Random matrix theories and chaotic dynamics

International Nuclear Information System (INIS)

Bohigas, O.

1991-01-01

A review of some of the main ideas, assumptions and results of the Wigner-Dyson type random matrix theories (RMT) which are relevant in the general context of 'Chaos and Quantum Physics' is presented. RMT are providing interesting and unexpected clues to connect classical dynamics with quantum phenomena. It is this aspect which will be emphasised and, concerning the main body of RMT, the author will restrict himself to a minimum. However, emphasis will be put on some generalizations of the 'canonical' random matrix ensembles that increase their flexibility, rendering the incorporation of relevant physical constraints possible. (R.P.) 112 refs., 35 figs., 5 tabs

Random matrix theory and analysis of nucleus-nucleus collision at high energies

International Nuclear Information System (INIS)

Shahaliev, E.I.; Inst. of Radiation Problems, Baku; ); Kuznetsov, A.A.; Suleymanov, M.K.; ); Teryaev, O.V.; )

2006-01-01

A novel method for analysis of experimental data obtained at relativistic nucleus-nucleus collisions is proposed. The method, based on the ideas of Random Matrix Theory, is applied to detect systematic errors that occur at measurements of momentum distributions of emitted particles. The unfolded momentum distribution is well described by the Gaussian orthogonal ensemble of random matrices, when the uncertainty in the momentum distribution is maximal. The method is free from unwanted background contributions [ru

Random matrix theory with an external source

CERN Document Server

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.

Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory

KAUST Repository

Suliman, Mohamed Abdalla Elhag; Ballal, Tarig; Kammoun, Abla; Al-Naffouri, Tareq Y.

2016-01-01

random matrix theory are applied to derive the near-optimum regularizer that minimizes the mean-squared error of the estimator. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods for various

Random matrix theory

CERN Document Server

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

Social patterns revealed through random matrix theory

Science.gov (United States)

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.

A random matrix approach to language acquisition

International Nuclear Information System (INIS)

Nicolaidis, A; Kosmidis, Kosmas; Argyrakis, Panos

2009-01-01

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

A random matrix approach to language acquisition

Science.gov (United States)

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.

Random matrix model for disordered conductors

Indian Academy of Sciences (India)

In the interpretation of transport properties of mesoscopic systems, the multichannel ... One defines the random matrix model with N eigenvalues 0. λТ ..... With heuristic arguments, using the ideas pertaining to Dyson Coulomb gas analogy,.

Random matrix theory in nuclear structure: past, present and future

International Nuclear Information System (INIS)

Kota, V.K.B.

2012-01-01

Random matrix theory (RMT) introduced by Wigner in 50's to describe statistical properties of slow-neutron resonances in heavy nuclei such as 232 Th, was developed further in the 60's by Dyson, Mehta, Porter and others and in the 70's by French, Pandey, Bohigas and others. Going beyond this, the demonstration that level fluctuations of quantum analogues of classically chaotic few-degrees-of-freedom systems follow random matrix theory (integrable systems follow Poisson as shown by Berry) in 1984 by Bohigas and others on one hand and the recognition from 1995 onwards that two-body random matrix ensembles derived from shell model have wide ranging applications on the other, defined new directions in RMT applications in nuclear physics. Growth points in RMT in nuclear physics are: (i) analysis of nuclear data looking for order-chaos transitions and symmetry (Time-reversal, Parity, Isospin) breaking; (ii) analysis of shell model driven embedded (or two-body) random matrix ensembles giving statistical properties generated by random interactions in the presence of a mean-field; (iii) statistical nuclear spectroscopy generated by embedded ensembles for level densities, occupancies, GT strengths, transition strength sums and so on; (iv) the new paradigm of regular structures generated by random interactions as brought out by studies using various nuclear models; (v) random matrix theory for nuclear reactions with particular reference to open quantum systems; (vi) RMT results from nuclear physics to atomic physics, mesoscopic physics and quantum information science. Topics (i)-(vi) emphasizing recent results are discussed. (author)

Parametric Level Statistics in Random Matrix Theory: Exact Solution

International Nuclear Information System (INIS)

Kanzieper, E.

1999-01-01

During recent several years, the theory of non-Gaussian random matrix ensembles has experienced a sound progress motivated by new ideas in quantum chromodynamics (QCD) and mesoscopic physics. Invariant non-Gaussian random matrix models appear to describe universal features of low-energy part of the spectrum of Dirac operator in QCD, and electron level statistics in normal conducting-superconducting hybrid structures. They also serve as a basis for constructing the toy models of universal spectral statistics expected at the edge of the metal-insulator transition. While conventional spectral statistics has received a detailed study in the context of RMT, quite a bit is known about parametric level statistics in non-Gaussian random matrix models. In this communication we report about exact solution to the problem of parametric level statistics in unitary invariant, U(N), non-Gaussian ensembles of N x N Hermitian random matrices with either soft or strong level confinement. The solution is formulated within the framework of the orthogonal polynomial technique and is shown to depend on both the unfolded two-point scalar kernel and the level confinement through a double integral transformation which, in turn, provides a constructive tool for description of parametric level correlations in non-Gaussian RMT. In the case of soft level confinement, the formalism developed is potentially applicable to a study of parametric level statistics in an important class of random matrix models with finite level compressibility expected to describe a disorder-induced metal-insulator transition. In random matrix ensembles with strong level confinement, the solution presented takes a particular simple form in the thermodynamic limit: In this case, a new intriguing connection relation between the parametric level statistics and the scalar two-point kernel of an unperturbed ensemble is demonstrated to emerge. Extension of the results obtained to higher-order parametric level statistics is

Random matrix ensembles for PT-symmetric systems

International Nuclear Information System (INIS)

Graefe, Eva-Maria; Mudute-Ndumbe, Steve; Taylor, Matthew

2015-01-01

Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting PT-symmetry. Here we show that there is a one-to-one correspondence between complex PT-symmetric matrices and split-complex and split-quaternionic versions of Hermitian matrices. We introduce two new random matrix ensembles of (a) Gaussian split-complex Hermitian; and (b) Gaussian split-quaternionic Hermitian matrices, of arbitrary sizes. We conjecture that these ensembles represent universality classes for PT-symmetric matrices. For the case of 2 × 2 matrices we derive analytic expressions for the joint probability distributions of the eigenvalues, the one-level densities and the level spacings in the case of real eigenvalues. (fast track communication)

Universality in random matrix theory and chiral symmetry breaking in QCD

International Nuclear Information System (INIS)

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.)

Random matrix approach to cross correlations in financial data

Science.gov (United States)

Plerou, Vasiliki; Gopikrishnan, Parameswaran; Rosenow, Bernd; Amaral, Luís A.; Guhr, Thomas; Stanley, H. Eugene

2002-06-01

We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994-1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996-1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962-1996. We test the statistics of the eigenvalues λi of C against a ``null hypothesis'' - a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [λ-,λ+] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices-implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these ``deviating eigenvectors'' are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.

Embedded random matrix ensembles in quantum physics

CERN Document Server

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...

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...

A random matrix model of relaxation

International Nuclear Information System (INIS)

Lebowitz, J L; Pastur, L

2004-01-01

We consider a two-level system, S 2 , coupled to a general n level system, S n , via a random matrix. We derive an integral representation for the mean reduced density matrix ρ(t) of S 2 in the limit n → ∞, and we identify a model of S n which possesses some of the properties expected for macroscopic thermal reservoirs. In particular, it yields the Gibbs form for ρ(∞). We also consider an analog of the van Hove limit and obtain a master equation (Markov dynamics) for the evolution of ρ(t) on an appropriate time scale

Subcritical Multiplicative Chaos for Regularized Counting Statistics from Random Matrix Theory

Science.gov (United States)

Lambert, Gaultier; Ostrovsky, Dmitry; Simm, Nick

2018-05-01

For an {N × N} Haar distributed random unitary matrix U N , we consider the random field defined by counting the number of eigenvalues of U N in a mesoscopic arc centered at the point u on the unit circle. We prove that after regularizing at a small scale {ɛN > 0}, the renormalized exponential of this field converges as N \\to ∞ to a Gaussian multiplicative chaos measure in the whole subcritical phase. We discuss implications of this result for obtaining a lower bound on the maximum of the field. We also show that the moments of the total mass converge to a Selberg-like integral and by taking a further limit as the size of the arc diverges, we establish part of the conjectures in Ostrovsky (Nonlinearity 29(2):426-464, 2016). By an analogous construction, we prove that the multiplicative chaos measure coming from the sine process has the same distribution, which strongly suggests that this limiting object should be universal. Our approach to the L 1-phase is based on a generalization of the construction in Berestycki (Electron Commun Probab 22(27):12, 2017) to random fields which are only asymptotically Gaussian. In particular, our method could have applications to other random fields coming from either random matrix theory or a different context.

Enumeration of RNA complexes via random matrix theory

DEFF Research Database (Denmark)

Andersen, Jørgen E; Chekhov, Leonid O.; Penner, Robert C

2013-01-01

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......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...

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 ...

Pseudo-Hermitian random matrix theory

International Nuclear Information System (INIS)

Srivastava, S.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. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Random matrix analysis of human EEG data

Czech Academy of Sciences Publication Activity Database

Šeba, Petr

2003-01-01

Roč. 91, - (2003), s. 198104-1 - 198104-4 ISSN 0031-9007 R&D Projects: GA ČR GA202/02/0088 Institutional research plan: CEZ:AV0Z1010914 Keywords : random matrix theory * EEG signal Subject RIV: BE - Theoretical Physics Impact factor: 7.035, year: 2003

Universality in chaos: Lyapunov spectrum and random matrix theory.

Science.gov (United States)

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

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

Universality in chaos: Lyapunov spectrum and random matrix theory

Science.gov (United States)

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

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

Random matrix theory for pseudo-Hermitian systems: Cyclic blocks

Indian Academy of Sciences (India)

Abstract. We discuss the relevance of random matrix theory for pseudo-Hermitian sys- tems, and, for Hamiltonians that break parity P and time-reversal invariance T. In an attempt to understand the random Ising model, we present the treatment of cyclic asym- metric matrices with blocks and show that the nearest-neighbour ...

A random-matrix theory of the number sense.

Science.gov (United States)

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).

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.

A random matrix approach to credit risk.

Science.gov (United States)

Münnix, Michael C; Schäfer, Rudi; 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.

Universality of correlation functions in random matrix models of QCD

International Nuclear Information System (INIS)

Jackson, A.D.; Sener, M.K.; Verbaarschot, J.J.M.

1997-01-01

We demonstrate the universality of the spectral correlation functions of a QCD inspired random matrix model that consists of a random part having the chiral structure of the QCD Dirac operator and a deterministic part which describes a schematic temperature dependence. We calculate the correlation functions analytically using the technique of Itzykson-Zuber integrals for arbitrary complex supermatrices. An alternative exact calculation for arbitrary matrix size is given for the special case of zero temperature, and we reproduce the well-known Laguerre kernel. At finite temperature, the microscopic limit of the correlation functions are calculated in the saddle-point approximation. The main result of this paper is that the microscopic universality of correlation functions is maintained even though unitary invariance is broken by the addition of a deterministic matrix to the ensemble. (orig.)

Gravitational lensing by eigenvalue distributions of random matrix models

Science.gov (United States)

Martínez Alonso, Luis; Medina, Elena

2018-05-01

We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We prove that these models can be applied to describe lensing by systems of edge-on galaxies. We illustrate our analysis with the Gaussian and the quartic unitary matrix ensembles.

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

Science.gov (United States)

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

2016-11-01

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

Random matrix theory of multi-antenna communications: the Ricean channel

International Nuclear Information System (INIS)

Moustakas, Aris L; Simon, Steven H

2005-01-01

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

Accurate Quasiparticle Spectra from the T-Matrix Self-Energy and the Particle-Particle Random Phase Approximation.

Science.gov (United States)

Zhang, Du; Su, Neil Qiang; Yang, Weitao

2017-07-20

The GW self-energy, especially G 0 W 0 based on the particle-hole random phase approximation (phRPA), is widely used to study quasiparticle (QP) energies. Motivated by the desirable features of the particle-particle (pp) RPA compared to the conventional phRPA, we explore the pp counterpart of GW, that is, the T-matrix self-energy, formulated with the eigenvectors and eigenvalues of the ppRPA matrix. We demonstrate the accuracy of the T-matrix method for molecular QP energies, highlighting the importance of the pp channel for calculating QP spectra.

2 × 2 random matrix ensembles with reduced symmetry: from Hermitian to PT -symmetric matrices

International Nuclear Information System (INIS)

Gong Jiangbin; Wang Qinghai

2012-01-01

A possibly fruitful extension of conventional random matrix ensembles is proposed by imposing symmetry constraints on conventional Hermitian matrices or parity–time (PT)-symmetric matrices. To illustrate the main idea, we first study 2 × 2 complex Hermitian matrix ensembles with O(2)-invariant constraints, yielding novel level-spacing statistics such as singular distributions, the half-Gaussian distribution, distributions interpolating between the GOE (Gaussian orthogonal ensemble) distribution and half-Gaussian distributions, as well as the gapped-GOE distribution. Such a symmetry-reduction strategy is then used to explore 2 × 2 PT-symmetric matrix ensembles with real eigenvalues. In particular, PT-symmetric random matrix ensembles with U(2) invariance can be constructed, with the conventional complex Hermitian random matrix ensemble being a special case. In two examples of PT-symmetric random matrix ensembles, the level-spacing distributions are found to be the standard GUE (Gaussian unitary ensemble) statistics or the ‘truncated-GUE’ statistics. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

Enumeration of RNA complexes via random matrix theory.

Science.gov (United States)

Andersen, Jørgen E; Chekhov, Leonid O; Penner, Robert C; Reidys, Christian M; Sułkowski, Piotr

2013-04-01

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)=x2/2-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 the number of chord diagrams of fixed genus with specified numbers of backbones and chords as well as the number of cells in Riemann's moduli spaces for bordered surfaces of fixed topological type.

Blind Measurement Selection: A Random Matrix Theory Approach

KAUST Repository

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.

The Golden-Thompson inequality: Historical aspects and random matrix applications

International Nuclear Information System (INIS)

Forrester, Peter J.; Thompson, Colin J.

2014-01-01

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

Parametric level correlations in random-matrix models

International Nuclear Information System (INIS)

Weidenmueller, Hans A

2005-01-01

We show that parametric level correlations in random-matrix theories are closely related to a breaking of the symmetry between the advanced and the retarded Green functions. The form of the parametric level correlation function is the same as for the disordered case considered earlier by Simons and Altshuler and is given by the graded trace of the commutator of the saddle-point solution with the particular matrix that describes the symmetry breaking in the actual case of interest. The strength factor differs from the case of disorder. It is determined solely by the Goldstone mode. It is essentially given by the number of levels that are strongly mixed as the external parameter changes. The factor can easily be estimated in applications

Random matrix analysis of the QCD sign problem for general topology

International Nuclear Information System (INIS)

Bloch, Jacques; Wettig, Tilo

2009-01-01

Motivated by the important role played by the phase of the fermion determinant in the investigation of the sign problem in lattice QCD at nonzero baryon density, we derive an analytical formula for the average phase factor of the fermion determinant for general topology in the microscopic limit of chiral random matrix theory at nonzero chemical potential, for both the quenched and the unquenched case. The formula is a nontrivial extension of the expression for zero topology derived earlier by Splittorff and Verbaarschot. Our analytical predictions are verified by detailed numerical random matrix simulations of the quenched theory.

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

Science.gov (United States)

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.

Non-Hermitian Extensions of Wishart Random Matrix Ensembles

International Nuclear Information System (INIS)

Akemann, G.

2011-01-01

We briefly review the solution of three ensembles of non-Hermitian random matrices generalizing the Wishart-Laguerre (also called chiral) ensembles. These generalizations are realized as Gaussian two-matrix models, where the complex eigenvalues of the product of the two independent rectangular matrices are sought, with the matrix elements of both matrices being either real, complex or quaternion real. We also present the more general case depending on a non-Hermiticity parameter, that allows us to interpolate between the corresponding three Hermitian Wishart ensembles with real eigenvalues and the maximally non-Hermitian case. All three symmetry classes are explicitly solved for finite matrix size N x M for all complex eigenvalue correlations functions (and real or mixed correlations for real matrix elements). These are given in terms of the corresponding kernels built from orthogonal or skew-orthogonal Laguerre polynomials in the complex plane. We then present the corresponding three Bessel kernels in the complex plane in the microscopic large-N scaling limit at the origin, both at weak and strong non-Hermiticity with M - N ≥ 0 fixed. (author)

Spectral statistics in semiclassical random-matrix ensembles

International Nuclear Information System (INIS)

Feingold, M.; Leitner, D.M.; Wilkinson, M.

1991-01-01

A novel random-matrix ensemble is introduced which mimics the global structure inherent in the Hamiltonian matrices of autonomous, ergodic systems. Changes in its parameters induce a transition between a Poisson and a Wigner distribution for the level spacings, P(s). The intermediate distributions are uniquely determined by a single scaling variable. Semiclassical constraints force the ensemble to be in a regime with Wigner P(s) for systems with more than two freedoms

Anderson localization through Polyakov loops: Lattice evidence and random matrix model

International Nuclear Information System (INIS)

Bruckmann, Falk; Schierenberg, Sebastian; Kovacs, Tamas G.

2011-01-01

We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such ''wrong'' Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.

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

Science.gov (United States)

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

2018-05-01

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

Matrix method for acoustic levitation simulation.

Science.gov (United States)

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.

Response matrix method for large LMFBR analysis

International Nuclear Information System (INIS)

King, M.J.

1977-06-01

The feasibility of using response matrix techniques for computational models of large LMFBRs is examined. Since finite-difference methods based on diffusion theory have generally found a place in fast-reactor codes, a brief review of their general matrix foundation is given first in order to contrast it to the general strategy of response matrix methods. Then, in order to present the general method of response matrix technique, two illustrative examples are given. Matrix algorithms arising in the application to large LMFBRs are discussed, and the potential of the response matrix method is explored for a variety of computational problems. Principal properties of the matrices involved are derived with a view to application of numerical methods of solution. The Jacobi iterative method as applied to the current-balance eigenvalue problem is discussed

Exploring multicollinearity using a random matrix theory approach.

Science.gov (United States)

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.

Method of forming a ceramic matrix composite and a ceramic matrix component

Science.gov (United States)

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.

Matrix product approach for the asymmetric random average process

International Nuclear Information System (INIS)

Zielen, F; Schadschneider, A

2003-01-01

We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest-neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called beta densities, of all local interactions leading to steady states of product measure form are rigorously derived. This also completes an outstanding proof given in a previous publication. Then we present an alternative solution for the processes with factorized stationary states by using a matrix product ansatz. Due to continuous state variables we obtain a matrix algebra in the form of a functional equation which can be solved exactly

Some open problems in random matrix theory and the theory of integrable systems

OpenAIRE

Deift, Percy

2007-01-01

We describe a list of open problems in random matrix theory and integrable systems which was presented at the conference ``Integrable Systems, Random Matrices, and Applications'' at the Courant Institute in May 2006.

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)

1998-12-31

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)

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)

Number-conserving random phase approximation with analytically integrated matrix elements

International Nuclear Information System (INIS)

Kyotoku, M.; Schmid, K.W.; Gruemmer, F.; Faessler, A.

1990-01-01

In the present paper a number conserving random phase approximation is derived as a special case of the recently developed random phase approximation in general symmetry projected quasiparticle mean fields. All the occurring integrals induced by the number projection are performed analytically after writing the various overlap and energy matrices in the random phase approximation equation as polynomials in the gauge angle. In the limit of a large number of particles the well-known pairing vibration matrix elements are recovered. We also present a new analytically number projected variational equation for the number conserving pairing problem

Random matrix theory and fund of funds portfolio optimisation

Science.gov (United States)

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.

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

Science.gov (United States)

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

2008-07-01

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

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.

Random matrix theory and portfolio optimization in Moroccan stock exchange

Science.gov (United States)

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.

Raney Distributions and Random Matrix Theory

Science.gov (United States)

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.

Volatility of an Indian stock market: A random matrix approach

International Nuclear Information System (INIS)

Kulkarni, V.; Deo, N.

2006-07-01

We examine volatility of an Indian stock market in terms of aspects like participation, synchronization of stocks and quantification of volatility using the random matrix approach. Volatility pattern of the market is found using the BSE index for the three-year period 2000- 2002. Random matrix analysis is carried out using daily returns of 70 stocks for several time windows of 85 days in 2001 to (i) do a brief comparative analysis with statistics of eigenvalues and eigenvectors of the matrix C of correlations between price fluctuations, in time regimes of different volatilities. While a bulk of eigenvalues falls within RMT bounds in all the time periods, we see that the largest (deviating) eigenvalue correlates well with the volatility of the index, the corresponding eigenvector clearly shows a shift in the distribution of its components from volatile to less volatile periods and verifies the qualitative association between participation and volatility (ii) observe that the Inverse participation ratio for the last eigenvector is sensitive to market fluctuations (the two quantities are observed to anti correlate significantly) (iii) set up a variability index, V whose temporal evolution is found to be significantly correlated with the volatility of the overall market index. MIRAMAR (author)

Numerical methods in matrix computations

CERN Document Server

Björck, Åke

2015-01-01

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work. Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.

Skew-orthogonal polynomials and random matrix theory

CERN Document Server

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 ...

Study of RNA structures with a connection to random matrix theory

International Nuclear Information System (INIS)

Bhadola, Pradeep; Deo, Nivedita

2015-01-01

This manuscript investigates the level of complexity and thermodynamic properties of the real RNA structures and compares the properties with the random RNA sequences. A discussion on the similarities of thermodynamical properties of the real structures with the non linear random matrix model of RNA folding is presented. The structural information contained in the PDB file is exploited to get the base pairing information. The complexity of an RNA structure is defined by a topological quantity called genus which is calculated from the base pairing information. Thermodynamic analysis of the real structures is done numerically. The real structures have a minimum free energy which is very small compared to the randomly generated sequences of the same length. This analysis suggests that there are specific patterns in the structures which are preserved during the evolution of the sequences and certain sequences are discarded by the evolutionary process. Further analyzing the sequences of a fixed length reveal that the RNA structures exist in ensembles i.e. although all the sequences in the ensemble have different series of nucleotides (sequence) they fold into structures that have the same pairs of hydrogen bonding as well as the same minimum free energy. The specific heat of the RNA molecule is numerically estimated at different lengths. The specific heat curve with temperature shows a bump and for some RNA, a double peak behavior is observed. The same behavior is seen in the study of the random matrix model with non linear interaction of RNA folding. The bump in the non linear matrix model can be controlled by the change in the interaction strength.

Comparison of Experimental Methods for Estimating Matrix Diffusion Coefficients for Contaminant Transport Modeling

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.

The J-Matrix Method Developments and Applications

CERN Document Server

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.

The finite element response matrix method

International Nuclear Information System (INIS)

Nakata, H.; Martin, W.R.

1983-02-01

A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt

Combinatorial theory of the semiclassical evaluation of transport moments. I. Equivalence with the random matrix approach

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.

Character expansion methods for matrix models of dually weighted graphs

International Nuclear Information System (INIS)

Kazakov, V.A.; Staudacher, M.; Wynter, T.

1996-01-01

We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large N limit of the Itzykson-Zuber formula. We illustrate and check our methods by analysing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphs possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problem of phase transitions from random to flat lattices. (orig.). With 4 figs

Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

Science.gov (United States)

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.

Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

International Nuclear Information System (INIS)

Pato, Mauricio P; Oshanin, Gleb

2013-01-01

We study the probability distribution function P (β) n (w) of the Schmidt-like random variable w = x 2 1 /(∑ j=1 n x 2 j /n), where x j , (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 (β) (w)∼√((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. (paper)

Quantification of uncertainties in turbulence modeling: A comparison of physics-based and random matrix theoretic approaches

International Nuclear Information System (INIS)

Wang, Jian-Xun; Sun, Rui; Xiao, Heng

2016-01-01

Highlights: • Compared physics-based and random matrix methods to quantify RANS model uncertainty. • Demonstrated applications of both methods in channel ow over periodic hills. • Examined the amount of information introduced in the physics-based approach. • Discussed implications to modeling turbulence in both near-wall and separated regions. - Abstract: 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, e.g., those with non-parallel shear layers or strong mean flow curvature. Quantification of these large uncertainties originating from the modeled Reynolds stresses has attracted attention in the 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 maximum entropy, which is an alternative for model-form uncertainty quantification in RANS simulations. This method has better mathematical rigorousness and provides the most non-committal prior distributions without introducing artificial constraints. On the other hand, the physics-based approach has the advantages of being more flexible to incorporate available physical insights. In this work, we compare and discuss the advantages and disadvantages of the two approaches on model-form uncertainty quantification. In addition, we utilize the random matrix theoretic approach to assess and possibly improve the specification of priors used in the physics-based approach. The comparison is conducted through a test case using a canonical flow, the flow past

Efficient sparse matrix-matrix multiplication for computing periodic responses by shooting method on Intel Xeon Phi

Science.gov (United States)

Stoykov, S.; Atanassov, E.; Margenov, S.

2016-10-01

Many of the scientific applications involve sparse or dense matrix operations, such as solving linear systems, matrix-matrix products, eigensolvers, etc. In what concerns structural nonlinear dynamics, the computations of periodic responses and the determination of stability of the solution are of primary interest. Shooting method iswidely used for obtaining periodic responses of nonlinear systems. The method involves simultaneously operations with sparse and dense matrices. One of the computationally expensive operations in the method is multiplication of sparse by dense matrices. In the current work, a new algorithm for sparse matrix by dense matrix products is presented. The algorithm takes into account the structure of the sparse matrix, which is obtained by space discretization of the nonlinear Mindlin's plate equation of motion by the finite element method. The algorithm is developed to use the vector engine of Intel Xeon Phi coprocessors. It is compared with the standard sparse matrix by dense matrix algorithm and the one developed by Intel MKL and it is shown that by considering the properties of the sparse matrix better algorithms can be developed.

A nodal method based on matrix-response method

International Nuclear Information System (INIS)

Rocamora Junior, F.D.; Menezes, A.

1982-01-01

A nodal method based in the matrix-response method, is presented, and its application to spatial gradient problems, such as those that exist in fast reactors, near the core - blanket interface, is investigated. (E.G.) [pt

Localized motion in random matrix decomposition of complex financial systems

Science.gov (United States)

Jiang, Xiong-Fei; Zheng, Bo; Ren, Fei; Qiu, Tian

2017-04-01

With the random matrix theory, we decompose the multi-dimensional time series of complex financial systems into a set of orthogonal eigenmode functions, which are classified into the market mode, sector mode, and random mode. In particular, the localized motion generated by the business sectors, plays an important role in financial systems. Both the business sectors and their impact on the stock market are identified from the localized motion. We clarify that the localized motion induces different characteristics of the time correlations for the stock-market index and individual stocks. With a variation of a two-factor model, we reproduce the return-volatility correlations of the eigenmodes.

A wave propagation matrix method in semiclassical theory

International Nuclear Information System (INIS)

Lee, S.Y.; Takigawa, N.

1977-05-01

A wave propagation matrix method is used to derive the semiclassical formulae of the multiturning point problem. A phase shift matrix and a barrier transformation matrix are introduced to describe the processes of a particle travelling through a potential well and crossing a potential barrier respectively. The wave propagation matrix is given by the products of phase shift matrices and barrier transformation matrices. The method to study scattering by surface transparent potentials and the Bloch wave in solids is then applied

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.

A Matrix Splitting Method for Composite Function Minimization

KAUST Repository

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.

A Matrix Splitting Method for Composite Function Minimization

KAUST Repository

Yuan, Ganzhao; Zheng, Wei-Shi; Ghanem, Bernard

2016-01-01

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.

Thermodynamics of protein folding: a random matrix formulation.

Science.gov (United States)

Shukla, Pragya

2010-10-20

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters, e.g. the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows, however, that the evolution of the statistical measures, e.g. Gibbs free energy, heat capacity, and entropy, is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies. © 2010 IOP Publishing Ltd

Supplementary Appendix for: Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory

KAUST Repository

Suliman, Mohamed Abdalla Elhag; Ballal, Tarig; Kammoun, Abla; Alnaffouri, Tareq Y.

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 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...

ABCD Matrix Method a Case Study

CERN Document Server

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...

