Diffusion method in random matrix theory
Grela, Jacek
2016-01-01
We introduce a calculational tool useful in computing ratios and products of characteristic polynomials averaged over Gaussian measures with an external source. The method is based on Dyson’s Brownian motion and Grassmann/complex integration formulas for determinants. The resulting formulas are exact for finite matrix size N and form integral representations convenient for large N asymptotics. Quantities obtained by the method are interpreted as averages over standard matrix models. We provide several explicit and novel calculations with special emphasis on the β =2 Girko-Ginibre ensembles.
Optimization of MIMO Systems Capacity Using Large Random Matrix Methods
Directory of Open Access Journals (Sweden)
Philippe Loubaton
2012-11-01
Full Text Available This paper provides a comprehensive introduction of large random matrix methods for input covariance matrix optimization of mutual information of MIMO systems. It is first recalled informally how large system approximations of mutual information can be derived. Then, the optimization of the approximations is discussed, and important methodological points that are not necessarily covered by the existing literature are addressed, including the strict concavity of the approximation, the structure of the argument of its maximum, the accuracy of the large system approach with regard to the number of antennas, or the justification of iterative water-filling optimization algorithms. While the existing papers have developed methods adapted to a specific model, this contribution tries to provide a unified view of the large system approximation approach.
Non-hermitian random matrix theory: Method of hermitian reduction
Energy Technology Data Exchange (ETDEWEB)
Feinberg, J. [California Univ., Santa Barbara, CA (United States). Inst. for Theoretical Physics; Zee, A. [California Univ., Santa Barbara, CA (United States). Inst. for Theoretical Physics]|[Institute for Advanced Study, Olden Lane, Princeton, NJ 08540 (United States)
1997-11-03
We consider random non-hermitian matrices in the large-N limit. The power of analytic function theory cannot be brought to bear directly to analyze non-hermitian random matrices, in contrast to hermitian random matrices. To overcome this difficulty, we show that associated to each ensemble of non-hermitian matrices there is an auxiliary ensemble of random hermitian matrices which can be analyzed by the usual methods. We then extract the Green function and the density of eigenvalues of the non-hermitian ensemble from those of the auxiliary ensemble. We apply this ``method of hermitization`` to several examples, and discuss a number of related issues. (orig.). 25 refs.
Quasiclassical Random Matrix Theory
Prange, R. E.
1996-01-01
We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry, [as with Dyson's circular unitary ensemble], we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, th...
Indian Academy of Sciences (India)
chaos to galaxies. We demonstrate the applicability of random matrix theory for networks by pro- viding a new dimension to complex systems research. We show that in spite of huge differences ... as mentioned earlier, different types of networks can be constructed based on the nature of connections. For example,.
The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights
Kaymak, Vural; Kieburg, Mario; Guhr, Thomas
2014-07-01
In the past few years, the supersymmetry method has been generalized to real symmetric, Hermitian, and Hermitian self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic groups, respectively. We extend this supersymmetry approach to chiral random matrix theory invariant under the three chiral unitary groups in a unifying way. Thereby we generalize a projection formula providing a direct link and, hence, a ‘short cut’ between the probability density in ordinary space and that in superspace. We emphasize that this point was one of the main problems and shortcomings of the supersymmetry method, since only implicit dualities between ordinary space and superspace were known before. To provide examples, we apply this approach to the calculation of the supersymmetric analogue of a Lorentzian (Cauchy) ensemble and an ensemble with a quartic potential. Moreover, we consider the partially quenched partition function of the three chiral Gaussian ensembles corresponding to four-dimensional continuum quantum chromodynamics. We identify a natural splitting of the chiral Lagrangian in its lowest order into a part for the physical mesons and a part associated with source terms generating the observables, e.g. the level density of the Dirac operator.
Random matrix improved subspace clustering
Couillet, Romain
2017-03-06
This article introduces a spectral method for statistical subspace clustering. The method is built upon standard kernel spectral clustering techniques, however carefully tuned by theoretical understanding arising from random matrix findings. We show in particular that our method provides high clustering performance while standard kernel choices provably fail. An application to user grouping based on vector channel observations in the context of massive MIMO wireless communication networks is provided.
Deift, Percy
2009-01-01
This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derive
spam: A Sparse Matrix R Package with Emphasis on MCMC Methods for Gaussian Markov Random Fields
Directory of Open Access Journals (Sweden)
Reinhard Furrer
2010-10-01
Full Text Available spam is an R package for sparse matrix algebra with emphasis on a Cholesky factorization of sparse positive definite matrices. The implemantation of spam is based on the competing philosophical maxims to be competitively fast compared to existing tools and to be easy to use, modify and extend. The first is addressed by using fast Fortran routines and the second by assuring S3 and S4 compatibility. One of the features of spam is to exploit the algorithmic steps of the Cholesky factorization and hence to perform only a fraction of the workload when factorizing matrices with the same sparsity structure. Simulations show that exploiting this break-down of the factorization results in a speed-up of about a factor 5 and memory savings of about a factor 10 for large matrices and slightly smaller factors for huge matrices. The article is motivated with Markov chain Monte Carlo methods for Gaussian Markov random fields, but many other statistical applications are mentioned that profit from an efficient Cholesky factorization as well.
Random matrix theory within superstatistics
Abul-Magd, A. Y.
2005-01-01
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the method by calculating the level density, the nearest-neighbor-spacing distributions and the two-level co...
Energy Technology Data Exchange (ETDEWEB)
Macedo-Junior, A.F. [Departamento de Fisica, Laboratorio de Fisica Teorica e Computacional, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil)]. E-mail: ailton@df.ufpe.br; Macedo, A.M.S. [Departamento de Fisica, Laboratorio de Fisica Teorica e Computacional, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil)
2006-09-25
We study a class of Brownian-motion ensembles obtained from the general theory of Markovian stochastic processes in random-matrix theory. The ensembles admit a complete classification scheme based on a recent multivariable generalization of classical orthogonal polynomials and are closely related to Hamiltonians of Calogero-Sutherland-type quantum systems. An integral transform is proposed to evaluate the n-point correlation function for a large class of initial distribution functions. Applications of the classification scheme and of the integral transform to concrete physical systems are presented in detail.
Developments in Random Matrix Theory
Snaith, N. C.; Forrester, P. J.; Verbaarschot, J. J. M.
2003-01-01
In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given.
Energy Technology Data Exchange (ETDEWEB)
Jackson, A.D. [Niels Bohr Inst., Copenhagen (Denmark)
1998-08-10
Chiral random matrix theory has recently been shown to provide a tool useful for both modeling chiral symmetry restoration in QCD and for providing analytic descriptions of the microscopic spectral content of lattice gauge simulations. The basic ideas of chiral random matrix theory and some recent results are discussed. (orig.) 24 refs.
Supersymmetry in random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kieburg, Mario
2010-05-04
I study the applications of supersymmetry in random matrix theory. I generalize the supersymmetry method and develop three new approaches to calculate eigenvalue correlation functions. These correlation functions are averages over ratios of characteristic polynomials. In the first part of this thesis, I derive a relation between integrals over anti-commuting variables (Grassmann variables) and differential operators with respect to commuting variables. With this relation I rederive Cauchy- like integral theorems. As a new application I trace the supermatrix Bessel function back to a product of two ordinary matrix Bessel functions. In the second part, I apply the generalized Hubbard-Stratonovich transformation to arbitrary rotation invariant ensembles of real symmetric and Hermitian self-dual matrices. This extends the approach for unitarily rotation invariant matrix ensembles. For the k-point correlation functions I derive supersymmetric integral expressions in a unifying way. I prove the equivalence between the generalized Hubbard-Stratonovich transformation and the superbosonization formula. Moreover, I develop an alternative mapping from ordinary space to superspace. After comparing the results of this approach with the other two supersymmetry methods, I obtain explicit functional expressions for the probability densities in superspace. If the probability density of the matrix ensemble factorizes, then the generating functions exhibit determinantal and Pfaffian structures. For some matrix ensembles this was already shown with help of other approaches. I show that these structures appear by a purely algebraic manipulation. In this new approach I use structures naturally appearing in superspace. I derive determinantal and Pfaffian structures for three types of integrals without actually mapping onto superspace. These three types of integrals are quite general and, thus, they are applicable to a broad class of matrix ensembles. (orig.)
Octonions in random matrix theory
Forrester, Peter J.
2016-01-01
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random by symmetry considerations. Only for $N=2$ is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for $N...
Superstatistics in Random Matrix Theory
Abul-Magd, A. Y.
2011-01-01
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed several attempts to extend RMT to describe quantum systems with mixed regular-chaotic dynamics. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented other versions of the theory that keep...
Octonions in random matrix theory
Forrester, Peter J.
2017-04-01
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random matrices by symmetry considerations. Only for N=2 is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for N=3. We then proceed to consider the matrix structure X†X, when X has random octonion entries. Analytic results are obtained from N=2, but are observed to break down in the 3×3 case.
Random matrix theory and multivariate statistics
Diaz-Garcia, Jose A.; Jáimez, Ramon Gutiérrez
2009-01-01
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases the classical random matrix ensembles, are proposed. Some properties of these classes of ensemble are analysed. In addition, the random matrix ensemble approach is extended and a unified theory proposed for the study of distributions for real normed divisio...
Supersymmetry in Random Matrix Theory
Guhr, Thomas
2010-01-01
Supersymmetry is nowadays indispensable for many problems in Random Matrix Theory. It is presented here with an emphasis on conceptual and structural issues. An introduction to supermathematics is given. The Hubbard-Stratonovich transformation as well as its generalization and superbosonization are explained. The supersymmetric non-linear sigma model, Brownian motion in superspace and the color-flavor transformation are discussed.
Staggered chiral random matrix theory
Osborn, James C.
2010-01-01
We present a random matrix theory (RMT) for the staggered lattice QCD Dirac operator. The staggered RMT is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.
Energy Technology Data Exchange (ETDEWEB)
Suleymanov, Mais [CIIT, Islamabad (Pakistan); Shahaliev, Ehtiram [HEPL, JINR, Dubna (Russian Federation)
2009-07-01
Over the last 25 years a lot of efforts have been made to search for new phases of strongly interacting matter. Heavy ion collisions are of great importance since they open a way to reproduce these phases in the Earth laboratory. But in this case the volume of information increases sharply as well as the background information. A method was introduced a method on the basic of Random Matrix Theory to study the fluctuations of neutron resonances in compound nuclei which doesn't depend on the background of measurements. To analyze the energetic levels of compound nuclei the function of distances between two energetic levels p(s{sub i}) is defined as the general distributions for probability of all kinds of ensembles. At values of the index of universality {nu}=0 it will change to Poisson type distributions pointing to absence of any correlations in the system and at the values of {nu}=1 it will change to Wigner type behavior directing to some correlation in the studying ensemble. We discuss that the experimental study of the behavior of p(s{sub i}) distribution for secondary particles could give a signal on the phase transitions.
Superstatistics in Random Matrix Theory
Directory of Open Access Journals (Sweden)
A.Y. Abul-Magd
2012-12-01
Full Text Available Random matrix theory (RMT provides a successful model for quantum systems, whose classical counterpart has chaotic dynamics. It is based on two assumptions: (1 matrix-element independence, and (2 base invariance. The last decade witnessed several attempts to extend RMT to describe quantum systems with mixed regular-chaotic dynamics. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors have presented other versions of the theory that keep base invariance at the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or by following the basic prescription of the recently suggested concept of superstatistics. The latter concept was introduced as a generalization of equilibrium thermodynamics to describe non-equilibrium systems by allowing the temperature to fluctuate. We here review the superstatistical generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments on billiards modeling systems in transition from order to chaos.
A random matrix theory of decoherence
Energy Technology Data Exchange (ETDEWEB)
Gorin, T [Departamento de FIsica, Universidad de Guadalajara, Blvd Marcelino GarcIa Barragan y Calzada OlImpica, Guadalajara CP 44840, JalIsco (Mexico); Pineda, C [Institut fuer Physik und Astronomie, University of Potsdam, 14476 Potsdam (Germany); Kohler, H [Fachbereich Physik, Universitaet Duisburg-Essen, D-47057 Duisburg (Germany); Seligman, T H [Instituto de Ciencias FIsicas, Universidad Nacional Autonoma de Mexico (Mexico)], E-mail: thomas.gorin@red.cucei.udg.mx, E-mail: carlospgmat03@gmail.com
2008-11-15
Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix arising from the ensemble induced, in contrast to previous studies where the average values of purity, concurrence and entropy were considered; we further discuss when one or the other approach is relevant. The two approaches agree in the limit of large environments. Analytic results for the average density matrix and its purity are presented in linear response approximation. The two-qubit system is analysed, mainly numerically, in more detail.
Logarithmic universality in random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Splittorff, K. E-mail: split@alf.nbi.dk
1999-05-24
Universality in unitary invariant random matrix ensembles with complex matrix elements is considered. We treat two general ensembles which have a determinant factor in the weight. These ensembles are relevant, e.g., for spectra of the Dirac operator in QCD. In addition to the well established universality with respect to the choice of potential, we prove that microscopic spectral correlators are unaffected when the matrix in the determinant is replaced by an expansion in powers of the matrix. We refer to this invariance as logarithmic universality. The result is used in proving that a simple random matrix model with Ginsparg-Wilson symmetry has the same microscopic spectral correlators as chiral random matrix theory.
Importance of randomness in biological networks: A random matrix ...
Indian Academy of Sciences (India)
2015-01-29
Jan 29, 2015 ... We show that in spite of huge differences these interaction networks, representing real-world systems, posses from random matrix models, the spectral properties of the underlying matrices of these networks follow random matrix theory bringing them into the same universality class. We further demonstrate ...
Supersymmetric SYK model and random matrix theory
Li, Tianlin; Liu, Junyu; Xin, Yuan; Zhou, Yehao
2017-06-01
In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the N=1 supersymmetric generalization of Sachdev-Ye-Kitaev (SYK) model, a toy model for two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. The time-dependent evolution of the spectral form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic hamiltonian with supersymmetry.
Jackson, Dan; White, Ian R; Riley, Richard D
2013-03-01
Multivariate meta-analysis is becoming more commonly used. Methods for fitting the multivariate random effects model include maximum likelihood, restricted maximum likelihood, Bayesian estimation and multivariate generalisations of the standard univariate method of moments. Here, we provide a new multivariate method of moments for estimating the between-study covariance matrix with the properties that (1) it allows for either complete or incomplete outcomes and (2) it allows for covariates through meta-regression. Further, for complete data, it is invariant to linear transformations. Our method reduces to the usual univariate method of moments, proposed by DerSimonian and Laird, in a single dimension. We illustrate our method and compare it with some of the alternatives using a simulation study and a real example. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Jackson, Dan; White, Ian R; Riley, Richard D
2013-01-01
Multivariate meta-analysis is becoming more commonly used. Methods for fitting the multivariate random effects model include maximum likelihood, restricted maximum likelihood, Bayesian estimation and multivariate generalisations of the standard univariate method of moments. Here, we provide a new multivariate method of moments for estimating the between-study covariance matrix with the properties that (1) it allows for either complete or incomplete outcomes and (2) it allows for covariates through meta-regression. Further, for complete data, it is invariant to linear transformations. Our method reduces to the usual univariate method of moments, proposed by DerSimonian and Laird, in a single dimension. We illustrate our method and compare it with some of the alternatives using a simulation study and a real example. PMID:23401213
Matrix Methods to Analytic Geometry.
Bandy, C.
1982-01-01
The use of basis matrix methods to rotate axes is detailed. It is felt that persons who have need to rotate axes often will find that the matrix method saves considerable work. One drawback is that most students first learning to rotate axes will not yet have studied linear algebra. (MP)
Random matrix model for disordered conductors
Indian Academy of Sciences (India)
Keywords. Disordered conductors; random matrix theory; Dyson's Coulomb gas model. ... An interesting random walk problem associated with the joint probability distribution of the ensuing ensemble is discussed and its connection with level dynamics is brought out. It is further proved that Dyson's Coulomb gas analogy ...
Random matrix theory and symmetric spaces
Energy Technology Data Exchange (ETDEWEB)
Caselle, M.; Magnea, U
2004-05-01
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero-Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.
Random matrix techniques in quantum information theory
Collins, Benoît; Nechita, Ion
2016-01-01
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Random matrix techniques in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Collins, Benoît, E-mail: collins@math.kyoto-u.ac.jp [Department of Mathematics, Kyoto University, Kyoto 606-8502 (Japan); Département de Mathématique et Statistique, Université d’Ottawa, 585 King Edward, Ottawa, Ontario K1N6N5 (Canada); CNRS, Lyon (France); Nechita, Ion, E-mail: nechita@irsamc.ups-tlse.fr [Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching (Germany); Laboratoire de Physique Théorique, CNRS, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse (France)
2016-01-15
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
A random matrix approach to language acquisition
Nicolaidis, A.; Kosmidis, Kosmas; Argyrakis, Panos
2009-12-01
Since language is tied to cognition, we expect the linguistic structures to reflect patterns that we encounter in nature and are analyzed by physics. Within this realm we investigate the process of lexicon acquisition, using analytical and tractable methods developed within physics. A lexicon is a mapping between sounds and referents of the perceived world. This mapping is represented by a matrix and the linguistic interaction among individuals is described by a random matrix model. There are two essential parameters in our approach. The strength of the linguistic interaction β, which is considered as a genetically determined ability, and the number N of sounds employed (the lexicon size). Our model of linguistic interaction is analytically studied using methods of statistical physics and simulated by Monte Carlo techniques. The analysis reveals an intricate relationship between the innate propensity for language acquisition β and the lexicon size N, N~exp(β). Thus a small increase of the genetically determined β may lead to an incredible lexical explosion. Our approximate scheme offers an explanation for the biological affinity of different species and their simultaneous linguistic disparity.
Effective Lagrangians and chiral random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Halasz, M.A.; Verbaarschot, J.J.M. [Department of Physics, State University of New York, Stony Brook, New York 11794 (United States)
1995-08-15
Recently, sum rules were derived for the inverse eigenvalues of the Dirac operator. They were obtained in two different ways: (i) starting from the low-energy effective Lagrangian and (ii) starting from a random matrix theory with the symmetries of the Dirac operator. This suggests that the effective theory can be obtained directly from the random matrix theory. Previously, this was shown for three or more colors with fundamental fermions. In this paper we construct the effective theory from a random matrix theory for two colors in the fundamental representation and for an arbitrary number of colors in the adjoint representation. We construct a fermionic partition function for Majorana fermions in Euclidean spacetime. Their reality condition is formulated in terms of complex conjugation of the second kind.
Random matrix theory with an external source
Brézin, Edouard
2016-01-01
This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.
Quark Spectra, Topology, and Random Matrix Theory
Energy Technology Data Exchange (ETDEWEB)
Edwards, R.G.; Heller, U.M. [SCRI, Florida State University, Tallahassee, Florida 32306-4130 (United States); Kiskis, J. [Department of Physics, University of California, Davis, California 95616 (United States); Narayanan, R. [Department of Physics, Building 510A, Brookhaven National Laboratory, P.O. Box 5000, Upton, New York 11973 (United States)
1999-05-01
Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice overlap Dirac operator provides a nonperturbative, ultraviolet-regularized description of quarks with the correct chiral symmetry. Properties of the spectrum of this operator and their relation to random matrix theory are studied here. In particular, the predictions from chiral random matrix theory in topologically nontrivial gauge field sectors are tested for the first time. {copyright} {ital 1999} {ital The American Physical Society}
Construction of random perfect phylogeny matrix
Directory of Open Access Journals (Sweden)
Mehdi Sadeghi
2010-11-01
Full Text Available Mehdi Sadeghi1,2, Hamid Pezeshk4, Changiz Eslahchi3,5, Sara Ahmadian6, Sepideh Mah Abadi61National Institute of Genetic Engineering and Biotechnology, Tehran, Iran; 2School of Computer Science, 3School of Mathematics, Institute for Research in Fundamental Sciences (IPM, Tehran, Iran; 4School of Mathematics, Statistics and Computer Sciences, Center of Excellence in Biomathematics, College of Science, University of Tehran, Tehran, Iran; 5Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran; 6Department of Computer Engineering, Sharif University of Technology, Tehran, IranPurpose: Interest in developing methods appropriate for mapping increasing amounts of genome-wide molecular data are increasing rapidly. There is also an increasing need for methods that are able to efficiently simulate such data.Patients and methods: In this article, we provide a graph-theory approach to find the necessary and sufficient conditions for the existence of a phylogeny matrix with k nonidentical haplotypes, n single nucleotide polymorphisms (SNPs, and a population size of m for which the minimum allele frequency of each SNP is between two specific numbers a and b.Results: We introduce an O(max(n2, nm algorithm for the random construction of such a phylogeny matrix. The running time of any algorithm for solving this problem would be Ω (nm.Conclusion: We have developed software, RAPPER, based on this algorithm, which is available at http://bioinf.cs.ipm.ir/softwares/RAPPER.Keywords: perfect phylogeny, minimum allele frequency (MAF, tree, recursive algorithm
Statistical properties of random matrix product states
Garnerone, Silvano; de Oliveira, Thiago R.; Haas, Stephan; Zanardi, Paolo
2010-11-01
We study the set of random matrix product states (RMPS) introduced by Garnerone, de Oliveira, and Zanardi [S. Garnerone, T. R. de Oliveira, and P. Zanardi, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.81.032336 81, 032336 (2010)] as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical investigation of the properties of RMPS. We calculate the average state of the ensemble in the nonhomogeneous case, and numerically check the validity of this result. We also suggest using RMPS as a tool to approximate properties of general quantum random states. The numerical simulations presented here support the accuracy and efficiency of this approximation. These results suggest that any generalized canonical state can be approximated with high probability by the reduced density matrix of a RMPS, if the average matrix product states coincide with the associated microcanonical ensemble.
Embedded random matrix ensembles in quantum physics
Kota, V K B
2014-01-01
Although used with increasing frequency in many branches of physics, random matrix ensembles are not always sufficiently specific to account for important features of the physical system at hand. One refinement which retains the basic stochastic approach but allows for such features consists in the use of embedded ensembles. The present text is an exhaustive introduction to and survey of this important field. Starting with an easy-to-read introduction to general random matrix theory, the text then develops the necessary concepts from the beginning, accompanying the reader to the frontiers of present-day research. With some notable exceptions, to date these ensembles have primarily been applied in nuclear spectroscopy. A characteristic example is the use of a random two-body interaction in the framework of the nuclear shell model. Yet, topics in atomic physics, mesoscopic physics, quantum information science and statistical mechanics of isolated finite quantum systems can also be addressed using these ensemb...
Social patterns revealed through random matrix theory
Sarkar, Camellia; Jalan, Sarika
2014-11-01
Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real-world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in particular time frame affects the decisions of individuals rendering them more freedom of choice in situations of financial security. While the structural organization of networks remains the same throughout all datasets, random matrix theory provides insight into the interaction pattern of individuals of the society in situations of crisis. It has also been contemplated that individual accountability in terms of weighted interactions remains as a key to success unless segregation of tasks comes into play.
Random matrix theory for underwater sound propagation
Hegewisch, K. C.; Tomsovic, S.
2012-02-01
Ocean acoustic propagation can be formulated as a wave guide with a weakly random medium generating multiple scattering. Twenty years ago, this was recognized as a quantum chaos problem, and yet random matrix theory, one pillar of quantum or wave chaos studies, has never been introduced into the subject. The modes of the wave guide provide a representation for the propagation, which in the parabolic approximation is unitary. Scattering induced by the ocean's internal waves leads to a power-law random banded unitary matrix ensemble for long-range deep-ocean acoustic propagation. The ensemble has similarities, but differs, from those introduced for studying the Anderson metal-insulator transition. The resulting long-range propagation ensemble statistics agree well with those of full wave propagation using the parabolic equation.
A Random Matrix Approach to Credit Risk
Guhr, Thomas
2014-01-01
We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided. PMID:24853864
A random matrix approach to credit risk.
Directory of Open Access Journals (Sweden)
Michael C Münnix
Full Text Available We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.
Random Matrix Theory and Elliptic Curves
2014-11-24
lecture on random matrix models for elliptic curves at the combined meeting of the Australian and New Zealand mathematical societies Melbourne, Australia...organizer). Associated with the Chichely meeting will be a special volume of the Philosophical Transactions of the Royal Society (the world’s oldest...Distribution A: Approved for public release; distribution is unlimited. 5 USE OF SUPPORT 8 • JPK was awarded a Royal Society Wolfson Research Merit
Pseudo-Hermitian random matrix theory
Srivastava, S. C. L.; Jain, S. R.
2013-02-01
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statistical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available.
Pseudo-Hermitian random matrix theory
Srivastava, Shashi C. L.; Jain, S. R.
2013-01-01
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statistical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available.
Vertices from replica in a random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Brezin, E [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond 75231, Paris Cedex 05 (France); Hikami, S [Department of Basic Sciences, University of Tokyo, Meguro-ku, Komaba, Tokyo 153 (Japan)
2007-11-09
Kontsevich's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In a subsequent work Okounkov rederived these results from the edge behavior of a Gaussian matrix integral. In our work we consider the correlation functions of vertices in a Gaussian random matrix theory, with an external matrix source. We deal with operator products of the form <{pi}{sub i=1}{sup n}1/N tr M{sup k{sub i}}>, in a 1/N expansion. For large values of the powers k{sub i}, in an appropriate scaling limit relating large k's to large N, universal scaling functions are derived. Furthermore, we show that the replica method applied to characteristic polynomials of the random matrices, together with a duality exchanging N and the number of points, provides a new way to recover Kontsevich's results on these intersection numbers.
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
Ambainis, Andris; Harrow, Aram W.; Hastings, Matthew B.
2012-02-01
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in {(mathbb {C}^d)^{⊗ k}}, where k and p/ d k are fixed while d → ∞. When k = 1, the Marčenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ({(1+sqrt{p/d^k})^2}) but the smallest eigenvalue {(min(0,1-sqrt{p/d^k})^2)} and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately {(1+sqrt{p/d^k})^2} and the spectral density approaches that of the Marčenko-Pastur law, generalizing the random matrix theory result to the random tensor case. Our bound on the largest eigenvalue has implications both for sampling from a particular heavy-tailed distribution and for a recently proposed quantum data-hiding and correlation-locking scheme due to Leung and Winter. Since the matrices we consider have neither independent entries nor unitary invariance, we need to develop new techniques for their analysis. The main contribution of this paper is to give three different methods for analyzing mixtures of random product states: a diagrammatic approach based on Gaussian integrals, a combinatorial method that looks at the cycle decompositions of permutations and a recursive method that uses a variant of the Schwinger-Dyson equations.
Fuzzy Field Theory as a Random Matrix Model
Tekel, Juraj
This dissertation considers the theory of scalar fields on fuzzy spaces from the point of view of random matrices. First we define random matrix ensembles, which are natural description of such theory. These ensembles are new and the novel feature is a presence of kinetic term in the probability measure, which couples the random matrix to a set of external matrices and thus breaks the original symmetry. Considering the case of a free field ensemble, which is generalization of a Gaussian matrix ensemble, we develop a technique to compute expectation values of the observables of the theory based on explicit Wick contractions and we write down recursion rules for these. We show that the eigenvalue distribution of the random matrix follows the Wigner semicircle distribution with a rescaled radius. We also compute distributions of the matrix Laplacian of the random matrix given by the new term and demonstrate that the eigenvalues of these two matrices are correlated. We demonstrate the robustness of the method by computing expectation values and distributions for more complicated observables. We then consider the ensemble corresponding to an interacting field theory, with a quartic interaction. We use the same method to compute the distribution of the eigenvalues and show that the presence of the kinetic terms rescales the distribution given by the original theory, which is a polynomially deformed Wigner semicircle. We compute the eigenvalue distribution of the matrix Laplacian and the joint distribution up to second order in the correlation and we show that the correlation between the two changes from the free field case. Finally, as an application of these results, we compute the phase diagram of the fuzzy scalar field theory, we find multiscaling which stabilizes this diagram in the limit of large matrices and compare it with the results obtained numerically and by considering the kinetic part as a perturbation.
Agarwal, Jayant P; Mendenhall, Shaun D; Anderson, Layla A; Ying, Jian; Boucher, Kenneth M; Liu, Ting; Neumayer, Leigh A
2015-01-01
Recent literature has focused on the advantages and disadvantages of using acellular dermal matrix in breast reconstruction. Many of the reported data are from low level-of-evidence studies, leaving many questions incompletely answered. The present randomized trial provides high-level data on the incidence and severity of complications in acellular dermal matrix breast reconstruction between two commonly used types of acellular dermal matrix. A prospective randomized trial was conducted to compare outcomes of immediate staged tissue expander breast reconstruction using either AlloDerm or DermaMatrix. The impact of body mass index, smoking, diabetes, mastectomy type, radiation therapy, and chemotherapy on outcomes was analyzed. Acellular dermal matrix biointegration was analyzed clinically and histologically. Patient satisfaction was assessed by means of preoperative and postoperative surveys. Logistic regression models were used to identify predictors of complications. This article reports on the study design, surgical technique, patient characteristics, and preoperative survey results, with outcomes data in a separate report. After 2.5 years, we successfully enrolled and randomized 128 patients (199 breasts). The majority of patients were healthy nonsmokers, with 41 percent of patients receiving radiation therapy and 49 percent receiving chemotherapy. Half of the mastectomies were prophylactic, with nipple-sparing mastectomy common in both cancer and prophylactic cases. Preoperative survey results indicate that patients were satisfied with their premastectomy breast reconstruction education. Results from the Breast Reconstruction Evaluation Using Acellular Dermal Matrix as a Sling Trial will assist plastic surgeons in making evidence-based decisions regarding acellular dermal matrix-assisted tissue expander breast reconstruction. Therapeutic, II.
Overlap Dirac operator, eigenvalues and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Edwards, Robert G.; Heller, Urs M.; Kiskis, Joe; Narayanan, Rajamani
2000-03-01
The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are tested.
Random matrix approach to categorical data analysis
Patil, Aashay; Santhanam, M. S.
2015-09-01
Correlation and similarity measures are widely used in all the areas of sciences and social sciences. Often the variables are not numbers but are instead qualitative descriptors called categorical data. We define and study similarity matrix, as a measure of similarity, for the case of categorical data. This is of interest due to a deluge of categorical data, such as movie ratings, top-10 rankings, and data from social media, in the public domain that require analysis. We show that the statistical properties of the spectra of similarity matrices, constructed from categorical data, follow random matrix predictions with the dominant eigenvalue being an exception. We demonstrate this approach by applying it to the data for Indian general elections and sea level pressures in the North Atlantic ocean.
Heavy-tailed chiral random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kanazawa, Takuya [iTHES Research Group and Quantum Hadron Physics Laboratory, RIKEN,Wako, Saitama, 351-0198 (Japan)
2016-05-27
We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model analytically and obtain the microscopic spectral density and the smallest eigenvalue distribution for an arbitrary number of flavors and arbitrary quark masses. Exotic behaviors such as non-decoupling of heavy flavors and a power-law tail of the smallest eigenvalue distribution are illustrated.
Open quantum systems and random matrix theory
Mulhall, Declan
2015-01-01
A simple model for open quantum systems is analyzed with random matrix theory. The system is coupled to the continuum in a minimal way. In this paper the effect on the level statistics of opening the system is seen. In particular the Δ3(L ) statistic, the width distribution and the level spacing are examined as a function of the strength of this coupling. The emergence of a super-radiant transition is observed. The level spacing and Δ3(L ) statistics exhibit the signatures of missed levels or intruder levels as the super-radiant state is formed.
Heavy-tailed chiral random matrix theory
Kanazawa, Takuya
2016-05-01
We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model analytically and obtain the microscopic spectral density and the smallest eigenvalue distribution for an arbitrary number of flavors and arbitrary quark masses. Exotic behaviors such as non-decoupling of heavy flavors and a power-law tail of the smallest eigenvalue distribution are illustrated.
Pseudo-Hermitian random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Srivastava, S.C.L. [RIBFG, Variable Energy Cyclotron Centre, 1/AF Bidhan nagar, Kolkata-700 064 (India); Jain, S.R. [NPD, Bhabha Atomic Research Centre, Mumbai-400 085 (India)
2013-02-15
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statistical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
2016-07-01
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.
Energy Technology Data Exchange (ETDEWEB)
Nagata, Keitaro [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Nishimura, Jun [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Department of Particle and Nuclear Physics, School of High Energy Accelerator Science,Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba 305-0801 (Japan); Shimasaki, Shinji [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2016-07-14
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.
Deghosting based on the transmission matrix method
Wang, Benfeng; Wu, Ru-Shan; Chen, Xiaohong
2017-12-01
As the developments of seismic exploration and subsequent seismic exploitation advance, marine acquisition systems with towed streamers become an important seismic data acquisition method. But the existing air–water reflective interface can generate surface related multiples, including ghosts, which can affect the accuracy and performance of the following seismic data processing algorithms. Thus, we derive a deghosting method from a new perspective, i.e. using the transmission matrix (T-matrix) method instead of inverse scattering series. The T-matrix-based deghosting algorithm includes all scattering effects and is convergent absolutely. Initially, the effectiveness of the proposed method is demonstrated using synthetic data obtained from a designed layered model, and its noise-resistant property is also illustrated using noisy synthetic data contaminated by random noise. Numerical examples on complicated data from the open SMAART Pluto model and field marine data further demonstrate the validity and flexibility of the proposed method. After deghosting, low frequency components are recovered reasonably and the fake high frequency components are attenuated, and the recovered low frequency components will be useful for the subsequent full waveform inversion. The proposed deghosting method is currently suitable for two-dimensional towed streamer cases with accurate constant depth information and its extension into variable-depth streamers in three-dimensional cases will be studied in the future.
Random Vector and Matrix Theories: A Renormalization Group Approach
Zinn-Justin, Jean
2014-09-01
Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix theory, tackled with increasingly sophisticated mathematical methods and number of matrix models have been solved exactly. However, the somewhat paradoxical situation is that either models can be solved exactly or little can be said. Since the solved models display critical points and universal properties, it is tempting to use renormalization group ideas to determine universal properties, without solving models explicitly. Initiated by Br\\'ezin and Zinn-Justin, the approach has led to encouraging results, first for matrix integrals and then quantum mechanics with matrices, but has not yet become a universal tool as initially hoped. In particular, general quantum field theories with matrix fields require more detailed investigations. To better understand some of the encountered difficulties, we first apply analogous ideas to the simpler O(N) symmetric vector models, models that can be solved quite generally in the large N limit. Unlike other attempts, our method is a close extension of Br\\'ezin and Zinn-Justin. Discussing vector and matrix models with similar approximation scheme, we notice that in all cases (vector and matrix integrals, vector and matrix path integrals in the local approximation), at leading order, non-trivial fixed points satisfy the same universal algebraic equation, and this is the main result of this work. However, its precise meaning and role have still to be better understood.
Action correlations and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Smilansky, Uzy; Verdene, Basile [Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100 (Israel)
2003-03-28
The correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin, and which appear in the spectra of actions of the classical periodic orbits of the corresponding classical systems. We review this duality and the semiclassical theory which brings it about. The conjecture that the quantum spectral statistics are described in terms of random matrix theory, leads to the proposition that the classical two-point correlation function is also given in terms of a universal function. We study in detail the spectrum of actions of the Baker map, and use it to illustrate the steps needed to reveal the classical correlations, their origin and their relation to symbolic dynamics00.
Quantum graphs and random-matrix theory
Pluhař, Z.; Weidenmüller, H. A.
2015-07-01
For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P,Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size.
Raney Distributions and Random Matrix Theory
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.
Random matrix theory and three-dimensional QCD
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, J.J.M.; Zahed, I. (Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States))
1994-10-24
We suggest that the spectral properties near zero virtuality of three-dimensional QCD follow from a Hermitian random matrix model. The exact spectral density is derived for this family of random matrix models for both even and odd number of fermions. New sum rules for the inverse powers of the eigenvalues of the Dirac operator are obtained. The issue of anomalies in random matrix theories is discussed.
Neutron resonance data exclude random matrix theory
Koehler, P. E.; Bečvář, F.; Krtička, M.; Guber, K. H.; Ullmann, J. L.
2013-02-01
Almost since the time it was formulated, the overwhelming consensus has been that random matrix theory (RMT) is in excellent agreement with neutron resonance data. However, over the past few years, we have obtained new neutron-width data at Oak Ridge and Los Alamos National Laboratories that are in stark disagreement with this theory. We also have reanalyzed neutron widths in the most famous data set, the nuclear data ensemble (NDE), and found that it is seriously flawed, and, when analyzed carefully, excludes RMT with high confidence. More recently, we carefully examined energy spacings for these same resonances in the NDE using the $\\Delta_{3}$ statistic. We conclude that the data can be found to either confirm or refute the theory depending on which nuclides and whether known or suspected p-wave resonances are included in the analysis, in essence confirming results of our neutron-width analysis of the NDE. We also have examined radiation widths resulting from our Oak Ridge and Los Alamos measurements, and find that in some cases they do not agree with RMT. Although these disagreements presently are not understood, they could have broad impact on basic and applied nuclear physics, from nuclear astrophysics to nuclear criticality safety.
Neutron resonance data exclude random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Koehler, P.E. [Physics Division, Oak Ridge National Laboratory, MailStop 6356, Oak Ridge, Tennessee 37831 (United States); Becvar, F.; Krticka, M. [Charles University, Faculty of Mathematics and Physics, 180 00 Prague 8 (Czech Republic); Guber, K.H. [Reactor and Nuclear Systems Division, Oak Ridge National Laboratory, Mail Stop 6356, Oak Ridge, Tennessee 37831 (United States); Ullmann, J.L. [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2013-02-15
Almost since the time it was formulated, the overwhelming consensus has been that random matrix theory (RMT) is in excellent agreement with neutron resonance data. However, over the past few years, we have obtained new neutron-width data at Oak Ridge and Los Alamos National Laboratories that are in stark disagreement with this theory. We also have reanalyzed neutron widths in the most famous data set, the nuclear data ensemble (NDE), and found that it is seriously flawed, and, when analyzed carefully, excludes RMT with high confidence. More recently, we carefully examined energy spacings for these same resonances in the NDE using the {Delta}{sub 3} statistic. We conclude that the data can be found to either confirm or refute the theory depending on which nuclides and whether known or suspected p-wave resonances are included in the analysis, in essence confirming results of our neutron-width analysis of the NDE. We also have examined radiation widths resulting from our Oak Ridge and Los Alamos measurements, and find that in some cases they do not agree with RMT. Although these disagreements presently are not understood, they could have broad impact on basic and applied nuclear physics, from nuclear astrophysics to nuclear criticality safety. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Group theory for embedded random matrix ensembles
Kota, V. K. B.
2015-04-01
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say m fermions (or bosons) in N single particle states and interacting with say k-body interactions, we have EGUE(k) [embedded GUE of k-body interactions) with GUE embedding and the embedding algebra is U(N). In this paper, using EGUE(k) representation for a Hamiltonian that is fc-body and an independent EGUE(t) representation for a transition operator that is t-body and employing the embedding U(N) algebra, finite-N formulas for moments up to order four are derived, for the first time, for the transition strength densities (transition strengths multiplied by the density of states at the initial and final energies). In the asymptotic limit, these formulas reduce to those derived for the EGOE version and establish that in general bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extension of these results for other types of transition operators and EGUE ensembles with further symmetries are discussed.
Corner Transfer Matrix Renormalization Group Method
Nishino, T.; Okunishi, K.
1995-01-01
We propose a new fast numerical renormalization group method,the corner transfer matrix renormalization group (CTMRG) method, which is based on a unified scheme of Baxter's corner transfer matrix method and White's density matrix renormalization groupmethod. The key point is that a product of four corner transfer matrices gives the densitymatrix. We formulate the CTMRG method as a renormalization of 2D classical models.
Discrete Painlev\\'e equations and random matrix averages
Forrester, P. J.; Witte, N. S.
2003-01-01
The $\\tau$-function theory of Painlev\\'e systems is used to derive recurrences in the rank $n$ of certain random matrix averages over U(n). These recurrences involve auxilary quantities which satisfy discrete Painlev\\'e equations. The random matrix averages include cases which can be interpreted as eigenvalue distributions at the hard edge and in the bulk of matrix ensembles with unitary symmetry. The recurrences are illustrated by computing the value of a sequence of these distributions as $...
Nonequilibrium random matrix theory: Transition probabilities
Pedro, Francisco Gil; Westphal, Alexander
2017-03-01
In this paper we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
Matrix Krylov subspace methods for image restoration
Directory of Open Access Journals (Sweden)
khalide jbilou
2015-09-01
Full Text Available In the present paper, we consider some matrix Krylov subspace methods for solving ill-posed linear matrix equations and in those problems coming from the restoration of blurred and noisy images. Applying the well known Tikhonov regularization procedure leads to a Sylvester matrix equation depending the Tikhonov regularized parameter. We apply the matrix versions of the well known Krylov subspace methods, namely the Least Squared (LSQR and the conjugate gradient (CG methods to get approximate solutions representing the restored images. Some numerical tests are presented to show the effectiveness of the proposed methods.
On the Subspace Projected Approximate Matrix method
Brandts, J.H.; Reis da Silva, R.
2015-01-01
We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method of computing a few eigenvalues of a Hermitian matrix A. It falls in the category of inner-outer iteration methods and aims to reduce the costs of
Particle diagrams and embedded many-body random matrix theory
Small, R. A.; Müller, S.
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ≤m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k=m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k=m,3k=m,...,nk=m.
Spectral rigidity of vehicular streams (random matrix theory approach)
Energy Technology Data Exchange (ETDEWEB)
Krbalek, Milan [Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Prague (Czech Republic); Seba, Petr [Doppler Institute for Mathematical Physics and Applied Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Prague (Czech Republic)
2009-08-28
Using a method originally developed for the random matrix theory, we derive an approximate mathematical formula for the number variance {delta}{sub N}(L) describing the rigidity of particle ensembles with a power-law repulsion. The resulting relation is compared with the relevant statistics of the single-vehicle data measured on the Dutch freeway A9. The detected value of the inverse temperature {beta}, which can be identified as a coefficient of the mental strain of the car drivers, is then discussed in detail with the relation to the traffic density {rho} and flow J.
Application of Random Matrix Theory to Complex Networks
Rai, Aparna; Jalan, Sarika
The present article provides an overview of recent developments in spectral analysis of complex networks under random matrix theory framework. Adjacency matrix of unweighted networks, reviewed here, differ drastically from a random matrix, as former have only binary entries. Remarkably, short range correlations in corresponding eigenvalues of such matrices exhibit Gaussian orthogonal statistics of RMT and thus bring them into the universality class. Spectral rigidity of spectra provides measure of randomness in underlying networks. We will consider several examples of model networks vastly studied in last two decades. To the end we would provide potential of RMT framework and obtained results to understand and predict behavior of complex systems with underlying network structure.
Charting an Inflationary Landscape with Random Matrix Theory
Energy Technology Data Exchange (ETDEWEB)
Marsh, M.C. David [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP (United Kingdom); McAllister, Liam [Department of Physics, Cornell University, Ithaca, NY 14853 (United States); Pajer, Enrico [Department of Physics, Princeton University, Princeton, NJ 08544 (United States); Wrase, Timm, E-mail: david.marsh1@physics.ox.ac.uk, E-mail: mcallister@cornell.edu, E-mail: epajer@princeton.edu, E-mail: timm.wrase@stanford.edu [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305 (United States)
2013-11-01
We construct a class of random potentials for N >> 1 scalar fields using non-equilibrium random matrix theory, and then characterize multifield inflation in this setting. By stipulating that the Hessian matrices in adjacent coordinate patches are related by Dyson Brownian motion, we define the potential in the vicinity of a trajectory. This method remains computationally efficient at large N, permitting us to study much larger systems than has been possible with other constructions. We illustrate the utility of our approach with a numerical study of inflation in systems with up to 100 coupled scalar fields. A significant finding is that eigenvalue repulsion sharply reduces the duration of inflation near a critical point of the potential: even if the curvature of the potential is fine-tuned to be small at the critical point, small cross-couplings in the Hessian cause the curvature to grow in the neighborhood of the critical point.
Quantum Chaos and Random Matrix Theory Some New Results
Smilansky, U
1996-01-01
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which are the quantum versions of area preserving maps. The relevant Random Matrix ensembles are the Circular ensembles. The resulting semiclassical expressions depend on the symmetry of the system with respect to time reversal, and on a classical parameter $\\mu = tr U -1$ where U is the classical 1-step evolution operator. For system without time reversal symmetry, we are able to reproduce the exact Random Matrix predictions in the limit $\\mu \\to 0$. For systems with time reversal symmetry we can reproduce only some of the features of Random Matrix Theory. For both classes we obtain the leading corrections in $\\mu$. The semiclassical theory for integrable systems is also developed, resulting in expressions which reproduce the theory for the Poissonian ensemble to leading order i...
Vibrations in glasses and Euclidean random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Grigera, T.S.; Martin-Mayor, V.; Parisi, G. [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Rome (Italy); INFN Sezione di Roma - INFM Unita di Roma, Rome (Italy); Verrocchio, P. [Dipartimento di Fisica, Universita di Trento, Povo, Trento (Italy); INFM Unita di Trento, Trento (Italy)
2002-03-11
We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin peak, boson peak and secondary peak), Euclidean random matrix theory provides a single and fairly simple theoretical framework for their explanation. (author)
Random matrix model for disordered conductors
Indian Academy of Sciences (India)
1. Introduction. Matrix models are being successfully employed in a variety of domains of physics includ- ing studies on heavy nuclei [1], mesoscopic disordered conductors [2,3], two-dimensional quantum gravity [4], and chaotic quantum systems [5]. Universal conductance fluctuations in metals [6] and spectral fluctuations in ...
Spectra of large time-lagged correlation matrices from random matrix theory
Nowak, Maciej A.; Tarnowski, Wojciech
2017-06-01
We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing the methods of free random variables and diagrammatic techniques, we solve a general random matrix problem, namely the spectrum of a matrix \\frac{1}{T}XA{{X}\\dagger} , where X is an N× T Gaussian random matrix and A is any T× T , not necessarily symmetric (Hermitian) matrix. Using this result, we study the spectral features of the large lagged correlation matrices as a function of the depth of the time-lag. We also analyze the properties of left and right eigenvector correlations for the time-lagged matrices. We positively verify our results by the numerical simulations.
