the Mean-Variance (MV) model are used to evaluate the effectiveness of this improvement. Stability analysis shows the effect of two kinds of correlation matrices on the estimation error of portfolio weights. The observed scale behaviors are significant to risk management and could be used to optimize the portfolio selection.

Bacterial pathogen gene abundance and relation to recreational water quality at seven Great Lakes beaches.

PubMed

Oster, Ryan J; Wijesinghe, Rasanthi U; Haack, Sheridan K; Fogarty, Lisa R; Tucker, Taaja R; Riley, Stephen C

2014-12-16

Quantitative assessment of bacterial pathogens, their geographic variability, and distribution in various matrices at Great Lakes beaches are limited. Quantitative PCR (qPCR) was used to test for genes from E. coli O157:H7 (eaeO157), shiga-toxin producing E. coli (stx2), Campylobacter jejuni (mapA), Shigella spp. (ipaH), and a Salmonella enterica-specific (SE) DNA sequence at seven Great Lakes beaches, in algae, water, and sediment. Overall, detection frequencies were mapA>stx2>ipaH>SE>eaeO157. Results were highly variable among beaches and matrices; some correlations with environmental conditions were observed for mapA, stx2, and ipaH detections. Beach seasonal mean mapA abundance in water was correlated with beach seasonal mean log10 E. coli concentration. At one beach, stx2 gene abundance was positively correlated with concurrent daily E. coli concentrations. Concentration distributions for stx2, ipaH, and mapA within algae, sediment, and water were statistically different (Non-Detect and Data Analysis in R). Assuming 10, 50, or 100% of gene copies represented viable and presumably infective cells, a quantitative microbial risk assessment tool developed by Michigan State University indicated a moderate probability of illness for Campylobacter jejuni at the study beaches, especially where recreational water quality criteria were exceeded. Pathogen gene quantification may be useful for beach water quality management.

Comparison of chemical-activated luciferase gene expression bioassay and gas chromatography for PCB determination in human serum and follicular fluid.

PubMed Central

Pauwels, A; Cenijn, P H; Schepens, P J; Brouwer, A

2000-01-01

We assessed exposure to dioxin-like compounds using chemical and bioassay analysis in different matrices in a female population. A total of 106 serum and 9 follicular fluid samples were collected from infertile women attending Centers for Reproductive Medicine in Belgium from 1996 to 1998. Major polychlorinated biphenyl (PCB) congeners were quantified by chemical analysis using gas chromatography with electron-capture detection, and the chemical-activated luciferase gene expression (CALUX) bioassay was used to determine the total dioxin-like toxic equivalence (TEQ) of mixtures of polyhalogenated aromatic hydrocarbons present in body fluids, such as serum and follicular fluid. To the best of our knowledge, this is the first investigation to determine TEQ values by the CALUX bioassay in follicular fluid. The TEQ levels in both matrices are well correlated (r = 0.83, p = 0.02). As the chemical and bioassay analysis executed in this study do not cover the same span of polyhalogenated aromatic hydrocarbons, we did not expect totally correlated results. Moreover, the sample workup and quantification of the analytes differed completely. Nonetheless, the TEQ values in human extracts correlated well with the sum of four major PCB congeners chemically determined in both serum and follicular fluid. These results indicate that the CALUX bioassay may serve as a simple, relatively inexpensive prescreening tool for exposure assessment in epidemiologic surveys. Images Figure 1 Figure 2 PMID:10856030

The failing measurement of attitudes: How semantic determinants of individual survey responses come to replace measures of attitude strength.

PubMed

Arnulf, Jan Ketil; Larsen, Kai Rune; Martinsen, Øyvind Lund; Egeland, Thore

2018-01-12

The traditional understanding of data from Likert scales is that the quantifications involved result from measures of attitude strength. Applying a recently proposed semantic theory of survey response, we claim that survey responses tap two different sources: a mixture of attitudes plus the semantic structure of the survey. Exploring the degree to which individual responses are influenced by semantics, we hypothesized that in many cases, information about attitude strength is actually filtered out as noise in the commonly used correlation matrix. We developed a procedure to separate the semantic influence from attitude strength in individual response patterns, and compared these results to, respectively, the observed sample correlation matrices and the semantic similarity structures arising from text analysis algorithms. This was done with four datasets, comprising a total of 7,787 subjects and 27,461,502 observed item pair responses. As we argued, attitude strength seemed to account for much information about the individual respondents. However, this information did not seem to carry over into the observed sample correlation matrices, which instead converged around the semantic structures offered by the survey items. This is potentially disturbing for the traditional understanding of what survey data represent. We argue that this approach contributes to a better understanding of the cognitive processes involved in survey responses. In turn, this could help us make better use of the data that such methods provide.

Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

NASA Astrophysics Data System (ADS)

Pato, Mauricio P.; Oshanin, Gleb

2013-03-01

We study the probability distribution function P(β)n(w) of the Schmidt-like random variable w = x21/(∑j = 1nx2j/n), where xj, (j = 1, 2, …, n), are unordered eigenvalues of a given n × n β-Gaussian random matrix, β being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual (randomly chosen) eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n → ∞ and for arbitrary β the distribution P(β)n(w) converges to the Marčenko-Pastur form, i.e. is defined as P_{n}^{( \\beta )}(w) \\sim \\sqrt{(4 - w)/w} for w ∈ [0, 4] and equals zero outside of the support, despite the fact that formally w is defined on the interval [0, n]. Furthermore, for Gaussian unitary ensembles (β = 2) we present exact explicit expressions for P(β = 2)n(w) which are valid for arbitrary n and analyse their behaviour.

Genetic diversity of popcorn genotypes using molecular analysis.

PubMed

Resh, F S; Scapim, C A; Mangolin, C A; Machado, M F P S; do Amaral, A T; Ramos, H C C; Vivas, M

2015-08-19

In this study, we analyzed dominant molecular markers to estimate the genetic divergence of 26 popcorn genotypes and evaluate whether using various dissimilarity coefficients with these dominant markers influences the results of cluster analysis. Fifteen random amplification of polymorphic DNA primers produced 157 amplified fragments, of which 65 were monomorphic and 92 were polymorphic. To calculate the genetic distances among the 26 genotypes, the complements of the Jaccard, Dice, and Rogers and Tanimoto similarity coefficients were used. A matrix of Dij values (dissimilarity matrix) was constructed, from which the genetic distances among genotypes were represented in a more simplified manner as a dendrogram generated using the unweighted pair-group method with arithmetic average. Clusters determined by molecular analysis generally did not group material from the same parental origin together. The largest genetic distance was between varieties 17 (UNB-2) and 18 (PA-091). In the identification of genotypes with the smallest genetic distance, the 3 coefficients showed no agreement. The 3 dissimilarity coefficients showed no major differences among their grouping patterns because agreement in determining the genotypes with large, medium, and small genetic distances was high. The largest genetic distances were observed for the Rogers and Tanimoto dissimilarity coefficient (0.74), followed by the Jaccard coefficient (0.65) and the Dice coefficient (0.48). The 3 coefficients showed similar estimations for the cophenetic correlation coefficient. Correlations among the matrices generated using the 3 coefficients were positive and had high magnitudes, reflecting strong agreement among the results obtained using the 3 evaluated dissimilarity coefficients.

Discrete Painlevé equations for a class of PVI τ-functions given as U(N) averages

NASA Astrophysics Data System (ADS)

Forrester, P. J.; Witte, N. S.

2005-09-01

In a recent work, difference equations (Laguerre-Freud equations) for the bi-orthogonal polynomials and related quantities corresponding to the weight on the unit circle w(z)=\\prod^m_{j=1}(z-z_j(t))^{\\rho_j} were derived. It is shown here that in the case m = 3, these difference equations, when applied to the calculation of the underlying U(N) average, reduce to a coupled system identifiable with that obtained by Adler and van Moerbeke, using the methods of the Toeplitz lattice and Virasoro constraints. Moreover, it is shown that this coupled system can be reduced to yield the discrete fifth Painlevé equation dPV as it occurs in the theory of the sixth Painlevé system. Methods based on affine Weyl group symmetries of Bäcklund transformations have previously yielded the dPV equation, but with different parameters for the same problem. We find an explicit mapping between the two forms. Applications of our results are made to give recurrences for the gap probabilities and moments in the circular unitary ensemble of random matrices, and to the diagonal spin-spin correlation function of the square lattice Ising model.

On Statistics of Bi-Orthogonal Eigenvectors in Real and Complex Ginibre Ensembles: Combining Partial Schur Decomposition with Supersymmetry

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.

2018-06-01

We suggest a method of studying the joint probability density (JPD) of an eigenvalue and the associated `non-orthogonality overlap factor' (also known as the `eigenvalue condition number') of the left and right eigenvectors for non-selfadjoint Gaussian random matrices of size {N× N} . First we derive the general finite N expression for the JPD of a real eigenvalue {λ} and the associated non-orthogonality factor in the real Ginibre ensemble, and then analyze its `bulk' and `edge' scaling limits. The ensuing distribution is maximally heavy-tailed, so that all integer moments beyond normalization are divergent. A similar calculation for a complex eigenvalue z and the associated non-orthogonality factor in the complex Ginibre ensemble is presented as well and yields a distribution with the finite first moment. Its `bulk' scaling limit yields a distribution whose first moment reproduces the well-known result of Chalker and Mehlig (Phys Rev Lett 81(16):3367-3370, 1998), and we provide the `edge' scaling distribution for this case as well. Our method involves evaluating the ensemble average of products and ratios of integer and half-integer powers of characteristic polynomials for Ginibre matrices, which we perform in the framework of a supersymmetry approach. Our paper complements recent studies by Bourgade and Dubach (The distribution of overlaps between eigenvectors of Ginibre matrices, 2018. arXiv:1801.01219).

Vertices cannot be hidden from quantum spatial search for almost all random graphs

NASA Astrophysics Data System (ADS)

Glos, Adam; Krawiec, Aleksandra; Kukulski, Ryszard; Puchała, Zbigniew

2018-04-01

In this paper, we show that all nodes can be found optimally for almost all random Erdős-Rényi G(n,p) graphs using continuous-time quantum spatial search procedure. This works for both adjacency and Laplacian matrices, though under different conditions. The first one requires p=ω (log ^8(n)/n), while the second requires p≥ (1+ɛ )log (n)/n, where ɛ >0. The proof was made by analyzing the convergence of eigenvectors corresponding to outlying eigenvalues in the \\Vert \\cdot \\Vert _∞ norm. At the same time for p<(1-ɛ )log (n)/n, the property does not hold for any matrix, due to the connectivity issues. Hence, our derivation concerning Laplacian matrix is tight.