An Efficient GPU General Sparse Matrix-Matrix Multiplication for Irregular Data

DEFF Research Database (Denmark)

Liu, Weifeng; Vinter, Brian

2014-01-01

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method, breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM algorithm has to handle extra...... irregularity from three aspects: (1) the number of the nonzero entries in the result sparse matrix is unknown in advance, (2) very expensive parallel insert operations at random positions in the result sparse matrix dominate the execution time, and (3) load balancing must account for sparse data in both input....... Load balancing builds on the number of the necessary arithmetic operations on the nonzero entries and is guaranteed in all stages. Compared with the state-of-the-art GPU SpGEMM methods in the CUSPARSE library and the CUSP library and the latest CPU SpGEMM method in the Intel Math Kernel Library, our...

The finite element response Matrix method

International Nuclear Information System (INIS)

Nakata, H.; Martin, W.R.

1983-01-01

A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed

Random 2D Composites and the Generalized Method of Schwarz

Directory of Open Access Journals (Sweden)

Vladimir Mityushev

2015-01-01

Full Text Available Two-phase composites with nonoverlapping inclusions randomly embedded in matrix are investigated. A straightforward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value problems are solved for all locations of inclusions, that is, for all events of the considered probabilistic space C by the generalized method of Schwarz. Second, the effective properties are calculated in analytical form and averaged over C. This method is related to the traditional method based on the average probabilistic values involving the n-point correlation functions. However, we avoid computation of the correlation functions and compute their weighted moments of high orders by an indirect method which does not address the correlation functions. The effective properties are exactly expressed through these moments. It is proved that the generalized method of Schwarz converges for an arbitrary multiply connected doubly periodic domain and for an arbitrary contrast parameter. The proposed method yields an algorithm which can be applied with symbolic computations. The Torquato-Milton parameter ζ1 is exactly written for circular inclusions.

On the equilibrium state of a small system with random matrix coupling to its environment

Science.gov (United States)

Lebowitz, J. L.; Pastur, L.

2015-07-01

We consider a random matrix model of interaction between a small n-level system, S, and its environment, a N-level heat reservoir, R. The interaction between S and R is modeled by a tensor product of a fixed n× n matrix and a N× N Hermitian random matrix. We show that under certain ‘macroscopicity’ conditions on R, the reduced density matrix of the system {{ρ }S}=T{{r}R}ρ S\\cup R(eq), is given by ρ S(c)˜ exp \\{-β {{H}S}\\}, where HS is the Hamiltonian of the isolated system. This holds for all strengths of the interaction and thus gives some justification for using ρ S(c) to describe some nano-systems, like biopolymers, in equilibrium with their environment (Seifert 2012 Rep. Prog. Phys. 75 126001). Our results extend those obtained previously in (Lebowitz and Pastur 2004 J. Phys. A: Math. Gen. 37 1517-34) (Lebowitz et al 2007 Contemporary Mathematics (Providence RI: American Mathematical Society) pp 199-218) for a special two-level system.

POLLA-NESC, Resonance Parameter R-Matrix to S-Matrix Conversion by Reich-Moore Method

International Nuclear Information System (INIS)

Saussure, G. de; Perez, R.B.

1975-01-01

1 - Description of problem or function: The program transforms a set of r-matrix nuclear resonance parameters into a set of equivalent s-matrix (or Kapur-Peierls) resonance parameters. 2 - Method of solution: The program utilizes the multilevel formalism of Reich and Moore and avoids diagonalization of the level matrix. The parameters are obtained by a direct partial fraction expansion of the Reich-Moore expression of the collision matrix. This approach appears simpler and faster when the number of fission channels is known and small. The method is particularly useful when a large number of levels must be considered because it does not require diagonalization of a large level matrix. 3 - Restrictions on the complexity of the problem: By DIMENSION statements, the program is limited to maxima of 100 levels and 5 channels

Optimized Projection Matrix for Compressive Sensing

Directory of Open Access Journals (Sweden)

Jianping Xu

2010-01-01

Full Text Available Compressive sensing (CS is mainly concerned with low-coherence pairs, since the number of samples needed to recover the signal is proportional to the mutual coherence between projection matrix and sparsifying matrix. Until now, papers on CS always assume the projection matrix to be a random matrix. In this paper, aiming at minimizing the mutual coherence, a method is proposed to optimize the projection matrix. This method is based on equiangular tight frame (ETF design because an ETF has minimum coherence. It is impossible to solve the problem exactly because of the complexity. Therefore, an alternating minimization type method is used to find a feasible solution. The optimally designed projection matrix can further reduce the necessary number of samples for recovery or improve the recovery accuracy. The proposed method demonstrates better performance than conventional optimization methods, which brings benefits to both basis pursuit and orthogonal matching pursuit.

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.

Methods for converging correlation energies within the dielectric matrix formalism

Science.gov (United States)

Dixit, Anant; Claudot, Julien; Gould, Tim; Lebègue, Sébastien; Rocca, Dario

2018-03-01

Within the dielectric matrix formalism, the random-phase approximation (RPA) and analogous methods that include exchange effects are promising approaches to overcome some of the limitations of traditional density functional theory approximations. The RPA-type methods however have a significantly higher computational cost, and, similarly to correlated quantum-chemical methods, are characterized by a slow basis set convergence. In this work we analyzed two different schemes to converge the correlation energy, one based on a more traditional complete basis set extrapolation and one that converges energy differences by accounting for the size-consistency property. These two approaches have been systematically tested on the A24 test set, for six points on the potential-energy surface of the methane-formaldehyde complex, and for reaction energies involving the breaking and formation of covalent bonds. While both methods converge to similar results at similar rates, the computation of size-consistent energy differences has the advantage of not relying on the choice of a specific extrapolation model.

Accurate single-scattering simulation of ice cloud using the invariant-imbedding T-matrix method and the physical-geometric optics method

Science.gov (United States)

Sun, B.; Yang, P.; Kattawar, G. W.; Zhang, X.

2017-12-01

The ice cloud single-scattering properties can be accurately simulated using the invariant-imbedding T-matrix method (IITM) and the physical-geometric optics method (PGOM). The IITM has been parallelized using the Message Passing Interface (MPI) method to remove the memory limitation so that the IITM can be used to obtain the single-scattering properties of ice clouds for sizes in the geometric optics regime. Furthermore, the results associated with random orientations can be analytically achieved once the T-matrix is given. The PGOM is also parallelized in conjunction with random orientations. The single-scattering properties of a hexagonal prism with height 400 (in units of lambda/2*pi, where lambda is the incident wavelength) and an aspect ratio of 1 (defined as the height over two times of bottom side length) are given by using the parallelized IITM and compared to the counterparts using the parallelized PGOM. The two results are in close agreement. Furthermore, the integrated single-scattering properties, including the asymmetry factor, the extinction cross-section, and the scattering cross-section, are given in a completed size range. The present results show a smooth transition from the exact IITM solution to the approximate PGOM result. Because the calculation of the IITM method has reached the geometric regime, the IITM and the PGOM can be efficiently employed to accurately compute the single-scattering properties of ice cloud in a wide spectral range.

Embedded random matrix ensembles from nuclear structure and their recent applications

Science.gov (United States)

Kota, V. K. B.; Chavda, N. D.

Embedded random matrix ensembles generated by random interactions (of low body rank and usually two-body) in the presence of a one-body mean field, introduced in nuclear structure physics, are now established to be indispensable in describing statistical properties of a large number of isolated finite quantum many-particle systems. Lie algebra symmetries of the interactions, as identified from nuclear shell model and the interacting boson model, led to the introduction of a variety of embedded ensembles (EEs). These ensembles with a mean field and chaos generating two-body interaction generate in three different stages, delocalization of wave functions in the Fock space of the mean-field basis states. The last stage corresponds to what one may call thermalization and complex nuclei, as seen from many shell model calculations, lie in this region. Besides briefly describing them, their recent applications to nuclear structure are presented and they are (i) nuclear level densities with interactions; (ii) orbit occupancies; (iii) neutrinoless double beta decay nuclear transition matrix elements as transition strengths. In addition, their applications are also presented briefly that go beyond nuclear structure and they are (i) fidelity, decoherence, entanglement and thermalization in isolated finite quantum systems with interactions; (ii) quantum transport in disordered networks connected by many-body interactions with centrosymmetry; (iii) semicircle to Gaussian transition in eigenvalue densities with k-body random interactions and its relation to the Sachdev-Ye-Kitaev (SYK) model for majorana fermions.

Unified approach to numerical transfer matrix methods for disordered systems: applications to mixed crystals and to elasticity percolation

International Nuclear Information System (INIS)

Lemieux, M.A.; Breton, P.; Tremblay, A.M.S.

1985-01-01

It is shown that the Negative Eigenvalue Theorem and transfer matrix methods may be considered within a unified framework and generalized to compute projected densities of states or, more generally, any linear combination of matrix elements of the inverse of large symmetric random matrices. As examples of applications, extensive simulations for one- and two-mode behaviour in the Raman spectrum of one-dimensional mixed crystals and a finite-size analysis of critical exponents for the central force percolation universality class are presented

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.

Analysis of aeroplane boarding via spacetime geometry and random matrix theory

International Nuclear Information System (INIS)

Bachmat, E; Berend, D; Sapir, L; Skiena, S; Stolyarov, N

2006-01-01

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)

On the remarkable spectrum of a non-Hermitian random matrix model

International Nuclear Information System (INIS)

Holz, D E; Orland, H; Zee, A

2003-01-01

A non-Hermitian random matrix model proposed a few years ago has a remarkably intricate spectrum. Various attempts have been made to understand the spectrum, but even its dimension is not known. Using the Dyson-Schmidt equation, we show that the spectrum consists of a non-denumerable set of lines in the complex plane. Each line is the support of the spectrum of a periodic Hamiltonian, obtained by the infinite repetition of any finite sequence of the disorder variables. Our approach is based on the 'theory of words'. We make a complete study of all four-letter words. The spectrum is complicated because our matrix contains everything that will ever be written in the history of the universe, including this particular paper

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.

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.

Rotationally invariant family of Levy-like random matrix ensembles

International Nuclear Information System (INIS)

Choi, Jinmyung; Muttalib, K A

2009-01-01

We introduce a family of rotationally invariant random matrix ensembles characterized by a parameter λ. While λ = 1 corresponds to well-known critical ensembles, we show that λ ≠ 1 describes 'Levy-like' ensembles, characterized by power-law eigenvalue densities. For λ > 1 the density is bounded, as in Gaussian ensembles, but λ < 1 describes ensembles characterized by densities with long tails. In particular, the model allows us to evaluate, in terms of a novel family of orthogonal polynomials, the eigenvalue correlations for Levy-like ensembles. These correlations differ qualitatively from those in either the Gaussian or the critical ensembles. (fast track communication)

Mueller matrix polarimetry for the characterization of complex ...

Indian Academy of Sciences (India)

Scattering; polarization; Mueller matrix; wave propagation in random media; ... Initial biomedical applications of this novel general method for polarimetry analysis in random media are also presented. ... Pramana – Journal of Physics | News.

A semi-supervised method to detect seismic random noise with fuzzy GK clustering

International Nuclear Information System (INIS)

Hashemi, Hosein; Javaherian, Abdolrahim; Babuska, Robert

2008-01-01

We present a new method to detect random noise in seismic data using fuzzy Gustafson–Kessel (GK) clustering. First, using an adaptive distance norm, a matrix is constructed from the observed seismic amplitudes. The next step is to find centres of ellipsoidal clusters and construct a partition matrix which determines the soft decision boundaries between seismic events and random noise. The GK algorithm updates the cluster centres in order to iteratively minimize the cluster variance. Multiplication of the fuzzy membership function with values of each sample yields new sections; we name them 'clustered sections'. The seismic amplitude values of the clustered sections are given in a way to decrease the level of noise in the original noisy seismic input. In pre-stack data, it is essential to study the clustered sections in a f–k domain; finding the quantitative index for weighting the post-stack data needs a similar approach. Using the knowledge of a human specialist together with the fuzzy unsupervised clustering, the method is a semi-supervised random noise detection. The efficiency of this method is investigated on synthetic and real seismic data for both pre- and post-stack data. The results show a significant improvement of the input noisy sections without harming the important amplitude and phase information of the original data. The procedure for finding the final weights of each clustered section should be carefully done in order to keep almost all the evident seismic amplitudes in the output section. The method interactively uses the knowledge of the seismic specialist in detecting the noise

Universality in invariant random-matrix models: Existence near the soft edge

International Nuclear Information System (INIS)

Kanzieper, E.; Freilikher, V.

1997-01-01

We consider two non-Gaussian ensembles of large Hermitian random matrices with strong level confinement and show that near the soft edge of the spectrum both scaled density of states and eigenvalue correlations follow so-called Airy laws inherent in the Gaussian unitary ensemble. This suggests that the invariant one-matrix models should display universal eigenvalue correlations in the soft-edge scaling limit. copyright 1997 The American Physical Society

Dynamic Output Feedback Control for Nonlinear Networked Control Systems with Random Packet Dropout and Random Delay

Directory of Open Access Journals (Sweden)

Shuiqing Yu

2013-01-01

Full Text Available This paper investigates the dynamic output feedback control for nonlinear networked control systems with both random packet dropout and random delay. Random packet dropout and random delay are modeled as two independent random variables. An observer-based dynamic output feedback controller is designed based upon the Lyapunov theory. The quantitative relationship of the dropout rate, transition probability matrix, and nonlinear level is derived by solving a set of linear matrix inequalities. Finally, an example is presented to illustrate the effectiveness of the proposed method.

Matrix-based image reconstruction methods for tomography

International Nuclear Information System (INIS)

Llacer, J.; Meng, J.D.

1984-10-01

Matrix methods of image reconstruction have not been used, in general, because of the large size of practical matrices, ill condition upon inversion and the success of Fourier-based techniques. An exception is the work that has been done at the Lawrence Berkeley Laboratory for imaging with accelerated radioactive ions. An extension of that work into more general imaging problems shows that, with a correct formulation of the problem, positron tomography with ring geometries results in well behaved matrices which can be used for image reconstruction with no distortion of the point response in the field of view and flexibility in the design of the instrument. Maximum Likelihood Estimator methods of reconstruction, which use the system matrices tailored to specific instruments and do not need matrix inversion, are shown to result in good preliminary images. A parallel processing computer structure based on multiple inexpensive microprocessors is proposed as a system to implement the matrix-MLE methods. 14 references, 7 figures

On characteristic polynomials for a generalized chiral random matrix ensemble with a source

Science.gov (United States)

Fyodorov, Yan V.; Grela, Jacek; Strahov, Eugene

2018-04-01

We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a N× N random matrix taken from a L-deformed chiral Gaussian Unitary Ensemble with an external source Ω. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Fyodorov (2017 arXiv:1710.04699), is briefly discussed as a motivation to study asymptotics of these objects in the case of external source proportional to the identity matrix. In particular, for an associated complex bulk/chiral edge scaling regime we retrieve the kernel related to Bessel/Macdonald functions.

A Golub-Kahan-type reduction method for matrix pairs

NARCIS (Netherlands)

Hochstenbach, M.E.; Reichel, L.; Yu, X.

2015-01-01

We describe a novel method for reducing a pair of large matrices {A;B} to a pair of small matrices {H;K}. The method is an extension of Golub-Kahan bidiagonalization to matrix pairs, and simplifies to the latter method when B is the identity matrix. Applications to Tikhonov regularization of large

A Golub-Kahan-type reduction method for matrix pairs

NARCIS (Netherlands)

Hochstenbach, M.E.; Reichel, L.; Yu, X.

2015-01-01

We describe a novel method for reducing a pair of large matrices {A,B} to a pair of small matrices {H,K}. The method is an extension of Golub–Kahan bidiagonalization to matrix pairs, and simplifies to the latter method when B is the identity matrix. Applications to Tikhonov regularization of large

The Matrix Method of Representation, Analysis and Classification of Long Genetic Sequences

Directory of Open Access Journals (Sweden)

Ivan V. Stepanyan

2017-01-01

Full Text Available The article is devoted to a matrix method of comparative analysis of long nucleotide sequences by means of presenting each sequence in the form of three digital binary sequences. This method uses a set of symmetries of biochemical attributes of nucleotides. It also uses the possibility of presentation of every whole set of N-mers as one of the members of a Kronecker family of genetic matrices. With this method, a long nucleotide sequence can be visually represented as an individual fractal-like mosaic or another regular mosaic of binary type. In contrast to natural nucleotide sequences, artificial random sequences give non-regular patterns. Examples of binary mosaics of long nucleotide sequences are shown, including cases of human chromosomes and penicillins. The obtained results are then discussed.

From polymers to quantum gravity: Triple-scaling in rectangular random matrix models

International Nuclear Information System (INIS)

Myers, R.C.; Periwal, V.

1993-01-01

Rectangular NxM matrix models can be solved in several qualitatively distinct large-N limits, since two independent parameters govern the size of the matrix. Regarded as models of random surfaces, these matrix models interpolate between branched polymer behaviour and two-dimensional quantum gravity. We solve such models in a 'triple-scaling' regime in this paper, with N and M becoming large independently. A correspondence between phase transitions and singularities of mappings from R 2 to R 2 is indicated. At different critical points, the scaling behaviour is determined by (i) two decoupled ordinary differential equations; (ii) an ordinary differential equation and a finite-difference equation; or (iii) two coupled partial differential equations. The Painleve II equation arises (in conjunction with a difference equation) at a point associated with branched polymers. For critical points described by partial differential equations, there are dual weak-coupling/strong-coupling expansions. It is conjectured that the new physics is related to microscopic topology fluctuations. (orig.)

Factorisations for partition functions of random Hermitian matrix models

International Nuclear Information System (INIS)

Jackson, D.M.; Visentin, T.I.

1996-01-01

The partition function Z N , for Hermitian-complex matrix models can be expressed as an explicit integral over R N , where N is a positive integer. Such an integral also occurs in connection with random surfaces and models of two dimensional quantum gravity. We show that Z N can be expressed as the product of two partition functions, evaluated at translated arguments, for another model, giving an explicit connection between the two models. We also give an alternative computation of the partition function for the φ 4 -model.The approach is an algebraic one and holds for the functions regarded as formal power series in the appropriate ring. (orig.)

Pre-form ceramic matrix composite cavity and method of forming and method of forming a ceramic matrix composite component

Science.gov (United States)

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.

A random matrix approach to the crossover of energy-level statistics from Wigner to Poisson

International Nuclear Information System (INIS)

Datta, Nilanjana; Kunz, Herve

2004-01-01

We analyze a class of parametrized random matrix models, introduced by Rosenzweig and Porter, which is expected to describe the energy level statistics of quantum systems whose classical dynamics varies from regular to chaotic as a function of a parameter. We compute the generating function for the correlations of energy levels, in the limit of infinite matrix size. The crossover between Poisson and Wigner statistics is measured by a renormalized coupling constant. The model is exactly solved in the sense that, in the limit of infinite matrix size, the energy-level correlation functions and their generating function are given in terms of a finite set of integrals

A random matrix model for elliptic curve L-functions of finite conductor

International Nuclear Information System (INIS)

Dueñez, E; Huynh, D K; Keating, J P; Snaith, N C; Miller, S J

2012-01-01

We propose a random-matrix model for families of elliptic curve L-functions of finite conductor. A repulsion of the critical zeros of these L-functions away from the centre of the critical strip was observed numerically by Miller (2006 Exp. Math. 15 257–79); such behaviour deviates qualitatively from the conjectural limiting distribution of the zeros (for large conductors this distribution is expected to approach the one-level density of eigenvalues of orthogonal matrices after appropriate rescaling). Our purpose here is to provide a random-matrix model for Miller’s surprising discovery. We consider the family of even quadratic twists of a given elliptic curve. The main ingredient in our model is a calculation of the eigenvalue distribution of random orthogonal matrices whose characteristic polynomials are larger than some given value at the symmetry point in the spectra. We call this sub-ensemble of SO(2N) the excised orthogonal ensemble. The sieving-off of matrices with small values of the characteristic polynomial is akin to the discretization of the central values of L-functions implied by the formulae of Waldspurger and Kohnen–Zagier. The cut-off scale appropriate to modelling elliptic curve L-functions is exponentially small relative to the matrix size N. The one-level density of the excised ensemble can be expressed in terms of that of the well-known Jacobi ensemble, enabling the former to be explicitly calculated. It exhibits an exponentially small (on the scale of the mean spacing) hard gap determined by the cut-off value, followed by soft repulsion on a much larger scale. Neither of these features is present in the one-level density of SO(2N). When N → ∞ we recover the limiting orthogonal behaviour. Our results agree qualitatively with Miller’s discrepancy. Choosing the cut-off appropriately gives a model in good quantitative agreement with the number-theoretical data. (paper)

Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.

Science.gov (United States)

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.

Comparison of matrix methods for elastic wave scattering problems

International Nuclear Information System (INIS)

Tsao, S.J.; Varadan, V.K.; Varadan, V.V.

1983-01-01

This article briefly describes the T-matrix method and the MOOT (method of optimal truncation) of elastic wave scattering as they apply to A-D, SH- wave problems as well as 3-D elastic wave problems. Two methods are compared for scattering by elliptical cylinders as well as oblate spheroids of various eccentricity as a function of frequency. Convergence, and symmetry of the scattering cross section are also compared for ellipses and spheroidal cavities of different aspect ratios. Both the T-matrix approach and the MOOT were programmed on an AMDHL 470 computer using double precision arithmetic. Although the T-matrix method and MOOT are not always in agreement, it is in no way implied that any of the published results using MOOT are in error

Orthogonal polynomials and random matrices

CERN Document Server

Deift, Percy

2000-01-01

This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.

Refractive index inversion based on Mueller matrix method

Science.gov (United States)

Fan, Huaxi; Wu, Wenyuan; Huang, Yanhua; Li, Zhaozhao

2016-03-01

Based on Stokes vector and Jones vector, the correlation between Mueller matrix elements and refractive index was studied with the result simplified, and through Mueller matrix way, the expression of refractive index inversion was deduced. The Mueller matrix elements, under different incident angle, are simulated through the expression of specular reflection so as to analyze the influence of the angle of incidence and refractive index on it, which is verified through the measure of the Mueller matrix elements of polished metal surface. Research shows that, under the condition of specular reflection, the result of Mueller matrix inversion is consistent with the experiment and can be used as an index of refraction of inversion method, and it provides a new way for target detection and recognition technology.

Correlated random-phase approximation from densities and in-medium matrix elements

Energy Technology Data Exchange (ETDEWEB)

Trippel, Richard; Roth, Robert [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany)

2016-07-01

The random-phase approximation (RPA) as well as the second RPA (SRPA) are established tools for the study of collective excitations in nuclei. Addressing the well known lack of correlations, we derived a universal framework for a fully correlated RPA based on the use of one- and two-body densities. We apply densities from coupled cluster theory and investigate the impact of correlations. As an alternative approach to correlations we use matrix elements transformed via in-medium similarity renormalization group (IM-SRG) in combination with RPA and SRPA. We find that within SRPA the use of IM-SRG matrix elements leads to the disappearance of instabilities of low-lying states. For the calculations we use normal-ordered two- plus three-body interactions derived from chiral effective field theory. We apply different Hamiltonians to a number of doubly-magic nuclei and calculate electric transition strengths.

Direct determination of scattering time delays using the R-matrix propagation method

International Nuclear Information System (INIS)

Walker, R.B.; Hayes, E.F.

1989-01-01

A direct method for determining time delays for scattering processes is developed using the R-matrix propagation method. The procedure involves the simultaneous generation of the global R matrix and its energy derivative. The necessary expressions to obtain the energy derivative of the S matrix are relatively simple and involve many of the same matrix elements required for the R-matrix propagation method. This method is applied to a simple model for a chemical reaction that displays sharp resonance features. The test results of the direct method are shown to be in excellent agreement with the traditional numerical differentiation method for scattering energies near the resonance energy. However, for sharp resonances the numerical differentiation method requires calculation of the S-matrix elements at many closely spaced energies. Since the direct method presented here involves calculations at only a single energy, one is able to generate accurate energy derivatives and time delays much more efficiently and reliably

The covariance matrix of the Potts model: A random cluster analysis

International Nuclear Information System (INIS)

Borgs, C.; Chayes, J.T.

1996-01-01

We consider the covariance matrix, G mn = q 2 x ,m); δ(σ y ,n)>, of the d-dimensional q-states Potts model, rewriting it in the random cluster representation of Fortuin and Kasteleyn. In many of the q ordered phases, we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances, thereby attributing algebraic significance to these stochastic geometric quantities. We also show that the correlation length and the correlation length corresponding to the decay rate of one on the eigenvalues in the same as the inverse decay rate of the diameter of finite clusters. For dimension of d=2, we show that this correlation length and the correlation length of two-point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two. For systems with first-order transitions, this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self-dual point β o . For systems with second order transitions, this relation implies the equality of the correlation length exponents from above below threshold, as well as an amplitude ratio of two. In the course of proving the above results, we establish several properties of independent interest, including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions, and left continuity of the two-dimensional free boundary condition percolation probability at β o . We also introduce DLR equations for the random cluster model and use them to establish ergodicity of the free measure. In order to prove these results, we introduce a new class of events which we call decoupling events and two inequalities for these events

The Matrix Element Method at Next-to-Leading Order

OpenAIRE

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...

PCT Uncertainty Analysis Using Unscented Transform with Random Orthogonal Matrix

Energy Technology Data Exchange (ETDEWEB)

Fynana, Douglas A.; Ahn, Kwang-Il [KAERI, Daejeon (Korea, Republic of); Lee, John C. [Univ. of Michigan, Michigan (United States)

2015-05-15

Most Best Estimate Plus Uncertainty (BEPU) methods employ nonparametric order statistics through Wilks' formula to quantify uncertainties of best estimate simulations of nuclear power plant (NPP) transients. 95%/95% limits, the 95''t{sup h} percentile at a 95% confidence level, are obtained by randomly sampling all uncertainty contributors through conventional Monte Carlo (MC). Advantages are simple implementation of MC sampling of input probability density functions (pdfs) and limited computational expense of 1''s{sup t}, 2''n{sup d}, and 3''r{sup d} order Wilks' formula requiring only 59, 93, or 124 simulations, respectively. A disadvantage of small sample size is large sample to sample variation of statistical estimators. This paper presents a new efficient sampling based algorithm for accurate estimation of mean and variance of the output parameter pdf. The algorithm combines a deterministic sampling method, the unscented transform (UT), with random sampling through the generation of a random orthogonal matrix (ROM). The UT guarantees the mean, covariance, and 3''r{sup d} order moments of the multivariate input parameter distributions are exactly preserved by the sampled input points and the orthogonal transformation of the points by a ROM guarantees the sample error of all 4''t{sup h} order and higher moments are unbiased. The UT with ROM algorithm is applied to the uncertainty quantification of the peak clad temperature (PCT) during a large break loss-of-coolant accident (LBLOCA) in an OPR1000 NPP to demonstrate the applicability of the new algorithm to BEPU. This paper presented a new algorithm combining the UT with ROM for efficient multivariate parameter sampling that ensures sample input covariance and 3''r{sup d} order moments are exactly preserved and 4''th moment errors are small and unbiased. The advantageous sample properties guarantee higher order accuracy and

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...... 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...... by the cumulant neglect closure method applied at the fourth order level....

Finding a Hadamard matrix by simulated annealing of spin vectors

Science.gov (United States)

Bayu Suksmono, Andriyan

2017-05-01

Reformulation of a combinatorial problem into optimization of a statistical-mechanics system enables finding a better solution using heuristics derived from a physical process, such as by the simulated annealing (SA). In this paper, we present a Hadamard matrix (H-matrix) searching method based on the SA on an Ising model. By equivalence, an H-matrix can be converted into a seminormalized Hadamard (SH) matrix, whose first column is unit vector and the rest ones are vectors with equal number of -1 and +1 called SH-vectors. We define SH spin vectors as representation of the SH vectors, which play a similar role as the spins on Ising model. The topology of the lattice is generalized into a graph, whose edges represent orthogonality relationship among the SH spin vectors. Starting from a randomly generated quasi H-matrix Q, which is a matrix similar to the SH-matrix without imposing orthogonality, we perform the SA. The transitions of Q are conducted by random exchange of {+, -} spin-pair within the SH-spin vectors that follow the Metropolis update rule. Upon transition toward zeroth energy, the Q-matrix is evolved following a Markov chain toward an orthogonal matrix, at which the H-matrix is said to be found. We demonstrate the capability of the proposed method to find some low-order H-matrices, including the ones that cannot trivially be constructed by the Sylvester method.