Low-temperature random matrix theory at the soft edge
Energy Technology Data Exchange (ETDEWEB)
Edelman, Alan [Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Persson, Per-Olof [Department of Mathematics, University of California, Berkeley, California 94720 (United States); Sutton, Brian D. [Department of Mathematics, Randolph-Macon College, Ashland, Virginia 23005 (United States)
2014-06-15
“Low temperature” random matrix theory is the study of random eigenvalues as energy is removed. In standard notation, β is identified with inverse temperature, and low temperatures are achieved through the limit β → ∞. In this paper, we derive statistics for low-temperature random matrices at the “soft edge,” which describes the extreme eigenvalues for many random matrix distributions. Specifically, new asymptotics are found for the expected value and standard deviation of the general-β Tracy-Widom distribution. The new techniques utilize beta ensembles, stochastic differential operators, and Riccati diffusions. The asymptotics fit known high-temperature statistics curiously well and contribute to the larger program of general-β random matrix theory.
Low-temperature random matrix theory at the soft edge
Edelman, Alan; Persson, Per-Olof; Sutton, Brian D.
2014-06-01
"Low temperature" random matrix theory is the study of random eigenvalues as energy is removed. In standard notation, β is identified with inverse temperature, and low temperatures are achieved through the limit β → ∞. In this paper, we derive statistics for low-temperature random matrices at the "soft edge," which describes the extreme eigenvalues for many random matrix distributions. Specifically, new asymptotics are found for the expected value and standard deviation of the general-β Tracy-Widom distribution. The new techniques utilize beta ensembles, stochastic differential operators, and Riccati diffusions. The asymptotics fit known high-temperature statistics curiously well and contribute to the larger program of general-β random matrix theory.
Matrix method for acoustic levitation simulation.
Andrade, Marco A B; Perez, Nicolas; Buiochi, Flavio; Adamowski, Julio C
2011-08-01
A matrix method is presented for simulating acoustic levitators. A typical acoustic levitator consists of an ultrasonic transducer and a reflector. The matrix method is used to determine the potential for acoustic radiation force that acts on a small sphere in the standing wave field produced by the levitator. The method is based on the Rayleigh integral and it takes into account the multiple reflections that occur between the transducer and the reflector. The potential for acoustic radiation force obtained by the matrix method is validated by comparing the matrix method results with those obtained by the finite element method when using an axisymmetric model of a single-axis acoustic levitator. After validation, the method is applied in the simulation of a noncontact manipulation system consisting of two 37.9-kHz Langevin-type transducers and a plane reflector. The manipulation system allows control of the horizontal position of a small levitated sphere from -6 mm to 6 mm, which is done by changing the phase difference between the two transducers. The horizontal position of the sphere predicted by the matrix method agrees with the horizontal positions measured experimentally with a charge-coupled device camera. The main advantage of the matrix method is that it allows simulation of non-symmetric acoustic levitators without requiring much computational effort.
A generalization of random matrix theory and its application to statistical physics
Wang, Duan; Zhang, Xin; Horvatic, Davor; Podobnik, Boris; Eugene Stanley, H.
2017-02-01
To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities.
Random-matrix theory of quantum transport
Energy Technology Data Exchange (ETDEWEB)
Beenakker, C.W. [Instituut-Lorentz, University of Leiden, 2300 RA Leiden, (The Netherlands)
1997-07-01
This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined region with a chaotic classical dynamics, which is coupled to two electron reservoirs via point contacts. The disordered wire also connects two reservoirs, either directly or via a point contact or tunnel barrier. One of the two reservoirs may be in the superconducting state, in which case conduction involves Andreev reflection at the interface with the superconductor. In the case of the quantum dot, the distribution of the scattering matrix is given by either Dyson{close_quote}s circular ensemble for ballistic point contacts or the Poisson kernel for point contacts containing a tunnel barrier. In the case of the disordered wire, the distribution of the scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation. The equivalence is discussed with the nonlinear {sigma} model, which is a supersymmetric field theory of localization. The distribution of scattering matrices is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction. {copyright} {ital 1997} {ital The American Physical Society}
Typicality in random matrix product states
Garnerone, Silvano; de Oliveira, Thiago R.; Zanardi, Paolo
2010-03-01
Recent results suggest that the use of ensembles in statistical mechanics may not be necessary for isolated systems, since typically the states of the Hilbert space would have properties similar to those of the ensemble. Nevertheless, it is often argued that most of the states of the Hilbert space are nonphysical and not good descriptions of realistic systems. Therefore, to better understand the actual power of typicality it is important to ask if it is also a property of a set of physically relevant states. Here we address this issue, studying if and how typicality emerges in the set of matrix product states. We show analytically that typicality occurs for the expectation value of subsystems’ observables when the rank of the matrix product state scales polynomially with the size of the system with a power greater than 2. We illustrate this result numerically and present some indications that typicality may appear already for a linear scaling of the rank of the matrix product state.
Considering Horn’s parallel analysis from a random matrix theory point of view
Saccenti, Edoardo; Timmerman, Marieke E.
Horn’s parallel analysis is a widely used method for assessing the number of principal components and common factors. We discuss the theoretical foundations of parallel analysis for principal components based on a covariance matrix by making use of arguments from random matrix theory. In particular,
Considering Horn’s Parallel Analysis from a Random Matrix Theory Point of View
Saccenti, Edoardo; Timmerman, Marieke E.
2017-01-01
Horn’s parallel analysis is a widely used method for assessing the number of principal components and common factors. We discuss the theoretical foundations of parallel analysis for principal components based on a covariance matrix by making use of arguments from random matrix theory. In
Random matrix theory for pseudo-Hermitian systems: Cyclic blocks
Indian Academy of Sciences (India)
We discuss the relevance of random matrix theory for pseudo-Hermitian systems, and, for Hamiltonians that break parity and time-reversal invariance . In an attempt to understand the random Ising model, we present the treatment of cyclic asymmetric matrices with blocks and show that the nearest-neighbour spacing ...
Random matrix theory for heavy-tailed time series
DEFF Research Database (Denmark)
Heiny, Johannes
2017-01-01
This paper is a review of recent results for large random matrices with heavy-tailed entries. First, we outline the development of and some classical results in random matrix theory. We focus on large sample covariance matrices, their limiting spectral distributions, the asymptotic behavior...... of their largest and smallest eigenvalues and their eigenvectors. The limits significantly depend on the finite or infiniteness of the fourth moment of the entries of the random matrix. We compare the results for these two regimes which give rise to completely different asymptotic theories. Finally, the limits...
Interface matrix method in AFEN framework
Energy Technology Data Exchange (ETDEWEB)
Pogosbekyan, Leonid; Cho, Jin Young; Kim, Young Jin [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-12-31
In this study, we extend the application of the interface-matrix(IM) method for reflector modeling to Analytic Flux Expansion Nodal (AFEN) method. This include the modifications of the surface-averaged net current continuity and the net leakage balance conditions for IM method in accordance with AFEN formula. AFEN-interface matrix (AFEN-IM) method has been tested against ZION-1 benchmark problem. The numerical result of AFEN-IM method shows 1.24% of maximum error and 0.42% of root-mean square error in assembly power distribution, and 0.006% {Delta} k of neutron multiplication factor. This result proves that the interface-matrix method for reflector modeling can be useful in AFEN method. 3 refs., 4 figs. (Author)
Random discrete Schroedinger operators from random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Breuer, Jonathan [Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Forrester, Peter J [Department of Mathematics and Statistics, University of Melbourne, Parkville, Vic 3010 (Australia); Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute, Rehovot 76100 (Israel)
2007-02-02
We investigate random, discrete Schroedinger operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature {beta}. They are similar to the class of 'critical' random Schroedinger operators with random potentials which diminish as vertical bar x vertical bar{sup -1/2}. We show that as a function of {beta} they undergo a transition from a regime of (power-law) localized eigenstates with a pure point spectrum for {beta} < 2 to a regime of extended states with a singular continuous spectrum for {beta} {>=} 2. (fast track communication)
Cleaning large correlation matrices: Tools from Random Matrix Theory
Bun, Joël; Bouchaud, Jean-Philippe; Potters, Marc
2017-01-01
This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marčenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.
Matrix Recipes for Hard Thresholding Methods
Kyrillidis, Anastasios
2012-01-01
Given a set of possibly corrupted and incomplete linear measurements, we leverage low-dimensional models to best explain the data for provable solution quality in inversion. A non-exhaustive list of examples includes sparse vector and low-rank matrix approximation. Most of the well-known low dimensional models are inherently non-convex. However, recent approaches prefer convex surrogates that "relax" the problem in order to establish solution uniqueness and stability. In this paper, we tackle the linear inverse problems revolving around low-rank matrices by preserving their non-convex structure. To this end, we present and analyze a new set of sparse and low-rank recovery algorithms within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic "ingredients" for different configurations to achieve complexity vs. accuracy tradeoffs. Moreover, we propose acceleration schemes by utilizing memory-based techniques and randomized, $\\epsilon$-approximate, low-rank pr...
From gap probabilities in random matrix theory to eigenvalue expansions
Bothner, Thomas
2016-02-01
We present a method to derive asymptotics of eigenvalues for trace-class integral operators K :{L}2(J;{{d}}λ )\\circlearrowleft , acting on a single interval J\\subset {{R}}, which belongs to the ring of integrable operators (Its et al 1990 Int. J. Mod. Phys. B 4 1003-37 ). Our emphasis lies on the behavior of the spectrum \\{{λ }i(J)\\}{}i=0∞ of K as | J| \\to ∞ and i is fixed. We show that this behavior is intimately linked to the analysis of the Fredholm determinant {det}(I-γ K){| }{L2(J)} as | J| \\to ∞ and γ \\uparrow 1 in a Stokes type scaling regime. Concrete asymptotic formulæ are obtained for the eigenvalues of Airy and Bessel kernels in random matrix theory. Dedicated to Percy Deift and Craig Tracy on the occasion of their 70th birthdays.
Vempala, Santosh S
2005-01-01
Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout. Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neig...
Blind Measurement Selection: A Random Matrix Theory Approach
Elkhalil, Khalil
2016-12-14
This paper considers the problem of selecting a set of $k$ measurements from $n$ available sensor observations. The selected measurements should minimize a certain error function assessing the error in estimating a certain $m$ dimensional parameter vector. The exhaustive search inspecting each of the $n\\\\choose k$ possible choices would require a very high computational complexity and as such is not practical for large $n$ and $k$. Alternative methods with low complexity have recently been investigated but their main drawbacks are that 1) they require perfect knowledge of the measurement matrix and 2) they need to be applied at the pace of change of the measurement matrix. To overcome these issues, we consider the asymptotic regime in which $k$, $n$ and $m$ grow large at the same pace. Tools from random matrix theory are then used to approximate in closed-form the most important error measures that are commonly used. The asymptotic approximations are then leveraged to select properly $k$ measurements exhibiting low values for the asymptotic error measures. Two heuristic algorithms are proposed: the first one merely consists in applying the convex optimization artifice to the asymptotic error measure. The second algorithm is a low-complexity greedy algorithm that attempts to look for a sufficiently good solution for the original minimization problem. The greedy algorithm can be applied to both the exact and the asymptotic error measures and can be thus implemented in blind and channel-aware fashions. We present two potential applications where the proposed algorithms can be used, namely antenna selection for uplink transmissions in large scale multi-user systems and sensor selection for wireless sensor networks. Numerical results are also presented and sustain the efficiency of the proposed blind methods in reaching the performances of channel-aware algorithms.
Nonextensive random-matrix theory based on Kaniadakis entropy
Abul-Magd, A. Y.
2006-01-01
The joint eigenvalue distributions of random-matrix ensembles are derived by applying the principle maximum entropy to the Renyi, Abe and Kaniadakis entropies. While the Renyi entropy produces essentially the same matrix-element distributions as the previously obtained expression by using the Tsallis entropy, and the Abe entropy does not lead to a closed form expression, the Kaniadakis entropy leads to a new generalized form of the Wigner surmise that describes a transition of the spacing dis...
Enumeration of RNA complexes via random matrix theory
DEFF Research Database (Denmark)
Andersen, Jørgen E; Chekhov, Leonid O.; Penner, Robert C
2013-01-01
In the present article, we review a derivation of the numbers of RNA complexes of an arbitrary topology. These numbers are encoded in the free energy of the Hermitian matrix model with potential V(x)=x(2)/2 - stx/(1 - tx), where s and t are respective generating parameters for the number of RNA...... molecules and hydrogen bonds in a given complex. The free energies of this matrix model are computed using the so-called topological recursion, which is a powerful new formalism arising from random matrix theory. These numbers of RNA complexes also have profound meaning in mathematics: they provide...
Error Analysis of Band Matrix Method
Taniguchi, Takeo; Soga, Akira
1984-01-01
Numerical error in the solution of the band matrix method based on the elimination method in single precision is investigated theoretically and experimentally, and the behaviour of the truncation error and the roundoff error is clarified. Some important suggestions for the useful application of the band solver are proposed by using the results of above error analysis.
Random matrix analysis for gene interaction networks in cancer cells
Kikkawa, Ayumi
2016-01-01
Motivation: The investigation of topological modifications of the gene interaction networks in cancer cells is essential for understanding the desease. We study gene interaction networks in various human cancer cells with the random matrix theory. This study is based on the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by Bayesian network algorithms from 256 microarray experimental data downloaded from NCBI GEO. The original GEO data are provided by the high-throughput microarray expression experiments on various human cancer cells. We apply the random matrix theory to the computationally inferred gene interaction networks in TCNG in order to detect the universality in the topology of the gene interaction networks in cancer cells. Results: We found the universal behavior in almost one half of the 256 gene interaction networks in TCNG. The distribution of nearest neighbor level spacing of the gene interaction matrix becomes the Wigner distribution when the net...
Optimum allocation in multivariate stratified random sampling: Stochastic matrix optimisation
Diaz-Garcia, Jose A.; Ramos-Quiroga, Rogelio
2011-01-01
The allocation problem for multivariate stratified random sampling as a problem of stochastic matrix integer mathematical programming is considered. With these aims the asymptotic normality of sample covariance matrices for each strata is established. Some alternative approaches are suggested for its solution. An example is solved by applying the proposed techniques.
QCD Dirac spectra with and without random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Damgaard, P.H. [Niels Bohr Institute, Copenhagen (Denmark)
1999-07-01
Recent work on the spectrum of the Euclidean Dirac operator spectrum show that the exact microscopic spectral density can be computed in both random matrix theory, and directly from field theory. Exact relations to effective Lagrangians with additional quark species form the bridge between the two formulations. (author)
Partial Discharge Detection and Recognition in Random Matrix Theory Paradigm
National Research Council Canada - National Science Library
Luo, Lingen; Han, Bei; Chen, Jingde; Sheng, Gehao; Jiang, Xiuchen
.... Take advantage of the affluent results from random matrix theory (RMT), such as eigenvalue analysis, M-P law, the ring law, and so on, a novel methodology in RMT paradigm is proposed for fast PD pulse detection in this paper...
Applications of Random Matrix Ensembles in Nuclear Systems
Duras, Maciej M.
2003-01-01
The random matrix ensembles (RME), especially Gaussian RME and Ginibre RME, are applied to nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated.
Random matrix theory approach to vibrations near the jamming transition
Beltukov, Y. M.
2015-03-01
It has been shown that the dynamical matrix M describing harmonic oscillations in granular media can be represented in the form M = AA T, where the rows of the matrix A correspond to the degrees of freedom of individual granules and its columns correspond to elastic contacts between granules. Such a representation of the dynamical matrix makes it possible to estimate the density of vibrational states with the use of the random matrix theory. The found density of vibrational states is approximately constant in a wide frequency range ω- < ω < ω+, which is determined by the ratio of the number of degrees of freedom to the total number of contacts in the system, which is in good agreement with the results of the numerical experiments.
Aluminium matrix composites fabricated by infiltration method
L.A. Dobrzański; M. Kremzer; A.J. Nowak; Nagel, A.
2009-01-01
Purpose: The aim of this work is to examine the structure and properties of metal matrix composites obtained by infiltration method of porous ceramic preforms by liquid aluminium alloy.Design/methodology/approach: Ceramic preforms were manufactured by the sintering method of ceramic powder. The preform material consists of powder Condea Al2O3 CL 2500, however, as the pore forming the carbon fibers Sigrafil C10 M250 UNS were used. Then ceramic preforms were infiltrated with liquid eutectic EN ...
Porcine collagen matrix for treating gingival recession. Randomized clinical trial.
Directory of Open Access Journals (Sweden)
Yuri Castro
2014-03-01
Full Text Available Achieving root coverage after exposure caused by gingival recession is one of the main goals of reconstructive periodontal surgery. Even though a large variety of techniques and mucogingival grafting procedures are available, their long-term results are not clear yet. Therefore, this study aimed to compare clinical effectiveness of the porcine collagen matrix with subepithelial connective graft for treating Miller class I and II gingival recessions. Materials and methods: The randomized clinical trial included twelve patients assigned to two groups. In the first group (experimental, six patients were treated using collagen matrix (mean age, 54.3±5.6 years; mean recession 2. 67±1.03mm. Another group (control of six patients was treated using connective grafts (mean age, 57.1± 2.7 years; mean recession 4.33±1.03mm. All patients underwent periodontal evaluation and pre-surgical preparation including oral hygiene instruction and supragingival scaling. Gingival recessions were exposed through partial thickness flaps where the grafts and matrices were placed. Patients were assessed periodically until complete healing of tissue. Results: Root coverage parameters, amount of keratinized gingiva, gingival biotype and clinical attachment level were evaluated. The root coverage percentage for the group using connective graft was 24.7±13.5% and 16.6±26.8% for the one treated with the matrix. The amount of increased keratinized tissue was 4.33±2.06mm and 4.5±0.83mm for the control and experimental group respectively. Both groups increased gingival biotypes from thin to thick at 100%. The final clinical attachment level was 4.17±3.17±04mm for the control group and 0.98mm for the experimental group. There were significant differences between the outcome of gingival recession and clinical attachment. Conclusion: Results indicate both techniques, besides being predictable, are useful for improving clinical parameters when treating gingival recessions
A Secure LFSR Based Random Measurement Matrix for Compressive Sensing
George, Sudhish N.; Pattathil, Deepthi P.
2014-11-01
In this paper, a novel approach for generating the secure measurement matrix for compressive sensing (CS) based on linear feedback shift register (LFSR) is presented. The basic idea is to select the different states of LFSR as the random entries of the measurement matrix and normalize these values to get independent and identically distributed (i.i.d.) random variables with zero mean and variance , where N is the number of input samples. The initial seed for the LFSR system act as the key to the user to provide security. Since the measurement matrix is generated from the LFSR system, and memory overload to store the measurement matrix is avoided in the proposed system. Moreover, the proposed system can provide security maintaining the robustness to noise of the CS system. The proposed system is validated through different block-based CS techniques of images. To enhance security, the different blocks of images are measured with different measurement matrices so that the proposed encryption system can withstand known plaintext attack. A modulo division circuit is used to reseed the LFSR system to generate multiple random measurement matrices, whereby after each fundamental period of LFSR, the feedback polynomial of the modulo circuit is modified in terms of a chaotic value. The proposed secure robust CS paradigm for images is subjected to several forms of attacks and is proven to be resistant against the same. From experimental analysis, it is proven that the proposed system provides better performance than its counterparts.
Random matrix approach to the distribution of genomic distance.
Alexeev, Nikita; Zograf, Peter
2014-08-01
The cycle graph introduced by Bafna and Pevzner is an important tool for evaluating the distance between two genomes, that is, the minimal number of rearrangements needed to transform one genome into another. We interpret this distance in topological terms and relate it to the random matrix theory. Namely, the number of genomes at a given 2-break distance from a fixed one (the Hultman number) is represented by a coefficient in the genus expansion of a matrix integral over the space of complex matrices with the Gaussian measure. We study generating functions for the Hultman numbers and prove that the two-break distance distribution is asymptotically normal.
Random matrix theory and portfolio optimization in Moroccan stock exchange
El Alaoui, Marwane
2015-09-01
In this work, we use random matrix theory to analyze eigenvalues and see if there is a presence of pertinent information by using Marčenko-Pastur distribution. Thus, we study cross-correlation among stocks of Casablanca Stock Exchange. Moreover, we clean correlation matrix from noisy elements to see if the gap between predicted risk and realized risk would be reduced. We also analyze eigenvectors components distributions and their degree of deviations by computing the inverse participation ratio. This analysis is a way to understand the correlation structure among stocks of Casablanca Stock Exchange portfolio.
Nonextensive random-matrix theory based on Kaniadakis entropy
Abul-Magd, A. Y.
2007-02-01
The joint eigenvalue distributions of random-matrix ensembles are derived by applying the principle maximum entropy to the Rényi, Abe and Kaniadakis entropies. While the Rényi entropy produces essentially the same matrix-element distributions as the previously obtained expression by using the Tsallis entropy, and the Abe entropy does not lead to a closed form expression, the Kaniadakis entropy leads to a new generalized form of the Wigner surmise that describes a transition of the spacing distribution from chaos to order. This expression is compared with the corresponding expression obtained by assuming Tsallis' entropy as well as the results of a previous numerical experiment.
Nonextensive random-matrix theory based on Kaniadakis entropy
Energy Technology Data Exchange (ETDEWEB)
Abul-Magd, A.Y. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)]. E-mail: a_y_abul_magd@hotmail.com
2007-02-12
The joint eigenvalue distributions of random-matrix ensembles are derived by applying the principle maximum entropy to the Renyi, Abe and Kaniadakis entropies. While the Renyi entropy produces essentially the same matrix-element distributions as the previously obtained expression by using the Tsallis entropy, and the Abe entropy does not lead to a closed form expression, the Kaniadakis entropy leads to a new generalized form of the Wigner surmise that describes a transition of the spacing distribution from chaos to order. This expression is compared with the corresponding expression obtained by assuming Tsallis' entropy as well as the results of a previous numerical experiment.
van der Heijden, P.G.M.; Cruyff, Maarten; Bockenholt, U.
2014-01-01
In survey research it is often problematic to ask people sensitive questions because they may refuse to answer or they may provide a socially desirable answer that does not reveal their true status on the sensitive question. To solve this problem Warner (1965) proposed randomized response (RR). Here
Super Yang-Mills theory as a random matrix model
Energy Technology Data Exchange (ETDEWEB)
Siegel, W. [Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794-3840 (United States)
1995-07-15
We generalize the Gervais-Neveu gauge to four-dimensional {ital N}=1 superspace. The model describes an {ital N}=2 super Yang-Mills theory. All chiral superfields ({ital N}=2 matter and ghost multiplets) exactly cancel to all loops. The remaining Hermitian scalar superfield (matrix) has a renormalizable massive propagator and simplified vertices. These properties are associated with {ital N}=1 supergraphs describing a superstring theory on a random lattice world sheet. We also consider all possible finite matrix models, and find they have a universal large-color limit. These could describe gravitational strings if the matrix-model coupling is fixed to unity, for exact electric-magnetic self-duality.
ABCD Matrix Method a Case Study
Seidov, Zakir F; Yahalom, Asher
2004-01-01
In the Israeli Electrostatic Accelerator FEL, the distance between the accelerator's end and the wiggler's entrance is about 2.1 m, and 1.4 MeV electron beam is transported through this space using four similar quadrupoles (FODO-channel). The transfer matrix method (ABCD matrix method) was used for simulating the beam transport, a set of programs is written in the several programming languages (MATHEMATICA, MATLAB, MATCAD, MAPLE) and reasonable agreement is demonstrated between experimental results and simulations. Comparison of ABCD matrix method with the direct "numerical experiments" using EGUN, ELOP, and GPT programs with and without taking into account the space-charge effects showed the agreement to be good enough as well. Also the inverse problem of finding emittance of the electron beam at the S1 screen position (before FODO-channel), by using the spot image at S2 screen position (after FODO-channel) as function of quad currents, is considered. Spot and beam at both screens are described as tilted eel...
Random matrix theory, interacting particle systems and integrable systems
Forrester, Peter
2014-01-01
Random matrix theory is at the intersection of linear algebra, probability theory and integrable systems, and has a wide range of applications in physics, engineering, multivariate statistics and beyond. This volume is based on a Fall 2010 MSRI program which generated the solution of long-standing questions on universalities of Wigner matrices and beta-ensembles and opened new research directions especially in relation to the KPZ universality class of interacting particle systems and low-rank perturbations. The book contains review articles and research contributions on all these topics, in addition to other core aspects of random matrix theory such as integrability and free probability theory. It will give both established and new researchers insights into the most recent advances in the field and the connections among many subfields.
Density Functional Approach and Random Matrix Theory in Proteogenesis
Yamanaka, Masanori
2017-02-01
We study the energy-level statistics of amino acids by random matrix theory. The molecular orbital and the Kohn-Sham orbital energies are calculated using ab initio and density-functional formalisms for 20 different amino acids. To generate statistical data, we performed a multipoint calculation on 10000 molecular structures produced via a molecular dynamics simulation. For the valence orbitals, the energy-level statistics exhibit repulsion, but the universality in the random matrix cannot be determined. For the unoccupied orbitals, the energy-level statistics indicate an intermediate distribution between the Gaussian orthogonal ensemble and the semi-Poisson statistics for all 20 different amino acids. These amino acids are considered to be in a type of critical state.
Finitely connected vector spin systems with random matrix interactions
Energy Technology Data Exchange (ETDEWEB)
Coolen, A C C [Department of Mathematics, King' s College London, The Strand, London WC2R 2LS (United Kingdom); Skantzos, N S [Institute for Theoretical Physics, Celestijnenlaan 200D, Katholieke Universiteit Leuven, B-3001 (Belgium); Castillo, I Perez [Rudolf Peierls Center for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP (United Kingdom); Vicente, C J Perez [Departament de FIsica Fonamental, Facultat de FIsica, Universitat de Barcelona, 08028 Barcelona (Spain); Hatchett, J P L [Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Hirosawa 2-1, Wako-Shi, Saitama 351-0198 (Japan); Wemmenhove, B [Department of Medical Physics and Biophysics, Radboud University Nijmegen, Geert Grooteplein 21, NL 6525 EZ Nijmegen (Netherlands); Nikoletopoulos, T [Department of Mathematics, King' s College London, The Strand, London WC2R 2LS (United Kingdom)
2005-09-30
We use finite connectivity equilibrium replica theory to solve models of finitely connected unit-length vectorial spins, with random pair-interactions which are of the orthogonal matrix type. Finitely connected spin models, although still of a mean-field nature, can be regarded as a convenient level of description in between fully connected and finite-dimensional ones. Since the spins are continuous and the connectivity c remains finite in the thermodynamic limit, the replica-symmetric order parameter is a functional. The general theory is developed for arbitrary values of the dimension d of the spins, and arbitrary choices of the ensemble of random orthogonal matrices. We calculate phase diagrams and the values of moments of the order parameter explicitly for d = 2 (finitely connected XY spins with random chiral interactions) and for d = 3 (finitely connected classical Heisenberg spins with random chiral interactions). Numerical simulations are shown to support our predictions quite satisfactorily.
Wigner surmise for mixed symmetry classes in random matrix theory
Schierenberg, Sebastian; Bruckmann, Falk; Wettig, Tilo
2012-06-01
We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes or between integrable and nonintegrable systems. We derive analytical formulas for the spacing distributions of 2×2 or 4×4 matrices and show numerically that they provide very good approximations for those of random matrices with large dimension. This generalizes the Wigner surmise, which is valid for pure ensembles that are recovered as limits of the mixed ensembles. We show how the coupling parameters of small and large matrices must be matched depending on the local eigenvalue density.
Inner structure of vehicular ensembles and random matrix theory
Krbálek, Milan; Hobza, Tomáš
2016-05-01
We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded spectra of DUE matrices) with the time-clearance distribution extracted from various areas of the flux-density diagram (evaluated from original traffic data measured on Czech expressways with high occupancies) we demonstrate that the set of classical systems showing an universality associated with Random Matrix Ensembles can be extended by traffic systems.
Random matrix theory in biological nuclear magnetic resonance spectroscopy.
Lacelle, S
1984-01-01
The statistical theory of energy levels or random matrix theory is presented in the context of the analysis of chemical shifts of nuclear magnetic resonance (NMR) spectra of large biological systems. Distribution functions for the spacing between nearest-neighbor energy levels are discussed for uncorrelated, correlated, and random superposition of correlated energy levels. Application of this approach to the NMR spectra of a vitamin, an antibiotic, and a protein demonstrates the state of correlation of an ensemble of energy levels that characterizes each system. The detection of coherent and dissipative structures in proteins becomes feasible with this statistical spectroscopic technique. PMID:6478032
Random-matrix theory of Majorana fermions and topological superconductors
Beenakker, C. W. J.
2015-07-01
The theory of random matrices originated half a century ago as a universal description of the spectral statistics of atoms and nuclei, dependent only on the presence or absence of fundamental symmetries. Applications to quantum dots (artificial atoms) followed, stimulated by developments in the field of quantum chaos, as well as applications to Andreev billiards—quantum dots with induced superconductivity. Superconductors with topologically protected subgap states, Majorana zero modes, and Majorana edge modes, provide a new arena for applications of random-matrix theory. These recent developments are reviewed, with an emphasis on electrical and thermal transport properties that can probe the Majorana fermions.
Chiral random matrix theory and effective theories of QCD
Energy Technology Data Exchange (ETDEWEB)
Takahashi, K.; Iida, S
2000-05-08
The correlations of the QCD Dirac eigenvalues are studied with use of an extended chiral random matrix model. The inclusion of spatial dependence which the original model lacks enables us to investigate the effects of diffusion modes. We get analytical expressions of level correlation functions with non-universal behavior caused by diffusion modes which is characterized by Thouless energy. Pion mode is shown to be responsible for these diffusion effects when QCD vacuum is considered a disordered medium.
Chiral Random Matrix Theory and Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Damgaard, Poul H, E-mail: phdamg@nbi.dk [Niels Bohr International Academy and Discovery Center, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark)
2011-04-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Comparing lattice Dirac operators with Random Matrix Theory
Energy Technology Data Exchange (ETDEWEB)
Farchioni, F.; Hipt, I.; Lang, C.B
2000-03-01
We study the eigenvalue spectrum of different lattice Dirac operators (staggered, fixed point, overlap) and discuss their dependence on the topological sectors. Although the model is 2D (the Schwinger model with massless fermions) our observations indicate possible problems in 4D applications. In particular misidentification of the smallest eigenvalues due to non-identification of the topological sector may hinder successful comparison with Random Matrix Theory (RMT)
Random matrix theory and the spectra of overlap fermions
Energy Technology Data Exchange (ETDEWEB)
Shcheredin, S.; Bietenholz, W.; Chiarappa, T.; Jansen, K.; Nagai, K.-I
2004-03-01
The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at topological charge {nu} = 0, {+-} 1 and {+-}2, and found agreement with those predictions -- at least for the first non-zero eigenvalue -- if the volume exceeds about (1.2 fm){sup 4}.
Page 1 contents v Random matrix theory and the statistical ...
Indian Academy of Sciences (India)
contents v. Random matrix theory and the statistical mechanics of disordered systems , k. & & & è è & e * * • • • * * * * * * * w * • • s • * • * • • a • » • • • • • • • • « • « Jitendra C Parikh 467—476. Statistical Physics. On information, negentropy and thermostatistics.... C G Chakrabarti 65-72. Connectivity constant of the kagomé lattice.
Generalized Random Matrix Theory:. a Mathematical Probe for Complexity
Shukla, Pragya
2012-07-01
The ubiquitous presence of complexity in nature makes it necessary to seek new mathematical tools which can probe physical systems beyond linear or perturbative approximations. The random matrix theory is one such tool in which the statistical behavior of a system is modeled by an ensemble of its replicas. This paper is an attempt to review the basic aspects of the theory in a simplified language, aimed at students from diverse areas of physics.
Quantized gauge theory on the fuzzy sphere as random matrix model
Energy Technology Data Exchange (ETDEWEB)
Steinacker, Harold E-mail: harold.steinacker@physik.uni-muenchen.de
2004-02-16
U(n) Yang-Mills theory on the fuzzy sphere S{sup 2}{sub N} is quantized using random matrix methods. The gauge theory is formulated as a matrix model for a single Hermitian matrix subject to a constraint, and a potential with two degenerate minima. This allows to reduce the path integral over the gauge fields to an integral over eigenvalues, which can be evaluated for large N. The partition function of U(n) Yang-Mills theory on the classical sphere is recovered in the large N limit, as a sum over instanton contributions. The monopole solutions are found explicitly.
Full simulation of chiral random matrix theory at nonzero chemical potential by complex Langevin
Mollgaard, A.; Splittorff, K.
2015-02-01
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at nonzero chemical potential. The successful match with the analytic prediction for the chiral condensate is established through a shift of matrix integration variables and choosing a polar representation for the new matrix elements before complexification. Furthermore, we test the proposal to work with a Langevin-time-dependent quark mass and find that it allows us to control the fluctuations of the phase of the fermion determinant throughout the Langevin trajectory.
Forecasting Using Random Subspace Methods
T. Boot (Tom); D. Nibbering (Didier)
2016-01-01
textabstractRandom subspace methods are a novel approach to obtain accurate forecasts in high-dimensional regression settings. We provide a theoretical justification of the use of random subspace methods and show their usefulness when forecasting monthly macroeconomic variables. We focus on two
On the Marginal Distribution of the Diagonal Blocks in a Blocked Wishart Random Matrix
Directory of Open Access Journals (Sweden)
Kjetil B. Halvorsen
2016-01-01
Full Text Available Let A be a (m1+m2×(m1+m2 blocked Wishart random matrix with diagonal blocks of orders m1×m1 and m2×m2. The goal of the paper is to find the exact marginal distribution of the two diagonal blocks of A. We find an expression for this marginal density involving the matrix-variate generalized hypergeometric function. We became interested in this problem because of an application in spatial interpolation of random fields of positive definite matrices, where this result will be used for parameter estimation, using composite likelihood methods.
Chiral random matrix theory and the spectrum of the Dirac operator near zero virtuality
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, J. [State Univ. of New York, Stony Brook, NY (United States). Dept. of Physics
1994-01-01
We study the spectrum of the QCD Dirac operator near zero virtuality. We argue that it can be described by a random matrix theory with the chiral structure of QCD. In the large N limit, this model reduces to the low energy limit of the QCD partition function put forward by Leutwyler and Smilga. We conjecture that the microscopic limit of its spectral density is universal and reproduces that of QCD. Using random matrix methods we obtain its exact analytical expression. This results is compared to numerically calculated spectra for a liquid of instantons, and we find a very satisfactory agreement. (author). 26 refs., 2 figs.
Large N (=3) neutrinos and random matrix theory
Bai, Yang; Torroba, Gonzalo
2012-12-01
The large N limit has been successfully applied to QCD, leading to qualitatively correct results even for N = 3. In this work, we propose to treat the number N = 3 of Standard Model generations as a large number. Specifically, we apply this idea to the neutrino anarchy scenario and study neutrino physics using Random Matrix Theory, finding new results in both areas. For neutrino physics, we obtain predictions for the masses and mixing angles as a function of the generation number N. The Seesaw mechanism produces a hierarchy of order 1 /N 3 between the lightest and heaviest neutrino, and a θ 13 mixing angle of order 1 /N, in parametric agreement with experimental data when N goes to 3. For Random Matrix Theory, this motivates the introduction of a new type of ensemble of random matrices, the "Seesaw ensemble." Basic properties of such matrices are studied, including the eigenvalue density and the interpretation as a Coulomb gas system. Besides its mathematical interest, the Seesaw ensemble may be useful in random systems where two hierarchical scales exist.
A fixed point method to compute solvents of matrix polynomials
Marcos, Fernando; Pereira, Edgar
2009-01-01
Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricial elements of the matrix polynomial are considered separately as complex polynomials. Numerical examples illustrate the method presented.
Inner structure of vehicular ensembles and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Krbálek, Milan, E-mail: milan.krbalek@fjfi.cvut.cz; Hobza, Tomáš
2016-05-06
Highlights: • New class of random matrices (DUE) is proposed and analyzed in detail. • Approximation formula for level spacing distribution in DUE ensembles is analytically derived. • Connection between DUE and vehicular systems (analogical to a well-known link between GUE and Mexico buses) is presented. • It is shown that LS distribution of DUE matrices is the same as clearance distribution measured on expressways. - Abstract: We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded spectra of DUE matrices) with the time-clearance distribution extracted from various areas of the flux-density diagram (evaluated from original traffic data measured on Czech expressways with high occupancies) we demonstrate that the set of classical systems showing an universality associated with Random Matrix Ensembles can be extended by traffic systems.
Analytical techniques for instrument design - matrix methods
Energy Technology Data Exchange (ETDEWEB)
Robinson, R.A. [Los Alamos National Lab., NM (United States)
1997-09-01
We take the traditional Cooper-Nathans approach, as has been applied for many years for steady-state triple-axis spectrometers, and consider its generalisation to other inelastic scattering spectrometers. This involves a number of simple manipulations of exponentials of quadratic forms. In particular, we discuss a toolbox of matrix manipulations that can be performed on the 6- dimensional Cooper-Nathans matrix: diagonalisation (Moller-Nielsen method), coordinate changes e.g. from ({Delta}k{sub I},{Delta}k{sub F} to {Delta}E, {Delta}Q & 2 dummy variables), integration of one or more variables (e.g. over such dummy variables), integration subject to linear constraints (e.g. Bragg`s Law for analysers), inversion to give the variance-covariance matrix, and so on. We show how these tools can be combined to solve a number of important problems, within the narrow-band limit and the gaussian approximation. We will argue that a generalised program that can handle multiple different spectrometers could (and should) be written in parallel to the Monte-Carlo packages that are becoming available. We will also discuss the complementarity between detailed Monte-Carlo calculations and the approach presented here. In particular, Monte-Carlo methods traditionally simulate the real experiment as performed in practice, given a model scattering law, while the Cooper-Nathans method asks the inverse question: given that a neutron turns up in a particular spectrometer configuration (e.g. angle and time of flight), what is the probability distribution of possible scattering events at the sample? The Monte-Carlo approach could be applied in the same spirit to this question.
Exploring multicollinearity using a random matrix theory approach.
Feher, Kristen; Whelan, James; Müller, Samuel
2012-01-01
Clustering of gene expression data is often done with the latent aim of dimension reduction, by finding groups of genes that have a common response to potentially unknown stimuli. However, what is poorly understood to date is the behaviour of a low dimensional signal embedded in high dimensions. This paper introduces a multicollinear model which is based on random matrix theory results, and shows potential for the characterisation of a gene cluster's correlation matrix. This model projects a one dimensional signal into many dimensions and is based on the spiked covariance model, but rather characterises the behaviour of the corresponding correlation matrix. The eigenspectrum of the correlation matrix is empirically examined by simulation, under the addition of noise to the original signal. The simulation results are then used to propose a dimension estimation procedure of clusters from data. Moreover, the simulation results warn against considering pairwise correlations in isolation, as the model provides a mechanism whereby a pair of genes with `low' correlation may simply be due to the interaction of high dimension and noise. Instead, collective information about all the variables is given by the eigenspectrum.
Random matrix theory and fund of funds portfolio optimisation
Conlon, T.; Ruskin, H. J.; Crane, M.
2007-08-01
The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper, random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The inverse participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.
Method of producing a hybrid matrix fiber composite
Deteresa, Steven J [Livermore, CA; Lyon, Richard E [Absecon, NJ; Groves, Scott E [Brentwood, CA
2006-03-28
Hybrid matrix fiber composites having enhanced compressive performance as well as enhanced stiffness, toughness and durability suitable for compression-critical applications. The methods for producing the fiber composites using matrix hybridization. The hybrid matrix fiber composites comprised of two chemically or physically bonded matrix materials, whereas the first matrix materials are used to impregnate multi-filament fibers formed into ribbons and the second matrix material is placed around and between the fiber ribbons that are impregnated with the first matrix material and both matrix materials are cured and solidified.
Random Matrix Theory of Rigidity in Soft Matter
Yamanaka, Masanori
2015-06-01
We study the rigidity or softness of soft matter using the characteristic scale of coupling formation developed in random matrix theory. The eigensystems of the timescale-dependent cross-correlation matrix, which are obtained from the time series data of the atomic coordinates of a protein produced by the all-atom molecular dynamics of the solvent, are analyzed. As an example, we present a result for a protein lysozyme, PDBID:1AKI. We find that there are at least three different time scales involved in the coupling formation of correlated sectors of atoms and at least two different time scales for the size of the correlated sectors. These five time scales coexist simultaneously. We compare the results with those of the normal mode analysis and find a crossover of the distribution of the dominant vibrational components.
Taste breaking in staggered fermions from random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Osborna, James C
2004-03-01
We discuss the construction of a chiral random matrix model for staggered fermions. This model includes O(a{sup 2}) corrections to the continuum limit of staggered fermions and is related to the zero momentum limit of the Lee-Sharpe Lagrangian for staggered fermions. The naive construction based on a specific expansion in lattice spacing (a) of the Dirac matrix produces the term which gives the dominant contribution to the observed taste splitting in the pion masses. A more careful analysis can include extra terms which are also consistent with the symmetries of staggered fermions. Lastly I will mention possible uses of the model including studies of topology and fractional powers of the fermion determinant.
A random-matrix theory of the number sense.
Hannagan, T; Nieder, A; Viswanathan, P; Dehaene, S
2017-02-19
Number sense, a spontaneous ability to process approximate numbers, has been documented in human adults, infants and newborns, and many other animals. Species as distant as monkeys and crows exhibit very similar neurons tuned to specific numerosities. How number sense can emerge in the absence of learning or fine tuning is currently unknown. We introduce a random-matrix theory of self-organized neural states where numbers are coded by vectors of activation across multiple units, and where the vector codes for successive integers are obtained through multiplication by a fixed but random matrix. This cortical implementation of the 'von Mises' algorithm explains many otherwise disconnected observations ranging from neural tuning curves in monkeys to looking times in neonates and cortical numerotopy in adults. The theory clarifies the origin of Weber-Fechner's Law and yields a novel and empirically validated prediction of multi-peak number neurons. Random matrices constitute a novel mechanism for the emergence of brain states coding for quantity.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).
Matrix and discrepancy view of generalized random and quasirandom graphs
Directory of Open Access Journals (Sweden)
Bolla Marianna
2016-01-01
Full Text Available We will discuss how graph based matrices are capable to find classification of the graph vertices with small within- and between-cluster discrepancies. The structural eigenvalues together with the corresponding spectral subspaces of the normalized modularity matrix are used to find a block-structure in the graph. The notions are extended to rectangular arrays of nonnegative entries and to directed graphs. We also investigate relations between spectral properties, multiway discrepancies, and degree distribution of generalized random graphs. These properties are regarded as generalized quasirandom properties, and we conjecture and partly prove that they are also equivalent for certain deterministic graph sequences, irrespective of stochastic models.
Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers
Li, Huanan; Suwunnarat, Suwun; Fleischmann, Ragnar; Schanz, Holger; Kottos, Tsampikos
2017-01-01
We employ random matrix theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength γCPA and energy ECPA, for which a CPA occurs, are expressed in terms of the eigenmodes of the isolated cavity—thus carrying over the information about the chaotic nature of the target—and their coupling to a finite number of scattering channels. Our results are tested against numerical calculations using complex networks of resonators and chaotic graphs as CPA cavities.
U(1) staggered Dirac operator and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Berg, Bernd A.; Markum, Harald; Pullirsch, Rainer; Wettig, Tilo
2000-03-01
We investigate the spectrum of the staggered Dirac operator in 4d quenched U(1) lattice gauge theory and its relationship to random matrix theory. In the confined as well as in the Coulomb phase the nearest-neighbor spacing distribution of the unfolded eigenvalues is well described by the chiral unitary ensemble. The same is true for the distribution of the smallest eigenvalue and the microscopic spectral density in the confined phase. The physical origin of the chiral condensate in this phase deserves further study.
Application of random matrix theory to biological networks
Energy Technology Data Exchange (ETDEWEB)
Luo Feng [Department of Computer Science, Clemson University, 100 McAdams Hall, Clemson, SC 29634 (United States); Department of Pathology, U.T. Southwestern Medical Center, 5323 Harry Hines Blvd. Dallas, TX 75390-9072 (United States); Zhong Jianxin [Department of Physics, Xiangtan University, Hunan 411105 (China) and Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)]. E-mail: zhongjn@ornl.gov; Yang Yunfeng [Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Scheuermann, Richard H. [Department of Pathology, U.T. Southwestern Medical Center, 5323 Harry Hines Blvd. Dallas, TX 75390-9072 (United States); Zhou Jizhong [Department of Botany and Microbiology, University of Oklahoma, Norman, OK 73019 (United States) and Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)]. E-mail: zhouj@ornl.gov
2006-09-25
We show that spectral fluctuation of interaction matrices of a yeast protein-protein interaction network and a yeast metabolic network follows the description of the Gaussian orthogonal ensemble (GOE) of random matrix theory (RMT). Furthermore, we demonstrate that while the global biological networks evaluated belong to GOE, removal of interactions between constituents transitions the networks to systems of isolated modules described by the Poisson distribution. Our results indicate that although biological networks are very different from other complex systems at the molecular level, they display the same statistical properties at network scale. The transition point provides a new objective approach for the identification of functional modules.
Complex Langevin dynamics for chiral random matrix theory
Mollgaard, A.; Splittorff, K.
2013-12-01
We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass, the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.
Index Theorem and Random Matrix Theory for Improved Staggered Quarks
Energy Technology Data Exchange (ETDEWEB)
Follana, E. [Department of Physics and Astronomy, University of Glasgow (United Kingdom); Hart, A. [School of Physics, University of Edinburgh (United Kingdom); Davies, C.T.H. [Department of Physics and Astronomy, University of Glasgow (United Kingdom)
2006-03-15
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD. We find a clear separation of the spectrum of eigenvalues into high chirality, would-be zero modes and others, in accordance with the Index Theorem. We find the expected clustering of the non-zero modes into quartets as we approach the continuum limit. The predictions of random matrix theory for the epsilon regime are well reproduced. We conclude that improved staggered quarks near the continuum limit respond correctly to QCD topology.