Surnames in Bolivia: a study of the population of Bolivia through isonymy.

PubMed

Rodriguez-Larralde, Alvaro; Dipierri, José; Gomez, Emma Alfaro; Scapoli, Chiara; Mamolini, Elisabetta; Salvatorelli, Germano; De Lorenzi, Sonia; Carrieri, Alberto; Barrai, Italo

2011-02-01

In Bolivia, the Hispanic dual surname system is used. To describe the isonymic structure of Bolivia, the surname distribution of 12,139,448 persons registered in the 2006 census data was studied in 9 districts and 112 provinces of the nation, for a total of 23,244,064 surnames. The number of different surnames found was 174,922. Matrices of isonymic distances between the administrative units (districts and provinces) were constructed and tested for correlation with geographic distance. In the 112 provinces, isonymic distances were correlated with geographic distance (r = 0.545 ± 0.011 for Euclidean, 0.501 ± 0.012 for Nei's, and 0.556 ± 0.010 for Lasker's distance). The multiple regression of the surname effective number (α), equivalent to the allele effective number in a genetic system, was nonsignificant on latitude and longitude; however, it was highly significant and negative on altitude (r = -0.72). Because the Andes extend from north to south in west-central Bolivia, random inbreeding was lowest in the eastern districts, and highest in mountainous western Bolivia. Average α for the provinces was 122 ± 2; for the districts, it was 216 ± 29, and for the whole of Bolivia it was 213. The geographical distribution of α in the provinces is compatible with the settlement of subsequent groups of migrants moving from east and north toward the center and south of Bolivia. The relative frequency of indigenous surnames is correlated positively with altitude. This suggests that the country was populated by recent low-density demic diffusion over a low-density indigenous population. This may have been a common phenomenon in the immigration to tropical South America. 2010 Wiley-Liss, Inc.

Evaluating Exposure-Response Associations for Non-Hodgkin Lymphoma with Varying Methods of Assigning Cumulative Benzene Exposure in the Shanghai Women's Health Study.

PubMed

Friesen, Melissa C; Bassig, Bryan A; Vermeulen, Roel; Shu, Xiao-Ou; Purdue, Mark P; Stewart, Patricia A; Xiang, Yong-Bing; Chow, Wong-Ho; Ji, Bu-Tian; Yang, Gong; Linet, Martha S; Hu, Wei; Gao, Yu-Tang; Zheng, Wei; Rothman, Nathaniel; Lan, Qing

2017-01-01

To provide insight into the contributions of exposure measurements to job exposure matrices (JEMs), we examined the robustness of an association between occupational benzene exposure and non-Hodgkin lymphoma (NHL) to varying exposure assessment methods. NHL risk was examined in a prospective population-based cohort of 73087 women in Shanghai. A mixed-effects model that combined a benzene JEM with >60000 short-term, area benzene inspection measurements was used to derive two sets of measurement-based benzene estimates: 'job/industry-specific' estimates (our presumed best approach) were derived from the model's fixed effects (year, JEM intensity rating) and random effects (occupation, industry); 'calibrated JEM' estimates were derived using only the fixed effects. 'Uncalibrated JEM' (using the ordinal JEM ratings) and exposure duration estimates were also calculated. Cumulative exposure for each subject was calculated for each approach based on varying exposure definitions defined using the JEM's probability ratings. We examined the agreement between the cumulative metrics and evaluated changes in the benzene-NHL associations. For our primary exposure definition, the job/industry-specific estimates were moderately to highly correlated with all other approaches (Pearson correlation 0.61-0.89; Spearman correlation > 0.99). All these metrics resulted in statistically significant exposure-response associations for NHL, with negligible gain in model fit from using measurement-based estimates. Using more sensitive or specific exposure definitions resulted in elevated but non-significant associations. The robust associations observed here with varying benzene assessment methods provide support for a benzene-NHL association. While incorporating exposure measurements did not improve model fit, the measurements allowed us to derive quantitative exposure-response curves. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

Handling Correlations between Covariates and Random Slopes in Multilevel Models

ERIC Educational Resources Information Center

Bates, Michael David; Castellano, Katherine E.; Rabe-Hesketh, Sophia; Skrondal, Anders

2014-01-01

This article discusses estimation of multilevel/hierarchical linear models that include cluster-level random intercepts and random slopes. Viewing the models as structural, the random intercepts and slopes represent the effects of omitted cluster-level covariates that may be correlated with included covariates. The resulting correlations between…

Accurate Simulation and Detection of Coevolution Signals in Multiple Sequence Alignments

PubMed Central

Ackerman, Sharon H.; Tillier, Elisabeth R.; Gatti, Domenico L.

2012-01-01

Background While the conserved positions of a multiple sequence alignment (MSA) are clearly of interest, non-conserved positions can also be important because, for example, destabilizing effects at one position can be compensated by stabilizing effects at another position. Different methods have been developed to recognize the evolutionary relationship between amino acid sites, and to disentangle functional/structural dependencies from historical/phylogenetic ones. Methodology/Principal Findings We have used two complementary approaches to test the efficacy of these methods. In the first approach, we have used a new program, MSAvolve, for the in silico evolution of MSAs, which records a detailed history of all covarying positions, and builds a global coevolution matrix as the accumulated sum of individual matrices for the positions forced to co-vary, the recombinant coevolution, and the stochastic coevolution. We have simulated over 1600 MSAs for 8 protein families, which reflect sequences of different sizes and proteins with widely different functions. The calculated coevolution matrices were compared with the coevolution matrices obtained for the same evolved MSAs with different coevolution detection methods. In a second approach we have evaluated the capacity of the different methods to predict close contacts in the representative X-ray structures of an additional 150 protein families using only experimental MSAs. Conclusions/Significance Methods based on the identification of global correlations between pairs were found to be generally superior to methods based only on local correlations in their capacity to identify coevolving residues using either simulated or experimental MSAs. However, the significant variability in the performance of different methods with different proteins suggests that the simulation of MSAs that replicate the statistical properties of the experimental MSA can be a valuable tool to identify the coevolution detection method that is most effective in each case. PMID:23091608

Ultrasonic nebulization extraction/low pressure photoionization mass spectrometry for direct analysis of chemicals in matrices.

PubMed

Liu, Chengyuan; Zhu, Yanan; Zhou, Zhongyue; Yang, Jiuzhong; Qi, Fei; Pan, Yang

2015-09-03

A novel ultrasonic nebulization extraction/low-pressure photoionization (UNE-LPPI) system has been designed and employed for the rapid mass spectrometric analysis of chemicals in matrices. An ultrasonic nebulizer was used to extract the chemicals in solid sample and nebulize the solvent in the nebulization cell. Aerosols formed by ultrasonic were evaporated by passing through a transferring tube, and desolvated chemicals were ionized by the emitted light (10.6 eV) from a Krypton discharge lamp at low pressure (∼68 Pa). First, a series of semi/non-volatile compounds with different polarities, such as polycyclic aromatic hydrocarbons (PAHs), amino acids, dipeptides, drugs, nucleic acids, alkaloids, and steroids were used to test the system. Then, the quantification capability of UNE-LPPI was checked with: 1) pure chemicals, such as 9,10-phenanthrenequinone and 1,4-naphthoquinone dissolved in solvent; 2) soil powder spiked with different amounts of phenanthrene and pyrene. For pure chemicals, the correlation coefficient (R(2)) for the standard curve of 9,10-phenanthrenequinone in the range of 3 ng-20 μg mL(-1) was 0.9922, and the measured limits of detection (LOD) was 1 ng ml(-1). In the case of soil powder, linear relationships for phenanthrene and pyrene from 10 to 400 ng mg(-1) were obtained with correlation coefficients of 0.9889 and 0.9893, respectively. At last, the feasibility of UNE-LPPI for the detection of chemicals in real matrices such as tablets and biological tissues (tea, Citrus aurantium peel and sage (Salvia officinalis) leaf) were successfully demonstrated. Copyright © 2015 Elsevier B.V. All rights reserved.

Novel electrospun nanofibrous matrices prepared from poly(lactic acid)/poly(butylene adipate) blends for controlled release formulations of an anti-rheumatoid agent.

PubMed

Siafaka, Panoraia I; Barmbalexis, Panagiotis; Bikiaris, Dimitrios N

2016-06-10

In the present work, a series of novel formulations consisting of poly(lactic acid)/poly(butylene adipate) (PLA/PBAd) electrospun blends was examined as controlled release matrices for Leflunomide's active metabolite, Teriflunomide (TFL). The mixtures were prepared using different ratios of PLA and PBAd in order to produce nanofibrous matrices with different characteristics. Miscibility studies of the blended polymeric fibers were performed through differential scanning calorimetry (DSC) and X-ray diffractometry (XRD). Hydrolytic degradation in the prepared fibers was evaluated at 37°C using a phosphate buffered saline solution. Different concentrations of (TFL) (5, 10, 15wt.%) were incorporated into nanofibers for examining the drug release behavior in simulated body fluids (SBF), at 37°C. The drug-loaded nanofibrous formulations were further characterized by Fourier Transform Infrared Spectroscopy (FTIR) spectroscopy, DSC and XRD. Gel permeation chromatography (GPC) analysis was used to evaluate the mechanism of TFL release. Artificial neural networks (ANN) and multi-linear-regression (MLR) models were used to evaluate the effect of % content of PBAd (X1) and TFL (X2) on an initial burst effect and a dissolution behavior. It was found that PLA/PBAd nanofibers have different diameters depending on the ratio of used polyesters and added drug. TFL was incorporated in an amorphous form inside the polymeric nanofibers. In vitro release studies reveal that a drug release behavior is correlated with the size of the nanofibers, drug loading and matrix degradation after a specific time. ANN dissolution modeling showed increased correlation efficacy compared to MLR. Copyright © 2016 Elsevier B.V. All rights reserved.

Fetal exposure markers of dioxins and dioxin-like PCBs.