Mechanical properties of unidirectional and randomly oriented kenaf bast fibre composites using polypropylene resin matrix

International Nuclear Information System (INIS)

Sharifah Hanisah Syed Abd Aziz; Khairul Zaman Mohd Dahlan

2004-01-01

Fibres are known to confer strength and rigidity to the weak and brittle matrix and currently, research in composite materials is being directed at using natural fibers instead of synthetic fibres. In this work long and random kenaf fibers were used in the as-received condition and alkalized with a 0.06M NaOH solution. They were combined with polypropylene thin sheets and hot-pressed to form natural fibre composites. The mechanical properties of the composites were investigated to observe the effect of fibre alignment, fibre treatment, and the method of moulding technique used. A general trend was observed whereby alkalized and long fibre composites give higher flexural modulus and flexural strength compared with random mat and untreated fibres. The long fibre composites also gave a higher work of fracture. However, the correlation between fibre surface treatment and the work of fracture was less clear. The method of moulding used also need to be improved to optimize the performance of the composites manufactured as the overall mechanical test result showed some irregularities. Pre-irradiation on the polypropylene pellets before the composite is manufactured will be considered as one of the mechanism in enhancing the mechanical performance of the composites in future work. (Author)

Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains

Science.gov (United States)

Zhao, Yan; Stratt, Richard M.

2018-05-01

Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory.

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...... method here is implemented by programming in VHDL language. Finally, the novel method in this paper is verified by experiments....

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.

Application of the R-matrix method to photoionization of molecules.

Science.gov (United States)

Tashiro, Motomichi

2010-04-07

The R-matrix method has been used for theoretical calculation of electron collision with atoms and molecules for long years. The method was also formulated to treat photoionization process, however, its application has been mostly limited to photoionization of atoms. In this work, we implement the R-matrix method to treat molecular photoionization problem based on the UK R-matrix codes. This method can be used for diatomic as well as polyatomic molecules, with multiconfigurational description for electronic states of both target neutral molecule and product molecular ion. Test calculations were performed for valence electron photoionization of nitrogen (N(2)) as well as nitric oxide (NO) molecules. Calculated photoionization cross sections and asymmetry parameters agree reasonably well with the available experimental results, suggesting usefulness of the method for molecular photoionization.

Gauge cooling for the singular-drift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD

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.

Three-body forces for electrons by the S-matrix method

International Nuclear Information System (INIS)

Margaritelli, R.

1989-01-01

A electromagnetic three-body potential between eletrons is derived by the S-matrix method. This potential can be compared up to a certain point with other electromagnetic potentials (obtained by other methods) encountered in the literature. However, since the potential derived here is far more complete than others, this turns direct comparison with the potentials found in the literature somewhat difficult. These calculations allow a better understanding of the S-matrix method as applied to problems which involve the calculations of three-body nuclear forces (these calculations are performed in order to understand the 3 He form factor). Furthermore, these results enable us to decide between two discrepant works which derive the two-pion exchange three-body potential, both by the S-matrix method. (author) [pt

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

Directory of Open Access Journals (Sweden)

James M. Cheverud

2007-03-01

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

Hybrid transfer-matrix FDTD method for layered periodic structures.

Science.gov (United States)

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 nodal method based on the response-matrix method

International Nuclear Information System (INIS)

Cunha Menezes Filho, A. da; Rocamora Junior, F.D.

1983-02-01

A nodal approach based on the Response-Matrix method is presented with the purpose of investigating the possibility of mixing two different allocations in the same problem. It is found that the use of allocation of albedo combined with allocation of direct reflection produces good results for homogeneous fast reactor configurations. (Author) [pt

A framework for general sparse matrix-matrix multiplication on GPUs and heterogeneous processors

DEFF Research Database (Denmark)

Liu, Weifeng; Vinter, Brian

2015-01-01

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM implementation has to handle...... extra irregularity from three aspects: (1) the number of nonzero entries in the resulting sparse matrix is unknown in advance, (2) very expensive parallel insert operations at random positions in the resulting sparse matrix dominate the execution time, and (3) load balancing must account for sparse data...... memory space and efficiently utilizes the very limited on-chip scratchpad memory. Parallel insert operations of the nonzero entries are implemented through the GPU merge path algorithm that is experimentally found to be the fastest GPU merge approach. Load balancing builds on the number of necessary...

Fluctuation, stationarity, and ergodic properties of random-matrix ensembles

International Nuclear Information System (INIS)

Pandey, A.

1979-01-01

The properties of random-matrix ensembles and the application of such ensembles to energy-level fluctuations and strength fluctuations are discussed. The two-point correlation function for complex spectra described by the three standard Gaussian ensembles is calculated, and its essential simplicity, displayed by an elementary procedure that derives from the dominance of binary correlations. The resultant function is exact for the unitary case and a very good approximation to the orthogonal and symplectic cases. The same procedure yields the spectrum for a Gaussian orthogonal ensemble (GOE) deformed by a pairing interaction. Several extensions are given and relationships to other problems of current interest are discussed. The standard fluctuation measures are rederived for the GOE, and their extensions to the unitary and symplectic cases are given. The measures are shown to derive, for the most part, from the two-point function, and new relationships between them are established, answering some long-standing questions. Some comparisons with experimental values are also made. All the cluster functions, and therefore the fluctuation measures, are shown to be stationary and strongly ergodic, thus justifying the use of random matrices for individual spectra. Strength fluctuations in the orthogonal ensemble are also considered. The Porter-Thomas distribution in its various forms is rederived and its ergodicity is established

Matrix method for two-dimensional waveguide mode solution

Science.gov (United States)

Sun, Baoguang; Cai, Congzhong; Venkatesh, Balajee Seshasayee

2018-05-01

In this paper, we show that the transfer matrix theory of multilayer optics can be used to solve the modes of any two-dimensional (2D) waveguide for their effective indices and field distributions. A 2D waveguide, even composed of numerous layers, is essentially a multilayer stack and the transmission through the stack can be analysed using the transfer matrix theory. The result is a transfer matrix with four complex value elements, namely A, B, C and D. The effective index of a guided mode satisfies two conditions: (1) evanescent waves exist simultaneously in the first (cladding) layer and last (substrate) layer, and (2) the complex element D vanishes. For a given mode, the field distribution in the waveguide is the result of a 'folded' plane wave. In each layer, there is only propagation and absorption; at each boundary, only reflection and refraction occur, which can be calculated according to the Fresnel equations. As examples, we show that this method can be used to solve modes supported by the multilayer step-index dielectric waveguide, slot waveguide, gradient-index waveguide and various plasmonic waveguides. The results indicate the transfer matrix method is effective for 2D waveguide mode solution in general.

Theoretical treatment of molecular photoionization based on the R-matrix method

International Nuclear Information System (INIS)

Tashiro, Motomichi

2012-01-01

The R-matrix method was implemented to treat molecular photoionization problem based on the UK R-matrix codes. This method was formulated to treat photoionization process long before, however, its application has been mostly limited to photoionization of atoms. Application of the method to valence photoionization as well as inner-shell photoionization process will be presented.

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

Science.gov (United States)

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.

Modeling Transport in Fractured Porous Media with the Random-Walk Particle Method: The Transient Activity Range and the Particle-Transfer Probability

International Nuclear Information System (INIS)

Lehua Pan; G.S. Bodvarsson

2001-01-01

Multiscale features of transport processes in fractured porous media make numerical modeling a difficult task, both in conceptualization and computation. Modeling the mass transfer through the fracture-matrix interface is one of the critical issues in the simulation of transport in a fractured porous medium. Because conventional dual-continuum-based numerical methods are unable to capture the transient features of the diffusion depth into the matrix (unless they assume a passive matrix medium), such methods will overestimate the transport of tracers through the fractures, especially for the cases with large fracture spacing, resulting in artificial early breakthroughs. We have developed a new method for calculating the particle-transfer probability that can capture the transient features of diffusion depth into the matrix within the framework of the dual-continuum random-walk particle method (RWPM) by introducing a new concept of activity range of a particle within the matrix. Unlike the multiple-continuum approach, the new dual-continuum RWPM does not require using additional grid blocks to represent the matrix. It does not assume a passive matrix medium and can be applied to the cases where global water flow exists in both continua. The new method has been verified against analytical solutions for transport in the fracture-matrix systems with various fracture spacing. The calculations of the breakthrough curves of radionuclides from a potential repository to the water table in Yucca Mountain demonstrate the effectiveness of the new method for simulating 3-D, mountain-scale transport in a heterogeneous, fractured porous medium under variably saturated conditions

Gaussian random-matrix process and universal parametric correlations in complex systems

International Nuclear Information System (INIS)

Attias, H.; Alhassid, Y.

1995-01-01

We introduce the framework of the Gaussian random-matrix process as an extension of Dyson's Gaussian ensembles and use it to discuss the statistical properties of complex quantum systems that depend on an external parameter. We classify the Gaussian processes according to the short-distance diffusive behavior of their energy levels and demonstrate that all parametric correlation functions become universal upon the appropriate scaling of the parameter. The class of differentiable Gaussian processes is identified as the relevant one for most physical systems. We reproduce the known spectral correlators and compute eigenfunction correlators in their universal form. Numerical evidence from both a chaotic model and weakly disordered model confirms our predictions

Efficient computation method of Jacobian matrix

International Nuclear Information System (INIS)

Sasaki, Shinobu

1995-05-01

As well known, the elements of the Jacobian matrix are complex trigonometric functions of the joint angles, resulting in a matrix of staggering complexity when we write it all out in one place. This article addresses that difficulties to this subject are overcome by using velocity representation. The main point is that its recursive algorithm and computer algebra technologies allow us to derive analytical formulation with no human intervention. Particularly, it is to be noted that as compared to previous results the elements are extremely simplified throughout the effective use of frame transformations. Furthermore, in case of a spherical wrist, it is shown that the present approach is computationally most efficient. Due to such advantages, the proposed method is useful in studying kinematically peculiar properties such as singularity problems. (author)

The response-matrix based AFEN method for the hexagonal geometry

International Nuclear Information System (INIS)

Noh, Jae Man; Kim, Keung Koo; Zee, Sung Quun; Joo, Hyung Kook; Cho, Byng Oh; Jeong, Hyung Guk; Cho, Jin Young

1998-03-01

The analytic function expansion nodal (AFEN) method, developed to overcome the limitations caused by the transverse integration, has been successfully to predict the neutron behavior in the hexagonal core as well as rectangular core. In the hexagonal node, the transverse leakage resulted from the transverse integration has some singular terms such as delta-function and step-functions near the node center line. In most nodal methods using the transverse integration, the accuracy of nodal method is degraded because the transverse leakage is approximated as a smooth function across the node center line by ignoring singular terms. However, the AFEN method in which there is no transverse leakage term in deriving nodal coupling equations keeps good accuracy for hexagonal node. In this study, the AFEN method which shows excellent accuracy in the hexagonal core analyses is reformulated as a response matrix form. This form of the AFEN method can be implemented easily to nodal codes based on the response matrix method. Therefore, the Coarse Mesh Rebalance (CMR) acceleration technique which is one of main advantages of the response matrix method can be utilized for the AFEN method. The response matrix based AFEN method has been successfully implemented into the MASTER code and its accuracy and computational efficiency were examined by analyzing the two- and three- dimensional benchmark problem of VVER-440. Based on the results, it can be concluded that the newly formulated AFEN method predicts accurately the assembly powers (within 0.2% average error) as well as the effective multiplication factor (within 0.2% average error) as well as the effective multiplication factor (within 20 pcm error). In addition, the CMR acceleration technique is quite efficient in reducing the computation time of the AFEN method by 8 to 10 times. (author). 22 refs., 1 tab., 4 figs

Analytical techniques for instrument design - matrix methods

International Nuclear Information System (INIS)

Robinson, R.A.

1997-01-01

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 (Δk I ,Δk F to ΔE, ΔQ ampersand 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

Matrix-based system reliability method and applications to bridge networks

International Nuclear Information System (INIS)

Kang, W.-H.; Song Junho; Gardoni, Paolo

2008-01-01

Using a matrix-based system reliability (MSR) method, one can estimate the probabilities of complex system events by simple matrix calculations. Unlike existing system reliability methods whose complexity depends highly on that of the system event, the MSR method describes any general system event in a simple matrix form and therefore provides a more convenient way of handling the system event and estimating its probability. Even in the case where one has incomplete information on the component probabilities and/or the statistical dependence thereof, the matrix-based framework enables us to estimate the narrowest bounds on the system failure probability by linear programming. This paper presents the MSR method and applies it to a transportation network consisting of bridge structures. The seismic failure probabilities of bridges are estimated by use of the predictive fragility curves developed by a Bayesian methodology based on experimental data and existing deterministic models of the seismic capacity and demand. Using the MSR method, the probability of disconnection between each city/county and a critical facility is estimated. The probability mass function of the number of failed bridges is computed as well. In order to quantify the relative importance of bridges, the MSR method is used to compute the conditional probabilities of bridge failures given that there is at least one city disconnected from the critical facility. The bounds on the probability of disconnection are also obtained for cases with incomplete information

Random matrix model of adiabatic quantum computing

International Nuclear Information System (INIS)

Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.

2005-01-01

We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of random matrix theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances - i.e., those having a critical ratio of clauses to variables - the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to nonadiabatic Landau-Zener-type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size

Transfer matrix method for four-flux radiative transfer.

Science.gov (United States)

Slovick, Brian; Flom, Zachary; Zipp, Lucas; Krishnamurthy, Srini

2017-07-20

We develop a transfer matrix method for four-flux radiative transfer, which is ideally suited for studying transport through multiple scattering layers. The model predicts the specular and diffuse reflection and transmission of multilayer composite films, including interface reflections, for diffuse or collimated incidence. For spherical particles in the diffusion approximation, we derive closed-form expressions for the matrix coefficients and show remarkable agreement with numerical Monte Carlo simulations for a range of absorption values and film thicknesses, and for an example multilayer slab.

Google matrix analysis of directed networks

Science.gov (United States)

Ermann, Leonardo; Frahm, Klaus M.; Shepelyansky, Dima L.

2015-10-01

In the past decade modern societies have developed enormous communication and social networks. Their classification and information retrieval processing has become a formidable task for the society. Because of the rapid growth of the World Wide Web, and social and communication networks, new mathematical methods have been invented to characterize the properties of these networks in a more detailed and precise way. Various search engines extensively use such methods. It is highly important to develop new tools to classify and rank a massive amount of network information in a way that is adapted to internal network structures and characteristics. This review describes the Google matrix analysis of directed complex networks demonstrating its efficiency using various examples including the World Wide Web, Wikipedia, software architectures, world trade, social and citation networks, brain neural networks, DNA sequences, and Ulam networks. The analytical and numerical matrix methods used in this analysis originate from the fields of Markov chains, quantum chaos, and random matrix theory.

Probabilistic homogenization of random composite with ellipsoidal particle reinforcement by the iterative stochastic finite element method

Science.gov (United States)

Sokołowski, Damian; Kamiński, Marcin

2018-01-01

This study proposes a framework for determination of basic probabilistic characteristics of the orthotropic homogenized elastic properties of the periodic composite reinforced with ellipsoidal particles and a high stiffness contrast between the reinforcement and the matrix. Homogenization problem, solved by the Iterative Stochastic Finite Element Method (ISFEM) is implemented according to the stochastic perturbation, Monte Carlo simulation and semi-analytical techniques with the use of cubic Representative Volume Element (RVE) of this composite containing single particle. The given input Gaussian random variable is Young modulus of the matrix, while 3D homogenization scheme is based on numerical determination of the strain energy of the RVE under uniform unit stretches carried out in the FEM system ABAQUS. The entire series of several deterministic solutions with varying Young modulus of the matrix serves for the Weighted Least Squares Method (WLSM) recovery of polynomial response functions finally used in stochastic Taylor expansions inherent for the ISFEM. A numerical example consists of the High Density Polyurethane (HDPU) reinforced with the Carbon Black particle. It is numerically investigated (1) if the resulting homogenized characteristics are also Gaussian and (2) how the uncertainty in matrix Young modulus affects the effective stiffness tensor components and their PDF (Probability Density Function).

Dirac operator, chirality and random matrix theory

International Nuclear Information System (INIS)

Pullirsch, R.

2001-05-01

Quantum Chromodynamics (QCD) is considered to be the correct theory which describes quarks and gluons and, thus, all strong interaction phenomena from the fundamental forces of nature. However, important properties of QCD such as the physical mechanism of color confinement and the spontaneous breaking of chiral symmetry are still not completely understood and under extensive discussion. Analytical calculations are limited, because in the low-energy regime where quarks are confined, application of perturbation theory is restricted due to the large gluon coupling. A powerful tool to investigate numerically and analytically the non-perturbative region is provided by the lattice formulation of QCD. From Monte Carlo simulations of lattice QCD we know that chiral symmetry is restored above a critical temperature. As the chiral condensate is connected to the spectral density of the Dirac operator via the Banks-Casher relation, the QCD Dirac spectrum is an interesting object for detailed studies. In search for an analytical expression of the infrared limit of the Dirac spectrum it has been realized that chiral random-matrix theory (chRMT) is a suitable tool to compare with the distribution and the correlations of the small Dirac eigenvalues. Further, it has been shown that the correlations of eigenvalues on the scale of mean level spacings are universal for complex physical systems and are given by random-matrix theory (Rm). This has been formulated as the Baghouse-Giannoni-Schmit conjecture which states that spectral correlations of a classically chaotic system are given by RMT on the quantum level. The aim of this work is to analyze the relationship between chiral phase transitions and chaos to order transitions in quantum field theories. We study the eigenvalues of the Dirac operator for Quantum Electrodynamics (QED) with compact gauge group U(1) on the lattice. This theory shows chiral symmetry breaking and confinement in the strong coupling region. Although being

A stochastic method for computing hadronic matrix elements

Energy Technology Data Exchange (ETDEWEB)

Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus). Computational-based Science and Technology Research Center; Dinter, Simon; Drach, Vincent [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Jansen, Karl [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Hadjiyiannakou, Kyriakos [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Renner, Dru B. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Collaboration: European Twisted Mass Collaboration

2013-02-15

We present a stochastic method for the calculation of baryon three-point functions that is more versatile compared to the typically used sequential method. We analyze the scaling of the error of the stochastically evaluated three-point function with the lattice volume and find a favorable signal-to-noise ratio suggesting that our stochastic method can be used efficiently at large volumes to compute hadronic matrix elements.

Low Complexity Precoder and Receiver Design for Massive MIMO Systems: A Large System Analysis using Random Matrix Theory

KAUST Repository

Sifaou, Houssem

2016-01-01

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

Response Matrix Method Development Program at Savannah River Laboratory

International Nuclear Information System (INIS)

Sicilian, J.M.

1976-01-01

The Response Matrix Method Development Program at Savannah River Laboratory (SRL) has concentrated on the development of an effective system of computer codes for the analysis of Savannah River Plant (SRP) reactors. The most significant contribution of this program to date has been the verification of the accuracy of diffusion theory codes as used for routine analysis of SRP reactor operation. This paper documents the two steps carried out in achieving this verification: confirmation of the accuracy of the response matrix technique through comparison with experiment and Monte Carlo calculations; and establishment of agreement between diffusion theory and response matrix codes in situations which realistically approximate actual operating conditions

Optimization of the Dutch Matrix Test by Random Selection of Sentences From a Preselected Subset

Directory of Open Access Journals (Sweden)

Rolph Houben

2015-04-01

Full Text Available Matrix tests are available for speech recognition testing in many languages. For an accurate measurement, a steep psychometric function of the speech materials is required. For existing tests, it would be beneficial if it were possible to further optimize the available materials by increasing the function’s steepness. The objective is to show if the steepness of the psychometric function of an existing matrix test can be increased by selecting a homogeneous subset of recordings with the steepest sentence-based psychometric functions. We took data from a previous multicenter evaluation of the Dutch matrix test (45 normal-hearing listeners. Based on half of the data set, first the sentences (140 out of 311 with a similar speech reception threshold and with the steepest psychometric function (≥9.7%/dB were selected. Subsequently, the steepness of the psychometric function for this selection was calculated from the remaining (unused second half of the data set. The calculation showed that the slope increased from 10.2%/dB to 13.7%/dB. The resulting subset did not allow the construction of enough balanced test lists. Therefore, the measurement procedure was changed to randomly select the sentences during testing. Random selection may interfere with a representative occurrence of phonemes. However, in our material, the median phonemic occurrence remained close to that of the original test. This finding indicates that phonemic occurrence is not a critical factor. The work highlights the possibility that existing speech tests might be improved by selecting sentences with a steep psychometric function.

Simulation of quantum systems with random walks: A new algorithm for charged systems

International Nuclear Information System (INIS)

Ceperley, D.

1983-01-01

Random walks with branching have been used to calculate exact properties of the ground state of quantum many-body systems. In this paper, a more general Green's function identity is derived which relates the potential energy, a trial wavefunction, and a trial density matrix to the rules of a branched random walk. It is shown that an efficient algorithm requires a good trial wavefunction, a good trial density matrix, and a good sampling of this density matrix. An accurate density matrix is constructed for Coulomb systems using the path integral formula. The random walks from this new algorithm diffuse through phase space an order of magnitude faster than the previous Green's Function Monte Carlo method. In contrast to the simple diffusion Monte Carlo algorithm, it is exact method. Representative results are presented for several molecules

Iterative approach as alternative to S-matrix in modal methods

Science.gov (United States)

Semenikhin, Igor; Zanuccoli, Mauro

2014-12-01

The continuously increasing complexity of opto-electronic devices and the rising demands of simulation accuracy lead to the need of solving very large systems of linear equations making iterative methods promising and attractive from the computational point of view with respect to direct methods. In particular, iterative approach potentially enables the reduction of required computational time to solve Maxwell's equations by Eigenmode Expansion algorithms. Regardless of the particular eigenmodes finding method used, the expansion coefficients are computed as a rule by scattering matrix (S-matrix) approach or similar techniques requiring order of M3 operations. In this work we consider alternatives to the S-matrix technique which are based on pure iterative or mixed direct-iterative approaches. The possibility to diminish the impact of M3 -order calculations to overall time and in some cases even to reduce the number of arithmetic operations to M2 by applying iterative techniques are discussed. Numerical results are illustrated to discuss validity and potentiality of the proposed approaches.

Characteristics of quantum open systems: free random variables approach

International Nuclear Information System (INIS)

Gudowska-Nowak, E.; Papp, G.; Brickmann, J.

1998-01-01

Random Matrix Theory provides an interesting tool for modelling a number of phenomena where noises (fluctuations) play a prominent role. Various applications range from the theory of mesoscopic systems in nuclear and atomic physics to biophysical models, like Hopfield-type models of neural networks and protein folding. Random Matrix Theory is also used to study dissipative systems with broken time-reversal invariance providing a setup for analysis of dynamic processes in condensed, disordered media. In the paper we use the Random Matrix Theory (RMT) within the formalism of Free Random Variables (alias Blue's functions), which allows to characterize spectral properties of non-Hermitean ''Hamiltonians''. The relevance of using the Blue's function method is discussed in connection with application of non-Hermitean operators in various problems of physical chemistry. (author)

Introducing two Random Forest based methods for cloud detection in remote sensing images

Science.gov (United States)

Ghasemian, Nafiseh; Akhoondzadeh, Mehdi

2018-07-01

Cloud detection is a necessary phase in satellite images processing to retrieve the atmospheric and lithospheric parameters. Currently, some cloud detection methods based on Random Forest (RF) model have been proposed but they do not consider both spectral and textural characteristics of the image. Furthermore, they have not been tested in the presence of snow/ice. In this paper, we introduce two RF based algorithms, Feature Level Fusion Random Forest (FLFRF) and Decision Level Fusion Random Forest (DLFRF) to incorporate visible, infrared (IR) and thermal spectral and textural features (FLFRF) including Gray Level Co-occurrence Matrix (GLCM) and Robust Extended Local Binary Pattern (RELBP_CI) or visible, IR and thermal classifiers (DLFRF) for highly accurate cloud detection on remote sensing images. FLFRF first fuses visible, IR and thermal features. Thereafter, it uses the RF model to classify pixels to cloud, snow/ice and background or thick cloud, thin cloud and background. DLFRF considers visible, IR and thermal features (both spectral and textural) separately and inserts each set of features to RF model. Then, it holds vote matrix of each run of the model. Finally, it fuses the classifiers using the majority vote method. To demonstrate the effectiveness of the proposed algorithms, 10 Terra MODIS and 15 Landsat 8 OLI/TIRS images with different spatial resolutions are used in this paper. Quantitative analyses are based on manually selected ground truth data. Results show that after adding RELBP_CI to input feature set cloud detection accuracy improves. Also, the average cloud kappa values of FLFRF and DLFRF on MODIS images (1 and 0.99) are higher than other machine learning methods, Linear Discriminate Analysis (LDA), Classification And Regression Tree (CART), K Nearest Neighbor (KNN) and Support Vector Machine (SVM) (0.96). The average snow/ice kappa values of FLFRF and DLFRF on MODIS images (1 and 0.85) are higher than other traditional methods. The

A New Method of Creating Technology/Function Matrix for Systematic Innovation without Expert

Directory of Open Access Journals (Sweden)

Tien-Yuan Cheng

2012-02-01

Full Text Available The technology/function matrix is comprised by specific technologies and functions, and through the technology/function matrix we can known what the technologies with functions have opportunities for innovation of product or technology. However, the technology/function matrix is very difficult to create, because the patents need to be read, analyzed and categorized into the technology/function matrix always more than hundreds or thousands. In this research, I propose a method to create a technology/function matrix just need to execute patent search without reading and analyzing patents. Through the proposed method anyone can create a technology/function matrix in a short time without experts’ help even if there are thousands of thousands of patents need to be read and analyzed.

The mesoscopic conductance of disordered rings, its random matrix theory and the generalized variable range hopping picture

International Nuclear Information System (INIS)

Stotland, Alexander; Peer, Tal; Cohen, Doron; Budoyo, Rangga; Kottos, Tsampikos

2008-01-01

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)

Matrix completion by deep matrix factorization.

Science.gov (United States)

Fan, Jicong; Cheng, Jieyu

2018-02-01

Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations. In this paper, a novel method called deep matrix factorization (DMF) is proposed for nonlinear matrix completion. Different from conventional matrix completion methods that are based on linear latent variable models, DMF is on the basis of a nonlinear latent variable model. DMF is formulated as a deep-structure neural network, in which the inputs are the low-dimensional unknown latent variables and the outputs are the partially observed variables. In DMF, the inputs and the parameters of the multilayer neural network are simultaneously optimized to minimize the reconstruction errors for the observed entries. Then the missing entries can be readily recovered by propagating the latent variables to the output layer. DMF is compared with state-of-the-art methods of linear and nonlinear matrix completion in the tasks of toy matrix completion, image inpainting and collaborative filtering. The experimental results verify that DMF is able to provide higher matrix completion accuracy than existing methods do and DMF is applicable to large matrices. Copyright © 2017 Elsevier Ltd. All rights reserved.

Nucleon matrix elements using the variational method in lattice QCD

International Nuclear Information System (INIS)

Dragos, J.; Kamleh, W.; Leinweber, D.B.; Zanotti, J.M.; Rakow, P.E.L.; Young, R.D.; Adelaide Univ., SA

2016-06-01

The extraction of hadron matrix elements in lattice QCD using the standard two- and threepoint correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current g_A, the scalar current g_S and the quark momentum fraction left angle x right angle of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.

Random matrix theory and higher genus integrability: the quantum chiral Potts model

International Nuclear Information System (INIS)

Angles d'Auriac, J.Ch.; Maillard, J.M.; Viallet, C.M.

2002-01-01

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)

A simplified method for random vibration analysis of structures with random parameters

International Nuclear Information System (INIS)

Ghienne, Martin; Blanzé, Claude

2016-01-01

Piezoelectric patches with adapted electrical circuits or viscoelastic dissipative materials are two solutions particularly adapted to reduce vibration of light structures. To accurately design these solutions, it is necessary to describe precisely the dynamical behaviour of the structure. It may quickly become computationally intensive to describe robustly this behaviour for a structure with nonlinear phenomena, such as contact or friction for bolted structures, and uncertain variations of its parameters. The aim of this work is to propose a non-intrusive reduced stochastic method to characterize robustly the vibrational response of a structure with random parameters. Our goal is to characterize the eigenspace of linear systems with dynamic properties considered as random variables. This method is based on a separation of random aspects from deterministic aspects and allows us to estimate the first central moments of each random eigenfrequency with a single deterministic finite elements computation. The method is applied to a frame with several Young's moduli modeled as random variables. This example could be expanded to a bolted structure including piezoelectric devices. The method needs to be enhanced when random eigenvalues are closely spaced. An indicator with no additional computational cost is proposed to characterize the ’’proximity” of two random eigenvalues. (paper)

Study on the Dynamics of Laser Gyro Strapdown Inertial Measurement Unit System Based on Transfer Matrix Method for Multibody System

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.

Marine wind data presentation using wind transition matrix

Digital Repository Service at National Institute of Oceanography (India)

Mascarenhas, A.J.; Gouveia, A.D.; Desai, R.G.P.