Random matrix theory and QCD at nonzero chemical potential
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, J.J.M. [State Univ. of New York, Stony Brook, NY (United States). Dept. of Physics and Astronomy
1998-11-02
In this lecture we give a brief review of chiral random matrix theory (chRMT) and its applications to QCD at nonzero chemical potential. We present both analytical arguments involving chiral perturbation theory and numerical evidence from lattice QCD simulations showing that correlations of the smallest Dirac eigenvalues are described by chRMT. We discuss the range of validity of chRMT and emphasize the importance of universality. For chRMT`s at {mu}{ne}0 we identify universal properties of the Dirac eigenvalues and study the effect of quenching on the distribution of Yang-Lee zeros. (orig.) 86 refs.
Skew-orthogonal polynomials and random matrix theory
Ghosh, Saugata
2009-01-01
Orthogonal polynomials satisfy a three-term recursion relation irrespective of the weight function with respect to which they are defined. This gives a simple formula for the kernel function, known in the literature as the Christoffel-Darboux sum. The availability of asymptotic results of orthogonal polynomials and the simple structure of the Christoffel-Darboux sum make the study of unitary ensembles of random matrices relatively straightforward. In this book, the author develops the theory of skew-orthogonal polynomials and obtains recursion relations which, unlike orthogonal polynomials, depend on weight functions. After deriving reduced expressions, called the generalized Christoffel-Darboux formulas (GCD), he obtains universal correlation functions and non-universal level densities for a wide class of random matrix ensembles using the GCD. The author also shows that once questions about higher order effects are considered (questions that are relevant in different branches of physics and mathematics) the ...
The Riccati transfer matrix method. [for computerized structural analysis
Horner, G. C.; Pilkey, W. D.
1977-01-01
The Riccati transfer matrix method is a new technique for analyzing structural members. This new technique makes use of an existing large catalog of transfer matrices for various structural members such as rotating shafts. The numerical instability encountered when calculating high resonant frequencies, static response of a flexible member on a stiff foundation, or the response of a long member by the transfer matrix method is eliminated by the Riccati transfer matrix method. The computational time and storage requirements of the Riccati transfer matrix method are about half the values for the transfer matrix method. A rotating shaft analysis demonstrates the numerical accuracy of the method.
Spectra of empirical autocorrelation matrices: A random-matrix-theory-inspired perspective
Jamali, Tayeb; Jafari, G. R.
2015-07-01
We construct an autocorrelation matrix of a time series and analyze it based on the random-matrix theory (RMT) approach. The autocorrelation matrix is capable of extracting information which is not easily accessible by the direct analysis of the autocorrelation function. In order to provide a precise conclusion based on the information extracted from the autocorrelation matrix, the results must be first evaluated. In other words they need to be compared with some sort of criterion to provide a basis for the most suitable and applicable conclusions. In the context of the present study, the criterion is selected to be the well-known fractional Gaussian noise (fGn). We illustrate the applicability of our method in the context of stock markets. For the former, despite the non-Gaussianity in returns of the stock markets, a remarkable agreement with the fGn is achieved.
Novel Modulation Method for Multidirectional Matrix Converter
Directory of Open Access Journals (Sweden)
Saman Toosi
2014-01-01
Full Text Available This study presents a new modulation method for multidirectional matrix converter (MDMC, based on the direct duty ratio pulse width modulation (DDPWM. In this study, a new structure of MDMC has been proposed to control the power flow direction through the stand-alone battery based system and hybrid vehicle. The modulation method acts based on the average voltage over one switching period concept. Therefore, in order to determine the duty ratio for each switch, the instantaneous input voltages are captured and compared with triangular waveform continuously. By selecting the proper switching pattern and changing the slope of the carriers, the sinusoidal input current can be synthesized with high power factor and desired output voltage. The proposed system increases the discharging time of the battery by injecting the power to the system from the generator and battery at the same time. Thus, it makes the battery life longer and saves more energy. This paper also derived necessary equation for proposed modulation method as well as detail of analysis and modulation algorithm. The theoretical and modulation concepts presented have been verified in MATLAB simulation.
Novel modulation method for multidirectional matrix converter.
Toosi, Saman; Misron, Norhisam; Hanamoto, Tsuyoshi; Bin Aris, Ishak; Radzi, Mohd Amran Mohd; Yamada, Hiroaki
2014-01-01
This study presents a new modulation method for multidirectional matrix converter (MDMC), based on the direct duty ratio pulse width modulation (DDPWM). In this study, a new structure of MDMC has been proposed to control the power flow direction through the stand-alone battery based system and hybrid vehicle. The modulation method acts based on the average voltage over one switching period concept. Therefore, in order to determine the duty ratio for each switch, the instantaneous input voltages are captured and compared with triangular waveform continuously. By selecting the proper switching pattern and changing the slope of the carriers, the sinusoidal input current can be synthesized with high power factor and desired output voltage. The proposed system increases the discharging time of the battery by injecting the power to the system from the generator and battery at the same time. Thus, it makes the battery life longer and saves more energy. This paper also derived necessary equation for proposed modulation method as well as detail of analysis and modulation algorithm. The theoretical and modulation concepts presented have been verified in MATLAB simulation.
The Matrix Element Method and Vector-Like Quark Searches
Morrison, Benjamin
2016-01-01
In my time at the CERN summer student program, I worked on applying the matrix element method to vector-like quark identification. I worked in the ATLAS University of Geneva group under Dr. Olaf Nackenhorst. I developed automated plotting tools with ROOT, a script for implementing and optimizing generated matrix element calculation code, and kinematic transforms for the matrix element method.
Statistics of resonances and delay times in random media: beyond random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kottos, Tsampikos [Department of Physics, Wesleyan University, Middletown, CT 06459-0155 (United States); Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073 Goettingen (Germany)
2005-12-09
We review recent developments in quantum scattering from mesoscopic systems. Various spatial geometries whose closed analogues show diffusive, localized or critical behaviour are considered. These are the features that cannot be described by the universal random matrix theory results. Instead, one has to go beyond this approximation and incorporate them in a non-perturbative way. Here, we pay particular attention to the traces of these non-universal characteristics, in the distribution of the Wigner delay times and resonance widths. The former quantity captures time-dependent aspects of quantum scattering while the latter is associated with the poles of the scattering matrix.
Random matrix theory for transition strengths: Applications and open questions
Kota, V. K. B.
2017-12-01
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different) and so on. Using embedded ensembles (EE), there are efforts to derive a good statistical theory for transition strengths. With m fermions (or bosons) in N mean-field single particle levels and interacting via two-body forces, we have with GOE embedding, the so called EGOE(1+2). Now, the transition strength density (transition strength multiplied by the density of states at the initial and final energies) is a convolution of the density generated by the mean-field one-body part with a bivariate spreading function due to the two-body interaction. Using the embedding U(N) algebra, it is established, for a variety of transition operators, that the spreading function, for sufficiently strong interactions, is close to a bivariate Gaussian. Also, as the interaction strength increases, the spreading function exhibits a transition from bivariate Breit-Wigner to bivariate Gaussian form. In appropriate limits, this EE theory reduces to the polynomial theory of Draayer, French and Wong on one hand and to the theory due to Flambaum and Izrailev for one-body transition operators on the other. Using spin-cutoff factors for projecting angular momentum, the theory is applied to nuclear matrix elements for neutrinoless double beta decay (NDBD). In this paper we will describe: (i) various developments in the EE theory for transition strengths; (ii) results for nuclear matrix elements for 130Te and 136Xe NDBD; (iii) important open questions in the current form of the EE theory.
Index Theorem and Random Matrix Theory for Improved Staggered Quarks
Energy Technology Data Exchange (ETDEWEB)
Follana, E. [Department of Physics and Astronomy, University of Glasgow, G12 8QQ Glasgow (United Kingdom)
2005-03-15
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum of eigenvalues into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the Index Theorem, and their chirality expectation value is large. The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that improvement of the fermionic and gauge actions moves the staggered quarks closer to the continuum limit where they respond correctly to QCD topology.
Random matrix theory of a chaotic Andreev quantum dot
Energy Technology Data Exchange (ETDEWEB)
Altland, A.; Zirnbauer, M.R. [Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str.77, 50937 Koeln (Germany)
1996-04-01
A new universality class distinct from the standard Wigner-Dyson class is identified. This class is realized by putting a metallic quantum dot in contact with a superconductor, while applying a magnetic field so as to make the pairing field effectively vanish on average. A random-matrix description of the spectral and transport properties of such a quantum dot is proposed. The weak-localization correction to the tunnel conductance is nonzero and results from the depletion of the density of states due to the coupling with the superconductor. Semiclassically, the depletion is caused by a singular mode of phase-coherent long-range propagation of particles and holes. {copyright} {ital 1996 The American Physical Society.}
Perturbation treatment of symmetry breaking within random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Carvalho, J.X. de [Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden (Germany); Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, S.P. (Brazil); Hussein, M.S. [Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden (Germany); Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, S.P. (Brazil)], E-mail: mhussein@mpipks-dresden.mpg.de; Pato, M.P.; Sargeant, A.J. [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, S.P. (Brazil)
2008-07-07
We discuss the applicability, within the random matrix theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both two-fold and three-fold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequencies is considered to be missing in the sample. Our findings are relevant for symmetry violation studies in general.
Large-Nc Gauge Theory and Chiral Random Matrix Theory
Hanada, Masanori; Lee, Jong-Wan; Yamada, Norikazu
Effective theory approaches and the large-Nc limit are useful for studying the strongly coupled gauge theories. In this talk we consider how the chiral random matrix theory (χRMT) can be used in the study of large-Nc gauge theories. It turns out the parameter regions, in which each of these two approaches are valid, are different. Still, however, we show that the breakdown of chiral symmetry can be detected by combining the large-Nc argument and the χRMT with some cares. As a demonstration, we numerically study the four dimensional SU(Nc) gauge theory with Nf = 2 heavy adjoint fermions on a 24 lattice by using Monte-Carlo simulations, which is related to the infinite volume lattice through the Eguchi-Kawai equivalence.
Luo, Feng; Yang, Yunfeng; Zhong, Jianxin; Gao, Haichun; Khan, Latifur; Thompson, Dorothea K; Zhou, Jizhong
2007-01-01
Background Large-scale sequencing of entire genomes has ushered in a new age in biology. One of the next grand challenges is to dissect the cellular networks consisting of many individual functional modules. Defining co-expression networks without ambiguity based on genome-wide microarray data is difficult and current methods are not robust and consistent with different data sets. This is particularly problematic for little understood organisms since not much existing biological knowledge can be exploited for determining the threshold to differentiate true correlation from random noise. Random matrix theory (RMT), which has been widely and successfully used in physics, is a powerful approach to distinguish system-specific, non-random properties embedded in complex systems from random noise. Here, we have hypothesized that the universal predictions of RMT are also applicable to biological systems and the correlation threshold can be determined by characterizing the correlation matrix of microarray profiles using random matrix theory. Results Application of random matrix theory to microarray data of S. oneidensis, E. coli, yeast, A. thaliana, Drosophila, mouse and human indicates that there is a sharp transition of nearest neighbour spacing distribution (NNSD) of correlation matrix after gradually removing certain elements insider the matrix. Testing on an in silico modular model has demonstrated that this transition can be used to determine the correlation threshold for revealing modular co-expression networks. The co-expression network derived from yeast cell cycling microarray data is supported by gene annotation. The topological properties of the resulting co-expression network agree well with the general properties of biological networks. Computational evaluations have showed that RMT approach is sensitive and robust. Furthermore, evaluation on sampled expression data of an in silico modular gene system has showed that under-sampled expressions do not affect the
Luo, Feng; Yang, Yunfeng; Zhong, Jianxin; Gao, Haichun; Khan, Latifur; Thompson, Dorothea K; Zhou, Jizhong
2007-08-14
Large-scale sequencing of entire genomes has ushered in a new age in biology. One of the next grand challenges is to dissect the cellular networks consisting of many individual functional modules. Defining co-expression networks without ambiguity based on genome-wide microarray data is difficult and current methods are not robust and consistent with different data sets. This is particularly problematic for little understood organisms since not much existing biological knowledge can be exploited for determining the threshold to differentiate true correlation from random noise. Random matrix theory (RMT), which has been widely and successfully used in physics, is a powerful approach to distinguish system-specific, non-random properties embedded in complex systems from random noise. Here, we have hypothesized that the universal predictions of RMT are also applicable to biological systems and the correlation threshold can be determined by characterizing the correlation matrix of microarray profiles using random matrix theory. Application of random matrix theory to microarray data of S. oneidensis, E. coli, yeast, A. thaliana, Drosophila, mouse and human indicates that there is a sharp transition of nearest neighbour spacing distribution (NNSD) of correlation matrix after gradually removing certain elements insider the matrix. Testing on an in silico modular model has demonstrated that this transition can be used to determine the correlation threshold for revealing modular co-expression networks. The co-expression network derived from yeast cell cycling microarray data is supported by gene annotation. The topological properties of the resulting co-expression network agree well with the general properties of biological networks. Computational evaluations have showed that RMT approach is sensitive and robust. Furthermore, evaluation on sampled expression data of an in silico modular gene system has showed that under-sampled expressions do not affect the recovery of gene
Energy Technology Data Exchange (ETDEWEB)
Conte, Elio [Department of Pharmacology and Human Physiology and Tires, Center for Innovative Technologies for Signal Detection and Processing, University of Bari (Italy); School of Advanced International Studies on Theoretical and Nonlinear Methodologies-Bari (Italy)], E-mail: elio.conte@fastwebnet.it; Khrennikov, Andrei [International Center for Mathematical Modelling in Physics and Cognitive Sciences, M.S.I., University of Vaexjoe, S-35195 (Sweden); Federici, Antonio [Department of Pharmacology and Human Physiology and Tires, Center for Innovative Technologies for Signal Detection and Processing, University of Bari (Italy); Zbilut, Joseph P. [Department of Molecular Biophysics and Physiology, Rush University Medical Center, 1653W Congress, Chicago, IL 60612 (United States)
2009-09-15
We develop a new method for analysis of fundamental brain waves as recorded by the EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given. We also discuss the link of such formulation with H. Weiss and V. Weiss golden ratio found in the brain, and with El Naschie fractal Cantorian space-time theory.
Method of forming a ceramic matrix composite and a ceramic matrix component
de Diego, Peter; Zhang, James
2017-05-30
A method of forming a ceramic matrix composite component includes providing a formed ceramic member having a cavity, filling at least a portion of the cavity with a ceramic foam. The ceramic foam is deposited on a barrier layer covering at least one internal passage of the cavity. The method includes processing the formed ceramic member and ceramic foam to obtain a ceramic matrix composite component. Also provided is a method of forming a ceramic matrix composite blade and a ceramic matrix composite component.
Random matrix theory and the sixth Painleve equation
Energy Technology Data Exchange (ETDEWEB)
Forrester, P J; Witte, N S [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia)
2006-09-29
A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realized by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determinants. These distributions are well known to be {tau}-functions for Painleve systems, allowing for the former to be characterized as the solution of certain nonlinear equations. We consider the random matrix ensembles for which the nonlinear equation is the {sigma} form of P{sub VI}. Known results are reviewed, as is their implication by way of series expansions for the distributions. New results are given for the boundary conditions in the neighbourhood of the fixed singularities at t = 0, 1, {infinity} of {sigma}P{sub VI} displayed by a generalization of the generating function for the distributions. The structure of these expansions is related to Jimbo's general expansions for the {tau}-function of {sigma}P{sub VI} in the neighbourhood of its fixed singularities, and this theory is itself put in its context of the linear isomonodromy problem relating to P{sub VI}.
Universality of S-matrix correlations for deterministic plus random Hamiltonians.
Mae, N; Iida, S
2001-04-01
We study S-matrix correlations for random matrix ensembles with a Hamiltonian H=H(0)+straight phi, in which H0 is a deterministic NxN matrix and straight phi belongs to a Gaussian random matrix ensemble. Using Efetov's supersymmetry formalism, we show that in the limit N-->infinity correlation functions of S-matrix elements are universal on the scale of the local mean level spacing: the dependence of H0 enters into these correlation functions only through the average S matrix and the average level density. This statement applies to each of the three symmetry classes (unitary, orthogonal, and symplectic).
Testing the Predictions of Random Matrix Theory in Low Loss Wave Chaotic Scattering Systems
Yeh, Jen-Hao; Antonsen, Thomas; Ott, Edward; Anlage, Steven
2013-03-01
Wave chaos is a field where researchers apply random matrix theory (RMT) to predict the statistics of wave properties in complicated wave scattering systems. The RMT predictions have successfully demonstrated universality of the distributions of these wave properties, which only depend on the loss parameter of the system and the physical symmetry. Examination of these predictions in very low loss systems is interesting because extreme limits for the distribution functions and other predictions are encountered. Therefore, we use a wave-chaotic superconducting cavity to establish a low loss environment and test RMT predictions, including the statistics of the scattering (S) matrix and the impedance (Z) matrix, the universality (or lack thereof) of the Z- and S-variance ratios, and the statistics of the proper delay times of the Wigner-Smith time-delay matrix. We have applied an in-situ microwave calibration method (Thru-Reflection-Line method) to calibrate the cryostat system, and we also applied the random coupling model to remove the system-specific features. Our experimental results of different properties agree with the RMT predictions. This work is funded by the ONR/Maryland AppEl Center Task A2 (contract No. N000140911190), the AFOSR under grant FA95500710049, and Center for Nanophysics and Advanced Materials.
Suliman, Mohamed
2016-01-01
In this supplementary appendix we provide proofs and additional simulation results that complement the paper (constrained perturbation regularization approach for signal estimation using random matrix theory).
Random matrix approach to the dynamics of stock inventory variations
Zhou, Wei-Xing; Mu, Guo-Hua; Kertész, János
2012-09-01
It is well accepted that investors can be classified into groups owing to distinct trading strategies, which forms the basic assumption of many agent-based models for financial markets when agents are not zero-intelligent. However, empirical tests of these assumptions are still very rare due to the lack of order flow data. Here we adopt the order flow data of Chinese stocks to tackle this problem by investigating the dynamics of inventory variations for individual and institutional investors that contain rich information about the trading behavior of investors and have a crucial influence on price fluctuations. We find that the distributions of cross-correlation coefficient Cij have power-law forms in the bulk that are followed by exponential tails, and there are more positive coefficients than negative ones. In addition, it is more likely that two individuals or two institutions have a stronger inventory variation correlation than one individual and one institution. We find that the largest and the second largest eigenvalues (λ1 and λ2) of the correlation matrix cannot be explained by random matrix theory and the projections of investors' inventory variations on the first eigenvector u(λ1) are linearly correlated with stock returns, where individual investors play a dominating role. The investors are classified into three categories based on the cross-correlation coefficients CV R between inventory variations and stock returns. A strong Granger causality is unveiled from stock returns to inventory variations, which means that a large proportion of individuals hold the reversing trading strategy and a small part of individuals hold the trending strategy. Our empirical findings have scientific significance in the understanding of investors' trading behavior and in the construction of agent-based models for emerging stock markets.
Systems and methods for deactivating a matrix converter
Ransom, Ray M.
2013-04-02
Systems and methods are provided for deactivating a matrix conversion module. An electrical system comprises an alternating current (AC) interface, a matrix conversion module coupled to the AC interface, an inductive element coupled between the AC interface and the matrix conversion module, and a control module. The control module is coupled to the matrix conversion module, and in response to a shutdown condition, the control module is configured to operate the matrix conversion module to deactivate the first conversion module when a magnitude of a current through the inductive element is less than a threshold value.
Advances in random matrix theory, zeta functions, and sphere packing
Hales, T. C.; Sarnak, P.; Pugh, M. C.
2000-01-01
Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks. PMID:11058156
Random matrix theory filters and currency portfolio optimisation
Daly, J.; Crane, M.; Ruskin, H. J.
2010-04-01
Random matrix theory (RMT) filters have recently been shown to improve the optimisation of financial portfolios. This paper studies the effect of three RMT filters on realised portfolio risk, using bootstrap analysis and out-of-sample testing. We considered the case of a foreign exchange and commodity portfolio, weighted towards foreign exchange, and consisting of 39 assets. This was intended to test the limits of RMT filtering, which is more obviously applicable to portfolios with larger numbers of assets. We considered both equally and exponentially weighted covariance matrices, and observed that, despite the small number of assets involved, RMT filters reduced risk in a way that was consistent with a much larger S&P 500 portfolio. The exponential weightings indicated showed good consistency with the value suggested by Riskmetrics, in contrast to previous results involving stocks. This decay factor, along with the low number of past moves preferred in the filtered, equally weighted case, displayed a trend towards models which were reactive to recent market changes. On testing portfolios with fewer assets, RMT filtering provided less or no overall risk reduction. In particular, no long term out-of-sample risk reduction was observed for a portfolio consisting of 15 major currencies and commodities.
Randomized Block Cubic Newton Method
Doikov, Nikita
2018-02-12
We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN) method, which in each iteration builds a model of the objective function formed as the sum of the natural models of its three components: a linear model with a quadratic regularizer for the differentiable term, a quadratic model with a cubic regularizer for the twice differentiable term, and perfect (proximal) model for the nonsmooth term. Our method in each iteration minimizes the model over a random subset of blocks of the search variable. RBCN is the first algorithm with these properties, generalizing several existing methods, matching the best known bounds in all special cases. We establish ${\\\\cal O}(1/\\\\epsilon)$, ${\\\\cal O}(1/\\\\sqrt{\\\\epsilon})$ and ${\\\\cal O}(\\\\log (1/\\\\epsilon))$ rates under different assumptions on the component functions. Lastly, we show numerically that our method outperforms the state-of-the-art on a variety of machine learning problems, including cubically regularized least-squares, logistic regression with constraints, and Poisson regression.
Method of making molten carbonate fuel cell ceramic matrix tape
Maricle, Donald L.; Putnam, Gary C.; Stewart, Jr., Robert C.
1984-10-23
A method of making a thin, flexible, pliable matrix material for a molten carbonate fuel cell is described. The method comprises admixing particles inert in the molten carbonate environment with an organic polymer binder and ceramic particle. The composition is applied to a mold surface and dried, and the formed compliant matrix material removed.
An improved 4-step commutation method application for matrix converter
DEFF Research Database (Denmark)
Guo, Yu; Guo, Yougui; Deng, Wenlang
2014-01-01
A novel four-step commutation method is proposed for matrix converter cell, 3 phase inputs to 1 phase output in this paper, which is obtained on the analysis of published commutation methods for matrix converter. The first and fourth step can be shorter than the second or third one. The discussed...
Novaes, Marcel
2015-06-01
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = - iħS†dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
Energy Technology Data Exchange (ETDEWEB)
Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Ave. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
Distribution of local density of states in superstatistical random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Abul-Magd, A.Y. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)]. E-mail: a_y_abul_magd@hotmail.com
2007-07-02
We expose an interesting connection between the distribution of local spectral density of states arising in the theory of disordered systems and the notion of superstatistics introduced by Beck and Cohen and recently incorporated in random matrix theory. The latter represents the matrix-element joint probability density function as an average of the corresponding quantity in the standard random-matrix theory over a distribution of level densities. We show that this distribution is in reasonable agreement with the numerical calculation for a disordered wire, which suggests to use the results of theory of disordered conductors in estimating the parameter distribution of the superstatistical random-matrix ensemble.
On the Riccati transfer matrix method for repetitive structures
Stephen, N.G.
2010-01-01
The Riccati transfer matrix method is employed in the elastostatic analysis of a repetitive structure subject to various loadings; the eigenvalues of particular terms featuring in the recursive relationships show why the method is numerically stable
Non-equilibrium random matrix theory. Transition probabilities
Energy Technology Data Exchange (ETDEWEB)
Pedro, Francisco Gil [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie
2016-06-15
In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
Diffusion MRI noise mapping using random matrix theory
Veraart, Jelle; Fieremans, Els; Novikov, Dmitry S.
2016-01-01
Purpose To estimate the spatially varying noise map using a redundant magnitude MR series. Methods We exploit redundancy in non-Gaussian multi-directional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices. The bulk of PCA eigenvalues, arising due to noise, is described by the universal Marchenko-Pastur distribution, parameterized by the noise level. This allows us to estimate noise level in a local neighborhood based on the singular value decomposition of a matrix combining neighborhood voxels and diffusion directions. Results We present a model-independent local noise mapping method capable of estimating noise level down to about 1% error. In contrast to current state-of-the art techniques, the resultant noise maps do not show artifactual anatomical features that often reflect physiological noise, the presence of sharp edges, or a lack of adequate a priori knowledge of the expected form of MR signal. Conclusions Simulations and experiments show that typical diffusion MRI data exhibit sufficient redundancy that enables accurate, precise, and robust estimation of the local noise level by interpreting the PCA eigenspectrum in terms of the Marchenko-Pastur distribution. PMID:26599599
Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation
DEFF Research Database (Denmark)
Brouwer, Thomas; Frellsen, Jes; Liò, Pietro
2017-01-01
In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri...
A Matrix Splitting Method for Composite Function Minimization
Yuan, Ganzhao
2016-12-07
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes and analyzes a new Matrix Splitting Method (MSM) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method and the Successive Over-Relaxation method for solving linear systems in the literature. Incorporating a new Gaussian elimination procedure, the matrix splitting method achieves state-of-the-art performance. For convex problems, we establish the global convergence, convergence rate, and iteration complexity of MSM, while for non-convex problems, we prove its global convergence. Finally, we validate the performance of our matrix splitting method on two particular applications: nonnegative matrix factorization and cardinality regularized sparse coding. Extensive experiments show that our method outperforms existing composite function minimization techniques in term of both efficiency and efficacy.
Directory of Open Access Journals (Sweden)
Wanxing Sheng
2016-05-01
Full Text Available In this paper, a reactive power optimization method based on historical data is investigated to solve the dynamic reactive power optimization problem in distribution network. In order to reflect the variation of loads, network loads are represented in a form of random matrix. Load similarity (LS is defined to measure the degree of similarity between the loads in different days and the calculation method of the load similarity of load random matrix (LRM is presented. By calculating the load similarity between the forecasting random matrix and the random matrix of historical load, the historical reactive power optimization dispatching scheme that most matches the forecasting load can be found for reactive power control usage. The differences of daily load curves between working days and weekends in different seasons are considered in the proposed method. The proposed method is tested on a standard 14 nodes distribution network with three different types of load. The computational result demonstrates that the proposed method for reactive power optimization is fast, feasible and effective in distribution network.
A non-parametric permutation method for assessing agreement for distance matrix observations.
Røislien, Jo; Samset, Eigil
2014-01-30
Distance matrix data are occurring ever more frequently in medical research, particularly in fields such as genetics, DNA research, and image analysis. We propose a non-parametric permutation method for assessing agreement when the data under study are distance matrices. We apply agglomerative hierarchical clustering and accompanying dendrograms to visualize the internal structure of the matrix observations. The accompanying test is based on random permutations of the elements within individual matrix observations and the corresponding matrix mean of these permutations. We compare the within-matrix element sum of squares (WMESS) for the observed mean against the WMESS for the permutation means. The methodology is exemplified using simulations and real data from magnetic resonance imaging. Copyright © 2013 John Wiley & Sons, Ltd.
A nonlinearity compensation method for a matrix converter drive
DEFF Research Database (Denmark)
Lee, Kyo-Beum; Blaabjerg, Frede
2005-01-01
This paper presents a new method to compensate the nonlinearities for matrix converter drives. The nonlinearities of matrix converter drives such as commutation delay, turn-on and turn-off time of the switching devices, and on-state switching device voltage drop is corrected by a new matrix...... using a 3-kW matrix converter system without a speed sensor. Experimental results show the proposed method provides good compensating characteristics....... converter model using the direction of current. The proposed method does not need any additional hardware or complicated software and it is easy to realize by applying the algorithm to the conventional vector control. The proposed compensation method is applied for high-performance induction motor drives...
An iterative method to invert the LTSn matrix
Energy Technology Data Exchange (ETDEWEB)
Cardona, A.V.; Vilhena, M.T. de [UFRGS, Porto Alegre (Brazil)
1996-12-31
Recently Vilhena and Barichello proposed the LTSn method to solve, analytically, the Discrete Ordinates Problem (Sn problem) in transport theory. The main feature of this method consist in the application of the Laplace transform to the set of Sn equations and solve the resulting algebraic system for the transport flux. Barichello solve the linear system containing the parameter s applying the definition of matrix invertion exploiting the structure of the LTSn matrix. In this work, it is proposed a new scheme to invert the LTSn matrix, decomposing it in blocks and recursively inverting this blocks.
Method to measure soil matrix infiltration in forest soil
Zhang, Jing; Lei, Tingwu; Qu, Liqin; Chen, Ping; Gao, Xiaofeng; Chen, Chao; Yuan, Lili; Zhang, Manliang; Su, Guangxu
2017-09-01
Infiltration of water into forest soil commonly involves infiltration through the matrix body and preferential passages. Determining the matrix infiltration process is important in partitioning water infiltrating into the soil through the soil body and macropores to evaluate the effects of soil and water conservation practices on hillslope hydrology and watershed sedimentation. A new method that employs a double-ring infiltrometer was applied in this study to determine the matrix infiltration process in forest soil. Field experiments were conducted in a forest field on the Loess Plateau at Tianshui Soil and Water Conservation Experimental Station. Nylon cloth was placed on the soil surface in the inner ring and between the inner and outer rings of infiltrometers. A thin layer of fine sands were placed onto the nylon cloth to shelter the macropores and ensure that water infiltrates the soil through the matrix only. Brilliant Blue tracers were applied to examine the exclusion of preferential flow occurrences in the measured soil body. The infiltration process was measured, computed, and recorded through procedures similar to those of conventional methods. Horizontal and vertical soil profiles were excavated to check the success of the experiment and ensure that preferential flow did not occur in the measured soil column and that infiltration was only through the soil matrix. The infiltration processes of the replicates of five plots were roughly the same, thereby indicating the feasibility of the methodology to measure soil matrix infiltration. The measured infiltration curves effectively explained the transient process of soil matrix infiltration. Philip and Kostiakov models fitted the measured data well, and all the coefficients of determination were greater than 0.9. The wetted soil bodies through excavations did not present evidence of preferential flow. Therefore, the proposed method can determine the infiltration process through the forest soil matrix. This
Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory
Suliman, Mohamed; Ballal, Tarig; Kammoun, Abla; Al-Naffouri, Tareq Y.
2016-12-01
In this supplementary appendix we provide proofs and additional extensive simulations that complement the analysis of the main paper (constrained perturbation regularization approach for signal estimation using random matrix theory).
Density of state in a complex random matrix theory with external source
Energy Technology Data Exchange (ETDEWEB)
Hikami, S. [Department of Pure and Applied Sciences, University of Tokyo, Meguro-ku, Komaba, Tokyo (Japan); Pnini, R. [Department of Pure and Applied Sciences, University of Tokyo, Meguro-ku, Komaba, Tokyo (Japan); CREST, Japan Science and Technology Cooperation (Japan)
1998-09-04
The density of state for a complex NxN random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained. (author). Letter-to-the-editor.
Successive Over Relaxation Method Which Uses Matrix Norms for ...
African Journals Online (AJOL)
An algorithm for S.O.R functional iteration which uses matrix norms for the Jacobi iteration matrices rather than the usual Power method, feasible in Newton Operator for the solution of nonlinear system of equations is proposed. We modified the S.O.R. iterative method known as Multiphase S.O.R. method for Newton ...
Spectrum of the QCD Dirac operator and chiral random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, J. (Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States))
1994-04-18
We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of the classical random matrix ensembles of Dyson we have three different cases: the chiral orthogonal ensemble, the chiral unitary ensemble, and the chiral symplectic ensemble. They correspond to gauge groups SU(2) in the fundamental representation, SU([ital N][sub [ital c
A random matrix approach to RNA folding with interaction
Indian Academy of Sciences (India)
2015-11-27
Nov 27, 2015 ... In the matrix model of RNA [G Vernizzi, H Orland and A Zee, Phys. Rev. Lett. 94, 168103 (2005)] we introduce external interactions on n bases in the action of the partition function where ≤ and is the length of the polymer chain. The RNA structures found in the model can be separated into two ...
A random matrix approach to RNA folding with interaction
Indian Academy of Sciences (India)
Abstract. In the matrix model of RNA [G Vernizzi, H Orland and A Zee, Phys. Rev. Lett. 94, 168103 (2005)] we introduce external interactions on n bases in the action of the partition function where n ≤ L and L is the length of the polymer chain. The RNA structures found in the model can be separated into two regimes: (i) 0 ...
Osorio, Ivan; Lai, Ying-Cheng
2011-09-01
We present a general method to analyze multichannel time series that are becoming increasingly common in many areas of science and engineering. Of particular interest is the degree of synchrony among various channels, motivated by the recognition that characterization of synchrony in a system consisting of many interacting components can provide insights into its fundamental dynamics. Often such a system is complex, high-dimensional, nonlinear, nonstationary, and noisy, rendering unlikely complete synchronization in which the dynamical variables from individual components approach each other asymptotically. Nonetheless, a weaker type of synchrony that lasts for a finite amount of time, namely, phase synchronization, can be expected. Our idea is to calculate the average phase-synchronization times from all available pairs of channels and then to construct a matrix. Due to nonlinearity and stochasticity, the matrix is effectively random. Moreover, since the diagonal elements of the matrix can be arbitrarily large, the matrix can be singular. To overcome this difficulty, we develop a random-matrix based criterion for proper choosing of the diagonal matrix elements. Monitoring of the eigenvalues and the determinant provides a powerful way to assess changes in synchrony. The method is tested using a prototype nonstationary noisy dynamical system, electroencephalogram (scalp) data from absence seizures for which enhanced cortico-thalamic synchrony is presumed, and electrocorticogram (intracranial) data from subjects having partial seizures with secondary generalization for which enhanced local synchrony is similarly presumed.
The Matrix Element Method at Next-to-Leading Order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-01-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of...
The matrix element method at next-to-leading order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-11-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory, for electro-weak final states. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of unweighted next-to-leading order events. As examples of the application of our next-to-leading order matrix element method we consider the measurement of the mass of the Z boson and also the search for the Higgs boson in the four lepton channel.
Discovering cell types in flow cytometry data with random matrix theory
Shen, Yang; Nussenblatt, Robert; Losert, Wolfgang
Flow cytometry is a widely used experimental technique in immunology research. During the experiments, peripheral blood mononuclear cells (PBMC) from a single patient, labeled with multiple fluorescent stains that bind to different proteins, are illuminated by a laser. The intensity of each stain on a single cell is recorded and reflects the amount of protein expressed by that cell. The data analysis focuses on identifying specific cell types related to a disease. Different cell types can be identified by the type and amount of protein they express. To date, this has most often been done manually by labelling a protein as expressed or not while ignoring the amount of expression. Using a cross correlation matrix of stain intensities, which contains both information on the proteins expressed and their amount, has been largely ignored by researchers as it suffers from measurement noise. Here we present an algorithm to identify cell types in flow cytometry data which uses random matrix theory (RMT) to reduce noise in a cross correlation matrix. We demonstrate our method using a published flow cytometry data set. Compared with previous analysis techniques, we were able to rediscover relevant cell types in an automatic way. Department of Physics, University of Maryland, College Park, MD 20742.
The J-Matrix Method Developments and Applications
Alhaidari, Abdulaziz D; Heller, Eric J; Abdelmonem, Mohamed S
2008-01-01
This volume aims to provide the fundamental knowledge to appreciate the advantages of the J-matrix method and to encourage its use and further development. The J-matrix method is an algebraic method of quantum scattering with substantial success in atomic and nuclear physics. The accuracy and convergence property of the method compares favourably with other successful scattering calculation methods. Despite its thirty-year long history new applications are being found for the J-matrix method. This book gives a brief account of the recent developments and some selected applications of the method in atomic and nuclear physics. New findings are reported in which experimental results are compared to theoretical calculations. Modifications, improvements and extensions of the method are discussed using the language of the J-matrix. The volume starts with a Foreword by the two co-founders of the method, E.J. Heller and H.A. Yamani and it contains contributions from 24 prominent international researchers.
Hybrid transfer-matrix FDTD method for layered periodic structures.
Deinega, Alexei; Belousov, Sergei; Valuev, Ilya
2009-03-15
A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new method is tested by comparing computed transmission spectra of a 32-layered photonic crystal composed of spherical or ellipsoidal scatterers with the results of direct FDTD and layer-multiple-scattering calculations.
A study of stepped acoustic resonator with transfer matrix method
Min, Qi; He, Wan-Quan; Wang, Quan-Biao; Tian, Jia-Jin; Zhang, Qing-You
2014-07-01
Transfer matrix method was applied in the study of stepped acoustic resonators. Transfer matrix method was more competent in comparison with analytic method to investigate the acoustic properties of stepped acoustic resonator, especially multi-step acoustic resonator. With the help of the numerical solution, the resonance frequencies, the phase angles and the radiation impedances of stepped acoustic resonators which consisted of one to five sub-tubes were studied theoretically and experimentally. The numerical solutions were in excellent agreement with the experimental results.
Modelling of packet traffic with matrix analytic methods
DEFF Research Database (Denmark)
Andersen, Allan T.
1995-01-01
network services i.e. 800 and 900 calls and advanced mobile communication services. The Markovian Arrival Process (MAP) has been used as a versatile tool to model the packet arrival process. Applying the MAP facilitates the use of Matrix Analytic methods to obtain performance measures associated......-scales. In this study we show that 8-16 state MAPs are able to capture this very variable behaviour over several timescales. The queueing behaviour of these MAPs has been analyzed with Matrix Analytic methods. The results correspond to those obtained by trace driven simulations of measured LAN traffic. It is shown...... process. A heuristic formula for the tail behaviour of a single server queue fed by a superposition of renewal processes has been evaluated. The evaluation was performed by applying Matrix Analytic methods. The heuristic formula has applications in the Call Admission Control (CAC) procedure of the future...
Random-matrix-theory approach to mesoscopic fluctuations of heat current
Schmidt, Martin; Kottos, Tsampikos; Shapiro, Boris
2013-08-01
We consider an ensemble of fully connected networks of N oscillators coupled harmonically with random springs and show, using random-matrix-theory considerations, that both the average phonon heat current and its variance are scale invariant and take universal values in the large N limit. These anomalous mesoscopic fluctuations is the hallmark of strong correlations between normal modes.
Random matrix theory of multi-antenna communications: the Ricean channel
Energy Technology Data Exchange (ETDEWEB)
Moustakas, Aris L [Department of Physics, University of Athens, Panepistimiopolis, Athens 15784 (Greece); Simon, Steven H [Bell Labs, Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974 (United States)
2005-12-09
The use of multi-antenna arrays in wireless communications through disordered media promises huge increases in the information transmission rate. It is therefore important to analyse the information capacity of such systems in realistic situations of microwave transmission, where the statistics of the transmission amplitudes (channel) may be coloured. Here, we present an approach that provides analytic expressions for the statistics, i.e. the moments of the distribution, of the mutual information for general Gaussian channel statistics. The mathematical method applies tools developed originally in the context of coherent wave propagation in disordered media, such as random matrix theory and replicas. Although it is valid formally for large antenna numbers, this approach produces extremely accurate results even for arrays with as few as two antennas. We also develop a method to analytically optimize over the input signal distribution, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel. The emphasis of this paper is on elucidating the novel mathematical methods used. We do this by analysing a specific case when the channel matrix is a complex Gaussian with arbitrary mean and unit covariance, which is usually called the Ricean channel.
Telfeyan, Katherine; Ware, S Doug; Reimus, Paul W; Birdsell, Kay H
2018-02-01
Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired. Copyright © 2018 Elsevier B.V. All rights reserved.
Mesh-matrix analysis method for electromagnetic launchers
Elliott, David G.
1989-01-01
The mesh-matrix method is a procedure for calculating the current distribution in the conductors of electromagnetic launchers with coil or flat-plate geometry. Once the current distribution is known the launcher performance can be calculated. The method divides the conductors into parallel current paths, or meshes, and finds the current in each mesh by matrix inversion. The author presents procedures for writing equations for the current and voltage relations for a few meshes to serve as a pattern for writing the computer code. An available subroutine package provides routines for field and flux coefficients and equation solution.
A General Method of Empirical Q-matrix Validation.
de la Torre, Jimmy; Chiu, Chia-Yi
2016-06-01
In contrast to unidimensional item response models that postulate a single underlying proficiency, cognitive diagnosis models (CDMs) posit multiple, discrete skills or attributes, thus allowing CDMs to provide a finer-grained assessment of examinees' test performance. A common component of CDMs for specifying the attributes required for each item is the Q-matrix. Although construction of Q-matrix is typically performed by domain experts, it nonetheless, to a large extent, remains a subjective process, and misspecifications in the Q-matrix, if left unchecked, can have important practical implications. To address this concern, this paper proposes a discrimination index that can be used with a wide class of CDM subsumed by the generalized deterministic input, noisy "and" gate model to empirically validate the Q-matrix specifications by identifying and replacing misspecified entries in the Q-matrix. The rationale for using the index as the basis for a proposed validation method is provided in the form of mathematical proofs to several relevant lemmas and a theorem. The feasibility of the proposed method was examined using simulated data generated under various conditions. The proposed method is illustrated using fraction subtraction data.
Analysis of Nonlinear Dynamics by Square Matrix Method
Energy Technology Data Exchange (ETDEWEB)
Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II
2016-07-25
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.
Random matrix theory for pseudo-Hermitian systems: Cyclic blocks
Indian Academy of Sciences (India)
tems, and, for Hamiltonians that break parity P and time-reversal invariance T. In an attempt to understand the ... Keywords. Random matrices; circulants; quantum chaos; PT symmetry; pseudo-. Hermiticity. ... local fluctuation properties of complex quantum systems have universal properties, independent of the details of the ...
Schmessane, Andrea; Laboratory of matter out equilibrium Team
2012-11-01
Wave localization explains how a perturbation is trapped by the randomness present in a propagation medium. As it propagates, the localized wave amplitude decreases strongly by multiple internal reflections with randomly positioned scatterers, effectively trapping the perturbation inside the random region. The characteristic length where a localized wave is propagated before being extinguish by randomness is called localization length. We carried experiments in a quasi-onedimensional channel with random bottom in a shallow water regime for surface gravity water waves, using a Perfilometry Fourier Transform method, which enables us to obtain global surface measurements. We discuss keys aspects of the control of variables, the experimental setup and the implementation of the measurement method. Thus, we can control, measure and evaluate fundamental variables present in the localization phenomenon such as the type of randomness, scattering intensity and sample length, which allows us to characterize wave localization. We use the scattering matrix method to compare the experimental measurements with theoretical and numerical predictions, using the Lyapunov exponent of the scattering matrix, and discuss their agreement. Conicyt
Mueller coherency matrix method for contrast image in tissue polarimetry
Arce-Diego, J. L.; Fanjul-Vélez, F.; Samperio-García, D.; Pereda-Cubián, D.
2007-07-01
In this work, we propose the use of the Mueller Coherency matrix of biological tissues in order to increase the information from tissue images and so their contrast. This method involves different Mueller Coherency matrix based parameters, like the eigenvalues analysis, the entropy factor calculation, polarization components crosstalks, linear and circular polarization degrees, hermiticity or the Quaternions analysis in case depolarisation properties of tissue are sufficiently low. All these parameters make information appear clearer and so increase image contrast, so pathologies like cancer could be detected in a sooner stage of development. The election will depend on the concrete pathological process under study. This Mueller Coherency matrix method can be applied to a single tissue point, or it can be combined with a tomographic technique, so as to obtain a 3D representation of polarization contrast parameters in pathological tissues. The application of this analysis to concrete diseases can lead to tissue burn depth estimation or cancer early detection.
Universality in random matrix theory and chiral symmetry breaking in QCD
Energy Technology Data Exchange (ETDEWEB)
Akemann, G.
2000-05-01
In this work we review the topic of random matrix model universality with particular stress on its application to the study of chiral symmetry breaking in QCD. We highlight the role of microscopic and macroscopic matrix model correlation functions played in the description of the deep infrared eigenvalue spectrum of the Dirac operator. The universal microscopic correlation functions are presented for all three chiral symmetry breaking patterns, and the corresponding random matrix universality proofs are given for massless and massive fermions in a unified way. These analytic results have been widely confirmed from QCD lattice data and we present a comparison with the most recent analytic calculations describing data for dynamical SU(2) staggered fermions. The microscopic matrix model results are then re-expressed in terms of the finite-volume partition functions of Leutwyler and Smilga, where some of these expressions have been recently obtained using field theory only. The macroscopic random matrix universality is reviewed for the most simplest examples of bosonic and supersymmetric models. We also give an example for a non-universal deformation of a random matrix model - the restricted trace ensemble. (orig.)
Generalized Jones matrix method for homogeneous biaxial samples.
Ortega-Quijano, Noé; Fade, Julien; Alouini, Mehdi
2015-08-10
The generalized Jones matrix (GJM) is a recently introduced tool to describe linear transformations of three-dimensional light fields. Based on this framework, a specific method for obtaining the GJM of uniaxial anisotropic media was recently presented. However, the GJM of biaxial media had not been tackled so far, as the previous method made use of a simplified rotation matrix that lacks a degree of freedom in the three-dimensional rotation, thus being not suitable for calculating the GJM of biaxial media. In this work we propose a general method to derive the GJM of arbitrarily-oriented homogeneous biaxial media. It is based on the differential generalized Jones matrix (dGJM), which is the three-dimensional counterpart of the conventional differential Jones matrix. We show that the dGJM provides a simple and elegant way to describe uniaxial and biaxial media, with the capacity to model multiple simultaneous optical effects. The practical usefulness of this method is illustrated by the GJM modeling of the polarimetric properties of a negative uniaxial KDP crystal and a biaxial KTP crystal for any three-dimensional sample orientation. The results show that this method constitutes an advantageous and straightforward way to model biaxial media, which show a growing relevance for many interesting applications.
Monaghan, Philip Harold; Delvaux, John McConnell; Taxacher, Glenn Curtis
2015-06-09
A pre-form CMC cavity and method of forming pre-form CMC cavity for a ceramic matrix component includes providing a mandrel, applying a base ply to the mandrel, laying-up at least one CMC ply on the base ply, removing the mandrel, and densifying the base ply and the at least one CMC ply. The remaining densified base ply and at least one CMC ply form a ceramic matrix component having a desired geometry and a cavity formed therein. Also provided is a method of forming a CMC component.