PubMed

Lampa, Erik; Eguchi, Akifumi; Todaka, Emiko; Mori, Chisato

2018-04-01

Fetal exposure to polychlorinated biphenyls (PCBs), polychlorinated-p-dibenzodioxins (PCDDs), and polychlorinated dibenzofurans (PCDFs) have been associated with a number of adverse health outcomes. Although the placenta acts as a barrier between the mother and the fetus, these contaminants transfer through the placenta exposing the fetus. Several studies have investigated placental transfer, but few have assessed the co-variation among these contaminants. Maternal blood, cord blood, and cord tissue were collected from 41 Japanese mother-infant pairs and analyzed for dioxin-like PCBs and PCDD/Fs. Hierarchical cluster analysis followed by principal component analysis were used to assess the co-variation. Two stable clusters of dioxin-like PCBs were found in maternal and cord blood. One cluster of low/medium chlorinated dioxin-like PCBs was present in all three matrices with 2,3',4,4',5-PeCB(#118) and 3,3',4,4',5-PeCB(#126) explaining the majority of the clusters' variances. Medium/high chlorinated dioxin-like PCBs clustered in maternal blood and cord blood but not in cord tissue. 2,3,4,4',5-PeCB(#114) and 2,3,3',4,4',5,5'-HpCB(#189) explained the majority of the clusters' variances. There was a substantial correlation between the sum of dioxin-like PCBs and total PCDD/F in all three matrices. The sum of the four suggested PCBs plus 3,3',4,4'-TeCB(#77) correlated well with total PCDD/F in all three matrices. Apart from the dioxin-like PCBs, little co-variation existed among the studied contaminants. The five PCBs can be used as fetal exposure markers for dioxin and dioxin-like PCBs in maternal and cord blood respectively. In cord tissue, more higher chlorinated dioxin-like PCBs need to be measured as well.

Minimal Spanning Tree Graphs and Power Like Scaling in FOREX Networks

NASA Astrophysics Data System (ADS)

Górski, A. Z.; Kwapień, J.; Oświęcimka, P.; Drożdż, S.

2008-09-01

Correlation matrices of foreign exchange rate time series are investigated for 60 world currencies. Minimal spanning tree graphs for the gold, silver and platinum are presented. Inverse power like scaling is discussed for these graphs as well as for four distinct currency groups (major, liquid, less liquid and non-tradable). The worst scaling was found for USD and related currencies.

Factor Analysis with EM Algorithm Never Gives Improper Solutions when Sample Covariance and Initial Parameter Matrices Are Proper

ERIC Educational Resources Information Center

Adachi, Kohei

2013-01-01

Rubin and Thayer ("Psychometrika," 47:69-76, 1982) proposed the EM algorithm for exploratory and confirmatory maximum likelihood factor analysis. In this paper, we prove the following fact: the EM algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one,…

Investigation of global and local network properties of music perception with culturally different styles of music.

PubMed

Li, Yan; Rui, Xue; Li, Shuyu; Pu, Fang

2014-11-01

Graph theoretical analysis has recently become a popular research tool in neuroscience, however, there have been very few studies on brain responses to music perception, especially when culturally different styles of music are involved. Electroencephalograms were recorded from ten subjects listening to Chinese traditional music, light music and western classical music. For event-related potentials, phase coherence was calculated in the alpha band and then constructed into correlation matrices. Clustering coefficients and characteristic path lengths were evaluated for global properties, while clustering coefficients and efficiency were assessed for local network properties. Perception of light music and western classical music manifested small-world network properties, especially with a relatively low proportion of weights of correlation matrices. For local analysis, efficiency was more discernible than clustering coefficient. Nevertheless, there was no significant discrimination between Chinese traditional and western classical music perception. Perception of different styles of music introduces different network properties, both globally and locally. Research into both global and local network properties has been carried out in other areas; however, this is a preliminary investigation aimed at suggesting a possible new approach to brain network properties in music perception. Copyright © 2014 Elsevier Ltd. All rights reserved.

HiCRep: assessing the reproducibility of Hi-C data using a stratum-adjusted correlation coefficient.

PubMed

Yang, Tao; Zhang, Feipeng; Yardımcı, Galip Gürkan; Song, Fan; Hardison, Ross C; Noble, William Stafford; Yue, Feng; Li, Qunhua

2017-11-01

Hi-C is a powerful technology for studying genome-wide chromatin interactions. However, current methods for assessing Hi-C data reproducibility can produce misleading results because they ignore spatial features in Hi-C data, such as domain structure and distance dependence. We present HiCRep, a framework for assessing the reproducibility of Hi-C data that systematically accounts for these features. In particular, we introduce a novel similarity measure, the stratum adjusted correlation coefficient (SCC), for quantifying the similarity between Hi-C interaction matrices. Not only does it provide a statistically sound and reliable evaluation of reproducibility, SCC can also be used to quantify differences between Hi-C contact matrices and to determine the optimal sequencing depth for a desired resolution. The measure consistently shows higher accuracy than existing approaches in distinguishing subtle differences in reproducibility and depicting interrelationships of cell lineages. The proposed measure is straightforward to interpret and easy to compute, making it well-suited for providing standardized, interpretable, automatable, and scalable quality control. The freely available R package HiCRep implements our approach. © 2017 Yang et al.; Published by Cold Spring Harbor Laboratory Press.

Power laws for the backscattering matrices in the case of lidar sensing of cirrus clouds

NASA Astrophysics Data System (ADS)

Kustova, Natalia V.; Konoshonkin, Alexander V.; Borovoi, Anatoli; Okamoto, Hajime; Sato, Kaori; Katagiri, Shuichiro

2017-11-01

The data bank for the backscattering matrixes of cirrus clouds that was calculated earlier by the authors and was available in the internet for free access has been replaced in the case of randomly oriented crystals by simple analytic equations. Four microphysical ratios conventionally measured by lidars have been calculated for different shapes and the effective size of the crystals. These values could be used for retrieving shapes of the crystals in cirrus clouds.

IEEE International Symposium Information Theory, held at Santa Monica California, February 9-12, 1981.

DTIC Science & Technology

1981-01-01

Channel and study permutation codes as a special case. ,uch a code is generated by an initial vector x, a group G of orthogonal n by n matrices, and a...random-access components, is introduced and studied . Under this scheme, the network stations are divided into groups , each of which is assigned a...IEEE INFORMATION THEORY GROUP CO-SPONSORED BY: UNION RADIO SCIENTIFIQUE INTERNATIONALE IEEE Catalog Number 81 CH 1609-7 IT 𔃻. 81 ~20 04Q SECURITY

Relationships between the Kaufman Brief Intelligence Test and the Wechsler Adult Intelligence Scale-Third Edition.

PubMed

Walters, Steven O; Weaver, Kenneth A

2003-06-01

The Kaufman Brief Intelligence Test detects learning problems of young students and is a screen for whether a more comprehensive test of intelligence is needed. A study to assess whether this test was valid as an adult intelligence test was conducted with 20 undergraduate psychology majors. The correlations between the Kaufman Brief Intelligence Test's Composite, Vocabulary, and Matrices test scores and their corresponding Wechsler Adult Intelligence Scale-Third Edition test scores, the Full Scale (r=.88), Verbal (r=.77), and Performance scores (r=.87), indicated very strong relationships. In addition, no significant differences were obtained between the Composite, Vocabulary, and Matrices means of the Kaufman Brief Intelligence Test and the Full Scale, Verbal, and Performance means of the WAIS-III. The Kaufman Brief Intelligence Test appears to be a valid test of intelligence for adults.

Oscillating-Flow Regenerator Test Rig: Hardware and Theory With Derived Correlations for Screens and Felts

NASA Technical Reports Server (NTRS)

Gedeon, D.; Wood, J. G.

1996-01-01

A number of wire mesh and metal felt test samples, with a range of porosities, yield generic correlations for friction factor, Nusselt number, enhanced axial conduction ratio, and overall heat flux ratio. This information is directed primarily toward stirling cycle regenerator modelers, but will be of use to anyone seeking to better model fluid flow through these porous materials. Behind these results lies an oscillating-flow test rig, which measures pumping dissipation and thermal energy transport in sample matrices, and several stages of data-reduction software, which correlate instantaneous values for the above dimensionless groups. Within the software, theoretical model reduces instantaneous quantifies from cycle-averaged measurables using standard parameter estimation techniques.

Correlation Study of PVDF Membrane Morphology with Protein Adsorption: Quantitative Analysis by FTIR/ATR Technique

NASA Astrophysics Data System (ADS)

Ideris, N.; Ahmad, A. L.; Ooi, B. S.; Low, S. C.

2018-05-01

Microporous PVDF membranes were used as protein capture matrices in immunoassays. Because the most common labels in immunoassays were detected based on the colour change, an understanding of how protein concentration varies on different PVDF surfaces was needed. Herein, the correlation between the membrane pore size and protein adsorption was systematically investigated. Five different PVDF membrane morphologies were prepared and FTIR/ATR was employed to accurately quantify the surface protein concentration on membranes with small pore sizes. SigmaPlot® was used to find a suitable curve fit for protein adsorption and membrane pore size, with a high correlation coefficient, R2, of 0.9971.

An Analysis of the Max-Min Texture Measure.

DTIC Science & Technology

1982-01-01

PANC 33 D2 Confusion Matrices for Scene A, IR 34 D3 Confusion Matrices for Scene B, PANC 35 D4 Confusion Matrices for Scene B, IR 36 D5 Confusion...Matrices for Scene C, PANC 37 D6 Confusion Matrices for Scene C, IR 38 D7 Confusion Matrices for Scene E, PANC 39 D8 Confusion Matrices for Scene E, IR 40...D9 Confusion Matrices for Scene H, PANC 41 DIO Confusion Matrices for Scene H, JR 42 3 .D 10CnuinMtie o cn ,IR4 AN ANALYSIS OF THE MAX-MIN TEXTURE

Kernel-Correlated Levy Field Driven Forward Rate and Application to Derivative Pricing

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

Bo Lijun; Wang Yongjin; Yang Xuewei, E-mail: xwyangnk@yahoo.com.cn

2013-08-01

We propose a term structure of forward rates driven by a kernel-correlated Levy random field under the HJM framework. The kernel-correlated Levy random field is composed of a kernel-correlated Gaussian random field and a centered Poisson random measure. We shall give a criterion to preclude arbitrage under the risk-neutral pricing measure. As applications, an interest rate derivative with general payoff functional is priced under this pricing measure.

Projection correlation between two random vectors.