One of the methods to simulate the random wind behaviour through time is to use historical wind data presented in the form of wind transition matrix. Here it is assumed that, the probability that the wind will shift from one direction to another...

A New Pseudoinverse Matrix Method For Balancing Chemical Equations And Their Stability

International Nuclear Information System (INIS)

Risteski, Ice B.

2008-01-01

In this work is given a new pseudoniverse matrix method for balancing chemical equations. Here offered method is founded on virtue of the solution of a Diophantine matrix equation by using of a Moore-Penrose pseudoinverse matrix. The method has been tested on several typical chemical equations and found to be very successful for the all equations in our extensive balancing research. This method, which works successfully without any limitations, also has the capability to determine the feasibility of a new chemical reaction, and if it is feasible, then it will balance the equation. Chemical equations treated here possess atoms with fractional oxidation numbers. Also, in the present work are introduced necessary and sufficient criteria for stability of chemical equations over stability of their extended matrices

Chosen interval methods for solving linear interval systems with special type of matrix

Science.gov (United States)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

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 ...

On a novel matrix method for three-dimensional photoelasticity

International Nuclear Information System (INIS)

Theocaris, P.S.; Gdoutos, E.E.

1978-01-01

A non-destructive method for the photoelastic determination of three-dimensional stress distributions, based on the Mueller and Jones calculi, is developed. The differential equations satisfied by the Stokes and Jones vectors, when a polarized light beam passes through a photoelastic model, presenting rotation of the secondary principal stress directions, are established in matrix form. The Peano-Baker method is used for the solution of these differential equations in a matrix series form, establishing the elements of the Mueller and Jones matrices of the photoelastic model. These matrices are experimentally determined by using different wavelengths in conjunction with Jones' 'equivalence theorem'. The Neumann equations are immediately deduced from the above-mentioned differential equations. (orig.) [de

On the efficiency of a randomized mirror descent algorithm in online optimization problems

Science.gov (United States)

Gasnikov, A. V.; Nesterov, Yu. E.; Spokoiny, V. G.

2015-04-01

A randomized online version of the mirror descent method is proposed. It differs from the existing versions by the randomization method. Randomization is performed at the stage of the projection of a subgradient of the function being optimized onto the unit simplex rather than at the stage of the computation of a subgradient, which is common practice. As a result, a componentwise subgradient descent with a randomly chosen component is obtained, which admits an online interpretation. This observation, for example, has made it possible to uniformly interpret results on weighting expert decisions and propose the most efficient method for searching for an equilibrium in a zero-sum two-person matrix game with sparse matrix.

Nonlinear response matrix methods for radiative transfer

International Nuclear Information System (INIS)

Miller, W.F. Jr.; Lewis, E.E.

1987-01-01

A nonlinear response matrix formalism is presented for the solution of time-dependent radiative transfer problems. The essential feature of the method is that within each computational cell the temperature is calculated in response to the incoming photons from all frequency groups. Thus the updating of the temperature distribution is placed within the iterative solution of the spaceangle transport problem, instead of being placed outside of it. The method is formulated for both grey and multifrequency problems and applied in slab geometry. The method is compared to the more conventional source iteration technique. 7 refs., 1 fig., 4 tabs

Measuring methods of matrix diffusion

International Nuclear Information System (INIS)

Muurinen, A.; Valkiainen, M.

1988-03-01

In Finland the spent nuclear fuel is planned to be disposed of at large depths in crystalline bedrock. The radionuclides which are dissolved in the groundwater may be able to diffuse into the micropores of the porous rock matrix and thus be withdrawn from the flowing water in the fractures. This phenomenon is called matrix diffusion. A review over matrix diffusion is presented in the study. The main interest is directed to the diffusion of non-sorbing species. The review covers diffusion experiments and measurements of porosity, pore size, specific surface area and water permeability

An integrating factor matrix method to find first integrals

International Nuclear Information System (INIS)

Saputra, K V I; Quispel, G R W; Van Veen, L

2010-01-01

In this paper we develop an integrating factor matrix method to derive conditions for the existence of first integrals. We use this novel method to obtain first integrals, along with the conditions for their existence, for two- and three-dimensional Lotka-Volterra systems with constant terms. The results are compared to previous results obtained by other methods.

J-matrix method of scattering in one dimension: The nonrelativistic theory

International Nuclear Information System (INIS)

Alhaidari, A.D.; Bahlouli, H.; Abdelmonem, M.S.

2009-01-01

We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.

A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix

KAUST Repository

Hu, Zongliang; Dong, Kai; Dai, Wenlin; Tong, Tiejun

2017-01-01

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

KAUST Repository

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.

A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix.

Science.gov (United States)

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.

Random matrix theory for transition strengths: Applications and open questions

Science.gov (United States)

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.

Improvement of the Convergence of the Invariant Imbedding T-Matrix Method

Science.gov (United States)

Zhai, S.; Panetta, R. L.; Yang, P.

2017-12-01

The invariant imbedding T-matrix method (IITM) is based on an electromagnetic volume integral equation to compute the T-matrix of an arbitrary scattering particle. A free-space Green's function is chosen as the integral kernel and thus each source point is placed in an imaginary vacuum spherical shell extending from the center to that source point. The final T-matrix (of the largest circumscribing sphere) is obtained through an iterative relation that, layer by layer, computes the T-matrix from the particle center to the outermost shell. On each spherical shell surface, an integration of the product of the refractive index 𝜀(𝜃, 𝜑) and vector spherical harmonics must be performed, resulting in the so-called U-matrix, which directly leads to the T-matrix on the spherical surface. Our observations indicate that the matrix size and sparseness are determined by the particular refractive index function 𝜀(𝜃, 𝜑). If 𝜀(𝜃, 𝜑) is an analytic function on the surface, then the matrix elements resulting from the integration decay rapidly, leading to sparse matrix; if 𝜀(𝜃, 𝜑) is not (for example, contains jump discontinuities), then the matrix elements decay slowly, leading to a large dense matrix. The intersection between an irregular scatterer and each spherical shell can leave jump discontinuities in 𝜀(𝜃, 𝜑) distributed over the shell surface. The aforementioned feature is analogous to the Gibbs phenomenon appearing in the orthogonal expansion of non-smooth functions with Hermitian eigenfunctions (complex exponential, Legendre, Bessel,...) where poor convergence speed is a direct consequence of the slow decay rate of the expansion coefficients. Various methods have been developed to deal with this slow convergence in the presence of discontinuities. Among the different approaches the most practical one may be a spectral filter: a filter is applied on the

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.

Independent random sampling methods

CERN Document Server

Martino, Luca; Míguez, Joaquín

2018-01-01

This book systematically addresses the design and analysis of efficient techniques for independent random sampling. Both general-purpose approaches, which can be used to generate samples from arbitrary probability distributions, and tailored techniques, designed to efficiently address common real-world practical problems, are introduced and discussed in detail. In turn, the monograph presents fundamental results and methodologies in the field, elaborating and developing them into the latest techniques. The theory and methods are illustrated with a varied collection of examples, which are discussed in detail in the text and supplemented with ready-to-run computer code. The main problem addressed in the book is how to generate independent random samples from an arbitrary probability distribution with the weakest possible constraints or assumptions in a form suitable for practical implementation. The authors review the fundamental results and methods in the field, address the latest methods, and emphasize the li...

Control method for multi-input multi-output non-Gaussian random vibration test with cross spectra consideration

Directory of Open Access Journals (Sweden)

Ronghui ZHENG

2017-12-01

Full Text Available A control method for Multi-Input Multi-Output (MIMO non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multi-output kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well. Keywords: Cross spectra, Kurtosis control, Multi-input multi-output, Non-Gaussian, Random vibration test

Decomposition of spectra in EPR dosimetry using the matrix method

International Nuclear Information System (INIS)

Sholom, S.V.; Chumak, V.V.

2003-01-01

The matrix method of EPR spectra decomposition is developed and adapted for routine application in retrospective EPR dosimetry with teeth. According to this method, the initial EPR spectra are decomposed (using methods of matrix algebra) into several reference components (reference matrices) that are specific for each material. Proposed procedure has been tested on the example of tooth enamel. Reference spectra were a spectrum of an empty sample tube and three standard signals of enamel (two at g=2.0045, both for the native signal and one at g perpendicular =2.0018, g parallel =1.9973 for the dosimetric signal). Values of dosimetric signals obtained using the given method have been compared with data obtained by manual manipulation of spectra, and good coincidence was observed. This allows considering the proposed method as potent for application in routine EPR dosimetry

The time-dependent density matrix renormalisation group method

Science.gov (United States)

Ma, Haibo; Luo, Zhen; Yao, Yao

2018-04-01

Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule.

Standard test method for translaminar fracture toughness of laminated and pultruded polymer matrix composite materials

CERN Document Server

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...

Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles

International Nuclear Information System (INIS)

Forrester, P.J.; Witte, N.S.

2000-01-01

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form a(s) e-b(s) for a simply related to a Painleve transcendent and b its anti-derivative. A formula consisting of the sum of two such terms is given for the symplectic case (Hermitian matrices with real quaternion elements)

On matrix realization of random surfaces

International Nuclear Information System (INIS)

Sasaki, Misao; Suzuki, Hiroshi.

1990-12-01

The large N one-matrix model with a potential, V(φ) = φ 2 /2 + g 4 φ 4 /N + g 6 φ 6 /N 2 is carefully investigated using the orthogonal polynomial method. We present a numerical method to solve the recurrence relation and evaluate the recursion coefficients r k (k = 1,2,3,...) of the orthogonal polynomials at large N. We find that for g 6 /g 4 2 > 1/2 there is no m = 2 solution which can be expressed as a smooth function of k/N in the limit N → ∞. This means that the assumption of smoothness of r k at N → ∞ near the critical point, which was essential to derive the string susceptibility and the string equation, is broken even at the tree level of the genus expansion by adding the φ 6 -term. We have also observed the free energy around the (expected) critical point to confirm that the system does not have the desired criticality as pure gravity. Our (discouraging) results for m = 2 are complementary to previous analyses by the saddle point method. On the other hand, for the case m = 3 (g 6 /g 4 2 = 4/5), we find a well-behaved solution which coincides with the result by Brezin et al.. To strengthen the validity of our numerical scheme, we present in appendix a non-perturbative solution for m = 1 which obeys the so-called type-II string equation proposed by Demeterfi et al.. (author)

A collocation finite element method with prior matrix condensation

International Nuclear Information System (INIS)

Sutcliffe, W.J.

1977-01-01

For thin shells with general loading, sixteen degrees of freedom have been used for a previous finite element solution procedure using a Collocation method instead of the usual variational based procedures. Although the number of elements required was relatively small, nevertheless the final matrix for the simultaneous solution of all unknowns could become large for a complex compound structure. The purpose of the present paper is to demonstrate a method of reducing the final matrix size, so allowing solution for large structures with comparatively small computer storage requirements while retaining the accuracy given by high order displacement functions. Collocation points, a number are equilibrium conditions which must be satisfied independently of the overall compatibility of forces and deflections for a complete structure. (Auth.)

Convergence analysis of modulus-based matrix splitting iterative methods for implicit complementarity problems.

Science.gov (United States)

Wang, An; Cao, Yang; Shi, Quan

2018-01-01

In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra Appl. 23:629-641, 2016). New convergence conditions are presented when the system matrix is a positive-definite matrix and an [Formula: see text]-matrix, respectively.

Comprehensive T-Matrix Reference Database: A 2012 - 2013 Update

Science.gov (United States)

Mishchenko, Michael I.; Videen, Gorden; Khlebtsov, Nikolai G.; Wriedt, Thomas

2013-01-01

The T-matrix method is one of the most versatile, efficient, and accurate theoretical techniques widely used for numerically exact computer calculations of electromagnetic scattering by single and composite particles, discrete random media, and particles imbedded in complex environments. This paper presents the fifth update to the comprehensive database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2012. It also lists several earlier publications not incorporated in the original database, including Peter Waterman's reports from the 1960s illustrating the history of the T-matrix approach and demonstrating that John Fikioris and Peter Waterman were the true pioneers of the multi-sphere method otherwise known as the generalized Lorenz - Mie theory.

Random matrix theory filters and currency portfolio optimisation

Science.gov (United States)

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.

Removal of Stationary Sinusoidal Noise from Random Vibration Signals.

Energy Technology Data Exchange (ETDEWEB)

Johnson, Brian; Cap, Jerome S.

2018-02-01

In random vibration environments, sinusoidal line noise may appear in the vibration signal and can affect analysis of the resulting data. We studied two methods which remove stationary sine tones from random noise: a matrix inversion algorithm and a chirp-z transform algorithm. In addition, we developed new methods to determine the frequency of the tonal noise. The results show that both of the removal methods can eliminate sine tones in prefabricated random vibration data when the sine-to-random ratio is at least 0.25. For smaller ratios down to 0.02 only the matrix inversion technique can remove the tones, but the metrics to evaluate its effectiveness also degrade. We also found that using fast Fourier transforms best identified the tonal noise, and determined that band-pass-filtering the signals prior to the process improved sine removal. When applied to actual vibration test data, the methods were not as effective at removing harmonic tones, which we believe to be a result of mixed-phase sinusoidal noise.

A discrete ordinate response matrix method for massively parallel computers

International Nuclear Information System (INIS)

Hanebutte, U.R.; Lewis, E.E.

1991-01-01

A discrete ordinate response matrix method is formulated for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices which result from the diamond-differenced equations are utilized in a factored form which minimizes memory requirements and significantly reduces the required number of algorithm utilizes massive parallelism by assigning each spatial node to a processor. The algorithm is accelerated effectively by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red/black iterations. The method has been implemented on a 16k Connection Machine-2, and S 8 and S 16 solutions have been obtained for fixed-source benchmark problems in X--Y geometry

Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition

OpenAIRE

Canali, C. M.

1995-01-01

We consider a family of random matrix ensembles (RME) invariant under similarity transformations and described by the probability density $P({\\bf H})= \\exp[-{\\rm Tr}V({\\bf H})]$. Dyson's mean field theory (MFT) of the corresponding plasma model of eigenvalues is generalized to the case of weak confining potential, $V(\\epsilon)\\sim {A\\over 2}\\ln ^2(\\epsilon)$. The eigenvalue statistics derived from MFT are shown to deviate substantially from the classical Wigner-Dyson statistics when $A

Convergence Improvement of Response Matrix Method with Large Discontinuity Factors

International Nuclear Information System (INIS)

Yamamoto, Akio

2003-01-01

In the response matrix method, a numerical divergence problem has been reported when extremely small or large discontinuity factors are utilized in the calculations. In this paper, an alternative response matrix formulation to solve the divergence problem is discussed, and properties of iteration matrixes are investigated through eigenvalue analyses. In the conventional response matrix formulation, partial currents between adjacent nodes are assumed to be discontinuous, and outgoing partial currents are converted into incoming partial currents by the discontinuity factor matrix. Namely, the partial currents of the homogeneous system (i.e., homogeneous partial currents) are treated in the conventional response matrix formulation. In this approach, the spectral radius of an iteration matrix for the partial currents may exceed unity when an extremely small or large discontinuity factor is used. Contrary to this, an alternative response matrix formulation using heterogeneous partial currents is discussed in this paper. In the latter approach, partial currents are assumed to be continuous between adjacent nodes, and discontinuity factors are directly considered in the coefficients of a response matrix. From the eigenvalue analysis of the iteration matrix for the one-group, one-dimensional problem, the spectral radius for the heterogeneous partial current formulation does not exceed unity even if an extremely small or large discontinuity factor is used in the calculation; numerical stability of the alternative formulation is superior to the conventional one. The numerical stability of the heterogeneous partial current formulation is also confirmed by the two-dimensional light water reactor core analysis. Since the heterogeneous partial current formulation does not require any approximation, the converged solution exactly reproduces the reference solution when the discontinuity factors are directly derived from the reference calculation

A matrix-inversion method for gamma-source mapping from gamma-count data - 59082

International Nuclear Information System (INIS)

Bull, Richard K.; Adsley, Ian; Burgess, Claire

2012-01-01

Gamma ray counting is often used to survey the distribution of active waste material in various locations. Ideally the output from such surveys would be a map of the activity of the waste. In this paper a simple matrix-inversion method is presented. This allows an array of gamma-count data to be converted to an array of source activities. For each survey area the response matrix is computed using the gamma-shielding code Microshield [1]. This matrix links the activity array to the count array. The activity array is then obtained via matrix inversion. The method was tested on artificially-created arrays of count-data onto which statistical noise had been added. The method was able to reproduce, quite faithfully, the original activity distribution used to generate the dataset. The method has been applied to a number of practical cases, including the distribution of activated objects in a hot cell and to activated Nimonic springs amongst fuel-element debris in vaults at a nuclear plant. (authors)

Normalization sum rule and spontaneous breaking of U(N) invariance in random matrix ensembles

International Nuclear Information System (INIS)

Canali, C.M.; Kravtsov, V.E.

1995-03-01

It is shown that the two-level correlation function R(s,s') in the invariant random matrix ensembles (RME) with soft confinement exhibits a ''ghost peak'' at s approx. -s'. This lifts the sum rule prohibition for the level number variance to have a Poisson-like term var(n) = ηn that is typical of RME with broken U(N) symmetry. Thus we conclude that the U(N) invariance is broken spontaneously in the RME with soft confinement, η playing the role of an order-parameter. (author). 16 refs, 1 fig

NONLINEAR PLANT PIECEWISE-CONTINUOUS MODEL MATRIX PARAMETERS ESTIMATION

Directory of Open Access Journals (Sweden)

Roman L. Leibov

2017-09-01

Full Text Available This paper presents a nonlinear plant piecewise-continuous model matrix parameters estimation technique using nonlinear model time responses and random search method. One of piecewise-continuous model application areas is defined. The results of proposed approach application for aircraft turbofan engine piecewisecontinuous model formation are presented

Algebraic methods in random matrices and enumerative geometry

CERN Document Server

Eynard, Bertrand

2008-01-01

We review the method of symplectic invariants recently introduced to solve matrix models loop equations, and further extended beyond the context of matrix models. For any given spectral curve, one defined a sequence of differential forms, and a sequence of complex numbers Fg . We recall the definition of the invariants Fg, and we explain their main properties, in particular symplectic invariance, integrability, modularity,... Then, we give several example of applications, in particular matrix models, enumeration of discrete surfaces (maps), algebraic geometry and topological strings, non-intersecting brownian motions,...

Non-equilibrium random matrix theory. Transition probabilities

International Nuclear Information System (INIS)

Pedro, Francisco Gil; Westphal, Alexander

2016-06-01

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.

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.

On efficient randomized algorithms for finding the PageRank vector

Science.gov (United States)

Gasnikov, A. V.; Dmitriev, D. Yu.

2015-03-01

Two randomized methods are considered for finding the PageRank vector; in other words, the solution of the system p T = p T P with a stochastic n × n matrix P, where n ˜ 107-109, is sought (in the class of probability distributions) with accuracy ɛ: ɛ ≫ n -1. Thus, the possibility of brute-force multiplication of P by the column is ruled out in the case of dense objects. The first method is based on the idea of Markov chain Monte Carlo algorithms. This approach is efficient when the iterative process p {/t+1 T} = p {/t T} P quickly reaches a steady state. Additionally, it takes into account another specific feature of P, namely, the nonzero off-diagonal elements of P are equal in rows (this property is used to organize a random walk over the graph with the matrix P). Based on modern concentration-of-measure inequalities, new bounds for the running time of this method are presented that take into account the specific features of P. In the second method, the search for a ranking vector is reduced to finding the equilibrium in the antagonistic matrix game where S n (1) is a unit simplex in ℝ n and I is the identity matrix. The arising problem is solved by applying a slightly modified Grigoriadis-Khachiyan algorithm (1995). This technique, like the Nazin-Polyak method (2009), is a randomized version of Nemirovski's mirror descent method. The difference is that randomization in the Grigoriadis-Khachiyan algorithm is used when the gradient is projected onto the simplex rather than when the stochastic gradient is computed. For sparse matrices P, the method proposed yields noticeably better results.

Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Vector case

International Nuclear Information System (INIS)

Doicu, A.; Trautmann, T.

2009-01-01

The paper is devoted to the extension of the matrix-exponential formalism for the scalar radiative transfer to the vector case. Using basic results of the theory of matrix-exponential functions we provide a compact and versatile formulation of the vector radiative transfer. As in the scalar case, we operate with the concept of the layer equation incorporating the level values of the Stokes vector. The matrix exponentials which enter in the expression of the layer equation are computed by using the matrix eigenvalue method and the Pade approximation. A discussion of the computational efficiency of the proposed method for both an aerosol-loaded atmosphere as well as a cloudy atmosphere is also provided

Proper comparison among methods using a confusion matrix

CSIR Research Space (South Africa)

Salmon

2015-07-01

Full Text Available -1 IGARSS 2015, Milan, Italy, 26-31 July 2015 Proper comparison among methods using a confusion matrix 1,2 B.P. Salmon, 2,3 W. Kleynhans, 2,3 C.P. Schwegmann and 1J.C. Olivier 1School of Engineering and ICT, University of Tasmania, Australia 2...

A nonlinearity compensation method for a matrix converter drive

DEFF Research Database (Denmark)

Lee, Kyo-Beum; Blaabjerg, Frede

2005-01-01

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...... using a 3-kW matrix converter system without a speed sensor. Experimental results show the proposed method provides good compensating characteristics....

Matrix-exponential distributions in applied probability

CERN Document Server

Bladt, Mogens

2017-01-01

This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution is obtained through replacing the intensity parameter in an exponential distribution by a matrix. The ME distributions can also be identified as the class of non-negative distributions with rational Laplace transforms. If the matrix has the structure of a sub-intensity matrix for a Markov jump process we obtain a PH distribution which allows for nice probabilistic interpretations facilitating the derivation of exact solutions and closed form formulas. The full potential of ME and PH unfolds in their use in stochastic modelling. Several chapters on generic applications, like renewal theory, random walks and regenerative processes, are included together with some specific examples from queueing theory and insurance risk. We emphasize our intention towards applications by including an extensive treatment on statistical methods for PH distribu...

Upscaling solute transport in naturally fractured porous media with the continuous time random walk method

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.

A Novel Measurement Matrix Optimization Approach for Hyperspectral Unmixing

Directory of Open Access Journals (Sweden)

Su Xu

2017-01-01

Full Text Available Each pixel in the hyperspectral unmixing process is modeled as a linear combination of endmembers, which can be expressed in the form of linear combinations of a number of pure spectral signatures that are known in advance. However, the limitation of Gaussian random variables on its computational complexity or sparsity affects the efficiency and accuracy. This paper proposes a novel approach for the optimization of measurement matrix in compressive sensing (CS theory for hyperspectral unmixing. Firstly, a new Toeplitz-structured chaotic measurement matrix (TSCMM is formed by pseudo-random chaotic elements, which can be implemented by a simple hardware; secondly, rank revealing QR factorization with eigenvalue decomposition is presented to speed up the measurement time; finally, orthogonal gradient descent method for measurement matrix optimization is used to achieve optimal incoherence. Experimental results demonstrate that the proposed approach can lead to better CS reconstruction performance with low extra computational cost in hyperspectral unmixing.

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

Science.gov (United States)

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

2017-03-02

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

A Predictive-Control-Based Over-Modulation Method for Conventional Matrix Converters

DEFF Research Database (Denmark)

Zhang, Guanguan; Yang, Jian; Sun, Yao

2018-01-01

To increase the voltage transfer ratio of the matrix converter and improve the input/output current performance simultaneously, an over-modulation method based on predictive control is proposed in this paper, where the weighting factor is selected by an automatic adjusting mechanism, which is able...... to further enhance the system performance promptly. This method has advantages like the maximum voltage transfer ratio can reach 0.987 in the experiments; the total harmonic distortion of the input and output current are reduced, and the losses in the matrix converter are decreased. Moreover, the specific...

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

Protein structure estimation from NMR data by matrix completion.

Science.gov (United States)

Li, Zhicheng; Li, Yang; Lei, Qiang; Zhao, Qing

2017-09-01

Knowledge of protein structures is very important to understand their corresponding physical and chemical properties. Nuclear Magnetic Resonance (NMR) spectroscopy is one of the main methods to measure protein structure. In this paper, we propose a two-stage approach to calculate the structure of a protein from a highly incomplete distance matrix, where most data are obtained from NMR. We first randomly "guess" a small part of unobservable distances by utilizing the triangle inequality, which is crucial for the second stage. Then we use matrix completion to calculate the protein structure from the obtained incomplete distance matrix. We apply the accelerated proximal gradient algorithm to solve the corresponding optimization problem. Furthermore, the recovery error of our method is analyzed, and its efficiency is demonstrated by several practical examples.

Generating quantitative models describing the sequence specificity of biological processes with the stabilized matrix method

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.

Analytical techniques for instrument design - Matrix methods

International Nuclear Information System (INIS)

Robinson, R.A.

1997-01-01

The authors take the traditional Cooper-Nathans approach, as has been applied for many years for steady-state triple-axis spectrometers, and consider its generalization to other inelastic scattering spectrometers. This involves a number of simple manipulations of exponentials of quadratic forms. In particular, they discuss a toolbox of matrix manipulations that can be performed on the 6-dimensional Cooper-Nathans matrix. They show how these tools can be combined to solve a number of important problems, within the narrow-band limit and the gaussian approximation. They will argue that a generalized program that can handle multiple different spectrometers could (and should) be written in parallel to the Monte-Carlo packages that are becoming available. They 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

Fractal fluctuations and quantum-like chaos in the brain by analysis of variability of brain waves: A new method based on a fractal variance function and random matrix theory: A link with El Naschie fractal Cantorian space-time and V. Weiss and H. Weiss golden ratio in brain

International Nuclear Information System (INIS)

Conte, Elio; Khrennikov, Andrei; Federici, Antonio; Zbilut, Joseph P.

2009-01-01

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.

On the density of eigenvalues of a random matrix; Concernant la densite des racines caracteristiques d'une matrice stochastique

Energy Technology Data Exchange (ETDEWEB)

Mehta, M. L. [Institute of Fundamental Research Bombay (India); Gaudin, M. [Commissariat a l' energie atomique et aux energies alternatives - CEA, Centre d' Etudes Nucleaires de Saclay, Gif-sur-Yvette (France)

1960-07-01

An exact expression for the density of eigenvalues of a random- matrix is derived. When the order of the matrix becomes infinite, it can be seen very directly that it goes over to Wigner's 'semi-circle law'. Reprint of a paper published in 'Nuclear Physics' 18, 1960, p. 420-427 [French] On deduit une expression precise pour la densite des racines caracteristiques d'une matrice stochastique. Quand l'ordre de la matrice devient infini, on peut voir facilement qu'elle obeit a la loi dite 'semi-circulaire' de Wigner. Reproduction d'un article publie dans 'Nuclear Physics' 18, 1960, p. 420-427.

A method simulating random magnetic field in interplanetary space by an autoregressive method

International Nuclear Information System (INIS)

Kato, Masahito; Sakai, Takasuke

1985-01-01

With an autoregressive method, we tried to generate the random noise fitting in with the power spectrum which can be analytically Fouriertransformed into an autocorrelation function. Although we can not directly compare our method with FFT by Owens (1978), we can only point out the following; FFT method should determine at first the number of data points N, or the total length to be generated and we cannot generate random data more than N. Because, beyond the NΔy, the generated data repeats the same pattern as below NΔy, where Δy = minimum interval for random noise. So if you want to change or increase N after generating the random noise, you should start the generation from the first step. The characteristic of the generated random number may depend upon the number of N, judging from the generating method. Once the prediction error filters are determined, our method can produce successively the random numbers, that is, we can possibly extend N to infinite without any effort. (author)

Money creation process in a random redistribution model

Science.gov (United States)

Chen, Siyan; Wang, Yougui; Li, Keqiang; Wu, Jinshan

2014-01-01

In this paper, the dynamical process of money creation in a random exchange model with debt is investigated. The money creation kinetics are analyzed by both the money-transfer matrix method and the diffusion method. From both approaches, we attain the same conclusion: the source of money creation in the case of random exchange is the agents with neither money nor debt. These analytical results are demonstrated by computer simulations.

Monte Carlo method for random surfaces

International Nuclear Information System (INIS)

Berg, B.

1985-01-01

Previously two of the authors proposed a Monte Carlo method for sampling statistical ensembles of random walks and surfaces with a Boltzmann probabilistic weight. In the present paper we work out the details for several models of random surfaces, defined on d-dimensional hypercubic lattices. (orig.)

Novel image analysis methods for quantification of in situ 3-D tendon cell and matrix strain.

Science.gov (United States)

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.

Random Numbers and Monte Carlo Methods

Science.gov (United States)

Scherer, Philipp O. J.