Induced Dimension Reduction Method for Solving Linear Matrix Equations
Astudillo Rengifo, R.A.; van Gijzen, M.B.
2016-01-01
This paper discusses the solution of large-scale linear matrix equations using the Induced Dimension reduction method (IDR(s)). IDR(s) was originally presented to solve system of linear equations, and is based on the IDR(s) theorem. We generalize the IDR(s) theorem to solve linear problems in any
Induced Dimension Reduction method for solving linear matrix equations
Astudillo, R.; Van Gijzen, M.B.
2015-01-01
This paper discusses the solution of large-scale linear matrix equations using the Induced Dimension reduction method (IDR(s)). IDR(s) was originally presented to solve system of linear equations, and is based on the IDR(s) theorem. We generalize the IDR(s) theorem to solve linear problems in any
Matrix factorization method for the Hamiltonian structure of ...
Indian Academy of Sciences (India)
We demonstrate that the process of matrix factorization provides a systematic mathematical method to investigate the Hamiltonian structure of non-linear evolution equations characterized by hereditary operators with Nijenhuis property. Author Affiliations. S Ghosh1 B Talukdar1 S Chakraborti2. Department of Physics ...
Haar Wavelet Operational Matrix Method for Fractional Oscillation Equations
Directory of Open Access Journals (Sweden)
Umer Saeed
2014-01-01
Full Text Available We utilized the Haar wavelet operational matrix method for fractional order nonlinear oscillation equations and find the solutions of fractional order force-free and forced Duffing-Van der Pol oscillator and higher order fractional Duffing equation on large intervals. The results are compared with the results obtained by the other technique and with exact solution.
Mussard, Bastien; Jansen, Georg; Angyan, Janos
2016-01-01
Starting from the general expression for the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the co...
A trivial observation on time reversal in random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kaplan, L [Department of Physics, Tulane University, New Orleans, LA (United States); Leyvraz, F [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico (Mexico); Pineda, C [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico (Mexico); Seligman, T H [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico (Mexico)
2007-12-07
It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is time-reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models. (fast track communication)
Skew-orthogonal polynomials, differential systems and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Saugata [Abdus Salam ICTP, Strada Costiera 11, 34100, Trieste (Italy)
2007-01-26
We study skew-orthogonal polynomials with respect to the weight function exp [ - 2V(x)], with V(x) = {sigma}{sup 2d}{sub K=1}(u{sub K}/K)x{sup K}, u{sub 2d} > 0, d > 0. A finite subsequence of such skew-orthogonal polynomials arising in the study of orthogonal and symplectic ensembles of random matrices satisfies a system of differential-difference-deformation equation. The vectors formed by such subsequence have the rank equal to the degree of the potential in the quaternion sense. These solutions satisfy certain compatibility condition and hence admit a simultaneous fundamental system of solutions.
Yamanaka, Masanori
2013-08-01
We apply the random matrix theory to analyze the molecular dynamics simulation of macromolecules, such as proteins. The eigensystem of the cross-correlation matrix for the time series of the atomic coordinates is analyzed. We study a data set with seven different sampling intervals to observe the characteristic motion at each time scale. In all cases, the unfolded eigenvalue spacings are in agreement with the predictions of random matrix theory. In the short-time scale, the cross-correlation matrix has the universal properties of the Gaussian orthogonal ensemble. The eigenvalue distribution and inverse participation ratio have a crossover behavior between the universal and nonuniversal classes, which is distinct from the known results such as the financial time series. Analyzing the inverse participation ratio, we extract the correlated cluster of atoms and decompose it to subclusters.
Widening the Scope of R-matrix Methods
Energy Technology Data Exchange (ETDEWEB)
Thompson, Ian J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Dimitriou, Paraskevi [IAEA, Vienna (Austria); DeBoer, Richard J. [Nieuwland Science Hall, Notre Dame, IN (United States); Kunieda, Satoshi [Nuclear Data Center (JAEA), Tokai (Japan); Paris, Mark [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Thompson, Ian [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Trkov, Andrej [IAEA, Vienna (Austria)
2016-03-01
A Consultant’s Meeting was held at the IAEA Headquarters, from 7 to 9 December 2015, to discuss the status of R-matrix codes currently used in calculations of charged-particle induced reaction cross sections at low energies. The ultimate goal was to initiate an international effort, coordinated by the IAEA, to evaluate charged-particle induced reactions in the resolved-resonance region. Participants reviewed the capabilities of the codes, the different implementations of R-matrix theory and translatability of the R-matrix parameters, the evaluation methods and suitable data formats for broader dissemination. The details of the presentations and technical discussions, as well as the actions that were proposed to achieve the goal of the meeting are summarized in this report.
InstantLabs® Salmonella species detection method: matrix extension.
Sharma, Neil; Bambusch, Lauren; Le, Thu; Morey, Amit; Hayman, Melinda; Montez, Sergio J
2014-01-01
The performance of InstantLabs® Salmonella Species Food Safety Kit to detect Salmonella in four food matrixes was validated against the International Organization for Standardization (ISO) reference method 6579:2002. The matrixes (raw ground beef, raw chicken breast, raw ground chicken, and lettuce) were inoculated with low levels of Salmonella (Salmonella. Samples were validated using 375 g (meat) or 25 g (lettuce and poultry) test portions enriched in FASTGRO TM SE at 42±1 °C for 12 h and 10 h, respectively. All samples were confirmed using the ISO reference method, regardless of initial-screen result. The InstantLabs test method was shown to perform as well as or better than the reference method for the detection of Salmonella species in ground beef, chicken breast, ground chicken, and lettuce. Inclusivity and exclusivity testing revealed no false negatives among the 100 Salmonella serovars and no false positives among the 30 non-Salmonella species examined, respectively.
A New Method for Preparation of Metal Matrix Nanocomposites
Padhi, Payodhar; Panigrahi, S. C.; Ghosh, Sudipto
2008-10-01
Particulate metal matrix composites (MMCs) can involve ceramic particulates ranging in size from few nanometers to 500 μm. Particulates are added to the metal matrix for strengthening. In particular, addition of nanoparticles, even in quantities as small as 2 weight percent can enhance the hardness or yield strength by a factor as high as 2. There are several methods for the production of metal matrix nanocomposites including mechanical alloying , vertex process and spray deposition. However, the above processes are expensive. Solidification processing is a relatively cheaper route. However, during solidification processing nanoparticulates tend to agglomerate as a result of van der Waals forces and thus proper dispersion of the nano-particulate in metal matrix is a challenge. Yang et al dispersed nanoparticles in metal matrix by ultrasonic casting. However their technique has several drawbacks such as the oscillating probe, which is in direct contact with liquid metal, may dissolve in the liquid metal and contaminate it. Moreover, the extent of dispersion is not uniform. It is maximum near the probe and gradually decreases as one move away from the probe. Lastly in the method developed by Yang et al, the oscillating probe is removed from the liquid metal before cooling and solidification begin. This may lead to partial reagglomeration of nanoparticles. To overcome these difficulties a non-contact method, where the ultrasonic probe is not in direct contact with the liquid metal, was attempted to disperse nano-sized Al2O3 particulates in aluminum matrix. In this method the mold was subjected to ultrasonic vibration. Hardness measurements and microstructural studies using HRTEM were carried out on samples taken from different locations of the nanocomposite ingot cast by the non-contact method. Commercially pure liquid aluminum was used as matrix of the composite. The Al2O3 nano-powder was prepared by ball milling for 22 hr. The nanopowders were characterized using
Denoising of diffusion MRI using random matrix theory
Veraart, Jelle; Novikov, Dmitry S.; Christiaens, Daan; Ades-aron, Benjamin; Sijbers, Jan; Fieremans, Els
2016-01-01
We introduce and evaluate a post-processing technique for fast denoising diffusion-weighted MR images. By exploiting the intrinsic redundancy in diffusion MRI using universal properties of the eigenspectrum of random covariance matrices, we remove noise-only principal components, thereby enabling signal-to-noise ratio enhancements, yielding parameter maps of improved quality for visual, quantitative, and statistical interpretation. By studying statistics of residuals, we demonstrate that the technique suppresses local signal fluctuations that solely originate from thermal noise rather than from other sources such as anatomical detail. Furthermore, we achieve improved precision in the estimation of diffusion parameters and fiber orientations in the human brain without compromising the accuracy and/or spatial resolution. PMID:27523449
An Alternative Method for Computing Mean and Covariance Matrix of Some Multivariate Distributions
Radhakrishnan, R.; Choudhury, Askar
2009-01-01
Computing the mean and covariance matrix of some multivariate distributions, in particular, multivariate normal distribution and Wishart distribution are considered in this article. It involves a matrix transformation of the normal random vector into a random vector whose components are independent normal random variables, and then integrating…
Diffusion MRI noise mapping using random matrix theory
National Research Council Canada - National Science Library
Veraart, Jelle; Fieremans, Els; Novikov, Dmitry S
2016-01-01
.... Methods We exploit redundancy in non-Gaussian distributed multidirectional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices...
Alternating proximal gradient method for nonnegative matrix factorization
Xu, Yangyang
2011-01-01
Nonnegative matrix factorization has been widely applied in face recognition, text mining, as well as spectral analysis. This paper proposes an alternating proximal gradient method for solving this problem. With a uniformly positive lower bound assumption on the iterates, any limit point can be proved to satisfy the first-order optimality conditions. A Nesterov-type extrapolation technique is then applied to accelerate the algorithm. Though this technique is at first used for convex program, it turns out to work very well for the non-convex nonnegative matrix factorization problem. Extensive numerical experiments illustrate the efficiency of the alternating proximal gradient method and the accleration technique. Especially for real data tests, the accelerated method reveals high superiority to state-of-the-art algorithms in speed with comparable solution qualities.
The Random Material Point Method
Wang, B.; Vardon, P.J.; Hicks, M.A.
2017-01-01
The material point method is a finite element variant which allows the material, represented by a point-wise discretization, to move through the background mesh. This means that large deformations, such as those observed post slope failure, can be computed. By coupling this material level
Wang, Jian-Xun; Xiao, Heng
2016-01-01
Numerical models based on Reynolds-Averaged Navier-Stokes (RANS) equations are widely used in engineering turbulence modeling. However, the RANS predictions have large model-form uncertainties for many complex flows. Quantification of these large uncertainties originating from the modeled Reynolds stresses has attracted attention in turbulence modeling community. Recently, a physics-based Bayesian framework for quantifying model-form uncertainties has been proposed with successful applications to several flows. Nonetheless, how to specify proper priors without introducing unwarranted, artificial information remains challenging to the current form of the physics-based approach. Another recently proposed method based on random matrix theory provides the prior distributions with the maximum entropy, which is an alternative for model-form uncertainty quantification in RANS simulations. In this work, we utilize the random matrix theoretic approach to assess and possibly improve the specification of priors used in ...
Extrapolation techniques applied to matrix methods in neutron diffusion problems
Mccready, Robert R
1956-01-01
A general matrix method is developed for the solution of characteristic-value problems of the type arising in many physical applications. The scheme employed is essentially that of Gauss and Seidel with appropriate modifications needed to make it applicable to characteristic-value problems. An iterative procedure produces a sequence of estimates to the answer; and extrapolation techniques, based upon previous behavior of iterants, are utilized in speeding convergence. Theoretically sound limits are placed on the magnitude of the extrapolation that may be tolerated. This matrix method is applied to the problem of finding criticality and neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron-diffusion equations is treated. Results for this example are indicated.
The Matrix Element Method in the LHC era
Wertz, Sébastien
2017-03-01
The Matrix Element Method (MEM) is a powerful multivariate method allowing to maximally exploit the experimental and theoretical information available to an analysis. The method is reviewed in depth, and several recent applications of the MEM at LHC experiments are discussed, such as searches for rare processes and measurements of Standard Model observables in Higgs and Top physics. Finally, a new implementation of the MEM is presented. This project builds on established phase-space parametrisations known to greatly improve the speed of the calculations, and aims at a much improved modularity and maintainability compared to previous software, easing the use of the MEM for high-statistics data analyses.
Universality in Chiral Random Matrix Theory at {beta} = 1 and {beta} = 4
Energy Technology Data Exchange (ETDEWEB)
Sener, M.K.; Verbaarschot, J.J. [Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794 (United States)
1998-07-01
In this paper the kernel for the spectral correlation functions of invariant chiral random matrix ensembles with real ({beta}=1 ) and quaternion real ({beta}=4 ) matrix elements is expressed in terms of the kernel of the corresponding complex Hermitian random matrix ensembles ({beta}=2 ). Such identities are exact in case of a Gaussian probability distribution and, under certain smoothness assumptions, they are shown to be valid asymptotically for an arbitrary finite polynomial potential. They are proved by means of a construction proposed by Brezin and Neuberger. Universal behavior of the eigenvalues close to zero for all three chiral ensembles then follows from microscopic universality for {beta}=2 as shown by Akemann, Damgaard, Magnea, and Nishigaki. {copyright} {ital 1998} {ital The American Physical Society}
Non-extensive random matrix theory--a bridge connecting chaotic and regular dynamics
Energy Technology Data Exchange (ETDEWEB)
Abul-Magd, A.Y. [Faculty of Science, Zagazig University, Zagazig (Egypt)]. E-mail: a_y_abul_magd@hotmail.com
2004-11-29
We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis' q-parametrized entropy. We discuss the dependence of the spacing distribution on q using a non-extensive generalization of Wigner's surmises for ensembles belonging to the orthogonal, unitary and symplectic symmetry universal classes.
Photodissociation in quantum chaotic systems: Random-matrix theory of cross-section fluctuations
Energy Technology Data Exchange (ETDEWEB)
Fyodorov, Y.V. [Fachbereich Physik, Universitaet-GH Essen, D-45117 Essen (Germany); Alhassid, Y. [Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520 (United States)
1998-11-01
Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum chaos. {copyright} {ital 1998} {ital The American Physical Society}
Random matrix theory and discrete moments of the Riemann zeta function
Energy Technology Data Exchange (ETDEWEB)
Hughes, C P [Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
2003-03-28
We calculate the discrete moments of the characteristic polynomial of a random unitary matrix, evaluated a small distance away from an eigenangle. Such results allow us to make conjectures about similar moments for the Riemann zeta function, and provide a uniform approach to understanding moments of the zeta function and its derivative.
Open problems in applying random-matrix theory to nuclear reactions
Weidenmüller, H. A.
2014-09-01
Problems in applying random-matrix theory (RMT) to nuclear reactions arise in two domains. To justify the approach, statistical properties of isolated resonances observed experimentally must agree with RMT predictions. That agreement is less striking than would be desirable. In the implementation of the approach, the range of theoretically predicted observables is too narrow.
Energy Technology Data Exchange (ETDEWEB)
Hehl, H.
2002-07-01
This thesis has studied the range of validity of the chiral random matrix theory in QCD on the example of the quenched staggered Dirac operator. The eigenvalues of this operator in the neighbourhood of zero are essential for the understanding of the spontaneous breaking of the chiral symmetry and the phase transition connected with this. The phase transition cannot be understood in the framework of perturbation theory, so that the formulation of QCD on the lattice has been chosen as the only non-perturbative approach. In order to circumvent both the problem of the fermion doubling and to study chiral properties on the lattice with acceptable numerical effort, quenched Kogut-Susskind fermions have been applied. The corresponding Dirac operator can be completely diagonalized by the Lanczos procedure of Cullum and Willoughby. Monte carlo simulations on hypercubic lattice have been performed and the Dirac operators of very much configurations diagonalized at different lattice lengths and coupling constants. The eigenvalue correlations on the microscopic scale are completely described by the chiral random matrix theory for the topological sector zero, which has been studied by means of the distribution of the smallest eigenvalue, the microscopic spectral density and the corresponding 2-point correlation function. The found universal behaviour shows, that on the scale of the lowest eigenvalue only completely general properties of the theory are important, but not the full dynamics. In order to determine the energy scale, from which the chiral random matrix theory losses its validity, - the Thouless energy - with the scalar susceptibilities observables have been analyzed, which are because of their spectral mass dependence sensitive on this. For each combination of the lattice parameter so the deviation point has been identified.
Energy Technology Data Exchange (ETDEWEB)
Telfeyan, Katherine Christina [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ware, Stuart Douglas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Reimus, Paul William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Birdsell, Kay Hanson [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-11-06
Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.
Preasymptotic convergence of randomized Kaczmarz method
Jiao, Yuling; Jin, Bangti; Lu, Xiliang
2017-12-01
Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the initial error is smooth (e.g. sourcewise representation), the result explains the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.
Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II
Deift, Percy
2017-03-01
We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de Recherches Mathématiques, Montréal, June 7-11, 2015. We also describe progress that has been made on problems in an earlier list presented by the author on the occasion of his 60^{th} birthday in 2005 (see [Deift P., Contemp. Math., Vol. 458, Amer. Math. Soc., Providence, RI, 2008, 419-430, arXiv:0712.0849]).
On an Integrated Transfer Matrix method for multiply connected mufflers
Vijayasree, N. K.; Munjal, M. L.
2012-04-01
The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Exact solution of some linear matrix equations using algebraic methods
Djaferis, T. E.; Mitter, S. K.
1977-01-01
A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.
Low-temperature chemistry using the R-matrix method
Tennyson, Jonathan; Rivlin, Tom
2016-01-01
Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as th...
Method of making metal matrix composites reinforced with ceramic particulates
Cornie, James A.; Kattamis, Theodoulos; Chambers, Brent V.; Bond, Bruce E.; Varela, Raul H.
1989-01-01
Composite materials and methods for making such materials are disclosed in which dispersed ceramic particles are at chemical equilibrium with a base metal matrix, thereby permitting such materials to be remelted and subsequently cast or otherwise processed to form net weight parts and other finished (or semi-finished) articles while maintaining the microstructure and mechanical properties (e.g. wear resistance or hardness) of the original composite. The composite materials of the present invention are composed of ceramic particles in a base metal matrix. The ceramics are preferably carbides of titanium, zirconium, tungsten, molybdenum or other refractory metals. The base metal can be iron, nickel, cobalt, chromium or other high temperature metal and alloys thereof. For ferrous matrices, alloys suitable for use as the base metal include cast iron, carbon steels, stainless steels and iron-based superalloys.
Method of making metal matrix composites reinforced with ceramic particulates
Cornie, J.A.; Kattamis, T.; Chambers, B.V.; Bond, B.E.; Varela, R.H.
1989-08-01
Composite materials and methods for making such materials are disclosed in which dispersed ceramic particles are at chemical equilibrium with a base metal matrix, thereby permitting such materials to be remelted and subsequently cast or otherwise processed to form net weight parts and other finished (or semi-finished) articles while maintaining the microstructure and mechanical properties (e.g. wear resistance or hardness) of the original composite. The composite materials of the present invention are composed of ceramic particles in a base metal matrix. The ceramics are preferably carbides of titanium, zirconium, tungsten, molybdenum or other refractory metals. The base metal can be iron, nickel, cobalt, chromium or other high temperature metal and alloys thereof. For ferrous matrices, alloys suitable for use as the base metal include cast iron, carbon steels, stainless steels and iron-based superalloys. 2 figs.
A global test for gene‐gene interactions based on random matrix theory
Amos, Christopher I.; Moore, Jason H.
2016-01-01
ABSTRACT Statistical interactions between markers of genetic variation, or gene‐gene interactions, are believed to play an important role in the etiology of many multifactorial diseases and other complex phenotypes. Unfortunately, detecting gene‐gene interactions is extremely challenging due to the large number of potential interactions and ambiguity regarding marker coding and interaction scale. For many data sets, there is insufficient statistical power to evaluate all candidate gene‐gene interactions. In these cases, a global test for gene‐gene interactions may be the best option. Global tests have much greater power relative to multiple individual interaction tests and can be used on subsets of the markers as an initial filter prior to testing for specific interactions. In this paper, we describe a novel global test for gene‐gene interactions, the global epistasis test (GET), that is based on results from random matrix theory. As we show via simulation studies based on previously proposed models for common diseases including rheumatoid arthritis, type 2 diabetes, and breast cancer, our proposed GET method has superior performance characteristics relative to existing global gene‐gene interaction tests. A glaucoma GWAS data set is used to demonstrate the practical utility of the GET method. PMID:27386793
Energy Technology Data Exchange (ETDEWEB)
Berkolaiko, G., E-mail: berko@math.tamu.edu [Department of Mathematics, Texas A and M University, College Station, Texas 77843-3368 (United States); Kuipers, J., E-mail: Jack.Kuipers@physik.uni-regensburg.de [Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)
2013-11-15
To study electronic transport through chaotic quantum dots, there are two main theoretical approaches. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other treats the transport in the semiclassical approximation and studies correlations among sets of classical trajectories. There are established evaluation procedures within the semiclassical evaluation that, for several linear and nonlinear transport moments to which they were applied, have always resulted in the agreement with random matrix predictions. We prove that this agreement is universal: any semiclassical evaluation within the accepted procedures is equivalent to the evaluation within random matrix theory. The equivalence is shown by developing a combinatorial interpretation of the trajectory sets as ribbon graphs (maps) with certain properties and exhibiting systematic cancellations among their contributions. Remaining trajectory sets can be identified with primitive (palindromic) factorisations whose number gives the coefficients in the corresponding expansion of the moments of random matrices. The equivalence is proved for systems with and without time reversal symmetry.
Berkolaiko, G.; Kuipers, J.
2013-11-01
To study electronic transport through chaotic quantum dots, there are two main theoretical approaches. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other treats the transport in the semiclassical approximation and studies correlations among sets of classical trajectories. There are established evaluation procedures within the semiclassical evaluation that, for several linear and nonlinear transport moments to which they were applied, have always resulted in the agreement with random matrix predictions. We prove that this agreement is universal: any semiclassical evaluation within the accepted procedures is equivalent to the evaluation within random matrix theory. The equivalence is shown by developing a combinatorial interpretation of the trajectory sets as ribbon graphs (maps) with certain properties and exhibiting systematic cancellations among their contributions. Remaining trajectory sets can be identified with primitive (palindromic) factorisations whose number gives the coefficients in the corresponding expansion of the moments of random matrices. The equivalence is proved for systems with and without time reversal symmetry.
Fleming, H. E.
1977-01-01
Linear numerical inversion methods applied to atmospheric remote sounding generally can be categorized in two ways: (1) iterative, and (2) inverse matrix methods. However, these two categories are not unrelated; a duality exists between them. In other words, given an iterative scheme, a corresponding inverse matrix method exists, and conversely. This duality concept is developed for the more familiar linear methods. The iterative duals are compared with the classical linear iterative approaches and their differences analyzed. The importance of the initial profile in all methods is stressed. Calculations using simulated data are made to compare accuracies and to examine the dependence of the solution on the initial profile.
Matrix-valued polynomials in Lanczos type methods
Energy Technology Data Exchange (ETDEWEB)
Simoncini, V. [Universita di Padova (Italy); Gallopoulos, E. [Univ. of Illinois, Urbana, IL (United States)
1994-12-31
It is well known that convergence properties of iterative methods can be derived by studying the behavior of the residual polynomial over a suitable domain of the complex plane. Block Krylov subspace methods for the solution of linear systems A[x{sub 1},{hor_ellipsis}, x{sub s}] = [b{sub 1},{hor_ellipsis}, b{sub s}] lead to the generation of residual polynomials {phi}{sub m} {element_of} {bar P}{sub m,s} where {bar P}{sub m,s} is the subset of matrix-valued polynomials of maximum degree m and size s such that {phi}{sub m}(0) = I{sub s}, R{sub m} := B - AX{sub m} = {phi}{sub m}(A) {circ} R{sub 0}, where {phi}{sub m}(A) {circ} R{sub 0} := R{sub 0} - A{summation}{sub j=0}{sup m-1} A{sup j}R{sub 0}{xi}{sub j}, {xi}{sub j} {element_of} R{sup sxs}. An effective method has to balance adequate approximation with economical computation of iterates defined by the polynomial. Matrix valued polynomials can be used to improve the performance of block methods. Another approach is to solve for a single right-hand side at a time and use the generated information in order to update the approximations of the remaining systems. In light of this, a more general scheme is as follows: A subset of residuals (seeds) is selected and a block short term recurrence method is used to compute approximate solutions for the corresponding systems. At the same time the generated matrix valued polynomial is implicitly applied to the remaining residuals. Subsequently a new set of seeds is selected and the process is continued as above, till convergence of all right-hand sides. The use of a quasi-minimization technique ensures a smooth convergence behavior for all systems. In this talk the authors discuss the implementation of this class of algorithms and formulate strategies for the selection of parameters involved in the computation. Experiments and comparisons with other methods will be presented.
Thimble regularization at work: From toy models to chiral random matrix theories
Di Renzo, F.; Eruzzi, G.
2015-10-01
We apply the Lefschetz thimble formulation of field theories to a couple of different problems. We first address the solution of a complex zero-dimensional ϕ4 theory. Although very simple, this toy model makes us appreciate a few key issues of the method. In particular, we will solve the model by a correct accounting of all the thimbles giving a contribution to the partition function and we will discuss a number of algorithmic solutions to simulate this (simple) model. We will then move to a chiral random matrix (CRM) theory. This is a somehow more realistic setting, giving us once again the chance to tackle the same couple of fundamental questions: How many thimbles contribute to the solution? How can we make sure that we correctly sample configurations on the thimble? Since the exact result is known for the observable we study (a condensate), we can verify that, in the region of parameters we studied, only one thimble contributes and that the algorithmic solution that we set up works well, despite its very crude nature. The deviation of results from phase quenched ones highlights that in a certain region of parameter space there is a quite important sign problem. In view of this, the success of our thimble approach is quite a significant one.
Thimble regularization at work: from toy models to chiral random matrix theories
Di Renzo, Francesco
2015-01-01
We apply the Lefschetz thimble formulation of field theories to a couple of different problems. We first address the solution of a complex 0-dimensional phi^4 theory. Although very simple, this toy-model makes us appreciate a few key issues of the method. In particular, we will solve the model by a correct accounting of all the thimbles giving a contribution to the partition function and we will discuss a number of algorithmic solutions to simulate this (simple) model. We will then move to a chiral random matrix (CRM) theory. This is a somehow more realistic setting, giving us once again the chance to tackle the same couple of fundamental questions: how many thimbles contribute to the solution? how can we make sure that we correctly sample configurations on the thimble? Since the exact result is known for the observable we study (a condensate), we can verify that, in the region of parameters we studied, only one thimble contributes and that the algorithmic solution that we set up works well, despite its very ...
Kanazawa, Takuya; Wettig, Tilo
2014-10-01
We generalize QCD at asymptotically large isospin chemical potential to an arbitrary even number of flavors. We also allow for small quark chemical potentials, which stress the coincident Fermi surfaces of the paired quarks and lead to a sign problem in Monte Carlo simulations. We derive the corresponding low-energy effective theory in both p- and ɛ-expansion and quantify the severity of the sign problem. We construct the random matrix theory describing our physical situation and show that it can be mapped to a known random matrix theory at low baryon density so that new insights can be gained without additional calculations. In particular, we explain the Silver Blaze phenomenon at high isospin density. We also introduce stressed singular values of the Dirac operator and relate them to the pionic condensate. Finally we comment on extensions of our work to two-color QCD.
Surprising Pfaffian factorizations in random matrix theory with Dyson index β = 2
Kieburg, Mario
2012-03-01
In recent decades, determinants and Pfaffians were found for eigenvalue correlations of various random matrix ensembles. These structures simplify the average over a large number of ratios of characteristic polynomials to integrations over one and two characteristic polynomials only. Up to now it was thought that determinants occur for ensembles with Dyson index β = 2, whereas Pfaffians only for ensembles with β = 1, 4. We derive a non-trivial Pfaffian determinant for β = 2 random matrix ensembles which is similar to the one for β = 1, 4. Thus, it unveils a hidden universality of this structure. We also give a general relation between the orthogonal polynomials related to the determinantal structure and the skew-orthogonal polynomials corresponding to the Pfaffian. As a particular example, we consider the chiral unitary ensembles in great detail.
Random matrix theory and the zeros of {zeta}'(s)
Energy Technology Data Exchange (ETDEWEB)
Mezzadri, Francesco [School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK (United Kingdom)
2003-03-28
We study the density of the roots of the derivative of the characteristic polynomial Z(U, z) of an N x N random unitary matrix with distribution given by Haar measure on the unitary group. Based on previous random matrix theory models of the Riemann zeta function {zeta}(s), this is expected to be an accurate description for the horizontal distribution of the zeros of {zeta}'(s) to the right of the critical line. We show that as N {yields} {infinity} the fraction of the roots of Z'(U, z) that lie in the region 1 - x/(N - 1) {<=} vertical bar z vertical bar < 1 tends to a limit function. We derive asymptotic expressions for this function in the limits x {yields} {infinity} and x {yields} 0 and compare them with numerical experiments.
Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory
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.
The intersection numbers of the p-spin curves from random matrix theory
Brézin, E.; Hikami, S.
2013-02-01
The intersection numbers of p-spin curves are computed through correlation functions of Gaussian ensembles of random matrices in an external matrix source. The p-dependence of intersection numbers is determined as polynomial in p; the large p behavior is also considered. The analytic continuation of intersection numbers to negative values of p is discussed in relation to SL(2,R)/U(1) black hole sigma model.
Application of random matrix theory to microarray data for discovering functional gene modules
Energy Technology Data Exchange (ETDEWEB)
Luo, F. [Xiangtan University, Xiangtan Hunan, China; Zhong, Jianxin [ORNL; Yang, Y. F. [unknown; Zhou, Jizhong [ORNL
2006-03-01
We show that spectral fluctuation of coexpression correlation matrices of yeast gene microarray profiles follows the description of the Gaussian orthogonal ensemble (GOE) of the random matrix theory (RMT) and removal of small values of the correlation coefficients results in a transition from the GOE statistics to the Poisson statistics of the RMT. This transition is directly related to the structural change of the gene expression network from a global network to a network of isolated modules.
Analysis of aeroplane boarding via spacetime geometry and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Bachmat, E [Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105 (Israel); Berend, D [Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105 (Israel); Sapir, L [Department of Management and Industrial Engineering, Ben-Gurion University, Beer-Sheva 84105 (Israel); Skiena, S [Department of Computer science, SUNY at Stony Brook, Stony Brook, NY 11794 (United States); Stolyarov, N [Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105 (Israel)
2006-07-21
We show that aeroplane boarding can be asymptotically modelled by two-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are closely related to random matrix theory. The models can be used to explain why some commonly practiced airline boarding policies are ineffective and even detrimental. (letter to the editor)
UA(1) breaking and phase transition in chiral random matrix model
Sano, T.; Fujii, H.; Ohtani, M
2009-01-01
We propose a chiral random matrix model which properly incorporates the flavor-number dependence of the phase transition owing to the \\UA(1) anomaly term. At finite temperature, the model shows the second-order phase transition with mean-field critical exponents for two massless flavors, while in the case of three massless flavors the transition turns out to be of the first order. The topological susceptibility satisfies the anomalous \\UA(1) Ward identity and decreases gradually with the temp...
Method of manufacturing a matrix for the detection of mismatches
Ershov, Gennady Moiseevich; Mirzabekov, Andrei Darievich
1998-01-01
This method for preparing micromatrices consists in applying a specially-patterned intermediate layer of laser-absorbing substance on a solid support. The configuration of the sublayer fully corresponds to the topology of the manufactured matrix. The intermediate layer is further covered by a continuous layer of gel , the gel and the material of the support being transparent towards laser radiation. The gel layer is irradiated by a laser beam for a time needed to evaporate simultaneously the gel in the places immediately above the laser-absorbing sublayer and the sublayer itself. Oligonucleotides from a chosen set are then attached to the formed gel `cells`, one oligonucleotide to each cell. This method is intended for use in biotechnology, specifically for deciphering the nucleotide sequence of DNA.
Transient Analysis of Hysteresis Queueing Model Using Matrix Geometric Method
Directory of Open Access Journals (Sweden)
Wajiha Shah
2011-10-01
Full Text Available Various analytical methods have been proposed for the transient analysis of a queueing system in the scalar domain. In this paper, a vector domain based transient analysis is proposed for the hysteresis queueing system with internal thresholds for the efficient and numerically stable analysis. In this system arrival rate of customer is controlled through the internal thresholds and the system is analyzed as a quasi-birth and death process through matrix geometric method with the combination of vector form Runge-Kutta numerical procedure which utilizes the special matrices. An arrival and service process of the system follows a Markovian distribution. We analyze the mean number of customers in the system when the system is in transient state against varying time for a Markovian distribution. The results show that the effect of oscillation/hysteresis depends on the difference between the two internal threshold values.
Berkolaiko, Gregory; Kuipers, Jack
2012-04-01
Electronic transport through chaotic quantum dots exhibits universal, system-independent properties, consistent with random-matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the classical scattering trajectories. Correlations between such trajectories can be organized diagrammatically and have been shown to yield universal answers for some observables. Here, we develop the general combinatorial treatment of the semiclassical diagrams, through a connection to factorizations of permutations. We show agreement between the semiclassical and random matrix approaches to the moments of the transmission eigenvalues. The result is valid for all moments to all orders of the expansion in inverse channel number for all three main symmetry classes (with and without time-reversal symmetry and spin-orbit interaction) and extends to nonlinear statistics. This finally explains the applicability of random-matrix theory to chaotic quantum transport in terms of the underlying dynamics as well as providing semiclassical access to the probability density of the transmission eigenvalues.
Spectral properties of the Wilson-Dirac operator and random matrix theory
Kieburg, Mario; Verbaarschot, Jacobus J. M.; Zafeiropoulos, Savvas
2013-11-01
Random matrix theory has been successfully applied to lattice quantum chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson-Dirac operator. In this paper, we study the infrared spectrum of the Wilson-Dirac operator via random matrix theory including the three leading order a2 correction terms that appear in the corresponding chiral Lagrangian. A derivation of the joint probability density of the eigenvalues is presented. This result is used to calculate the density of the complex eigenvalues, the density of the real eigenvalues, and the distribution of the chiralities over the real eigenvalues. A detailed discussion of these quantities shows how each low-energy constant affects the spectrum. Especially we consider the limit of small and large (which is almost the mean field limit) lattice spacing. Comparisons with Monte Carlo simulations of the random matrix theory show a perfect agreement with the analytical predictions. Furthermore we present some quantities which can be easily used for comparison of lattice data and the analytical results.
Analogies between random matrix ensembles and the one-component plasma in two-dimensions
Directory of Open Access Journals (Sweden)
Peter J. Forrester
2016-03-01
Full Text Available The eigenvalue PDF for some well known classes of non-Hermitian random matrices — the complex Ginibre ensemble for example — can be interpreted as the Boltzmann factor for one-component plasma systems in two-dimensional domains. We address this theme in a systematic fashion, identifying the plasma system for the Ginibre ensemble of non-Hermitian Gaussian random matrices G, the spherical ensemble of the product of an inverse Ginibre matrix and a Ginibre matrix G1−1G2, and the ensemble formed by truncating unitary matrices, as well as for products of such matrices. We do this when each has either real, complex or real quaternion elements. One consequence of this analogy is that the leading form of the eigenvalue density follows as a corollary. Another is that the eigenvalue correlations must obey sum rules known to characterise the plasma system, and this leads us to an exhibit of an integral identity satisfied by the two-particle correlation for real quaternion matrices in the neighbourhood of the real axis. Further random matrix ensembles investigated from this viewpoint are self dual non-Hermitian matrices, in which a previous study has related to the one-component plasma system in a disk at inverse temperature β=4, and the ensemble formed by the single row and column of quaternion elements from a member of the circular symplectic ensemble.
Aspects of fabrication aluminium matrix heterophase composites by suspension method
Dolata, A. J.; Dyzia, M.
2012-05-01
Composites with an aluminium alloy matrix (AlMMC) exhibit several advantageous properties such as good strength, stiffness, low density, resistance and dimensional stability to elevated temperatures, good thermal expansion coefficient and particularly high resistance to friction wear. Therefore such composites are more and more used in modern engineering constructions. Composites reinforced with hard ceramic particles (Al2O3, SiC) are gradually being implemented into production in automotive or aircraft industries. Another application of AlMMC is in the electronics industry, where the dimensional stability and capacity to absorb and remove heat is used in radiators. However the main problems are still: a reduction of production costs, developing methods of composite material tests and final product quality assessment, standardisation, development of recycling and mechanical processing methods. AlMMC production technologies, based on liquid-phase methods, and the shaping of products by casting methods, belong to the cheapest production methods. Application of a suspension method for the production of composites with heterophase reinforcement may turn out to be a new material and technological solution. The article presents the material and technological aspects of the transfer procedures for the production of composite suspensions from laboratory scale to a semi-industrial scale.
Chemical Decellularization Methods and Its Effects on Extracellular Matrix
Directory of Open Access Journals (Sweden)
Amir Hossein Akbari Zahmati
2017-08-01
Full Text Available Background: Extracellular matrix (ECM produced by tissue decellularization processes as a biological scaffold due to its unique properties compared to other scaffolds for migration and implantation of stem cells have been used successfully in the field of tissue engineering and regenerative medicine in the last years. The objective of this manuscript was to provide an overview of the chemical decellularization methods, evaluation of decellularized ECM and the potential effect of the chemical decellularization agents on the biochemical composition. Methods: We searched in Google Scholar, PubMed, Scopus, and Science Direct. The literature search was done by using the following keywords: “ECM, biologic scaffold, decellularization, chemical methods, tissue engineering.” We selected articles have been published from 2000 to 2016, and 15 full texts and 97 abstracts were reviewed. Results:Employing an optimization method to minimize damage to the ECM ultrastructure as for a result of the lack of reduction in mechanical properties and also the preservation of essential proteins such as laminin, fibronectin, Glycosaminoglycans (GAGs, growth factor is required. Various methods include chemical, physical and enzymatic technics were studied. However, on each of these methods can have undesirable effects on ECM. Conclusion: It is suggested that instead of the Sodium dodecyl sulfate (SDS which have high strength degradation, we can use zwitterionic separately or in combination with SDS. Tributyl phosphate (TBP due to its unique properties can be used in decellularization process.
Teaching Improvement Model Designed with DEA Method and Management Matrix
Montoneri, Bernard
2014-01-01
This study uses student evaluation of teachers to design a teaching improvement matrix based on teaching efficiency and performance by combining management matrix and data envelopment analysis. This matrix is designed to formulate suggestions to improve teaching. The research sample consists of 42 classes of freshmen following a course of English…
A note on the multiple-recursive matrix method for generating pseudorandom vectors
Bishoi, Susil Kumar; Haran, Himanshu Kumar; Hasan, Sartaj Ul
2016-01-01
The multiple-recursive matrix method for generating pseudorandom vectors was introduced by Niederreiter (Linear Algebra Appl. 192 (1993), 301-328). We propose an algorithm for finding an efficient primitive multiple-recursive matrix method. Moreover, for improving the linear complexity, we introduce a tweak on the contents of the primitive multiple-recursive matrix method.
Liu, Yuanyuan; Jiao, L C; Shang, Fanhua; Yin, Fei; Liu, F
2013-12-01
In recent years, matrix rank minimization problems have aroused considerable interests from machine learning, data mining and computer vision communities. All of these problems can be solved via their convex relaxations which minimize the trace norm instead of the rank of the matrix, and have to be solved iteratively and involve singular value decomposition (SVD) at each iteration. Therefore, those algorithms for trace norm minimization problems suffer from high computation cost of multiple SVDs. In this paper, we propose an efficient Matrix Bi-Factorization (MBF) method to approximate the original trace norm minimization problem and mitigate the computation cost of performing SVDs. The proposed MBF method can be used to address a wide range of low-rank matrix recovery and completion problems such as low-rank and sparse matrix decomposition (LRSD), low-rank representation (LRR) and low-rank matrix completion (MC). We also present three small scale matrix trace norm models for LRSD, LRR and MC problems, respectively. Moreover, we develop two concrete linearized proximal alternative optimization algorithms for solving the above three problems. Experimental results on a variety of synthetic and real-world data sets validate the efficiency, robustness and effectiveness of our MBF method comparing with the state-of-the-art trace norm minimization algorithms. Copyright © 2013 Elsevier Ltd. All rights reserved.
Moments of the transmission eigenvalues, proper delay times and random matrix theory II
Mezzadri, F.; Simm, N. J.
2012-05-01
We systematically study the first three terms in the asymptotic expansions of the moments of the transmission eigenvalues and proper delay times as the number of quantum channels n in the leads goes to infinity. The computations are based on the assumption that the Landauer-Büttiker scattering matrix for chaotic ballistic cavities can be modelled by the circular ensembles of random matrix theory. The starting points are the finite-n formulae that we recently discovered [F. Mezzadri and N. J. Simm, "Moments of the transmission eigenvalues, proper delay times and random matrix theory," J. Math. Phys. 52, 103511 (2011)], 10.1063/1.3644378. Our analysis includes all the symmetry classes β ∈ {1, 2, 4}; in addition, it applies to the transmission eigenvalues of Andreev billiards, whose symmetry classes were classified by Zirnbauer ["Riemannian symmetric superspaces and their origin in random-matrix theory," J. Math. Phys. 37(10), 4986 (1996)], 10.1063/1.531675 and Altland and Zirnbauer ["Random matrix theory of a chaotic Andreev quantum dot," Phys. Rev. Lett. 76(18), 3420 (1996), 10.1103/PhysRevLett.76.3420; Altland and Zirnbauer "Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures," Phys. Rev. B 55(2), 1142 (1997)], 10.1103/PhysRevB.55.1142. Where applicable, our results are in complete agreement with the semiclassical theory of mesoscopic systems developed by Berkolaiko et al. ["Full counting statistics of chaotic cavities from classical action correlations," J. Phys. A: Math. Theor. 41(36), 365102 (2008)], 10.1088/1751-8113/41/36/365102 and Berkolaiko and Kuipers ["Moments of the Wigner delay times," J. Phys. A: Math. Theor. 43(3), 035101 (2010), 10.1088/1751-8113/43/3/035101; Berkolaiko and Kuipers "Transport moments beyond the leading order," New J. Phys. 13(6), 063020 (2011)], 10.1088/1367-2630/13/6/063020. Our approach also applies to the Selberg-like integrals. We calculate the first two terms in their asymptotic expansion
Methods and analysis of realizing randomized grouping.
Hu, Liang-Ping; Bao, Xiao-Lei; Wang, Qi
2011-07-01
Randomization is one of the four basic principles of research design. The meaning of randomization includes two aspects: one is to randomly select samples from the population, which is known as random sampling; the other is to randomly group all the samples, which is called randomized grouping. Randomized grouping can be subdivided into three categories: completely, stratified and dynamically randomized grouping. This article mainly introduces the steps of complete randomization, the definition of dynamic randomization and the realization of random sampling and grouping by SAS software.
On the Transfer Matrix of the Modified Power Method
Zhang, Peng; Lee, Hyunsuk; Lee, Deokjung
2018-01-01
The characteristics of the Transfer Matrix (TM) introduced in the modified power method (MPM) have been studied. Because it can be easily mistaken as the Fission Matrix (FM), the differences between the FM and TM are discussed. Theoretically, it can be concluded that the FM is eigenmode dependent unless a very fine mesh is adopted for the FM tally, whereas the TM is based on the coarse mesh and it can give the correct higher eigenmode solutions if the exact weight cancellation can be done. This is confirmed by comparing the analytical solutions of a one-dimensional monoenergetic homogeneous diffusion problem with the solutions of the 2-by-2 FM and TM. It is further confirmed by the numerical tests that the FM tallied with a coarse mesh cannot give correct higher mode solutions, and the FM tallied with i th mode neutron weights but on a coarse mesh can only give a correct i th mode solution. The numerical tests also confirm that the TM of various sizes, when different numbers of modes are considered, can give the first several eigenmode solutions correctly and consistently with the same fine mesh based weight cancellation. The impact of the mesh size on the results of the MPM has also been investigated. In practice, the FM only requires the fundamental mode neutron source, but the TM requires simulating the first several eigenmode fission sources explicitly. The FM and the TM can be used to accelerate the convergence of the fundamental mode. The FM uses its fundamental eigenvector to adjust the neutron weights. The TM is used to calculate the combination coefficients which can then be used to update the neutron sources. All the comparisons clearly prove that the TM is different from the FM and that the TM requires further investigation.
Kanazawa, Takuya; Yamamoto, Arata
2016-01-01
We apply QCD-inspired techniques to study nonrelativistic N -component degenerate fermions with attractive interactions. By analyzing the singular-value spectrum of the fermion matrix in the Lagrangian, we derive several exact relations that characterize spontaneous symmetry breaking U (1 )×SU (N )→Sp (N ) through bifermion condensates. These are nonrelativistic analogues of the Banks-Casher relation and the Smilga-Stern relation in QCD. Nonlocal order parameters are also introduced and their spectral representations are derived, from which a nontrivial constraint on the phase diagram is obtained. The effective theory of soft collective excitations is derived, and its equivalence to random matrix theory is demonstrated in the ɛ regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.
Riemannian symmetric superspaces and their origin in random-matrix theory
Energy Technology Data Exchange (ETDEWEB)
Zirnbauer, M.R. [Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, California 93106 (United States)
1996-10-01
Gaussian random-matrix ensembles defined over the tangent spaces of the large families of Cartan{close_quote}s symmetric spaces are considered. Such ensembles play a central role in mesoscopic physics, as they describe the universal ergodic limit of disordered and chaotic single-particle systems. The generating function for the spectral correlations of each ensemble is reduced to an integral over a Riemannian symmetric superspace in the limit of large matrix dimension. Such a space is defined as a pair ({ital G}/{ital H},{ital M}{sub {ital r}}), where {ital G}/{ital H} is a complex-analytic graded manifold homogeneous with respect to the action of a complex Lie supergroup {ital G}, and {ital M}{sub {ital r}} is a maximal Riemannian submanifold of the support of {ital G}/{ital H}. {copyright} {ital 1996 American Institute of Physics.}
On matrix diffusion: formulations, solution methods and qualitative effects
Carrera, Jesús; Sánchez-Vila, Xavier; Benet, Inmaculada; Medina, Agustín; Galarza, Germán; Guimerà, Jordi
Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φm2RmDm / Lm2, whereas late-time behavior (long tracer tests) depends only on φmRm, and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. RésuméLa diffusion matricielle est un phénomène reconnu maintenant comme un mécanisme de transport important. Malheureusement, la prise en compte de la diffusion matricielle complique la simulation du transport de soluté. Ce problème a conduit à des formulations simplifiées, en partie à cause de la méthode de résolution. Il s'en est suivi une certaine confusion sur la façon de poser correctement le problème. L'un des objectifs de ce travail est de trouver une certaine unité parmi les formulations et les méthodes de résolution. C'est ainsi que certaines propriétés asymptotiques de la diffusion matricielle ont été dérivées. En particulier, le comportement à l'origine (expériences de traçage courtes) dépend uniquement du terme φm2RmDm / Lm2, alors que le comportement à long terme
Matrix element method for high performance computing platforms
Grasseau, G.; Chamont, D.; Beaudette, F.; Bianchini, L.; Davignon, O.; Mastrolorenzo, L.; Ochando, C.; Paganini, P.; Strebler, T.
