Permuting sparse rectangular matrices into block-diagonal form

Energy Technology Data Exchange (ETDEWEB)

Aykanat, Cevdet; Pinar, Ali; Catalyurek, Umit V.

2002-12-09

This work investigates the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for the solution of the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Besides proposing the models to represent sparse matrices and investigating related combinatorial problems, we provide a detailed survey of relevant literature to bridge the gap between different societies, investigate existing techniques for partitioning and propose new ones, and finally present a thorough empirical study of these techniques. Our experiments on a wide range of matrices, using state-of-the-art graph and hypergraph partitioning tools MeTiS and PaT oH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and run time.

Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts

Science.gov (United States)

Noble, J. H.; Lubasch, M.; Stevens, J.; Jentschura, U. D.

2017-12-01

We describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices, A ̲ =A̲T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product 〈 u ̲ , v ̲ 〉 ∗ =∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generalized Householder transformations (first step). An iterative, generalized QL decomposition of the tridiagonal matrix employing an implicit shift converges toward diagonal form (second step). The QL algorithm employs iterative deflation techniques when a machine-precision zero is encountered "prematurely" on the super-/sub-diagonal. The algorithm allows for a reliable and computationally efficient computation of resonance and antiresonance energies which emerge from complex-scaled Hamiltonians, and for the numerical determination of the real energy eigenvalues of pseudo-Hermitian and PT-symmetric Hamilton matrices. Numerical reference values are provided.

Lanczos Tridiagonalization and Core Problems

Czech Academy of Sciences Publication Activity Database

Hnětynková, Iveta; Strakoš, Zdeněk

2007-01-01

Roč. 421, č. 2-3 (2007), s. 243-251 ISSN 0024-3795 R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z10300504 Keywords : linear approximation problem * orthogonal transformation * core problem * Golub-Kahan bidiagonalization * Lanczos tridiagonalization * Jacobi matrix Subject RIV: BA - General Mathematics Impact factor: 0.702, year: 2007

A hybrid method for the parallel computation of Green's functions

International Nuclear Information System (INIS)

Petersen, Dan Erik; Li Song; Stokbro, Kurt; Sorensen, Hans Henrik B.; Hansen, Per Christian; Skelboe, Stig; Darve, Eric

2009-01-01

Quantum transport models for nanodevices using the non-equilibrium Green's function method require the repeated calculation of the block tridiagonal part of the Green's and lesser Green's function matrices. This problem is related to the calculation of the inverse of a sparse matrix. Because of the large number of times this calculation needs to be performed, this is computationally very expensive even on supercomputers. The classical approach is based on recurrence formulas which cannot be efficiently parallelized. This practically prevents the solution of large problems with hundreds of thousands of atoms. We propose new recurrences for a general class of sparse matrices to calculate Green's and lesser Green's function matrices which extend formulas derived by Takahashi and others. We show that these recurrences may lead to a dramatically reduced computational cost because they only require computing a small number of entries of the inverse matrix. Then, we propose a parallelization strategy for block tridiagonal matrices which involves a combination of Schur complement calculations and cyclic reduction. It achieves good scalability even on problems of modest size.

Arikan and Alamouti matrices based on fast block-wise inverse Jacket transform

Science.gov (United States)

Lee, Moon Ho; Khan, Md Hashem Ali; Kim, Kyeong Jin

2013-12-01

Recently, Lee and Hou (IEEE Signal Process Lett 13: 461-464, 2006) proposed one-dimensional and two-dimensional fast algorithms for block-wise inverse Jacket transforms (BIJTs). Their BIJTs are not real inverse Jacket transforms from mathematical point of view because their inverses do not satisfy the usual condition, i.e., the multiplication of a matrix with its inverse matrix is not equal to the identity matrix. Therefore, we mathematically propose a fast block-wise inverse Jacket transform of orders N = 2 k , 3 k , 5 k , and 6 k , where k is a positive integer. Based on the Kronecker product of the successive lower order Jacket matrices and the basis matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse and fast algorithms of Arikan polar binary and Alamouti multiple-input multiple-output (MIMO) non-binary matrices, which are obtained from BIJTs, they can be applied in areas such as 3GPP physical layer for ultra mobile broadband permutation matrices design, first-order q-ary Reed-Muller code design, diagonal channel design, diagonal subchannel decompose for interference alignment, and 4G MIMO long-term evolution Alamouti precoding design.

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

Science.gov (United States)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

A tridiagonal parsimonious higher order multivariate Markov chain model

Science.gov (United States)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, we present a tridiagonal parsimonious higher-order multivariate Markov chain model (TPHOMMCM). Moreover, estimation method of the parameters in TPHOMMCM is give. Numerical experiments illustrate the effectiveness of TPHOMMCM.

Recursive tridiagonalization of infinite dimensional Hamiltonians

International Nuclear Information System (INIS)

Haydock, R.; Oregon Univ., Eugene, OR

1989-01-01

Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)

A Fast parallel tridiagonal algorithm for a class of CFD applications

Science.gov (United States)

Moitra, Stuti; Sun, Xian-He

1996-01-01

The parallel diagonal dominant (PDD) algorithm is an efficient tridiagonal solver. This paper presents for study a variation of the PDD algorithm, the reduced PDD algorithm. The new algorithm maintains the minimum communication provided by the PDD algorithm, but has a reduced operation count. The PDD algorithm also has a smaller operation count than the conventional sequential algorithm for many applications. Accuracy analysis is provided for the reduced PDD algorithm for symmetric Toeplitz tridiagonal (STT) systems. Implementation results on Langley's Intel Paragon and IBM SP2 show that both the PDD and reduced PDD algorithms are efficient and scalable.

A general approach to analyse preconditioners two-by-two block matrices

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe

2012-01-01

Roč. 19, č. 2 (2012), s. 1-20 ISSN 1070-5325 R&D Projects: GA ČR GA105/09/1830 Institutional research plan: CEZ:AV0Z30860518 Keywords : block preconditioning * nonsymmetric matrices * saddle point systems Subject RIV: BA - General Mathematics Impact factor: 1.202, year: 2012 http://www.quosafulltext.com/sc_ddm/sc_ddm.jsp

A Perron–Frobenius theory for block matrices associated to a multiplex network

International Nuclear Information System (INIS)

Romance, Miguel; Solá, Luis; Flores, Julio; García, Esther; García del Amo, Alejandro; Criado, Regino

2015-01-01

The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector of the multiplex network in terms of the Perron eigenvectors of its layers

A Perron-Frobenius theory for block matrices associated to a multiplex network

Science.gov (United States)

Romance, Miguel; Solá, Luis; Flores, Julio; García, Esther; García del Amo, Alejandro; Criado, Regino

2015-03-01

The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector of the multiplex network in terms of the Perron eigenvectors of its layers.

Solution of the nonrelativistic wave equation using the tridiagonal representation approach

Science.gov (United States)

Alhaidari, A. D.

2017-07-01

We choose a complete set of square integrable functions as a basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent linear wave operator is tridiagonal and symmetric. Consequently, the matrix wave equation becomes a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. The recursion relation is then solved exactly in terms of orthogonal polynomials in the energy. Some of these polynomials are not found in the mathematics literature. The asymptotics of these polynomials give the phase shift for the continuous energy scattering states and the spectrum for the discrete energy bound states. Depending on the space and boundary conditions, the basis functions are written in terms of either the Laguerre or Jacobi polynomials. The tridiagonal requirement limits the number of potential functions that yield exact solutions of the wave equation. Nonetheless, the class of exactly solvable problems in this approach is larger than the conventional class (see, for example, Table XII in the text). We also give very accurate results for cases where the wave operator matrix is not tridiagonal but its elements could be evaluated either exactly or numerically with high precision.

A hybrid method for the parallel computation of Green’s functions

DEFF Research Database (Denmark)

Petersen, Dan Erik; Li, Song; Stokbro, Kurt

2009-01-01

Quantum transport models for nanodevices using the non-equilibrium Green’s function method require the repeated calculation of the block tridiagonal part of the Green’s and lesser Green’s function matrices. This problem is related to the calculation of the inverse of a sparse matrix. Because of t...

A Parallel Prefix Algorithm for Almost Toeplitz Tridiagonal Systems

Science.gov (United States)

Sun, Xian-He; Joslin, Ronald D.

1995-01-01

A compact scheme is a discretization scheme that is advantageous in obtaining highly accurate solutions. However, the resulting systems from compact schemes are tridiagonal systems that are difficult to solve efficiently on parallel computers. Considering the almost symmetric Toeplitz structure, a parallel algorithm, simple parallel prefix (SPP), is proposed. The SPP algorithm requires less memory than the conventional LU decomposition and is efficient on parallel machines. It consists of a prefix communication pattern and AXPY operations. Both the computation and the communication can be truncated without degrading the accuracy when the system is diagonally dominant. A formal accuracy study has been conducted to provide a simple truncation formula. Experimental results have been measured on a MasPar MP-1 SIMD machine and on a Cray 2 vector machine. Experimental results show that the simple parallel prefix algorithm is a good algorithm for symmetric, almost symmetric Toeplitz tridiagonal systems and for the compact scheme on high-performance computers.

Replica Fourier Tansforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

Science.gov (United States)

de Dominicis, C.; Carlucci, D. M.; Temesvári, T.

1997-01-01

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices M^{α β;γ^δ}, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work. On montre que l'analyse d'objets vivant sur un arbre ultramétrique, en particulier, la diagonalisation par blocs d'une matrice M^{α β;γ^δ} dépendant de 4-répliques, se simplifie de façon dramatique si l'on introduit les opérations appropriées sur ces objets. Ce sont les Transformées de Fourier de Répliques sur un arbre ultramétrique. Ces transformations sont définies et utilisées dans le présent travail.

Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe

2013-01-01

Roč. 45, č. 45 (2013), s. 45-67. ISBN 978-1-4614-7171-4. ISSN 2194-1009 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : two-by-two block-structured matrices * preconditioning * complex-valued system * Cahn-Hilliard phase-field model * optimal control Subject RIV: BA - General Mathematics http://link.springer.com/chapter/10.1007/978-1-4614-7172-1_3

Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices

Czech Academy of Sciences Publication Activity Database

Hnětynková, Iveta; Plešinger, M.

2015-01-01

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

Incomplete block factorization preconditioning for indefinite elliptic problems

Energy Technology Data Exchange (ETDEWEB)

Guo, Chun-Hua [Univ. of Calgary, Alberta (Canada)

1996-12-31

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small. And this factorization can serve as an efficient preconditioner. Some efforts are made to estimate the eigenvalues of the preconditioned matrix. Numerical results are also given.

The Antitriangular Factorization of Saddle Point Matrices

KAUST Repository

Pestana, J.

2014-01-01

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

MAIA, Eigenvalues for MHD Equation of Tokamak Plasma Stability Problems

International Nuclear Information System (INIS)

Tanaka, Y.; Azumi, M.; Kurita, G.; Tsunematsu, T.; Takeda, T.

1986-01-01

1 - Description of program or function: This program solves an eigenvalue problem zBx=Ax where A and B are real block tri-diagonal matrices. This eigenvalue problem is derived from a reduced set of linear resistive MHD equations which is often employed to study tokamak plasma stability problem. 2 - Method of solution: Both the determinant and inverse iteration methods are employed. 3 - Restrictions on the complexity of the problem: The eigenvalue z must be real

Special matrices of mathematical physics stochastic, circulant and Bell matrices

CERN Document Server

Aldrovandi, R

2001-01-01

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

Preconditioning of matrices partitioned in 2 x 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Blaheta, Radim

2010-01-01

Roč. 17, č. 5 (2010), s. 787-810 ISSN 1070-5325 R&D Projects: GA ČR GA105/09/1830 Institutional research plan: CEZ:AV0Z30860518 Keywords : iterative solution methods * saddle point problems * preconditioning block matrices * domain decomposition * heterogeneous problems * regularization Subject RIV: JC - Computer Hardware ; Software Impact factor: 1.163, year: 2010 http://onlinelibrary.wiley.com/doi/10.1002/nla.v17:5/issuetoc

A hybrid method for the parallel computation of Green's functions

DEFF Research Database (Denmark)

Petersen, Dan Erik; Li, Song; Stokbro, Kurt

2009-01-01

of the large number of times this calculation needs to be performed, this is computationally very expensive even on supercomputers. The classical approach is based on recurrence formulas which cannot be efficiently parallelized. This practically prevents the solution of large problems with hundreds...... of thousands of atoms. We propose new recurrences for a general class of sparse matrices to calculate Green's and lesser Green's function matrices which extend formulas derived by Takahashi and others. We show that these recurrences may lead to a dramatically reduced computational cost because they only...... require computing a small number of entries of the inverse matrix. Then. we propose a parallelization strategy for block tridiagonal matrices which involves a combination of Schur complement calculations and cyclic reduction. It achieves good scalability even on problems of modest size....

Encoders for block-circulant LDPC codes

Science.gov (United States)

Divsalar, Dariush (Inventor); Abbasfar, Aliazam (Inventor); Jones, Christopher R. (Inventor); Dolinar, Samuel J. (Inventor); Thorpe, Jeremy C. (Inventor); Andrews, Kenneth S. (Inventor); Yao, Kung (Inventor)

2009-01-01

Methods and apparatus to encode message input symbols in accordance with an accumulate-repeat-accumulate code with repetition three or four are disclosed. Block circulant matrices are used. A first method and apparatus make use of the block-circulant structure of the parity check matrix. A second method and apparatus use block-circulant generator matrices.

Numerical solutions of stochastic Lotka-Volterra equations via operational matrices

Directory of Open Access Journals (Sweden)

F. Hosseini Shekarabi

2016-03-01

Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.

Orthogonal polynomials derived from the tridiagonal representation approach

Science.gov (United States)

Alhaidari, A. D.

2018-01-01

The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials whose properties give the structure and dynamics of the corresponding physical system. For a certain range of parameters, one of these polynomials has a mix of continuous and discrete spectra making it suitable for describing physical systems with both scattering and bound states. In this work, we define these polynomials by their recursion relations and highlight some of their properties using numerical means. Due to the prime significance of these polynomials in physics, we hope that our short expose will encourage experts in the field of orthogonal polynomials to study them and derive their properties (weight functions, generating functions, asymptotics, orthogonality relations, zeros, etc.) analytically.

Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions

International Nuclear Information System (INIS)

Barrios, Dolores; Lopez, Guillermo L; Martinez-Finkelshtein, A; Torrano, Emilio

1999-01-01

The approximability of the resolvent of an operator induced by a band matrix by the resolvents of its finite-dimensional sections is studied. For bounded perturbations of self-adjoint matrices a positive result is obtained. The convergence domain of the sequence of resolvents can be described in this case in terms of matrices involved in the representation. This result is applied to tridiagonal complex matrices to establish conditions for the convergence of Chebyshev continued fractions on sets in the complex domain. In the particular case of compact perturbations this result is improved and a connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is established

Morphology-properties relationship on nanocomposite films based on poly(styrene-block-diene-block-styrene copolymers and silver nanoparticles

Directory of Open Access Journals (Sweden)

2011-02-01

Full Text Available A comparative study on the self-assembled nanostructured morphology and the rheological and mechanical properties of four different triblock copolymers, based on poly(styrene-block-diene-block-styrene and poly(styrene-block-diene-block-styrene matrices, and of their respective nanocomposites with 1 wt% silver nanoparticles, is reported in this work. In order to obtain well-dispersed nanoparticles in the block copolymer matrix, dodecanethiol was used as surfactant, showing good affinity with both nanoparticles and the polystyrene phase of the matrices as predicted by the solubility parameters calculated based on Hoftyzer and Van Krevelen theory. The block copolymer with the highest PS content shows the highest tensile modulus and tensile strength, but also the smallest elongation at break. When silver nanoparticles treated with surfactant were added to the block copolymer matrices, each system studied shows higher mechanical properties due to the good dispersion and the good interface of Ag nanoparticles in the matrices. Furthermore, it has been shown that semiempirical models such as Guth and Gold equation and Halpin-Tsai model can be used to predict the tensile modulus of the analyzed nanocomposites.

Linear algebra and matrices topics for a second course

CERN Document Server

Shapiro, Helene

2015-01-01

Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first c...

Threshold partitioning of sparse matrices and applications to Markov chains

Energy Technology Data Exchange (ETDEWEB)

Choi, Hwajeong; Szyld, D.B. [Temple Univ., Philadelphia, PA (United States)

1996-12-31

It is well known that the order of the variables and equations of a large, sparse linear system influences the performance of classical iterative methods. In particular if, after a symmetric permutation, the blocks in the diagonal have more nonzeros, classical block methods have a faster asymptotic rate of convergence. In this paper, different ordering and partitioning algorithms for sparse matrices are presented. They are modifications of PABLO. In the new algorithms, in addition to the location of the nonzeros, the values of the entries are taken into account. The matrix resulting after the symmetric permutation has dense blocks along the diagonal, and small entries in the off-diagonal blocks. Parameters can be easily adjusted to obtain, for example, denser blocks, or blocks with elements of larger magnitude. In particular, when the matrices represent Markov chains, the permuted matrices are well suited for block iterative methods that find the corresponding probability distribution. Applications to three types of methods are explored: (1) Classical block methods, such as Block Gauss Seidel. (2) Preconditioned GMRES, where a block diagonal preconditioner is used. (3) Iterative aggregation method (also called aggregation/disaggregation) where the partition obtained from the ordering algorithm with certain parameters is used as an aggregation scheme. In all three cases, experiments are presented which illustrate the performance of the methods with the new orderings. The complexity of the new algorithms is linear in the number of nonzeros and the order of the matrix, and thus adding little computational effort to the overall solution.

An efficient parallel algorithm for the solution of a tridiagonal linear system of equations

Science.gov (United States)

Stone, H. S.

1971-01-01

Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

Self-orthogonal codes from some bush-type Hadamard matrices ...

African Journals Online (AJOL)

By means of a construction method outlined by Harada and Tonchev, we determine some non-binary self-orthogonal codes obtained from the row span of orbit matrices of Bush-type Hadamard matrices that admit a xed-point-free and xed-block-free automorphism of prime order. We show that the code [20; 15; 4]5 obtained ...

The Antitriangular Factorization of Saddle Point Matrices

KAUST Repository

Pestana, J.; Wathen, A. J.

2014-01-01

Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle

Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks

Directory of Open Access Journals (Sweden)

Enming Dong

2014-01-01

Full Text Available Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.

THE ALGORITHM AND PROGRAM OF M-MATRICES SEARCH AND STUDY

Directory of Open Access Journals (Sweden)

Y. N. Balonin

2013-05-01

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

Higher dimensional unitary braid matrices: Construction, associated structures and entanglements

International Nuclear Information System (INIS)

Abdesselam, B.; Chakrabarti, A.; Dobrev, V.K.; Mihov, S.G.

2007-03-01

We construct (2n) 2 x (2n) 2 unitary braid matrices R-circumflex for n ≥ 2 generalizing the class known for n = 1. A set of (2n) x (2n) matrices (I, J,K,L) are defined. R-circumflex is expressed in terms of their tensor products (such as K x J), leading to a canonical formulation for all n. Complex projectors P ± provide a basis for our real, unitary R-circumflex. Baxterization is obtained. Diagonalizations and block- diagonalizations are presented. The loss of braid property when R-circumflex (n > 1) is block-diagonalized in terms of R-circumflex (n = 1) is pointed out and explained. For odd dimension (2n + 1) 2 x (2n + 1) 2 , a previously constructed braid matrix is complexified to obtain unitarity. R-circumflexLL- and R-circumflexTT- algebras, chain Hamiltonians, potentials for factorizable S-matrices, complex non-commutative spaces are all studied briefly in the context of our unitary braid matrices. Turaev construction of link invariants is formulated for our case. We conclude with comments concerning entanglements. (author)

Stabilization and solidification of Pb in cement matrices

International Nuclear Information System (INIS)

Gollmann, Maria A.C.; Silva, Marcia M. da; Santos, Joao H. Z. dos; Masuero, Angela B.

2010-01-01

Pb was incorporated to a series of cement matrices, which were submitted to different cure time and pH. Pb content leached to aqueous solution was monitored by atomic absorption spectroscopy. The block resistance was evaluated by unconfined compressive strength at 7 and 28 ages. Data are discussed in terms of metal mobility along the cement block monitored by X-ray fluorescence (XRF) spectrometry. The Pb incorporated matrices have shown that a long cure time is more suitable for avoiding metal leaching. For a longer cure period the action of the metal is higher and there is a decreasing in the compressive strength. The XRF analyses show that there is a lower Ca concentration in the matrix in which Pb was added. (author)

Parallel computation for solving the tridiagonal linear system of equations

International Nuclear Information System (INIS)

Ishiguro, Misako; Harada, Hiroo; Fujii, Minoru; Fujimura, Toichiro; Nakamura, Yasuhiro; Nanba, Katsumi.

1981-09-01

Recently, applications of parallel computation for scientific calculations have increased from the need of the high speed calculation of large scale programs. At the JAERI computing center, an array processor FACOM 230-75 APU has installed to study the applicability of parallel computation for nuclear codes. We made some numerical experiments by using the APU on the methods of solution of tridiagonal linear equation which is an important problem in scientific calculations. Referring to the recent papers with parallel methods, we investigate eight ones. These are Gauss elimination method, Parallel Gauss method, Accelerated parallel Gauss method, Jacobi method, Recursive doubling method, Cyclic reduction method, Chebyshev iteration method, and Conjugate gradient method. The computing time and accuracy were compared among the methods on the basis of the numerical experiments. As the result, it is found that the Cyclic reduction method is best both in computing time and accuracy and the Gauss elimination method is the second one. (author)

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

Science.gov (United States)

Shcherbina, Mariya; Shcherbina, Tatyana

2018-02-01

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

Malware analysis using visualized image matrices.

Science.gov (United States)

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

2014-01-01

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

Malware Analysis Using Visualized Image Matrices

Directory of Open Access Journals (Sweden)

KyoungSoo Han

2014-01-01

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

A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements

KAUST Repository

Chávez, Gustavo

2017-03-17

A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N) arithmetic complexity and O(NlogN) memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the $$\\\\mathcal{H}$$ -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $$\\\\mathcal{H}$$ -LU and that it can tackle problems where algebraic multigrid fails to converge.

Basket Option Pricing Using GP-GPU Hardware Acceleration

KAUST Repository

Douglas, Craig C.; Lee, Hyoseop

2010-01-01

We introduce a basket option pricing problem arisen in financial mathematics. We discretized the problem based on the alternating direction implicit (ADI) method and parallel cyclic reduction is applied to solve the set of tridiagonal matrices

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

KAUST Repository

Boukaram, W.

2015-03-25

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

Inverse m-matrices and ultrametric matrices

CERN Document Server

Dellacherie, Claude; San Martin, Jaime

2014-01-01

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

Unitary tridiagonalization in M(4, C)

Indian Academy of Sciences (India)

Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45

Abstract. A question of interest in linear algebra is whether all n × n complex matrices can be unitarily ... passing, we also provide another elementary proof for the n = 3 case. 2. Some Lemmas. We need ... also use the letter A to denote the unique linear transformation determined by the matrix. A = [aij ] (satisfying Aej = ∑n.

Sums of the squares of terms of sequence {un }{ un }{ un}

Indian Academy of Sciences (India)

The second order linear recurrences of the Fibonacci ...... [18] Kilic E and Tasci D, On the permanents of some tridiagonal matrices with applications ... [23] Lee G-Y, k-Lucas numbers and associated bipartite graphs, Linear Algebra Appl. 320.

Wilson loop invariants from WN conformal blocks

Directory of Open Access Journals (Sweden)

Oleg Alekseev

2015-12-01

Full Text Available Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.

'Leonard pairs' in classical mechanics

International Nuclear Information System (INIS)

Zhedanov, Alexei; Korovnichenko, Alyona

2002-01-01

Leonard pairs (LP) are matrices with the property of mutual tri-diagonality. We introduce and study a classical analogue of LP. We show that corresponding classical 'Leonard' dynamical variables satisfy non-linear relations of the AW-type with respect to Poisson brackets. (author)

Finding column depedencies in sparse matrices over $ F_ 2 $ by block Wiedemann

NARCIS (Netherlands)

O. Penninga

1998-01-01

textabstractLarge systems of linear equations over $mathbb{F_2$ with sparse coefficient matrices have to be solved as a part of integer factorization with sieve-based methods such as in the Number Field Sieve algorithm. In this report, we first discuss the Wiedemann algorithm to solve these systems

Plasma turbulence calculations on the Intel iPSC/860 (rx) hypercube

International Nuclear Information System (INIS)

Lynch, V.E.; Ruiter, J.R.

1990-01-01

One approach to improving the real-time efficiency of plasma turbulence calculations is to use a parallel algorithm. A serial algorithm used for plasma turbulence calculations was modified to allocate a radial region in each node. In this way, convolutions at a fixed radius are performed in parallel, and communication is limited to boundary values for each radial region. For a semi-implicity numerical scheme (tridiagonal matrix solver), there is a factor of 3 improvement in efficiency with the Intel iPSC/860 machine using 64 processors over a single-processor Cray-II. For block-tridiagonal matrix cases (fully implicit code), a second parallelization takes place. The Fourier components are distributed in nodes. In each node, the block-tridiagonal matrix is inverted for each of allocated Fourier components. The algorithm for this second case has not yet been optimized. 10 refs., 4 figs

Extended abstract: Partial row projection methods

Energy Technology Data Exchange (ETDEWEB)

Bramley, R.; Lee, Y. [Indiana Univ., Bloomington, IN (United States)

1996-12-31

Accelerated row projection (RP) algorithms for solving linear systems Ax = b are a class of iterative methods which in theory converge for any nonsingular matrix. RP methods are by definition ones that require finding the orthogonal projection of vectors onto the null space of block rows of the matrix. The Kaczmarz form, considered here because it has a better spectrum for iterative methods, has an iteration matrix that is the product of such projectors. Because straightforward Kaczmarz method converges slowly for practical problems, typically an outer CG acceleration is applied. Definiteness, symmetry, or localization of the eigenvalues, of the coefficient matrix is not required. In spite of this robustness, work has generally been limited to structured systems such as block tridiagonal matrices because unlike many iterative solvers, RP methods cannot be implemented by simply supplying a matrix-vector multiplication routine. Finding the orthogonal projection of vectors onto the null space of block rows of the matrix in practice requires accessing the actual entries in the matrix. This report introduces a new partial RP algorithm which retains advantages of the RP methods.

Fusion algebra and fusing matrices

International Nuclear Information System (INIS)

Gao Yihong; Li Miao; Yu Ming.

1989-09-01

We show that the Wilson line operators in topological field theories form a fusion algebra. In general, the fusion algebra is a relation among the fusing (F) matrices. In the case of the SU(2) WZW model, some special F matrix elements are found in this way, and the remaining F matrix elements are then determined up to a sign. In addition, the S(j) modular transformation of the one point blocks on the torus is worked out. Our results are found to agree with those obtained from the quantum group method. (author). 24 refs

The q-Onsager algebra and multivariable q-special functions

Science.gov (United States)

Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei

2017-09-01

Two sets of mutually commuting q-difference operators x i and y j , i,j=1,...,N such that x i and y i generate a homomorphic image of the q-Onsager algebra for each i are introduced. The common polynomial eigenfunctions of each set are found to be entangled product of elementary Pochhammer functions in N variables and N+3 parameters. Under certain conditions on the parameters, they form two ‘dual’ bases of polynomials in N variables. The action of each operator with respect to its dual basis is block tridiagonal. The overlap coefficients between the two dual bases are expressed as entangled products of q-Racah polynomials and satisfy an orthogonality relation. The overlap coefficients between either one of these bases and the multivariable monomial basis are also considered. One obtains in this case entangled products of dual q-Krawtchouk polynomials. Finally, the ‘split’ basis in which the two families of operators act as block bidiagonal matrices is also provided.

Parallelization of mathematical library for generalized eigenvalue problem for real band matrices

International Nuclear Information System (INIS)

Tanaka, Yasuhisa.