Many-body problems often involve the calculation of integrals of very high dimension which cannot be treated by standard methods. For the calculation of thermodynamic averages Monte Carlo methods are very useful which sample the integration volume at randomly chosen points. After summarizing some basic statistics, we discuss algorithms for the generation of pseudo-random numbers with given probability distribution which are essential for all Monte Carlo methods. We show how the efficiency of Monte Carlo integration can be improved by sampling preferentially the important configurations. Finally the famous Metropolis algorithm is applied to classical many-particle systems. Computer experiments visualize the central limit theorem and apply the Metropolis method to the traveling salesman problem.

The Effect of Matrix Method on Anxiety and Attitude Toward Methamphetamine and Crack Abuse in Males Referring to Addiction Treatment Centers in Tonkabon, Iran

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.

Comprehensive T-matrix Reference Database: A 2009-2011 Update

Science.gov (United States)

Zakharova, Nadezhda T.; Videen, G.; Khlebtsov, Nikolai G.

2012-01-01

The T-matrix method is one of the most versatile and efficient theoretical techniques widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper presents an update to the comprehensive database of peer-reviewed T-matrix publications compiled by us previously and includes the publications that appeared since 2009. It also lists several earlier publications not included in the original database.

Comprehensive T-Matrix Reference Database: A 2007-2009 Update

Science.gov (United States)

Mishchenko, Michael I.; Zakharova, Nadia T.; Videen, Gorden; Khlebtsov, Nikolai G.; Wriedt, Thomas

2010-01-01

The T-matrix method is among the most versatile, efficient, and widely used theoretical techniques for the numerically exact computation of electromagnetic scattering by homogeneous and composite particles, clusters of particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper presents an update to the comprehensive database of T-matrix publications compiled by us previously and includes the publications that appeared since 2007. It also lists several earlier publications not included in the original database.

Another method for a global fit of the Cabibbo-Kobayashi-Maskawa matrix

International Nuclear Information System (INIS)

Dita, Petre

2005-01-01

Recently we proposed a novel method for doing global fits on the entries of the Cabibbo-Kobayashi-Maskawa matrix. The new used ingredients were a clear relationship between the entries of the CKM matrix and the experimental data, as well as the use of the necessary and sufficient condition the data have to satisfy in order to find a unitary matrix compatible with them. This condition writes as -1 ≤ cosδ ≤1 where δ is the phase that accounts for CP violation. Numerical results are provided for the CKM matrix entries, the mixing angles between generations and all the angles of the standard unitarity triangle. (author)

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...... history interviews have advantages over other qualitative methods, and offers one alternative to the conventional survey tool....... 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...

The Dirac operator on a finite domain and the R-matrix method

International Nuclear Information System (INIS)

Grant, I P

2008-01-01

Relativistic effects in electron-atom collisions and photo-excitation and -ionization processes increase in importance as the atomic number of the target atom grows and spin-dependent effects increase. A relativistic treatment in which electron motion is described using the Dirac Hamiltonian is then desirable. A version of the popular nonrelativistic R-matrix package incorporating terms from the Breit-Pauli Hamiltonian has been used for modelling such processes for some years. The fully relativistic Dirac R-matrix method has been less popular, but is becoming increasingly relevant for applications to heavy ion targets, where the need to use relativistic wavefunctions is more obvious. The Dirac R-matrix method has been controversial ever since it was first proposed by Goertzel (1948 Phys. Rev. 73 1463-6), and it is therefore important to confirm that recent elaborate and costly applications of the method, such as, Badnell et al (2004 J. Phys. B: At. Mol. Phys. 37 4589) and Ballance and Griffin (2007 J. Phys. B: At. Mol. Opt. Phys. 40 247-58), rest on secure foundations. The first part of this paper analyses the structure of the two-point boundary-value problem for the Dirac operator on a finite domain, from which we construct a unified derivation of the Schroedinger (nonrelativistic) and Dirac (relativistic) R-matrix methods. Suggestions that the usual relativistic theory is not well founded are shown to be without foundation

A transfer-matrix method for spatially modulated structures

International Nuclear Information System (INIS)

Surda, A.

1991-03-01

A cluster transfer-matrix method convenient for calculation of spatially modulated structures of a wide class of lattice-gas models is developed. The method formulates the problem of calculation of the partition function in terms of non-linear mapping of effective multi-site fields. It is applied to a lattice-gas model qualitatively describing the system of oxygen atoms in the basal planes of high-temperature superconductors. The properties of an incommensurate structure occurring at intermediate temperatures are discussed in detail. (author). 21 refs, 15 figs

Application of unfolding transformation in the random matrix theory to analyze in vivo neuronal spike firing during awake and anesthetized conditions

Directory of Open Access Journals (Sweden)

Risako Kato

2018-03-01

Full Text Available General anesthetics decrease the frequency and density of spike firing. This effect makes it difficult to detect spike regularity. To overcome this problem, we developed a method utilizing the unfolding transformation which analyzes the energy level statistics in the random matrix theory. We regarded the energy axis as time axis of neuron spike and analyzed the time series of cortical neural firing in vivo. Unfolding transformation detected regularities of neural firing while changes in firing densities were associated with pentobarbital. We found that unfolding transformation enables us to compare firing regularity between awake and anesthetic conditions on a universal scale. Keywords: Unfolding transformation, Spike-timing, Regularity

Solution of the Multigroup-Diffusion equation by the response matrix method

International Nuclear Information System (INIS)

Oliveira, C.R.E.

1980-10-01

A preliminary analysis of the response matrix method is made, considering its application to the solution of the multigroup diffusion equations. The one-dimensional formulation is presented and used to test some flux expansions, seeking the application of the method to the two-dimensional problem. This formulation also solves the equations that arise from the integro-differential synthesis algorithm. The slow convergence of the power method, used to solve the eigenvalue problem, and its acceleration by means of the Chebyshev polynomial method, are also studied. An algorithm for the estimation of the dominance ratio is presented, based on the residues of two successive iteration vectors. This ratio, which is not known a priori, is fundamental for the efficiency of the method. Some numerical problems are solved, testing the 1D formulation of the response matrix method, its application to the synthesis algorithm and also, at the same time, the algorithm to accelerate the source problem. (Author) [pt

A pedagogical derivation of the matrix element method in particle physics data analysis

Science.gov (United States)

Sumowidagdo, Suharyo

2018-03-01

The matrix element method provides a direct connection between the underlying theory of particle physics processes and detector-level physical observables. I am presenting a pedagogically-oriented derivation of the matrix element method, drawing from elementary concepts in probability theory, statistics, and the process of experimental measurements. The level of treatment should be suitable for beginning research student in phenomenology and experimental high energy physics.

Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Scalar case

International Nuclear Information System (INIS)

Doicu, A.; Trautmann, T.

2009-01-01

We present a discrete-ordinate algorithm using the matrix-exponential solution for pseudo-spherical radiative transfer. Following the finite-element technique we introduce the concept of layer equation and formulate the discrete radiative transfer problem in terms of the level values of the radiance. The layer quantities are expressed by means of matrix exponentials, which are computed by using the matrix eigenvalue method and the Pade approximation. These solution methods lead to a compact and versatile formulation of the radiative transfer. Simulated nadir and limb radiances for an aerosol-loaded atmosphere and a cloudy atmosphere are presented along with a discussion of the model intercomparisons and timings

Modelling of packet traffic with matrix analytic methods

DEFF Research Database (Denmark)

Andersen, Allan T.

1995-01-01

BISDN network. The heuristic formula did not seem to yield substantially better results than already available approximations. Finally, some results for the finite capacity BMAP/G/1 queue have been obtained. The steady state probability vector of the embedded chain is found by a direct method where...... 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...

Graphene-Reinforced Aluminum Matrix Composites: A Review of Synthesis Methods and Properties

Science.gov (United States)

Chen, Fei; Gupta, Nikhil; Behera, Rakesh K.; Rohatgi, Pradeep K.

2018-03-01

Graphene-reinforced aluminum (Gr-Al) matrix nanocomposites (NCs) have attracted strong interest from both research and industry in high-performance weight-sensitive applications. Due to the vastly different bonding characteristics of the Al matrix (metallic) and graphene (in-plane covalent + inter-plane van der Waals), the graphene phase has a general tendency to agglomerate and phase separate in the metal matrix, which is detrimental for the mechanical and chemical properties of the composite. Thus, synthesis of Gr-Al NCs is extremely challenging. This review summarizes the different methods available to synthesize Gr-Al NCs and the resulting properties achieved in these NCs. Understanding the effect of processing parameters on the realized properties opens up the possibility of tailoring the synthesis methods to achieve the desired properties for a given application.

Graphene-Reinforced Aluminum Matrix Composites: A Review of Synthesis Methods and Properties

Science.gov (United States)

Chen, Fei; Gupta, Nikhil; Behera, Rakesh K.; Rohatgi, Pradeep K.

2018-06-01

Graphene-reinforced aluminum (Gr-Al) matrix nanocomposites (NCs) have attracted strong interest from both research and industry in high-performance weight-sensitive applications. Due to the vastly different bonding characteristics of the Al matrix (metallic) and graphene (in-plane covalent + inter-plane van der Waals), the graphene phase has a general tendency to agglomerate and phase separate in the metal matrix, which is detrimental for the mechanical and chemical properties of the composite. Thus, synthesis of Gr-Al NCs is extremely challenging. This review summarizes the different methods available to synthesize Gr-Al NCs and the resulting properties achieved in these NCs. Understanding the effect of processing parameters on the realized properties opens up the possibility of tailoring the synthesis methods to achieve the desired properties for a given application.

Random matrix approach to the dynamics of stock inventory variations

International Nuclear Information System (INIS)

Zhou Weixing; Mu Guohua; Kertész, János

2012-01-01

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 C ij 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 (λ 1 and λ 2 ) of the correlation matrix cannot be explained by random matrix theory and the projections of investors' inventory variations on the first eigenvector u(λ 1 ) 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 C VR 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. (paper)

Random matrix approach to the dynamics of stock inventory variations

Science.gov (United States)

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.

Energy-dependent applications of the transfer matrix method

International Nuclear Information System (INIS)

Oeztunali, O.I.; Aronson, R.

1975-01-01

The transfer matrix method is applied to energy-dependent neutron transport problems for multiplying and nonmultiplying media in one-dimensional plane geometry. Experimental cross sections are used for total, elastic, and inelastic scattering and fission. Numerical solutions are presented for the problem of a unit point isotropic source in an infinite medium of water and for the problem of the critical 235 U slab with finite water reflectors. No iterations were necessary in this method. Numerical results obtained are consistent with physical considerations and compare favorably with the moments method results for the problem of the unit point isotropic source in an infinite water medium. (U.S.)

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......-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synthetic and real...

Multiple resonance compensation for betatron coupling and its equivalence with matrix method

CERN Document Server

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...

Understanding effects of matrix protease and matrix organization on directional persistence and translational speed in three-dimensional cell migration.

Science.gov (United States)

Zaman, Muhammad H; Matsudaira, Paul; Lauffenburger, Douglas A

2007-01-01

Recent studies have shown significant differences in migration mechanisms between two- and three-dimensional environments. While experiments have suggested a strong dependence of in vivo migration on both structure and proteolytic activity, the underlying biophysics of such dependence has not been studied adequately. In addition, the existing models of persistent random walk migration are primarily based on two-dimensional movement and do not account for the effect of proteolysis or matrix inhomogeneity. Using lattice Monte Carlo methods, we present a model to study the role of matrix metallo-proteases (MMPs) on directional persistence and speed. The simulations account for a given cell's ability to deform as well as to digest the matrix as the cell moves in three dimensions. Our results show a bimodal dependence of speed and persistence on matrix pore size and suggest high sensitivity on MMP activity, which is in very good agreement with experimental studies carried out in 3D matrices.

A Literature Study of Matrix Element Influenced to the Result of Analysis Using Absorption Atomic Spectroscopy Method (AAS)

International Nuclear Information System (INIS)

Tyas-Djuhariningrum

2004-01-01

The gold sample analysis can be deviated more than >10% to those thrue value caused by the matrix element. So that the matrix element character need to be study in order to reduce the deviation. In rock samples, the matrix elements can cause self quenching, self absorption and ionization process, so there is a result analysis error. In the rock geochemical process, the elements of the same group at the periodic system have the tendency to be together because of their same characteristic. In absorption Atomic Spectroscopy analysis, the elements associate can absorb primer energy with similar wave length so that it can cause deviation in the result interpretation. The aim of study is to predict matrix element influences from rock sample with application standard method for reducing deviation. In quantitative way, assessment of primer light intensity that will be absorbed is proportional to the concentration atom in the sample that relationship between photon intensity with concentration in part per million is linier (ppm). These methods for eliminating matrix elements influence consist of three methods : external standard method, internal standard method, and addition standard method. External standard method for all matrix element, internal standard method for elimination matrix element that have similar characteristics, addition standard methods for elimination matrix elements in Au, Pt samples. The third of standard posess here accuracy are about 95-97%. (author)

Convergence of a random walk method for the Burgers equation

International Nuclear Information System (INIS)

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

A method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix

International Nuclear Information System (INIS)

Godfrin, Elena

1990-01-01

This paper presents a method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix using adequate partitions of the complete matrix. This type of matrix is very usual in quantum mechanics and, more specifically, in solid state physics (e.g., interfaces and superlattices), when the tight-binding approximation is used. The efficiency of the method is analyzed comparing the required CPU time and work-area for different usual techniques. (Author)

Reactor calculation in coarse mesh by finite element method applied to matrix response method

International Nuclear Information System (INIS)

Nakata, H.

1982-01-01

The finite element method is applied to the solution of the modified formulation of the matrix-response method aiming to do reactor calculations in coarse mesh. Good results are obtained with a short running time. The method is applicable to problems where the heterogeneity is predominant and to problems of evolution in coarse meshes where the burnup is variable in one same coarse mesh, making the cross section vary spatially with the evolution. (E.G.) [pt

NLTE steady-state response matrix method.

Science.gov (United States)

Faussurier, G.; More, R. M.

2000-05-01

A connection between atomic kinetics and non-equilibrium thermodynamics has been recently established by using a collisional-radiative model modified to include line absorption. The calculated net emission can be expressed as a non-local thermodynamic equilibrium (NLTE) symmetric response matrix. In the paper, this connection is extended to both cases of the average-atom model and the Busquet's model (RAdiative-Dependent IOnization Model, RADIOM). The main properties of the response matrix still remain valid. The RADIOM source function found in the literature leads to a diagonal response matrix, stressing the absence of any frequency redistribution among the frequency groups at this order of calculation.

Steady- and transient-state analysis of fully ceramic microencapsulated fuel with randomly dispersed tristructural isotropic particles via two-temperature homogenized model-I: Theory and method

International Nuclear Information System (INIS)

Lee, Yoon Hee; Cho, Bum Hee; Cho, Nam Zin

2016-01-01

As a type of accident-tolerant fuel, fully ceramic microencapsulated (FCM) fuel was proposed after the Fukushima accident in Japan. The FCM fuel consists of tristructural isotropic particles randomly dispersed in a silicon carbide (SiC) matrix. For a fuel element with such high heterogeneity, we have proposed a two-temperature homogenized model using the particle transport Monte Carlo method for the heat conduction problem. This model distinguishes between fuel-kernel and SiC matrix temperatures. Moreover, the obtained temperature profiles are more realistic than those of other models. In Part I of the paper, homogenized parameters for the FCM fuel in which tristructural isotropic particles are randomly dispersed in the fine lattice stochastic structure are obtained by (1) matching steady-state analytic solutions of the model with the results of particle transport Monte Carlo method for heat conduction problems, and (2) preserving total enthalpies in fuel kernels and SiC matrix. The homogenized parameters have two desirable properties: (1) they are insensitive to boundary conditions such as coolant bulk temperatures and thickness of cladding, and (2) they are independent of operating power density. By performing the Monte Carlo calculations with the temperature-dependent thermal properties of the constituent materials of the FCM fuel, temperature-dependent homogenized parameters are obtained

Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations

NARCIS (Netherlands)

Jarlebring, E.; Hochstenbach, M.E.

2009-01-01

Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called

Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles

International Nuclear Information System (INIS)

Akemann, G.; Bender, M.

2010-01-01

We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class. The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane. These are orthogonal with respect to a non-Gaussian weight including a modified Bessel function of the second kind, and we give an elementary proof for this. In the large n limit, the eigenvalue statistics at the spectral edge close to the real axis are described by the same family of kernels interpolating between Airy and Poisson that was recently found by one of the authors for the elliptic Ginibre ensemble. We conclude that this scaling limit is universal, appearing for two different non-Hermitian random matrix ensembles with unitary symmetry. As a second result we give an equivalent form for the interpolating Airy kernel in terms of a single real integral, similar to representations for the asymptotic kernel in the bulk and at the hard edge of the spectrum. This makes its structure as a one-parameter deformation of the Airy kernel more transparent.

Agar/gelatin bilayer gel matrix fabricated by simple thermo-responsive sol-gel transition method.

Science.gov (United States)

Wang, Yifeng; Dong, Meng; Guo, Mengmeng; Wang, Xia; Zhou, Jing; Lei, Jian; Guo, Chuanhang; Qin, Chaoran

2017-08-01

We present a simple and environmentally-friendly method to generate an agar/gelatin bilayer gel matrix for further biomedical applications. In this method, the thermally responsive sol-gel transitions of agar and gelatin combined with the different transition temperatures are exquisitely employed to fabricate the agar/gelatin bilayer gel matrix and achieve separate loading for various materials (e.g., drugs, fluorescent materials, and nanoparticles). Importantly, the resulting bilayer gel matrix provides two different biopolymer environments (a polysaccharide environment vs a protein environment) with a well-defined border, which allows the loaded materials in different layers to retain their original properties (e.g., magnetism and fluorescence) and reduce mutual interference. In addition, the loaded materials in the bilayer gel matrix exhibit an interesting release behavior under the control of thermal stimuli. Consequently, the resulting agar/gelatin bilayer gel matrix is a promising candidate for biomedical applications in drug delivery, controlled release, fluorescence labeling, and bio-imaging. Copyright © 2017 Elsevier B.V. All rights reserved.

A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D Methods

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.

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

An interlaboratory comparison of methods for measuring rock matrix porosity

International Nuclear Information System (INIS)

Rasilainen, K.; Hellmuth, K.H.; Kivekaes, L.; Ruskeeniemi, T.; Melamed, A.; Siitari-Kauppi, M.

1996-09-01

An interlaboratory comparison study was conducted for the available Finnish methods of rock matrix porosity measurements. The aim was first to compare different experimental methods for future applications, and second to obtain quality assured data for the needs of matrix diffusion modelling. Three different versions of water immersion techniques, a tracer elution method, a helium gas through-diffusion method, and a C-14-PMMA method were tested. All methods selected for this study were established experimental tools in the respective laboratories, and they had already been individually tested. Rock samples for the study were obtained from a homogeneous granitic drill core section from the natural analogue site at Palmottu. The drill core section was cut into slabs that were expected to be practically identical. The subsamples were then circulated between the different laboratories using a round robin approach. The circulation was possible because all methods were non-destructive, except the C-14-PMMA method, which was always the last method to be applied. The possible effect of drying temperature on the measured porosity was also preliminarily tested. These measurements were done in the order of increasing drying temperature. Based on the study, it can be concluded that all methods are comparable in their accuracy. The selection of methods for future applications can therefore be based on practical considerations. Drying temperature seemed to have very little effect on the measured porosity, but a more detailed study is needed for definite conclusions. (author) (4 refs.)

Efficient Tridiagonal Preconditioner for the Matrix-Free Truncated Newton Method

Czech Academy of Sciences Publication Activity Database

Lukšan, Ladislav; Vlček, Jan

2014-01-01

Roč. 235, 25 May (2014), s. 394-407 ISSN 0096-3003 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : unconstrained optimization * large scale optimization * matrix-free truncated Newton method * preconditioned conjugate gradient method * preconditioners obtained by the directional differentiation * numerical algorithms Subject RIV: BA - General Mathematics Impact factor: 1.551, year: 2014

Method of computer algebraic calculation of the matrix elements in the second quantization language

International Nuclear Information System (INIS)

Gotoh, Masashi; Mori, Kazuhide; Itoh, Reikichi

1995-01-01

An automated method by the algebraic programming language REDUCE3 for specifying the matrix elements expressed in second quantization language is presented and then applied to the case of the matrix elements in the TDHF theory. This program works in a very straightforward way by commuting the electron creation and annihilation operator (a † and a) until these operators have completely vanished from the expression of the matrix element under the appropriate elimination conditions. An improved method using singlet generators of unitary transformations in the place of the electron creation and annihilation operators is also presented. This improvement reduces the time and memory required for the calculation. These methods will make programming in the field of quantum chemistry much easier. 11 refs., 1 tab

A massively parallel discrete ordinates response matrix method for neutron transport

International Nuclear Information System (INIS)

Hanebutte, U.R.; Lewis, E.E.

1992-01-01

In this paper a discrete ordinates response matrix method is formulated with anisotropic scattering for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices that result from the diamond-differenced equations are utilized in a factored form that minimizes memory requirements and significantly reduces the number of arithmetic operations required per node. The red-black solution algorithm utilizes massive parallelism by assigning each spatial node to one or more processors. The algorithm is accelerated by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red-black iterations. The method is implemented on a 16K Connection Machine-2, and S 8 and S 16 solutions are obtained for fixed-source benchmark problems in x-y geometry

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects.

Science.gov (United States)

Mussard, Bastien; Rocca, Dario; Jansen, Georg; Ángyán, János G

2016-05-10

Starting from the general expression for the ground state correlation energy in the adiabatic-connection fluctuation-dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case, the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed, and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental for improvement over direct RPA results.

Eigenvalue distribution of large random matrices

CERN Document Server

Pastur, Leonid

2011-01-01

Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important refer...

Chaos and random matrices in supersymmetric SYK

Science.gov (United States)

Hunter-Jones, Nicholas; Liu, Junyu

2018-05-01

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

The MIXMAX random number generator

Science.gov (United States)

Savvidy, Konstantin G.

2015-11-01

In this paper, we study the randomness properties of unimodular matrix random number generators. Under well-known conditions, these discrete-time dynamical systems have the highly desirable K-mixing properties which guarantee high quality random numbers. It is found that some widely used random number generators have poor Kolmogorov entropy and consequently fail in empirical tests of randomness. These tests show that the lowest acceptable value of the Kolmogorov entropy is around 50. Next, we provide a solution to the problem of determining the maximal period of unimodular matrix generators of pseudo-random numbers. We formulate the necessary and sufficient condition to attain the maximum period and present a family of specific generators in the MIXMAX family with superior performance and excellent statistical properties. Finally, we construct three efficient algorithms for operations with the MIXMAX matrix which is a multi-dimensional generalization of the famous cat-map. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to recursively compute its characteristic polynomial with O(N2) operations, and third, to apply skips of large number of steps S to the sequence in O(N2 log(S)) operations.

Random matrix theory for analyzing the brain functional network in attention deficit hyperactivity disorder

Science.gov (United States)

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.

Randomized Block Cubic Newton Method

KAUST Repository

Doikov, Nikita; Richtarik, Peter

2018-01-01

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.

Randomized Block Cubic Newton Method

KAUST Repository

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.

Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

Directory of Open Access Journals (Sweden)

Fengjiao Wu

2016-01-01

Full Text Available The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. Furthermore, the proposed method has good robustness which can process external random disturbances and uncertain parameters. Finally, the validity and superiority are proved by the numerical simulations.

On the use of transition matrix methods with extended ensembles.

Science.gov (United States)

Escobedo, Fernando A; Abreu, Charlles R A

2006-03-14

Different extended ensemble schemes for non-Boltzmann sampling (NBS) of a selected reaction coordinate lambda were formulated so that they employ (i) "variable" sampling window schemes (that include the "successive umbrella sampling" method) to comprehensibly explore the lambda domain and (ii) transition matrix methods to iteratively obtain the underlying free-energy eta landscape (or "importance" weights) associated with lambda. The connection between "acceptance ratio" and transition matrix methods was first established to form the basis of the approach for estimating eta(lambda). The validity and performance of the different NBS schemes were then assessed using as lambda coordinate the configurational energy of the Lennard-Jones fluid. For the cases studied, it was found that the convergence rate in the estimation of eta is little affected by the use of data from high-order transitions, while it is noticeably improved by the use of a broader window of sampling in the variable window methods. Finally, it is shown how an "elastic" window of sampling can be used to effectively enact (nonuniform) preferential sampling over the lambda domain, and how to stitch the weights from separate one-dimensional NBS runs to produce a eta surface over a two-dimensional domain.

Steady- and Transient-State Analyses of Fully Ceramic Microencapsulated Fuel with Randomly Dispersed Tristructural Isotropic Particles via Two-Temperature Homogenized Model—I: Theory and Method

Directory of Open Access Journals (Sweden)

Yoonhee Lee

2016-06-01

Full Text Available As a type of accident-tolerant fuel, fully ceramic microencapsulated (FCM fuel was proposed after the Fukushima accident in Japan. The FCM fuel consists of tristructural isotropic particles randomly dispersed in a silicon carbide (SiC matrix. For a fuel element with such high heterogeneity, we have proposed a two-temperature homogenized model using the particle transport Monte Carlo method for the heat conduction problem. This model distinguishes between fuel-kernel and SiC matrix temperatures. Moreover, the obtained temperature profiles are more realistic than those of other models. In Part I of the paper, homogenized parameters for the FCM fuel in which tristructural isotropic particles are randomly dispersed in the fine lattice stochastic structure are obtained by (1 matching steady-state analytic solutions of the model with the results of particle transport Monte Carlo method for heat conduction problems, and (2 preserving total enthalpies in fuel kernels and SiC matrix. The homogenized parameters have two desirable properties: (1 they are insensitive to boundary conditions such as coolant bulk temperatures and thickness of cladding, and (2 they are independent of operating power density. By performing the Monte Carlo calculations with the temperature-dependent thermal properties of the constituent materials of the FCM fuel, temperature-dependent homogenized parameters are obtained.

Comprehensive Thematic T-Matrix Reference Database: A 2014-2015 Update

Science.gov (United States)

Mishchenko, Michael I.; Zakharova, Nadezhda; Khlebtsov, Nikolai G.; Videen, Gorden; Wriedt, Thomas

2015-01-01

The T-matrix method is one of the most versatile and efficient direct computer solvers of the macroscopic Maxwell equations and is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper is the seventh update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2013. It also lists a number of earlier publications overlooked previously.

IMPACT OF MATRIX INVERSION ON THE COMPLEXITY OF THE FINITE ELEMENT METHOD

Directory of Open Access Journals (Sweden)

M. Sybis

2016-04-01

Full Text Available Purpose. The development of a wide construction market and a desire to design innovative architectural building constructions has resulted in the need to create complex numerical models of objects having increasingly higher computational complexity. The purpose of this work is to show that choosing a proper method for solving the set of equations can improve the calculation time (reduce the complexity by a few levels of magnitude. Methodology. The article presents an analysis of the impact of matrix inversion algorithm on the deflection calculation in the beam, using the finite element method (FEM. Based on the literature analysis, common methods of calculating set of equations were determined. From the found solutions the Gaussian elimination, LU and Cholesky decomposition methods have been implemented to determine the effect of the matrix inversion algorithm used for solving the equations set on the number of computational operations performed. In addition, each of the implemented method has been further optimized thereby reducing the number of necessary arithmetic operations. Findings. These optimizations have been performed on the use of certain properties of the matrix, such as symmetry or significant number of zero elements in the matrix. The results of the analysis are presented for the division of the beam to 5, 50, 100 and 200 nodes, for which the deflection has been calculated. Originality. The main achievement of this work is that it shows the impact of the used methodology on the complexity of solving the problem (or equivalently, time needed to obtain results. Practical value. The difference between the best (the less complex and the worst (the most complex is in the row of few orders of magnitude. This result shows that choosing wrong methodology may enlarge time needed to perform calculation significantly.

A Combined Weighting Method Based on Hybrid of Interval Evidence Fusion and Random Sampling

Directory of Open Access Journals (Sweden)

Ying Yan

2017-01-01

Full Text Available Due to the complexity of system and lack of expertise, epistemic uncertainties may present in the experts’ judgment on the importance of certain indices during group decision-making. A novel combination weighting method is proposed to solve the index weighting problem when various uncertainties are present in expert comments. Based on the idea of evidence theory, various types of uncertain evaluation information are uniformly expressed through interval evidence structures. Similarity matrix between interval evidences is constructed, and expert’s information is fused. Comment grades are quantified using the interval number, and cumulative probability function for evaluating the importance of indices is constructed based on the fused information. Finally, index weights are obtained by Monte Carlo random sampling. The method can process expert’s information with varying degrees of uncertainties, which possesses good compatibility. Difficulty in effectively fusing high-conflict group decision-making information and large information loss after fusion is avertible. Original expert judgments are retained rather objectively throughout the processing procedure. Cumulative probability function constructing and random sampling processes do not require any human intervention or judgment. It can be implemented by computer programs easily, thus having an apparent advantage in evaluation practices of fairly huge index systems.