PubMed

Zhu, Liping; Xu, Kai; Li, Runze; Zhong, Wei

2017-12-01

We propose the use of projection correlation to characterize dependence between two random vectors. Projection correlation has several appealing properties. It equals zero if and only if the two random vectors are independent, it is not sensitive to the dimensions of the two random vectors, it is invariant with respect to the group of orthogonal transformations, and its estimation is free of tuning parameters and does not require moment conditions on the random vectors. We show that the sample estimate of the projection correction is [Formula: see text]-consistent if the two random vectors are independent and root-[Formula: see text]-consistent otherwise. Monte Carlo simulation studies indicate that the projection correlation has higher power than the distance correlation and the ranks of distances in tests of independence, especially when the dimensions are relatively large or the moment conditions required by the distance correlation are violated.

Tumor cell invasion of collagen matrices requires coordinate lipid agonist-induced G-protein and membrane-type matrix metalloproteinase-1-dependent signaling.

PubMed

Fisher, Kevin E; Pop, Andreia; Koh, Wonshill; Anthis, Nicholas J; Saunders, W Brian; Davis, George E

2006-12-08

Lysophosphatidic acid (LPA) and sphingosine 1-phosphate (S1P) are bioactive lipid signaling molecules implicated in tumor dissemination. Membrane-type matrix metalloproteinase 1 (MT1-MMP) is a membrane-tethered collagenase thought to be involved in tumor invasion via extracellular matrix degradation. In this study, we investigated the molecular requirements for LPA- and S1P-regulated tumor cell migration in two dimensions (2D) and invasion of three-dimensional (3D) collagen matrices and, in particular, evaluated the role of MT1-MMP in this process. LPA stimulated while S1P inhibited migration of most tumor lines in Boyden chamber assays. Conversely, HT1080 fibrosarcoma cells migrated in response to both lipids. HT1080 cells also markedly invaded 3D collagen matrices (approximatly 700 microm over 48 hours) in response to either lipid. siRNA targeting of LPA1 and Rac1, or S1P1, Rac1, and Cdc42 specifically inhibited LPA- or S1P-induced HT1080 invasion, respectively. Analysis of LPA-induced HT1080 motility on 2D substrates vs. 3D matrices revealed that synthetic MMP inhibitors markedly reduced the distance (approximately 125 microm vs. approximately 45 microm) and velocity of invasion (approximately 0.09 microm/min vs. approximately 0.03 microm/min) only when cells navigated 3D matrices signifying a role for MMPs exclusively in invasion. Additionally, tissue inhibitors of metalloproteinases (TIMPs)-2, -3, and -4, but not TIMP-1, blocked lipid agonist-induced invasion indicating a role for membrane-type (MT)-MMPs. Furthermore, MT1-MMP expression in several tumor lines directly correlated with LPA-induced invasion. HEK293s, which neither express MT1-MMP nor invade in the presence of LPA, were transfected with MT1-MMP cDNA, and subsequently invaded in response to LPA. When HT1080 cells were seeded on top of or within collagen matrices, siRNA targeting of MT1-MMP, but not other MMPs, inhibited lipid agonist-induced invasion establishing a requisite role for MT1-MMP in this process. LPA is a fundamental regulator of MT1-MMP-dependent tumor cell invasion of 3D collagen matrices. In contrast, S1P appears to act as an inhibitory stimulus in most cases, while stimulating only select tumor lines. MT1-MMP is required only when tumor cells navigate 3D barriers and not when cells migrate on 2D substrata. We demonstrate that tumor cells require coordinate regulation of LPA/S1P receptors and Rho GTPases to migrate, and additionally, require MT1-MMP in order to invade collagen matrices during neoplastic progression.

Extensive characterizations of bacteria isolated from catheterized urine and stone matrices in patients with nephrolithiasis.

PubMed

Tavichakorntrakool, Ratree; Prasongwattana, Vitoon; Sungkeeree, Seksit; Saisud, Phitsamai; Sribenjalux, Pipat; Pimratana, Chaowat; Bovornpadungkitti, Sombat; Sriboonlue, Pote; Thongboonkerd, Visith

2012-11-01

Urinary tract infections are generally known to be associated with nephrolithiasis, particularly struvite stone, in which the most common microbe found is urea-splitting bacterium, i.e. Proteus mirabilis. However, our observation indicated that it might not be the case of stone formers in Thailand. We therefore extensively characterized microorganisms associated with all types of kidney stones. A total of 100 kidney stone formers (59 males and 41 females) admitted for elective percutaneous nephrolithotomy were recruited and microorganisms isolated from catheterized urine and cortex and nidus of their stones were analyzed. From 100 stone formers recruited, 36 cases had a total of 45 bacterial isolates cultivated from their catheterized urine and/or stone matrices. Among these 36 cases, chemical analysis by Fourier-transformed infrared spectroscopy revealed that 8 had the previously classified 'infection-induced stones', whereas the other 28 cases had the previously classified 'metabolic stones'. Calcium oxalate (in either pure or mixed form) was the most common and found in 64 and 75% of the stone formers with and without bacterial isolates, respectively. Escherichia coli was the most common bacterium (approximately one-third of all bacterial isolates) found in urine and stone matrices (both nidus and periphery). Linear regression analysis showed significant correlation (r = 0.860, P < 0.001) between bacterial types in urine and stone matrices. Multidrug resistance was frequently found in these isolated bacteria. Moreover, urea test revealed that only 31% were urea-splitting bacteria, whereas the majority (69%) had negative urea test. Our data indicate that microorganisms are associated with almost all chemical types of kidney stones and urea-splitting bacteria are not the major causative microorganisms found in urine and stone matrices of the stone formers in Thailand. These data may lead to rethinking and a new roadmap for future research regarding the role of microorganisms in kidney stone formation.

Real-Time Cytotoxicity Assay for Rapid and Sensitive Detection of Ricin from Complex Matrices

PubMed Central

Pauly, Diana; Worbs, Sylvia; Kirchner, Sebastian; Shatohina, Olena; Dorner, Martin B.; Dorner, Brigitte G.

2012-01-01

Background In the context of a potential bioterrorist attack sensitive and fast detection of functionally active toxins such as ricin from complex matrices is necessary to be able to start timely countermeasures. One of the functional detection methods currently available for ricin is the endpoint cytotoxicity assay, which suffers from a number of technical deficits. Methodology/Findings This work describes a novel online cytotoxicity assay for the detection of active ricin and Ricinus communis agglutinin, that is based on a real-time cell electronic sensing system and impedance measurement. Characteristic growth parameters of Vero cells were monitored online and used as standardized viability control. Upon incubation with toxin the cell status and the cytotoxic effect were visualized using a characteristic cell index–time profile. For ricin, tested in concentrations of 0.06 ng/mL or above, a concentration-dependent decrease of cell index correlating with cytotoxicity was recorded between 3.5 h and 60 h. For ricin, sensitive detection was determined after 24 h, with an IC50 of 0.4 ng/mL (for agglutinin, an IC50 of 30 ng/mL was observed). Using functionally blocking antibodies, the specificity for ricin and agglutinin was shown. For detection from complex matrices, ricin was spiked into several food matrices, and an IC50 ranging from 5.6 to 200 ng/mL was observed. Additionally, the assay proved to be useful in detecting active ricin in environmental sample materials, as shown for organic fertilizer containing R. communis material. Conclusions/Significance The cell-electrode impedance measurement provides a sensitive online detection method for biologically active cytotoxins such as ricin. As the cell status is monitored online, the assay can be standardized more efficiently than previous approaches based on endpoint measurement. More importantly, the real-time cytotoxicity assay provides a fast and easy tool to detect active ricin in complex sample matrices. PMID:22532852

Determination of the optimal number of components in independent components analysis.

PubMed

Kassouf, Amine; Jouan-Rimbaud Bouveresse, Delphine; Rutledge, Douglas N

2018-03-01

Independent components analysis (ICA) may be considered as one of the most established blind source separation techniques for the treatment of complex data sets in analytical chemistry. Like other similar methods, the determination of the optimal number of latent variables, in this case, independent components (ICs), is a crucial step before any modeling. Therefore, validation methods are required in order to decide about the optimal number of ICs to be used in the computation of the final model. In this paper, three new validation methods are formally presented. The first one, called Random_ICA, is a generalization of the ICA_by_blocks method. Its specificity resides in the random way of splitting the initial data matrix into two blocks, and then repeating this procedure several times, giving a broader perspective for the selection of the optimal number of ICs. The second method, called KMO_ICA_Residuals is based on the computation of the Kaiser-Meyer-Olkin (KMO) index of the transposed residual matrices obtained after progressive extraction of ICs. The third method, called ICA_corr_y, helps to select the optimal number of ICs by computing the correlations between calculated proportions and known physico-chemical information about samples, generally concentrations, or between a source signal known to be present in the mixture and the signals extracted by ICA. These three methods were tested using varied simulated and experimental data sets and compared, when necessary, to ICA_by_blocks. Results were relevant and in line with expected ones, proving the reliability of the three proposed methods. Copyright © 2017 Elsevier B.V. All rights reserved.

Periodic GMP Matrices

NASA Astrophysics Data System (ADS)

Eichinger, Benjamin

2016-07-01

We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP matrices. They form a certain Generalization of matrices related to the strong Moment Problem. This class allows us to give a parametrization of almost periodic finite gap Jacobi matrices by periodic GMP matrices. Moreover, due to their structural similarity we can carry over numerous results from the direct and inverse spectral theory of periodic Jacobi matrices to the class of periodic GMP matrices. In particular, we prove an analogue of the remarkable ''magic formula'' for this new class.

The correlation of low-velocity impact resistance of graphite-fiber-reinforced composites with matrix properties

NASA Technical Reports Server (NTRS)

Bowles, K. J.

1986-01-01

Summarized are basic studies that were conducted to correlate the impact resistance of graphite-fiber-reinforced composites with polymer matrix properties. Three crosslinked epoxy resins and a linear polysulfone were selected as composite matrices. As a group, these resins possess a significantly large range of mechanical properties. The mechanical properties of the resins and their respective composites were measured. Neat resin specimens and unidirectional and crossply composite specimens were impact tested with an instrumented dropweight tester. Impact resistances of the specimens were assessed on the basis of loading capability, energy absorption, and extent of damage.