1997-05-01

This research has focused on a parallelization of the mathematical library for a generalized eigenvalue problem for real band matrices on IBM SP and Hitachi SR2201. The origin of the library is LASO (Lanczos Algorithm with Selective Orthogonalization), which was developed on the basis of Block Lanczos method for standard eigenvalue problem for real band matrices at Texas University. We adopted D.O.F. (Degree Of Freedom) decomposition method for a parallelization of this library, and evaluated its parallel performance. (author)

Conditioning analysis of block incomplete factorization and its application to elliptic equations

NARCIS (Netherlands)

Lu, H.; Axelsson, Owe

1997-01-01

The paper deals with eigenvalue estimates for block incomplete fac- torization methods for symmetric matrices. First, some previous results on upper bounds for the maximum eigenvalue of preconditioned matrices are generalized to each eigenvalue. Second, upper bounds for the maximum eigenvalue of the

NANOSTRUCTURED METAL OXIDE CATALYSTS VIA BUILDING BLOCK SYNTHESES

Energy Technology Data Exchange (ETDEWEB)

Craig E. Barnes

2013-03-05

A broadly applicable methodology has been developed to prepare new single site catalysts on silica supports. This methodology requires of three critical components: a rigid building block that will be the main structural and compositional component of the support matrix; a family of linking reagents that will be used to insert active metals into the matrix as well as cross link building blocks into a three dimensional matrix; and a clean coupling reaction that will connect building blocks and linking agents together in a controlled fashion. The final piece of conceptual strategy at the center of this methodology involves dosing the building block with known amounts of linking agents so that the targeted connectivity of a linking center to surrounding building blocks is obtained. Achieving targeted connectivities around catalytically active metals in these building block matrices is a critical element of the strategy by which single site catalysts are obtained. This methodology has been demonstrated with a model system involving only silicon and then with two metal-containing systems (titanium and vanadium). The effect that connectivity has on the reactivity of atomically dispersed titanium sites in silica building block matrices has been investigated in the selective oxidation of phenols to benezoquinones. 2-connected titanium sites are found to be five times as active (i.e. initial turnover frequencies) than 4-connected titanium sites (i.e. framework titanium sites).

Inconsistent Distances in Substitution Matrices can be Avoided by Properly Handling Hydrophobic Residues

Directory of Open Access Journals (Sweden)

J. Baussand

2008-01-01

Full Text Available The adequacy of substitution matrices to model evolutionary relationships between amino acid sequences can be numerically evaluated by checking the mathematical property of triangle inequality for all triplets of residues. By converting substitution scores into distances, one can verify that a direct path between two amino acids is shorter than a path passing through a third amino acid in the amino acid space modeled by the matrix. If the triangle inequality is not verified, the intuition is that the evolutionary signal is not well modeled by the matrix, that the space is locally inconsistent and that the matrix construction was probably based on insufficient biological data. Previous analysis on several substitution matrices revealed that the number of triplets violating the triangle inequality increases with sequence divergence. Here, we compare matrices which are dedicated to the alignment of highly divergent proteins. The triangle inequality is tested on several classical substitution matrices as well as in a pair of “complementary” substitution matrices recording the evolutionary pressures inside and outside hydrophobic blocks in protein sequences. The analysis proves the crucial role of hydrophobic residues in substitution matrices dedicated to the alignment of distantly related proteins.

Physical properties of the Schur complement of local covariance matrices

International Nuclear Information System (INIS)

Haruna, L F; Oliveira, M C de

2007-01-01

General properties of global covariance matrices representing bipartite Gaussian states can be decomposed into properties of local covariance matrices and their Schur complements. We demonstrate that given a bipartite Gaussian state ρ 12 described by a 4 x 4 covariance matrix V, the Schur complement of a local covariance submatrix V 1 of it can be interpreted as a new covariance matrix representing a Gaussian operator of party 1 conditioned to local parity measurements on party 2. The connection with a partial parity measurement over a bipartite quantum state and the determination of the reduced Wigner function is given and an operational process of parity measurement is developed. Generalization of this procedure to an n-partite Gaussian state is given, and it is demonstrated that the n - 1 system state conditioned to a partial parity projection is given by a covariance matrix such that its 2 x 2 block elements are Schur complements of special local matrices

Duality relations between SU(N)k and SU(k)NWZW models and their braid matrices

International Nuclear Information System (INIS)

Naculich, S.G.; Schnitzer, H.J.

1990-01-01

Dual relations are found between the primary fields, correlators, and conformal blocks of SU(N) k and SU(k) N WZW models, which in turn imply dual relations between the braid matrices of the two theories. These results are a consequence of the fact that the spaces of conformal blocks of SU(N) k and SU(k) N correlation functions are dual. (orig.)

Averaging operations on matrices

Indian Academy of Sciences (India)

2014-07-03

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

Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks

OpenAIRE

Chorazkiewicz, Damian; Hadasz, Leszek

2008-01-01

We construct, generalizing appropriately the method applied by J. Teschner in the case of the Virasoro conformal blocks, the braiding and fusion matrices of the Neveu-Schwarz super-conformal blocks. Their properties allow for an explicit verification of the bootstrap equation in the NS sector of the N=1 supersymmetric Liouville field theory.

Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks

International Nuclear Information System (INIS)

Chorazkiewicz, Damian; Hadasz, Leszek

2009-01-01

We construct, generalizing appropriately the method applied by J. Teschner in the case of the Virasoro conformal blocks, the braiding and fusion matrices of the Neveu-Schwarz super-conformal blocks. Their properties allow for an explicit verification of the bootstrap equation in the NS sector of the N = 1 supersymmetric Liouville field theory.

A GPU-accelerated semi-implicit fractional-step method for numerical solutions of incompressible Navier-Stokes equations

Science.gov (United States)

Ha, Sanghyun; Park, Junshin; You, Donghyun

2018-01-01

Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. The Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution methods used in the semi-implicit fractional-step method take advantage of multiple tridiagonal matrices whose inversion is known as the major bottleneck for acceleration on a typical multi-core machine. A novel implementation of the semi-implicit fractional-step method designed for GPU acceleration of the incompressible Navier-Stokes equations is presented. Aspects of the programing model of Compute Unified Device Architecture (CUDA), which are critical to the bandwidth-bound nature of the present method are discussed in detail. A data layout for efficient use of CUDA libraries is proposed for acceleration of tridiagonal matrix inversion and fast Fourier transform. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while the Navier-Stokes equations are computed on a GPU. Performance of the present method using CUDA is assessed by comparing the speed of solving three tridiagonal matrices using ADI with the speed of solving one heptadiagonal matrix using a conjugate gradient method. An overall speedup of 20 times is achieved using a Tesla K40 GPU in comparison with a single-core Xeon E5-2660 v3 CPU in simulations of turbulent boundary-layer flow over a flat plate conducted on over 134 million grids. Enhanced performance of 48 times speedup is reached for the same problem using a Tesla P100 GPU.

The chiral Gaussian two-matrix ensemble of real asymmetric matrices

International Nuclear Information System (INIS)

Akemann, G; Phillips, M J; Sommers, H-J

2010-01-01

We solve a family of Gaussian two-matrix models with rectangular N x (N + ν) matrices, having real asymmetric matrix elements and depending on a non-Hermiticity parameter μ. Our model can be thought of as the chiral extension of the real Ginibre ensemble, relevant for Dirac operators in the same symmetry class. It has the property that its eigenvalues are either real, purely imaginary or come in complex conjugate eigenvalue pairs. The eigenvalue joint probability distribution for our model is explicitly computed, leading to a non-Gaussian distribution including K-Bessel functions. All n-point density correlation functions are expressed for finite N in terms of a Pfaffian form. This contains a kernel involving Laguerre polynomials in the complex plane as a building block which was previously computed by the authors. This kernel can be expressed in terms of the kernel for complex non-Hermitian matrices, generalizing the known relation among ensembles of Hermitian random matrices. Compact expressions are given for the density at finite N as an example, as well as its microscopic large-N limits at the origin for fixed ν at strong and weak non-Hermiticity.

Identification of fractional-order systems with time delays using block pulse functions

Science.gov (United States)

Tang, Yinggan; Li, Ning; Liu, Minmin; Lu, Yao; Wang, Weiwei

2017-07-01

In this paper, a novel method based on block pulse functions is proposed to identify continuous-time fractional-order systems with time delays. First, the operational matrices of block pulse functions for fractional integral operator and time delay operator are derived. Then, these operational matrices are applied to convert the continuous-time fractional-order systems with time delays to an algebraic equation. Finally, the system's parameters along with the differentiation orders and the time delays are all simultaneously estimated through minimizing a quadric error function. The proposed method reduces the computation complexity of the identification process, and also it does not require the system's differentiation orders to be commensurate. The effectiveness of the proposed method are demonstrated by several numerical examples.

Selection of appropriate conditioning matrices for the safe disposal of radioactive waste

International Nuclear Information System (INIS)

Vance, E.R.

2002-01-01

The selection of appropriate solid conditioning matrices or wasteforms for the safe disposal of radioactive waste is dictated by many factors. The overriding issue is that the matrix incorporating the radionuclides, together with a set of engineered barriers in a near-surface or deep geological repository, should prevent significant groundwater transport of radionuclides to the biosphere. For high-level waste (HLW) from nuclear fuel reprocessing, the favored matrices are glasses, ceramics and glass-ceramics. Borosilicate glasses are presently being used in some countries, but there are strong scientific arguments why ceramics based on assemblages of natural minerals are advantageous for HLW. Much research has been carried out in the last 40 years around the world, and different matrices are more suitable than others for a given waste composition. However a major stumbling block for HLW immobilisation is the mall number of approved geological repositories for such matrices. The most appropriate matrices for Intermediate and low-level wastes are contentious and the selection criteria are not very well defined. The candidate matrices for these latter wastes are cements, bitumen, geopolymers, glasses, glass-ceramics and ceramics. After discussing the pros and cons of various candidate matrices for given kinds of radioactive wastes, the SYNROC research program at ANSTO will be briefly surveyed. Some of the potential applications of this work using a variety of SYNROC derivatives will be given. Finally the basic research program at ANSTO on radioactive waste immobilisation will be summarised. This comprises mainly work on solid state chemistry to understand ionic valences and co-ordinations for the chemical design of wasteforms, aqueous durability to study the pH and temperature dependence of solid-water reactions, radiation damage effects on structure and solid-water reactions. (Author)

Infinite matrices and sequence spaces

CERN Document Server

Cooke, Richard G

2014-01-01

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

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 ...

Nonconventional concrete hollow blocks evaluation by destructive and non-destructive testing

Directory of Open Access Journals (Sweden)

M.S. Rodrigues

Full Text Available The aim of this study was to evaluate cementitious matrices properties by partial replacement of Portland cement by silica fume (SF or by rice husk ash (RHA, and their application in nonbearing hollow blocks, tested by destructive and non-destructive methods. The following mixtures were produced: reference (100% of Portland cement and Portland cement replacement (10% by mass with SF or RHA. The non-destructive testing showed that the highest values of UPV were obtained for SF-based blocks and RHA-based blocks. The destructive test showed better results for SF-based blocks, but there was no statistical difference between the RHA-based and control ones.

On reflectionless equi-transmitting matrices

Directory of Open Access Journals (Sweden)

Pavel Kurasov

2014-01-01

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

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 ...

Improving Conductivity Image Quality Using Block Matrix-based Multiple Regularization (BMMR Technique in EIT: A Simulation Study

Directory of Open Access Journals (Sweden)

Tushar Kanti Bera

2011-06-01

Full Text Available A Block Matrix based Multiple Regularization (BMMR technique is proposed for improving conductivity image quality in EIT. The response matrix (JTJ has been partitioned into several sub-block matrices and the highest eigenvalue of each sub-block matrices has been chosen as regularization parameter for the nodes contained by that sub-block. Simulated boundary data are generated for circular domain with circular inhomogeneity and the conductivity images are reconstructed in a Model Based Iterative Image Reconstruction (MoBIIR algorithm. Conductivity images are reconstructed with BMMR technique and the results are compared with the Single-step Tikhonov Regularization (STR and modified Levenberg-Marquardt Regularization (LMR methods. It is observed that the BMMR technique reduces the projection error and solution error and improves the conductivity reconstruction in EIT. Result show that the BMMR method also improves the image contrast and inhomogeneity conductivity profile and hence the reconstructed image quality is enhanced. ;doi:10.5617/jeb.170 J Electr Bioimp, vol. 2, pp. 33-47, 2011

Braiding properties of the N = 1 super-conformal blocks (Ramond sector)

Science.gov (United States)

Chorążkiewicz, Damian; Hadasz, Leszek; Jaskólski, Zbigniew

2011-11-01

Using a super scalar field representation of the chiral vertex operators we develop a general method of calculating braiding matrices for all types of N = 1 superconformal 4-point blocks involving Ramond external weights. We give explicit analytic formulae in a number of cases.

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

Science.gov (United States)

Waller, Niels G

2016-01-01

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

A biclustering algorithm for binary matrices based on penalized Bernoulli likelihood

KAUST Repository

Lee, Seokho

2013-01-31

We propose a new biclustering method for binary data matrices using the maximum penalized Bernoulli likelihood estimation. Our method applies a multi-layer model defined on the logits of the success probabilities, where each layer represents a simple bicluster structure and the combination of multiple layers is able to reveal complicated, multiple biclusters. The method allows for non-pure biclusters, and can simultaneously identify the 1-prevalent blocks and 0-prevalent blocks. A computationally efficient algorithm is developed and guidelines are provided for specifying the tuning parameters, including initial values of model parameters, the number of layers, and the penalty parameters. Missing-data imputation can be handled in the EM framework. The method is tested using synthetic and real datasets and shows good performance. © 2013 Springer Science+Business Media New York.

Exact solution of corner-modified banded block-Toeplitz eigensystems

International Nuclear Information System (INIS)

Cobanera, Emilio; Alase, Abhijeet; Viola, Lorenza; Ortiz, Gerardo

2017-01-01

Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified . Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz , independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix , whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev. (paper)

Double stochastic matrices in quantum mechanics

International Nuclear Information System (INIS)

Louck, J.D.