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

Science.gov (United States)

Bourlier, Christophe; Kubické, Gildas; Déchamps, Nicolas

2008-04-01

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

A comparison of companion matrix methods to find roots of a trigonometric polynomial

Science.gov (United States)

Boyd, John P.

2013-08-01

A trigonometric polynomial is a truncated Fourier series of the form fN(t)≡∑j=0Naj cos(jt)+∑j=1N bj sin(jt). It has been previously shown by the author that zeros of such a polynomial can be computed as the eigenvalues of a companion matrix with elements which are complex valued combinations of the Fourier coefficients, the "CCM" method. However, previous work provided no examples, so one goal of this new work is to experimentally test the CCM method. A second goal is introduce a new alternative, the elimination/Chebyshev algorithm, and experimentally compare it with the CCM scheme. The elimination/Chebyshev matrix (ECM) algorithm yields a companion matrix with real-valued elements, albeit at the price of usefulness only for real roots. The new elimination scheme first converts the trigonometric rootfinding problem to a pair of polynomial equations in the variables (c,s) where c≡cos(t) and s≡sin(t). The elimination method next reduces the system to a single univariate polynomial P(c). We show that this same polynomial is the resultant of the system and is also a generator of the Groebner basis with lexicographic ordering for the system. Both methods give very high numerical accuracy for real-valued roots, typically at least 11 decimal places in Matlab/IEEE 754 16 digit floating point arithmetic. The CCM algorithm is typically one or two decimal places more accurate, though these differences disappear if the roots are "Newton-polished" by a single Newton's iteration. The complex-valued matrix is accurate for complex-valued roots, too, though accuracy decreases with the magnitude of the imaginary part of the root. The cost of both methods scales as O(N3) floating point operations. In spite of intimate connections of the elimination/Chebyshev scheme to two well-established technologies for solving systems of equations, resultants and Groebner bases, and the advantages of using only real-valued arithmetic to obtain a companion matrix with real-valued elements

Replica methods for loopy sparse random graphs

International Nuclear Information System (INIS)

Coolen, ACC

2016-01-01

I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)

A Control Method of Current Type Matrix Converter for Plasma Control Coil Power Supply

International Nuclear Information System (INIS)

Shimada, K.; Matsukawa, M.; Kurihara, K.; Jun-ichi Itoh

2006-01-01

In exploration to a tokamak fusion reactor, the control of plasma instabilities of high β plasma such as neoclassical tearing mode (NTM), resistive wall mode (RWM) etc., is the key issue for steady-state sustainment. One of the proposed methods to avoid suppressing RWM is that AC current having a phase to work for reduction the RWM growth is generated in a coil (sector coil) equipped spirally on the plasma vacuum vessel. To stabilize RWM, precise and fast real-time feedback control of magnetic field with proper amplitude and frequency is necessary. This implies that an appropriate power supply dedicated for such an application is expected to be developed. A matrix converter as one of power supply candidates for this purpose could provide a solution The matrix converter, categorized in an AC/AC direct converter composed of nine bi-directional current switches, has a great feature that a large energy storage element is unnecessary in comparison with a standard existing AC/AC indirect converter, which is composed of an AC/DC converter and a DC/AC inverter. It is also advantageous in cost and size of its applications. Fortunately, a voltage type matrix converter has come to be available at the market recently, while a current type matrix converter, which is advantageous for fast control of the large-inductance coil current, has been unavailable. On the background above mentioned, we proposed a new current type matrix converter and its control method applicable to a power supply with fast response for suppressing plasma instabilities. Since this converter is required with high accuracy control, the gate control method is adopted to three-phase switching method using middle phase to reduce voltage and current waveforms distortion. The control system is composed of VME-bus board with DSP (Digital Signal Processor) and FPGA (Field Programmable Gate Array) for high speed calculation and control. This paper describes the control method of a current type matrix converter

Efficient Training Methods for Conditional Random Fields

National Research Council Canada - National Science Library

Sutton, Charles A

2008-01-01

.... In this thesis, I investigate efficient training methods for conditional random fields with complex graphical structure, focusing on local methods which avoid propagating information globally along the graph...

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

Directory of Open Access Journals (Sweden)

Thomas Gomez

2018-04-01

Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

Strategy BMT Al-Ittihad Using Matrix IE, Matrix SWOT 8K, Matrix SPACE and Matrix TWOS

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Nofrizal Nofrizal

2018-03-01

Full Text Available This research aims to formulate and select BMT Al-Ittihad Rumbai strategy to face the changing of business environment both from internal environment such as organization resources, finance, member and external business such as competitor, economy, politics and others. This research method used Analysis of EFAS, IFAS, IE Matrix, SWOT-8K Matrix, SPACE Matrix and TWOS Matrix. our hope from this research it can assist BMT Al-Ittihad in formulating and selecting strategies for the sustainability of BMT Al-Ittihad in the future. The sample in this research is using purposive sampling technique that is the manager and leader of BMT Al-IttihadRumbaiPekanbaru. The result of this research shows that the position of BMT Al-Ittihad using IE Matrix, SWOT-8K Matrix and SPACE Matrix is in growth position, stabilization and aggressive. The choice of strategy after using TWOS Matrix is market penetration, market development, vertical integration, horizontal integration, and stabilization (careful.

Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation.

Science.gov (United States)

van Aggelen, Helen; Yang, Yang; Yang, Weitao

2014-05-14

Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H2, and eliminates delocalization errors in H2(+) and other single-bond systems. It gives surprisingly good non-bonded interaction energies--competitive with the ph-RPA--with the correct R(-6) asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations.

Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation

International Nuclear Information System (INIS)

Aggelen, Helen van; Yang, Yang; Yang, Weitao

2014-01-01

Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H 2 , and eliminates delocalization errors in H 2 + and other single-bond systems. It gives surprisingly good non-bonded interaction energies – competitive with the ph-RPA – with the correct R −6 asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations

The current matrix elements from HAL QCD method

Science.gov (United States)

Watanabe, Kai; Ishii, Noriyoshi

2018-03-01

HAL QCD method is a method to construct a potential (HAL QCD potential) that reproduces the NN scattering phase shift faithful to the QCD. The HAL QCD potential is obtained from QCD by eliminating the degrees of freedom of quarks and gluons and leaving only two particular hadrons. Therefor, in the effective quantum mechanics of two nucleons defined by HAL QCD potential, the conserved current consists not only of the nucleon current but also an extra current originating from the potential (two-body current). Though the form of the two-body current is closely related to the potential, it is not straight forward to extract the former from the latter. In this work, we derive the the current matrix element formula in the quantum mechanics defined by the HAL QCD potential. As a first step, we focus on the non-relativistic case. To give an explicit example, we consider a second quantized non-relativistic two-channel coupling model which we refer to as the original model. From the original model, the HAL QCD potential for the open channel is constructed by eliminating the closed channel in the elastic two-particle scattering region. The current matrix element formula is derived by demanding the effective quantum mechanics defined by the HAL QCD potential to respond to the external field in the same way as the original two-channel coupling model.

A real-space stochastic density matrix approach for density functional electronic structure.

Science.gov (United States)

Beck, Thomas L

2015-12-21

The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

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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.

A 2D/1D coupling neutron transport method based on the matrix MOC and NEM methods

International Nuclear Information System (INIS)

Zhang, H.; Zheng, Y.; Wu, H.; Cao, L.

2013-01-01

A new 2D/1D coupling method based on the matrix MOC method (MMOC) and nodal expansion method (NEM) is proposed for solving the three-dimensional heterogeneous neutron transport problem. The MMOC method, used for radial two-dimensional calculation, constructs a response matrix between source and flux with only one sweep and then solves the linear system by using the restarted GMRES algorithm instead of the traditional trajectory sweeping process during within-group iteration for angular flux update. Long characteristics are generated by using the customization of commercial software AutoCAD. A one-dimensional diffusion calculation is carried out in the axial direction by employing the NEM method. The 2D and ID solutions are coupled through the transverse leakage items. The 3D CMFD method is used to ensure the global neutron balance and adjust the different convergence properties of the radial and axial solvers. A computational code is developed based on these theories. Two benchmarks are calculated to verify the coupling method and the code. It is observed that the corresponding numerical results agree well with references, which indicates that the new method is capable of solving the 3D heterogeneous neutron transport problem directly. (authors)

A 2D/1D coupling neutron transport method based on the matrix MOC and NEM methods

Energy Technology Data Exchange (ETDEWEB)

Zhang, H.; Zheng, Y.; Wu, H.; Cao, L. [School of Nuclear Science and Technology, Xi' an Jiaotong University, No. 28, Xianning West Road, Xi' an, Shaanxi 710049 (China)

2013-07-01

A new 2D/1D coupling method based on the matrix MOC method (MMOC) and nodal expansion method (NEM) is proposed for solving the three-dimensional heterogeneous neutron transport problem. The MMOC method, used for radial two-dimensional calculation, constructs a response matrix between source and flux with only one sweep and then solves the linear system by using the restarted GMRES algorithm instead of the traditional trajectory sweeping process during within-group iteration for angular flux update. Long characteristics are generated by using the customization of commercial software AutoCAD. A one-dimensional diffusion calculation is carried out in the axial direction by employing the NEM method. The 2D and ID solutions are coupled through the transverse leakage items. The 3D CMFD method is used to ensure the global neutron balance and adjust the different convergence properties of the radial and axial solvers. A computational code is developed based on these theories. Two benchmarks are calculated to verify the coupling method and the code. It is observed that the corresponding numerical results agree well with references, which indicates that the new method is capable of solving the 3D heterogeneous neutron transport problem directly. (authors)

The Wasteland of Random Supergravities

OpenAIRE

Marsh, David; McAllister, Liam; Wrase, Timm

2011-01-01

We show that in a general \\cal{N} = 1 supergravity with N \\gg 1 scalar fields, an exponentially small fraction of the de Sitter critical points are metastable vacua. Taking the superpotential and Kahler potential to be random functions, we construct a random matrix model for the Hessian matrix, which is well-approximated by the sum of a Wigner matrix and two Wishart matrices. We compute the eigenvalue spectrum analytically from the free convolution of the constituent spectra and find that in ...

A Method of Erasing Data Using Random Number Generators

OpenAIRE

井上,正人

2012-01-01

Erasing data is an indispensable step for disposal of computers or external storage media. Except physical destruction, erasing data means writing random information on entire disk drives or media. We propose a method which erases data safely using random number generators. These random number generators create true random numbers based on quantum processes.

Quantitative evaluation of the matrix effect in bioanalytical methods based on LC-MS: A comparison of two approaches.

Science.gov (United States)

Rudzki, Piotr J; Gniazdowska, Elżbieta; Buś-Kwaśnik, Katarzyna

2018-06-05

Liquid chromatography coupled to mass spectrometry (LC-MS) is a powerful tool for studying pharmacokinetics and toxicokinetics. Reliable bioanalysis requires the characterization of the matrix effect, i.e. influence of the endogenous or exogenous compounds on the analyte signal intensity. We have compared two methods for the quantitation of matrix effect. The CVs(%) of internal standard normalized matrix factors recommended by the European Medicines Agency were evaluated against internal standard normalized relative matrix effects derived from Matuszewski et al. (2003). Both methods use post-extraction spiked samples, but matrix factors require also neat solutions. We have tested both approaches using analytes of diverse chemical structures. The study did not reveal relevant differences in the results obtained with both calculation methods. After normalization with the internal standard, the CV(%) of the matrix factor was on average 0.5% higher than the corresponding relative matrix effect. The method adopted by the European Medicines Agency seems to be slightly more conservative in the analyzed datasets. Nine analytes of different structures enabled a general overview of the problem, still, further studies are encouraged to confirm our observations. Copyright © 2018 Elsevier B.V. All rights reserved.

Statistics of stationary points of random finite polynomial potentials

International Nuclear Information System (INIS)

Mehta, Dhagash; Niemerg, Matthew; Sun, Chuang

2015-01-01

The stationary points (SPs) of the potential energy landscapes (PELs) of multivariate random potentials (RPs) have found many applications in many areas of Physics, Chemistry and Mathematical Biology. However, there are few reliable methods available which can find all the SPs accurately. Hence, one has to rely on indirect methods such as Random Matrix theory. With a combination of the numerical polynomial homotopy continuation method and a certification method, we obtain all the certified SPs of the most general polynomial RP for each sample chosen from the Gaussian distribution with mean 0 and variance 1. While obtaining many novel results for the finite size case of the RP, we also discuss the implications of our results on mathematics of random systems and string theory landscapes. (paper)

Bunches of random cross-correlated sequences

International Nuclear Information System (INIS)

Maystrenko, A A; Melnik, S S; Pritula, G M; Usatenko, O V

2013-01-01

The statistical properties of random cross-correlated sequences constructed by the convolution method (likewise referred to as the Rice or the inverse Fourier transformation) are examined. We clarify the meaning of the filtering function—the kernel of the convolution operator—and show that it is the value of the cross-correlation function which describes correlations between the initial white noise and constructed correlated sequences. The matrix generalization of this method for constructing a bunch of N cross-correlated sequences is presented. Algorithms for their generation are reduced to solving the problem of decomposition of the Fourier transform of the correlation matrix into a product of two mutually conjugate matrices. Different decompositions are considered. The limits of weak and strong correlations for the one-point probability and pair correlation functions of sequences generated by the method under consideration are studied. Special cases of heavy-tailed distributions of the generated sequences are analyzed. We show that, if the filtering function is rather smooth, the distribution function of generated variables has the Gaussian or Lévy form depending on the analytical properties of the distribution (or characteristic) functions of the initial white noise. Anisotropic properties of statistically homogeneous random sequences related to the asymmetry of a filtering function are revealed and studied. These asymmetry properties are expressed in terms of the third- or fourth-order correlation functions. Several examples of the construction of correlated chains with a predefined correlation matrix are given. (paper)

Taming the pion condensation in QCD at finite baryon density: a numerical test in a random matrix model

Energy Technology Data Exchange (ETDEWEB)

Aoki, Sinya [Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan); Hanada, Masanori [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan); The Hakubi Center for Advanced Research, Kyoto University,Yoshida Ushinomiyacho, Sakyo-ku, Kyoto 606-8501 (Japan); Nakamura, Atsushi [Research Institute for Information Science and Education, Hiroshima University,Higashi-Hiroshima 739-8527 (Japan)

2015-05-14

In the Monte Carlo study of QCD at finite baryon density based upon the phase reweighting method, the pion condensation in the phase-quenched theory and associated zero-mode prevent us from going to the low-temperature high-density region. We propose a method to circumvent them by a simple modification of the density of state method. We first argue that the standard version of the density of state method, which is invented to solve the overlapping problem, is effective only for a certain ‘good’ class of observables. We then modify it so as to solve the overlap problem for ‘bad’ observables as well. While, in the standard version of the density of state method, we usually constrain an observable we are interested in, we fix a different observable in our new method which has a sharp peak at some particular value characterizing the correct vacuum of the target theory. In the finite-density QCD, such an observable is the pion condensate. The average phase becomes vanishingly small as the value of the pion condensate becomes large, hence it is enough to consider configurations with π{sup +}≃0, where the zero mode does not appear. We demonstrate an effectiveness of our method by using a toy model (the chiral random matrix theory) which captures the properties of finite-density QCD qualitatively. We also argue how to apply our method to other theories including finite-density QCD. Although the example we study numerically is based on the phase reweighting method, the same idea can be applied to more general reweighting methods and we show how this idea can be applied to find a possible QCD critical point.

Evaluation of the streaming-matrix method for discrete-ordinates duct-streaming calculations

International Nuclear Information System (INIS)

Clark, B.A.; Urban, W.T.; Dudziak, D.J.

1983-01-01

A new deterministic streaming technique called the Streaming Matrix Hybrid Method (SMHM) is applied to two realistic duct-shielding problems. The results are compared to standard discrete-ordinates and Monte Carlo calculations. The SMHM shows promise as an alternative deterministic streaming method to standard discrete-ordinates

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

Science.gov (United States)

Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua

2016-07-01

On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.

Statistical methods in nuclear theory

International Nuclear Information System (INIS)

Shubin, Yu.N.

1974-01-01

The paper outlines statistical methods which are widely used for describing properties of excited states of nuclei and nuclear reactions. It discusses physical assumptions lying at the basis of known distributions between levels (Wigner, Poisson distributions) and of widths of highly excited states (Porter-Thomas distribution, as well as assumptions used in the statistical theory of nuclear reactions and in the fluctuation analysis. The author considers the random matrix method, which consists in replacing the matrix elements of a residual interaction by random variables with a simple statistical distribution. Experimental data are compared with results of calculations using the statistical model. The superfluid nucleus model is considered with regard to superconducting-type pair correlations

A Fast and Effective Block Adjustment Method with Big Data

Directory of Open Access Journals (Sweden)

ZHENG Maoteng

2017-02-01

Full Text Available To deal with multi-source, complex and massive data in photogrammetry, and solve the high memory requirement and low computation efficiency of irregular normal equation caused by the randomly aligned and large scale datasets, we introduce the preconditioned conjugate gradient combined with inexact Newton method to solve the normal equation which do not have strip characteristics due to the randomly aligned images. We also use an effective sparse matrix compression format to compress the big normal matrix, a brand new workflow of bundle adjustment is developed. Our method can avoid the direct inversion of the big normal matrix, the memory requirement of the normal matrix is also decreased by the proposed sparse matrix compression format. Combining all these techniques, the proposed method can not only decrease the memory requirement of normal matrix, but also largely improve the efficiency of bundle adjustment while maintaining the same accuracy as the conventional method. Preliminary experiment results show that the bundle adjustment of a dataset with about 4500 images and 9 million image points can be done in only 15 minutes while achieving sub-pixel accuracy.

A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers

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Jiang-Xia Nan

2010-09-01

Full Text Available The intuitionistic fuzzy set (IF-set has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs. Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example.

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

Science.gov (United States)

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.

Invariant Imbedding T-Matrix Method for Axial Symmetric Hydrometeors with Extreme Aspect Ratios

Science.gov (United States)

Pelissier, C.; Clune, T.; Kuo, K. S.; Munchak, S. J.; Adams, I. S.

2017-12-01

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.

NewIn-situ synthesis method of magnesium matrix composites reinforced with TiC particulates

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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.

Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

CERN Document Server

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. .

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.

Algebraic method for analysis of nonlinear systems with a normal matrix

International Nuclear Information System (INIS)

Konyaev, Yu.A.; Salimova, A.F.

2014-01-01

A promising method has been proposed for analyzing a class of quasilinear nonautonomous systems of differential equations whose matrix can be represented as a sum of nonlinear normal matrices, which makes it possible to analyze stability without using the Lyapunov functions [ru

Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory

Science.gov (United States)

Kos, Pavel; Ljubotina, Marko; Prosen, Tomaž

2018-04-01

A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985), 10.1098/rspa.1985.0078] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K (t ) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004), 10.1103/PhysRevLett.93.014103]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the "many-body localized phase" and "ergodic phase." In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K (t ) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1 /2 models in a periodically kicking transverse field. In particular, we relate K (t ) to partition functions of a class of twisted classical Ising models on a ring of size t ; hence, the leading-order RMT behavior

Improved determination of hadron matrix elements using the variational method

International Nuclear Information System (INIS)

Dragos, J.; Kamleh, W.; Leinweber, D.B.; Zanotti, J.M.; Rakow, P.E.L.; Young, R.D.; Adelaide Univ.

2015-11-01

The extraction of hadron form factors in lattice QCD using the standard two- and three-point correlator functions has its limitations. One of the most commonly studied sources of systematic error is excited state contamination, which occurs when correlators are contaminated with results from higher energy excitations. We apply the variational method to calculate the axial vector current g A and compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.

Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

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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.

[Three-dimensional parallel collagen scaffold promotes tendon extracellular matrix formation].

Science.gov (United States)

Zheng, Zefeng; Shen, Weiliang; Le, Huihui; Dai, Xuesong; Ouyang, Hongwei; Chen, Weishan

2016-03-01

To investigate the effects of three-dimensional parallel collagen scaffold on the cell shape, arrangement and extracellular matrix formation of tendon stem cells. Parallel collagen scaffold was fabricated by unidirectional freezing technique, while random collagen scaffold was fabricated by freeze-drying technique. The effects of two scaffolds on cell shape and extracellular matrix formation were investigated in vitro by seeding tendon stem/progenitor cells and in vivo by ectopic implantation. Parallel and random collagen scaffolds were produced successfully. Parallel collagen scaffold was more akin to tendon than random collagen scaffold. Tendon stem/progenitor cells were spindle-shaped and unified orientated in parallel collagen scaffold, while cells on random collagen scaffold had disorder orientation. Two weeks after ectopic implantation, cells had nearly the same orientation with the collagen substance. In parallel collagen scaffold, cells had parallel arrangement, and more spindly cells were observed. By contrast, cells in random collagen scaffold were disorder. Parallel collagen scaffold can induce cells to be in spindly and parallel arrangement, and promote parallel extracellular matrix formation; while random collagen scaffold can induce cells in random arrangement. The results indicate that parallel collagen scaffold is an ideal structure to promote tendon repairing.

Matrix-variational method: an efficient approach to bound state eigenproblems

International Nuclear Information System (INIS)

Gerck, E.; d'Oliveira, A.B.

1978-11-01

A new matrix-variational method for solving the radial Schroedinger equation is described. It consists in obtaining an adjustable matrix formulation for the boundary value differential equation, using a set of three functions that obey the boundary conditions. These functions are linearly combined at every three adjacents points to fit the true unknown eigenfunction by a variational technique. With the use of a new class of central differences, the exponential differences, tridiagonal or bidiagonal matrices are obtained. In the bidiagonal case, closed form expressions for the eigenvalues are given for the Coulomb, harmonic, linear, square-root and logarithmic potentials. The values obtained are within 0.1% of the true numerical value. The eigenfunction can be calculated using the eigenvectors to reconstruct the linear combination of the set functions [pt

Finite-time stability of neutral-type neural networks with random time-varying delays

Science.gov (United States)

Ali, M. Syed; Saravanan, S.; Zhu, Quanxin

2017-11-01

This paper is devoted to the finite-time stability analysis of neutral-type neural networks with random time-varying delays. The randomly time-varying delays are characterised by Bernoulli stochastic variable. This result can be extended to analysis and design for neutral-type neural networks with random time-varying delays. On the basis of this paper, we constructed suitable Lyapunov-Krasovskii functional together and established a set of sufficient linear matrix inequalities approach to guarantee the finite-time stability of the system concerned. By employing the Jensen's inequality, free-weighting matrix method and Wirtinger's double integral inequality, the proposed conditions are derived and two numerical examples are addressed for the effectiveness of the developed techniques.

Prognostic interaction patterns in diabetes mellitus II: A random-matrix-theory relation

Science.gov (United States)

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.

Response matrix method and its application to SCWR single channel stability analysis

International Nuclear Information System (INIS)

Zhao, Jiyun; Tseng, K.J.; Tso, C.P.

2011-01-01

To simulate the reactor system dynamic features during density wave oscillations (DWO), both the non-linear method and the linear method can be used. Although some transient information is lost through model linearization, the high computational efficiency and relatively accurate results make the linear analysis methodology attractive, especially for prediction of the onset of instability. In the linear stability analysis, the system models are simplified through linearization of the complex non-linear differential equations, and then, the linear differential equations are generally solved in the frequency domain through Laplace transformation. In this paper, a system response matrix method was introduced by directly solving the differential equations in the time domain. By using a system response matrix method, the complicated transfer function derivation, which must be done in the frequency domain method, can be avoided. Using the response matrix method, a model was developed and applied to the single channel or parallel channel type instability analyses of the typical proposed SCWR design. The sensitivity of the decay ratio (DR) to the axial mesh size was analyzed and it was found that the DR is not sensitive to mesh size once sufficient number of axial nodes is applied. To demonstrate the effects of the inlet orificing to the stability feature for the supercritical condition, the sensitivity of the stability to inlet orifice coefficient was conducted for hot channel. It is clearly shown that a higher inlet orifice coefficient will make the system more stable. The susceptibility of stability to operating parameters such as mass flow rate, power and system pressure was also performed. And the measure to improve the SCWR stability sensitivity to operating parameters was investigated. It was found that the SCWR stability sensitivity feature can be improved by carefully managing the inlet orifices and choosing proper operating parameters. (author)

Variational random phase approximation for the anharmonic oscillator

International Nuclear Information System (INIS)

Dukelsky, J.; Schuck, P.

1990-04-01

The recently derived Variational Random Phase Approximation is examined using the anharmonic oscillator model. Special attention is paid to the ground state RPA wave function and the convergence of the proposed truncation scheme to obtain the diagonal density matrix. Comparison with the standard Coupled Cluster method is made

EcmPred: Prediction of extracellular matrix proteins based on random forest with maximum relevance minimum redundancy feature selection

KAUST Repository

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.

Efficient Data Gathering Methods in Wireless Sensor Networks Using GBTR Matrix Completion

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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.

Statistical Analysis of the Figure of Merit of a Two-Level Thermoelectric System: A Random Matrix Approach

KAUST Repository

Abbout, Adel; Ouerdane, Henni; Goupil, Christophe

2016-01-01

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.

Statistical Analysis of the Figure of Merit of a Two-Level Thermoelectric System: A Random Matrix Approach

KAUST Repository

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.

A Solution Method for Linear and Geometrically Nonlinear MDOF Systems with Random Properties subject to Random Excitation

DEFF Research Database (Denmark)

Micaletti, R. C.; Cakmak, A. S.; Nielsen, Søren R. K.

structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficient and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random......A method for computing the lower-order moments of randomly-excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random...... initial conditions. This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases...

ECAP – New consolidation method for production of aluminium matrix composites with ceramic reinforcement

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.

Random sampling of quantum states: a survey of methods and some issues regarding the Overparametrized Method

International Nuclear Information System (INIS)

Maziero, Jonas

2015-01-01

The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here, we review some methods that may be used for performing that task. We start by presenting a simple procedure for generating random state vectors, for which the main tool is the random sampling of unbiased discrete probability distributions (DPD). Afterwards, the creation of random density matrices is addressed. In this context, we first present the standard method, which consists in using the spectral decomposition of a quantum state for getting RQS from random DPDs and random unitary matrices. In the sequence, the Bloch vector parametrization method is described. This approach, despite being useful in several instances, is not in general convenient for RQS generation. In the last part of the article, we regard the overparametrized method (OPM) and the related Ginibre and Bures techniques. The OPM can be used to create random positive semidefinite matrices with unit trace from randomly produced general complex matrices in a simple way that is friendly for numerical implementations. We consider a physically relevant issue related to the possible domains that may be used for the real and imaginary parts of the elements of such general complex matrices. Subsequently, a too fast concentration of measure in the quantum state space that appears in this parametrization is noticed. (author)

Methods for the visualization and analysis of extracellular matrix protein structure and degradation.

Science.gov (United States)

Leonard, Annemarie K; Loughran, Elizabeth A; Klymenko, Yuliya; Liu, Yueying; Kim, Oleg; Asem, Marwa; McAbee, Kevin; Ravosa, Matthew J; Stack, M Sharon

2018-01-01

This chapter highlights methods for visualization and analysis of extracellular matrix (ECM) proteins, with particular emphasis on collagen type I, the most abundant protein in mammals. Protocols described range from advanced imaging of complex in vivo matrices to simple biochemical analysis of individual ECM proteins. The first section of this chapter describes common methods to image ECM components and includes protocols for second harmonic generation, scanning electron microscopy, and several histological methods of ECM localization and degradation analysis, including immunohistochemistry, Trichrome staining, and in situ zymography. The second section of this chapter details both a common transwell invasion assay and a novel live imaging method to investigate cellular behavior with respect to collagen and other ECM proteins of interest. The final section consists of common electrophoresis-based biochemical methods that are used in analysis of ECM proteins. Use of the methods described herein will enable researchers to gain a greater understanding of the role of ECM structure and degradation in development and matrix-related diseases such as cancer and connective tissue disorders. © 2018 Elsevier Inc. All rights reserved.