Full-Duplex Bidirectional Secure Communications Under Perfect and Distributionally Ambiguous Eavesdropper's CSI

NASA Astrophysics Data System (ADS)

Li, Qiang; Zhang, Ying; Lin, Jingran; Wu, Sissi Xiaoxiao

2017-09-01

Consider a full-duplex (FD) bidirectional secure communication system, where two communication nodes, named Alice and Bob, simultaneously transmit and receive confidential information from each other, and an eavesdropper, named Eve, overhears the transmissions. Our goal is to maximize the sum secrecy rate (SSR) of the bidirectional transmissions by optimizing the transmit covariance matrices at Alice and Bob. To tackle this SSR maximization (SSRM) problem, we develop an alternating difference-of-concave (ADC) programming approach to alternately optimize the transmit covariance matrices at Alice and Bob. We show that the ADC iteration has a semi-closed-form beamforming solution, and is guaranteed to converge to a stationary solution of the SSRM problem. Besides the SSRM design, this paper also deals with a robust SSRM transmit design under a moment-based random channel state information (CSI) model, where only some roughly estimated first and second-order statistics of Eve's CSI are available, but the exact distribution or other high-order statistics is not known. This moment-based error model is new and different from the widely used bounded-sphere error model and the Gaussian random error model. Under the consider CSI error model, the robust SSRM is formulated as an outage probability-constrained SSRM problem. By leveraging the Lagrangian duality theory and DC programming, a tractable safe solution to the robust SSRM problem is derived. The effectiveness and the robustness of the proposed designs are demonstrated through simulations.

Atomistic modeling of thermomechanical properties of SWNT/Epoxy nanocomposites

NASA Astrophysics Data System (ADS)

Fasanella, Nicholas; Sundararaghavan, Veera

2015-09-01

Molecular dynamics simulations are performed to compute thermomechanical properties of cured epoxy resins reinforced with pristine and covalently functionalized carbon nanotubes. A DGEBA-DDS epoxy network was built using the ‘dendrimer’ growth approach where 75% of available epoxy sites were cross-linked. The epoxy model is verified through comparisons to experiments, and simulations are performed on nanotube reinforced cross-linked epoxy matrix using the CVFF force field in LAMMPS. Full stiffness matrices and linear coefficient of thermal expansion vectors are obtained for the nanocomposite. Large increases in stiffness and large decreases in thermal expansion were seen along the direction of the nanotube for both nanocomposite systems when compared to neat epoxy. The direction transverse to nanotube saw a 40% increase in stiffness due to covalent functionalization over neat epoxy at 1 K whereas the pristine nanotube system only saw a 7% increase due to van der Waals effects. The functionalized SWNT/epoxy nanocomposite showed an additional 42% decrease in thermal expansion along the nanotube direction when compared to the pristine SWNT/epoxy nanocomposite. The stiffness matrices are rotated over every possible orientation to simulate the effects of an isotropic system of randomly oriented nanotubes in the epoxy. The randomly oriented covalently functionalized SWNT/Epoxy nanocomposites showed substantial improvements over the plain epoxy in terms of higher stiffness (200% increase) and lower thermal expansion (32% reduction). Through MD simulations, we develop means to build simulation cells, perform annealing to reach correct densities, compute thermomechanical properties and compare with experiments.

Constructing acoustic timefronts using random matrix theory.

PubMed

Hegewisch, Katherine C; Tomsovic, Steven

2013-10-01

In a recent letter [Hegewisch and Tomsovic, Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering between acoustic modes due to sound speed fluctuations induced by the ocean's internal waves. The scattering exhibits a power-law decay as a function of the differences in mode numbers thereby generating a power-law, banded, random unitary matrix ensemble. This work gives a more complete account of that approach and extends the methods to the construction of an ensemble of acoustic timefronts. The result is a very efficient method for studying the statistical properties of timefronts at various propagation ranges that agrees well with propagation based on the parabolic equation. It helps identify which information about the ocean environment can be deduced from the timefronts and how to connect features of the data to that environmental information. It also makes direct connections to methods used in other disordered waveguide contexts where the use of random matrix theory has a multi-decade history.

Sequential time interleaved random equivalent sampling for repetitive signal.

PubMed

Zhao, Yijiu; Liu, Jingjing

2016-12-01

Compressed sensing (CS) based sampling techniques exhibit many advantages over other existing approaches for sparse signal spectrum sensing; they are also incorporated into non-uniform sampling signal reconstruction to improve the efficiency, such as random equivalent sampling (RES). However, in CS based RES, only one sample of each acquisition is considered in the signal reconstruction stage, and it will result in more acquisition runs and longer sampling time. In this paper, a sampling sequence is taken in each RES acquisition run, and the corresponding block measurement matrix is constructed using a Whittaker-Shannon interpolation formula. All the block matrices are combined into an equivalent measurement matrix with respect to all sampling sequences. We implemented the proposed approach with a multi-cores analog-to-digital converter (ADC), whose ADC cores are time interleaved. A prototype realization of this proposed CS based sequential random equivalent sampling method has been developed. It is able to capture an analog waveform at an equivalent sampling rate of 40 GHz while sampled at 1 GHz physically. Experiments indicate that, for a sparse signal, the proposed CS based sequential random equivalent sampling exhibits high efficiency.

Universal shocks in the Wishart random-matrix ensemble.

PubMed

Blaizot, Jean-Paul; Nowak, Maciej A; Warchoł, Piotr

2013-05-01

We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of N, the size of the matrix. In the large N limit, this equation generalizes the simple inviscid Burgers equation that has been obtained earlier for Hermitian or unitary matrices. The solution, through the method of characteristics, presents singularities that we relate to the precursors of shock formation in the Burgers equation. The finite N effects appear as a viscosity term in the Burgers equation. Using a scaling analysis of the complete equation for the characteristic polynomial, in the vicinity of the shocks, we recover in a simple way the universal Bessel oscillations (so-called hard-edge singularities) familiar in random-matrix theory.

Linear discriminant analysis with misallocation in training samples

NASA Technical Reports Server (NTRS)

Chhikara, R. (Principal Investigator); Mckeon, J.

1982-01-01

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general appraoch to modeling of mislocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained and the asymptotic first two moments of the two types of error rate given. Certain numerical results for the error rates are presented by considering the random and two non-random misallocation models. It is shown that when the allocation procedure for training samples is objectively formulated, the effect of misallocation on the error rates of the Bayes linear discriminant rule can almost be eliminated. If, however, this is not possible, the use of Fisher rule may be preferred over the Bayes rule.

Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems

PubMed Central

2015-01-01

We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement. PMID:25844072

Visualizing complex (hydrological) systems with correlation matrices

NASA Astrophysics Data System (ADS)

Haas, J. C.

2016-12-01

When trying to understand or visualize the connections of different aspects of a complex system, this often requires deeper understanding to start with, or - in the case of geo data - complicated GIS software. To our knowledge, correlation matrices have rarely been used in hydrology (e.g. Stoll et al., 2011; van Loon and Laaha, 2015), yet they do provide an interesting option for data visualization and analysis. We present a simple, python based way - using a river catchment as an example - to visualize correlations and similarities in an easy and colorful way. We apply existing and easy to use python packages from various disciplines not necessarily linked to the Earth sciences and can thus quickly show how different aquifers work or react, and identify outliers, enabling this system to also be used for quality control of large datasets. Going beyond earlier work, we add a temporal and spatial element, enabling us to visualize how a system reacts to local phenomena such as for example a river, or changes over time, by visualizing the passing of time in an animated movie. References: van Loon, A.F., Laaha, G.: Hydrological drought severity explained by climate and catchment characteristics, Journal of Hydrology 526, 3-14, 2015, Drought processes, modeling, and mitigation Stoll, S., Hendricks Franssen, H. J., Barthel, R., Kinzelbach, W.: What can we learn from long-term groundwater data to improve climate change impact studies?, Hydrology and Earth System Sciences 15(12), 3861-3875, 2011

Partition of environmental chemicals between maternal and fetal blood and tissues.

PubMed

Needham, Larry L; Grandjean, Philippe; Heinzow, Birger; Jørgensen, Poul J; Nielsen, Flemming; Patterson, Donald G; Sjödin, Andreas; Turner, Wayman E; Weihe, Pal

2011-02-01

Passage of environmental chemicals across the placenta has important toxicological consequences, as well as for choosing samples for analysis and for interpreting the results. To obtain systematic data, we collected in 2000 maternal and cord blood, cord tissue, placenta, and milk in connection with births in the Faroe Islands, where exposures to marine contaminants is increased. In 15 sample sets, we measured a total of 87 environmental chemicals, almost all of which were detected both in maternal and fetal tissues. The maternal serum lipid-based concentrations of organohalogen compounds averaged 1.7 times those of cord serum, 2.8 times those of cord tissue and placenta, and 0.7 those of milk. For organohalogen compounds detectable in all matrices, a high degree of correlation between concentrations in maternal serum and the other tissues investigated was generally observed (r(2) > 0.5). Greater degree of chlorination resulted in lower transfer from maternal serum into milk. Concentrations of pentachlorbenzene, γ-hexachlorocyclohexane, and several polychlorinated biphenyl congeners with low chlorination were higher in fetal samples and showed poor correlation with maternal levels. Perfluorinated compounds occurred in lower concentrations in cord serum than in maternal serum. Cadmium, lead, mercury, and selenium were all detected in fetal samples, but only mercury showed close correlations among concentrations in different matrices. Although the environmental chemicals examined pass through the placenta and are excreted into milk, partitions between maternal and fetal samples are not uniform.

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

PubMed

Fushiki, Tadayoshi

2009-07-01

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

Detecting a currency’s dominance using multivariate time series analysis

NASA Astrophysics Data System (ADS)

Syahidah Yusoff, Nur; Sharif, Shamshuritawati

2017-09-01

A currency exchange rate is the price of one country’s currency in terms of another country’s currency. There are four different prices; opening, closing, highest, and lowest can be achieved from daily trading activities. In the past, a lot of studies have been carried out by using closing price only. However, those four prices are interrelated to each other. Thus, the multivariate time series can provide more information than univariate time series. Therefore, the enthusiasm of this paper is to compare the results of two different approaches, which are mean vector and Escoufier’s RV coefficient in constructing similarity matrices of 20 world currencies. Consequently, both matrices are used to substitute the correlation matrix required by network topology. With the help of degree centrality measure, we can detect the currency’s dominance for both networks. The pros and cons for both approaches will be presented at the end of this paper.