1997-01-01

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

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

Science.gov (United States)

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

2013-01-01

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

Matrices and linear transformations

CERN Document Server

Cullen, Charles G

1990-01-01

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

Lambda-matrices and vibrating systems

CERN Document Server

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

1966-01-01

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

Manin matrices and Talalaev's formula

International Nuclear Information System (INIS)

Chervov, A; Falqui, G

2008-01-01

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

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-01-01

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

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-12-05

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

Numerical Simulation of Permeation from Deposited Droplets: Model Expansion

Science.gov (United States)

1992-04-01

tridiagonal matrices in Tables 3 through 8, we used the Thomas algorithm [18]. 10.1 Boundary Conditions. At the unwet portion of the upper surface, i.e...IJL)--CPRIME(I) 54 CONTINUE END IF DO060 I=10+1I,11 RI T DOS55 J=IJL-1 IF( I.EQ. I ) THEN DM(J)--2.0*CSTAR(I-I J)+2.0*(BETA-1 0)* CSTR (IJ) ELSE IF (I Q

Basket Option Pricing Using GP-GPU Hardware Acceleration

KAUST Repository

Douglas, Craig C.

2010-08-01

We introduce a basket option pricing problem arisen in financial mathematics. We discretized the problem based on the alternating direction implicit (ADI) method and parallel cyclic reduction is applied to solve the set of tridiagonal matrices generated by the ADI method. To reduce the computational time of the problem, a general purpose graphics processing units (GP-GPU) environment is considered. Numerical results confirm the convergence and efficiency of the proposed method. © 2010 IEEE.

MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD

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N. A. Balonin

2014-05-01

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

Modular transformations of conformal blocks in WZW models on Riemann surfaces of higher genus

International Nuclear Information System (INIS)

Miao Li; Ming Yu.

1989-05-01

We derive the modular transformations for conformal blocks in Wess-Zumino-Witten models on Riemann surfaces of higher genus. The basic ingredient consists of using the Chern-Simons theory developed by Witten. We find that the modular transformations generated by Dehn twists are linear combinations of Wilson line operators, which can be expressed in terms of braiding matrices. It can also be shown that modular transformation matrices for g > 0 Riemann surfaces depend only on those for g ≤ 3. (author). 13 refs, 15 figs

Intrinsic character of Stokes matrices

Science.gov (United States)

Gagnon, Jean-François; Rousseau, Christiane

2017-02-01

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

Hierarchical matrices algorithms and analysis

CERN Document Server

Hackbusch, Wolfgang

2015-01-01

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

Decorin-transforming growth factor- interaction regulates matrix organization and mechanical characteristics of three-dimensional collagen matrices.

Science.gov (United States)

Ferdous, Zannatul; Wei, Victoria Mariko; Iozzo, Renato; Höök, Magnus; Grande-Allen, Kathryn Jane

2007-12-07

The small leucine-rich proteoglycan decorin has been demonstrated to be a key regulator of collagen fibrillogenesis; decorin deficiencies lead to irregularly shaped collagen fibrils and weakened material behavior in postnatal murine connective tissues. In an in vitro investigation of the contributions of decorin to tissue organization and material behavior, model tissues were engineered by seeding embryonic fibroblasts, harvested from 12.5-13.5 days gestational aged decorin null (Dcn(-/-)) or wild-type mice, within type I collagen gels. The resulting three-dimensional collagen matrices were cultured for 4 weeks under static tension. The collagen matrices seeded with Dcn(-/-) cells exhibited greater contraction, cell density, ultimate tensile strength, and elastic modulus than those seeded with wild-type cells. Ultrastructurally, the matrices seeded with Dcn(-/-) cells contained a greater density of collagen. The decorin-null tissues contained more biglycan than control tissues, suggesting that this related proteoglycan compensated for the absence of decorin. The effect of transforming growth factor-beta (TGF-beta), which is normally sequestered by decorin, was also investigated in this study. The addition of TGF-beta1 to the matrices seeded with wild-type cells improved their contraction and mechanical strength, whereas blocking TGF-beta1 in the Dcn(-/-) cell-seeded matrices significantly reduced the collagen gel contraction. These results indicate that the inhibitory interaction between decorin and TGF-beta1 significantly influenced the matrix organization and material behavior of these in vitro model tissues.

Tetrodotoxin Detection by a Surface Plasmon Resonance Sensor in Pufferfish Matrices and Urine

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Allen D. Taylor

2011-01-01

Full Text Available Tetrodotoxin (TTX poisoning is most commonly associated with consumption of pufferfish. TTX is a low molecular weight (~319 Da neurotoxin that selectively blocks voltage-sensitive Na+-gated ion channels. The standard method accepted worldwide for monitoring TTX toxicity in food matrices is the mouse bioassay. Ethical concerns from live animal testing, low sample throughput, and analytical inaccuracies have led to the need for an alternative method. We have previously established that surface plasmon resonance (SPR sensors can quantify TTX in aqueous buffer samples by an antibody-based inhibition assay. In this paper, we report the extension of the assay for the detection of TTX in both clinical- and food-relevant matrices. The assay was optimized for application to three relevant complex matrices: pufferfish liver extract, pufferfish muscle extract, and human urine. Matrix effects are discussed and calibration curves are presented. Naturally contaminated pufferfish liver and muscle extracts were analyzed by the SPR method, and the data is compared to liquid-chromatography electrospray-ionization multiple reactions monitoring mass spectrometry (LC/ESI/MRM/MS data. Ten samples, including three from a poisoning incident, two control monkfish samples, and five toxic pufferfish samples, were analyzed using this method, and the data is compared to LC/ESI/MRM/MS analysis of the samples.

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

Energy Technology Data Exchange (ETDEWEB)

Wagner, C.

1996-12-31

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

Introduction to matrices and vectors

CERN Document Server

Schwartz, Jacob T

2001-01-01

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

Pathological rate matrices: from primates to pathogens

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Knight Rob

2008-12-01

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

Spectra of sparse random matrices

International Nuclear Information System (INIS)

Kuehn, Reimer

2008-01-01

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

Chemiluminescence in cryogenic matrices

Science.gov (United States)

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

1989-04-01

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

Skew-adjacency matrices of graphs

NARCIS (Netherlands)

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

2012-01-01

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

The invariant theory of matrices

CERN Document Server

Concini, Corrado De

2017-01-01

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

Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix

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Yanpeng Zheng

2015-01-01

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

Enhancing Understanding of Transformation Matrices

Science.gov (United States)

Dick, Jonathan; Childrey, Maria

2012-01-01

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

Modeling of Video Sequences by Gaussian Mixture: Application in Motion Estimation by Block Matching Method

Directory of Open Access Journals (Sweden)

Abdenaceur Boudlal

2010-01-01

Full Text Available This article investigates a new method of motion estimation based on block matching criterion through the modeling of image blocks by a mixture of two and three Gaussian distributions. Mixture parameters (weights, means vectors, and covariance matrices are estimated by the Expectation Maximization algorithm (EM which maximizes the log-likelihood criterion. The similarity between a block in the current image and the more resembling one in a search window on the reference image is measured by the minimization of Extended Mahalanobis distance between the clusters of mixture. Performed experiments on sequences of real images have given good results, and PSNR reached 3 dB.

Continuous tone printing in silicone from CNC milled matrices

Science.gov (United States)

Hoskins, S.; McCallion, P.

2014-02-01

Current research at the Centre for Fine Print Research (CFPR) at the University of the West of England, Bristol, is exploring the potential of creating coloured pictorial imagery from a continuous tone relief surface. To create the printing matrices the research team have been using CNC milled images where the height of the relief image is dictated by creating a tone curve and then milling this curve into a series of relief blocks from which the image is cast in a silicone ink. A translucent image is cast from each of the colour matrices and each colour is assembled - one on top of another - resulting is a colour continuous tone print, where colour tone is created by physical depth of colour. This process is a contemporary method of continuous tone colour printing based upon the Nineteenth Century black and white printing process of Woodburytype as developed by Walter Bentley Woodbury in 1865. Woodburytype is the only true continuous tone printing process invented, and although its delicate and subtle surfaces surpassed all other printing methods at the time. The process died out in the late nineteenth century as more expedient and cost effective methods of printing prevailed. New research at CFPR builds upon previous research that combines 19th Century Photomechanical techniques with digital technology to reappraise the potential of these processes.

Group inverses of M-matrices and their applications

CERN Document Server

Kirkland, Stephen J

2013-01-01

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

Inference for High-dimensional Differential Correlation Matrices.

Science.gov (United States)

Cai, T Tony; Zhang, Anru

2016-01-01

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

Phenomenological mass matrices with a democratic warp

International Nuclear Information System (INIS)

Kleppe, A.

2018-01-01

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

Diagonalization of the mass matrices

International Nuclear Information System (INIS)

Rhee, S.S.

1984-01-01

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

LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation

International Nuclear Information System (INIS)

Dongarra, J.J.

1979-01-01

1 - Description of problem or function: LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE: General, GB: General band, PO: Positive definite, PP: Positive definite packed, PB: Positive definite band, SI: Symmetric indefinite, SP: Symmetric indefinite packed, HI: Hermitian indefinite, HP: Hermitian indefinite packed, TR: Triangular, GT: General tridiagonal, PT: Positive definite tridiagonal, CH: Cholesky decomposition, QR: Orthogonal-triangular decomposition, SV: Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA: Factor, CO: Factor and estimate condition, SL: Solve, DI: Determinant and/or inverse and/or inertia, DC: Decompose, UD: Update, DD: Down-date, EX Exchange. The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z. SGE: FA, CO, SL, DI; SGB: FA, CO, SL, DI; SPO: FA, CO, SL, DI; SPP: FA, CO, SL, DI; SPB: FA, CO, SL, DI; SSI: FA, CO, SL, DI; SSP: FA, CO, SL, DI; CHI: FA, CO, SL, DI; CHP: FA, CO, SL, DI; STR

The construction of factorized S-matrices

International Nuclear Information System (INIS)

Chudnovsky, D.V.

1981-01-01

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

Matrices in Engineering Problems

CERN Document Server

Tobias, Marvin

2011-01-01

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

A Brief Historical Introduction to Matrices and Their Applications

Science.gov (United States)

Debnath, L.

2014-01-01

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

Fibroblast Cluster Formation on 3D Collagen Matrices Requires Cell Contraction-Dependent Fibronectin Matrix Organization

Science.gov (United States)

da Rocha-Azevedo, Bruno; Ho, Chin-Han; Grinnell, Frederick

2012-01-01

Fibroblasts incubated on 3D collagen matrices in serum or lysophosphatidic acid (LPA)-containing medium self-organize into clusters through a mechanism that requires cell contraction. However, in platelet-derived growth factor (PDGF)-containing medium, cells migrate as individuals and do not form clusters even though they constantly encounter each other. Here, we present evidence that a required function of cell contraction in clustering is formation of fibronectin fibrillar matrix. We found that in serum or LPA but not in PDGF or basal medium, cells organized FN (both serum and cellular) into a fibrillar, detergent-insoluble matrix. Cell clusters developed concomitant with FN matrix formation. FN fibrils accumulated beneath cells and along the borders of cell clusters in regions of cell-matrix tension. Blocking Rho kinase or myosin II activity prevented FN matrix assembly and cell clustering. Using siRNA silencing and function-blocking antibodies and peptides, we found that cell clustering and FN matrix assembly required α5β1 integrins and fibronectin. Cells were still able to exert contractile force and compact the collagen matrix under the latter conditions, which showed that contraction was not sufficient for cell clustering to occur. Our findings provide new insights into how procontractile (serum/LPA) and promigratory (PDGF) growth factor environments can differentially regulate FN matrix assembly by fibroblasts interacting with collagen matrices and thereby influence mesenchymal cell morphogenetic behavior under physiologic circumstances such as wound repair, morphogenesis and malignancy. PMID:23117111

Fibroblast cluster formation on 3D collagen matrices requires cell contraction dependent fibronectin matrix organization.

Science.gov (United States)

da Rocha-Azevedo, Bruno; Ho, Chin-Han; Grinnell, Frederick

2013-02-15

Fibroblasts incubated on 3D collagen matrices in serum or lysophosphatidic acid (LPA)-containing medium self-organize into clusters through a mechanism that requires cell contraction. However, in platelet-derived growth factor (PDGF)-containing medium, cells migrate as individuals and do not form clusters even though they constantly encounter each other. Here, we present evidence that a required function of cell contraction in clustering is formation of fibronectin (FN) fibrillar matrix. We found that in serum or LPA but not in PDGF or basal medium, cells organized FN (both serum and cellular) into a fibrillar, detergent-insoluble matrix. Cell clusters developed concomitant with FN matrix formation. FN fibrils accumulated beneath cells and along the borders of cell clusters in regions of cell-matrix tension. Blocking Rho kinase or myosin II activity prevented FN matrix assembly and cell clustering. Using siRNA silencing and function-blocking antibodies and peptides, we found that cell clustering and FN matrix assembly required α5β1 integrins and fibronectin. Cells were still able to exert contractile force and compact the collagen matrix under the latter conditions, which showed that contraction was not sufficient for cell clustering to occur. Our findings provide new insights into how procontractile (serum/LPA) and promigratory (PDGF) growth factor environments can differentially regulate FN matrix assembly by fibroblasts interacting with collagen matrices and thereby influence mesenchymal cell morphogenetic behavior under physiologic circumstances such as wound repair, morphogenesis and malignancy. Copyright © 2012 Elsevier Inc. All rights reserved.

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

Science.gov (United States)

Fijany, Amir

1993-01-01

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Hypercyclic Abelian Semigroups of Matrices on Cn

International Nuclear Information System (INIS)

Ayadi, Adlene; Marzougui, Habib

2010-07-01

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

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

OpenAIRE

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

2013-01-01

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

Single and multiple object tracking using log-euclidean Riemannian subspace and block-division appearance model.

Science.gov (United States)

Hu, Weiming; Li, Xi; Luo, Wenhan; Zhang, Xiaoqin; Maybank, Stephen; Zhang, Zhongfei

2012-12-01

Object appearance modeling is crucial for tracking objects, especially in videos captured by nonstationary cameras and for reasoning about occlusions between multiple moving objects. Based on the log-euclidean Riemannian metric on symmetric positive definite matrices, we propose an incremental log-euclidean Riemannian subspace learning algorithm in which covariance matrices of image features are mapped into a vector space with the log-euclidean Riemannian metric. Based on the subspace learning algorithm, we develop a log-euclidean block-division appearance model which captures both the global and local spatial layout information about object appearances. Single object tracking and multi-object tracking with occlusion reasoning are then achieved by particle filtering-based Bayesian state inference. During tracking, incremental updating of the log-euclidean block-division appearance model captures changes in object appearance. For multi-object tracking, the appearance models of the objects can be updated even in the presence of occlusions. Experimental results demonstrate that the proposed tracking algorithm obtains more accurate results than six state-of-the-art tracking algorithms.