2015-12-01
Lot of efforts have been devoted by ATLAS and CMS teams to improve the quality of LHC events analysis with the Matrix Element Method (MEM). Up to now, very few implementations try to face up the huge computing resources required by this method. We propose here a highly parallel version, combining MPI and OpenCL, which makes the MEM exploitation reachable for the whole CMS datasets with a moderate cost. In the article, we describe the status of two software projects under development, one focused on physics and one focused on computing. We also showcase their preliminary performance obtained with classical multi-core processors, CUDA accelerators and MIC co-processors. This let us extrapolate that with the help of 6 high-end accelerators, we should be able to reprocess the whole LHC run 1 within 10 days, and that we have a satisfying metric for the upcoming run 2. The future work will consist in finalizing a single merged system including all the physics and all the parallelism infrastructure, thus optimizing implementation for best hardware platforms.
Random matrix theory and higher genus integrability: the quantum chiral Potts model
Energy Technology Data Exchange (ETDEWEB)
Angles d' Auriac, J.Ch. [Centre de Recherches sur les Tres Basses Temperatures, BP 166, Grenoble (France)]. E-mail: dauriac@polycnrs-gre.fr; Maillard, J.M.; Viallet, C.M. [LPTHE, Tour 16, Paris (France)]. E-mails: maillard@lpthe.jussieu.fr; viallet@lpthe.jussieu.fr
2002-06-14
We perform a random matrix theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L 8. Our analysis gives clear evidence of a Gaussian orthogonal ensemble (GOE) statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore, a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of 'higher genus integrability'. (author)
Energy Technology Data Exchange (ETDEWEB)
Akemann, G.; Kanzieper, E
2001-03-01
The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low-energy correlation functions of all three chiral symmetry breaking patterns (labeled by the Dyson index {beta} = 1, 2 and 4) on the same footing, offering a unifying description of massive QCD Dirac spectra. RMT universality is explicitly proven for all three symmetry classes and the results are compared to the available lattice data for {beta} = 4.
Lattice QCD in the {epsilon}-regime and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Giusti, L.; Luescher, M. [CERN, Geneva (Switzerland); Weisz, P. [Max-Planck-Institut fuer Physik, Muenchen (Germany); Wittig, H. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2003-11-01
In the {epsilon}-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-precision numerical data obtained from quenched lattice QCD for a range of lattice spacings and volumes. While no complete matching is observed, the results agree with theoretical expectations at volumes larger than about 5 fm{sup 4}. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Edwards, R.G.; Heller, U.M. [SCRI, Florida State University, Tallahassee, Florida 32306-4130 (United States); Narayanan, R. [Department of Physics, Building 510A, Brookhaven National Laboratory, P. O. Box 5000, Upton, New York 11973 (United States)
1999-10-01
The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and symplectic ensembles. Lattice gauge theory with staggered fermions has verified two of the cases so far, unitary and symplectic, with staggered fermions in the fundamental representation of SU(3) and SU(2). We verify the missing case here, namely orthogonal, with staggered fermions in the adjoint representation of SU(N{sub c}), N{sub c}=2,3. {copyright} {ital 1999} {ital The American Physical Society}
Lattice QCD in the {epsilon}-regime and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Giusti, Leonardo; Luescher, Martin [CERN, Theory Division, Geneva (Switzerland)]. E-mail addresses: leonardo.giusti@cern.ch; luscher@mail.cern.ch; Weisz, Peter [Max-Planck-Institut fuer Physik, Munich (Germany)]. E-mail: pew@dmumpiwh.mppmu.mpg.de; Wittig, Hartmut [DESY, Theory Group, Hamburg (Germany)]. E-mail: hartmut.wittig@desy.de
2003-11-01
In the {epsilon}-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-precision numerical data obtained from quenched lattice QCD for a range of lattice spacings and volumes. While no complete matching is observed, the results agree with theoretical expectations at volumes larger than about 5 fm{sup 4}. (author)
Slope failure analysis using the random material point method
Wang, B.; Hicks, M.A.; Vardon, P.J.
2016-01-01
The random material point method (RMPM), which combines random field theory and the material point method (MPM), is proposed. It differs from the random finite-element method (RFEM), by assigning random field (cell) values to material points that are free to move relative to the computational grid
Analysis of symmetry breaking in quartz blocks using superstatistical random-matrix theory
Abul-Magd, A. Y.; Mazen, S. A.; Abdel-Mageed, M.
2012-06-01
We study the symmetry breaking of acoustic resonances measured by Ellegaard et al. (1996) [1] in quartz blocks. The observed resonance spectra show a gradual transition from a superposition of two uncoupled components, one for each symmetry realization, to a single component that is well represented by a Gaussian orthogonal ensemble (GOE) of random matrices. We discuss the applicability of superstatistical random-matrix theory to the final stages of the symmetry-breaking transition. A comparison is made between the formula from superstatistics and that from a previous work by Abd El-Hady et al. (2002) [7], which describes the same data by introducing a third GOE component. Our results suggest that the inverse chi-squared superstatistics could be used for studying the whole symmetry-breaking process.
Stochastic finite element method with simple random elements
Starkloff, Hans-Jörg
2008-01-01
We propose a variant of the stochastic finite element method, where the random elements occuring in the problem formulation are approximated by simple random elements, i.e. random elements with only a finite number of possible values.
A top quark mass measurement using a matrix element method
Energy Technology Data Exchange (ETDEWEB)
Linacre, Jacob Thomas [St. John' s College, Annapolis, MD (United States)
2009-01-01
A measurement of the mass of the top quark is presented, using top-antitop pair (t$\\bar{t}$) candidate events for the lepton+jets decay channel. The measurement makes use of Tevatron p$\\bar{p}$ collision data at centre-of-mass energy √s = 1.96 TeV, collected at the CDF detector. The top quark mass is measured by employing an unbinned maximum likelihood method where the event probability density functions are calculated using signal (t$\\bar{t}$) and background (W+jets) matrix elements, as well as a set of parameterised jet-to-parton mapping functions. The likelihood function is maximised with respect to the top quark mass, the fraction of signal events, and a correction to the jet energy scale (JES) of the calorimeter jets. The simultaneous measurement of the JES correction (Δ_{JES}) provides an in situ jet energy calibration based on the known mass of the hadronically decaying W boson. Using 578 lepton+jets candidate events corresponding to 3.2 fb ^{-1} of integrated luminosity, the top quark mass is measured to be m_{t} = 172.4± 1.4 (stat+Δ_{JES}) ±1.3 (syst) GeV=c^{2}, one of the most precise single measurements to date.
Global Fits of the CKM Matrix with the SCAN Method
Eigen, G; Hitlin, D G; Porter, F C
2015-01-01
We present a Scan Method analysis of the allowed region of the rho bar - eta bar plane using the latest input measurements of the CKM matrix elements, sin 2 beta, B0(s,d) mixing, epsilon(K), alpha and gamma. In this approach, we make no assumptions as to the distribution of theory uncertainties; rather, we scan over the range of plausible theoretical uncertainties and determine confidence level contours in the rho bar eta bar plane. We determine alpha from branching fraction and CP asymmetry measurements of B decays to all light pseudoscalar-pseudoscalar, pesudoscalar-vector, vector-vector and a1-psudoscalar mesons and determine gamma from D(*)K(*), D(*) pi and D rho modes, thereby including correlations between the angles of the unitarity triangle. We parametrize the individual decay amplitudes in terms of color-allowed tree, color-suppressed tree, gluonic penguin, singlet penguin, electroweak penguin, as well as W-exchange and W-annihilation amplitudes. Our procedure accounts for all correlations among the ...
A bi-diagonal method for finding the determinant of a matrix | Aminu ...
African Journals Online (AJOL)
The determinant of a matrix always depends on the concept of row or column. That is to evaluate the determinant of a matrix using several existing methods we use rows and column. In this paper we introduce the concept of false-determinant which is the determinant obtained using the diagonal elements of a matrix instead ...
Random projection and SVD methods in hyperspectral imaging
Zhang, Jiani
Hyperspectral imaging provides researchers with abundant information with which to study the characteristics of objects in a scene. Processing the massive hyperspectral imagery datasets in a way that efficiently provides useful information becomes an important issue. In this thesis, we consider methods which reduce the dimension of hyperspectral data while retaining as much useful information as possible. Traditional deterministic methods for low-rank approximation are not always adaptable to process huge datasets in an effective way, and therefore probabilistic methods are useful in dimension reduction of hyperspectral images. In this thesis, we begin by generally introducing the background and motivations of this work. Next, we summarize the preliminary knowledge and the applications of SVD and PCA. After these descriptions, we present a probabilistic method, randomized Singular Value Decomposition (rSVD), for the purposes of dimension reduction, compression, reconstruction, and classification of hyperspectral data. We discuss some variations of this method. These variations offer the opportunity to obtain a more accurate reconstruction of the matrix whose singular values decay gradually, to process matrices without target rank, and to obtain the rSVD with only one single pass over the original data. Moreover, we compare the method with Compressive-Projection Principle Component Analysis (CPPCA). From the numerical results, we can see that rSVD has better performance in compression and reconstruction than truncated SVD and CPPCA. We also apply rSVD to classification methods for the hyperspectral data provided by the National Geospatial-Intelligence Agency (NGA).
A Robust Method to Improve Stability in Matrix Converters
DEFF Research Database (Denmark)
Liu, F.; Klumpner, Christian; Blaabjerg, Frede
2004-01-01
The last few years witness a high interest in the use of matrix converter technology in AC/AC power conversion. This paper is focusing on its stability issues. It analyzes the instability reason and reveals that the harmonics interaction of its input current and input voltage is the main cause...... of instability. The matrix converter stability can be improved by decoupling its input current with the input voltage. A modulation strategy is presented that satisfies the idea. The difference of the strategy compared with the traditional one only concerns on the definition of the reference angle for the input...... current vector. A matrix converter model that takes the switching behavior and effects related with the digital implementations into consideration is developed for evaluation of the strategy. The simulation results show that the proposed strategy can highly improve the matrix converter stability...
Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.
Sztepanacz, Jacqueline L; Blows, Mark W
2017-07-01
The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix. Copyright © 2017 by the Genetics Society of America.
Random matrix theory and acoustic resonances in plates with an approximate symmetry
Energy Technology Data Exchange (ETDEWEB)
Andersen, A.; Ellegaard, C.; Jackson, A. D.; Schaadt, K.
2001-06-01
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum and the widths for acoustic resonances in thin aluminum plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using their measured widths. We compare the spectral statistics of each mode class with results for the Gaussian orthogonal ensemble. By cutting a slit of increasing depth on one face of the plate, we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed. Presenting the spectral fluctuation statistics and the distribution of widths for the resonances, we find that this transition is well described by the random matrix model.
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.
Analysis of the {sup 238}U resonance parameters using random-matrix theory
Energy Technology Data Exchange (ETDEWEB)
Courcelle, A. [CEA Cadarache, 13 - Saint Paul lez Durance (France); Derrien, H.; Leal, L.C.; Larson, N.M. [Oak Ridge National Laboratory, Oak Ridge, TN (United States)
2005-07-01
Random-matrix theories (RMTs) provide valuable statistical tools to analyze neutron-resonance data. The predictive power of the random-matrix theories, which do not contain any adjustable parameters, is striking, and the application is rather simple and fast. A new evaluation of {sup 238}U resonance parameters has recently been performed at the Oak Ridge National Laboratory; the objective of this paper is to illustrate the use of RMT in the field of resonance-parameter evaluation with the newly evaluated {sup 239}U energy levels and widths. Several statistics were computed using the s-wave resonances up to 20 keV and compared to the Gaussian Orthogonal Ensemble predictions. It is shown that a good agreement is observed between RMT and the experimental data up to 2.5 keV. The F-Dyson statistic was especially investigated because of its claimed ability to detect locally missed and spurious levels in the sample (p-resonances contamination or unresolved multiplets). As expected, the entire set of evaluated {sup 238}U s-wave resonances up to 20 keV disagrees significantly with the theory. There are two reasons for this: First, it is difficult to distinguish s- and p-wave resonances in the analysis. Secondly, especially above 10 keV, it is impossible to determine reliable resonance energies from the available experimental data. It is concluded that the use of RMT can help nuclear data specialists to improve their evaluations in the resonance range. (authors)
Kappa-Deformed Random-Matrix Theory Based on Kaniadakis Statistics
Abul-Magd, A. Y.; Abdel-Mageed, M.
We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index κ (Boltzmann-Gibbs entropy is recovered in the limit κ → 0), we propose the non-Gaussian deformations (κ ≠ 0) of the conventional orthogonal and unitary ensembles of random matrices. The joint eigenvalue distributions for the κ-deformed ensembles are derived by applying the principle maximum entropy to Kaniadakis entropy. The resulting distribution functions are base invariant as they depend on the matrix elements in a trace form. Using these expressions, we introduce a new generalized form of the Wigner surmise valid for nearly-chaotic mixed systems, where a basis-independent description is still expected to hold. We motivate the necessity of such generalization by the need to describe the transition of the spacing distribution from chaos to order, at least in the initial stage. We show several examples about the use of the generalized Wigner surmise to the analysis of the results of a number of previous experiments and numerical experiments. Our results suggest the entropic index κ as a measure for deviation from the state of chaos. We also introduce a κ-deformed Porter-Thomas distribution of transition intensities, which fits the experimental data for mixed systems better than the commonly-used gamma-distribution.
Drouin-Chartier, Jean-Philippe; Tremblay, André J; Maltais-Giguère, Julie; Charest, Amélie; Guinot, Léa; Rioux, Laurie-Eve; Labrie, Steve; Britten, Michel; Lamarche, Benoît; Turgeon, Sylvie L; Couture, Patrick
2017-12-01
Background: In a simulated gastrointestinal environment, the cheese matrix modulates dairy fat digestion. However, to our knowledge, the impact of the cheese matrix on postprandial lipemia in humans has not yet been evaluated.Objective: In healthy subjects, we compared the impact of dairy fat provided from firm cheese, soft cream cheese, and butter on the postprandial response at 4 h and on the incremental area under the curve (iAUC) of plasma triglycerides.Design: Forty-three healthy subjects were recruited to this randomized, crossover, controlled trial. In random order at intervals of 14 d and after a 12-h fast, subjects ingested 33 g fat from a firm cheese (young cheddar), a soft cream cheese (cream cheese), or butter (control) incorporated into standardized meals that were matched for macronutrient content. Plasma concentrations of triglycerides were measured immediately before the meal and 2, 4, 6, and 8 h after the meal.Results: Cheddar cheese, cream cheese, and butter induced similar increases in triglyceride concentrations at 4 h (change from baseline: +59%, +59%, and +62%, respectively; P = 0.9). No difference in the triglyceride iAUC0-8 h (P-meal = 0.9) was observed between the 3 meals. However, at 2 h, the triglyceride response caused by the cream cheese (change from baseline: +44%) was significantly greater than that induced by butter (change from baseline: +24%; P = 0.002) and cheddar cheese (change from baseline: +16%; P = 0.0004). At 6 h, the triglyceride response induced by cream cheese was significantly attenuated compared with that induced by cheddar cheese (change from baseline: +14% compared with +42%; P = 0.0004).Conclusion: This study demonstrates that the cheese matrix modulates the impact of dairy fat on postprandial lipemia in healthy subjects. This trial was registered at clinicaltrials.gov as NCT02623790. © 2017 American Society for Nutrition.
Meyle, Joerg; Hoffmann, Thomas; Topoll, Heinz; Heinz, Bernd; Al-Machot, Eli; Jervøe-Storm, Pia-Merete; Jepsen, Søren; Eickholz, Peter; Meiss, Christian
2011-01-01
Abstract Objectives: Comparison of clinical and radiographic outcomes of a combination of enamel matrix derivatives (EMD) and a synthetic bone graft (SBG) with EMD alone in wide and deep 1- and 2- wall intrabony defects 12 months after treatment. Method: In 73 patients with chronic periodontitis and one intrabony lesion, defects were randomly assigned to EMD/SBG (test) or EMD (control). Bone sounding, attachment levels, probing pocket depths, bleeding on probing and recessions w...
Modal generation of the design parameters of an elastic spacecraft by the random search method
Titov, B. A.
A method for the modal generation of the dynamic properties of an elastic spacecraft is proposed which is based on algorithms of random search in the space of design parameters. A practical implementation of this approach is illustrated by an example. It is shown that the modal parameter generation procedure based on the random search solves the problem of parameter selection. However, as in any other method, the accuracy of the computation of matrix elements is largely determined by the initial set of permissible values and the number of random samples in determining the subgradient of the objective function.
2016-05-11
AFRL-AFOSR-JP-TR-2016-0046 Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization U Kang Korea...Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386...AOARD Grant FA2386-14-1-4036 “Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization” 29
Reflection Matrix Method for Controlling Light After Reflection From a Diffuse Scattering Surface
2016-12-22
REFLECTION MATRIX METHOD FOR CONTROLLING LIGHT AFTER REFLECTION FROM A DIFFUSE SCATTERING SURFACE DISSERTATION Kenneth W. Burgi, Major, USAF AFIT-ENP...work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENP-DS-16-D-011 REFLECTION MATRIX METHOD FOR...ENP-DS-16-D-011 REFLECTION MATRIX METHOD FOR CONTROLLING LIGHT AFTER REFLECTION FROM A DIFFUSE SCATTERING SURFACE DISSERTATION Kenneth W. Burgi, BS
A T Matrix Method Based upon Scalar Basis Functions
Mackowski, D.W.; Kahnert, F. M.; Mishchenko, Michael I.
2013-01-01
A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.
Wang, Rong; Wang, Li; Yang, Yong; Li, Jiajia; Wu, Ying; Lin, Pan
2016-11-01
Attention deficit hyperactivity disorder (ADHD) is the most common childhood neuropsychiatric disorder and affects approximately 6 -7 % of children worldwide. Here, we investigate the statistical properties of undirected and directed brain functional networks in ADHD patients based on random matrix theory (RMT), in which the undirected functional connectivity is constructed based on correlation coefficient and the directed functional connectivity is measured based on cross-correlation coefficient and mutual information. We first analyze the functional connectivity and the eigenvalues of the brain functional network. We find that ADHD patients have increased undirected functional connectivity, reflecting a higher degree of linear dependence between regions, and increased directed functional connectivity, indicating stronger causality and more transmission of information among brain regions. More importantly, we explore the randomness of the undirected and directed functional networks using RMT. We find that for ADHD patients, the undirected functional network is more orderly than that for normal subjects, which indicates an abnormal increase in undirected functional connectivity. In addition, we find that the directed functional networks are more random, which reveals greater disorder in causality and more chaotic information flow among brain regions in ADHD patients. Our results not only further confirm the efficacy of RMT in characterizing the intrinsic properties of brain functional networks but also provide insights into the possibilities RMT offers for improving clinical diagnoses and treatment evaluations for ADHD patients.
MUSCLE MRI SEGMENTATION USING RANDOM WALKER METHOD
Directory of Open Access Journals (Sweden)
A. V. Shukelovich
2013-01-01
Full Text Available A technique of marker set construction for muscle MRI segmentation using random walker approach is introduced. The possibility of clinician’s manual labor amount reduction and random walker algorithm optimization is studied.
Transformation Matrix for Time Discretization Based on Tustin’s Method
Directory of Open Access Journals (Sweden)
Yiming Jiang
2014-01-01
Full Text Available This paper studies rules in transformation of transfer function through time discretization. A method of using transformation matrix to realize bilinear transform (also known as Tustin’s method is presented. This method can be described as the conversion between the coefficients of transfer functions, which are expressed as transform by certain matrix. For a polynomial of degree n, the corresponding transformation matrix of order n exists and is unique. Furthermore, the transformation matrix can be decomposed into an upper triangular matrix multiplied with another lower triangular matrix. And both have obvious regularity. The proposed method can achieve rapid bilinear transform used in automatic design of digital filter. The result of numerical simulation verifies the correctness of the theoretical results. Moreover, it also can be extended to other similar problems. Example in the last throws light on this point.
Empirical evaluation of gradient methods for matrix learning vector quantization
LeKander, M.; Biehl, M.; Vries, H. de
2017-01-01
Generalized Matrix Learning Vector Quantization (GMLVQ) critically relies on the use of an optimization algorithm to train its model parameters. We test various schemes for automated control of learning rates in gradient-based training. We evaluate these algorithms in terms of their achieved
Nishigaki, Shinsuke M.
2012-12-01
Schierenberg [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.061130 85, 061130 (2012)] recently applied the Wigner surmise, i.e., substitution of ∞×∞ matrices by their 2×2 counterparts for the computation of level spacing distributions, to random matrix ensembles in transition between two universality classes. I examine the accuracy and the range of validity of the surmise for the crossover between the Gaussian orthogonal and unitary ensembles by contrasting them with the large-N results that I evaluated using the Nyström-type method for the Fredholm determinant. The surmised expression at the best-fitting parameter provides a good approximation for 0≲s≲2, i.e., the validity range of the original surmise.
A Random Matrix Approach for Quantifying Model-Form Uncertainties in Turbulence Modeling
Xiao, Heng; Ghanem, Roger G
2016-01-01
With the ever-increasing use of Reynolds-Averaged Navier--Stokes (RANS) simulations in mission-critical applications, the quantification of model-form uncertainty in RANS models has attracted attention in the turbulence modeling community. Recently, a physics-based, nonparametric approach for quantifying model-form uncertainty in RANS simulations has been proposed, where Reynolds stresses are projected to physically meaningful dimensions and perturbations are introduced only in the physically realizable limits. However, a challenge associated with this approach is to assess the amount of information introduced in the prior distribution and to avoid imposing unwarranted constraints. In this work we propose a random matrix approach for quantifying model-form uncertainties in RANS simulations with the realizability of the Reynolds stress guaranteed. Furthermore, the maximum entropy principle is used to identify the probability distribution that satisfies the constraints from available information but without int...
Random matrix theory for the analysis of the performance of an analog computer: a scaling theory
Energy Technology Data Exchange (ETDEWEB)
Ben-Hur, Asa; Feinberg, Joshua; Fishman, Shmuel; Siegelmann, Hava T
2004-03-22
The phase space flow of a dynamical system, leading to the solution of linear programming (LP) problems, is explored as an example of complexity analysis in an analog computation framework. In this framework, computation by physical devices and natural systems, evolving in continuous phase space and time (in contrast to the digital computer where these are discrete), is explored. A Gaussian ensemble of LP problems is studied. The convergence time of a flow to the fixed point representing the optimal solution, is computed. The cumulative distribution function of the convergence time is calculated in the framework of random matrix theory (RMT) in the asymptotic limit of large problem size. It is found to be a scaling function, of the form obtained in the theories of critical phenomena and Anderson localization. It demonstrates a correspondence between problems of computer science and physics.
Random matrix theory and spectral sum rules for the Dirac operator in QCD
Energy Technology Data Exchange (ETDEWEB)
Shuryak, E.V. (Dept. of Physics, SUNY, Stony Brook, NY (United States)); Verbaarschot, J.J.M. (Dept. of Physics, SUNY, Stony Brook, NY (United States))
1993-07-12
We construct a random matrix model that, in the large-N limit, reduces to the low-energy limit of the QCD partition function put forward by Leutwyler and Smilga. This equivalence holds for an arbitrary number of flavors and any value of the QCD vacuum angle. In this model, moments of the inverse squares of eigenvalues of the Dirac operator obey sum rules, which we conjecture to be universal. In other words, the validity of the sum rules depends only on the symmetries of the theory but not on its details. To illustrate this point we show that the sum rules hold for an interacting liquid of instantons. The physical interpretations is that the way the thermodynamic limit of the spectral density near zero is approached is universal. However, its value, i.e. the chiral condensate, is not. (orig.)
Transmission eigenvalue densities and moments in chaotic cavities from random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Vivo, Pierpaolo [School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH (United Kingdom); Vivo, Edoardo [Universita degli Studi di Parma, Dipartimento di Fisica Teorica, Viale GP Usberti n.7/A (Parco Area delle Scienze), Parma (Italy)
2008-03-28
We point out that the transmission eigenvalue density and higher order correlation functions in chaotic cavities for an arbitrary number of incoming and outgoing leads (N{sub 1}, N{sub 2}) are analytically known from the Jacobi ensemble of random matrix theory. Using this result and a simple linear statistic, we give an exact and non-perturbative expression for moments of the form ({lambda}{sup m}{sub 1}) for m > -|N{sub 1} - N{sub 2}| - 1 and {beta} = 2, thus improving the existing results in the literature. Secondly, we offer an independent derivation of the average density and higher order correlation function for {beta} = 2, 4 which does not make use of the orthogonal polynomials technique. This result may be relevant for an efficient numerical implementation avoiding determinants. (fast track communication)
Odd-flavored QCD{sub 3} and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Christiansen, Jesper E-mail: jeschris@nbi.dk
1999-05-10
We consider QCD{sub 3} with an odd number of flavors in the mesoscopic scaling region where the field theory finite-volume partition function is equivalent to a random matrix theory partition function. We argue that the theory is parity invariant at the classical level if an odd number of masses are zero. By introducing so-called pseudo-orthogonal polynomials we are able to relate the kernel to the kernel of the chiral unitary ensemble with {beta} = 2 in the sector of topological charge {nu} = ((1)/(2)). We prove universality and are able to write the kernel in the microscopic limit in terms of field theory finite-volume partition functions.
Random matrix theory and acoustic resonances in plates with an approximate symmetry
DEFF Research Database (Denmark)
Andersen, Anders Peter; Ellegaard, C.; Jackson, A.D.
2001-01-01
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum...... and the widths for acoustic resonances in thin aluminum plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using...... their measured widths. We compare the spectral statistics of each mode class with results for the Gaussian orthogonal ensemble. By cutting a slit of increasing depth on one face of the plate, we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed. Presenting...
Energy Technology Data Exchange (ETDEWEB)
Liu, Yizhuang, E-mail: yizhuang.liu@stonybrook.edu [Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800 (United States); Nowak, Maciej A., E-mail: maciej.a.nowak@uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, PL-30348 Krakow (Poland); Zahed, Ismail, E-mail: ismail.zahed@stonybrook.edu [Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800 (United States)
2016-08-15
We derive an exact formula for the stochastic evolution of the characteristic determinant of a class of deformed Wishart matrices following from a chiral random matrix model of QCD at finite chemical potential. In the WKB approximation, the characteristic determinant describes a sharp droplet of eigenvalues that deforms and expands at large stochastic times. Beyond the WKB limit, the edges of the droplet are fuzzy and described by universal edge functions. At the chiral point, the characteristic determinant in the microscopic limit is universal. Remarkably, the physical chiral condensate at finite chemical potential may be extracted from current and quenched lattice Dirac spectra using the universal edge scaling laws, without having to solve the QCD sign problem.
Directory of Open Access Journals (Sweden)
Sette Alessandro
2005-05-01
Full Text Available Abstract Background Many processes in molecular biology involve the recognition of short sequences of nucleic-or amino acids, such as the binding of immunogenic peptides to major histocompatibility complex (MHC molecules. From experimental data, a model of the sequence specificity of these processes can be constructed, such as a sequence motif, a scoring matrix or an artificial neural network. The purpose of these models is two-fold. First, they can provide a summary of experimental results, allowing for a deeper understanding of the mechanisms involved in sequence recognition. Second, such models can be used to predict the experimental outcome for yet untested sequences. In the past we reported the development of a method to generate such models called the Stabilized Matrix Method (SMM. This method has been successfully applied to predicting peptide binding to MHC molecules, peptide transport by the transporter associated with antigen presentation (TAP and proteasomal cleavage of protein sequences. Results Herein we report the implementation of the SMM algorithm as a publicly available software package. Specific features determining the type of problems the method is most appropriate for are discussed. Advantageous features of the package are: (1 the output generated is easy to interpret, (2 input and output are both quantitative, (3 specific computational strategies to handle experimental noise are built in, (4 the algorithm is designed to effectively handle bounded experimental data, (5 experimental data from randomized peptide libraries and conventional peptides can easily be combined, and (6 it is possible to incorporate pair interactions between positions of a sequence. Conclusion Making the SMM method publicly available enables bioinformaticians and experimental biologists to easily access it, to compare its performance to other prediction methods, and to extend it to other applications.
Macroscopic and microscopic (non-)universality of compact support random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Akemann, G.; Vernizzi, G
2000-09-11
A random matrix model with a {sigma}-model like constraint, the restricted trace ensemble (RTE), is solved in the large-n limit. In the macroscopic limit the smooth connected two-point resolvent G(z,w) is found to be non-universal, extending previous results from monomial to arbitrary polynomial potentials. Using loop equation techniques we give a closed though non-universal expression for G(z,w), which extends recursively to all higher k-point resolvents. These findings are in contrast to the usual unconstrained one-matrix model. However, in the microscopic large-n limit, which probes only correlations at distance of the mean level spacing, we are able to show that the constraint does not modify the universal sine-law. In the case of monomial potentials V(M)=M{sup 2p}, we provide a relation valid for finite-n between the k-point correlation function of the RTE and the unconstrained model. In the microscopic large-n limit they coincide which proves the microscopic universality of RTEs.
Global financial indices and twitter sentiment: A random matrix theory approach
García, A.
2016-11-01
We use Random Matrix Theory (RMT) approach to analyze the correlation matrix structure of a collection of public tweets and the corresponding return time series associated to 20 global financial indices along 7 trading months of 2014. In order to quantify the collection of tweets, we constructed daily polarity time series from public tweets via sentiment analysis. The results from RMT analysis support the fact of the existence of true correlations between financial indices, polarities, and the mixture of them. Moreover, we found a good agreement between the temporal behavior of the extreme eigenvalues of both empirical data, and similar results were found when computing the inverse participation ratio, which provides an evidence about the emergence of common factors in global financial information whether we use the return or polarity data as a source. In addition, we found a very strong presumption that polarity Granger causes returns of an Indonesian index for a long range of lag trading days, whereas for Israel, South Korea, Australia, and Japan, the predictive information of returns is also presented but with less presumption. Our results suggest that incorporating polarity as a financial indicator may open up new insights to understand the collective and even individual behavior of global financial indices.
A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation
Danabasoglu, G.; Biringen, S.
1989-01-01
The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.
The band method and inverse problems for orthogonal matrix functions of Szego-Krein type
Kaashoek, M.A.; Lerer, L.
2012-01-01
A band method approach for solving inverse problems for certain orthogonal functions is developed. The inverse theorems for Szego-Kreǐn matrix polynomials and for Kreǐn orthogonal entire matrix functions are obtained as corollaries of the band method results. Other examples, including a
A Chebyshev matrix method for the spatial modes of the Orr-Sommerfeld equation
Danabasoglu, Gokhan; Biringen, Sedat
1990-01-01
The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blasius boundary layer. The problems is linearized by the companion matrix technique for semiinfinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.
Energy Technology Data Exchange (ETDEWEB)
Lara-Curzio, E.; Ferber, M.K. [Oak Ridge National Lab., TN (United States); Jenkins, M.G. [Washington Univ., Seattle, WA (United States). Dept. of Mechanical Engineering
1994-05-01
Requirements for thermomechanical characterization of ceramic matrix composite materials are reviewed. Feasibility of adapting existent room temperature test methods for polymer and metal matrix composites to test ceramic matrix composites at room and elevated temperatures is investigated.
Gaussian Beam Propagation in a Kerr Type Metamaterial Medium Using ABCD Matrix Method
Keshavarz, A.; Naseri, M.
2016-08-01
In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps. Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.
Random matrix theory, the exceptional Lie groups and L-functions
Energy Technology Data Exchange (ETDEWEB)
Keating, J P [School of Mathematics, University of Bristol, Bristol BS8 1TW, UK (United Kingdom); Linden, N [School of Mathematics, University of Bristol, Bristol BS8 1TW, UK (United Kingdom); Rudnick, Z [Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
2003-03-28
There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of L-functions. These connections are extended here to non-classical groups. We focus on an explicit example: the exceptional Lie group G{sub 2}. The value distributions for characteristic polynomials associated with the 7- and 14-dimensional representations of G{sub 2}, defined with respect to the uniform invariant (Haar) measure, are calculated using two of the Macdonald constant term identities. A one-parameter family of L-functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the seven-dimensional representation of G{sub 2}. The random matrix calculations extend to all exceptional Lie groups.
Klopp, Frédéric
The purpose of this paper is to study the transition from the classical to the quantum asymptotics for the integrated density of states of an unbounded random Jacobi matrix. Therefore, we give precise results on the behavior of the tail of the integrated density of states near infinity. We study the evolution of these asymptotics when the decay of the tail of the distribution of the random potential increases. Résumé. Cet article est consacré à l'étude de la transition entre le régime classique et le régime quantique pour la densité d'états intégrée d'une matrice de Jacobi aléatoire non bornée. Pour cela nous donnons des asymptotiques précises du comportement de la densité d'états intégrée au voisinage de l'infini. De plus, nous étudions le comportement de cette asymptotique lorsque la décroissance à l'infini de la distribution du potentiel aléatoire augmente.
Individual Differences Methods for Randomized Experiments
Tucker-Drob, Elliot M.
2011-01-01
Experiments allow researchers to randomly vary the key manipulation, the instruments of measurement, and the sequences of the measurements and manipulations across participants. To date, however, the advantages of randomized experiments to manipulate both the aspects of interest and the aspects that threaten internal validity have been primarily…
Extreme learning machines for regression based on V-matrix method.
Yang, Zhiyong; Zhang, Taohong; Lu, Jingcheng; Su, Yuan; Zhang, Dezheng; Duan, Yaowu
2017-10-01
This paper studies the joint effect of V-matrix, a recently proposed framework for statistical inferences, and extreme learning machine (ELM) on regression problems. First of all, a novel algorithm is proposed to efficiently evaluate the V-matrix. Secondly, a novel weighted ELM algorithm called V-ELM is proposed based on the explicit kernel mapping of ELM and the V-matrix method. Though V-matrix method could capture the geometrical structure of training data, it tends to assign a higher weight to instance with smaller input value. In order to avoid this bias, a novel method called VI-ELM is proposed by minimizing both the regression error and the V-matrix weighted error simultaneously. Finally, experiment results on 12 real world benchmark datasets show the effectiveness of our proposed methods.
New theory of superfluidity. Method of equilibrium density matrix
Bondarev, Boris
2014-01-01
The variational theory of equilibrium boson system state to have been previously developed by the author under the density matrix formalism is applicable for researching equilibrium states and thermodynamic properties of the quantum Bose gas which consists of zero-spin particles. Particle pulse distribution function is obtained and duly employed for calculation of chemical potential, internal energy and gas capacity temperature dependences. It is found that specific phase transition, which is similar to transition of liquid helium to its superfluid state, occurs at the temperature exceeding that of the Bose condensation.
Liu, Ying; Shi, Xiao-Wei; Liu, E-Hu; Sheng, Long-Sheng; Qi, Lian-Wen; Li, Ping
2012-09-07
Various analytical technologies have been developed for quantitative determination of marker compounds in herbal medicines (HMs). One important issue is matrix effects that must be addressed in method validation for different detections. Unlike biological fluids, blank matrix samples for calibration are usually unavailable for HMs. In this work, practical approaches for minimizing matrix effects in HMs analysis were proposed. The matrix effects in quantitative analysis of five saponins from Panax notoginseng were assessed using high-performance liquid chromatography (HPLC). Matrix components were found to interfere with the ionization of target analytes when mass spectrometry (MS) detection were employed. To compensate the matrix signal suppression/enhancement, two matrix-matched methods, standard addition method with the target-knockout extract and standard superposition method with a HM extract were developed and tested in this work. The results showed that the standard superposition method is simple and practical for overcoming matrix effects for quantitative analysis of HMs. Moreover, the interference components were observed to interfere with light scattering of target analytes when evaporative light scattering detection (ELSD) was utilized for quantitative analysis of HMs but was not indicated when Ultraviolet detection (UV) were employed. Thus, the issue of interference effects should be addressed and minimized for quantitative HPLC-ELSD and HPLC-MS methodologies for quality control of HMs. Copyright © 2012 Elsevier B.V. All rights reserved.
Convergence of a random walk method for the Burgers equation
Energy Technology Data Exchange (ETDEWEB)
Roberts, S.
1985-10-01
In this paper we consider a random walk algorithm for the solution of Burgers' equation. The algorithm uses the method of fractional steps. The non-linear advection term of the equation is solved by advecting ''fluid'' particles in a velocity field induced by the particles. The diffusion term of the equation is approximated by adding an appropriate random perturbation to the positions of the particles. Though the algorithm is inefficient as a method for solving Burgers' equation, it does model a similar method, the random vortex method, which has been used extensively to solve the incompressible Navier-Stokes equations. The purpose of this paper is to demonstrate the strong convergence of our random walk method and so provide a model for the proof of convergence for more complex random walk algorithms; for instance, the random vortex method without boundaries.
Qing Liu; Zhihui Lai; Zongwei Zhou; Fangjun Kuang; Zhong Jin
2016-01-01
Low-rank matrix completion aims to recover a matrix from a small subset of its entries and has received much attention in the field of computer vision. Most existing methods formulate the task as a low-rank matrix approximation problem. A truncated nuclear norm has recently been proposed as a better approximation to the rank of matrix than a nuclear norm. The corresponding optimization method, truncated nuclear norm regularization (TNNR), converges better than the nuclear norm minimization-based methods. However, it is not robust to the number of subtracted singular values and requires a large number of iterations to converge. In this paper, a TNNR method based on weighted residual error (TNNR-WRE) for matrix completion and its extension model (ETNNR-WRE) are proposed. TNNR-WRE assigns different weights to the rows of the residual error matrix in an augmented Lagrange function to accelerate the convergence of the TNNR method. The ETNNR-WRE is much more robust to the number of subtracted singular values than the TNNR-WRE, TNNR alternating direction method of multipliers, and TNNR accelerated proximal gradient with Line search methods. Experimental results using both synthetic and real visual data sets show that the proposed TNNR-WRE and ETNNR-WRE methods perform better than TNNR and Iteratively Reweighted Nuclear Norm (IRNN) methods.
Matrix Effects in the Liquid Chromatography-Tandem Mass Spectrometry Method of Analysis.
Liu, H-C; Lin, D-L; McCurdy, H H
2013-03-01
Matrix effects are dependent on biological fluid, ionization type, and sample preparation method. Although matrix effects are observed for both ionization types, ESI is especially susceptible, while APCI has proved to be less vulnerable. Sample preparation method has a clear influence on matrix effects as does, in particular, the choice of internal standard. When matrix effects result in severe ion suppression or enhancement of the target analyte by co-eluting residual components, they are typically located in isolated regions of the chromatogram. Postcolumn infusion and postextraction addition methods have been developed for the assessments of matrix effects. Approaches used for eliminating, minimizing, or compensating for matrix effects include improved sample preparation and chromatographic separation, sample dilution, and the utilization of internal standards. Matrix effects may not always be fully circumventable because a perfectly consistent matrix does not exist, but they can be significantly minimized and largely compensated for by various approaches, such as standard addition, matrixmatched calibration, and the use of isotopic analogs of the analytes as internal standards. Copyright © 2013 Central Police University.
The Matrix Completion Method for Phase Retrieval from Fractional Fourier Transform Magnitudes
Directory of Open Access Journals (Sweden)
Qi Luo
2016-01-01
Full Text Available Inspired by the implementation of the fractional Fourier transform (FRFT and its applications in optics, we address the problem of reconstructing a signal from its several FRFT magnitudes (or intensities. The matrix completion method is adopted here. Through numerical tests, the matrix completion method is proven effective in both noisy and noise-free situations. We also compare our method with the Gerchberg-Saxton (GS algorithm based on FRFT. Numerical tests show that the matrix completion method gains a certain advantage in recovering uniqueness and convergence over the GS algorithm in the noise-free case. Furthermore, in terms of noisy signals, the matrix completion method performs robustly and adding more measurements can generally increase accuracy of recovered signals.
Effect of Matrix Metalloproteinase-inhibiting Solutions and Aging Methods on Dentin Bond Strength.
Perote, Letícia C C Costa; Kamozaki, Maria Beatriz Beber; Gutierrez, Natália C; Tay, Franklin R; Pucci, Cesar R
2015-08-01
This study examined the effects of matrix metalloproteinase-inhibiting solutions and aging methods on the bond strength between resin composite and human dentin. Crown segments of 105 human non-carious molars were bonded using simulated pulpal pressure at 20 cm water pressure. The teeth were randomly split into 5 groups according to the solution applied: CG (control, no solution), CHX (0.2% chlorhexidine), EPE (10% ethanolic propolis extract), APE (aqueous propolis extract), and E (70% ethanol). Each solution was left on the acid-etched dentin for 1 min. Adper Single Bond 2 and resin composite (Filtek Z350 XT) were applied to all specimens. The 5 groups were subdivided according to the aging method: SI (sectioned immediately); S (storage in artificial saliva for 6 months); and T (thermomechanical aging with 240,000 mechanical cycles and 1000 thermal cycles). Specimens were sectioned into sticks and subjected to microtensile testing. Bond strength data were analyzed by two-factor ANOVA followed by a post-hoc Tukey's test (α=0.05). For the factor "solution", there was no significant difference among the groups (p=0.32). For the factor "aging method", significant differences were found (pmatrix metalloproteinase-inhibiting solutions on dentin as an adjunct to the application of an etch-and-rinse adhesive does not prevent the loss of bond strength after aging. Nevertheless, these solutions have no adverse effect on adhesion to tooth structure.
Isaacson, Sven; Luo, Feng; Feltus, Frank A.; Smith, Melissa C.
2013-01-01
The study of gene relationships and their effect on biological function and phenotype is a focal point in systems biology. Gene co-expression networks built using microarray expression profiles are one technique for discovering and interpreting gene relationships. A knowledge-independent thresholding technique, such as Random Matrix Theory (RMT), is useful for identifying meaningful relationships. Highly connected genes in the thresholded network are then grouped into modules that provide insight into their collective functionality. While it has been shown that co-expression networks are biologically relevant, it has not been determined to what extent any given network is functionally robust given perturbations in the input sample set. For such a test, hundreds of networks are needed and hence a tool to rapidly construct these networks. To examine functional robustness of networks with varying input, we enhanced an existing RMT implementation for improved scalability and tested functional robustness of human (Homo sapiens), rice (Oryza sativa) and budding yeast (Saccharomyces cerevisiae). We demonstrate dramatic decrease in network construction time and computational requirements and show that despite some variation in global properties between networks, functional similarity remains high. Moreover, the biological function captured by co-expression networks thresholded by RMT is highly robust. PMID:23409071
Large N_c volume reduction and chiral random matrix theory
Lee, J. W.; Hanada, M.; Yamada, N.
Motivated by recent progress on the understanding of the Eguchi-Kawai (EK) volume equivalence and growing interest in conformal window, we simultaneously use the large-Nc volume reduction and Chiral Random Matrix Theory (chRMT) to study the chiral symmetry breaking of four dimensional SU(Nc) gauge theory with adjoint fermions in the large Nc limit. Although some cares are required because the chRMT limit and 't Hooft limit are not compatible in general, we show that the breakdown of the chiral symmetry can be detected in large-Nc gauge theories. As a first step, we mainly focus on the quenched approximation to establish the methodology. We first confirm that heavy adjoint fermions, introduced as the center symmetry preserver, work as expected and thanks to them the volume reduction holds. Using massless overlap fermion as a probe, we then calculate the low-lying Dirac spectrum for fermion in the adjoint representation to compare to that of chRMT, and find that chiral symmetry is indeed broken in the quenched theory.
Disorder in gauge/gravity duality, pole spectrum statistics and random matrix theory
Saremi, Omid
2014-05-01
In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist phases where the nearest neighbor spacing distribution of the unfolded pole spectra of generic two-point correlators is Poisson. This closely resembles the localized phase of the Anderson Hamiltonian. We perform two tests on our statistical hypothesis. One is based on a statistic defined in the context of random matrix theory, the so-called \\overline{\\Delta _3}, or spectral rigidity, proposed by Dyson and Mehta. The second is a χ-squared test. In our model, the results of both tests are consistent with the hypothesis that the pole spectra of two-point functions can be at least in two distinct phases; first a regular sequence and second a completely uncorrelated sequence with a Poisson nearest neighbor spacing distribution.
Random-matrix theory of amplifying and absorbing resonators with {PT} or {PTT}^{\\prime } symmetry
Birchall, Christopher; Schomerus, Henning
2012-11-01
We formulate Gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical realizations of such systems we consider a {PT} or a {PTT}^{\\prime } time-reversal symmetry, which impose different constraints on magneto-optical effects, and then focus on five common settings. For each of these, we determine the eigenvalue distribution in the complex plane in the short-wavelength limit, which reveals that the fraction of real eigenvalues among all eigenvalues in the spectrum vanishes if all classical scales are kept fixed. Numerically, we find that the transition from real to complex eigenvalues in the various ensembles display a different dependence on the coupling strength between the two resonators. These differences can be linked to the level spacing statistics in the Hermitian limit of the considered models. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Asymptotic Analysis of Large Cooperative Relay Networks Using Random Matrix Theory
Directory of Open Access Journals (Sweden)
H. Poor
2008-04-01
Full Text Available Cooperative transmission is an emerging communication technology that takes advantage of the broadcast nature of wireless channels. In cooperative transmission, the use of relays can create a virtual antenna array so that multiple-input/multiple-output (MIMO techniques can be employed. Most existing work in this area has focused on the situation in which there are a small number of sources and relays and a destination. In this paper, cooperative relay networks with large numbers of nodes are analyzed, and in particular the asymptotic performance improvement of cooperative transmission over direction transmission and relay transmission is analyzed using random matrix theory. The key idea is to investigate the eigenvalue distributions related to channel capacity and to analyze the moments of this distribution in large wireless networks. A performance upper bound is derived, the performance in the low signal-to-noise-ratio regime is analyzed, and two approximations are obtained for high and low relay-to-destination link qualities, respectively. Finally, simulations are provided to validate the accuracy of the analytical results. The analysis in this paper provides important tools for the understanding and the design of large cooperative wireless networks.