Photophysical and lasing properties of new analogs of the boron-dipyrromethene laser dye pyrromethene 567 incorporated into or covalently bounded to solid matrices of poly(methyl methacrylate).

PubMed

López Arbeloa, F; Bañuelos Prieto, J; López Arbeloa, I; Costela, A; García-Moreno, I; Gómez, C; Amat-Guerri, F; Liras, M; Sastre, R

2003-07-01

The photophysical, lasing and thermostability properties of newly synthesized analogs of the commercial dye pyrromethene 567 (PM567) have been measured in polymeric matrices of poly(methyl methacrylate) both when used as a dopant and when covalently bounded to the polymeric chain. These analogs have an acetoxy or a polymerizable methacryloyloxy group at the end of a polymethylene chain at Position 8 of the PM567 chromophore core. Clear correlations between photophysical and lasing characteristics are observed. Linking chain lengths with three or more methylene units give the highest fluorescence quantum yields (as high as 0.89) and lasing efficiencies (as high as 41%). The covalent linkage of the chromophore to the polymeric chain via the methacryloyloxy group improves the photostability of the PM567 chromophore.

Solubility of gases and liquids in glassy polymers.

PubMed

De Angelis, Maria Grazia; Sarti, Giulio C

2011-01-01

This review discusses a macroscopic thermodynamic procedure to calculate the solubility of gases, vapors, and liquids in glassy polymers that is based on the general procedure provided by the nonequilibrium thermodynamics for glassy polymers (NET-GP) method. Several examples are presented using various nonequilibrium (NE) models including lattice fluid (NELF), statistical associating fluid theory (NE-SAFT), and perturbed hard sphere chain (NE-PHSC). Particular applications illustrate the calculation of infinite-dilution solubility coefficients in different glassy polymers and the prediction of solubility isotherms for different gases and vapors in pure polymers as well as in polymer blends. The determination of model parameters is discussed, and the predictive abilities of the models are illustrated. Attention is also given to the solubility of gas mixtures and solubility isotherms in nanocomposite mixed matrices. The fractional free volume determined from solubility data can be used to correlate solute diffusivities in mixed matrices.

Automatic Detection of Pearlite Spheroidization Grade of Steel Using Optical Metallography.

PubMed

Chen, Naichao; Chen, Yingchao; Ai, Jun; Ren, Jianxin; Zhu, Rui; Ma, Xingchi; Han, Jun; Ma, Qingqian

2016-02-01

To eliminate the effect of subjective factors during manually determining the pearlite spheroidization grade of steel by analysis of optical metallography images, a novel method combining image mining and artificial neural networks (ANN) is proposed. The four co-occurrence matrices of angular second moment, contrast, correlation, and entropy are adopted to objectively characterize the images. ANN is employed to establish a mathematical model between the four co-occurrence matrices and the corresponding spheroidization grade. Three materials used in coal-fired power plants (ASTM A315-B steel, ASTM A335-P12 steel, and ASTM A355-P11 steel) were selected as the samples to test the validity of our proposed method. The results indicate that the accuracies of the calculated spheroidization grades reach 99.05, 95.46, and 93.63%, respectively. Hence, our newly proposed method is adequate for automatically detecting the pearlite spheroidization grade of steel using optical metallography.

Influence of culture conditions and extracellular matrix alignment on human mesenchymal stem cells invasion into decellularized engineered tissues.

PubMed

Weidenhamer, Nathan K; Moore, Dusty L; Lobo, Fluvio L; Klair, Nathaniel T; Tranquillo, Robert T

2015-05-01

The variables that influence the in vitro recellularization potential of decellularized engineered tissues, such as cell culture conditions and scaffold alignment, have yet to be explored. The goal of this work was to explore the influence of insulin and ascorbic acid and extracellular matrix (ECM) alignment on the recellularization of decellularized engineered tissue by human mesenchymal stem cells (hMSCs). Aligned and non-aligned tissues were created by specifying the geometry and associated mechanical constraints to fibroblast-mediated fibrin gel contraction and remodelling using circular and C-shaped moulds. Decellularized tissues (matrices) of the same alignment were created by decellularization with detergents. Ascorbic acid promoted the invasion of hMSCs into the matrices due to a stimulated increase in motility and proliferation. Invasion correlated with hyaluronic acid secretion, α-smooth muscle actin expression and decreased matrix thickness. Furthermore, hMSCs invasion into aligned and non-aligned matrices was not different, although there was a difference in cell orientation. Finally, we show that hMSCs on the matrix surface appear to differentiate toward a smooth muscle cell or myofibroblast phenotype with ascorbic acid treatment. These results inform the strategy of recellularizing decellularized engineered tissue with hMSCs. Copyright © 2014 John Wiley & Sons, Ltd.

Tactile short-term memory in sensory-deprived individuals.

PubMed

Papagno, Costanza; Minniti, Giovanna; Mattavelli, Giulia C; Mantovan, Lara; Cecchetto, Carlo

2017-02-01

To verify whether loosing a sense or two has consequences on a spared sensory modality, namely touch, and whether these consequences depend on practice or are biologically determined, we investigated 13 deafblind participants, 16 deaf participants, 15 blind participants, and 13 matched normally sighted and hearing controls on a tactile short-term memory task, using checkerboard matrices of increasing length in which half of the squares were made up of a rough texture and half of a smooth one. Time of execution of a fixed matrix, number of correctly reproduced matrices, largest matrix correctly reproduced and tactile span were recorded. The three groups of sensory-deprived individuals did not differ in any measure, while blind and deaf participants outscored controls in all parameters except time of execution; the difference approached significance for deafblind people compared to controls only in one measure, namely correctly reproduced matrices. In blind and deafblind participants, performance negatively correlated with age of Braille acquisition, the older being the subject when acquiring Braille, the lower the performance, suggesting that practice plays a role. However, the fact that deaf participants, who did not share tactile experience, performed similarly to blind participants and significantly better than controls highlights that practice cannot be the only contribution to better tactile memory.

Evaluation of the default-mode network by quantitative 15O-PET: comparative study between cerebral blood flow and oxygen consumption.

PubMed

Aoe, Jo; Watabe, Tadashi; Shimosegawa, Eku; Kato, Hiroki; Kanai, Yasukazu; Naka, Sadahiro; Matsunaga, Keiko; Isohashi, Kayako; Tatsumi, Mitsuaki; Hatazawa, Jun

2018-06-22

Resting-state functional MRI (rs-fMRI) has revealed the existence of a default-mode network (DMN) based on spontaneous oscillations of the blood oxygenation level-dependent (BOLD) signal. The BOLD signal reflects the deoxyhemoglobin concentration, which depends on the relationship between the regional cerebral blood flow (CBF) and the cerebral metabolic rate of oxygen (CMRO 2 ). However, these two factors cannot be separated in BOLD rs-fMRI. In this study, we attempted to estimate the functional correlations in the DMN by means of quantitative 15 O-labeled gases and water PET, and to compare the contribution of the CBF and CMRO 2 to the DMN. Nine healthy volunteers (5 men and 4 women; mean age, 47.0 ± 1.2 years) were studied by means of 15 O-O 2 , 15 O-CO gases and 15 O-water PET. Quantitative CBF and CMRO 2 images were generated by an autoradiographic method and transformed into MNI standardized brain template. Regions of interest were placed on normalized PET images according to the previous rs-fMRI study. For the functional correlation analysis, the intersubject Pearson's correlation coefficients (r) were calculated for all pairs in the brain regions and correlation matrices were obtained for CBF and CMRO 2 , respectively. We defined r > 0.7 as a significant positive correlation and compared the correlation matrices of CBF and CMRO 2 . Significant positive correlations (r > 0.7) were observed in 24 pairs of brain regions for the CBF and 22 pairs of brain regions for the CMRO 2 . Among them, 12 overlapping networks were observed between CBF and CMRO 2 . Correlation analysis of CBF led to the detection of more brain networks as compared to that of CMRO 2 , indicating that the CBF can capture the state of the spontaneous activity with a higher sensitivity. We estimated the functional correlations in the DMN by means of quantitative PET using 15 O-labeled gases and water. The correlation matrix derived from the CBF revealed a larger number of brain networks as compared to that derived from the CMRO 2 , indicating that contribution to the functional correlation in the DMN is higher in the blood flow more than the oxygen consumption.

Structure-Function Network Mapping and Its Assessment via Persistent Homology

PubMed Central

2017-01-01

Understanding the relationship between brain structure and function is a fundamental problem in network neuroscience. This work deals with the general method of structure-function mapping at the whole-brain level. We formulate the problem as a topological mapping of structure-function connectivity via matrix function, and find a stable solution by exploiting a regularization procedure to cope with large matrices. We introduce a novel measure of network similarity based on persistent homology for assessing the quality of the network mapping, which enables a detailed comparison of network topological changes across all possible thresholds, rather than just at a single, arbitrary threshold that may not be optimal. We demonstrate that our approach can uncover the direct and indirect structural paths for predicting functional connectivity, and our network similarity measure outperforms other currently available methods. We systematically validate our approach with (1) a comparison of regularized vs. non-regularized procedures, (2) a null model of the degree-preserving random rewired structural matrix, (3) different network types (binary vs. weighted matrices), and (4) different brain parcellation schemes (low vs. high resolutions). Finally, we evaluate the scalability of our method with relatively large matrices (2514x2514) of structural and functional connectivity obtained from 12 healthy human subjects measured non-invasively while at rest. Our results reveal a nonlinear structure-function relationship, suggesting that the resting-state functional connectivity depends on direct structural connections, as well as relatively parsimonious indirect connections via polysynaptic pathways. PMID:28046127

Influence of chocolate matrix composition on cocoa flavan-3-ol bioaccessibility in vitro and bioavailability in humans.