Formal matrices

CERN Document Server

Krylov, Piotr

2017-01-01

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

ESTIMATION OF FUNCTIONALS OF SPARSE COVARIANCE MATRICES.

Science.gov (United States)

Fan, Jianqing; Rigollet, Philippe; Wang, Weichen

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

Computation of deformations and stresses in graphite blocks for HTR core survey purposes

International Nuclear Information System (INIS)

Besdo, Dieter; Theymann, W.

1975-01-01

Stresses and deformations in graphite fuel elements for HTRs are caused by the temperature distribution and by irradiation under influence of creep, shrinking, thermal strains, and elastic deformations. The global deformations and the stress distribution in a prismatic fuel-element containing regularly distributed axial holes for the coolant flow and the fuel sticks, can be computed in the following manner: the block with its holes is treated as an effective homogeneous continuum with an equivalent global behaviour. Assuming that the fourth-order-tensor of the elastic constants is proportional to the corresponding tensor in the constitutive equations for creep, only the effective strains are of interest. The values of temperature and dose may be given in n points of the block at certain points of time. Then, the inelastic nonthermal strains are integrated by a Runge-Kutta-procedure in the n points. When interpolated and combined with thermal strains, they are incompatible. Hence, they produce elastic deformations which cause creep and can be computed by use of a Ritz-polynomial-series by help of a specific principle of the minimum of potential energy. Excessive computing time can be avoided easily since the influence of the local variation of the elastic constants within the block is almost negligible and, therefore, of practically no importance for the determination of the elastic strains. By this reason some matrices can be calculated a priori, and the elastic deformations are obtained by multiplications of these matrices rather than inversions. Therefore, this method is particularly suited for the computation of deformations and stresses for reactor core survey purposes where a large number (up to 7000 blocks) have to be treated

Response to Comment on Preconditioning of matrices partitioned in 2 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Blaheta, Radim

2013-01-01

Roč. 20, č. 3 (2013), s. 536-539 ISSN 1070-5325 Institutional support: RVO:68145535 Keywords : saddle point matrices * inverses * preconditioning Subject RIV: BA - General Mathematics Impact factor: 1.424, year: 2013 http://onlinelibrary.wiley.com/doi/10.1002/nla.816/pdf

The modified Gauss diagonalization of polynomial matrices

International Nuclear Information System (INIS)

Saeed, K.

1982-10-01

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

Quantum Hilbert matrices and orthogonal polynomials

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Berg, Christian

2009-01-01

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

Discrete canonical transforms that are Hadamard matrices

International Nuclear Information System (INIS)

Healy, John J; Wolf, Kurt Bernardo

2011-01-01

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

Abel-grassmann's groupoids of modulo matrices

International Nuclear Information System (INIS)

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

2016-01-01

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

Free probability and random matrices

CERN Document Server

Mingo, James A

2017-01-01

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

Quantum matrices in two dimensions

International Nuclear Information System (INIS)

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

1991-01-01

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

Viscous hydrophilic injection matrices for serial crystallography

Directory of Open Access Journals (Sweden)

Gabriela Kovácsová

2017-07-01

Full Text Available Serial (femtosecond crystallography at synchrotron and X-ray free-electron laser (XFEL sources distributes the absorbed radiation dose over all crystals used for data collection and therefore allows measurement of radiation damage prone systems, including the use of microcrystals for room-temperature measurements. Serial crystallography relies on fast and efficient exchange of crystals upon X-ray exposure, which can be achieved using a variety of methods, including various injection techniques. The latter vary significantly in their flow rates – gas dynamic virtual nozzle based injectors provide very thin fast-flowing jets, whereas high-viscosity extrusion injectors produce much thicker streams with flow rates two to three orders of magnitude lower. High-viscosity extrusion results in much lower sample consumption, as its sample delivery speed is commensurate both with typical XFEL repetition rates and with data acquisition rates at synchrotron sources. An obvious viscous injection medium is lipidic cubic phase (LCP as it is used for in meso membrane protein crystallization. However, LCP has limited compatibility with many crystallization conditions. While a few other viscous media have been described in the literature, there is an ongoing need to identify additional injection media for crystal embedding. Critical attributes are reliable injection properties and a broad chemical compatibility to accommodate samples as heterogeneous and sensitive as protein crystals. Here, the use of two novel hydrogels as viscous injection matrices is described, namely sodium carboxymethyl cellulose and the thermo-reversible block polymer Pluronic F-127. Both are compatible with various crystallization conditions and yield acceptable X-ray background. The stability and velocity of the extruded stream were also analysed and the dependence of the stream velocity on the flow rate was measured. In contrast with previously characterized injection media, both new

Synchronous correlation matrices and Connes’ embedding conjecture

Energy Technology Data Exchange (ETDEWEB)

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

2016-01-15

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

Realm of Matrices

Indian Academy of Sciences (India)

IAS Admin

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

Virial expansion for almost diagonal random matrices

Science.gov (United States)

Yevtushenko, Oleg; Kravtsov, Vladimir E.

2003-08-01

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

A direct recursive residue generation method: application to photoionization of hydrogen in static electric fields

International Nuclear Information System (INIS)

Karlsson, H.O.; Goscinski, O.

1994-01-01

In studies of hydrogenic systems via the recursive residue generation method (RRGM) the major bottleneck is the matrix vector product HC, between the Hamiltonian matrix H and a Lanczos vector C. For highly excited states and/or strong perturbations the size of H grows fast leading to storage problems. By making use of direct methods, i.e. avoidance of explicit construction of large Hamiltonian matrices, such problems can be overcome. Utilizing the underlying analytical properties of the Laguerre basis e -λr L k 2l+2 (2λr) a direct RRGM (D-RRGM) for the unperturbed hydrogenic Hamiltonian is derived, changing the storage needs from scaling as N 2 to 4N where N is the number of radial functions for each factorized H o (l,m) block with the possibility of parallel processing. A further computational simplification is introduced by putting the expression for the photoionization (PI) cross section in the rational form conventionally used in the representation of density of states (DOS). This allows the construction of the PI cross section directly from the tridiagonal Lanczos matrix avoiding the explicit calculation of individual eigen values and eigenvectors. (Author)

Chequered surfaces and complex matrices

International Nuclear Information System (INIS)

Morris, T.R.; Southampton Univ.

1991-01-01

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

Intrinsic Density Matrices of the Nuclear Shell Model

International Nuclear Information System (INIS)

Deveikis, A.; Kamuntavichius, G.

1996-01-01

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

Random matrices and random difference equations

International Nuclear Information System (INIS)

Uppuluri, V.R.R.

1975-01-01

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

Quantum Entanglement and Reduced Density Matrices

Science.gov (United States)

Purwanto, Agus; Sukamto, Heru; Yuwana, Lila

2018-05-01

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

Approach method of the solutions of algebraic models of the N body problem

International Nuclear Information System (INIS)

Dufour, M.

1986-09-01

We have studied a class of algebraic eigenvalue problems that generate tridiagonal matrices. The Lipkin Hamiltonian was chosen as representative. Three methods have been implemented, whose extension to more general many body problems seems possible i) Degenerate Linked Cluster Theory (LCT), which disregards special symmetries of the interaction and defines a hierarchy of approximation based on model spaces at fixed number of particle-hole excitation of the unperturbed Hamiltonian. The method works for small perturbations but does not yield a complete description. ii) A new linearization method that replaces the matrix to be diagonalized by local (tangent) approximations by harmonic matrices. This method generalizes LCT and is a posteriori reminiscent of semi-classical ones. However of is simpler, more precise and yields a complete description of spectra. iii) A global way to characterize spectra based on Gershgorine-Hadamard disks [fr

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-11-01

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

S-matrices and integrability

International Nuclear Information System (INIS)

Bombardelli, Diego

2016-01-01

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

Matrices Aléatoires Tri-diagonales et Par Blocs.

OpenAIRE

MEKKI, Slimane

2014-01-01

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

Hierarchical quark mass matrices

International Nuclear Information System (INIS)

Rasin, A.

1998-02-01

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

Design of Packet-Based Block Codes with Shift Operators

Directory of Open Access Journals (Sweden)

Ilow Jacek

2010-01-01

Full Text Available This paper introduces packet-oriented block codes for the recovery of lost packets and the correction of an erroneous single packet. Specifically, a family of systematic codes is proposed, based on a Vandermonde matrix applied to a group of information packets to construct redundant packets, where the elements of the Vandermonde matrix are bit-level right arithmetic shift operators. The code design is applicable to packets of any size, provided that the packets within a block of information packets are of uniform length. In order to decrease the overhead associated with packet padding using shift operators, non-Vandermonde matrices are also proposed for designing packet-oriented block codes. An efficient matrix inversion procedure for the off-line design of the decoding algorithm is presented to recover lost packets. The error correction capability of the design is investigated as well. The decoding algorithm, based on syndrome decoding, to correct a single erroneous packet in a group of received packets is presented. The paper is equipped with examples of codes using different parameters. The code designs and their performance are tested using Monte Carlo simulations; the results obtained exhibit good agreement with the corresponding theoretical results.

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

Science.gov (United States)

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

2012-06-01

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

Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1981-01-01

Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

Graphs and matrices

CERN Document Server

Bapat, Ravindra B

2014-01-01

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

Bayesian Nonparametric Clustering for Positive Definite Matrices.

Science.gov (United States)

Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2016-05-01

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

On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers

Directory of Open Access Journals (Sweden)

Zhaolin Jiang

2014-01-01

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

Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems

KAUST Repository

Chávez, Gustavo

2017-12-15

We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions. Algorithmic synergies between Cyclic Reduction and hierarchical matrix arithmetic operations result in a solver that has O(kNlogN(logN+k2)) arithmetic complexity and O(k Nlog N) memory footprint, where N is the number of degrees of freedom and k is the rank of a block in the hierarchical approximation, and which exhibits substantial concurrency. We provide a baseline for performance and applicability by comparing with the multifrontal method with and without hierarchical semi-separable matrices, with algebraic multigrid and with the classic cyclic reduction method. Over a set of large-scale elliptic systems with features of nonsymmetry and indefiniteness, the robustness of the direct solvers extends beyond that of the multigrid solver, and relative to the multifrontal approach ACR has lower or comparable execution time and size of the factors, with substantially lower numerical ranks. ACR exhibits good strong and weak scaling in a distributed context and, as with any direct solver, is advantageous for problems that require the solution of multiple right-hand sides. Numerical experiments show that the rank k patterns are of O(1) for the Poisson equation and of O(n) for the indefinite Helmholtz equation. The solver is ideal in situations where low-accuracy solutions are sufficient, or otherwise as a preconditioner within an iterative method.

Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems

KAUST Repository

Chá vez, Gustavo; Turkiyyah, George; Zampini, Stefano; Ltaief, Hatem; Keyes, David E.

2017-01-01

We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions. Algorithmic synergies between Cyclic Reduction and hierarchical matrix arithmetic operations result in a solver that has O(kNlogN(logN+k2)) arithmetic complexity and O(k Nlog N) memory footprint, where N is the number of degrees of freedom and k is the rank of a block in the hierarchical approximation, and which exhibits substantial concurrency. We provide a baseline for performance and applicability by comparing with the multifrontal method with and without hierarchical semi-separable matrices, with algebraic multigrid and with the classic cyclic reduction method. Over a set of large-scale elliptic systems with features of nonsymmetry and indefiniteness, the robustness of the direct solvers extends beyond that of the multigrid solver, and relative to the multifrontal approach ACR has lower or comparable execution time and size of the factors, with substantially lower numerical ranks. ACR exhibits good strong and weak scaling in a distributed context and, as with any direct solver, is advantageous for problems that require the solution of multiple right-hand sides. Numerical experiments show that the rank k patterns are of O(1) for the Poisson equation and of O(n) for the indefinite Helmholtz equation. The solver is ideal in situations where low-accuracy solutions are sufficient, or otherwise as a preconditioner within an iterative method.

Immanant Conversion on Symmetric Matrices

Directory of Open Access Journals (Sweden)

Purificação Coelho M.

2014-01-01

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

The 'golden' matrices and a new kind of cryptography

International Nuclear Information System (INIS)

Stakhov, A.P.

2007-01-01

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

Advanced incomplete factorization algorithms for Stiltijes matrices

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

On Investigating GMRES Convergence using Unitary Matrices

Czech Academy of Sciences Publication Activity Database

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

2014-01-01

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

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

Science.gov (United States)

Lee, Ken Voon

2013-04-01

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

CONVERGENCE OF POWERS OF CONTROLLABLE INTUITIONISTIC FUZZY MATRICES

OpenAIRE

Riyaz Ahmad Padder; P. Murugadas

2016-01-01

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

Loop diagrams without γ matrices

International Nuclear Information System (INIS)

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

1993-01-01

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

Classification en référence à une matrice stochastique

OpenAIRE

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

2009-01-01

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

Capture Matrices Handbook

Science.gov (United States)

2014-04-01

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

Binary Positive Semidefinite Matrices and Associated Integer Polytopes

DEFF Research Database (Denmark)

Letchford, Adam N.; Sørensen, Michael Malmros

2012-01-01

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

Chain of matrices, loop equations and topological recursion

CERN Document Server

Orantin, Nicolas

2009-01-01

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

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

OpenAIRE

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

2017-01-01

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

Design of Packet-Based Block Codes with Shift Operators

Directory of Open Access Journals (Sweden)

Jacek Ilow

2010-01-01

Full Text Available This paper introduces packet-oriented block codes for the recovery of lost packets and the correction of an erroneous single packet. Specifically, a family of systematic codes is proposed, based on a Vandermonde matrix applied to a group of k information packets to construct r redundant packets, where the elements of the Vandermonde matrix are bit-level right arithmetic shift operators. The code design is applicable to packets of any size, provided that the packets within a block of k information packets are of uniform length. In order to decrease the overhead associated with packet padding using shift operators, non-Vandermonde matrices are also proposed for designing packet-oriented block codes. An efficient matrix inversion procedure for the off-line design of the decoding algorithm is presented to recover lost packets. The error correction capability of the design is investigated as well. The decoding algorithm, based on syndrome decoding, to correct a single erroneous packet in a group of n=k+r received packets is presented. The paper is equipped with examples of codes using different parameters. The code designs and their performance are tested using Monte Carlo simulations; the results obtained exhibit good agreement with the corresponding theoretical results.