A multi-platform evaluation of the randomized CX low-rank matrix factorization in Spark
Energy Technology Data Exchange (ETDEWEB)
Gittens, Alex; Kottalam, Jey; Yang, Jiyan; Ringenburg, Michael, F.; Chhugani, Jatin; Racah, Evan; Singh, Mohitdeep; Yao, Yushu; Fischer, Curt; Ruebel, Oliver; Bowen, Benjamin; Lewis, Norman, G.; Mahoney, Michael, W.; Krishnamurthy, Venkat; Prabhat, Mr
2017-07-27
We investigate the performance and scalability of the randomized CX low-rank matrix factorization and demonstrate its applicability through the analysis of a 1TB mass spectrometry imaging (MSI) dataset, using Apache Spark on an Amazon EC2 cluster, a Cray XC40 system, and an experimental Cray cluster. We implemented this factorization both as a parallelized C implementation with hand-tuned optimizations and in Scala using the Apache Spark high-level cluster computing framework. We obtained consistent performance across the three platforms: using Spark we were able to process the 1TB size dataset in under 30 minutes with 960 cores on all systems, with the fastest times obtained on the experimental Cray cluster. In comparison, the C implementation was 21X faster on the Amazon EC2 system, due to careful cache optimizations, bandwidth-friendly access of matrices and vector computation using SIMD units. We report these results and their implications on the hardware and software issues arising in supporting data-centric workloads in parallel and distributed environments.
Prognostic interaction patterns in diabetes mellitus II: A random-matrix-theory relation
Rai, Aparna; Pawar, Amit Kumar; Jalan, Sarika
2015-08-01
We analyze protein-protein interactions in diabetes mellitus II and its normal counterpart under the combined framework of random matrix theory and network biology. This disease is the fifth-leading cause of death in high-income countries and an epidemic in developing countries, affecting around 8 % of the total adult population in the world. Treatment at the advanced stage is difficult and challenging, making early detection a high priority in the cure of the disease. Our investigation reveals specific structural patterns important for the occurrence of the disease. In addition to the structural parameters, the spectral properties reveal the top contributing nodes from localized eigenvectors, which turn out to be significant for the occurrence of the disease. Our analysis is time-efficient and cost-effective, bringing a new horizon in the field of medicine by highlighting major pathways involved in the disease. The analysis provides a direction for the development of novel drugs and therapies in curing the disease by targeting specific interaction patterns instead of a single protein.
A computational method for prediction of matrix proteins in endogenous retroviruses.
Ma, Yucheng; Liu, Ruiling; Lv, Hongqiang; Han, Jiuqiang; Zhong, Dexing; Zhang, Xinman
2017-01-01
Human endogenous retroviruses (HERVs) encode active retroviral proteins, which may be involved in the progression of cancer and other diseases. Matrix protein (MA), in group-specific antigen genes (gag) of retroviruses, is associated with the virus envelope glycoproteins in most mammalian retroviruses and may be involved in virus particle assembly, transport and budding. However, the amount of annotated MAs in ERVs is still at a low level so far. No computational method to predict the exact start and end coordinates of MAs in gags has been proposed yet. In this paper, a computational method to identify MAs in ERVs is proposed. A divide and conquer technique was designed and applied to the conventional prediction model to acquire better results when dealing with gene sequences with various lengths. Initiation sites and termination sites were predicted separately and then combined according to their intervals. Three different algorithms were applied and compared: weighted support vector machine (WSVM), weighted extreme learning machine (WELM) and random forest (RF). G - mean (geometric mean of sensitivity and specificity) values of initiation sites and termination sites under 5-fold cross validation generated by random forest models are 0.9869 and 0.9755 respectively, highest among the algorithms applied. Our prediction models combine RF & WSVM algorithms to achieve the best prediction results. 98.4% of all the collected ERV sequences with complete MAs (125 in total) could be predicted exactly correct by the models. 94,671 HERV sequences from 118 families were scanned by the model, 104 new putative MAs were predicted in human chromosomes. Distributions of the putative MAs and optimizations of model parameters were also analyzed. The usage of our predicting method was also expanded to other retroviruses and satisfying results were acquired.
A computational method for prediction of matrix proteins in endogenous retroviruses.
Directory of Open Access Journals (Sweden)
Yucheng Ma
Full Text Available Human endogenous retroviruses (HERVs encode active retroviral proteins, which may be involved in the progression of cancer and other diseases. Matrix protein (MA, in group-specific antigen genes (gag of retroviruses, is associated with the virus envelope glycoproteins in most mammalian retroviruses and may be involved in virus particle assembly, transport and budding. However, the amount of annotated MAs in ERVs is still at a low level so far. No computational method to predict the exact start and end coordinates of MAs in gags has been proposed yet. In this paper, a computational method to identify MAs in ERVs is proposed. A divide and conquer technique was designed and applied to the conventional prediction model to acquire better results when dealing with gene sequences with various lengths. Initiation sites and termination sites were predicted separately and then combined according to their intervals. Three different algorithms were applied and compared: weighted support vector machine (WSVM, weighted extreme learning machine (WELM and random forest (RF. G - mean (geometric mean of sensitivity and specificity values of initiation sites and termination sites under 5-fold cross validation generated by random forest models are 0.9869 and 0.9755 respectively, highest among the algorithms applied. Our prediction models combine RF & WSVM algorithms to achieve the best prediction results. 98.4% of all the collected ERV sequences with complete MAs (125 in total could be predicted exactly correct by the models. 94,671 HERV sequences from 118 families were scanned by the model, 104 new putative MAs were predicted in human chromosomes. Distributions of the putative MAs and optimizations of model parameters were also analyzed. The usage of our predicting method was also expanded to other retroviruses and satisfying results were acquired.
Gemperline, Erin; Rawson, Stephanie; Li, Lingjun
2014-10-21
The matrix application technique is critical to the success of a matrix-assisted laser desorption/ionization (MALDI) experiment. This work presents a systematic study aiming to evaluate three different matrix application techniques for MALDI mass spectrometric imaging (MSI) of endogenous metabolites from legume plant, Medicago truncatula, root nodules. Airbrush, automatic sprayer, and sublimation matrix application methods were optimized individually for detection of metabolites in the positive ionization mode exploiting the two most widely used MALDI matrices, 2,5-dihydroxybenzoic acid (DHB) and α-cyano-4-hydroxycinnamic acid (CHCA). Analytical reproducibility and analyte diffusion were examined and compared side-by-side for each method. When using DHB, the optimized method developed for the automatic matrix sprayer system resulted in approximately double the number of metabolites detected when compared to sublimation and airbrush. The automatic sprayer method also showed more reproducible results and less analyte diffusion than the airbrush method. Sublimation matrix deposition yielded high spatial resolution and reproducibility but fewer analytes in the higher m/z range (500-1000 m/z). When the samples were placed in a humidity chamber after sublimation, there was enhanced detection of higher mass metabolites but increased analyte diffusion in the lower mass range. When using CHCA, the optimized automatic sprayer method and humidified sublimation method resulted in double the number of metabolites detected compared to standard airbrush method.
Using matrix summation method for three dimensional dose calculation in brachytherapy.
Zibandeh-Gorji, Mahmoud; Mowlavi, Ali Asghar; Mohammadi, Saeed
2012-01-01
The purpose of this study is to calculate radiation dose around a brachytherapy source in a water phantom for different seed locations or rotation the sources by the matrix summation method. Monte Carlo based codes like MCNP are widely used for performing radiation transport calculations and dose evaluation in brachytherapy. But for complicated situations, like using more than one source, moving or rotating the source, the routine Monte Carlo method for dose calculation needs a long time running. The MCNPX code has been used to calculate radiation dose around a (192)Ir brachytherapy source and saved in a 3D matrix. Then, we used this matrix to evaluate the absorbed dose in any point due to some sources or a source which shifted or rotated in some places by the matrix summation method. Three dimensional (3D) dose results and isodose curves were presented for (192)Ir source in a water cube phantom shifted for 10 steps and rotated for 45 and 90° based on the matrix summation method. Also, we applied this method for some arrays of sources. The matrix summation method can be used for 3D dose calculations for any brachytherapy source which has moved or rotated. This simple method is very fast compared to routine Monte Carlo based methods. In addition, it can be applied for dose optimization study.
Efficient randomized methods for stability analysis of fluids systems
Dawson, Scott; Rowley, Clarence
2016-11-01
We show that probabilistic algorithms that have recently been developed for the approximation of large matrices can be utilized to numerically evaluate the properties of linear operators in fluids systems. In particular, we present an algorithm that is well suited for optimal transient growth (i.e., nonmodal stability) analysis. For non-normal systems, such analysis can be important for analyzing local regions of convective instability, and in identifying high-amplitude transients that can trigger nonlinear instabilities. Our proposed algorithms are easy to wrap around pre-existing timesteppers for linearized forward and adjoint equations, are highly parallelizable, and come with known error bounds. Furthermore, they allow for efficient computation of optimal growth modes for numerous time horizons simultaneously. We compare the proposed algorithm to both direct matrix-forming and Krylov subspace approaches on a number of test problems. We will additionally discuss the potential for randomized methods to assist more broadly in the speed-up of algorithms for analyzing both fluids data and operators. Supported by AFOSR Grant FA9550-14-1-0289.
Ceramic Matrix Composites (CMC) Life Prediction Method Development
Levine, Stanley R.; Calomino, Anthony M.; Ellis, John R.; Halbig, Michael C.; Mital, Subodh K.; Murthy, Pappu L.; Opila, Elizabeth J.; Thomas, David J.; Thomas-Ogbuji, Linus U.; Verrilli, Michael J.
2000-01-01
Advanced launch systems (e.g., Reusable Launch Vehicle and other Shuttle Class concepts, Rocket-Based Combine Cycle, etc.), and interplanetary vehicles will very likely incorporate fiber reinforced ceramic matrix composites (CMC) in critical propulsion components. The use of CMC is highly desirable to save weight, to improve reuse capability, and to increase performance. CMC candidate applications are mission and cycle dependent and may include turbopump rotors, housings, combustors, nozzle injectors, exit cones or ramps, and throats. For reusable and single mission uses, accurate prediction of life is critical to mission success. The tools to accomplish life prediction are very immature and not oriented toward the behavior of carbon fiber reinforced silicon carbide (C/SiC), the primary system of interest for a variety of space propulsion applications. This paper describes an approach to satisfy the need to develop an integrated life prediction system for CMC that addresses mechanical durability due to cyclic and steady thermomechanical loads, and takes into account the impact of environmental degradation.
Novel image analysis methods for quantification of in situ 3-D tendon cell and matrix strain.
Fung, Ashley K; Paredes, J J; Andarawis-Puri, Nelly
2018-01-23
Macroscopic tendon loads modulate the cellular microenvironment leading to biological outcomes such as degeneration or repair. Previous studies have shown that damage accumulation and the phases of tendon healing are marked by significant changes in the extracellular matrix, but it remains unknown how mechanical forces of the extracellular matrix are translated to mechanotransduction pathways that ultimately drive the biological response. Our overarching hypothesis is that the unique relationship between extracellular matrix strain and cell deformation will dictate biological outcomes, prompting the need for quantitative methods to characterize the local strain environment. While 2-D methods have successfully calculated matrix strain and cell deformation, 3-D methods are necessary to capture the increased complexity that can arise due to high levels of anisotropy and out-of-plane motion, particularly in the disorganized, highly cellular, injured state. In this study, we validated the use of digital volume correlation methods to quantify 3-D matrix strain using images of naïve tendon cells, the collagen fiber matrix, and injured tendon cells. Additionally, naïve tendon cell images were used to develop novel methods for 3-D cell deformation and 3-D cell-matrix strain, which is defined as a quantitative measure of the relationship between matrix strain and cell deformation. The results support that these methods can be used to detect strains with high accuracy and can be further extended to an in vivo setting for observing temporal changes in cell and matrix mechanics during degeneration and healing. Copyright © 2017. Published by Elsevier Ltd.
Directory of Open Access Journals (Sweden)
Imjak Jeon
2011-01-01
Full Text Available Roll compaction was applied for the preparation of hydroxypropyl cellulose (HPC-based sustained-release matrix tablets. Matrix tablets made via roll compaction exhibited higher dosage uniformity and faster drug release than direct-compacted tablets. HPC viscosity grade, roll pressure, and milling speed affected tablet properties significantly. Roll compaction seems to be an adequate granulation method for the preparation of HPC-based matrix tablets due to the simplicity of the process, less handling difficulty from HPC tackiness as well as easier particle size targeting. Selecting the optimum ratio of plastic excipients and the particle size of starting materials can however be critical issues in this method.
Solution Methods for Structures with Random Properties Subject to Random Excitation
DEFF Research Database (Denmark)
Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.
This paper deals with the lower order statistical moments of the response of structures with random stiffness and random damping properties subject to random excitation. The arising stochastic differential equations (SDE) with random coefficients are solved by two methods, a second order...... perturbation approach and a Markovian method. The second order perturbation approach is grounded on the total probability theorem and can be compactly written. Moreover, the problem to be solved is independent of the dimension of the random variables involved. The Markovian approach suggests transforming...... the SDE with random coefficients with deterministic initial conditions to an equivalent nonlinear SDE with deterministic coefficient and random initial conditions. In both methods, the statistical moment equations are used. Hierarchy of statistical moments in the markovian approach is closed...
On the eigenvalue-eigenvector method for solution of the stationary discrete matrix Riccati equation
DEFF Research Database (Denmark)
Michelsen, Michael Locht
1979-01-01
The purpose of this correspondence is to point out that certain numerical problems encountered in the solution of the stationary discrete matrix Riccati equation by the eigenvalue-eigenvector method of Vanghan [1] can be avoided by a simple reformulation.......The purpose of this correspondence is to point out that certain numerical problems encountered in the solution of the stationary discrete matrix Riccati equation by the eigenvalue-eigenvector method of Vanghan [1] can be avoided by a simple reformulation....
An ensemble method with hybrid features to identify extracellular matrix proteins.
Yang, Runtao; Zhang, Chengjin; Gao, Rui; Zhang, Lina
2015-01-01
The extracellular matrix (ECM) is a dynamic composite of secreted proteins that play important roles in numerous biological processes such as tissue morphogenesis, differentiation and homeostasis. Furthermore, various diseases are caused by the dysfunction of ECM proteins. Therefore, identifying these important ECM proteins may assist in understanding related biological processes and drug development. In view of the serious imbalance in the training dataset, a Random Forest-based ensemble method with hybrid features is developed in this paper to identify ECM proteins. Hybrid features are employed by incorporating sequence composition, physicochemical properties, evolutionary and structural information. The Information Gain Ratio and Incremental Feature Selection (IGR-IFS) methods are adopted to select the optimal features. Finally, the resulting predictor termed IECMP (Identify ECM Proteins) achieves an balanced accuracy of 86.4% using the 10-fold cross-validation on the training dataset, which is much higher than results obtained by other methods (ECMPRED: 71.0%, ECMPP: 77.8%). Moreover, when tested on a common independent dataset, our method also achieves significantly improved performance over ECMPP and ECMPRED. These results indicate that IECMP is an effective method for ECM protein prediction, which has a more balanced prediction capability for positive and negative samples. It is anticipated that the proposed method will provide significant information to fully decipher the molecular mechanisms of ECM-related biological processes and discover candidate drug targets. For public access, we develop a user-friendly web server for ECM protein identification that is freely accessible at http://iecmp.weka.cc.
Directory of Open Access Journals (Sweden)
Lev-Tov Hadar
2013-01-01
Full Text Available Abstract Background Diabetic foot ulcers (DFUs represent a significant source of morbidity and an enormous financial burden. Standard care for DFUs involves systemic glucose control, ensuring adequate perfusion, debridement of nonviable tissue, off-loading, control of infection, local wound care and patient education, all administered by a multidisciplinary team. Unfortunately, even with the best standard of care (SOC available, only 24% or 30% of DFUs will heal at weeks 12 or 20, respectively. The extracellular matrix (ECM in DFUs is abnormal and its impairment has been proposed as a key target for new therapeutic devices. These devices intend to replace the aberrant ECM by implanting a matrix, either devoid of cells or enhanced with fibroblasts, keratinocytes or both as well as various growth factors. These new bioengineered skin substitutes are proposed to encourage angiogenesis and in-growth of new tissue, and to utilize living cells to generate cytokines needed for wound repair. To date, the efficacy of bioengineered ECM containing live cellular elements for improving healing above that of a SOC control group has not been compared with the efficacy of an ECM devoid of cells relative to the same SOC. Our hypothesis is that there is no difference in the improved healing effected by either of these two product types relative to SOC. Methods/Design To test this hypothesis we propose a randomized, single-blind, clinical trial with three arms: SOC, SOC plus Dermagraft® (bioengineered ECM containing living fibroblasts and SOC plus Oasis® (ECM devoid of living cells in patients with nonhealing DFUs. The primary outcome is the percentage of subjects that achieved complete wound closure by week 12. Discussion If our hypothesis is correct, then immense cost savings could be realized by using the orders-of-magnitude less expensive acellular ECM device without compromising patient health outcomes. The article describes the protocol proposed to test
Energy Technology Data Exchange (ETDEWEB)
Stotland, Alexander; Peer, Tal; Cohen, Doron [Department of Physics, Ben-Gurion University, Beer-Sheva 84005 (Israel); Budoyo, Rangga; Kottos, Tsampikos [Department of Physics, Wesleyan University, Middletown, CT 06459 (United States)
2008-07-11
The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming 'mesoscopic' circumstances the analysis of the electro-driven transitions shows similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to capture the essential ingredients of the problem, and leads to a generalized variable range hopping picture. (fast track communication)
Energy Technology Data Exchange (ETDEWEB)
Verbaarschot, Jacobus (Department of Physics, SUNY, Stony Brook, NY 11794 (United States))
1994-09-19
We study the spectrum of the QCD Dirac operator near zero virtuality for N[sub c] =2. According to a universality argument, it can be described by a random matrix theory with the chiral structure of QCD, but with real matrix elements.Using results derived by Mehta and Mahoux and Nagao and Wadati, we are able to obtain an analytical result for the microscopic spectral density that in turn is the generating function for Leutwyler-Smilga type spectral sum rules. ((orig.))
Methods of Manufacturing Bioactive Gels from Extracellular Matrix Material
Kentner, Kimberly (Inventor); Stuart, Katherine A. (Inventor); Janis, Abram D. (Inventor)
2017-01-01
The present invention is directed to methods of manufacturing bioactive gels from ECM material, i.e., gels which retain bioactivity, and can serve as scaffolds for preclinical and clinical tissue engineering and regenerative medicine approaches to tissue reconstruction. The manufacturing methods take advantage of a new recognition that bioactive gels from ECM material can be created by digesting particularized ECM material in an alkaline environment and neutralizing to provide bioactive gels.
Panuwet, Parinya; Hunter, Ronald E.; D’Souza, Priya E.; Chen, Xianyu; Radford, Samantha A.; Cohen, Jordan R.; Marder, M. Elizabeth; Kartavenka, Kostya; Ryan, P. Barry; Barr, Dana Boyd
2015-01-01
The ability to quantify levels of target analytes in biological samples accurately and precisely, in biomonitoring, involves the use of highly sensitive and selective instrumentation such as tandem mass spectrometers and a thorough understanding of highly variable matrix effects. Typically, matrix effects are caused by co-eluting matrix components that alter the ionization of target analytes as well as the chromatographic response of target analytes, leading to reduced or increased sensitivity of the analysis. Thus, before the desired accuracy and precision standards of laboratory data are achieved, these effects must be characterized and controlled. Here we present our review and observations of matrix effects encountered during the validation and implementation of tandem mass spectrometry-based analytical methods. We also provide systematic, comprehensive laboratory strategies needed to control challenges posed by matrix effects in order to ensure delivery of the most accurate data for biomonitoring studies assessing exposure to environmental toxicants. PMID:25562585
The Visual Matrix Method: Imagery and Affect in a Group-Based Research Setting
Directory of Open Access Journals (Sweden)
Lynn Froggett
2015-07-01
Full Text Available The visual matrix is a method for researching shared experience, stimulated by sensory material relevant to a research question. It is led by imagery, visualization and affect, which in the matrix take precedence over discourse. The method enables the symbolization of imaginative and emotional material, which might not otherwise be articulated and allows "unthought" dimensions of experience to emerge into consciousness in a participatory setting. We describe the process of the matrix with reference to the study "Public Art and Civic Engagement" (FROGGETT, MANLEY, ROY, PRIOR & DOHERTY, 2014 in which it was developed and tested. Subsequently, examples of its use in other contexts are provided. Both the matrix and post-matrix discussions are described, as is the interpretive process that follows. Theoretical sources are highlighted: its origins in social dreaming; the atemporal, associative nature of the thinking during and after the matrix which we describe through the Deleuzian idea of the rhizome; and the hermeneutic analysis which draws from object relations theory and the Lorenzerian tradition of scenic understanding. The matrix has been conceptualized as a "scenic rhizome" to account for its distinctive quality and hybrid origins in research practice. The scenic rhizome operates as a "third" between participants and the "objects" of contemplation. We suggest that some of the drawbacks of other group-based methods are avoided in the visual matrix—namely the tendency for inter-personal dynamics to dominate the event. URN: http://nbn-resolving.de/urn:nbn:de:0114-fqs150369
Fernando, Rohan L; Cheng, Hao; Garrick, Dorian J
2016-10-27
The mixed linear model employed for genomic best linear unbiased prediction (GBLUP) includes the breeding value for each animal as a random effect that has a mean of zero and a covariance matrix proportional to the genomic relationship matrix ([Formula: see text]), where the inverse of [Formula: see text] is required to set up the usual mixed model equations (MME). When only some animals have genomic information, genomic predictions can be obtained by an extension known as single-step GBLUP, where the covariance matrix of breeding values is constructed by combining the pedigree-based additive relationship matrix with [Formula: see text]. The inverse of the combined relationship matrix can be obtained efficiently, provided [Formula: see text] can be inverted. In some livestock species, however, the number [Formula: see text] of animals with genomic information exceeds the number of marker covariates used to compute [Formula: see text], and this results in a singular [Formula: see text]. For such a case, an efficient and exact method to obtain GBLUP and single-step GBLUP is presented here. Exact methods are already available to obtain GBLUP when [Formula: see text] is singular, but these require working with large dense matrices. Another approach is to modify [Formula: see text] to make it nonsingular by adding a small value to all its diagonals or regressing it towards the pedigree-based relationship matrix. This, however, results in the inverse of [Formula: see text] being dense and difficult to compute as [Formula: see text] grows. The approach presented here recognizes that the number r of linearly independent genomic breeding values cannot exceed the number of marker covariates, and the mixed linear model used here for genomic prediction only fits these r linearly independent breeding values as random effects. The exact method presented here was compared to Apy-GBLUP and to Apy single-step GBLUP, both of which are approximate methods that use a modified [Formula
[Optimization of cataplasm matrix with face-centered design-response surface method].
Liu, Shuzhi; Li, Junhong; Jin, Rixian; Du, Maobo
2009-12-01
To optimize the matrix formulation of cataplasm. Face-centered design was used in the experimental design, and response surface was produced in quadratic polynomial after data fitting in order to explore the impacts of Sodium Polyacrylate, Carbomer and the cross-linking agent on stickiness of cataplasm, optimize the prescription of the cataplasm matrix and perform the evaluation analysis. The multiple correlation coefficient (R2) and adjusted R2 in the fitting method using quadratic polynomial were 0.970 and 0. 952 (F = 53.953, P = 0.0001), respectively, and the model was significant different. The ratio of optimum proportion of Sodium Polyacrylate, Carbomer and the cross-linking agent in the matrix of cataplasm was determined, which was proved efficaciously. Face-centered design-response surface method is a simple method with good prediction result for the optimization of cataplasm matrix.
What role for qualitative methods in randomized experiments?
DEFF Research Database (Denmark)
Prowse, Martin; Camfield, Laura
2009-01-01
The vibrant debate on randomized experiments within international development has been slow to accept a role for qualitative methods within research designs. Whilst there are examples of how 'field visits' or descriptive analyses of context can play a complementary, but secondary, role...... to quantitative methods, little attention has been paid to the possibility of randomized experiments that allow a primary role to qualitative methods. This paper assesses whether a range of qualitative methods compromise the internal and external validity criteria of randomized experiments. It suggests that life...... history interviews have advantages over other qualitative methods, and offers one alternative to the conventional survey tool....
American Society for Testing and Materials. Philadelphia
2004-01-01
1.1 This test method covers the determination of translaminar fracture toughness, KTL, for laminated and pultruded polymer matrix composite materials of various ply orientations using test results from monotonically loaded notched specimens. 1.2 This test method is applicable to room temperature laboratory air environments. 1.3 Composite materials that can be tested by this test method are not limited by thickness or by type of polymer matrix or fiber, provided that the specimen sizes and the test results meet the requirements of this test method. This test method was developed primarily from test results of various carbon fiber – epoxy matrix laminates and from additional results of glass fiber – epoxy matrix, glass fiber-polyester matrix pultrusions and carbon fiber – bismaleimide matrix laminates (1-4, 6, 7). 1.4 A range of eccentrically loaded, single-edge-notch tension, ESE(T), specimen sizes with proportional planar dimensions is provided, but planar size may be variable and adjusted, with asso...
Matrix factorization method for the Hamiltonian structure of ...
Indian Academy of Sciences (India)
S Ghosh, B Talukdar and S Chakraborti. The Hamiltonian structure of non-linear evolution equations solvable by the inverse spectral method was discovered in 1971 by Zakharov and Faddeev [2] and by Gardner [3] who interpreted the Kortweg-de Vries (KdV) equation as a completely integrable Hamilto- nian system in an ...
Emergy Algebra: Improving Matrix Methods for Calculating Tranformities
Transformity is one of the core concepts in Energy Systems Theory and it is fundamental to the calculation of emergy. Accurate evaluation of transformities and other emergy per unit values is essential for the broad acceptance, application and further development of emergy method...
Lyophilic matrix method for dissolution and release studies of nanoscale particles.
Pessi, Jenni; Svanbäck, Sami; Lassila, Ilkka; Hæggström, Edward; Yliruusi, Jouko
2017-10-25
We introduce a system with a lyophilic matrix to aid dissolution studies of powders and particulate systems. This lyophilic matrix method (LM method) is based on the ability to discriminate between non-dissolved particles and the dissolved species. In the LM method the test substance is embedded in a thin lyophilic core-shell matrix. This permits rapid contact with the dissolution medium while minimizing dispersion of non-dissolved particles without presenting a substantial diffusion barrier. The method produces realistic dissolution and release results for particulate systems, especially those featuring nanoscale particles. By minimizing method-induced effects on the dissolution profile of nanopowders, the LM method overcomes shortcomings associated with current dissolution tests. Copyright © 2017 Elsevier B.V. All rights reserved.
A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix.
Hu, Zongliang; Dong, Kai; Dai, Wenlin; Tong, Tiejun
2017-09-21
The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.
A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix
Hu, Zongliang
2017-09-27
The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.
Symmetric Matrix Fields in the Finite Element Method
Directory of Open Access Journals (Sweden)
Gerard Awanou
2010-07-01
Full Text Available The theory of elasticity is used to predict the response of a material body subject to applied forces. In the linear theory, where the displacement is small, the stress tensor which measures the internal forces is the variable of primal importance. However the symmetry of the stress tensor which expresses the conservation of angular momentum had been a challenge for finite element computations. We review in this paper approaches based on mixed finite element methods.
Schilder, Jurnan; Ellenbroek, Marcel; de Boer, Andre
2017-01-01
In this work two different recursive solution procedures for flexible multibody systems are considered: the condensation method and the transfer matrix method. A comparison between these methods is made based on the equation of motion of an arbitrary 3D linear elastic body, in which the absolute
An Iterative Method for the Matrix Principal n-th Root
Lakić, Slobodan
1995-01-01
In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.
NewIn-situ synthesis method of magnesium matrix composites reinforced with TiC particulates
Directory of Open Access Journals (Sweden)
Zhang Xiuqing
2006-12-01
Full Text Available Magnesium matrix composites reinforced with TiC particulates was prepared using a new in-situ synthesis method of remelting and dilution technique. And measurements were performed on the composites. The results of x ray diffraction (XRD analysis confirmed that TiC particulates were synthesized during the sintering process, and they retained in magnesium matrix composites after the remelting and dilution processing. From the microstructure characterization and electron probe microanalysis (EPMA, we could see that fine TiC particulates distributed uniformly in the matrix material.
Hu, Jun; Li, Yang; Yang, Jing-Yu; Shen, Hong-Bin; Yu, Dong-Jun
2016-02-01
G-protein-coupled receptors (GPCRs) are important targets of modern medicinal drugs. The accurate identification of interactions between GPCRs and drugs is of significant importance for both protein function annotations and drug discovery. In this paper, a new sequence-based predictor called TargetGDrug is designed and implemented for predicting GPCR-drug interactions. In TargetGDrug, the evolutionary feature of GPCR sequence and the wavelet-based molecular fingerprint feature of drug are integrated to form the combined feature of a GPCR-drug pair; then, the combined feature is fed to a trained random forest (RF) classifier to perform initial prediction; finally, a novel drug-association-matrix-based post-processing procedure is applied to reduce potential false positive or false negative of the initial prediction. Experimental results on benchmark datasets demonstrate the efficacy of the proposed method, and an improvement of 15% in the Matthews correlation coefficient (MCC) was observed over independent validation tests when compared with the most recently released sequence-based GPCR-drug interactions predictor. The implemented webserver, together with the datasets used in this study, is freely available for academic use at http://csbio.njust.edu.cn/bioinf/TargetGDrug. Copyright © 2015 Elsevier Ltd. All rights reserved.
Li, Victor C.; Wang, Youjiang; Backer, Stanley
A MICROMECHANICAL model has been formulated for the post-cracking behavior of a brittle matrix composite reinforced with randomly distributed short fibers. This model incorporates the mechanics of pull-out of fibers which are inclined at an angle to the matrix crack plane and which undergo slip-weakening or slip-hardening during the pull-out process. In addition, the random location and orientation of fibers are accounted for. Comparisons of model predictions of post-cracking tension-softening behavior with experimental data appear to support the validity of the model. The model is used to examine the effects of fiber length, snubbing friction coefficient and interfacial bond behavior on composite post-cracking tensile properties. The scaling of the bridging fracture toughening with material parameters is discussed.
Roundtrip matrix method for calculating the leaky resonant modes of open nanophotonic structures
DEFF Research Database (Denmark)
de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper
2014-01-01
We present a numerical method for calculating quasi-normal modes of open nanophotonic structures. The method is based on scattering matrices and a unity eigenvalue of the roundtrip matrix of an internal cavity, and we develop it in detail with electromagnetic fields expanded on Bloch modes...... of periodic structures. This procedure is simpler to implement numerically and more intuitive than previous scattering matrix methods, and any routine based on scattering matrices can benefit from the method. We demonstrate the calculation of quasi-normal modes for two-dimensional photonic crystals where...
Method for encapsulating nanoparticles in a zeolite matrix
Coker, Eric N.
2007-12-11
A method for preparing a metal nanocluster composite material. A porous zeolitic material is treated with an aqueous metal compound solution to form a metal ion-exchanged zeolitic material, heated at a temperature ramp rate of less than 2.degree. C./min to an elevated temperature, cooled, contacted with an organic monomer and heating to induce polymerization, and heating the composite material to greater than 350.degree. C. under non-oxidizing conditions to form a metal nanocluster-carbon composite material with nanocluster sizes between approximately 0.6 nm and 10 nm.
DEFF Research Database (Denmark)
Cherchi, Elisabetta; Guevara, Cristian Angelo
2012-01-01
of parameters increases is usually known as the “curse of dimensionality” in the simulation methods. We investigate this problem in the case of the random coefficients Logit model. We compare the traditional Maximum Simulated Likelihood (MSL) method with two alternative estimation methods: the Expectation......–covariance matrix. Results show that indeed MSL suffers from lack of empirical identification as the dimensionality grows while EM deals much better with this estimation problem. On the other hand, the HH method, although not being simulation-based, showed poor performance with large dimensions, principally because......When the dimension of the vector of estimated parameters increases, simulation based methods become impractical, because the number of draws required for estimation grows exponentially with the number of parameters. In simulation methods, the lack of empirical identification when the number...
Cox, Jeris; Malik, Minnie; Britten, Joy; Lewis, Terrence; Catherino, William H
2018-02-01
In a prior randomized controlled study, patients treated with ulipristal acetate (UPA) or placebo for 3 months had a decrease in leiomyoma size. A total of 10 patients' tissue samples (5 placebo and 5 treated with 10 mg/d UPA) that underwent hysterectomy and tissue preservation were identified from this study. Quantitative real-time reverse transcriptase polymerase chain reaction and Western blotting were used to assess fold gene and protein expression of extracellular membrane (ECM) proteins: collagen 1A (COL1A), fibronectin (FN1), and versican (VCAN) of the samples. Confirmatory immunohistochemical analysis was performed. Changes in total matrix collagen were examined using Masson trichrome staining. Multiplex measurement of the matrix metalloproteinases (MMPs) and tissue inhibitor of metalloproteinases was performed. Compared to placebo-treated surgical specimens, 80% of the treated specimens showed decrease in VCAN protein, 60% showed decrease in FN1, but no consistent alteration in COL1A. This effect was also supported by immunohistochemistry where leiomyoma surgical specimens demonstrated decreased amount of FN1 and VCAN on UPA treatment. Increased MMP2 and decreased MMP9 in treated patient leiomyomas indicate both degradation of the matrix and inhibition of the pathway involved in matrix production. Treatment with UPA decreased fibroid volume in placebo-controlled, randomized trials. Treatment with UPA decreased gene expression and protein production in leiomyoma tissue, suggesting both an impact on water content and ECM protein concentration as a mechanism of ulipristal-mediated decrease in leiomyoma size.
Analysis and Synthesis of the Digital Structures by the Matrix Method
Psenicka, B.; Hospodka, J.
2011-01-01
This paper presents a general matrix algorithm for analysis of digital filters. The method proposed in this paper allows not only the analysis of the digital filters, but also the construction of new structures of the canonic or non-canonic digital filter. Equivalent filters of different structures can be found according to various matrix expansions. The structures can be calculated even from transfer function or from state-space matrices and with the additional advantage of requiring minimum...
Method for Analysis of Matrix Degradation by CCN2 Through the MMP/TIMP System.
McLennan, Susan V; Min, Danqing; Wang, Xiaoyu; Twigg, Stephen M
2017-01-01
Many studies have shown effects of members of the CCN family on matrix synthesis and accumulation but few have examined degradative pathways. This scarcity of information is in part due to the lack of suitable model systems. Here we describe methods for making rhCCN2 and also for the preparation of a biosynthetically labeled matrix substrate that can be used to measure the effect of CCN on cellular or secreted degradative pathways.
Imagining transitions in old age through the Visual Matrix method
DEFF Research Database (Denmark)
Liveng, Anne; Ramvi, Ellen; Froggett, Lynn
2017-01-01
and collective imagination. Through analysis of data extracts, on the three transitions, we illustrate oscillations between defending against the challenges of ageing and realism in facing the anxieties it can provoke. A recurring theme includes the finality of individual life and the inter......Dominant discourses of ageing are often confined to what is less painful to think about and therefore idealise or denigrate ageing and later life. We present findings from an exploratory psychosocial study, in a Nordic context, into three later-life transitions: from working life to retirement......, from mental health to dementia and from life to death. Because, for some, these topics are hard to bear and therefore defended against and routinely excluded from everyday awareness, we used a method led by imagery and affect–the Visual Matrix–to elicit participant s’ free associative personal...
The matrix method for radiological characterization of radioactive waste
Magistris, M
2007-01-01
Beam losses are responsible for material activation in some of the components of particle accelerators. The activation is caused by several nuclear processes and varies with the irradiation history and the characteristics of the material (namely chemical composition and size). Once at the end of their operational lifetime, these materials require radiological characterization. The radionuclide inventory depends on the particle spectrum, the irradiation history and the chemical composition of the material. As long as these factors are known and the material cross-sections are available, the induced radioactivity can be calculated analytically. However, these factors vary widely among different items of waste and sometimes they are only partially known. The European Laboratory for Particle Physics (CERN, Geneva) has been operating accelerators for high-energy physics for 50 years. Different methods for the evaluation of the radionuclide inventory are currently under investigation at CERN, including the so-calle...
Han, Rui-Qi; Xie, Wen-Jie; Xiong, Xiong; Zhang, Wei; Zhou, Wei-Xing
The correlation structure of a stock market contains important financial contents, which may change remarkably due to the occurrence of financial crisis. We perform a comparative analysis of the Chinese stock market around the occurrence of the 2008 crisis based on the random matrix analysis of high-frequency stock returns of 1228 Chinese stocks. Both raw correlation matrix and partial correlation matrix with respect to the market index in two time periods of one year are investigated. We find that the Chinese stocks have stronger average correlation and partial correlation in 2008 than in 2007 and the average partial correlation is significantly weaker than the average correlation in each period. Accordingly, the largest eigenvalue of the correlation matrix is remarkably greater than that of the partial correlation matrix in each period. Moreover, each largest eigenvalue and its eigenvector reflect an evident market effect, while other deviating eigenvalues do not. We find no evidence that deviating eigenvalues contain industrial sectorial information. Surprisingly, the eigenvectors of the second largest eigenvalues in 2007 and of the third largest eigenvalues in 2008 are able to distinguish the stocks from the two exchanges. We also find that the component magnitudes of the some largest eigenvectors are proportional to the stocks’ capitalizations.
Method of making carbon fiber-carbon matrix reinforced ceramic composites
Williams, Brian (Inventor); Benander, Robert (Inventor)
2007-01-01
A method of making a carbon fiber-carbon matrix reinforced ceramic composite wherein the result is a carbon fiber-carbon matrix reinforcement is embedded within a ceramic matrix. The ceramic matrix does not penetrate into the carbon fiber-carbon matrix reinforcement to any significant degree. The carbide matrix is a formed in situ solid carbide of at least one metal having a melting point above about 1850 degrees centigrade. At least when the composite is intended to operate between approximately 1500 and 2000 degrees centigrade for extended periods of time the solid carbide with the embedded reinforcement is formed first by reaction infiltration. Molten silicon is then diffused into the carbide. The molten silicon diffuses preferentially into the carbide matrix but not to any significant degree into the carbon-carbon reinforcement. Where the composite is intended to operate between approximately 2000 and 2700 degrees centigrade for extended periods of time such diffusion of molten silicon into the carbide is optional and generally preferred, but not essential.
Using the Matrix Method to Compute the Degrees of Freedom of Mechanisms
Directory of Open Access Journals (Sweden)
Kambiz Ghaemi Osgouie
2017-08-01
Full Text Available In this paper, some definitions and traditional formulas for calculating the mobility of mechanisms are represented, e.g. Grubler formula, Somov - Malyshev formula, and Buchsbaum - Freudenstei. It is discussed that there are certain cases in which they are too ambiguous and incorrect to use. However, a matrix method is suggested based on the rank of the Jacobian of the mechanism and its application is investigated. It is shown that the matrix method will definitely lead to a correct answer; however, it is lengthy and consumes more computational effort. It is shown that in the cases the traditional formulas give a wrong answer and the matrix method gives the correct mobility. To compare the methods, several examples are given including the four bar planar linkage, the augmented four bar linkage, University of Maryland manipulator, Cartesian parallel manipulator (CPM, delta robot, orthoglide robot, and H4 parallel robot.
Novel Direction Of Arrival Estimation Method Based on Coherent Accumulation Matrix Reconstruction
Directory of Open Access Journals (Sweden)
Li Lei
2015-04-01
Full Text Available Based on coherent accumulation matrix reconstruction, a novel Direction Of Arrival (DOA estimation decorrelation method of coherent signals is proposed using a small sample. First, the Signal to Noise Ratio (SNR is improved by performing coherent accumulation operation on an array of observed data. Then, according to the structure characteristics of the accumulated snapshot vector, the equivalent covariance matrix, whose rank is the same as the number of array elements, is constructed. The rank of this matrix is proved to be determined just by the number of incident signals, which realize the decorrelation of coherent signals. Compared with spatial smoothing method, the proposed method performs better by effectively avoiding aperture loss with high-resolution characteristics and low computational complexity. Simulation results demonstrate the efficiency of the proposed method.
A random spatial sampling method in a rural developing nation
Michelle C. Kondo; Kent D.W. Bream; Frances K. Barg; Charles C. Branas
2014-01-01
Nonrandom sampling of populations in developing nations has limitations and can inaccurately estimate health phenomena, especially among hard-to-reach populations such as rural residents. However, random sampling of rural populations in developing nations can be challenged by incomplete enumeration of the base population. We describe a stratified random sampling method...
A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics
Pujol, O.; Perez, J. P.
2007-01-01
The aim of this paper is to propose a synthetic approach to the transfer matrix method in classical and quantum physics. This method is an efficient tool to deal with complicated physical systems of practical importance in geometrical light or charged particle optics, classical electronics, mechanics, electromagnetics and quantum physics. Teaching…
Charge-constrained auxiliary-density-matrix methods for the Hartree–Fock exchange contribution
DEFF Research Database (Denmark)
Merlot, Patrick; Izsak, Robert; Borgoo, Alex
2014-01-01
Three new variants of the auxiliary-density-matrix method (ADMM) of Guidon, Hutter, and VandeVondele [J. Chem. Theory Comput. 6, 2348 (2010)] are presented with the common feature thatthey have a simplified constraint compared with the full orthonormality requirement of the earlier ADMM1 method...
Efficient Training Methods for Conditional Random Fields
2008-02-01
Learning (ICML), 2007. [63] Bruce G. Lindsay. Composite likelihood methods. Contemporary Mathematics, pages 221–239, 1988. 189 [64] Yan Liu , Jaime...graphical models: Approximate MCMC algorithms. In Conference on Uncertainty in Artificial Intelligence (UAI), 2004. [86] Ara V. Nefian, Luhong Liang, Xiaobo ...Pi, Liu Xiaoxiang, Crusoe Mao, and Kevin Murphy. A coupled HMM for audio-visual speech recognition. In IEEE Int’l Conference on Acoustics, Speech and
Electron-molecule collision calculations using the R-matrix method
Energy Technology Data Exchange (ETDEWEB)
Tennyson, Jonathan, E-mail: j.tennyson@ucl.ac.u [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom)
2010-06-15
The R-matrix method is an embedding procedure which is based on the division of space into an inner region where the physics is complicated and an outer region for which greatly simplified equations can be solved. The method developed out of nuclear physics, where the effects of the inner region were simply parametrized, into atomic and molecular physics, where the full problem can be formulated and hopefully solved ab initio. In atomic physics R-matrix based procedures are the method of choice for the ab initio calculation of electron collision parameters. There has been a number of R-matrix procedures developed to treat the low-energy electron-molecule collision problem or particular aspects of this problem. These methods have been extended to both positron physics and the R-matrix treatment of vibrational motion. The physical basis of the R-matrix method as well as its theoretical formulation are presented. Various electron scattering models within an R-matrix formulation including static exchange, static exchange plus polarization and close coupling are described with reference to various computational implementations of the method; these are compared to similar models used within other scattering methods. The need for a balanced treatment of the target and continuum wave functions is emphasised. Extensions of close-coupling based models into the intermediate energy regime using pseudo-states is discussed, as is the adaptation of R-matrix methods to problems involving photons. The numerical realisation of the R-matrix method is based on the adaptation of quantum chemistry codes in the inner region and asymptotic electron-atom scattering programs in the outer region. Use of bound state codes in scattering calculations raises issues involving continuum basis sets, appropriate orbitals, integral evaluation, orthogonalization, Hamiltonian construction and diagonalization which need to be addressed. The algorithms developed to resolve these issues are described as
Wang, Gang-Jin; Xie, Chi; Chen, Shou; Yang, Jiao-Jiao; Yang, Ming-Yan
2013-09-01
In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Marčenko-Pastur distribution.
Directory of Open Access Journals (Sweden)
Ayşe Betül Koç
2014-01-01
Full Text Available A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.
Trimpin, Sarah; Inutan, Ellen D
2013-05-01
An astonishingly simple new method to produce gas-phase ions of small molecules as well as proteins from the solid state under cold vacuum conditions is described. This matrix assisted ionization vacuum (MAIV) mass spectrometry (MS) method produces multiply charged ions similar to those that typify electrospray ionization (ESI) and uses sample preparation methods that are nearly identical to matrix-assisted laser desorption/ionization (MALDI). Unlike these established methods, MAIV does not require a laser or voltage for ionization, and unlike the recently introduced matrix assisted ionization inlet method, does not require added heat. MAIV-MS requires only introduction of a crystalline mixture of the analyte incorporated with a suitable small molecule matrix compound such as 3-nitrobenzonitrile directly to the vacuum of the mass spectrometer. Vacuum intermediate pressure MALDI sources and modified ESI sources successfully produce ions for analysis by MS with this method. As in ESI-MS, ion formation is continuous and, without a laser, little chemical background is observed. MAIV, operating from a surface offers the possibility of significantly improved sensitivity relative to atmospheric pressure ionization because ions are produced in the vacuum region of the mass spectrometer eliminating losses associated with ion transfer from atmospheric pressure to vacuum. Mechanistic aspects and potential applications for this new ionization method are discussed.
Genetic algorithms as global random search methods
Peck, Charles C.; Dhawan, Atam P.