PubMed

Neilson, Andrew P; George, Judy C; Janle, Elsa M; Mattes, Richard D; Rudolph, Ralf; Matusheski, Nathan V; Ferruzzi, Mario G

2009-10-28

Conflicting data exist regarding the influence of chocolate matrices on the bioavailability of epicatechin (EC) from cocoa. The objective of this study was to assess the bioavailability of EC from matrices varying in macronutrient composition and physical form. EC bioavailability was assessed from chocolate confections [reference dark chocolate (CDK), high sucrose (CHS), high milk protein (CMP)] and cocoa beverages [sucrose milk protein (BSMP), non-nutritive sweetener milk protein (BNMP)], in humans and in vitro. Six subjects consumed each product in a randomized crossover design, with serum EC concentrations monitored over 6 h post consumption. Areas under the serum concentration-time curve (AUC) were similar among chocolate matrices. However, AUCs were significantly increased for BSMP and BNMP (132 and 143 nM h) versus CMP (101 nM h). Peak serum concentrations (C(MAX)) were also increased for BSMP and BNMP (43 and 42 nM) compared to CDK and CMP (32 and 25 nM). Mean T(MAX) values were lower, although not statistically different, for beverages (0.9-1.1 h) versus confections (1.8-2.3 h), reflecting distinct shapes of the pharmacokinetic curves for beverages and confections. In vitro bioaccessibility and Caco-2 accumulation did not differ between treatments. These data suggest that bioavailability of cocoa flavan-3-ols is likely similar from typical commercial cocoa based foods and beverages, but that the physical form and sucrose content may influence T(MAX) and C(MAX).

Statistical theory of correlations in random packings of hard particles.

PubMed

Jin, Yuliang; Puckett, James G; Makse, Hernán A

2014-05-01

A random packing of hard particles represents a fundamental model for granular matter. Despite its importance, analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory. Here, we take inspiration from liquid theories for the n-particle angular correlation function to develop a formalism of random packings of hard particles from the bottom up. A progressive expansion into a shell of particles converges in the large layer limit under a Kirkwood-like approximation of higher-order correlations. We apply the formalism to hard disks and predict the density of two-dimensional random close packing (RCP), ϕ(rcp) = 0.85 ± 0.01, and random loose packing (RLP), ϕ(rlp) = 0.67 ± 0.01. Our theory also predicts a phase diagram and angular correlation functions that are in good agreement with experimental and numerical data.

Normative data for IQ, height and head circumference for children in Saudi Arabia.

PubMed

Batterjee, Adel A; Khaleefa, Omar; Ashaer, Khalil; Lynn, Richard

2013-07-01

Normative data are reported for intelligence, height and head circumference for a sample of 1553 6- to 15-year-olds in Saudi Arabia, and for the correlations between these variables. Intelligence was tested with the Standard Progressive Matrices, on which the Saudi sample obtained a British IQ of 76.2. There were no significant differences in means between boys and girls and differences in variability were inconsistent. The heights of the Saudi sample were generally lower than those of the American norms. The differences in head circumferences between the Saudi children and the American norms were inconsistent. Correlations between IQ and height were weaker than those found in other studies but correlations between IQ and head circumference were positive.

Inference from clustering with application to gene-expression microarrays.

PubMed

Dougherty, Edward R; Barrera, Junior; Brun, Marcel; Kim, Seungchan; Cesar, Roberto M; Chen, Yidong; Bittner, Michael; Trent, Jeffrey M

2002-01-01

There are many algorithms to cluster sample data points based on nearness or a similarity measure. Often the implication is that points in different clusters come from different underlying classes, whereas those in the same cluster come from the same class. Stochastically, the underlying classes represent different random processes. The inference is that clusters represent a partition of the sample points according to which process they belong. This paper discusses a model-based clustering toolbox that evaluates cluster accuracy. Each random process is modeled as its mean plus independent noise, sample points are generated, the points are clustered, and the clustering error is the number of points clustered incorrectly according to the generating random processes. Various clustering algorithms are evaluated based on process variance and the key issue of the rate at which algorithmic performance improves with increasing numbers of experimental replications. The model means can be selected by hand to test the separability of expected types of biological expression patterns. Alternatively, the model can be seeded by real data to test the expected precision of that output or the extent of improvement in precision that replication could provide. In the latter case, a clustering algorithm is used to form clusters, and the model is seeded with the means and variances of these clusters. Other algorithms are then tested relative to the seeding algorithm. Results are averaged over various seeds. Output includes error tables and graphs, confusion matrices, principal-component plots, and validation measures. Five algorithms are studied in detail: K-means, fuzzy C-means, self-organizing maps, hierarchical Euclidean-distance-based and correlation-based clustering. The toolbox is applied to gene-expression clustering based on cDNA microarrays using real data. Expression profile graphics are generated and error analysis is displayed within the context of these profile graphics. A large amount of generated output is available over the web.

Caustics, counting maps and semi-classical asymptotics

NASA Astrophysics Data System (ADS)

Ercolani, N. M.

2011-02-01

This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z0(t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain tied random walks on a 1D lattice, and the large time asymptotics of random matrix partition functions.

Stability conditions for exact-exchange Kohn-Sham methods and their relation to correlation energies from the adiabatic-connection fluctuation-dissipation theorem.

PubMed

Bleiziffer, Patrick; Schmidtel, Daniel; Görling, Andreas

2014-11-28

The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N2, O2, and the polyyne C10H2) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions.

The compositional mosaic of Fusarium species and their mycotoxins in unprocessed cereals, food and feed products in Belgium.

PubMed

Vanheule, Adriaan; Audenaert, Kris; De Boevre, Marthe; Landschoot, Sofie; Bekaert, Boris; Munaut, Françoise; Eeckhout, Mia; Höfte, Monica; De Saeger, Sarah; Haesaert, Geert

2014-07-02

Global food safety depends on continuous monitoring of food contaminants such as mycotoxins in cereals and cereal-derived products. Here, we combine this type of investigation with quantitative occurrence data on Fusarium infestation of these products in extensive correlation studies. Finally, this contributes to a thorough understanding of the presence, origin and physiology of Fusarium Head Blight (FHB) related mycotoxins and the correlations within their ranks. Two hundred and thirty-seven samples were analyzed from diverse cereal matrices, representing the most important stages of the cereal food and feed chain in Belgium. Food, feed and non-processed field samples were investigated, with a strong emphasis on whole-grain food products. Two approaches were pursued to estimate the full scope of FHB and its repercussions: UPLC-MS/MS was applied to detect twelve different mycotoxins, and Q-PCR was used to measure the presence of ten Fusarium species. We found that different matrices have different characteristic contamination profiles, and extensive correlation studies identified certain mycotoxins for future assessment (e.g. moniliformin produced by the Fusarium avenaceum/Fusarium tricinctum species group). The investigated harvest year of 2012 yielded many non-processed field materials containing elevated levels of deoxynivalenol (DON), while even in a so-called DON-year less prevalent toxins such as T-2 and HT-2 might be considered problematic due to their consistent co-occurrence with related mycotoxins. Our data illustrate complex interactions between the many Fusarium species that are responsible for FHB and their mycotoxins. Correlation studies demonstrate that consistent co-occurrence of mycotoxins is not to be neglected, and pinpoint issues for future surveillance and legislation. Copyright © 2014 Elsevier B.V. All rights reserved.

Protein structure similarity from Principle Component Correlation analysis.

PubMed

Zhou, Xiaobo; Chou, James; Wong, Stephen T C

2006-01-25

Owing to rapid expansion of protein structure databases in recent years, methods of structure comparison are becoming increasingly effective and important in revealing novel information on functional properties of proteins and their roles in the grand scheme of evolutionary biology. Currently, the structural similarity between two proteins is measured by the root-mean-square-deviation (RMSD) in their best-superimposed atomic coordinates. RMSD is the golden rule of measuring structural similarity when the structures are nearly identical; it, however, fails to detect the higher order topological similarities in proteins evolved into different shapes. We propose new algorithms for extracting geometrical invariants of proteins that can be effectively used to identify homologous protein structures or topologies in order to quantify both close and remote structural similarities. We measure structural similarity between proteins by correlating the principle components of their secondary structure interaction matrix. In our approach, the Principle Component Correlation (PCC) analysis, a symmetric interaction matrix for a protein structure is constructed with relationship parameters between secondary elements that can take the form of distance, orientation, or other relevant structural invariants. When using a distance-based construction in the presence or absence of encoded N to C terminal sense, there are strong correlations between the principle components of interaction matrices of structurally or topologically similar proteins. The PCC method is extensively tested for protein structures that belong to the same topological class but are significantly different by RMSD measure. The PCC analysis can also differentiate proteins having similar shapes but different topological arrangements. Additionally, we demonstrate that when using two independently defined interaction matrices, comparison of their maximum eigenvalues can be highly effective in clustering structurally or topologically similar proteins. We believe that the PCC analysis of interaction matrix is highly flexible in adopting various structural parameters for protein structure comparison.

Quantum correlation of fiber-based telecom-band photon pairs through standard loss and random media.

PubMed

Sua, Yong Meng; Malowicki, John; Lee, Kim Fook

2014-08-15

We study quantum correlation and interference of fiber-based telecom-band photon pairs with one photon of the pair experiencing multiple scattering in a random medium. We measure joint probability of two-photon detection for signal photon in a normal channel and idler photon in a channel, which is subjected to two independent conditions: standard loss (neutral density filter) and random media. We observe that both conditions degrade the correlation of signal and idler photons, and depolarization of the idler photon in random medium can enhance two-photon interference at certain relative polarization angles. Our theoretical calculation on two-photon polarization correlation and interference as a function of mean free path is in agreement with our experiment data. We conclude that quantum correlation of a polarization-entangled photon pair is better preserved than a polarization-correlated photon pair as one photon of the pair scatters through a random medium.

Robust, Adaptive Functional Regression in Functional Mixed Model Framework.

PubMed

Zhu, Hongxiao; Brown, Philip J; Morris, Jeffrey S

2011-09-01

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets.

Robust, Adaptive Functional Regression in Functional Mixed Model Framework

PubMed Central

Zhu, Hongxiao; Brown, Philip J.; Morris, Jeffrey S.

2012-01-01

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets. PMID:22308015

Canonical Naimark extension for generalized measurements involving sets of Pauli quantum observables chosen at random

NASA Astrophysics Data System (ADS)

Sparaciari, Carlo; Paris, Matteo G. A.

2013-01-01

We address measurement schemes where certain observables Xk are chosen at random within a set of nondegenerate isospectral observables and then measured on repeated preparations of a physical system. Each observable has a probability zk to be measured, with ∑kzk=1, and the statistics of this generalized measurement is described by a positive operator-valued measure. This kind of scheme is referred to as quantum roulettes, since each observable Xk is chosen at random, e.g., according to the fluctuating value of an external parameter. Here we focus on quantum roulettes for qubits involving the measurements of Pauli matrices, and we explicitly evaluate their canonical Naimark extensions, i.e., their implementation as indirect measurements involving an interaction scheme with a probe system. We thus provide a concrete model to realize the roulette without destroying the signal state, which can be measured again after the measurement or can be transmitted. Finally, we apply our results to the description of Stern-Gerlach-like experiments on a two-level system.