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science.

Science.gov (United States)

Marek, A; Blum, V; Johanni, R; Havu, V; Lang, B; Auckenthaler, T; Heinecke, A; Bungartz, H-J; Lederer, H

2014-05-28

Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N(3)) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on a few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the Eigenvalue soLvers for Petascale Applications (ELPA) library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the Scalable Linear Algebra PACKage (ScaLAPACK) library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g. Intel's MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPI-OpenMPI implementation available as well. Scalability beyond 10,000 CPU cores for problem

The Modern Origin of Matrices and Their Applications

Science.gov (United States)

Debnath, L.

2014-01-01

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

Flux Jacobian Matrices For Equilibrium Real Gases

Science.gov (United States)

Vinokur, Marcel

1990-01-01

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

Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs

KAUST Repository

Farrell, Patricio

2015-04-30

© 2015John Wiley & Sons, Ltd. Symmetric collocation methods with RBFs allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. This cost can be alleviated somewhat by considering compactly supported RBFs and a multiscale technique. But the condition number and sparsity will still deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction. Numerical results verify the effectiveness of the preconditioners.

Data depth and rank-based tests for covariance and spectral density matrices

KAUST Repository

Chau, Joris

2017-06-26

In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.

Data depth and rank-based tests for covariance and spectral density matrices

KAUST Repository

Chau, Joris; Ombao, Hernando; Sachs, Rainer von

2017-01-01

In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.

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

Science.gov (United States)

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

2016-08-01

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

Forecasting Covariance Matrices: A Mixed Frequency Approach

DEFF Research Database (Denmark)

Halbleib, Roxana; Voev, Valeri

This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows for flexi......This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...

Propositional matrices as alternative representation of truth values ...

African Journals Online (AJOL)

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

A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals

Directory of Open Access Journals (Sweden)

Pablo Soto-Quiros

2015-01-01

Full Text Available This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT: the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.

Wishart and anti-Wishart random matrices

International Nuclear Information System (INIS)

Janik, Romuald A; Nowak, Maciej A

2003-01-01

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

Information geometry of density matrices and state estimation

International Nuclear Information System (INIS)

Brody, Dorje C

2011-01-01

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

Supercritical fluid extraction behaviour of polymer matrices

International Nuclear Information System (INIS)

Sujatha, K.; Kumar, R.; Sivaraman, N.; Srinivasan, T.G.; Vasudeva Rao, P.R.

2007-01-01

Organic compounds present in polymeric matrices such as neoprene, surgical gloves and PVC were co-extracted during the removal of uranium using supercritical fluid extraction (SFE) technique. Hence SFE studies of these matrices were carried out to establish the extracted species using HPLC, IR and mass spectrometry techniques. The initial study indicated that uranium present in the extract could be purified from the co-extracted organic species. (author)

On K-Line and K x K Block Iterative Schemes for a Problem Arising in 3-D Elliptic Difference Equations.

Science.gov (United States)

1980-01-01

VPARTER. , STEUERWALT No 0I 76_C-03AI UNCLASSIFIED CSTR -374 ML M EMON~hEE 111112.08 12.5 111112 1.4 1 1. KWOCP RSLINTS CHR NA11~ L .R~l0 ___VRD I-l...4b) are obtained from the well known algorithm for solving diagonally dominant tridiagonal sys- tems; see (16, 10]. The monotonicity of the Ej and the

The BR eigenvalue algorithm

Energy Technology Data Exchange (ETDEWEB)

Geist, G.A. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.; Howell, G.W. [Florida Inst. of Tech., Melbourne, FL (United States). Dept. of Applied Mathematics; Watkins, D.S. [Washington State Univ., Pullman, WA (United States). Dept. of Pure and Applied Mathematics

1997-11-01

The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrowband, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the QR algorithm by a factor of 30--60 in computing time and a factor of over 100 in matrix storage space.

Fabrication of Aligned Carbon Nanotube/Polycaprolactone/Gelatin Nanofibrous Matrices for Schwann Cell Immobilization

Directory of Open Access Journals (Sweden)

Shiao-Wen Tsai

2014-01-01

Full Text Available In this study, we utilized a mandrel rotating collector consisting of two parallel, electrically conductive pieces of tape to fabricate aligned electrospun polycaprolactone/gelatin (PG and carbon nanotube/polycaprolactone/gelatin (PGC nanofibrous matrices. Furthermore, we examined the biological performance of the PGC nanofibrous and film matrices using an in vitro culture of RT4-D6P2T rat Schwann cells. Using cell adhesion tests, we found that carbon nanotube inhibited Schwann cell attachment on PGC nanofibrous and film matrices. However, the proliferation rates of Schwann cells were higher when they were immobilized on PGC nanofibrous matrices compared to PGC film matrices. Using western blot analysis, we found that NRG1 and P0 protein expression levels were higher for cells immobilized on PGC nanofibrous matrices compared to PG nanofibrous matrices. However, the carbon nanotube inhibited NRG1 and P0 protein expression in cells immobilized on PGC film matrices. Moreover, the NRG1 and P0 protein expression levels were higher for cells immobilized on PGC nanofibrous matrices compared to PGC film matrices. We found that the matrix topography and composition influenced Schwann cell behavior.

Nano-Fiber Reinforced Enhancements in Composite Polymer Matrices

Science.gov (United States)

Chamis, Christos C.

2009-01-01

Nano-fibers are used to reinforce polymer matrices to enhance the matrix dependent properties that are subsequently used in conventional structural composites. A quasi isotropic configuration is used in arranging like nano-fibers through the thickness to ascertain equiaxial enhanced matrix behavior. The nano-fiber volume ratios are used to obtain the enhanced matrix strength properties for 0.01,0.03, and 0.05 nano-fiber volume rates. These enhanced nano-fiber matrices are used with conventional fiber volume ratios of 0.3 and 0.5 to obtain the composite properties. Results show that nano-fiber enhanced matrices of higher than 0.3 nano-fiber volume ratio are degrading the composite properties.

Meet and Join Matrices in the Poset of Exponential Divisors

Indian Academy of Sciences (India)

... exponential divisor ( G C E D ) and the least common exponential multiple ( L C E M ) do not always exist. In this paper we embed this poset in a lattice. As an application we study the G C E D and L C E M matrices, analogues of G C D and L C M matrices, which are both special cases of meet and join matrices on lattices.

Joint Estimation of Multiple Precision Matrices with Common Structures.

Science.gov (United States)

Lee, Wonyul; Liu, Yufeng

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

Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

Science.gov (United States)

Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.

2017-11-01

Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.

On the norms of r-circulant matrices with generalized Fibonacci numbers

Directory of Open Access Journals (Sweden)

Amara Chandoul

2017-01-01

Full Text Available In this paper, we obtain a generalization of [6, 8]. Firstly, we consider the so-called r-circulant matrices with generalized Fibonacci numbers and then found lower and upper bounds for the Euclidean and spectral norms of these matrices. Afterwards, we present some bounds for the spectral norms of Hadamard and Kronecker product of these matrices.

Some uses of the symmetric Lanczos algorithm - and why it works!

Energy Technology Data Exchange (ETDEWEB)

Druskin, V.L. [Schlumberger-Doll Research, Ridgefield, CT (United States); Greenbaum, A. [Courant Institute of Mathematical Sciences, New York, NY (United States); Knizhnerman, L.A. [Central Geophysical Expedition, Moscow (Russian Federation)

1996-12-31

The Lanczos algorithm uses a three-term recurrence to construct an orthonormal basis for the Krylov space corresponding to a symmetric matrix A and a starting vector q{sub 1}. The vectors and recurrence coefficients produced by this algorithm can be used for a number of purposes, including solving linear systems Au = {var_phi} and computing the matrix exponential e{sup -tA}{var_phi}. Although the vectors produced in finite precision arithmetic are not orthogonal, we show why they can still be used effectively for these purposes. The reason is that the 2-norm of the residual is essentially determined by the tridiagonal matrix and the next recurrence coefficient produced by the finite precision Lanczos computation. It follows that if the same tridiagonal matrix and recurrence coefficient are produced by the exact Lanczos algorithm applied to some other problem, then exact arithmetic bounds on the residual for that problem will hold for the finite precision computation. In order to establish exact arithmetic bounds for the different problem, it is necessary to have some information about the eigenvalues of the new coefficient matrix. Here we make use of information already established in the literature, and we also prove a new result for indefinite matrices.

Numerical Aspects of Atomic Physics: Helium Basis Sets and Matrix Diagonalization

Science.gov (United States)

Jentschura, Ulrich; Noble, Jonathan

2014-03-01

We present a matrix diagonalization algorithm for complex symmetric matrices, which can be used in order to determine the resonance energies of auto-ionizing states of comparatively simple quantum many-body systems such as helium. The algorithm is based in multi-precision arithmetic and proceeds via a tridiagonalization of the complex symmetric (not necessarily Hermitian) input matrix using generalized Householder transformations. Example calculations involving so-called PT-symmetric quantum systems lead to reference values which pertain to the imaginary cubic perturbation (the imaginary cubic anharmonic oscillator). We then proceed to novel basis sets for the helium atom and present results for Bethe logarithms in hydrogen and helium, obtained using the enhanced numerical techniques. Some intricacies of ``canned'' algorithms such as those used in LAPACK will be discussed. Our algorithm, for complex symmetric matrices such as those describing cubic resonances after complex scaling, is faster than LAPACK's built-in routines, for specific classes of input matrices. It also offer flexibility in terms of the calculation of the so-called implicit shift, which is used in order to ``pivot'' the system toward the convergence to diagonal form. We conclude with a wider overview.

Hypersymmetric functions and Pochhammers of 2×2 nonautonomous matrices

Directory of Open Access Journals (Sweden)

A. F. Antippa

2004-01-01

Full Text Available We introduce the hypersymmetric functions of 2×2 nonautonomous matrices and show that they are related, by simple expressions, to the Pochhammers (factorial polynomials of these matrices. The hypersymmetric functions are generalizations of the associated elementary symmetric functions, and for a specific class of 2×2 matrices, having a high degree of symmetry, they reduce to these latter functions. This class of matrices includes rotations, Lorentz boosts, and discrete time generators for the harmonic oscillators. The hypersymmetric functions are defined over four sets of independent indeterminates using a triplet of interrelated binary partitions. We work out the algebra of this triplet of partitions and then make use of the results in order to simplify the expressions for the hypersymmetric functions for a special class of matrices. In addition to their obvious applications in matrix theory, in coupled difference equations, and in the theory of symmetric functions, the results obtained here also have useful applications in problems involving successive rotations, successive Lorentz transformations, discrete harmonic oscillators, and linear two-state systems.

An algorithmic characterization of P-matricity

OpenAIRE

Ben Gharbia , Ibtihel; Gilbert , Jean Charles

2013-01-01

International audience; It is shown that a matrix M is a P-matrix if and only if, whatever is the vector q, the Newton-min algorithm does not cycle between two points when it is used to solve the linear complementarity problem 0 ≤ x ⊥ (Mx+q) ≥ 0.; Nous montrons dans cet article qu'une matrice M est une P-matrice si, et seulement si, quel que soit le vecteur q, l'algorithme de Newton-min ne fait pas de cycle de deux points lorsqu'il est utilisé pour résoudre le problème de compl\\émentarité lin...

Partitioning sparse rectangular matrices for parallel processing

Energy Technology Data Exchange (ETDEWEB)

Kolda, T.G.

1998-05-01

The authors are interested in partitioning sparse rectangular matrices for parallel processing. The partitioning problem has been well-studied in the square symmetric case, but the rectangular problem has received very little attention. They will formalize the rectangular matrix partitioning problem and discuss several methods for solving it. They will extend the spectral partitioning method for symmetric matrices to the rectangular case and compare this method to three new methods -- the alternating partitioning method and two hybrid methods. The hybrid methods will be shown to be best.

Development of a high performance eigensolver on the peta-scale next generation supercomputer system

International Nuclear Information System (INIS)

Imamura, Toshiyuki; Yamada, Susumu; Machida, Masahiko

2010-01-01

For the present supercomputer systems, a multicore and multisocket processors are necessary to build a system, and choice of interconnection is essential. In addition, for effective development of a new code, high performance, scalable, and reliable numerical software is one of the key items. ScaLAPACK and PETSc are well-known software on distributed memory parallel computer systems. It is needless to say that highly tuned software towards new architecture like many-core processors must be chosen for real computation. In this study, we present a high-performance and high-scalable eigenvalue solver towards the next-generation supercomputer system, so called 'K-computer' system. We have developed two versions, the standard version (eigen s) and enhanced performance version (eigen sx), which are developed on the T2K cluster system housed at University of Tokyo. Eigen s employs the conventional algorithms; Householder tridiagonalization, divide and conquer (DC) algorithm, and Householder back-transformation. They are carefully implemented with blocking technique and flexible two-dimensional data-distribution to reduce the overhead of memory traffic and data transfer, respectively. Eigen s performs excellently on the T2K system with 4096 cores (theoretical peak is 37.6 TFLOPS), and it shows fine performance 3.0 TFLOPS with a two hundred thousand dimensional matrix. The enhanced version, eigen sx, uses more advanced algorithms; the narrow-band reduction algorithm, DC for band matrices, and the block Householder back-transformation with WY-representation. Even though this version is still on a test stage, it shows 4.7 TFLOPS with the same dimensional matrix on eigen s. (author)

Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations

KAUST Repository

Chavez, Gustavo Ivan

2017-07-10

This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST\\'s Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.

Topological expansion of the chain of matrices

International Nuclear Information System (INIS)

Eynard, B.; Ferrer, A. Prats

2009-01-01

We solve the loop equations to all orders in 1/N 2 , for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for the 1 and 2-matrix model, given by the symplectic invariants of [19]. As a consequence, we find the double scaling limit explicitly, and we discuss modular properties, large N asymptotics. We also briefly discuss the limit of an infinite chain of matrices (matrix quantum mechanics).