1995-01-01
Genetic algorithm behavior is described in terms of the construction and evolution of the sampling distributions over the space of candidate solutions. This novel perspective is motivated by analysis indicating that the schema theory is inadequate for completely and properly explaining genetic algorithm behavior. Based on the proposed theory, it is argued that the similarities of candidate solutions should be exploited directly, rather than encoding candidate solutions and then exploiting their similarities. Proportional selection is characterized as a global search operator, and recombination is characterized as the search process that exploits similarities. Sequential algorithms and many deletion methods are also analyzed. It is shown that by properly constraining the search breadth of recombination operators, convergence of genetic algorithms to a global optimum can be ensured.
A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate
Directory of Open Access Journals (Sweden)
Min Sun
2014-01-01
Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.
Directory of Open Access Journals (Sweden)
Tamer Ahmed El-Sayed
2017-01-01
Full Text Available The exact solution for multistepped Timoshenko beam is derived using a set of fundamental solutions. This set of solutions is derived to normalize the solution at the origin of the coordinates. The start, end, and intermediate boundary conditions involve concentrated masses and linear and rotational elastic supports. The beam start, end, and intermediate equations are assembled using the present normalized transfer matrix (NTM. The advantage of this method is that it is quicker than the standard method because the size of the complete system coefficient matrix is 4 × 4. In addition, during the assembly of this matrix, there are no inverse matrix steps required. The validity of this method is tested by comparing the results of the current method with the literature. Then the validity of the exact stepped analysis is checked using experimental and FE(3D methods. The experimental results for stepped beams with single step and two steps, for sixteen different test samples, are in excellent agreement with those of the three-dimensional finite element FE(3D. The comparison between the NTM method and the finite element method results shows that the modal percentage deviation is increased when a beam step location coincides with a peak point in the mode shape. Meanwhile, the deviation decreases when a beam step location coincides with a straight portion in the mode shape.
Methods for sample size determination in cluster randomized trials.
Rutterford, Clare; Copas, Andrew; Eldridge, Sandra
2015-06-01
The use of cluster randomized trials (CRTs) is increasing, along with the variety in their design and analysis. The simplest approach for their sample size calculation is to calculate the sample size assuming individual randomization and inflate this by a design effect to account for randomization by cluster. The assumptions of a simple design effect may not always be met; alternative or more complicated approaches are required. We summarise a wide range of sample size methods available for cluster randomized trials. For those familiar with sample size calculations for individually randomized trials but with less experience in the clustered case, this manuscript provides formulae for a wide range of scenarios with associated explanation and recommendations. For those with more experience, comprehensive summaries are provided that allow quick identification of methods for a given design, outcome and analysis method. We present first those methods applicable to the simplest two-arm, parallel group, completely randomized design followed by methods that incorporate deviations from this design such as: variability in cluster sizes; attrition; non-compliance; or the inclusion of baseline covariates or repeated measures. The paper concludes with methods for alternative designs. There is a large amount of methodology available for sample size calculations in CRTs. This paper gives the most comprehensive description of published methodology for sample size calculation and provides an important resource for those designing these trials. © The Author 2015. Published by Oxford University Press on behalf of the International Epidemiological Association.
The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations
Chakravarthy, S. R.; Anderson, D. A.; Salas, M. D.
1980-01-01
The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.
Inutan, Ellen D.; Trimpin, Sarah
2013-01-01
The introduction of electrospray ionization (ESI) and matrix-assisted laser desorption/ionization (MALDI) for the mass spectrometric analysis of peptides and proteins had a dramatic impact on biological science. We now report that a wide variety of compounds, including peptides, proteins, and protein complexes, are transported directly from a solid-state small molecule matrix to gas-phase ions when placed into the vacuum of a mass spectrometer without the use of high voltage, a laser, or added heat. This ionization process produces ions having charge states similar to ESI, making the method applicable for high performance mass spectrometers designed for atmospheric pressure ionization. We demonstrate highly sensitive ionization using intermediate pressure MALDI and modified ESI sources. This matrix and vacuum assisted soft ionization method is suitable for the direct surface analysis of biological materials, including tissue, via mass spectrometry. PMID:23242551
Decoupled Estimation of 2D DOA for Coherently Distributed Sources Using 3D Matrix Pencil Method
Directory of Open Access Journals (Sweden)
Tang Bin
2008-08-01
Full Text Available A new 2D DOA estimation method for coherently distributed (CD source is proposed. CD sources model is constructed by using Taylor approximation to the generalized steering vector (GSV, whereas the angular and angular spread are separated from signal pattern. The angular information is in the phase part of the GSV, and the angular spread information is in the module part of the GSV, thus enabling to decouple the estimation of 2D DOA from that of the angular spread. The array received data is used to construct three-dimensional (3D enhanced data matrix. The 2D DOA for coherently distributed sources could be estimated from the enhanced matrix by using 3D matrix pencil method. Computer simulation validated the efficiency of the algorithm.
Ushenko, Yu. A.; Prysyazhnyuk, V. P.; Gavrylyak, M. S.; Gorsky, M. P.; Bachinskiy, V. T.; Vanchuliak, O. Ya.
2015-02-01
A new information optical technique of diagnostics of the structure of polycrystalline films of blood plasma is proposed. The model of Mueller-matrix description of mechanisms of optical anisotropy of such objects as optical activity, birefringence, as well as linear and circular dichroism is suggested. The ensemble of informationally topical azimuthally stable Mueller-matrix invariants is determined. Within the statistical analysis of such parameters distributions the objective criteria of differentiation of films of blood plasma taken from healthy and patients with liver cirrhosis were determined. From the point of view of probative medicine the operational characteristics (sensitivity, specificity and accuracy) of the information-optical method of Mueller-matrix mapping of polycrystalline films of blood plasma were found and its efficiency in diagnostics of liver cirrhosis was demonstrated. Prospects of application of the method in experimental medicine to differentiate postmortem changes of the myocardial tissue was examined.
Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers
Li, Deng-Feng
2016-01-01
This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .
Directory of Open Access Journals (Sweden)
Gangli Chen
2013-01-01
Full Text Available The dynamic test precision of the strapdown inertial measurement unit (SIMU is the basis of estimating accurate motion of various vehicles such as warships, airplanes, spacecrafts, and missiles. So, it is paid great attention in the above fields to increase the dynamic precision of SIMU by decreasing the vibration of the vehicles acting on the SIMU. In this paper, based on the transfer matrix method for multibody system (MSTMM, the multibody system dynamics model of laser gyro strapdown inertial measurement unit (LGSIMU is developed; the overall transfer equation of the system is deduced automatically. The computational results show that the frequency response function of the LGSIMU got by the proposed method and Newton-Euler method have good agreements. Further, the vibration reduction performance and the attitude error responses under harmonic and random excitations are analyzed. The proposed method provides a powerful technique for studying dynamics of LGSIMU because of using MSTMM and its following features: without the global dynamics equations of the system, high programming, low order of system matrix, and high computational speed.
Cloke, Jonathan; Evans, Katharine; Crabtree, David; Hughes, Annette; Simpson, Helen; Holopainen, Jani; Wickstrand, Nina; Kauppinen, Mikko; Leon-Velarde, Carlos; Larson, Nathan; Dave, Keron; Chen, Yi; Ryser, Elliot; Carter, Mark
2016-01-01
The Thermo Scientific™ SureTect™ Listeria species assay is a new real-time PCR assay for the detection of all species of Listeria in food and environmental samples. The assay was originally certified as Performance Tested Methods(SM) (PTM) 071304 in 2013. This report details the method modification study undertaken to extend the performance claims of the assay for matrixes of raw ground turkey, raw ground pork, bagged lettuce, raw pork sausages, pasteurized 2% fat milk, raw cod, pasteurized brie cheese, and ice cream. The method modification study was conducted using the AOAC Research Institute (RI) PTM program to validate the SureTect PCR assay in comparison to the reference method detailed in ISO 11290-1:1996 including amendment 1:2004. All matrixes were tested by Thermo Fisher Scientific (Basingstoke, United Kingdom). In addition, three matrixes (raw cod, bagged lettuce, and pasteurized brie cheese) were analyzed independently as part of the AOAC RI-controlled independent laboratory study by the University of Guelph, Canada. Using probability of detection statistical analysis, there was no significant difference in the performance between the SureTect assay and the International Organization for Standardization reference method for any of the matrixes analyzed in this study.
Energy Technology Data Exchange (ETDEWEB)
Yang, Yang [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Aggelen, Helen van [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Department of Inorganic and Physical Chemistry, Ghent University, 9000 Ghent (Belgium); Yang, Weitao, E-mail: weitao.yang@duke.edu [Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708 (United States)
2013-12-14
Double, Rydberg, and charge transfer (CT) excitations have been great challenges for time-dependent density functional theory (TDDFT). Starting from an (N ± 2)-electron single-determinant reference, we investigate excitations for the N-electron system through the pairing matrix fluctuation, which contains information on two-electron addition/removal processes. We adopt the particle-particle random phase approximation (pp-RPA) and the particle-particle Tamm-Dancoff approximation (pp-TDA) to approximate the pairing matrix fluctuation and then determine excitation energies by the differences of two-electron addition/removal energies. This approach captures all types of interesting excitations: single and double excitations are described accurately, Rydberg excitations are in good agreement with experimental data and CT excitations display correct 1/R dependence. Furthermore, the pp-RPA and the pp-TDA have a computational cost similar to TDDFT and consequently are promising for practical calculations.
Matrix method for analysis of network accuracy based on the beam dynamic theory
Energy Technology Data Exchange (ETDEWEB)
Pupkov, Y.A.; Levashov, Y.I. [AN SSSR, Novosibirsk (Russian Federation). Inst. Yadernoj Fiziki
1996-01-01
Starting the development of the alignment system, surveyors have faced several questions in respect to the degree of accuracy, the length of the region of relative accuracy, the optimal smoothing curve not resulting in the orbit distortion, and the scheme of measurements and appropriate instruments. Aiming to give answers to these questions, matrix method was practically applied for VEPP-4 alignment system. By the analysis of elements of the matrix A, the particular elements to be aligned with higher accuracy and the places where special attention should be paid to the positioning of the vacuum chamber and other equipment were able to be determined. The matrix of the orbit distortion A enabled to perform an analysis of the sensitivity of the magnet system to certain Fourier frequencies in a distribution of the quad displacements. The spectral sensitivity of magnet system for harmonics was much reduced when the matrix A was replaced by A-I. It was found that the surveyor can determine the orbit distortion and reduce the number of elements requiring alignment by applying the matrix method in the realignment process. (M.N.)
Tsai, Ko-Fan; Chu, Shu-Chun
2016-09-19
The one-time ray-tracing optimization method is a fast way to design LED illumination systems [Opt. Express22, 5357 (2014)10.1364/OE.22.005357]. The method optimizes the performance of LED illumination systems by modifying the LEDs' luminous intensity distribution curve (LIDC) with a freeform lens, instead of modifying the illumination system structure. In finding the LEDs' LIDC for optimizing the illumination system's performance, the LEDs' LIDC found by means of a general gradient descent method can be trapped in a local solution. This study develops a matrix operation method to directly find the global solution of the LEDs' LIDC for the optimization of the illumination system's performance for any initial design of an illumination system structure. As compared with the gradient descent method, using the proposed characteristic matrix operation method to find the best LEDs' LIDC reduces the cost in time by several orders of magnitude. The proposed characteristic matrix operation method ensures that the one-time ray-tracing optimization method is an efficient and reliable method for designing LED illumination systems.
Muñoz, O.; Volten, H.; Hovenier, J.W.; Laan, E.; Roush, T.; Stam, D.
2008-01-01
We present laboratory measurements for Martian analog particles, consisting of palagonite. We measured all elements of the scattering matrix as functions of the scattering angle from 3 to 174 degrees at a wavelength of 632.8 nm. The results may be used in studies of the Martian atmosphere.
2015-08-24
Squared Error (MSE) tracking performance for direction of arrival estimation in the presence of noise and missing data; see Fig. 5. 6) We have...scatter in random directions, thereby hindering its passage. As the thickness of a slab of highly scattering random medium increases, this effect
Analysis of multitone holographic interference filters by use of a sparse Hill matrix method
Diehl, D.W.; George, N.
2004-01-01
A theory is presented for the application of Hill's matrix method to the calculation of the reflection and transmission spectra of multitone holographic interference filters in which the permittivity is modulated by a sum of repeating functions of arbitrary period. Such filters are important because
Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation
Directory of Open Access Journals (Sweden)
S. Balaji
2014-01-01
Full Text Available A Legendre wavelet operational matrix method (LWM is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.
A Simple DTC-SVM method for Matrix Converter Drives Using a Deadbeat Scheme
DEFF Research Database (Denmark)
Lee, Kyo-Beum; Blaabjerg, Frede; Lee, Kwang-Won
2005-01-01
In this paper, a simple direct torque control (DTC) method for sensorless matrix converter drives is proposed, which is characterized by a simple structure, minimal torque ripple and unity input power factor. Also a good sensorless speed-control performance in the low speed operation is obtained......, while maintaining constant switching frequency and fast torque dynamics. It is possible to combine the advantages of matrix converters with the advantages of the DTC strategy using space vector modulation a deadbeat algorithm in the stator flux reference frame. Experimental results are shown...
Lin, Hai-Lun; Cao, Yu-Fang
1988-01-01
A new superposition method is presented for evaluating the matrix representation of the generators in the unitary-group approach. This superposition method is based on the Weyl graphical method for the calculation of matrix elements; the latter is an extension of Harter's jawbone formula for the evaluation of the matrix elements of Ei,i-1 to the more general case Ei,j and can also deal with both fermion and boson.
Chang, Hsuan T; Shui, J-W; Lin, K-P
2017-02-01
In this paper, a joint multiple-image encryption and multiplexing system, which utilizes both the nonnegative matrix factorization (NMF) scheme and digital holography, is proposed. A number of images are transformed into noise-like digital holograms, which are then decomposed into a defined number of basis images and a corresponding weighting matrix using the NMF scheme. The determined basis images are similar to the digital holograms and appear as noise-like patterns, which are then stored as encrypted data and serve as the lock in an encryption system. On the other hand, the column vectors in the weighting matrix serve as the keys for the corresponding plain images or the addresses of the multiplexed images. Both the increased uniformity of the column weighting factors and the parameters used in the digital holography enhance the security of the distributed keys. The experimental results show that the proposed method can successfully perform multiple-image encryption with high-level security.
L1 -norm low-rank matrix factorization by variational Bayesian method.
Zhao, Qian; Meng, Deyu; Xu, Zongben; Zuo, Wangmeng; Yan, Yan
2015-04-01
The L1 -norm low-rank matrix factorization (LRMF) has been attracting much attention due to its wide applications to computer vision and pattern recognition. In this paper, we construct a new hierarchical Bayesian generative model for the L1 -norm LRMF problem and design a mean-field variational method to automatically infer all the parameters involved in the model by closed-form equations. The variational Bayesian inference in the proposed method can be understood as solving a weighted LRMF problem with different weights on matrix elements based on their significance and with L2 -regularization penalties on parameters. Throughout the inference process of our method, the weights imposed on the matrix elements can be adaptively fitted so that the adverse influence of noises and outliers embedded in data can be largely suppressed, and the parameters can be appropriately regularized so that the generalization capability of the problem can be statistically guaranteed. The robustness and the efficiency of the proposed method are substantiated by a series of synthetic and real data experiments, as compared with the state-of-the-art L1 -norm LRMF methods. Especially, attributed to the intrinsic generalization capability of the Bayesian methodology, our method can always predict better on the unobserved ground truth data than existing methods.
Directory of Open Access Journals (Sweden)
Qunyi Xie
2016-01-01
Full Text Available Content-based image retrieval has recently become an important research topic and has been widely used for managing images from repertories. In this article, we address an efficient technique, called MNGS, which integrates multiview constrained nonnegative matrix factorization (NMF and Gaussian mixture model- (GMM- based spectral clustering for image retrieval. In the proposed methodology, the multiview NMF scheme provides competitive sparse representations of underlying images through decomposition of a similarity-preserving matrix that is formed by fusing multiple features from different visual aspects. In particular, the proposed method merges manifold constraints into the standard NMF objective function to impose an orthogonality constraint on the basis matrix and satisfy the structure preservation requirement of the coefficient matrix. To manipulate the clustering method on sparse representations, this paper has developed a GMM-based spectral clustering method in which the Gaussian components are regrouped in spectral space, which significantly improves the retrieval effectiveness. In this way, image retrieval of the whole database translates to a nearest-neighbour search in the cluster containing the query image. Simultaneously, this study investigates the proof of convergence of the objective function and the analysis of the computational complexity. Experimental results on three standard image datasets reveal the advantages that can be achieved with the proposed retrieval scheme.
Free vibration characteristics of multiple load path blades by the transfer matrix method
Murthy, V. R.; Joshi, Arun M.
1986-01-01
The determination of free vibrational characteristics is basic to any dynamic design, and these characteristics can form the basis for aeroelastic stability analyses. Conventional helicopter blades are typically idealized as single-load-path blades, and the transfer matrix method is well suited to analyze such blades. Several current helicopter dynamic programs employ transfer matrices to analyze the rotor blades. In this paper, however, the transfer matrix method is extended to treat multiple-load-path blades, without resorting to an equivalent single-load-path approximation. With such an extension, these current rotor dynamic programs which employ the transfer matrix method can be modified with relative ease to account for the multiple load paths. Unlike the conventional blades, the multiple-load-path blades require the introduction of the axial degree-of-freedom into the solution process to account for the differential axial displacements of the different load paths. The transfer matrix formulation is validated through comparison with the finite-element solutions.
Directory of Open Access Journals (Sweden)
Laith K. Abbas
2014-01-01
Full Text Available In this paper, an approach based on transfer matrix method of linear multibody systems (MS-TMM is developed to analyze the free vibration of a multilevel beam, coupled by spring/dashpot systems attached to them in-span. The Euler-Bernoulli model is used for the transverse vibration of the beams, and the spring/dashpot system represents a simplified model of a viscoelastic material. MS-TMM reduces the dynamic problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundaries are composed of displacements, rotation angles, bending moments, and shear forces, which are partly known and partly unknown, and end up with reduced overall transfer matrix. Nontrivial solution requires the coefficient matrix to be singular to yield the required natural frequencies. This paper implements two novel algorithms based on the methodology by reducing the zero search of the reduced overall transfer matrix's determinate to a minimization problem and demonstrates a simple and robust algorithm being much more efficient than direct enumeration. The proposal method is easy to formulate, systematic to apply, and simple to code and can be extended to complex structures with any boundary conditions. Numerical results are presented to show the validity of the proposal method against the published literature.
A random spatial sampling method in a rural developing nation.
Kondo, Michelle C; Bream, Kent D W; Barg, Frances K; Branas, Charles C
2014-04-10
Nonrandom sampling of populations in developing nations has limitations and can inaccurately estimate health phenomena, especially among hard-to-reach populations such as rural residents. However, random sampling of rural populations in developing nations can be challenged by incomplete enumeration of the base population. We describe a stratified random sampling method using geographical information system (GIS) software and global positioning system (GPS) technology for application in a health survey in a rural region of Guatemala, as well as a qualitative study of the enumeration process. This method offers an alternative sampling technique that could reduce opportunities for bias in household selection compared to cluster methods. However, its use is subject to issues surrounding survey preparation, technological limitations and in-the-field household selection. Application of this method in remote areas will raise challenges surrounding the boundary delineation process, use and translation of satellite imagery between GIS and GPS, and household selection at each survey point in varying field conditions. This method favors household selection in denser urban areas and in new residential developments. Random spatial sampling methodology can be used to survey a random sample of population in a remote region of a developing nation. Although this method should be further validated and compared with more established methods to determine its utility in social survey applications, it shows promise for use in developing nations with resource-challenged environments where detailed geographic and human census data are less available.
Multi-Agent Methods for the Configuration of Random Nanocomputers
Lawson, John W.
2004-01-01
As computational devices continue to shrink, the cost of manufacturing such devices is expected to grow exponentially. One alternative to the costly, detailed design and assembly of conventional computers is to place the nano-electronic components randomly on a chip. The price for such a trivial assembly process is that the resulting chip would not be programmable by conventional means. In this work, we show that such random nanocomputers can be adaptively programmed using multi-agent methods. This is accomplished through the optimization of an associated high dimensional error function. By representing each of the independent variables as a reinforcement learning agent, we are able to achieve convergence must faster than with other methods, including simulated annealing. Standard combinational logic circuits such as adders and multipliers are implemented in a straightforward manner. In addition, we show that the intrinsic flexibility of these adaptive methods allows the random computers to be reconfigured easily, making them reusable. Recovery from faults is also demonstrated.
Modeling of wave propagation in drill strings using vibration transfer matrix methods.
Han, Je-Heon; Kim, Yong-Joe; Karkoub, Mansour
2013-09-01
In order to understand critical vibration of a drill bit such as stick-slip and bit-bounce and their wave propagation characteristics through a drill string system, it is critical to model the torsional, longitudinal, and flexural waves generated by the drill bit vibration. Here, a modeling method based on a vibration transfer matrix between two sets of structural wave variables at the ends of a constant cross-sectional, hollow, circular pipe is proposed. For a drill string system with multiple pipe sections, the total vibration transfer matrix is calculated by multiplying all individual matrices, each is obtained for an individual pipe section. Since drill string systems are typically extremely long, conventional numerical analysis methods such as a finite element method (FEM) require a large number of meshes, which makes it computationally inefficient to analyze these drill string systems numerically. The proposed "analytical" vibration transfer matrix method requires significantly low computational resources. For the validation of the proposed method, experimental and numerical data are obtained from laboratory experiments and FEM analyses conducted by using a commercial FEM package, ANSYS. It is shown that the modeling results obtained by using the proposed method are well matched with the experimental and numerical results.
Multiple resonance compensation for betatron coupling and its equivalence with matrix method
De Ninno, G
1999-01-01
Analyses of betatron coupling can be broadly divided into two categories: the matrix approach that decouples the single-turn matrix to reveal the normal modes and the hamiltonian approach that evaluates the coupling in terms of the action of resonances in perturbation theory. The latter is often regarded as being less exact but good for physical insight. The common opinion is that the correction of the two closest sum and difference resonances to the working point is sufficient to reduce the off-axis terms in the 4X4 single-turn matrix, but this is only partially true. The reason for this is explained, and a method is developed that sums to infinity all coupling resonances and, in this way, obtains results equivalent to the matrix approach. The two approaches is discussed with reference to the dynamic aperture. Finally, the extension of the summation method to resonances of all orders is outlined and the relative importance of a single resonance compared to all resonances of a given order is analytically desc...
A revised version of the transfer matrix method to analyze one-dimensional structures
Nitzsche, F.
1983-01-01
A new and general method to analyze both free and forced vibration characteristics of one-dimensional structures is discussed in this paper. This scheme links for the first time the classical transfer matrix method with the recently developed integrating matrix technique to integrate systems of differential equations. Two alternative approaches to the problem are presented. The first is based upon the lumped parameter model to account for the inertia properties of the structure. The second releases that constraint allowing a more precise description of the physical system. The free vibration of a straight uniform beam under different support conditions is analyzed to test the accuracy of the two models. Finally some results for the free vibration of a 12th order system representing a curved, rotating beam prove that the present method is conveniently extended to more complicated structural dynamics problems.
Invariant Imbedded T-Matrix Method for Axial Symmetric Hydrometeors with Extreme Aspect Ratios
Pelissier, Craig; Kuo, Kwo-Sen; Clune, Thomas; Adams, Ian; Munchak, Stephen
2017-01-01
The single-scattering properties (SSPs) of hydrometeors are the fundamental quantities for physics-based precipitation retrievals. Thus, efficient computation of their electromagnetic scattering is of great value. Whereas the semi-analytical T-Matrix methods are likely the most efficient for nonspherical hydrometeors with axial symmetry, they are not suitable for arbitrarily shaped hydrometeors absent of any significant symmetry, for which volume integral methods such as those based on Discrete Dipole Approximation (DDA) are required. Currently the two leading T-matrix methods are the Extended Boundary Condition Method (EBCM) and the Invariant Imbedding T-matrix Method incorporating Lorentz-Mie Separation of Variables (IITM+SOV). EBCM is known to outperform IITM+SOV for hydrometeors with modest aspect ratios. However, in cases when aspect ratios become extreme, such as needle-like particles with large height to diameter values, EBCM fails to converge. Such hydrometeors with extreme aspect ratios are known to be present in solid precipitation and their SSPs are required to model the radiative responses accurately. In these cases, IITM+SOV is shown to converge. An efficient, parallelized C++ implementation for both EBCM and IITM+SOV has been developed to conduct a performance comparison between EBCM, IITM+SOV, and DDSCAT (a popular implementation of DDA). We present the comparison results and discuss details. Our intent is to release the combined ECBM IITM+SOV software to the community under an open source license.
Workshop report on large-scale matrix diagonalization methods in chemistry theory institute
Energy Technology Data Exchange (ETDEWEB)
Bischof, C.H.; Shepard, R.L.; Huss-Lederman, S. [eds.
1996-10-01
The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems as well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configuration interaction (CI), intramolecular vibrational relaxation (IVR), and scattering problems. In atomic structure calculations using the Hartree-Fock method (SCF), the symmetric matrices can range from order hundreds to thousands. These matrices often include large clusters of eigenvalues which can be as much as 25% of the spectrum. However, if Cl methods are also used, the matrix size can be between 10{sup 4} and 10{sup 9} where only one or a few extremal eigenvalues and eigenvectors are needed. Working with very large matrices has lead to the development of
Random matrix theory of quantum transport in chaotic cavities with nonideal leads
Jarosz, Andrzej; Vidal, Pedro; Kanzieper, Eugene
2015-05-01
We determine the joint probability density function (JPDF) of reflection eigenvalues in three Dyson's ensembles of normal-conducting chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Expressing the JPDF in terms of hypergeometric functions of matrix arguments (labeled by the Dyson index β ), we further show that reflection eigenvalues form a determinantal ensemble at β =2 and a new type of a Pfaffian ensemble at β =4 . As an application, we derive a simple analytic expression for the concurrence distribution describing production of orbitally entangled electrons in chaotic cavities with tunnel point contacts when time-reversal symmetry is preserved.
A new compound control method for sine-on-random mixed vibration test
Zhang, Buyun; Wang, Ruochen; Zeng, Falin
2017-09-01
Vibration environmental test (VET) is one of the important and effective methods to provide supports for the strength design, reliability and durability test of mechanical products. A new separation control strategy was proposed to apply in multiple-input multiple-output (MIMO) sine on random (SOR) mixed mode vibration test, which is the advanced and intensive test type of VET. As the key problem of the strategy, correlation integral method was applied to separate the mixed signals which included random and sinusoidal components. The feedback control formula of MIMO linear random vibration system was systematically deduced in frequency domain, and Jacobi control algorithm was proposed in view of the elements, such as self-spectrum, coherence, and phase of power spectral density (PSD) matrix. Based on the excessive correction of excitation in sine vibration test, compression factor was introduced to reduce the excitation correction, avoiding the destruction to vibration table or other devices. The two methods were synthesized to be applied in MIMO SOR vibration test system. In the final, verification test system with the vibration of a cantilever beam as the control object was established to verify the reliability and effectiveness of the methods proposed in the paper. The test results show that the exceeding values can be controlled in the tolerance range of references accurately, and the method can supply theory and application supports for mechanical engineering.
Generalized Christoffel-Darboux formula for skew-orthogonal polynomials and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Saugata [Abdus Salam ICTP, Strada Costiera 11, 34100, Trieste (Italy)
2006-07-14
We obtain a generalized Christoffel-Darboux (GCD) formula for skew-orthogonal polynomials. Using this, we present an alternative derivation of the level density and two-point function for Gaussian orthogonal ensembles and Gaussian symplectic ensembles of random matrices.
CMV matrices in random matrix theory and integrable systems: a survey
Energy Technology Data Exchange (ETDEWEB)
Nenciu, Irina [Courant Institute, 251 Mercer St, New York, NY 10012 (United States)
2006-07-14
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.
A semi-analytical method for simulating matrix diffusion in numerical transport models.
Falta, Ronald W; Wang, Wenwen
2017-02-01
A semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates. Copyright © 2017 Elsevier B.V. All rights reserved.
Pan, Guangming; Wang, Shaochen; Zhou, Wang
2017-10-01
In this paper, we consider the asymptotic behavior of Xfn (n )≔∑i=1 nfn(xi ) , where xi,i =1 ,…,n form orthogonal polynomial ensembles and fn is a real-valued, bounded measurable function. Under the condition that Var Xfn (n )→∞ , the Berry-Esseen (BE) bound and Cramér type moderate deviation principle (MDP) for Xfn (n ) are obtained by using the method of cumulants. As two applications, we establish the BE bound and Cramér type MDP for linear spectrum statistics of Wigner matrix and sample covariance matrix in the complex cases. These results show that in the edge case (which means fn has a particular form f (x ) I (x ≥θn ) where θn is close to the right edge of equilibrium measure and f is a smooth function), Xfn (n ) behaves like the eigenvalues counting function of the corresponding Wigner matrix and sample covariance matrix, respectively.
Application of the Random Vortex Method to Natural Convection ...
African Journals Online (AJOL)
Natural convection flows in channels have been studied using numerical tools such as finite difference and finite element techniques. These techniques are much demanding in computer skills and memory. Random Vortex Element method which has been used successfully in fluid flow was adopted in this work in view of its ...
An efficient algorithm using matrix methods to solve wind tunnel force-balance equations
Smith, D. L.
1972-01-01
An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.
Extension of the noise propagation matrix method for higher mode solutions
Zhang, Peng; Lee, Hyunsuk; Lee, Deokjung
2017-09-01
The noise propagation matrix method (NPMM) has been extended to get higher mode solutions. Previous studies show that the NPMM can be used to compute the dominance ratio of a system. It is essentially the same as the Coarse Mesh Projection Method (CMPM), both of which use the noise propagation matrix (NPM) to determine the dominance ratio, either after finishing the Monte Carlo simulation or on-the-fly during the simulation. Since only the fundamental fission source information is explicitly utilized while the higher mode information is implicitly contained in the statistical noises, the NPMM can usually only give an approximate estimation of the dominance ratio after thousands of cycles. In this study, the NPMM is extended by simulating the higher modes explicitly, so that the dominance ratio estimation can be more accurate and efficient. Besides, the higher mode solutions can be obtained at the same time with good accuracy and efficiency.
Fault detection of helicopter gearboxes using the multi-valued influence matrix method
Chin, Hsinyung; Danai, Kourosh; Lewicki, David G.
1993-01-01
In this paper we investigate the effectiveness of a pattern classifying fault detection system that is designed to cope with the variability of fault signatures inherent in helicopter gearboxes. For detection, the measurements are monitored on-line and flagged upon the detection of abnormalities, so that they can be attributed to a faulty or normal case. As such, the detection system is composed of two components, a quantization matrix to flag the measurements, and a multi-valued influence matrix (MVIM) that represents the behavior of measurements during normal operation and at fault instances. Both the quantization matrix and influence matrix are tuned during a training session so as to minimize the error in detection. To demonstrate the effectiveness of this detection system, it was applied to vibration measurements collected from a helicopter gearbox during normal operation and at various fault instances. The results indicate that the MVIM method provides excellent results when the full range of faults effects on the measurements are included in the training set.
A Method of Q-Matrix Validation for the Linear Logistic Test Model.
Baghaei, Purya; Hohensinn, Christine
2017-01-01
The linear logistic test model (LLTM) is a well-recognized psychometric model for examining the components of difficulty in cognitive tests and validating construct theories. The plausibility of the construct model, summarized in a matrix of weights, known as the Q-matrix or weight matrix, is tested by (1) comparing the fit of LLTM with the fit of the Rasch model (RM) using the likelihood ratio (LR) test and (2) by examining the correlation between the Rasch model item parameters and LLTM reconstructed item parameters. The problem with the LR test is that it is almost always significant and, consequently, LLTM is rejected. The drawback of examining the correlation coefficient is that there is no cut-off value or lower bound for the magnitude of the correlation coefficient. In this article we suggest a simulation method to set a minimum benchmark for the correlation between item parameters from the Rasch model and those reconstructed by the LLTM. If the cognitive model is valid then the correlation coefficient between the RM-based item parameters and the LLTM-reconstructed item parameters derived from the theoretical weight matrix should be greater than those derived from the simulated matrices.
A Novel Method to Implement the Matrix Pencil Super Resolution Algorithm for Indoor Positioning
Directory of Open Access Journals (Sweden)
Tariq Jamil Saifullah Khanzada
2011-10-01
Full Text Available This article highlights the estimation of the results for the algorithms implemented in order to estimate the delays and distances for the indoor positioning system. The data sets for the transmitted and received signals are captured at a typical outdoor and indoor area. The estimation super resolution algorithms are applied. Different state of art and super resolution techniques based algorithms are applied to avail the optimal estimates of the delays and distances between the transmitted and received signals and a novel method for matrix pencil algorithm is devised. The algorithms perform variably at different scenarios of transmitted and received positions. Two scenarios are experienced, for the single antenna scenario the super resolution techniques like ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique and theMatrix Pencil algorithms give optimal performance compared to the conventional techniques. In two antenna scenario RootMUSIC and Matrix Pencil algorithm performed better than other algorithms for the distance estimation, however, the accuracy of all the algorithms is worst than the single antenna scenario. In all cases our devised Matrix Pencil algorithm achieved the best estimation results.
Randomized Oversampling for Generalized Multiscale Finite Element Methods
Calo, Victor M.
2016-03-23
In this paper, we develop efficient multiscale methods for flows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approximates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the randomized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.
Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method
Directory of Open Access Journals (Sweden)
Hooman Fatoorehchi
2014-10-01
Full Text Available In this paper, we put forth a combined method for calculation of all real zeroes of a polynomial equation through the Adomian decomposition method equipped with a number of developed theorems from matrix algebra. These auxiliary theorems are associated with eigenvalues of matrices and enable convergence of the Adomian decomposition method toward different real roots of the target polynomial equation. To further improve the computational speed of our technique, a nonlinear convergence accelerator known as the Shanks transform has optionally been employed. For the sake of illustration, a number of numerical examples are given.
Energy Technology Data Exchange (ETDEWEB)
Geiger, S.; Cortis, A.; Birkholzer, J.T.
2010-04-01
Solute transport in fractured porous media is typically 'non-Fickian'; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with an advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.
Fast and accurate simulations of transmission-line metamaterials using transmission-matrix method
Ma, Hui Feng; Cui, Tie Jun; Chin, Jessie Yao; Cheng, Qiang
2009-01-01
Recently, two-dimensional (2D) periodically L and C loaded transmission-line (TL) networks have been applied to represent metamaterials. The commercial Agilent's Advanced Design System (ADS) is a commonly-used tool to simulate the TL metamaterials. However, it takes a lot of time to set up the TL network and perform numerical simulations using ADS, making the metamaterial analysis inefficient, especially for large-scale TL networks. In this paper, we propose transmission-matrix method (TMM) t...
Resistance of a 1D random chain: Hamiltonian version of the transfer matrix approach
Dossetti-Romero, V.; Izrailev, F. M.; Krokhin, A. A.
2004-01-01
We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We develop a new version of the transfer matrix approach based on the equivalency of a discrete Schrödinger equation and a two-dimensional Hamiltonian map describing a parametric kicked oscillator. In the two limiting cases of ballistic and localized regime we demonstrate how analytical results for the mean resistance and its second moment can be derived directly from the averaging over classical trajectories of the Hamiltonian map. We also discuss the implication of the single parameter scaling hypothesis to the resistance.
Standard Test Method for Tensile Properties of Fiber Reinforced Metal Matrix Composites
American Society for Testing and Materials. Philadelphia
1996-01-01
1.1 This test method covers the determination of the tensile properties of metal matrix composites reinforced by continuous and discontinuous high-modulus fibers. Nontraditional metal matrix composites as stated in also are covered in this test method. This test method applies to specimens loaded in a uniaxial manner tested in laboratory air at either room temperature or elevated temperatures. The types of metal matrix composites covered are: 1.1.1 Unidirectional - Any fiber-reinforced composite with all fibers aligned in a single direction. Continuous or discontinuous reinforcing fibers, longitudinal and transverse properties. 1.1.2 0/90 Balanced Crossply - A laminate composed of only 0 and 90 plies. This is not necessarily symmetric, continuous, or discontinuous reinforcing fibers. 1.1.3 Angleply Laminate - Any balanced laminate consisting of theta plies where theta is an acute angle with respect to a reference direction. Continuous reinforcing fibers without 0 reinforcing fibers (that is, (±45)ns, (±3...
Directory of Open Access Journals (Sweden)
Mateja Šnajdar Musa
2013-06-01
Full Text Available Aluminium based metal matrix composites are rapidly developing group of materials due to their unique combination of properties that include low weight, elevated strength, improved wear and corrosion resistance and relatively good ductility. This combination of properties is a result of mixing two groups of materials with rather different properties with aluminium as ductile matrix and different oxides and carbides added as reinforcement. Al2O3, SiC and ZrO2 are the most popular choices of reinforcement material. One of the most common methods for producing this type of metal matrix composites is powder metallurgy since it has many variations and also is relatively low-cost method. Many different techniques of compacting aluminium and ceramic powders have been previously investigated. Among those techniques equal channel angular pressing (ECAP stands out due to its beneficial influence on the main problem that arises during powder compaction and that is a non-uniform distribution of reinforcement particles. This paper gives an overview on ECAP method principles, advantages and produced powder composite properties.
Comparison between Two Methods to Calculate the Transition Matrix of Orbit Motion
Directory of Open Access Journals (Sweden)
Ana Paula Marins Chiaradia
2012-01-01
Full Text Available Two methods to evaluate the state transition matrix are implemented and analyzed to verify the computational cost and the accuracy of both methods. This evaluation represents one of the highest computational costs on the artificial satellite orbit determination task. The first method is an approximation of the Keplerian motion, providing an analytical solution which is then calculated numerically by solving Kepler's equation. The second one is a local numerical approximation that includes the effect of 2. The analysis is performed comparing these two methods with a reference generated by a numerical integrator. For small intervals of time (1 to 10 s and when one needs more accuracy, it is recommended to use the second method, since the CPU time does not excessively overload the computer during the orbit determination procedure. For larger intervals of time and when one expects more stability on the calculation, it is recommended to use the first method.
Takahashi, Tomoko; Thornton, Blair
2017-12-01
This paper reviews methods to compensate for matrix effects and self-absorption during quantitative analysis of compositions of solids measured using Laser Induced Breakdown Spectroscopy (LIBS) and their applications to in-situ analysis. Methods to reduce matrix and self-absorption effects on calibration curves are first introduced. The conditions where calibration curves are applicable to quantification of compositions of solid samples and their limitations are discussed. While calibration-free LIBS (CF-LIBS), which corrects matrix effects theoretically based on the Boltzmann distribution law and Saha equation, has been applied in a number of studies, requirements need to be satisfied for the calculation of chemical compositions to be valid. Also, peaks of all elements contained in the target need to be detected, which is a bottleneck for in-situ analysis of unknown materials. Multivariate analysis techniques are gaining momentum in LIBS analysis. Among the available techniques, principal component regression (PCR) analysis and partial least squares (PLS) regression analysis, which can extract related information to compositions from all spectral data, are widely established methods and have been applied to various fields including in-situ applications in air and for planetary explorations. Artificial neural networks (ANNs), where non-linear effects can be modelled, have also been investigated as a quantitative method and their applications are introduced. The ability to make quantitative estimates based on LIBS signals is seen as a key element for the technique to gain wider acceptance as an analytical method, especially in in-situ applications. In order to accelerate this process, it is recommended that the accuracy should be described using common figures of merit which express the overall normalised accuracy, such as the normalised root mean square errors (NRMSEs), when comparing the accuracy obtained from different setups and analytical methods.
Kandaswamy, Krishna Kumar Umar
2013-01-01
The extracellular matrix (ECM) is a major component of tissues of multicellular organisms. It consists of secreted macromolecules, mainly polysaccharides and glycoproteins. Malfunctions of ECM proteins lead to severe disorders such as marfan syndrome, osteogenesis imperfecta, numerous chondrodysplasias, and skin diseases. In this work, we report a random forest approach, EcmPred, for the prediction of ECM proteins from protein sequences. EcmPred was trained on a dataset containing 300 ECM and 300 non-ECM and tested on a dataset containing 145 ECM and 4187 non-ECM proteins. EcmPred achieved 83% accuracy on the training and 77% on the test dataset. EcmPred predicted 15 out of 20 experimentally verified ECM proteins. By scanning the entire human proteome, we predicted novel ECM proteins validated with gene ontology and InterPro. The dataset and standalone version of the EcmPred software is available at http://www.inb.uni-luebeck.de/tools-demos/Extracellular_matrix_proteins/EcmPred. © 2012 Elsevier Ltd.
Abbout, Adel
2016-08-05
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and connected through a low-density-of-states two-level quantum dot that acts as a conducting chaotic cavity. Our exact treatment of the chaotic behavior in such devices lies on the scattering matrix formalism and yields analytical expressions for the joint probability distribution functions of the Seebeck coefficient and the transmission profile, as well as the marginal distributions, at arbitrary Fermi energy. The scattering matrices belong to circular ensembles which we sample to numerically compute the transmission function, the Seebeck coefficient, and their relationship. The exact transport coefficients probability distributions are found to be highly non-Gaussian for small numbers of conduction modes, and the analytical and numerical results are in excellent agreement. The system performance is also studied, and we find that the optimum performance is obtained for half-transparent quantum dots; further, this optimum may be enhanced for systems with few conduction modes.
On the convergence of certain finite-difference schemes by an inverse-matrix method
Steger, J. L.; Warming, R. F.
1975-01-01
The inverse-matrix method of analyzing the convergence of the solution of a given system of finite-difference equations to the solution of the corresponding system of partial-differential equations is discussed and generalized. The convergence properties of a time- and space-centered differencing of the diffusion equation are analyzed as well as a staggered grid differencing of the Cauchy-Riemann equations. These two schemes are significant since they serve as simplified model algorithms for two recently developed methods used to calculate nonlinear aerodynamic flows.
Fast and accurate generation method of PSF-based system matrix for PET reconstruction
Sun, Xiao-Li; Yun, Ming-Kai; Li, Dao-Wu; Gao, Juan; Li, Mo-Han; Chai, Pei; Tang, Hao-Hui; Zhang, Zhi-Ming; Wei, Long
2016-01-01
Positional single photon incidence response (P-SPIR) theory is researched in this paper to generate more accurate PSF-contained system matrix simply and quickly. The method has been proved highly effective to improve the spatial resolution by applying to the Eplus-260 primate PET designed by the Institute of High Energy Physics of the Chinese Academy of Sciences(IHEP). Simultaneously, to meet the clinical needs, GPU acceleration is put to use. Basically, P-SPIR theory takes both incidence angle and incidence position by crystal subdivision instead of only incidence angle into consideration based on Geant4 Application for Emission Tomography (GATE). The simulation conforms to the actual response distribution and can be completed rapidly within less than 1s. Furthermore,two-block penetration and normalization of the response probability are raised to fit the reality. With PSF obtained, the homogenization model is analyzed to calculate the spread distribution of bins within a few minutes for system matrix genera...
Liu, Yan-Ping; Gu, Yu-Mei; Thijs, Lutgarde; Knapen, Marjo H J; Salvi, Erika; Citterio, Lorena; Petit, Thibault; Carpini, Simona Delli; Zhang, Zhenyu; Jacobs, Lotte; Jin, Yu; Barlassina, Cristina; Manunta, Paolo; Kuznetsova, Tatiana; Verhamme, Peter; Struijker-Boudier, Harry A; Cusi, Daniele; Vermeer, Cees; Staessen, Jan A
2015-02-01
Matrix Gla-protein is a vitamin K-dependent protein that strongly inhibits arterial calcification. Vitamin K deficiency leads to production of inactive nonphosphorylated and uncarboxylated matrix Gla protein (dp-ucMGP). The risk associated with dp-ucMGP in the population is unknown. In a Flemish population study, we measured circulating dp-ucMGP at baseline (1996-2011), genotyped MGP, recorded adverse health outcomes until December 31, 2012, and assessed the multivariable-adjusted associations of adverse health outcomes with dp-ucMGP. We applied a Mendelian randomization analysis using MGP genotypes as instrumental variables. Among 2318 participants, baseline dp-ucMGP averaged 3.61 μg/L. Over 14.1 years (median), 197 deaths occurred, 58 from cancer and 70 from cardiovascular disease; 85 participants experienced a coronary event. The risk of death and non-cancer mortality curvilinearly increased (P≤0.008) by 15.0% (95% confidence interval, 6.9-25.3) and by 21.5% (11.1-32.9) for a doubling of the nadir (1.43 and 0.97 μg/L, respectively). With higher dp-ucMGP, cardiovascular mortality log-linearly increased (hazard ratio for dp-ucMGP doubling, 1.14 [1.01-1.28]; P=0.027), but coronary events log-linearly decreased (0.93 [0.88-0.99]; P=0.021). dp-ucMGP levels were associated (P≤0.001) with MGP variants rs2098435, rs4236, and rs2430692. For non-cancer mortality and coronary events (P≤0.022), but not for total and cardiovascular mortality (P≥0.13), the Mendelian randomization analysis suggested causality. Higher dp-ucMGP predicts total, non-cancer and cardiovascular mortality, but lower coronary risk. For non-cancer mortality and coronary events, these associations are likely causal. © 2014 American Heart Association, Inc.
Freezing transitions and extreme values: random matrix theory, and disordered landscapes
Fyodorov, Yan V.; Keating, Jonathan P.
2014-01-01
We argue that the freezing transition scenario, previously conjectured to occur in the statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the characteristic polynomials pN(θ) of large N×N random unitary (circular unitary ensemble) matrices UN; i.e. the extreme value statistics of pN(θ) when . In addition, we argue that it leads to multi-fractal-like behaviour in the total length μN(x) of the intervals in which |pN(θ)|>Nx,x>0, in the same limit. We speculate that our results extend to the large values taken by the Riemann zeta function ζ(s) over stretches of the critical line of given constant length and present the results of numerical computations of the large values of ). Our main purpose is to draw attention to the unexpected connections between these different extreme value problems. PMID:24344336
Extremely Randomized Machine Learning Methods for Compound Activity Prediction.