Regulatory sequence analysis tools.

PubMed

van Helden, Jacques

2003-07-01

The web resource Regulatory Sequence Analysis Tools (RSAT) (http://rsat.ulb.ac.be/rsat) offers a collection of software tools dedicated to the prediction of regulatory sites in non-coding DNA sequences. These tools include sequence retrieval, pattern discovery, pattern matching, genome-scale pattern matching, feature-map drawing, random sequence generation and other utilities. Alternative formats are supported for the representation of regulatory motifs (strings or position-specific scoring matrices) and several algorithms are proposed for pattern discovery. RSAT currently holds >100 fully sequenced genomes and these data are regularly updated from GenBank.

Population Structure of the Primary Malaria Vector in South America, Anopheles darlingi, Using Isozyme, Random Amplified Polymorphic DNA, Internal Transcribed Spacer 2, and Morphologic Markers

DTIC Science & Technology

1999-01-01

distances and identities and Roger?’ genetic distances were clustered by the unweighted pair group method using arithmetic average ( UPGMA ) to produce...Seattle, WA) using the NEIGHBOR program with the UPGMA option and a phenogram was produced with DRAWGRAM, also in PHYLIP 3.X RAPDBOOT5’ was used to...generate 100 pseudoreplicate distance matrices, which were collapsed to form 100 trees with UPGMA . The bootstrap consensus tree was derived from the 100

Dynamical entropy via entropy of non-random matrices: application to stability and complexity in modelling ecosystems.

PubMed

Chakrabarti, C G; Ghosh, Koyel

2013-10-01

In the present paper we have first introduced a measure of dynamical entropy of an ecosystem on the basis of the dynamical model of the system. The dynamical entropy which depends on the eigenvalues of the community matrix of the system leads to a consistent measure of complexity of the ecosystem to characterize the dynamical behaviours such as the stability, instability and periodicity around the stationary states of the system. We have illustrated the theory with some model ecosystems. Copyright © 2013 Elsevier Inc. All rights reserved.

Treatment of Nuclear Data Covariance Information in Sample Generation

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

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

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.

On the Least-Squares Fitting of Correlated Data: a Priorivs a PosterioriWeighting

NASA Astrophysics Data System (ADS)

Tellinghuisen, Joel

1996-10-01

One of the methods in common use for analyzing large data sets is a two-step procedure, in which subsets of the full data are first least-squares fitted to a preliminary set of parameters, and the latter are subsequently merged to yield the final parameters. The second step of this procedure is properly a correlated least-squares fit and requires the variance-covariance matrices from the first step to construct the weight matrix for the merge. There is, however, an ambiguity concerning the manner in which the first-step variance-covariance matrices are assessed, which leads to different statistical properties for the quantities determined in the merge. The issue is one ofa priorivsa posterioriassessment of weights, which is an application of what was originally calledinternalvsexternal consistencyby Birge [Phys. Rev.40,207-227 (1932)] and Deming ("Statistical Adjustment of Data." Dover, New York, 1964). In the present work the simplest case of a merge fit-that of an average as obtained from a global fit vs a two-step fit of partitioned data-is used to illustrate that only in the case of a priori weighting do the results have the usually expected and desired statistical properties: normal distributions for residuals,tdistributions for parameters assessed a posteriori, and χ2distributions for variances.

Power balance and loss mechanism analysis in RF transmit coil arrays.

PubMed

Kuehne, Andre; Goluch, Sigrun; Waxmann, Patrick; Seifert, Frank; Ittermann, Bernd; Moser, Ewald; Laistler, Elmar

2015-10-01

To establish a framework for transmit array power balance calculations based on power correlation matrices to accurately quantify the loss contributions from different mechanisms such as coupling, lumped components, and radiation. Starting from Poynting's theorem, power correlation matrices are derived for all terms in the power balance, which is formulated as a matrix equation. Finite-difference time-domain simulations of two 7 T eight-channel head array coils at 297.2 MHz are used to verify the theoretical considerations and demonstrate their application. Care is taken to accurately incorporate all loss mechanisms. The power balance for static B1 phase shims as well as two-dimensional spatially selective transmit SENSE pulses is shown. The simulated power balance shows an excellent agreement with theory, with a maximum power imbalance of less than 0.11%. Power loss contributions from the different loss mechanisms vary significantly between the investigated setups, and depending on the excitation mode imposed on the coil. The presented approach enables a straightforward loss evaluation for an arbitrary excitation of transmit coil arrays. Worst-case power imbalance and losses are calculated in a straightforward manner. This allows for deeper insight into transmit array loss mechanisms, incorporation of radiated power components in specific absorption rate calculations and verification of electromagnetic simulations. © 2014 Wiley Periodicals, Inc.

Matrix decompositions of two-dimensional nuclear magnetic resonance spectra.

PubMed

Havel, T F; Najfeld, I; Yang, J X

1994-08-16

Two-dimensional NMR spectra are rectangular arrays of real numbers, which are commonly regarded as digitized images to be analyzed visually. If one treats them instead as mathematical matrices, linear algebra techniques can also be used to extract valuable information from them. This matrix approach is greatly facilitated by means of a physically significant decomposition of these spectra into a product of matrices--namely, S = PAPT. Here, P denotes a matrix whose columns contain the digitized contours of each individual peak or multiple in the one-dimensional spectrum, PT is its transpose, and A is an interaction matrix specific to the experiment in question. The practical applications of this decomposition are considered in detail for two important types of two-dimensional NMR spectra, double quantum-filtered correlated spectroscopy and nuclear Overhauser effect spectroscopy, both in the weak-coupling approximation. The elements of A are the signed intensities of the cross-peaks in a double quantum-filtered correlated spectrum, or the integrated cross-peak intensities in the case of a nuclear Overhauser effect spectrum. This decomposition not only permits these spectra to be efficiently simulated but also permits the corresponding inverse problems to be given an elegant mathematical formulation to which standard numerical methods are applicable. Finally, the extension of this decomposition to the case of strong coupling is given.

Matrix decompositions of two-dimensional nuclear magnetic resonance spectra.

PubMed Central

Havel, T F; Najfeld, I; Yang, J X

1994-01-01

Two-dimensional NMR spectra are rectangular arrays of real numbers, which are commonly regarded as digitized images to be analyzed visually. If one treats them instead as mathematical matrices, linear algebra techniques can also be used to extract valuable information from them. This matrix approach is greatly facilitated by means of a physically significant decomposition of these spectra into a product of matrices--namely, S = PAPT. Here, P denotes a matrix whose columns contain the digitized contours of each individual peak or multiple in the one-dimensional spectrum, PT is its transpose, and A is an interaction matrix specific to the experiment in question. The practical applications of this decomposition are considered in detail for two important types of two-dimensional NMR spectra, double quantum-filtered correlated spectroscopy and nuclear Overhauser effect spectroscopy, both in the weak-coupling approximation. The elements of A are the signed intensities of the cross-peaks in a double quantum-filtered correlated spectrum, or the integrated cross-peak intensities in the case of a nuclear Overhauser effect spectrum. This decomposition not only permits these spectra to be efficiently simulated but also permits the corresponding inverse problems to be given an elegant mathematical formulation to which standard numerical methods are applicable. Finally, the extension of this decomposition to the case of strong coupling is given. PMID:8058742

Exploring effective multiplicity in multichannel functional near-infrared spectroscopy using eigenvalues of correlation matrices

PubMed Central

Uga, Minako; Dan, Ippeita; Dan, Haruka; Kyutoku, Yasushi; Taguchi, Y-h; Watanabe, Eiju

2015-01-01

Abstract. Recent advances in multichannel functional near-infrared spectroscopy (fNIRS) allow wide coverage of cortical areas while entailing the necessity to control family-wise errors (FWEs) due to increased multiplicity. Conventionally, the Bonferroni method has been used to control FWE. While Type I errors (false positives) can be strictly controlled, the application of a large number of channel settings may inflate the chance of Type II errors (false negatives). The Bonferroni-based methods are especially stringent in controlling Type I errors of the most activated channel with the smallest p value. To maintain a balance between Types I and II errors, effective multiplicity (Meff) derived from the eigenvalues of correlation matrices is a method that has been introduced in genetic studies. Thus, we explored its feasibility in multichannel fNIRS studies. Applying the Meff method to three kinds of experimental data with different activation profiles, we performed resampling simulations and found that Meff was controlled at 10 to 15 in a 44-channel setting. Consequently, the number of significantly activated channels remained almost constant regardless of the number of measured channels. We demonstrated that the Meff approach can be an effective alternative to Bonferroni-based methods for multichannel fNIRS studies. PMID:26157982

Occurrence of perchlorate in groundwater, paired farmland soil, lettuce, and rhizosphere soil from Chengdu, China.

PubMed

Tang, Yulu; Zhong, Bifeng; Qu, Bing; Feng, Shujin; Ding, Sanglan; Su, Shijun; Li, Zhi; Gan, Zhiwei

2017-05-24

A total of 28 groundwater, paired farmland soil, lettuce, and its rhizosphere soil samples were collected from Chengdu, China to detect perchlorate levels and to evaluate the relationships of perchlorate concentrations among these matrices. The perchlorate concentrations in the groundwater, farmland soil, lettuce, and rhizosphere soil samples ranged from below detection limit to 60.2 μg L -1 , from below detection limit to 249 μg kg -1 dry weight (dw), from 2.07 to 1010 μg kg -1 wet weight, and from below detection limit to 314 μg kg -1 dw, respectively. Significant correlation was found in the perchlorate levels among the farmland soil, lettuce, and rhizosphere soil, suggesting that they have common pollution sources, or perchlorate might transfer from farmland soil-rhizosphere soil-plant. However, there is no significant correlation between groundwater and the other three matrices, indicating that infiltration from perchlorate contaminated farmland soil was not the predominant source for groundwater pollution in Chengdu. The perchlorate concentrations in the farmland soil and lettuce samples were significantly higher than those in the rhizosphere soil, primarily due to uptake of perchlorate through the rhizosphere micro-environment by lettuce, or accelerated degradation by rhizospheric microorganisms, which contributed more needs further investigation.