Newton`s iteration for inversion of Cauchy-like and other structured matrices

Energy Technology Data Exchange (ETDEWEB)

Pan, V.Y. [Lehman College, Bronx, NY (United States); Zheng, Ailong; Huang, Xiaohan; Dias, O. [CUNY, New York, NY (United States)

1996-12-31

We specify some initial assumptions that guarantee rapid refinement of a rough initial approximation to the inverse of a Cauchy-like matrix, by mean of our new modification of Newton`s iteration, where the input, output, and all the auxiliary matrices are represented with their short generators defined by the associated scaling operators. The computations are performed fast since they are confined to operations with short generators of the given and computed matrices. Because of the known correlations among various structured matrices, the algorithm is immediately extended to rapid refinement of rough initial approximations to the inverses of Vandermonde-like, Chebyshev-Vandermonde-like and Toeplitz-like matrices, where again, the computations are confined to operations with short generators of the involved matrices.

Agricultural matrices affect ground ant assemblage composition inside forest fragments.

Directory of Open Access Journals (Sweden)

Diego Santana Assis

Full Text Available The establishment of agricultural matrices generally involves deforestation, which leads to fragmentation of the remaining forest. This fragmentation can affect forest dynamics both positively and negatively. Since most animal species are affected, certain groups can be used to measure the impact of such fragmentation. This study aimed to measure the impacts of agricultural crops (matrices on ant communities of adjacent lower montane Atlantic rainforest fragments. We sampled nine forest fragments at locations surrounded by different agricultural matrices, namely: coffee (3 replicates; sugarcane (3; and pasture (3. At each site we installed pitfall traps along a 500 m transect from the interior of the matrix to the interior of the fragment (20 pitfall traps ~25 m apart. Each transect was partitioned into four categories: interior of the matrix; edge of the matrix; edge of the fragment; and interior of the fragment. For each sample site, we measured ant species richness and ant community composition within each transect category. Ant richness and composition differed between fragments and matrices. Each sample location had a specific composition of ants, probably because of the influence of the nature and management of the agricultural matrices. Species composition in the coffee matrix had the highest similarity to its corresponding fragment. The variability in species composition within forest fragments surrounded by pasture was greatest when compared with forest fragments surrounded by sugarcane or, to a lesser extent, coffee. Functional guild composition differed between locations, but the most representative guild was 'generalist' both in the agricultural matrices and forest fragments. Our results are important for understanding how agricultural matrices act on ant communities, and also, how these isolated forest fragments could act as an island of biodiversity in an 'ocean of crops'.

Agricultural matrices affect ground ant assemblage composition inside forest fragments.

Science.gov (United States)

Assis, Diego Santana; Dos Santos, Iracenir Andrade; Ramos, Flavio Nunes; Barrios-Rojas, Katty Elena; Majer, Jonathan David; Vilela, Evaldo Ferreira

2018-01-01

The establishment of agricultural matrices generally involves deforestation, which leads to fragmentation of the remaining forest. This fragmentation can affect forest dynamics both positively and negatively. Since most animal species are affected, certain groups can be used to measure the impact of such fragmentation. This study aimed to measure the impacts of agricultural crops (matrices) on ant communities of adjacent lower montane Atlantic rainforest fragments. We sampled nine forest fragments at locations surrounded by different agricultural matrices, namely: coffee (3 replicates); sugarcane (3); and pasture (3). At each site we installed pitfall traps along a 500 m transect from the interior of the matrix to the interior of the fragment (20 pitfall traps ~25 m apart). Each transect was partitioned into four categories: interior of the matrix; edge of the matrix; edge of the fragment; and interior of the fragment. For each sample site, we measured ant species richness and ant community composition within each transect category. Ant richness and composition differed between fragments and matrices. Each sample location had a specific composition of ants, probably because of the influence of the nature and management of the agricultural matrices. Species composition in the coffee matrix had the highest similarity to its corresponding fragment. The variability in species composition within forest fragments surrounded by pasture was greatest when compared with forest fragments surrounded by sugarcane or, to a lesser extent, coffee. Functional guild composition differed between locations, but the most representative guild was 'generalist' both in the agricultural matrices and forest fragments. Our results are important for understanding how agricultural matrices act on ant communities, and also, how these isolated forest fragments could act as an island of biodiversity in an 'ocean of crops'.

MALDI matrices for low molecular weight compounds: an endless story?

Science.gov (United States)

Calvano, Cosima Damiana; Monopoli, Antonio; Cataldi, Tommaso R I; Palmisano, Francesco

2018-04-23

Since its introduction in the 1980s, matrix-assisted laser desorption/ionization mass spectrometry (MALDI MS) has gained a prominent role in the analysis of high molecular weight biomolecules such as proteins, peptides, oligonucleotides, and polysaccharides. Its application to low molecular weight compounds has remained for long time challenging due to the spectral interferences produced by conventional organic matrices in the low m/z window. To overcome this problem, specific sample preparation such as analyte/matrix derivatization, addition of dopants, or sophisticated deposition technique especially useful for imaging experiments, have been proposed. Alternative approaches based on second generation (rationally designed) organic matrices, ionic liquids, and inorganic matrices, including metallic nanoparticles, have been the object of intense and continuous research efforts. Definite evidences are now provided that MALDI MS represents a powerful and invaluable analytical tool also for small molecules, including their quantification, thus opening new, exciting applications in metabolomics and imaging mass spectrometry. This review is intended to offer a concise critical overview of the most recent achievements about MALDI matrices capable of specifically address the challenging issue of small molecules analysis. Graphical abstract An ideal Book of matrices for MALDI MS of small molecules.

Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

Directory of Open Access Journals (Sweden)

Han Guo

2012-01-01

Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.

The recurrence sequences via Sylvester matrices

Science.gov (United States)

Karaduman, Erdal; Deveci, Ömür

2017-07-01

In this work, we define the Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by using the Slyvester matrices which are obtained from the characteristic polynomials of the Pell and Jacobsthal sequences and then, we study the sequences defined modulo m. Also, we obtain the cyclic groups and the semigroups from the generating matrices of these sequences when read modulo m and then, we derive the relationships among the orders of the cyclic groups and the periods of the sequences. Furthermore, we redefine Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by means of the elements of the groups and then, we examine them in the finite groups.

Quantitative mass spectrometry of unconventional human biological matrices

Science.gov (United States)

Dutkiewicz, Ewelina P.; Urban, Pawel L.

2016-10-01

The development of sensitive and versatile mass spectrometric methodology has fuelled interest in the analysis of metabolites and drugs in unconventional biological specimens. Here, we discuss the analysis of eight human matrices-hair, nail, breath, saliva, tears, meibum, nasal mucus and skin excretions (including sweat)-by mass spectrometry (MS). The use of such specimens brings a number of advantages, the most important being non-invasive sampling, the limited risk of adulteration and the ability to obtain information that complements blood and urine tests. The most often studied matrices are hair, breath and saliva. This review primarily focuses on endogenous (e.g. potential biomarkers, hormones) and exogenous (e.g. drugs, environmental contaminants) small molecules. The majority of analytical methods used chromatographic separation prior to MS; however, such a hyphenated methodology greatly limits analytical throughput. On the other hand, the mass spectrometric methods that exclude chromatographic separation are fast but suffer from matrix interferences. To enable development of quantitative assays for unconventional matrices, it is desirable to standardize the protocols for the analysis of each specimen and create appropriate certified reference materials. Overcoming these challenges will make analysis of unconventional human biological matrices more common in a clinical setting. This article is part of the themed issue 'Quantitative mass spectrometry'.

A Conceptual Cost Benefit Analysis of Tailings Matrices Use in Construction Applications

Directory of Open Access Journals (Sweden)

Mahmood Ali A.

2016-01-01

Full Text Available As part of a comprehensive research program, new tailings matrices are formulated of combinations of tailings and binder materials. The research program encompasses experimental and numerical analysis of the tailings matrices to investigate the feasibility of using them as construction materials in cold climates. This paper discusses a conceptual cost benefit analysis for the use of these new materials. It is shown here that the financial benefits of using the proposed new tailings matrices in terms of environmental sustainability are much higher when compared to normal sand matrices.

Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices

KAUST Repository

Lan, Shiwei

2017-11-08

Modeling covariance (and correlation) matrices is a challenging problem due to the large dimensionality and positive-definiteness constraint. In this paper, we propose a novel Bayesian framework based on decomposing the covariance matrix into variance and correlation matrices. The highlight is that the correlations are represented as products of vectors on unit spheres. We propose a variety of distributions on spheres (e.g. the squared-Dirichlet distribution) to induce flexible prior distributions for covariance matrices that go beyond the commonly used inverse-Wishart prior. To handle the intractability of the resulting posterior, we introduce the adaptive $\\\\Delta$-Spherical Hamiltonian Monte Carlo. We also extend our structured framework to dynamic cases and introduce unit-vector Gaussian process priors for modeling the evolution of correlation among multiple time series. Using an example of Normal-Inverse-Wishart problem, a simulated periodic process, and an analysis of local field potential data (collected from the hippocampus of rats performing a complex sequence memory task), we demonstrated the validity and effectiveness of our proposed framework for (dynamic) modeling covariance and correlation matrices.

An introduction to the theory of canonical matrices

CERN Document Server

Turnbull, H W

2004-01-01

Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory's principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations. 1952 edition. Index. Appendix. Historical notes. Bibliographies. 275 problems.

Complementary Set Matrices Satisfying a Column Correlation Constraint

OpenAIRE

Wu, Di; Spasojevic, Predrag

2006-01-01

Motivated by the problem of reducing the peak to average power ratio (PAPR) of transmitted signals, we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint. The design algorithm recursively builds a collection of $2^{t+1}$ mutually orthogonal (MO) complementary set matrices starting from a companion pair of sequences. We relate correlation properties of column sequences to that of the companion pair and illustrate how to select an appropriate...

Hamiltonian structure of isospectral deformation equation and semi-classical approximation to factorized S-matrices

International Nuclear Information System (INIS)

Chudnovsky, D.V.; Chudnovsky, G.V.

1980-01-01

We consider semi-classical approximation to factorized S-matrices. We show that this new class of matrices, called s-matrices, defines Hamiltonian structures for isospectral deformation equations. Concrete examples of factorized s-matrices are constructed and they are used to define Hamiltonian structure for general two-dimensional isospectral deformation systems. (orig.)

Self-assembly behavior of poly(fluorenyl styrene)-block-poly(2-vinyl pyridine) and their blends with single wall carbon nanotubes (SWCNT)

Science.gov (United States)

Mezzenga, Raffaele; Li, Chaoxu; Hsu, Jung-Ching; Chen, Wen-Chang; Sugiyama, Kenji; Hirao, Akira

2010-03-01

We describe a supramolecular strategy to disperse carbon nanotubes in block copolymer matrices. To achieve the desired functions and morphologies, comb-type architectures in which one and two fluorene units attached on the styrene ring of polystyrene-block-poly(2-vinyl pyridine) were studied. Depending on the pendant fluorene units, the block ratio, the casting solvent and thermal annealing history, multiple morphologies were found. The phase diagram, compared to PS-b-P2VP, was interpreted in terms of the conformational asymmetry arising from grafting of fluorene units of variable lengths. Hydrogen bonds between COOH-SWCNT and P2VP favor miscibility of SWCNT within P2VP domains and the blending of these two components is reflected both on the final morphologies and on the electron conductivity of the blends.

Some thoughts on positive definiteness in the consideration of nuclear data covariance matrices

Energy Technology Data Exchange (ETDEWEB)

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

1988-01-01

Some basic mathematical features of covariance matrices are reviewed, particularly as they relate to the property of positive difiniteness. Physical implications of positive definiteness are also discussed. Consideration is given to an examination of the origins of non-positive definite matrices, to procedures which encourage the generation of positive definite matrices and to the testing of covariance matrices for positive definiteness. Attention is also given to certain problems associated with the construction of covariance matrices using information which is obtained from evaluated data files recorded in the ENDF format. Examples are provided to illustrate key points pertaining to each of the topic areas covered.

Some thoughts on positive definiteness in the consideration of nuclear data covariance matrices

International Nuclear Information System (INIS)

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

1988-01-01

Some basic mathematical features of covariance matrices are reviewed, particularly as they relate to the property of positive difiniteness. Physical implications of positive definiteness are also discussed. Consideration is given to an examination of the origins of non-positive definite matrices, to procedures which encourage the generation of positive definite matrices and to the testing of covariance matrices for positive definiteness. Attention is also given to certain problems associated with the construction of covariance matrices using information which is obtained from evaluated data files recorded in the ENDF format. Examples are provided to illustrate key points pertaining to each of the topic areas covered

Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices

International Nuclear Information System (INIS)

Sechin, Ivan; Zotov, Andrei

2016-01-01

In this paper we propose versions of the associative Yang-Baxter equation and higher order R-matrix identities which can be applied to quantum dynamical R-matrices. As is known quantum non-dynamical R-matrices of Baxter-Belavin type satisfy this equation. Together with unitarity condition and skew-symmetry it provides the quantum Yang-Baxter equation and a set of identities useful for different applications in integrable systems. The dynamical R-matrices satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation between the dynamical and non-dynamical cases is described by the IRF (interaction-round-a-face)-Vertex transformation. An alternative approach to quantum (semi-)dynamical R-matrices and related quantum algebras was suggested by Arutyunov, Chekhov, and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The purpose of this paper is twofold. First, we prove that the ACF elliptic R-matrix satisfies the associative Yang-Baxter equation with shifted spectral parameters. Second, we directly prove a simple relation of the IRF-Vertex type between the Baxter-Belavin and the ACF elliptic R-matrices predicted previously by Avan and Rollet. It provides the higher order R-matrix identities and an explanation of the obtained equations through those for non-dynamical R-matrices. As a by-product we also get an interpretation of the intertwining transformation as matrix extension of scalar theta function likewise R-matrix is interpreted as matrix extension of the Kronecker function. Relations to the Gervais-Neveu-Felder equation and identities for the Felder’s elliptic R-matrix are also discussed.

Asymmetric correlation matrices: an analysis of financial data

Science.gov (United States)

Livan, G.; Rebecchi, L.

2012-06-01

We analyse the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non-symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrix to distinguish between noise and non-trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non-symmetric correlation matrix. We find several non trivial results when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.

No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices

KAUST Repository

Kammoun, Abla; Alouini, Mohamed-Slim

2016-01-01

This paper investigates the behaviour of the spectrum of generally correlated Gaussian random matrices whose columns are zero-mean independent vectors but have different correlations, under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace. Following the approach proposed in [1], we prove that under some mild conditions, there is no eigenvalue outside the limiting support of generally correlated Gaussian matrices. As an outcome of this result, we establish that the smallest singular value of these matrices is almost surely greater than zero. From a practical perspective, this control of the smallest singular value is paramount to applications from statistical signal processing and wireless communication, in which this kind of matrices naturally arise.