Czarnecki, Wojciech M; Podlewska, Sabina; Bojarski, Andrzej J
2015-11-09
Speed, a relatively low requirement for computational resources and high effectiveness of the evaluation of the bioactivity of compounds have caused a rapid growth of interest in the application of machine learning methods to virtual screening tasks. However, due to the growth of the amount of data also in cheminformatics and related fields, the aim of research has shifted not only towards the development of algorithms of high predictive power but also towards the simplification of previously existing methods to obtain results more quickly. In the study, we tested two approaches belonging to the group of so-called 'extremely randomized methods'-Extreme Entropy Machine and Extremely Randomized Trees-for their ability to properly identify compounds that have activity towards particular protein targets. These methods were compared with their 'non-extreme' competitors, i.e., Support Vector Machine and Random Forest. The extreme approaches were not only found out to improve the efficiency of the classification of bioactive compounds, but they were also proved to be less computationally complex, requiring fewer steps to perform an optimization procedure.
Energy Technology Data Exchange (ETDEWEB)
Agassi, D.; Ko, C.M.; Weidenmueller, H.A.
1977-09-06
A random-matrix model is used to describe the transformation of kinetic energy of relative motion into intrinsic excitation energy typical of a deeply inelastic heavy-ion collision. The random-matrix model is based upon statistical assumptions regarding the form factors coupling relative motion with intrinsic excitation of either fragment. Average cross sections are calculated by means of an ensemble average over the random matrix model. Summations over intermediate and final intrinsic spin values are performed. As a result, average cross sections are given by the asymptotic behavior of a probability density which in turn obeys a transport equation. In the transport equation there is no further reference to intrinsic spins. The physical and mathematical properties of this equation are exhibited.
Community structure discovery method based on the Gaussian kernel similarity matrix
Guo, Chonghui; Zhao, Haipeng
2012-03-01
Community structure discovery in complex networks is a popular issue, and overlapping community structure discovery in academic research has become one of the hot spots. Based on the Gaussian kernel similarity matrix and spectral bisection, this paper proposes a new community structure discovery method. First, by adjusting the Gaussian kernel parameter to change the scale of similarity, we can find the corresponding non-overlapping community structure when the value of the modularity is the largest relatively. Second, the changes of the Gaussian kernel parameter would lead to the unstable nodes jumping off, so with a slight change in method of non-overlapping community discovery, we can find the overlapping community nodes. Finally, synthetic data, karate club and political books datasets are used to test the proposed method, comparing with some other community discovery methods, to demonstrate the feasibility and effectiveness of this method.
PREDICTION OF RESERVOIR FLOW RATE OF DEZ DAM BY THE PROBABILITY MATRIX METHOD
Directory of Open Access Journals (Sweden)
Mohammad Hashem Kanani
2012-12-01
Full Text Available The data collected from the operation of existing storage reservoirs, could offer valuable information for the better allocation and management of fresh water rates for future use to mitigation droughts effect. In this paper the long-term Dez reservoir (IRAN water rate prediction is presented using probability matrix method. Data is analyzed to find the probability matrix of water rates in Dez reservoir based on the previous history of annual water entrance during the past and present years(40 years. The algorithm developed covers both, the overflow and non-overflow conditions in the reservoir. Result of this study shows that in non-overflow conditions the most exigency case is equal to 75%. This means that, if the reservoir is empty (the stored water is less than 100 MCM this year, it would be also empty by 75% next year. The stored water in the reservoir would be less than 300 MCM by 85% next year if the reservoir is empty this year. This percentage decreases to 70% next year if the water of reservoir is less than 300 MCM this year. The percentage also decreases to 5% next year if the reservoir is full this year. In overflow conditions the most exigency case is equal to 75% again. The reservoir volume would be less than 150 MCM by 90% next year, if it is empty this year. This percentage decreases to 70% if its water volume is less than 300 MCM and 55% if the water volume is less than 500 MCM this year. Result shows that too, if the probability matrix of water rates to a reservoir is multiplied by itself repeatedly; it converges to a constant probability matrix, which could be used to predict the long-term water rate of the reservoir. In other words, the probability matrix of series of water rates is changed to a steady probability matrix in the course of time, which could reflect the hydrological behavior of the watershed and could be easily used for the long-term prediction of water storage in the down stream reservoirs.
Limited-memory fast gradient descent method for graph regularized nonnegative matrix factorization.
Guan, Naiyang; Wei, Lei; Luo, Zhigang; Tao, Dacheng
2013-01-01
Graph regularized nonnegative matrix factorization (GNMF) decomposes a nonnegative data matrix X[Symbol:see text]R(m x n) to the product of two lower-rank nonnegative factor matrices, i.e.,W[Symbol:see text]R(m x r) and H[Symbol:see text]R(r x n) (r gradient direction with a non-optimal step size. Recently, a multiple step-sizes fast gradient descent (MFGD) method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton's method. However, the computational cost of MFGD is high because 1) the high-dimensional Hessian matrix is dense and costs too much memory; and 2) the Hessian inverse operator and its multiplication with gradient cost too much time. To overcome these deficiencies of MFGD, we propose an efficient limited-memory FGD (L-FGD) method for optimizing GNMF. In particular, we apply the limited-memory BFGS (L-BFGS) method to directly approximate the multiplication of the inverse Hessian and the gradient for searching the optimal step size in MFGD. The preliminary results on real-world datasets show that L-FGD is more efficient than both MFGD and MUR. To evaluate the effectiveness of L-FGD, we validate its clustering performance for optimizing KL-divergence based GNMF on two popular face image datasets including ORL and PIE and two text corpora including Reuters and TDT2. The experimental results confirm the effectiveness of L-FGD by comparing it with the representative GNMF solvers.
Limited-Memory Fast Gradient Descent Method for Graph Regularized Nonnegative Matrix Factorization
Guan, Naiyang; Wei, Lei; Luo, Zhigang; Tao, Dacheng
2013-01-01
Graph regularized nonnegative matrix factorization (GNMF) decomposes a nonnegative data matrix to the product of two lower-rank nonnegative factor matrices, i.e., and () and aims to preserve the local geometric structure of the dataset by minimizing squared Euclidean distance or Kullback-Leibler (KL) divergence between X and WH. The multiplicative update rule (MUR) is usually applied to optimize GNMF, but it suffers from the drawback of slow-convergence because it intrinsically advances one step along the rescaled negative gradient direction with a non-optimal step size. Recently, a multiple step-sizes fast gradient descent (MFGD) method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton's method. However, the computational cost of MFGD is high because 1) the high-dimensional Hessian matrix is dense and costs too much memory; and 2) the Hessian inverse operator and its multiplication with gradient cost too much time. To overcome these deficiencies of MFGD, we propose an efficient limited-memory FGD (L-FGD) method for optimizing GNMF. In particular, we apply the limited-memory BFGS (L-BFGS) method to directly approximate the multiplication of the inverse Hessian and the gradient for searching the optimal step size in MFGD. The preliminary results on real-world datasets show that L-FGD is more efficient than both MFGD and MUR. To evaluate the effectiveness of L-FGD, we validate its clustering performance for optimizing KL-divergence based GNMF on two popular face image datasets including ORL and PIE and two text corpora including Reuters and TDT2. The experimental results confirm the effectiveness of L-FGD by comparing it with the representative GNMF solvers. PMID:24204761
Extremely Randomized Machine Learning Methods for Compound Activity Prediction
Directory of Open Access Journals (Sweden)
Wojciech M. Czarnecki
2015-11-01
Full Text Available Speed, a relatively low requirement for computational resources and high effectiveness of the evaluation of the bioactivity of compounds have caused a rapid growth of interest in the application of machine learning methods to virtual screening tasks. However, due to the growth of the amount of data also in cheminformatics and related fields, the aim of research has shifted not only towards the development of algorithms of high predictive power but also towards the simplification of previously existing methods to obtain results more quickly. In the study, we tested two approaches belonging to the group of so-called ‘extremely randomized methods’—Extreme Entropy Machine and Extremely Randomized Trees—for their ability to properly identify compounds that have activity towards particular protein targets. These methods were compared with their ‘non-extreme’ competitors, i.e., Support Vector Machine and Random Forest. The extreme approaches were not only found out to improve the efficiency of the classification of bioactive compounds, but they were also proved to be less computationally complex, requiring fewer steps to perform an optimization procedure.
Simplified LCA and matrix methods in identifying the environmental aspects of a product system.
Hur, Tak; Lee, Jiyong; Ryu, Jiyeon; Kwon, Eunsun
2005-05-01
In order to effectively integrate environmental attributes into the product design and development processes, it is crucial to identify the significant environmental aspects related to a product system within a relatively short period of time. In this study, the usefulness of life cycle assessment (LCA) and a matrix method as tools for identifying the key environmental issues of a product system were examined. For this, a simplified LCA (SLCA) method that can be applied to Electrical and Electronic Equipment (EEE) was developed to efficiently identify their significant environmental aspects for eco-design, since a full scale LCA study is usually very detailed, expensive and time-consuming. The environmentally responsible product assessment (ERPA) method, which is one of the matrix methods, was also analyzed. Then, the usefulness of each method in eco-design processes was evaluated and compared using the case studies of the cellular phone and vacuum cleaner systems. It was found that the SLCA and the ERPA methods provided different information but they complemented each other to some extent. The SLCA method generated more information on the inherent environmental characteristics of a product system so that it might be useful for new design/eco-innovation when developing a completely new product or method where environmental considerations play a major role from the beginning. On the other hand, the ERPA method gave more information on the potential for improving a product so that it could be effectively used in eco-redesign which intends to alleviate environmental impacts of an existing product or process.
Directory of Open Access Journals (Sweden)
Hemmati Sabet
2015-11-01
Full Text Available Background Drug abuse is a major problem in the communities and has many harmful effects on human body. Objectives The current study aimed to compare the efficacy of matrix method on anxiety and attitude of male crack abusers referred to addiction treatment centers in Tonkabon, Iran, in 2014. Patients and Methods The current semi -experimental study included 1,000 males referred to addiction treatment centers in Tonkabon with crack abuse history in 2014. Based on Morgan sample volume formula, 278 males with anxiety and higher attitude to drug abuse were randomly selected from 1,000 males referred to addiction treatment centers in Tonkabon. Then, 30 subjects were reselected out of them and equally assigned into two groups of experimental and control, 15 subjects in each group. The experimental group received 24 sessions of 30 - 60 minutes matrix treatment method in group, but the control group received no training. At the end of training period the post-test was carried out. The research findings confirmed the efficacy of matrix method on anxiety and attitude to crack abuse among those referring to the addition treatment center. Results The single covariance analysis of ANCOVA indicated that the value of Eta about 72% of variance of anxiety variable and about 76% of variance of drug abuse variable are taken in to account for variable of group. The intervention was effective in reducing anxiety and attitude to crack in males. Evaluating the adjusted mean showed the effectiveness of matrix method on anxiety and attitude to crack abuse in males. Conclusions The research result showed that matrix method affected the reduction of methamphetamine and attitude to crack abuse in males referred to the addition treatment center.
Gainer, Patrick A.; Aiken, William S., Jr.
1959-01-01
A method is presented for shortening the computations required to determine the steady-state span loading on flexible wings in subsonic flight. The method makes use of tables of downwash factors to find the necessary aerodynamic-influence coefficients for the application of lifting-line theory. Explicit matrix equations of equilibrium are converted into a matrix power series with a finite number of terms by utilizing certain characteristic properties of matrices. The number of terms in the series is determined by a trial-and-error process dependent upon the required accuracy of the solution. Spanwise distributions of angle of attack, airload, shear, bending moment, and pitching moment are readily obtained as functions of qm(sub R) where q denotes the dynamic pressure and mR denotes the lift-curve slope of a rigid wing. This method is intended primarily to make it practical to solve steady-state aeroelastic problems on the ordinary manually operated desk calculators, but the method is also readily adaptable to automatic computing equipment.
Matrix solid phase dispersion method for determination of polycyclic aromatic hydrocarbons in moss.
Concha-Graña, Estefanía; Muniategui-Lorenzo, Soledad; De Nicola, Flavia; Aboal, Jesús R; Rey-Asensio, Ana Isabel; Giordano, Simonetta; Reski, Ralf; López-Mahía, Purificación; Prada-Rodríguez, Darío
2015-08-07
In this work a matrix solid-phase dispersion extraction method, followed by programmed temperature vaporization-gas chromatography-tandem mass spectrometry determination is proposed for the analysis of polycyclic aromatic hydrocarbons (PAHs) in moss samples. A devitalized, cultivated Sphagnum palustre L. moss clone obtained from the "Mossclone" EU-FP7 Project was used for the optimization and validation of the proposed method. Good trueness (84-116%), precision (intermediate precision lower than 11%) and sensitivity (quantitation limits lower than 1.7ngg(-1)) were obtained. The proposed method was compared with other procedures applied for this complex matrix, achieving a considerable reduction of sample amount, solvent volume and time consumption. The procedure was successfully tested for the analysis of PAHs in exposed moss clone samples for the monitoring of air pollution. Finally, the method was also tested for its suitability in the analysis of PAHs in other moss species as well as a lichen species. Copyright © 2015 Elsevier B.V. All rights reserved.
Dispersion curve extraction of Lamb waves in metallic plates by matrix pencil method
Chang, C. Y.; Yuan, F. G.
2017-04-01
Lamb wave dispersion curves for isotropic plates are extracted from measured sensor data by matrix pencil (MP) method. A piezoelectric wafer emits a linear chirp signal as broadband excitation to generate Lamb waves in isotropic plates. The propagating waves are measured at discrete locations along a wave ray direction with a sensor 1-D laser Doppler vibrometer (LDV). The out-of-plane velocities are first Fourier transformed into either space-frequency x-ω domain or wavenumber-time k-t domain. The matrix pencil method is then employed to extract the dispersion curves for various wave modes simultaneously. In addition, the phase and group velocity dispersion curves are deduced by the relation between wavenumber and frequency. In this research, the inspections for dispersion relations on isotropic plates are demonstrated and compared by two-dimensional Fourier transform (2D-FFT) and MP method. The results are confirmed by theoretical curves computed numerically. It has demonstrated that the MP method is robust in recognining/differentiating different wave modes, including higher order ones.
Leone, Frank A., Jr.
2015-01-01
A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.
Pyrolysis of organomercury compounds: investigation by the method of matrix isolation.
Maltsev, A K; Mikaelian, R G; Nefedov, O M; Hauge, R H; Margrave, J L
1971-12-01
The method of matrix isolation has been used to investigate mechanisms of gas-phase chemical reactions, in particular the pyrolysis of some organomercury compounds. A molecular beam of pyrolysis products was condensed simultaneously with a large excess of rare gas at temperatures from 5 to 15 degrees K to form a matrix that was subsequently studied by infrared spectroscopy. In the case of C(6)H(5)HgCCl(3), we found that pyrolysis in the temperature range 220-400 degrees C produced mainly dichlorocarbene. In addition, some trichloromethyl radical was observed and increased in relative importance at increased temperatures. Another identified product of pyrolysis was C(6)H(5)HgCl. In general, the same reactive intermediates, CCl(2) and CCl(3), were found from pyrolysis of Hg(CCl(3))(2) in the temperature range 250-500 degrees C, along with CCl(3)HgCl and HgCl(2). The identity of CCl(2) and CCl(2) was demonstrated by measurement of the relative intensities and isotopic splittings of stretching vibrations due to the chlorine isotopes. Isotopic patterns found for CCl(2) are: v(3) (745.8, 744.0, 741.8 cm(-1)), v(1) (719.5, 717.0, 714.9 cm(-1)) and for CCl(3) are: v(3) (897.8, 896.4, 895.2, 893.9 cm(-1)). Less dilution with the rare gas or warming of the matrix produced a decrease of CCl(2) and CCl(3) spectral bands and an increase of bands due to C(2)Cl(4), C(2)Cl(6), and other products. These results show the usefulness of matrix isolation in the study of such reactive species as CCl(2) produced by pyrolysis in the gas phase.
Xiang, Lei; Chen, Lei; Xiao, Tao; Mo, Ce-Hui; Li, Yan-Wen; Cai, Quan-Ying; Li, Hui; Zhou, Dong-Mei; Wong, Ming-Hung
2017-10-04
A robust method was developed for simultaneous determination of nine trace perfluoroalkyl carboxylic acids (PFCAs) in various edible crop matrices including cereal (grain), root vegetable (carrot), leafy vegetable (lettuce), and melon vegetable (pumpkin) using ultrasonic extraction followed by solid-phase extraction cleanup and high liquid chromatography-tandem mass spectrometry (HPLC-MS/MS). The varieties of extractants and cleanup cartridges, the usage of Supelclean graphitized carbon, and the matrix effect and its potential influencing factors were estimated to gain an optimal extraction procedure. The developed method presented high sensitivity and accuracy with the method detection limits and the recoveries at four fortification levels in various matrices ranging from 0.017 to 0.180 ng/g (dry weight) and from 70% to 114%, respectively. The successful application of the developed method to determine PFCAs in various crops sampled from several farms demonstrated its practicability for regular monitoring of PFCAs in real crops.
Electron-H2 Collisions Studied Using the Finite Element Z-Matrix Method
Huo, Winifred M.; Brown, David; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
We have applied the Z-matrix method, using a mixed basis of finite elements and Gaussians, to study e-H2 elastic and inelastic collisions. Special attention is paid to the quality of the basis set and the treatment of electron correlation. The calculated cross sections are invariant, to machine accuracy, with respect to the choice of parameters a, b, d, e as long as they satisfy Equation (3). However, the log derivative approach, i.e., the choice a = -e = 1, b = d = 0 appears to converge slightly faster than other choices. The cross sections agree well with previous theoretical results. Comparison will be made with available experimental data.
Method and apparatus for evaluating structural weakness in polymer matrix composites
Wachter, Eric A.; Fisher, Walter G.
1996-01-01
A method and apparatus for evaluating structural weaknesses in polymer matrix composites is described. An object to be studied is illuminated with laser radiation and fluorescence emanating therefrom is collected and filtered. The fluorescence is then imaged and the image is studied to determine fluorescence intensity over the surface of the object being studied and the wavelength of maximum fluorescent intensity. Such images provide a map of the structural integrity of the part being studied and weaknesses, particularly weaknesses created by exposure of the object to heat, are readily visible in the image.
DEFF Research Database (Denmark)
Withers, P.J.; Stobbs, W.M.; Pedersen, O.B.
1989-01-01
behaviour of short fibre metal matrix composites is predicted, and, taking the Al/SiC system as an example, compared with experiment. Finally, it is shown that relaxation phenomena play an important role in the development of internal stresses, and that the energetics and the resultant stress redistribution......Eshelby's equivalent inclusion approach is used to provide a rigorous theoretical basis for the prediction of the mechanical properties of short fibre composites. The equivalent inclusion construction which is central to this method is described in detail. The elastic, thermoelastic and plastic...
Systems and methods for commutating inductor current using a matrix converter
Ransom, Ray M; Kajouke, Lateef A; Perisic, Milun
2012-10-16
Systems and methods are provided for delivering current using a matrix converter in a vehicle. An electrical system comprises an AC interface, a first conversion module coupled to the AC interface, an inductive element coupled between the AC interface and the first conversion module, and a control module coupled to the first conversion module. The control module is configured to operate the first conversion module in a bidirectional operating mode to commutate current bidirectionally. When a magnitude of the current through the inductive element is greater than a first threshold value, the control module operates the conversion module in a unidirectional operating mode, wherein current is commutated unidirectionally.
A spectral method to detect community structure based on distance modularity matrix
Yang, Jin-Xuan; Zhang, Xiao-Dong
2017-08-01
There are many community organizations in social and biological networks. How to identify these community structure in complex networks has become a hot issue. In this paper, an algorithm to detect community structure of networks is proposed by using spectra of distance modularity matrix. The proposed algorithm focuses on the distance of vertices within communities, rather than the most weakly connected vertex pairs or number of edges between communities. The experimental results show that our method achieves better effectiveness to identify community structure for a variety of real-world networks and computer generated networks with a little more time-consumption.
Using the modified matrix element method to constrain Lμ-Lτ interactions
Elahi, Fatemeh; Martin, Adam
2017-07-01
In this paper, we explore the discriminatory power of the matrix element method (MEM) in constraining the Lμ-Lτ model at the LHC. The Z' boson associated with the spontaneously broken U (1 )Lμ-Lτ symmetry only interacts with the second and third generation of leptons at tree level, and is thus difficult to produce at the LHC. We argue that the best channels for discovering this Z' are in Z →4 μ and 2 μ + ET. Both these channels have a large number of kinematic observables, which strongly motivates the usage of a multivariate technique. The MEM is a multivariate analysis that uses the squared matrix element |M |2 to quantify the likelihood of the testing hypotheses. As the computation of the |M |2 requires knowing the initial and final state momenta and the model parameters, it is not commonly used in new physics searches. Conventionally, new parameters are estimated by maximizing the likelihood of the signal with respect to the background, and we outline scenarios in which this procedure is (in)effective. We illustrate that the new parameters can also be estimated by studying the |M |2 distributions, and, even if our parameter estimation is off, we can gain better sensitivity than cut-and-count methods. Additionally, unlike the conventional MEM, where one integrates over all unknown momenta in processes with ET, we show an example scenario where these momenta can be estimated using the process topology. This procedure, which we refer to as the "modified squared matrix element," is computationally much faster than the canonical matrix element method and maintains signal-background discrimination. Bringing the MEM and the aforementioned modifications to bear on the Lμ-Lτ model, we find that with 300 fb-1 of integrated luminosity, we are sensitive to the couplings of gZ'≳0.002 g1 and MZ'<20 GeV , and gZ'≳0.005 g1 and 20 GeV
DeCarvalho, N. V.; Chen, B. Y.; Pinho, S. T.; Baiz, P. M.; Ratcliffe, J. G.; Tay, T. E.
2013-01-01
A novel approach is proposed for high-fidelity modeling of progressive damage and failure in composite materials that combines the Floating Node Method (FNM) and the Virtual Crack Closure Technique (VCCT) to represent multiple interacting failure mechanisms in a mesh-independent fashion. In this study, the approach is applied to the modeling of delamination migration in cross-ply tape laminates. Delamination, matrix cracking, and migration are all modeled using fracture mechanics based failure and migration criteria. The methodology proposed shows very good qualitative and quantitative agreement with experiments.
DeCarvalho, Nelson V.; Chen, B. Y.; Pinho, Silvestre T.; Baiz, P. M.; Ratcliffe, James G.; Tay, T. E.
2013-01-01
A novel approach is proposed for high-fidelity modeling of progressive damage and failure in composite materials that combines the Floating Node Method (FNM) and the Virtual Crack Closure Technique (VCCT) to represent multiple interacting failure mechanisms in a mesh-independent fashion. In this study, the approach is applied to the modeling of delamination migration in cross-ply tape laminates. Delamination, matrix cracking, and migration are all modeled using fracture mechanics based failure and migration criteria. The methodology proposed shows very good qualitative and quantitative agreement with experiments.
Random-breakage mapping method applied to human DNA sequences
Lobrich, M.; Rydberg, B.; Cooper, P. K.; Chatterjee, A. (Principal Investigator)
1996-01-01
The random-breakage mapping method [Game et al. (1990) Nucleic Acids Res., 18, 4453-4461] was applied to DNA sequences in human fibroblasts. The methodology involves NotI restriction endonuclease digestion of DNA from irradiated calls, followed by pulsed-field gel electrophoresis, Southern blotting and hybridization with DNA probes recognizing the single copy sequences of interest. The Southern blots show a band for the unbroken restriction fragments and a smear below this band due to radiation induced random breaks. This smear pattern contains two discontinuities in intensity at positions that correspond to the distance of the hybridization site to each end of the restriction fragment. By analyzing the positions of those discontinuities we confirmed the previously mapped position of the probe DXS1327 within a NotI fragment on the X chromosome, thus demonstrating the validity of the technique. We were also able to position the probes D21S1 and D21S15 with respect to the ends of their corresponding NotI fragments on chromosome 21. A third chromosome 21 probe, D21S11, has previously been reported to be close to D21S1, although an uncertainty about a second possible location existed. Since both probes D21S1 and D21S11 hybridized to a single NotI fragment and yielded a similar smear pattern, this uncertainty is removed by the random-breakage mapping method.
Efficient Data Gathering Methods in Wireless Sensor Networks Using GBTR Matrix Completion
Directory of Open Access Journals (Sweden)
Donghao Wang
2016-09-01
Full Text Available To obtain efficient data gathering methods for wireless sensor networks (WSNs, a novel graph based transform regularized (GBTR matrix completion algorithm is proposed. The graph based transform sparsity of the sensed data is explored, which is also considered as a penalty term in the matrix completion problem. The proposed GBTR-ADMM algorithm utilizes the alternating direction method of multipliers (ADMM in an iterative procedure to solve the constrained optimization problem. Since the performance of the ADMM method is sensitive to the number of constraints, the GBTR-A2DM2 algorithm obtained to accelerate the convergence of GBTR-ADMM. GBTR-A2DM2 benefits from merging two constraint conditions into one as well as using a restart rule. The theoretical analysis shows the proposed algorithms obtain satisfactory time complexity. Extensive simulation results verify that our proposed algorithms outperform the state of the art algorithms for data collection problems in WSNs in respect to recovery accuracy, convergence rate, and energy consumption.
Directory of Open Access Journals (Sweden)
A.M. Yu
2012-01-01
Full Text Available Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45 in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical helical springs than that of cylindrical helical springs, which should be taken into consideration in the free vibration analysis of such springs.
The Random Ray Method for neutral particle transport
Energy Technology Data Exchange (ETDEWEB)
Tramm, John R., E-mail: jtramm@mit.edu [Massachusetts Institute of Technology, Department of Nuclear Science Engineering, 77 Massachusetts Avenue, 24-107, Cambridge, MA 02139 (United States); Argonne National Laboratory, Mathematics and Computer Science Department 9700 S Cass Ave, Argonne, IL 60439 (United States); Smith, Kord S., E-mail: kord@mit.edu [Massachusetts Institute of Technology, Department of Nuclear Science Engineering, 77 Massachusetts Avenue, 24-107, Cambridge, MA 02139 (United States); Forget, Benoit, E-mail: bforget@mit.edu [Massachusetts Institute of Technology, Department of Nuclear Science Engineering, 77 Massachusetts Avenue, 24-107, Cambridge, MA 02139 (United States); Siegel, Andrew R., E-mail: siegela@mcs.anl.gov [Argonne National Laboratory, Mathematics and Computer Science Department 9700 S Cass Ave, Argonne, IL 60439 (United States)
2017-08-01
A new approach to solving partial differential equations (PDEs) based on the method of characteristics (MOC) is presented. The Random Ray Method (TRRM) uses a stochastic rather than deterministic discretization of characteristic tracks to integrate the phase space of a problem. TRRM is potentially applicable in a number of transport simulation fields where long characteristic methods are used, such as neutron transport and gamma ray transport in reactor physics as well as radiative transfer in astrophysics. In this study, TRRM is developed and then tested on a series of exemplar reactor physics benchmark problems. The results show extreme improvements in memory efficiency compared to deterministic MOC methods, while also reducing algorithmic complexity, allowing for a sparser computational grid to be used while maintaining accuracy.
Reporting methods of blinding in randomized trials assessing nonpharmacological treatments.
Directory of Open Access Journals (Sweden)
Isabelle Boutron
2007-02-01
Full Text Available BACKGROUND: Blinding is a cornerstone of treatment evaluation. Blinding is more difficult to obtain in trials assessing nonpharmacological treatment and frequently relies on "creative" (nonstandard methods. The purpose of this study was to systematically describe the strategies used to obtain blinding in a sample of randomized controlled trials of nonpharmacological treatment. METHODS AND FINDINGS: We systematically searched in Medline and the Cochrane Methodology Register for randomized controlled trials (RCTs assessing nonpharmacological treatment with blinding, published during 2004 in high-impact-factor journals. Data were extracted using a standardized extraction form. We identified 145 articles, with the method of blinding described in 123 of the reports. Methods of blinding of participants and/or health care providers and/or other caregivers concerned mainly use of sham procedures such as simulation of surgical procedures, similar attention-control interventions, or a placebo with a different mode of administration for rehabilitation or psychotherapy. Trials assessing devices reported various placebo interventions such as use of sham prosthesis, identical apparatus (e.g., identical but inactivated machine or use of activated machine with a barrier to block the treatment, or simulation of using a device. Blinding participants to the study hypothesis was also an important method of blinding. The methods reported for blinding outcome assessors relied mainly on centralized assessment of paraclinical examinations, clinical examinations (i.e., use of video, audiotape, photography, or adjudications of clinical events. CONCLUSIONS: This study classifies blinding methods and provides a detailed description of methods that could overcome some barriers of blinding in clinical trials assessing nonpharmacological treatment, and provides information for readers assessing the quality of results of such trials.
Method Enabling Gene Expression Studies of Pathogens in a Complex Food Matrix
DEFF Research Database (Denmark)
Kjeldgaard, Jette; Henriksen, Sidsel; Cohn, Marianne Thorup
2011-01-01
We describe a simple method for stabilizing and extracting high-quality prokaryotic RNA from meat. Heat and salt stress of Escherichia coli and Salmonella spp. in minced meat reproducibly induced dnaK and otsB expression, respectively, as observed by quantitative reverse transcription-PCR (>5-fol...... relative changes). Thus, the method is applicable in studies of bacterial gene expression in a meat matrix.......We describe a simple method for stabilizing and extracting high-quality prokaryotic RNA from meat. Heat and salt stress of Escherichia coli and Salmonella spp. in minced meat reproducibly induced dnaK and otsB expression, respectively, as observed by quantitative reverse transcription-PCR (>5-fold...
A Numerical Matrix-Based method in Harmonic Studies in Wind Power Plants
DEFF Research Database (Denmark)
Dowlatabadi, Mohammadkazem Bakhshizadeh; Hjerrild, Jesper; Kocewiak, Łukasz Hubert
2016-01-01
In the low frequency range, there are some couplings between the positive- and negative-sequence small-signal impedances of the power converter due to the nonlinear and low bandwidth control loops such as the synchronization loop. In this paper, a new numerical method which also considers...... these couplings will be presented. The numerical data are advantageous to the parametric differential equations, because analysing the high order and complex transfer functions is very difficult, and finally one uses the numerical evaluation methods. This paper proposes a numerical matrix-based method, which...... is not only able to deal with those mentioned numerical data, but also it is able to consider all couplings between the positive and negative sequences....
Huang, Yanhui; Shen, Lin; Cai, Anhe; Xiao, Jing
2015-10-01
To investigate the effect of Chinese medicines using the warming Yang and removing blood stasis method on levels of matrix metalloproteinases (MMPs)/tissue inhibitor metalloproteinases (TIMPs) secreted by cultured endometrial cells from patients with endometriosis. Ectopic and eutopic endometrial cells obtaind from 15 endometriosis patients were cultured in vitro, and divided randomly into five groups: high dose; moderate dose; low dose; nemestran; blank control. The three dose groups were treated with a decoction prepared according to the principle of warming Yang and removing blood stasis; nemestran and 0.9% NaCl were administered to the nemestran group and balnk control group, respectively. Eutopic endometrial cells obtaind from 10 hysteromyoma patients were cultured in vitro, as the normal control group, 0.9% NaCl were administered to the normal control group. Cell culture supernatants were collected and levels of matrix metalloproteinase-1 (MMP-1), matrix metalloproteinase-2 (MMP-2), matrix metalloproteinase-9 (MMP-9), tissue inhibitor metalloproteinase-1 (TIMP-1) and tissue inhibitor metalloproteinase-2 (TIMP-2) detected by enzyme-linked immuno sorbent assay (ELISA). Compared with the normal control group, levels of MMP-1, MMP-2, and MMP-9 in eutopic and ectopic endometrium cell supernatants in the blank control group were increased, whereas levels of TIMP-1 and TIMP-2 were decreased (P method affects expression of MMPs and TIMPs.
An improved matrix separation method for characterization of ultrapure germanium (8N).
Reddy, M A; Shekhar, R; Jai Kumar, Sunil
2016-10-01
An improved matrix separation method has been described to characterize ultrapure germanium of 8N (99.999999%) purity. In this method, temperature of the reaction vessel in which in-situ generated chlorine gas reacts with germanium solid material directly is optimized to quantitatively remove Ge matrix from all its impurities. Optimized reaction temperature has been found to be 230±5°C. Recovery studies on more than 60 elements have been carried out at the optimized temperature. Recoveries of all the analytes except As, Se, Sn, Hg, Tl are found to be quantitative. The method has been examined for various amounts of Ge material and found to be suitable even for 10g of Ge sample and provides low parts per billion and trillion levels of process blanks. Determination of concentrations of impurities has been done by inductively coupled plasma quadrupole mass spectrometer (ICP-QMS) and high resolution continuum source graphite furnace atomic absorption spectrometer (HR-CS-GFAAS). In the absence of certified reference materials for ultrapure germanium, accuracy of the proposed method is established by spike recovery tests. Precision of this method is found to vary from 7% to 50% for concentrations between 4 and 0.004ngg(-1). Limits of detection (LOD) for the target analytes are found to be between 6 and 0.011ngmL(-1) or 1.8-0.003ngg(-1) for the proposed procedure. The method has been successfully applied for that characterization of ultrapure germanium material of 8N purity. Copyright © 2016 Elsevier B.V. All rights reserved.
Anderson, Lauren E; Inglehart, Marita R; El-Kholy, Karim; Eber, Robert; Wang, Hom-Lay
2014-08-01
This randomized controlled clinical pilot trial compared the efficacy of 2 soft tissue grafting methods for correcting esthetic discrepancies associated with definitively restored implant crowns. Thirteen patients presenting with implants displaying recession, thin biotype, concavity defects, or a combination thereof associated with single crowned dental implants randomly received subepithelial connective tissue grafts (SCTG) in the control group (N = 7) or acellular dermal matrix (ADM) allografts in the test group (N = 6), both under coronally positioned flaps. Data regarding soft tissue, hard tissue, esthetics, and quality of life (QoL) parameters were collected over 6 months. Both groups gained tissue thickness (SCTG: 63% and ADM: 105%), reduced concavity measures (SCTG: 82% and ADM: 96%), and improved recessions (SCTG: 40% and ADM: 28%) from baseline to 6 months. Clinicians determined improvement in esthetics for both groups (P = 0.001), unlike patients who did not change their esthetic ratings. No statistical differences were noted for QoL assessment; however, ADM subjects had more eventful wound healing (P = 0.021). Within the limitations of this study, both SCTG and ADM result in increased mucosal thickness, reduction in concavity dimensions, and have a potential for recession reduction on definitively restored dental implants.
Measurement of the top quark mass in the dilepton final state using the matrix element method
Energy Technology Data Exchange (ETDEWEB)
Grohsjean, Alexander [Ludwig Maximilian Univ., Munich (Germany)
2008-12-15
The top quark, discovered in 1995 by the CDF and D0 experiments at the Fermilab Tevatron Collider, is the heaviest known fundamental particle. The precise knowledge of its mass yields important constraints on the mass of the yet-unobserved Higgs boson and allows to probe for physics beyond the Standard Model. The first measurement of the top quark mass in the dilepton channel with the Matrix Element method at the D0 experiment is presented. After a short description of the experimental environment and the reconstruction chain from hits in the detector to physical objects, a detailed review of the Matrix Element method is given. The Matrix Element method is based on the likelihood to observe a given event under the assumption of the quantity to be measured, e.g. the mass of the top quark. The method has undergone significant modifications and improvements compared to previous measurements in the lepton+jets channel: the two undetected neutrinos require a new reconstruction scheme for the four-momenta of the final state particles, the small event sample demands the modeling of additional jets in the signal likelihood, and a new likelihood is designed to account for the main source of background containing tauonic Z decay. The Matrix Element method is validated on Monte Carlo simulated events at the generator level. For the measurement, calibration curves are derived from events that are run through the full D0 detector simulation. The analysis makes use of the Run II data set recorded between April 2002 and May 2008 corresponding to an integrated luminosity of 2.8 fb^{-1}. A total of 107 t$\\bar{t}$ candidate events with one electron and one muon in the final state are selected. Applying the Matrix Element method to this data set, the top quark mass is measured to be m_{top}^{Run IIa} = 170.6 ± 6.1(stat.)_{-1.5}^{+2.1}(syst.)GeV; m_{top}^{Run IIb} = 174.1 ± 4.4(stat.)_{-1.8}^{+2.5}(syst.)GeV; m
Validation of neutron current formulations for the response matrix method based on the SP3 theory
Energy Technology Data Exchange (ETDEWEB)
Tada, Kenichi, E-mail: k-tada@fermi.nucl.nagoya-u.ac.j [Department of Materials, Physics and Energy Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603 (Japan); Yamamoto, Akio; Yamane, Yoshihiro [Department of Materials, Physics and Energy Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603 (Japan); Kosaka, Shinya; Hirano, Gou [TEPCOSYSTEMS CORPORATION, 2-37-28, Eitai, Koto-ku, Tokyo 135-0034 (Japan)
2010-01-15
The pin-by-pin fine mesh BWR core analysis code SUBARU has been developed as a next-generation BWR core analysis code. SUBARU is based on the SP3 theory and the response matrix method is used for flux calculations. The SP3 theory consists of the 0th and 2nd order neutron fluxes. Therefore, the relations among the 0th and 2nd order partial neutron currents and the fluxes are required to apply the response matrix method. SUBARU is approximated the relations among the partial neutron currents and the fluxes are similar to that the diffusion theory. Our previous study revealed that the prediction accuracy of SUBARU is much higher than that of conventional core analysis codes. However, validity of the above approximation is not directly investigated so far. Therefore, relations among the partial neutron currents and the fluxes are theoretically derived and calculation results with the rigorous and the conventional formulations are compared. The calculation results indicate that the approximation of the conventional formulation is appropriate for the BWR core analysis.
A dynamic model of mobile concrete pump boom based on discrete time transfer matrix method
Ren, Wu; Wu, Yunxin; Zhang, Zhaowei
2013-12-01
Mobile concrete pump boom is typical multibody large-scale motion manipulator. Due to posture constantly change in working process, kinematic rule and dynamic characteristic are difficult to solve. A dynamics model of a mobile concrete pump boom is established based on discrete time transfer matrix method (DTTMM). The boom system is divided into sub-structure A and substructure B. Sub-structure A is composed by the 1st boom and hydraulic actuator as well as the support. And substructure B is consists of the other three booms and corresponding hydraulic actuators. In the model, the booms and links are regarded as rigid elements and the hydraulic cylinders are equivalent to spring-damper. The booms are driven by the controllable hydraulic actuators. The overall dynamic equation and transfer matrix of the model can be assembled by sub-structures A and B. To get a precise result, step size and integration parameters are studied then. Next the tip displacement is calculated and compared with the result of ADAMS software. The displacement and rotation angle curves of the proposed method fit well with the ADAMS model. Besides it is convenient in modeling and saves time. So it is suitable for mobile concrete pump boom real-time monitoring and dynamic analysis. All of these provide reference to boom optimize and engineering application of such mechanisms.
A Poisson likelihood approach to fake lepton estimation with the matrix method
Varnes, Erich W
2016-01-01
Many high-energy physics analyses require the presence of leptons from $W$, $Z$, or $H$ boson decay. For these analyses, signatures that mimic such leptons present a `fake lepton' background that must be estimated. Since the magnitude of this background depends strongly upon details of the detector response, it can be difficult to estimate with simulation. One data-driven approach is the `matrix method', in which two categories of leptons are defined (`loose' and `tight'), with the tight category being a subset of the loose category. Using the populations of leptons in each category in the analysis sample, and the efficiencies for both real and fake leptons in the loose category to satisfy the criteria for the tight category, the fake background yield can be estimated. This paper describes a Poisson likelihood implementation of the matrix method, which provides a more precise, reliable, and robust estimate of the fake background yield compared to an analytic solution. This implementation also provides a relia...
Sifaou, Houssem
2016-05-01
Massive MIMO systems are shown to be a promising technology for next generations of wireless communication networks. The realization of the attractive merits promised by massive MIMO systems requires advanced linear precoding and receiving techniques in order to mitigate the interference in downlink and uplink transmissions. This work considers the precoder and receiver design in massive MIMO systems. We first consider the design of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio (SINR) subject to a given power constraint. The analysis is carried out under the asymptotic regime in which the number of the BS antennas and that of the users grow large with a bounded ratio. This allows us to leverage tools from random matrix theory in order to approximate the parameters of the optimal linear precoder and receiver by their deterministic approximations. Such a result is of valuable practical interest, as it provides a handier way to implement the optimal precoder and receiver. To reduce further the complexity, we propose to apply the truncated polynomial expansion (TPE) concept on a per-user basis to approximate the inverse of large matrices that appear on the expressions of the optimal linear transceivers. Using tools from random matrix theory, we determine deterministic approximations of the SINR and the transmit power in the asymptotic regime. Then, the optimal per-user weight coe cients that solve the max-min SINR problem are derived. The simulation results show that the proposed precoder and receiver provide very close to optimal performance while reducing signi cantly the computational complexity. As a second part of this work, the TPE technique in a per-user basis is applied to the optimal linear precoding that minimizes the transmit power while satisfying a set of target SINR constraints. Due to the emerging research eld of green cellular networks, such a problem is receiving increasing interest nowadays. Closed
Comparing groups randomization and bootstrap methods using R
Zieffler, Andrew S; Long, Jeffrey D
2011-01-01
A hands-on guide to using R to carry out key statistical practices in educational and behavioral sciences research Computing has become an essential part of the day-to-day practice of statistical work, broadening the types of questions that can now be addressed by research scientists applying newly derived data analytic techniques. Comparing Groups: Randomization and Bootstrap Methods Using R emphasizes the direct link between scientific research questions and data analysis. Rather than relying on mathematical calculations, this book focus on conceptual explanations and
Energy Technology Data Exchange (ETDEWEB)
Guessous, N. E-mail: guessous_najib@hotmail.com; Akhmouch, M
2002-10-01
A higher analytical nodal method for the multigroup neutron diffusion equations, based on the transverse integration procedure, is presented. The discrete 1D equations are cast with the interface partial current techniques in response matrix formalism. The remaining Legendre coefficients of the transverse leakage moment are determined exactly in terms of the different neutron flux moments order in the reference node. In the weighted balance equations, the transverse leakage moments are linearly written in terms of the partial currents, facial and centered fluxes moments. The self-consistent is guaranteed. Furthermore, as the order k increase the neutronic balance in each node and the copulate between the adjacent cell are reinforced. The convergence order in L{sup 2}-norm is of O(h{sup k+3-{delta}k{sub 0}}) under smooth assumptions. The efficacy of the method is showed for 2D-PWR, 2D-IAEA LWR and 2D-LMFBR benchmark problems.
Directory of Open Access Journals (Sweden)
Yan Chen
2017-03-01
Full Text Available Based on the vectorised and cache optimised kernel, a parallel lower upper decomposition with a novel communication avoiding pivoting scheme is developed to solve dense complex matrix equations generated by the method of moments. The fine-grain data rearrangement and assembler instructions are adopted to reduce memory accessing times and improve CPU cache utilisation, which also facilitate vectorisation of the code. Through grouping processes in a binary tree, a parallel pivoting scheme is designed to optimise the communication pattern and thus reduces the solving time of the proposed solver. Two large electromagnetic radiation problems are solved on two supercomputers, respectively, and the numerical results demonstrate that the proposed method outperforms those in open source and commercial libraries.
Limited-memory fast gradient descent method for graph regularized nonnegative matrix factorization.
Directory of Open Access Journals (Sweden)
Naiyang Guan
Full Text Available Graph regularized nonnegative matrix factorization (GNMF decomposes a nonnegative data matrix X[Symbol:see text]R(m x n to the product of two lower-rank nonnegative factor matrices, i.e.,W[Symbol:see text]R(m x r and H[Symbol:see text]R(r x n (r < min {m,n} and aims to preserve the local geometric structure of the dataset by minimizing squared Euclidean distance or Kullback-Leibler (KL divergence between X and WH. The multiplicative update rule (MUR is usually applied to optimize GNMF, but it suffers from the drawback of slow-convergence because it intrinsically advances one step along the rescaled negative gradient direction with a non-optimal step size. Recently, a multiple step-sizes fast gradient descent (MFGD method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton's method. However, the computational cost of MFGD is high because 1 the high-dimensional Hessian matrix is dense and costs too much memory; and 2 the Hessian inverse operator and its multiplication with gradient cost too much time. To overcome these deficiencies of MFGD, we propose an efficient limited-memory FGD (L-FGD method for optimizing GNMF. In particular, we apply the limited-memory BFGS (L-BFGS method to directly approximate the multiplication of the inverse Hessian and the gradient for searching the optimal step size in MFGD. The preliminary results on real-world datasets show that L-FGD is more efficient than both MFGD and MUR. To evaluate the effectiveness of L-FGD, we validate its clustering performance for optimizing KL-divergence based GNMF on two popular face image datasets including ORL and PIE and two text corpora including Reuters and TDT2. The experimental results confirm the effectiveness of L-FGD by comparing it with the representative GNMF solvers.
Mukhamedzhanov, A. M.; Shubhchintak, Bertulani, C. A.
2017-08-01
In this paper we discuss the R -matrix approach to treat the subthreshold resonances for the single-level and one-channel and for the single-level and two-channel cases. In particular, the expression relating the asymptotic normalization coefficient (ANC) with the observable reduced width, when the subthreshold bound state is the only channel or coupled with an open channel, which is a resonance, is formulated. Since the ANC plays a very important role in nuclear astrophysics, these relations significantly enhance the power of the derived equations. We present the relationship between the resonance width and the ANC for the general case and consider two limiting cases: wide and narrow resonances. Different equations for the astrophysical S factors in the R -matrix approach are presented. After that we discuss the Trojan horse method (THM) formalism. The developed equations are obtained using the surface-integral formalism and the generalized R -matrix approach for the three-body resonant reactions. It is shown how the Trojan horse (TH) double-differential cross section can be expressed in terms of the on-the-energy-shell astrophysical S factor for the binary subreaction. Finally, we demonstrate how the THM can be used to calculate the astrophysical S factor for the neutron generator 13C(α ,n )16O in low-mass AGB stars. At astrophysically relevant energies this astrophysical S factor is controlled by the threshold level 1 /2+,Ex=6356 keV. Here, we reanalyzed recent TH data taking into account more accurately the three-body effects and using both assumptions that the threshold level is a subthreshold bound state or it is a resonance state.