An Efficient Local Correlation Matrix Decomposition Approach for the Localization Implementation of Ensemble-Based Assimilation Methods

Science.gov (United States)

Zhang, Hongqin; Tian, Xiangjun

2018-04-01

Ensemble-based data assimilation methods often use the so-called localization scheme to improve the representation of the ensemble background error covariance (Be). Extensive research has been undertaken to reduce the computational cost of these methods by using the localized ensemble samples to localize Be by means of a direct decomposition of the local correlation matrix C. However, the computational costs of the direct decomposition of the local correlation matrix C are still extremely high due to its high dimension. In this paper, we propose an efficient local correlation matrix decomposition approach based on the concept of alternating directions. This approach is intended to avoid direct decomposition of the correlation matrix. Instead, we first decompose the correlation matrix into 1-D correlation matrices in the three coordinate directions, then construct their empirical orthogonal function decomposition at low resolution. This procedure is followed by the 1-D spline interpolation process to transform the above decompositions to the high-resolution grid. Finally, an efficient correlation matrix decomposition is achieved by computing the very similar Kronecker product. We conducted a series of comparison experiments to illustrate the validity and accuracy of the proposed local correlation matrix decomposition approach. The effectiveness of the proposed correlation matrix decomposition approach and its efficient localization implementation of the nonlinear least-squares four-dimensional variational assimilation are further demonstrated by several groups of numerical experiments based on the Advanced Research Weather Research and Forecasting model.

Matrix algebra for linear models

CERN Document Server

Gruber, Marvin H J

2013-01-01

Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f

Correlated Random Systems Five Different Methods : CIRM Jean-Morlet Chair

CERN Document Server

Kistler, Nicola

2015-01-01

This volume presents five different methods recently developed to tackle the large scale behavior of highly correlated random systems, such as spin glasses, random polymers, local times and loop soups and random matrices. These methods, presented in a series of lectures delivered within the Jean-Morlet initiative (Spring 2013), play a fundamental role in the current development of probability theory and statistical mechanics. The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Models by N. Kistler, Isomorphism Theorems by J. Rosen and Spectral Properties of Wigner Matrices by B. Schlein. This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake. It is targeted at researchers, i...

A matrix contraction process

Science.gov (United States)

Wilkinson, Michael; Grant, John

2018-03-01

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

Matrix-type multiple reciprocity boundary element method for solving three-dimensional two-group neutron diffusion equations

International Nuclear Information System (INIS)

Itagaki, Masafumi; Sahashi, Naoki.

1997-01-01

The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)

A method for generating skewed random numbers using two overlapping uniform distributions

International Nuclear Information System (INIS)

Ermak, D.L.; Nasstrom, J.S.

1995-02-01

The objective of this work was to implement and evaluate a method for generating skewed random numbers using a combination of uniform random numbers. The method provides a simple and accurate way of generating skewed random numbers from the specified first three moments without an a priori specification of the probability density function. We describe the procedure for generating skewed random numbers from unifon-n random numbers, and show that it accurately produces random numbers with the desired first three moments over a range of skewness values. We also show that in the limit of zero skewness, the distribution of random numbers is an accurate approximation to the Gaussian probability density function. Future work win use this method to provide skewed random numbers for a Langevin equation model for diffusion in skewed turbulence

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...

Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods

Science.gov (United States)

Alexander, Steven; Coldwell, R. L.

2015-03-01

The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.

Solving Eigenvalue response matrix equations with Jacobian-Free Newton-Krylov methods

International Nuclear Information System (INIS)

Roberts, Jeremy A.; Forget, Benoit

2011-01-01

The response matrix method for reactor eigenvalue problems is motivated as a technique for solving coarse mesh transport equations, and the classical approach of power iteration (PI) for solution is described. The method is then reformulated as a nonlinear system of equations, and the associated Jacobian is derived. A Jacobian-Free Newton-Krylov (JFNK) method is employed to solve the system, using an approximate Jacobian coupled with incomplete factorization as a preconditioner. The unpreconditioned JFNK slightly outperforms PI, and preconditioned JFNK outperforms both PI and Steffensen-accelerated PI significantly. (author)

Random matrices and chaos in nuclear physics: Nuclear structure

International Nuclear Information System (INIS)

Weidenmueller, H. A.; Mitchell, G. E.

2009-01-01

Evidence for the applicability of random-matrix theory to nuclear spectra is reviewed. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately, quantum chaos) in nuclei whenever random-matrix predictions are fulfilled. An introduction into the basic concepts of random-matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random-matrix ensembles patterned after the shell model such as the embedded two-body ensemble, the two-body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground-state regions of strongly deformed nuclei.

Randomized Oversampling for Generalized Multiscale Finite Element Methods

KAUST Repository

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.

Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory

Science.gov (United States)

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.

Synthesizing (ZrAl3 + AlN)/Mg-Al composites by a 'matrix exchange' method

Science.gov (United States)

Gao, Tong; Li, Zengqiang; Hu, Kaiqi; Han, Mengxia; Liu, Xiangfa

2018-06-01

A method named 'matrix exchange' to synthesize ZrAl3 and AlN reinforced Mg-Al composite was developed in this paper. By inserting Al-10ZrN master alloy into Mg matrix and reheating the cooled ingot to 550 °C, Al and Mg atoms diffuse to the opposite side. As a result, liquid melt occurs once the interface areas reach to proper compositions. Then dissolved Al atoms react with ZrN, leading to the in-situ formation of ZrAl3 and AlN particles, while the Al matrix is finally replaced by Mg. This study provides a new insight for preparing Mg composites.

METHOD OF CONSTRUCTION OF GENETIC DATA CLUSTERS

Directory of Open Access Journals (Sweden)

N. A. Novoselova

2016-01-01

Full Text Available The paper presents a method of construction of genetic data clusters (functional modules using the randomized matrices. To build the functional modules the selection and analysis of the eigenvalues of the gene profiles correlation matrix is performed. The principal components, corresponding to the eigenvalues, which are significantly different from those obtained for the randomly generated correlation matrix, are used for the analysis. Each selected principal component forms gene cluster. In a comparative experiment with the analogs the proposed method shows the advantage in allocating statistically significant different-sized clusters, the ability to filter non- informative genes and to extract the biologically interpretable functional modules matching the real data structure.

A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level

International Nuclear Information System (INIS)

Kussmann, Jörg; Luenser, Arne; Beer, Matthias; Ochsenfeld, Christian

2015-01-01

An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r −2 instead of r −1 . The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure

DANTE, Activation Analysis Neutron Spectra Unfolding by Covariance Matrix Method

International Nuclear Information System (INIS)

Petilli, M.

1981-01-01

1 - Description of problem or function: The program evaluates activation measurements of reactor neutron spectra and unfolds the results for dosimetry purposes. Different evaluation options are foreseen: absolute or relative fluxes and different iteration algorithms. 2 - Method of solution: A least-square fit method is used. A correlation between available data and their uncertainties has been introduced by means of flux and activity variance-covariance matrices. Cross sections are assumed to be constant, i.e. with variance-covariance matrix equal to zero. The Lagrange multipliers method has been used for calculating the solution. 3 - Restrictions on the complexity of the problem: 9 activation experiments can be analyzed. 75 energy groups are accepted

Matrix removal in state of the art sample preparation methods for serum by charged aerosol detection and metabolomics-based LC-MS.

Science.gov (United States)

Schimek, Denise; Francesconi, Kevin A; Mautner, Anton; Libiseller, Gunnar; Raml, Reingard; Magnes, Christoph

2016-04-07

Investigations into sample preparation procedures usually focus on analyte recovery with no information provided about the fate of other components of the sample (matrix). For many analyses, however, and particularly those using liquid chromatography-mass spectrometry (LC-MS), quantitative measurements are greatly influenced by sample matrix. Using the example of the drug amitriptyline and three of its metabolites in serum, we performed a comprehensive investigation of nine commonly used sample clean-up procedures in terms of their suitability for preparing serum samples. We were monitoring the undesired matrix compounds using a combination of charged aerosol detection (CAD), LC-CAD, and a metabolomics-based LC-MS/MS approach. In this way, we compared analyte recovery of protein precipitation-, liquid-liquid-, solid-phase- and hybrid solid-phase extraction methods. Although all methods provided acceptable recoveries, the highest recovery was obtained by protein precipitation with acetonitrile/formic acid (amitriptyline 113%, nortriptyline 92%, 10-hydroxyamitriptyline 89%, and amitriptyline N-oxide 96%). The quantification of matrix removal by LC-CAD showed that the solid phase extraction method (SPE) provided the lowest remaining matrix load (48-123 μg mL(-1)), which is a 10-40 fold better matrix clean-up than the precipitation- or hybrid solid phase extraction methods. The metabolomics profiles of eleven compound classes, comprising 70 matrix compounds showed the trends of compound class removal for each sample preparation strategy. The collective data set of analyte recovery, matrix removal and matrix compound profile was used to assess the effectiveness of each sample preparation method. The best performance in matrix clean-up and practical handling of small sample volumes was showed by the SPE techniques, particularly HLB SPE. CAD proved to be an effective tool for revealing the considerable differences between the sample preparation methods. This detector can

A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics

Science.gov (United States)

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…

Current matrix element in HAL QCD's wavefunction-equivalent potential method

Science.gov (United States)

Watanabe, Kai; Ishii, Noriyoshi

2018-04-01

We give a formula to calculate a matrix element of a conserved current in the effective quantum mechanics defined by the wavefunction-equivalent potentials proposed by the HAL QCD collaboration. As a first step, a non-relativistic field theory with two-channel coupling is considered as the original theory, with which a wavefunction-equivalent HAL QCD potential is obtained in a closed analytic form. The external field method is used to derive the formula by demanding that the result should agree with the original theory. With this formula, the matrix element is obtained by sandwiching the effective current operator between the left and right eigenfunctions of the effective Hamiltonian associated with the HAL QCD potential. In addition to the naive one-body current, the effective current operator contains an additional two-body term emerging from the degrees of freedom which has been integrated out.

Randomly and Non-Randomly Missing Renal Function Data in the Strong Heart Study: A Comparison of Imputation Methods.

Directory of Open Access Journals (Sweden)

Nawar Shara

Full Text Available Kidney and cardiovascular disease are widespread among populations with high prevalence of diabetes, such as American Indians participating in the Strong Heart Study (SHS. Studying these conditions simultaneously in longitudinal studies is challenging, because the morbidity and mortality associated with these diseases result in missing data, and these data are likely not missing at random. When such data are merely excluded, study findings may be compromised. In this article, a subset of 2264 participants with complete renal function data from Strong Heart Exams 1 (1989-1991, 2 (1993-1995, and 3 (1998-1999 was used to examine the performance of five methods used to impute missing data: listwise deletion, mean of serial measures, adjacent value, multiple imputation, and pattern-mixture. Three missing at random models and one non-missing at random model were used to compare the performance of the imputation techniques on randomly and non-randomly missing data. The pattern-mixture method was found to perform best for imputing renal function data that were not missing at random. Determining whether data are missing at random or not can help in choosing the imputation method that will provide the most accurate results.

Exact solution of some linear matrix equations using algebraic methods

Science.gov (United States)

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.

Newton's method for solving a quadratic matrix equation with special coefficient matrices

International Nuclear Information System (INIS)

Seo, Sang-Hyup; Seo, Jong Hyun; Kim, Hyun-Min

2014-01-01

We consider the iterative method for solving a quadratic matrix equation with special coefficient matrices which arises in the quasi-birth-death problem. In this paper, we show that the elementwise minimal positive solvents to quadratic matrix equations can be obtained using Newton's method. We also prove that the convergence rate of the Newton iteration is quadratic if the Fréchet derivative at the elementwise minimal positive solvent is nonsingular. However, if the Fréchet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.(This is summarized a paper which is to appear in Honam Mathematical Journal.)

Matrix-Geometric Method for Queueing Model with State-Dependent Arrival of an Unreliable Server and PH Service

Directory of Open Access Journals (Sweden)

M.ReniSagaya Raj

2016-03-01

Full Text Available In this paper, we consider a state-dependent queueing system in which the system is subject to random breakdowns. Customer arrive at the system randomly following a Poisson process with state-dependent rates. Service times follows PH distribution and repair times are exponentially distributed. The server may fail to service with probability depending on the number of customer completed since the last repair. The main result of this paper is the matrix-geometric solution of the steady-state queue length from which many performance measurements of this queueing system like the stationary queue length distribution, waiting time distribution and the distribution of regular busy period, system utilization are obtained. Numerical examples are presented for both cases.

Google matrix of the citation network of Physical Review

Science.gov (United States)

Frahm, Klaus M.; Eom, Young-Ho; Shepelyansky, Dima L.

2014-05-01

We study the statistical properties of spectrum and eigenstates of the Google matrix of the citation network of Physical Review for the period 1893-2009. The main fraction of complex eigenvalues with largest modulus is determined numerically by different methods based on high-precision computations with up to p =16384 binary digits that allow us to resolve hard numerical problems for small eigenvalues. The nearly nilpotent matrix structure allows us to obtain a semianalytical computation of eigenvalues. We find that the spectrum is characterized by the fractal Weyl law with a fractal dimension df≈1. It is found that the majority of eigenvectors are located in a localized phase. The statistical distribution of articles in the PageRank-CheiRank plane is established providing a better understanding of information flows on the network. The concept of ImpactRank is proposed to determine an influence domain of a given article. We also discuss the properties of random matrix models of Perron-Frobenius operators.

Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications

Directory of Open Access Journals (Sweden)

Zhongtuan Zheng

2017-01-01

Full Text Available This paper investigates, both theoretically and numerically, preferential random walks (PRW on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW. Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.

Wishart and anti-Wishart random matrices

International Nuclear Information System (INIS)

Janik, Romuald A; Nowak, Maciej A

2003-01-01

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

A matrix structured LED backlight system with 2D-DHT local dimming method

Science.gov (United States)

Liu, Jia; Li, Yang; Du, Sidan

To reduce the number of the drivers in the conventional local dimming method for LCDs, a novel LED backlight local dimming system is proposed in this paper. The backlight of this system is generated by 2D discrete Hadamard transform and its matrix structured LED modules. Compared with the conventional 2D local dimming method, the proposed method costs much fewer drivers but with little degradation.

Description of elastic scattering in U-matrix method

International Nuclear Information System (INIS)

Edneral, V.F.; Troshin, S.M.; Tyurin, N.E.; Khrustalev, O.A.

1975-01-01

The elastic pp-scattering has been analyzed using a generalized reaction matrix (the U-matrix). A good agreement has been reached with the experimental total cross sections for the (pp) reaction beginning with an energy of 30 GeV and for the dsub(t)(dt)(pp) for four ISR energies [ru

Insight on agglomerates of gold nanoparticles in glass based on surface plasmon resonance spectrum: study by multi-spheres T-matrix method

Science.gov (United States)

Avakyan, L. A.; Heinz, M.; Skidanenko, A. V.; Yablunovski, K. A.; Ihlemann, J.; Meinertz, J.; Patzig, C.; Dubiel, M.; Bugaev, L. A.

2018-01-01

The formation of a localized surface plasmon resonance (SPR) spectrum of randomly distributed gold nanoparticles in the surface layer of silicate float glass, generated and implanted by UV ArF-excimer laser irradiation of a thin gold layer sputter-coated on the glass surface, was studied by the T-matrix method, which enables particle agglomeration to be taken into account. The experimental technique used is promising for the production of submicron patterns of plasmonic nanoparticles (given by laser masks or gratings) without damage to the glass surface. Analysis of the applicability of the multi-spheres T-matrix (MSTM) method to the studied material was performed through calculations of SPR characteristics for differently arranged and structured gold nanoparticles (gold nanoparticles in solution, particles pairs, and core-shell silver-gold nanoparticles) for which either experimental data or results of the modeling by other methods are available. For the studied gold nanoparticles in glass, it was revealed that the theoretical description of their SPR spectrum requires consideration of the plasmon coupling between particles, which can be done effectively by MSTM calculations. The obtained statistical distributions over particle sizes and over interparticle distances demonstrated the saturation behavior with respect to the number of particles under consideration, which enabled us to determine the effective aggregate of particles, sufficient to form the SPR spectrum. The suggested technique for the fitting of an experimental SPR spectrum of gold nanoparticles in glass by varying the geometrical parameters of the particles aggregate in the recurring calculations of spectrum by MSTM method enabled us to determine statistical characteristics of the aggregate: the average distance between particles, average size, and size distribution of the particles. The fitting strategy of the SPR spectrum presented here can be applied to nanoparticles of any nature and in various

A Brief Research Review for Improvement Methods the Wettability between Ceramic Reinforcement Particulate and Aluminium Matrix Composites

Science.gov (United States)

Razzaq, Alaa Mohammed; Majid, Dayang Laila Abang Abdul; Ishak, M. R.; B, Uday M.

2017-05-01

The development of new methods for addition fine ceramic powders to Al aluminium alloy melts, which would lead to more uniform distribution and effective incorporation of the reinforcement particles into the aluminium matrix alloy. Recently the materials engineering research has moved to composite materials from monolithic, adapting to the global need for lightweight, low cost, quality, and high performance advanced materials. Among the different methods, stir casting is one of the simplest ways of making aluminium matrix composites. However, it suffers from poor distribution and combination of the reinforcement ceramic particles in the metal matrix. These problems become significantly effect to reduce reinforcement size, more agglomeration and tendency with less wettability for the ceramic particles in the melt process. Many researchers have carried out different studies on the wettability between the metal matrix and dispersion phase, which includes added wettability agents, fluxes, preheating the reinforcement particles, coating the reinforcement particles, and use composting techniques. The enhancement of wettability of ceramic particles by the molten matrix alloy and the reinforcement particles distribution improvement in the solidified matrix is the main objective for many studies that will be discussed in this paper.

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

Energy Technology Data Exchange (ETDEWEB)

Blossier, Benoit [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Paris-XI Univ., 91 - Orsay (France). Lab. de Physique Theorique; Morte, Michele della [CERN, Geneva (Switzerland). Physics Dept.]|[Mainz Univ. (Germany). Inst. fuer Kernphysik; Hippel, Georg von; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Mendes, Tereza [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Sao Paulo Univ. (Brazil). IFSC

2009-02-15

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E{sub N+1}-E{sub n}) t). The gap E{sub N+1}-E{sub n} can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m{sub b} in HQET. (orig.)

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

International Nuclear Information System (INIS)

Blossier, Benoit; Mendes, Tereza; Sao Paulo Univ.

2009-02-01

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E N+1 -E n ) t). The gap E N+1 -E n can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m b in HQET. (orig.)

Determination of Dispersion Curves for Composite Materials with the Use of Stiffness Matrix Method

Directory of Open Access Journals (Sweden)

Barski Marek

2017-06-01

Full Text Available Elastic waves used in Structural Health Monitoring systems have strongly dispersive character. Therefore it is necessary to determine the appropriate dispersion curves in order to proper interpretation of a received dynamic response of an analyzed structure. The shape of dispersion curves as well as number of wave modes depends on mechanical properties of layers and frequency of an excited signal. In the current work, the relatively new approach is utilized, namely stiffness matrix method. In contrast to transfer matrix method or global matrix method, this algorithm is considered as numerically unconditionally stable and as effective as transfer matrix approach. However, it will be demonstrated that in the case of hybrid composites, where mechanical properties of particular layers differ significantly, obtaining results could be difficult. The theoretical relationships are presented for the composite plate of arbitrary stacking sequence and arbitrary direction of elastic waves propagation. As a numerical example, the dispersion curves are estimated for the lamina, which is made of carbon fibers and epoxy resin. It is assumed that elastic waves travel in the parallel, perpendicular and arbitrary direction to the fibers in lamina. Next, the dispersion curves are determined for the following laminate [0°, 90°, 0°, 90°, 0°, 90°, 0°, 90°] and hybrid [Al, 90°, 0°, 90°, 0°, 90°, 0°], where Al is the aluminum alloy PA38 and the rest of layers are made of carbon fibers and epoxy resin.

Rigidity percolation in dispersions with a structured viscoelastic matrix

NARCIS (Netherlands)

Wilbrink, M.W.L.; Michels, M.A.J.; Vellinga, W.P.; Meijer, H.E.H.

2005-01-01

This paper deals with rigidity percolation in composite materials consisting of a dispersion of mineral particles in a microstructured viscoelastic matrix. The viscoelastic matrix in this specific case is a hydrocarbon refinery residue. In a set of model random composites the mean interparticle

A novel method for morphological pleomorphism and heterogeneity quantitative measurement: Named cell feature level co-occurrence matrix.

Science.gov (United States)

Saito, Akira; Numata, Yasushi; Hamada, Takuya; Horisawa, Tomoyoshi; Cosatto, Eric; Graf, Hans-Peter; Kuroda, Masahiko; Yamamoto, Yoichiro

2016-01-01

Recent developments in molecular pathology and genetic/epigenetic analysis of cancer tissue have resulted in a marked increase in objective and measurable data. In comparison, the traditional morphological analysis approach to pathology diagnosis, which can connect these molecular data and clinical diagnosis, is still mostly subjective. Even though the advent and popularization of digital pathology has provided a boost to computer-aided diagnosis, some important pathological concepts still remain largely non-quantitative and their associated data measurements depend on the pathologist's sense and experience. Such features include pleomorphism and heterogeneity. In this paper, we propose a method for the objective measurement of pleomorphism and heterogeneity, using the cell-level co-occurrence matrix. Our method is based on the widely used Gray-level co-occurrence matrix (GLCM), where relations between neighboring pixel intensity levels are captured into a co-occurrence matrix, followed by the application of analysis functions such as Haralick features. In the pathological tissue image, through image processing techniques, each nucleus can be measured and each nucleus has its own measureable features like nucleus size, roundness, contour length, intra-nucleus texture data (GLCM is one of the methods). In GLCM each nucleus in the tissue image corresponds to one pixel. In this approach the most important point is how to define the neighborhood of each nucleus. We define three types of neighborhoods of a nucleus, then create the co-occurrence matrix and apply Haralick feature functions. In each image pleomorphism and heterogeneity are then determined quantitatively. For our method, one pixel corresponds to one nucleus feature, and we therefore named our method Cell Feature Level Co-occurrence Matrix (CFLCM). We tested this method for several nucleus features. CFLCM is showed as a useful quantitative method for pleomorphism and heterogeneity on histopathological image

Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry

International Nuclear Information System (INIS)

Birchall, Christopher; Schomerus, Henning

2012-01-01

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 ' 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’. (paper)

The random projection method

CERN Document Server

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...

Analysis of a wavelength selectable cascaded DFB laser based on the transfer matrix method

International Nuclear Information System (INIS)

Xie Hongyun; Chen Liang; Shen Pei; Sun Botao; Wang Renqing; Xiao Ying; You Yunxia; Zhang Wanrong

2010-01-01

A novel cascaded DFB laser, which consists of two serial gratings to provide selectable wavelengths, is presented and analyzed by the transfer matrix method. In this method, efficient facet reflectivity is derived from the transfer matrix built for each serial section and is then used to simulate the performance of the novel cascaded DFB laser through self-consistently solving the gain equation, the coupled wave equation and the current continuity equations. The simulations prove the feasibility of this kind of wavelength selectable laser and a corresponding designed device with two selectable wavelengths of 1.51 μm and 1.53 μm is realized by experiments on InP-based multiple quantum well structure. (semiconductor devices)

Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method.

Science.gov (United States)

Graf, Daniel; Beuerle, Matthias; Schurkus, Henry F; Luenser, Arne; Savasci, Gökcen; Ochsenfeld, Christian

2018-05-08

An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.

Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

OpenAIRE

Fengjiao Wu; Guitao Zhang; Zhengzhong Wang

2016-01-01

The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. ...

Black holes and random matrices

Energy Technology Data Exchange (ETDEWEB)

Cotler, Jordan S.; Gur-Ari, Guy [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Hanada, Masanori [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); The Hakubi Center for Advanced Research, Kyoto University,Kyoto 606-8502 (Japan); Polchinski, Joseph [Department of Physics, University of California,Santa Barbara, CA 93106 (United States); Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA 93106 (United States); Saad, Phil; Shenker, Stephen H. [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Stanford, Douglas [Institute for Advanced Study,Princeton, NJ 08540 (United States); Streicher, Alexandre [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Department of Physics, University of California,Santa Barbara, CA 93106 (United States); Tezuka, Masaki [Department of Physics, Kyoto University,Kyoto 606-8501 (Japan)

2017-05-22

We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function |Z(β+it)|{sup 2} as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.

Alternating optimization method based on nonnegative matrix factorizations for deep neural networks

OpenAIRE

Sakurai, Tetsuya; Imakura, Akira; Inoue, Yuto; Futamura, Yasunori

2016-01-01

The backpropagation algorithm for calculating gradients has been widely used in computation of weights for deep neural networks (DNNs). This method requires derivatives of objective functions and has some difficulties finding appropriate parameters such as learning rate. In this paper, we propose a novel approach for computing weight matrices of fully-connected DNNs by using two types of semi-nonnegative matrix factorizations (semi-NMFs). In this method, optimization processes are performed b...

Individual magnetization reversal of a square dot matrix by common current excitation

International Nuclear Information System (INIS)

Elyasi, Mehrdad; Bhatia, Charanjit S; Yang, Hyunsoo

2015-01-01

We have proposed a method for magnetization reversal of individual sites of a 2 by 2 matrix of perpendicularly magnetized dots by common current excitation. The spin-polarized current signal consists of a dc-biased ac part followed by a pure dc one. The amplitude of the dc and ac parts of the current, as well as the phase and duration of the ac current, determine the reversal sites through the magnetostatic interaction among the dots. We show that the individual selectivity in magnetization reversal occurs through two consecutive steps, dephasing of the matrix dyadic pairs dynamics followed by nonlinear dephasing of the individual elements. This method can be utilized to increase the storage density of magnetic random access memory by enabling common access for four or more bits. (paper)

Numerical Methods Application for Reinforced Concrete Elements-Theoretical Approach for Direct Stiffness Matrix Method

Directory of Open Access Journals (Sweden)

Sergiu Ciprian Catinas

2015-07-01

Full Text Available A detailed theoretical and practical investigation of the reinforced concrete elements is due to recent techniques and method that are implemented in the construction market. More over a theoretical study is a demand for a better and faster approach nowadays due to rapid development of the calculus technique. The paper above will present a study for implementing in a static calculus the direct stiffness matrix method in order capable to address phenomena related to different stages of loading, rapid change of cross section area and physical properties. The method is a demand due to the fact that in our days the FEM (Finite Element Method is the only alternative to such a calculus and FEM are considered as expensive methods from the time and calculus resources point of view. The main goal in such a method is to create the moment-curvature diagram in the cross section that is analyzed. The paper above will express some of the most important techniques and new ideas as well in order to create the moment curvature graphic in the cross sections considered.

Nuclear Matrix Elements for the $\\beta\\beta$ Decay of the $^{76}$Ge

CERN Document Server

Brown, B A; Horoi, M

2015-01-01

The nuclear matrix elements for two-neutrino double-beta (2 n$\\beta\\beta$ ) and zero-neutrino double-beta (0 n$\\beta\\beta$) decay of 76 Ge are evaluated in terms of the configuration interaction (CI), quasiparticle random phase approximation (QRPA) and interacting boson model (IBM) methods. We show that the decomposition of the matrix elements in terms of interemediate states in 74 Ge is dominated by ground state of this nucleus. We consider corrections to the CI results that arise from configurations admixtures involving orbitals out-side of the CI configuration space by using results from QRPA, many-body-perturbation theory, and the connections to related observables. The CI two-neutrino matrix element is reduced due to the inclusion of spin-orbit partners, and to many-body correlations connected with Gamow-Teller beta decay. The CI zero-neutrino matrix element for the heavy neutrino is enhanced due to particle-particle correlations that are connected with the odd-even oscillations in the nuclear masse...

Intercomparison of the GOS approach, superposition T-matrix method, and laboratory measurements for black carbon optical properties during aging

International Nuclear Information System (INIS)

He, Cenlin; Takano, Yoshi; Liou, Kuo-Nan; Yang, Ping; Li, Qinbin; Mackowski, Daniel W.

2016-01-01

We perform a comprehensive intercomparison of the geometric-optics surface-wave (GOS) approach, the superposition T-matrix method, and laboratory measurements for optical properties of fresh and coated/aged black carbon (BC) particles with complex structures. GOS and T-matrix calculations capture the measured optical (i.e., extinction, absorption, and scattering) cross sections of fresh BC aggregates, with 5–20% differences depending on particle size. We find that the T-matrix results tend to be lower than the measurements, due to uncertainty in theoretical approximations of realistic BC structures, particle property measurements, and numerical computations in the method. On the contrary, the GOS results are higher than the measurements (hence the T-matrix results) for BC radii 100 nm. We find good agreement (differences 100 nm. We find small deviations (≤10%) in asymmetry factors computed from the two methods for most BC coating structures and sizes, but several complex structures have 10–30% differences. This study provides the foundation for downstream application of the GOS approach in radiative transfer and climate studies. - Highlights: • The GOS and T-matrix methods capture laboratory measurements of BC optical properties. • The GOS results are consistent with the T-matrix results for BC optical properties. • BC optical properties vary remarkably with coating structures and sizes during aging.

Development of spectral history methods for pin-by-pin core analysis method using three-dimensional direct response matrix

International Nuclear Information System (INIS)

Mitsuyasu, T.; Ishii, K.; Hino, T.; Aoyama, M.

2009-01-01

Spectral history methods for pin-by-pin core analysis method using the three-dimensional direct response matrix have been developed. The direct response matrix is formalized by four sub-response matrices in order to respond to a core eigenvalue k and thus can be recomposed at each outer iteration in the core analysis. For core analysis, it is necessary to take into account the burn-up effect related to spectral history. One of the methods is to evaluate the nodal burn-up spectrum obtained using the out-going neutron current. The other is to correct the fuel rod neutron production rates obtained the pin-by-pin correction. These spectral history methods were tested in a heterogeneous system. The test results show that the neutron multiplication factor error can be reduced by half during burn-up, the nodal neutron production rates errors can be reduced by 30% or more. The root-mean-square differences between the relative fuel rod neutron production rate distributions can be reduced within 1.1% error. This means that these methods can accurately reflect the effects of intra- and inter-assembly heterogeneities during burn-up and can be used for core analysis. Core analysis with the DRM method was carried out for an ABWR quarter core and it was found that both thermal power and coolant-flow distributions were smoothly converged. (authors)

Chaos, complexity, and random matrices

Science.gov (United States)

Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu; Yoshida, Beni

2017-11-01

Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.

The Theory of Random Laser Systems

International Nuclear Information System (INIS)

Xunya Jiang

2002-01-01

Studies of random laser systems are a new direction with promising potential applications and theoretical interest. The research is based on the theories of localization and laser physics. So far, the research shows that there are random lasing modes inside the systems which is quite different from the common laser systems. From the properties of the random lasing modes, they can understand the phenomena observed in the experiments, such as multi-peak and anisotropic spectrum, lasing mode number saturation, mode competition and dynamic processes, etc. To summarize, this dissertation has contributed the following in the study of random laser systems: (1) by comparing the Lamb theory with the Letokhov theory, the general formulas of the threshold length or gain of random laser systems were obtained; (2) they pointed out the vital weakness of previous time-independent methods in random laser research; (3) a new model which includes the FDTD method and the semi-classical laser theory. The solutions of this model provided an explanation of the experimental results of multi-peak and anisotropic emission spectra, predicted the saturation of lasing modes number and the length of localized lasing modes; (4) theoretical (Lamb theory) and numerical (FDTD and transfer-matrix calculation) studies of the origin of localized lasing modes in the random laser systems; and (5) proposal of using random lasing modes as a new path to study wave localization in random systems and prediction of the lasing threshold discontinuity at mobility edge

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...

A novel image encryption algorithm based on synchronized random bit generated in cascade-coupled chaotic semiconductor ring lasers

Science.gov (United States)

Li, Jiafu; Xiang, Shuiying; Wang, Haoning; Gong, Junkai; Wen, Aijun

2018-03-01

In this paper, a novel image encryption algorithm based on synchronization of physical random bit generated in a cascade-coupled semiconductor ring lasers (CCSRL) system is proposed, and the security analysis is performed. In both transmitter and receiver parts, the CCSRL system is a master-slave configuration consisting of a master semiconductor ring laser (M-SRL) with cross-feedback and a solitary SRL (S-SRL). The proposed image encryption algorithm includes image preprocessing based on conventional chaotic maps, pixel confusion based on control matrix extracted from physical random bit, and pixel diffusion based on random bit stream extracted from physical random bit. Firstly, the preprocessing method is used to eliminate the correlation between adjacent pixels. Secondly, physical random bit with verified randomness is generated based on chaos in the CCSRL system, and is used to simultaneously generate the control matrix and random bit stream. Finally, the control matrix and random bit stream are used for the encryption algorithm in order to change the position and the values of pixels, respectively. Simulation results and security analysis demonstrate that the proposed algorithm is effective and able to resist various typical attacks, and thus is an excellent candidate for secure image communication application.

The augmented lagrange multipliers method for matrix completion from corrupted samplings with application to mixed Gaussian-impulse noise removal.

Directory of Open Access Journals (Sweden)

Fan Meng

Full Text Available This paper studies the problem of the restoration of images corrupted by mixed Gaussian-impulse noise. In recent years, low-rank matrix reconstruction has become a research hotspot in many scientific and engineering domains such as machine learning, image processing, computer vision and bioinformatics, which mainly involves the problem of matrix completion and robust principal component analysis, namely recovering a low-rank matrix from an incomplete but accurate sampling subset of its entries and from an observed data matrix with an unknown fraction of its entries being arbitrarily corrupted, respectively. Inspired by these ideas, we consider the problem of recovering a low-rank matrix from an incomplete sampling subset of its entries with an unknown fraction of the samplings contaminated by arbitrary errors, which is defined as the problem of matrix completion from corrupted samplings and modeled as a convex optimization problem that minimizes a combination of the nuclear norm and the l(1-norm in this paper. Meanwhile, we put forward a novel and effective algorithm called augmented Lagrange multipliers to exactly solve the problem. For mixed Gaussian-impulse noise removal, we regard it as the problem of matrix completion from corrupted samplings, and restore the noisy image following an impulse-detecting procedure. Compared with some existing methods for mixed noise removal, the recovery quality performance of our method is dominant if images possess low-rank features such as geometrically regular textures and similar structured contents; especially when the density of impulse noise is relatively high and the variance of Gaussian noise is small, our method can outperform the traditional methods significantly not only in the simultaneous removal of Gaussian noise and impulse noise, and the restoration ability for a low-rank image matrix, but also in the preservation of textures and details in the image.

Quantum mechanics in matrix form

CERN Document Server

Ludyk, Günter

2018-01-01

This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix  method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac´s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.

Examining drivers' eye glance patterns during distracted driving: Insights from scanning randomness and glance transition matrix.

Science.gov (United States)

Wang, Yuan; Bao, Shan; Du, Wenjun; Ye, Zhirui; Sayer, James R

2017-12-01

Visual attention to the driving environment is of great importance for road safety. Eye glance behavior has been used as an indicator of distracted driving. This study examined and quantified drivers' glance patterns and features during distracted driving. Data from an existing naturalistic driving study were used. Entropy rate was calculated and used to assess the randomness associated with drivers' scanning patterns. A glance-transition proportion matrix was defined to quantity visual search patterns transitioning among four main eye glance locations while driving (i.e., forward on-road, phone, mirrors and others). All measurements were calculated within a 5s time window under both cell phone and non-cell phone use conditions. Results of the glance data analyses showed different patterns between distracted and non-distracted driving, featured by a higher entropy rate value and highly biased attention transferring between forward and phone locations during distracted driving. Drivers in general had higher number of glance transitions, and their on-road glance duration was significantly shorter during distracted driving when compared to non-distracted driving. Results suggest that drivers have a higher scanning randomness/disorder level and shift their main attention from surrounding areas towards phone area when engaging in visual-manual tasks. Drivers' visual search patterns during visual-manual distraction with a high scanning randomness and a high proportion of eye glance transitions towards the location of the phone provide insight into driver distraction detection. This will help to inform the design of in-vehicle human-machine interface/systems. Copyright © 2017. Published by Elsevier Ltd.

Comparison of matrix exponential methods for fuel burnup calculations

International Nuclear Information System (INIS)

Oh, Hyung Suk; Yang, Won Sik

1999-01-01

Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7. (author). 11 refs., 4 figs., 2 tabs

On renormalization group flow in matrix model

International Nuclear Information System (INIS)

Gao, H.B.

1992-10-01

The renormalization group flow recently found by Brezin and Zinn-Justin by integrating out redundant entries of the (N+1)x(N+1) Hermitian random matrix is studied. By introducing explicitly the RG flow parameter, and adding suitable counter terms to the matrix potential of the one matrix model, we deduce some interesting properties of the RG trajectories. In particular, the string equation for the general massive model interpolating between the UV and IR fixed points turns out to be a consequence of RG flow. An ambiguity in the UV region of the RG trajectory is remarked to be related to the large order behaviour of the one matrix model. (author). 7 refs

Colloquium: Random matrices and chaos in nuclear spectra

International Nuclear Information System (INIS)

Papenbrock, T.; Weidenmueller, H. A.

2007-01-01

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

Calculation of the fast multiplication factor by the fission matrix method

International Nuclear Information System (INIS)

Naumov, V.A.; Rozin, S.G.; Ehl'perin, T.I.

1976-01-01

A variation of the Monte Carlo method to calculate an effective breeding factor of a nuclear reactor is described. The evaluation procedure of reactivity perturbations by the Monte Carlo method in the first order perturbation theory is considered. The method consists in reducing an integral neutron transport equation to a set of linear algebraic equations. The coefficients of this set are elements of a fission matrix. The fission matrix being a Grin function of the neutron transport equation, is evaluated by the Monte Carlo method. In the program realizing the suggested algorithm, the game for initial neutron energy of a fission spectrum and then for the region of neutron birth, ΔVsub(f)sup(i)has been played in proportion to the product of Σsub(f)sup(i)ΔVsub(f)sup(i), where Σsub(f)sup(i) is a macroscopic cross section in the region numbered at the birth energy. Further iterations of a space distribution of neutrons in the system are performed by the generation method. In the adopted scheme of simulation of neutron histories the emission of secondary neutrons is controlled by weights; it occurs at every collision and not only in the end on the history. The breeding factor is calculated simultaneously with the space distribution of neutron worth in the system relative to the fission process and neutron flux. Efficiency of the described procedure has been tested on the calculation of the breeding factor for the Godiva assembly, simulating a fast reactor with a hard spectrum. A high accuracy of calculations at moderate number of zones in the core and reasonable statistics has been stated

How random is a random vector?

International Nuclear Information System (INIS)

Eliazar, Iddo

2015-01-01

Over 80 years ago Samuel Wilks proposed that the “generalized variance” of a random vector is the determinant of its covariance matrix. To date, the notion and use of the generalized variance is confined only to very specific niches in statistics. In this paper we establish that the “Wilks standard deviation” –the square root of the generalized variance–is indeed the standard deviation of a random vector. We further establish that the “uncorrelation index” –a derivative of the Wilks standard deviation–is a measure of the overall correlation between the components of a random vector. Both the Wilks standard deviation and the uncorrelation index are, respectively, special cases of two general notions that we introduce: “randomness measures” and “independence indices” of random vectors. In turn, these general notions give rise to “randomness diagrams”—tangible planar visualizations that answer the question: How random is a random vector? The notion of “independence indices” yields a novel measure of correlation for Lévy laws. In general, the concepts and results presented in this paper are applicable to any field of science and engineering with random-vectors empirical data.

How random is a random vector?

Science.gov (United States)

Eliazar, Iddo

2015-12-01

Over 80 years ago Samuel Wilks proposed that the "generalized variance" of a random vector is the determinant of its covariance matrix. To date, the notion and use of the generalized variance is confined only to very specific niches in statistics. In this paper we establish that the "Wilks standard deviation" -the square root of the generalized variance-is indeed the standard deviation of a random vector. We further establish that the "uncorrelation index" -a derivative of the Wilks standard deviation-is a measure of the overall correlation between the components of a random vector. Both the Wilks standard deviation and the uncorrelation index are, respectively, special cases of two general notions that we introduce: "randomness measures" and "independence indices" of random vectors. In turn, these general notions give rise to "randomness diagrams"-tangible planar visualizations that answer the question: How random is a random vector? The notion of "independence indices" yields a novel measure of correlation for Lévy laws. In general, the concepts and results presented in this paper are applicable to any field of science and engineering with random-vectors empirical data.

Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix and Polymer Matrix Composite Structures

Science.gov (United States)

Nemeth, Noel N.; Bednarcyk, Brett A.; Pineda, Evan J.; Walton, Owen J.; Arnold, Steven M.

2016-01-01

Stochastic-based, discrete-event progressive damage simulations of ceramic-matrix composite and polymer matrix composite material structures have been enabled through the development of a unique multiscale modeling tool. This effort involves coupling three independently developed software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/ Life), and (3) the Abaqus finite element analysis (FEA) program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating unit cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC. Abaqus is used at the global scale to model the overall composite structure. An Abaqus user-defined material (UMAT) interface, referred to here as "FEAMAC/CARES," was developed that enables MAC/GMC and CARES/Life to operate seamlessly with the Abaqus FEA code. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events, which incrementally progress and lead to ultimate structural failure. This report describes the FEAMAC/CARES methodology and discusses examples that illustrate the performance of the tool. A comprehensive example problem, simulating the progressive damage of laminated ceramic matrix composites under various off-axis loading conditions and including a double notched tensile specimen geometry, is described in a separate report.

Teaching Improvement Model Designed with DEA Method and Management Matrix

Science.gov (United States)

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…

Empirical method for matrix effects correction in liquid samples

International Nuclear Information System (INIS)

Vigoda de Leyt, Dora; Vazquez, Cristina

1987-01-01

A simple method for the determination of Cr, Ni and Mo in stainless steels is presented. In order to minimize the matrix effects, the conditions of liquid system to dissolve stainless steels chips has been developed. Pure element solutions were used as standards. Preparation of synthetic solutions with all the elements of steel and also mathematic corrections are avoided. It results in a simple chemical operation which simplifies the method of analysis. The variance analysis of the results obtained with steel samples show that the three elements may be determined from the comparison with the analytical curves obtained with the pure elements if the same parameters in the calibration curves are used. The accuracy and the precision were checked against other techniques using the British Chemical Standards of the Bureau of Anlysed Samples Ltd. (England). (M.E.L.) [es

Love waves in functionally graded piezoelectric materials by stiffness matrix method.

Science.gov (United States)

Ben Salah, Issam; Wali, Yassine; Ben Ghozlen, Mohamed Hédi

2011-04-01

A numerical matrix method relative to the propagation of ultrasonic guided waves in functionally graded piezoelectric heterostructure is given in order to make a comparative study with the respective performances of analytical methods proposed in literature. The preliminary obtained results show a good agreement, however numerical approach has the advantage of conceptual simplicity and flexibility brought about by the stiffness matrix method. The propagation behaviour of Love waves in a functionally graded piezoelectric material (FGPM) is investigated in this article. It involves a thin FGPM layer bonded perfectly to an elastic substrate. The inhomogeneous FGPM heterostructure has been stratified along the depth direction, hence each state can be considered as homogeneous and the ordinary differential equation method is applied. The obtained solutions are used to study the effect of an exponential gradient applied to physical properties. Such numerical approach allows applying different gradient variation for mechanical and electrical properties. For this case, the obtained results reveal opposite effects. The dispersive curves and phase velocities of the Love wave propagation in the layered piezoelectric film are obtained for electrical open and short cases on the free surface, respectively. The effect of gradient coefficients on coupled electromechanical factor, on the stress fields, the electrical potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the well known heterostructure PZT-5H/SiO(2), the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Love wave propagation behaviour. Copyright © 2010 Elsevier B.V. All rights reserved.

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.

The nuclear reaction matrix

International Nuclear Information System (INIS)

Krenciglowa, E.M.; Kung, C.L.; Kuo, T.T.S.; Osnes, E.; and Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794)

1976-01-01

Different definitions of the reaction matrix G appropriate to the calculation of nuclear structure are reviewed and discussed. Qualitative physical arguments are presented in support of a two-step calculation of the G-matrix for finite nuclei. In the first step the high-energy excitations are included using orthogonalized plane-wave intermediate states, and in the second step the low-energy excitations are added in, using harmonic oscillator intermediate states. Accurate calculations of G-matrix elements for nuclear structure calculations in the Aapprox. =18 region are performed following this procedure and treating the Pauli exclusion operator Q 2 /sub p/ by the method of Tsai and Kuo. The treatment of Q 2 /sub p/, the effect of the intermediate-state spectrum and the energy dependence of the reaction matrix are investigated in detail. The present matrix elements are compared with various matrix elements given in the literature. In particular, close agreement is obtained with the matrix elements calculated by Kuo and Brown using approximate methods

The classical r-matrix method for nonlinear sigma-model

OpenAIRE

Sevostyanov, Alexey

1995-01-01

The canonical Poisson structure of nonlinear sigma-model is presented as a Lie-Poisson r-matrix bracket on coadjoint orbits. It is shown that the Poisson structure of this model is determined by some `hidden singularities' of the Lax matrix.

New computational method for non-LTE, the linear response matrix

International Nuclear Information System (INIS)

Fournier, K.B.; Grasiani, F.R.; Harte, J.A.; Libby, S.B.; More, R.M.; Zimmerman, G.B.

1998-01-01

My coauthors have done extensive theoretical and computational calculations that lay the ground work for a linear response matrix method to calculate non-LTE (local thermodynamic equilibrium) opacities. I will give briefly review some of their work and list references. Then I will describe what has been done to utilize this theory to create a computational package to rapidly calculate mild non-LTE emission and absorption opacities suitable for use in hydrodynamic calculations. The opacities are obtained by performing table look-ups on data that has been generated with a non-LTE package. This scheme is currently under development. We can see that it offers a significant computational speed advantage. It is suitable for mild non-LTE, quasi-steady conditions. And it offers a new insertion path for high-quality non-LTE data. Currently, the linear response matrix data file is created using XSN. These data files could be generated by more detailed and rigorous calculations without changing any part of the implementation in the hydro code. The scheme is running in Lasnex and is being tested and developed

An algorithm for seeking the optimum value of a function: 'random' method; Un algorithme de recherche de l'optimum d'une fonction: la methode random

Energy Technology Data Exchange (ETDEWEB)

Guais, J C [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1967-07-01

After a brief survey of classical techniques for static optimization, we present a Random seeking method for any function, of an arbitrary number of variables, with constraints. The resulting program is shown and illustrated by some examples. The comparison with classical methods points out the advantages of Random in some cases where analytic procedures fail or require too much calculation time. (author) [French] Apres une rapide revue des differents procedes actuels d'optimisation statique, on expose une methode de recherche aleatoire du minimum (ou du maximum) d'une fonction quelconque, definie sur un nombre theoriquement illimite de parametres independants, avec contraintes. Le programme resultant est presente. Il est illustre par quelques exemples simples et compare a des methodes d'optimisation classiques; Ceci montre en particulier que le programme RANDOM permet une recherche aisee d'extrema dans certains cas ou d'autres programmes ne conduisent pas a des solutions satisfaisantes ou bien demandent un temps calcul prohibitif. (auteur)

Dynamical correlations for circular ensembles of random matrices

International Nuclear Information System (INIS)

Nagao, Taro; Forrester, Peter

2003-01-01

Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue of antisymmetric Hermitian matrix initial conditions, Brownian dynamics toward the unitary symmetry is analyzed. The dynamical correlation functions of arbitrary number of Brownian particles at arbitrary number of times are shown to be written in the forms of quaternion determinants, similarly as in the case of Hermitian random matrix models

Parallel R-matrix computation

International Nuclear Information System (INIS)

Heggarty, J.W.

1999-06-01

response to the challenge of achieving parallel R-matrix computation. The primary objective was to develop parallel codes, targeted at multicomputers, that are capable of performing R-matrix calculations hitherto intractable using classic supercomputers. In particular, Fortran implementations of two internal region methods (the R-matrix Floquet method and the two-dimensional R-matrix propagation method) and three external region methods (the Light-Walker propagation method, the Baluja, Burke and Morgan propagation method and the Variable Phase Method) from four widely utilised R-matrix packages were investigated to ascertain whether, in these cases, parallel R-matrix computation was practicable and, if so, to determine the most effective way to port such codes to contemporary multicomputers. When attempting to develop the parallel codes, a number of computer aided automatic parallelization tools were investigated. These were found to be inadequate. Consequently, a parallelization approach was developed to provide simple guidelines for manual parallelization. This parallelization approach proved effective and efficient parallel versions of the five R-matrix codes were successfully developed. (author)

Radiation safety assessment of cobalt 60 external beam radiotherapy using the risk-matrix method

International Nuclear Information System (INIS)

Dumenigo, C; Vilaragut, J.J.; Ferro, R.; Guillen, A.; Ramirez, M.L.; Ortiz Lopez, P.; Rodriguez, M.; McDonnell, J.D.; Papadopulos, S.; Pereira, P.P.; Goncalvez, M.; Morales, J.; Larrinaga, E.; Lopez Morones, R.; Sanchez, R.; Delgado, J.M.; Sanchez, C.; Somoano, F.

2008-01-01

External beam radiotherapy is the only practice in which humans are placed directly in a radiation beam with the intention to deliver a very high dose. This is why safety in radiotherapy is very critical, and is a matter of interest to both radiotherapy departments and regulatory bodies. Accidental exposures have occurred throughout the world, thus showing the need for systematic safety assessments, capable to identify preventive measures and to minimize consequences of accidental exposure. Risk-matrix is a systematic approach which combines the relevant event features to assess the overall risk of each particular event. Once an event sequence is identified, questions such as how frequent the event, how severe the potential consequences and how reliable the existing safety measures are answered in a risk-matrix table. The ultimate goal is to achieve that the overall risk for events with severe consequences should always be low o very low. In the present study, the risk-matrix method has been applied to an hypothetical radiotherapy department, which could be equivalent to an upper level hospital of the Ibero American region, in terms of safety checks and preventive measures. The application of the method has identified 76 event sequences and revealed that the hypothetical radiotherapy department is sufficiently protected (low risk) against them, including 23 event sequences with severe consequences. The method has revealed that the risk of these sequences could grow to high level if certain specific preventive measures were degraded with time. This study has identified these preventive measures, thus facilitating a rational allocation of resources in regular controls to detect any loss of reliability. The method has proven to have an important practical value and is affordable at hospital level. The elaborated risk-matrix can be easily adapted to local circumstances, in terms of existing controls and safety measures. This approach can help hospitals to identify

The study of combining Latin Hypercube Sampling method and LU decomposition method (LULHS method) for constructing spatial random field

Science.gov (United States)

WANG, P. T.

2015-12-01

Groundwater modeling requires to assign hydrogeological properties to every numerical grid. Due to the lack of detailed information and the inherent spatial heterogeneity, geological properties can be treated as random variables. Hydrogeological property is assumed to be a multivariate distribution with spatial correlations. By sampling random numbers from a given statistical distribution and assigning a value to each grid, a random field for modeling can be completed. Therefore, statistics sampling plays an important role in the efficiency of modeling procedure. Latin Hypercube Sampling (LHS) is a stratified random sampling procedure that provides an efficient way to sample variables from their multivariate distributions. This study combines the the stratified random procedure from LHS and the simulation by using LU decomposition to form LULHS. Both conditional and unconditional simulations of LULHS were develpoed. The simulation efficiency and spatial correlation of LULHS are compared to the other three different simulation methods. The results show that for the conditional simulation and unconditional simulation, LULHS method is more efficient in terms of computational effort. Less realizations are required to achieve the required statistical accuracy and spatial correlation.

High-dimensional statistical inference: From vector to matrix

Science.gov (United States)

Zhang, Anru

estimator is easy to implement via convex programming and performs well numerically. The techniques and main results developed in the chapter also have implications to other related statistical problems. An application to estimation of spiked covariance matrices from one-dimensional random projections is considered. The results demonstrate that it is still possible to accurately estimate the covariance matrix of a high-dimensional distribution based only on one-dimensional projections. For the third part of the thesis, we consider another setting of low-rank matrix completion. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.

Batched QR and SVD Algorithms on GPUs with Applications in Hierarchical Matrix Compression

KAUST Repository

Halim Boukaram, Wajih

2017-09-14

We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used for its simplicity and inherent parallelism as a building block for the SVD of low rank blocks using randomized methods. We implement multiple kernels based on the level of the GPU memory hierarchy in which the matrices can reside and show substantial speedups against streamed cuSOLVER SVDs. The resulting batched routine is a key component of hierarchical matrix compression, opening up opportunities to perform H-matrix arithmetic efficiently on GPUs.

Batched QR and SVD Algorithms on GPUs with Applications in Hierarchical Matrix Compression

KAUST Repository

Halim Boukaram, Wajih; Turkiyyah, George; Ltaief, Hatem; Keyes, David E.

2017-01-01

We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used for its simplicity and inherent parallelism as a building block for the SVD of low rank blocks using randomized methods. We implement multiple kernels based on the level of the GPU memory hierarchy in which the matrices can reside and show substantial speedups against streamed cuSOLVER SVDs. The resulting batched routine is a key component of hierarchical matrix compression, opening up opportunities to perform H-matrix arithmetic efficiently on GPUs.

Analysis of random response of structure with uncertain parameters. Combination of substructure synthesis method and hierarchy method

International Nuclear Information System (INIS)

Iwatsubo, Takuzo; Kawamura, Shozo; Mori, Hiroyuki.

1995-01-01

In this paper, the method to obtain the random response of a structure with uncertain parameters is proposed. The proposed method is a combination of the substructure synthesis method and the hierarchy method. The concept of the proposed method is that the hierarchy equation of each substructure is obtained using the hierarchy method, and the hierarchy equation of the overall structure is obtained using the substructure synthesis method. Using the proposed method, the reduced order hierarchy equation can be obtained without analyzing the original whole structure. After the calculation of the mean square value of response, the reliability analysis can be carried out based on the first passage problem and Poisson's excursion rate. As a numerical example of structure, a simple piping system is considered. The damping constant of the support is considered as the uncertainty parameter. Then the random response is calculated using the proposed method. As a result, the proposed method is useful to analyze the random response in terms of the accuracy, computer storage and calculation time. (author)

Highly accelerated cardiac cine parallel MRI using low-rank matrix completion and partial separability model

Science.gov (United States)

Lyu, Jingyuan; Nakarmi, Ukash; Zhang, Chaoyi; Ying, Leslie

2016-05-01

This paper presents a new approach to highly accelerated dynamic parallel MRI using low rank matrix completion, partial separability (PS) model. In data acquisition, k-space data is moderately randomly undersampled at the center kspace navigator locations, but highly undersampled at the outer k-space for each temporal frame. In reconstruction, the navigator data is reconstructed from undersampled data using structured low-rank matrix completion. After all the unacquired navigator data is estimated, the partial separable model is used to obtain partial k-t data. Then the parallel imaging method is used to acquire the entire dynamic image series from highly undersampled data. The proposed method has shown to achieve high quality reconstructions with reduction factors up to 31, and temporal resolution of 29ms, when the conventional PS method fails.

Matrix models of 2d gravity

International Nuclear Information System (INIS)

Ginsparg, P.

1991-01-01

These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date

A METHOD TO ESTIMATE TEMPORAL INTERACTION IN A CONDITIONAL RANDOM FIELD BASED APPROACH FOR CROP RECOGNITION

Directory of Open Access Journals (Sweden)

P. M. A. Diaz

2016-06-01

Full Text Available This paper presents a method to estimate the temporal interaction in a Conditional Random Field (CRF based approach for crop recognition from multitemporal remote sensing image sequences. This approach models the phenology of different crop types as a CRF. Interaction potentials are assumed to depend only on the class labels of an image site at two consecutive epochs. In the proposed method, the estimation of temporal interaction parameters is considered as an optimization problem, whose goal is to find the transition matrix that maximizes the CRF performance, upon a set of labelled data. The objective functions underlying the optimization procedure can be formulated in terms of different accuracy metrics, such as overall and average class accuracy per crop or phenological stages. To validate the proposed approach, experiments were carried out upon a dataset consisting of 12 co-registered LANDSAT images of a region in southeast of Brazil. Pattern Search was used as the optimization algorithm. The experimental results demonstrated that the proposed method was able to substantially outperform estimates related to joint or conditional class transition probabilities, which rely on training samples.

Matrix elements and few-body calculations within the unitary correlation operator method

International Nuclear Information System (INIS)

Roth, R.; Hergert, H.; Papakonstantinou, P.

2005-01-01

We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges. (orig.)

Matrix elements and few-body calculations within the unitary correlation operator method

International Nuclear Information System (INIS)

Roth, R.; Hergert, H.; Papakonstantinou, P.; Neff, T.; Feldmeier, H.

2005-01-01

We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges

Hamiltonian formalism, quantization and S matrix for supergravity. [S matrix, canonical constraints

Energy Technology Data Exchange (ETDEWEB)

Fradkin, E S; Vasiliev, M A [AN SSSR, Moscow. Fizicheskij Inst.

1977-12-05

The canonical formalism for supergravity is constructed. The algebra of canonical constraints is found. The correct expression for the S matrix is obtained. Usual 'covariant methods' lead to an incorrect S matrix in supergravity since a new four-particle interaction of ghostfields survives in the Lagrangian expression of the S matrix.

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,...