No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices

KAUST Repository

Kammoun, Abla

2016-05-04

This paper investigates the behaviour of the spectrum of generally correlated Gaussian random matrices whose columns are zero-mean independent vectors but have different correlations, under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace. Following the approach proposed in [1], we prove that under some mild conditions, there is no eigenvalue outside the limiting support of generally correlated Gaussian matrices. As an outcome of this result, we establish that the smallest singular value of these matrices is almost surely greater than zero. From a practical perspective, this control of the smallest singular value is paramount to applications from statistical signal processing and wireless communication, in which this kind of matrices naturally arise.

Long-time leaching on full size radioactive waste blocks

International Nuclear Information System (INIS)

Bernard, Andre; Nomine, J.-C.; Cornec, Georges; Bonnet, Andre; Farges, Louis.

1980-12-01

Leaching is generally accepted as the fundamental characteristic when judging the quality of radioactive waste packaging. Long duration leaching tests have been carried out on full size waste blocks at the Commissariat a l'Energie Atomique. The monoliths studied are 200 litre cylinders made up of α, β and γ emitting liquid or solid waste embedded in cement or bitumen. Leaching takes place in accordance with rules based on I.A.E.A. recommendations embodying the specific concerns of safety and radiological capacity of storage sites. The tests are carried out at a Testing Station purpose built at Saclay. It includes several loops with instrumentation (volume: 3000 litres). The counting and analyses of the leached products have enabled the aggregated released fractions of the radionuclides and the structural and chemical modifications of the matrices to be assessed. The fractions of 137 Cs and 239 Pu released at 18 months are 10 -2 and 5x10 -6 for the cement coated wastes, and 10 -4 and 10 -5 for the bitumen coated wastes. The evaluation of the changes in the matrices made it possible, in particular, to observe the start of carbonation in the cement coated wastes. These trials are to be pursued for several years so as to obtain a better understanding of the exchange mechanics between the packaged wastes and the environment [fr

Adhesion and metabolic activity of human corneal cells on PCL based nanofiber matrices

Energy Technology Data Exchange (ETDEWEB)

Stafiej, Piotr; Küng, Florian [Department of Ophthalmology, Universität Erlangen-Nürnberg, Schwabachanlage 6, 91054 Erlangen (Germany); Institute of Polymer Materials, Universität Erlangen-Nürnberg, Martensstraße 7, 91054 Erlangen (Germany); Thieme, Daniel; Czugala, Marta; Kruse, Friedrich E. [Department of Ophthalmology, Universität Erlangen-Nürnberg, Schwabachanlage 6, 91054 Erlangen (Germany); Schubert, Dirk W. [Institute of Polymer Materials, Universität Erlangen-Nürnberg, Martensstraße 7, 91054 Erlangen (Germany); Fuchsluger, Thomas A., E-mail: thomas.fuchsluger@uk-erlangen.de [Department of Ophthalmology, Universität Erlangen-Nürnberg, Schwabachanlage 6, 91054 Erlangen (Germany)

2017-02-01

In this work, polycaprolactone (PCL) was used as a basic polymer for electrospinning of random and aligned nanofiber matrices. Our aim was to develop a biocompatible substrate for ophthalmological application to improve wound closure in defects of the cornea as replacement for human amniotic membrane. We investigated whether blending the hydrophobic PCL with poly (glycerol sebacate) (PGS) or chitosan (CHI) improves the biocompatibility of the matrices for cell expansion. Human corneal epithelial cells (HCEp) and human corneal keratocytes (HCK) were used for in vitro biocompatibility studies. After optimization of the electrospinning parameters for all blends, scanning electron microscopy (SEM), attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR), and water contact angle were used to characterize the different matrices. Fluorescence staining of the F-actin cytoskeleton of the cells was performed to analyze the adherence of the cells to the different matrices. Metabolic activity of the cells was measured by cell counting kit-8 (CCK-8) for 20 days to compare the biocompatibility of the materials. Our results show the feasibility of producing uniform nanofiber matrices with and without orientation for the used blends. All materials support adherence and proliferation of human corneal cell lines with oriented growth on aligned matrices. Although hydrophobicity of the materials was lowered by blending PCL, no increase in biocompatibility or proliferation, as was expected, could be measured. All tested matrices supported the expansion of human corneal cells, confirming their potential as substrates for biomedical applications. - Highlights: • PCL was blended with chitosan and poly(glycerol sebacate) for electrospinning. • Biocompatibility was proven with two human corneal cell lines. • Both cell lines adhered and proliferated on random and aligned nanofiber matrices. • Cytoskeletal orientation is shown on aligned nanofiber matrices. �

First results in the application of silicon photomultiplier matrices to small animal PET

Energy Technology Data Exchange (ETDEWEB)

Llosa, G. [University of Pisa, Department of Physics, Pisa (Italy)], E-mail: gabriela.llosa@pi.infn.it; Belcari, N.; Bisogni, M.G. [University of Pisa, Department of Physics, Pisa (Italy); INFN Pisa (Italy); Collazuol, G. [University of Pisa, Department of Physics, Pisa (Italy); Scuola Normale Superiore, Pisa (Italy); Marcatili, S. [University of Pisa, Department of Physics, Pisa (Italy); INFN Pisa (Italy); Boscardin, M.; Melchiorri, M.; Tarolli, A.; Piemonte, C.; Zorzi, N. [FBK irst, Trento (Italy); Barrillon, P.; Bondil-Blin, S.; Chaumat, V.; La Taille, C. de; Dinu, N.; Puill, V.; Vagnucci, J-F. [Laboratoire de l' Accelerateur Lineaire, IN2P3-CNRS, Orsay (France); Del Guerra, A. [University of Pisa, Department of Physics, Pisa (Italy); INFN Pisa (Italy)

2009-10-21

A very high resolution small animal PET scanner that employs matrices of silicon photomultipliers as photodetectors is under development at the University of Pisa and INFN Pisa. The first SiPM matrices composed of 16 (4x4)1mmx1mm pixel elements on a common substrate have been produced at FBK-irst, and are being evaluated for this application. The MAROC2 ASIC developed at LAL-Orsay has been employed for the readout of the SiPM matrices. The devices have been tested with pixelated and continuous LYSO crystals. The results show the good performance of the matrices and lead to the fabrication of matrices with 64 SiPM elements.

First results in the application of silicon photomultiplier matrices to small animal PET

International Nuclear Information System (INIS)

Llosa, G.; Belcari, N.; Bisogni, M.G.; Collazuol, G.; Marcatili, S.; Boscardin, M.; Melchiorri, M.; Tarolli, A.; Piemonte, C.; Zorzi, N.; Barrillon, P.; Bondil-Blin, S.; Chaumat, V.; La Taille, C. de; Dinu, N.; Puill, V.; Vagnucci, J-F.; Del Guerra, A.

2009-01-01

A very high resolution small animal PET scanner that employs matrices of silicon photomultipliers as photodetectors is under development at the University of Pisa and INFN Pisa. The first SiPM matrices composed of 16 (4x4)1mmx1mm pixel elements on a common substrate have been produced at FBK-irst, and are being evaluated for this application. The MAROC2 ASIC developed at LAL-Orsay has been employed for the readout of the SiPM matrices. The devices have been tested with pixelated and continuous LYSO crystals. The results show the good performance of the matrices and lead to the fabrication of matrices with 64 SiPM elements.

More about unphysical zeroes in quark mass matrices

Energy Technology Data Exchange (ETDEWEB)

Emmanuel-Costa, David, E-mail: david.costa@tecnico.ulisboa.pt [Departamento de Física and Centro de Física Teórica de Partículas - CFTP, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa (Portugal); González Felipe, Ricardo, E-mail: ricardo.felipe@tecnico.ulisboa.pt [Departamento de Física and Centro de Física Teórica de Partículas - CFTP, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa (Portugal); ISEL - Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, Rua Conselheiro Emídio Navarro, 1959-007 Lisboa (Portugal)

2017-01-10

We look for all weak bases that lead to texture zeroes in the quark mass matrices and contain a minimal number of parameters in the framework of the standard model. Since there are ten physical observables, namely, six nonvanishing quark masses, three mixing angles and one CP phase, the maximum number of texture zeroes in both quark sectors is altogether nine. The nine zero entries can only be distributed between the up- and down-quark sectors in matrix pairs with six and three texture zeroes or five and four texture zeroes. In the weak basis where a quark mass matrix is nonsingular and has six zeroes in one sector, we find that there are 54 matrices with three zeroes in the other sector, obtainable through right-handed weak basis transformations. It is also found that all pairs composed of a nonsingular matrix with five zeroes and a nonsingular and nondecoupled matrix with four zeroes simply correspond to a weak basis choice. Without any further assumptions, none of these pairs of up- and down-quark mass matrices has physical content. It is shown that all non-weak-basis pairs of quark mass matrices that contain nine zeroes are not compatible with current experimental data. The particular case of the so-called nearest-neighbour-interaction pattern is also discussed.

Basal Cell Carcinoma With Matrical Differentiation: Clinicopathologic, Immunohistochemical, and Molecular Biological Study of 22 Cases.

Science.gov (United States)

Kyrpychova, Liubov; Carr, Richard A; Martinek, Petr; Vanecek, Tomas; Perret, Raul; Chottová-Dvořáková, Magdalena; Zamecnik, Michal; Hadravsky, Ladislav; Michal, Michal; Kazakov, Dmitry V

2017-06-01

Basal cell carcinoma (BCC) with matrical differentiation is a fairly rare neoplasm, with about 30 cases documented mainly as isolated case reports. We studied a series of this neoplasm, including cases with an atypical matrical component, a hitherto unreported feature. Lesions coded as BCC with matrical differentiation were reviewed; 22 cases were included. Immunohistochemical studies were performed using antibodies against BerEp4, β-catenin, and epithelial membrane antigen (EMA). Molecular genetic studies using Ion AmpliSeq Cancer Hotspot Panel v2 by massively parallel sequencing on Ion Torrent PGM were performed in 2 cases with an atypical matrical component (1 was previously subjected to microdissection to sample the matrical and BCC areas separately). There were 13 male and 9 female patients, ranging in age from 41 to 89 years. Microscopically, all lesions manifested at least 2 components, a BCC area (follicular germinative differentiation) and areas with matrical differentiation. A BCC component dominated in 14 cases, whereas a matrical component dominated in 4 cases. Matrical differentiation was recognized as matrical/supramatrical cells (n=21), shadow cells (n=21), bright red trichohyaline granules (n=18), and blue-gray corneocytes (n=18). In 2 cases, matrical areas manifested cytologic atypia, and a third case exhibited an infiltrative growth pattern, with the tumor metastasizing to a lymph node. BerEP4 labeled the follicular germinative cells, whereas it was markedly reduced or negative in matrical areas. The reverse pattern was seen with β-catenin. EMA was negative in BCC areas but stained a proportion of matrical/supramatrical cells. Genetic studies revealed mutations of the following genes: CTNNB1, KIT, CDKN2A, TP53, SMAD4, ERBB4, and PTCH1, with some differences between the matrical and BCC components. It is concluded that matrical differentiation in BCC in most cases occurs as multiple foci. Rare neoplasms manifest atypia in the matrical areas

Dirac Matrices and Feynman’s Rest of the Universe

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Young S. Kim

2012-10-01

Full Text Available There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four γ matrices. These fifteen matrices can also serve as the generators of the group SL(4, r. The second set consists of ten generators of the Sp(4 group which Dirac derived from two coupled harmonic oscillators. It is shown possible to extend the symmetry of Sp(4 to that of SL(4, r if the area of the phase space of one of the oscillators is allowed to become smaller without a lower limit. While there are no restrictions on the size of phase space in classical mechanics, Feynman’s rest of the universe makes this Sp(4-to-SL(4, r transition possible. The ten generators are for the world where quantum mechanics is valid. The remaining five generators belong to the rest of the universe. It is noted that the groups SL(4, r and Sp(4 are locally isomorphic to the Lorentz groups O(3, 3 and O(3, 2 respectively. This allows us to interpret Feynman’s rest of the universe in terms of space-time symmetry.

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

Quantum Algorithms for Weighing Matrices and Quadratic Residues

OpenAIRE

van Dam, Wim

2000-01-01

In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is ignificantly lower than the classical one. It is pointed out that this scheme captures both Bernstein & Vazirani's inner-product protocol, as well as Grover's search algorithm. In the second part of the ar...

Empowering first year (post-matric) students in basic research skills ...

African Journals Online (AJOL)

Post-matric students from under-resourced (historically disadvantaged) black high schools generally encounter difficulties in their academic work at university. The study reported here was intended to empower first year (post-matric) students from these schools with basic research skills in a bid to counteract the effects of ...

Applicability of non-invasively collected matrices for human biomonitoring

Directory of Open Access Journals (Sweden)

Nickmilder Marc

2009-03-01

Full Text Available Abstract With its inclusion under Action 3 in the Environment and Health Action Plan 2004–2010 of the European Commission, human biomonitoring is currently receiving an increasing amount of attention from the scientific community as a tool to better quantify human exposure to, and health effects of, environmental stressors. Despite the policy support, however, there are still several issues that restrict the routine application of human biomonitoring data in environmental health impact assessment. One of the main issues is the obvious need to routinely collect human samples for large-scale surveys. Particularly the collection of invasive samples from susceptible populations may suffer from ethical and practical limitations. Children, pregnant women, elderly, or chronically-ill people are among those that would benefit the most from non-invasive, repeated or routine sampling. Therefore, the use of non-invasively collected matrices for human biomonitoring should be promoted as an ethically appropriate, cost-efficient and toxicologically relevant alternative for many biomarkers that are currently determined in invasively collected matrices. This review illustrates that several non-invasively collected matrices are widely used that can be an valuable addition to, or alternative for, invasively collected matrices such as peripheral blood sampling. Moreover, a well-informed choice of matrix can provide an added value for human biomonitoring, as different non-invasively collected matrices can offer opportunities to study additional aspects of exposure to and effects from environmental contaminants, such as repeated sampling, historical overview of exposure, mother-child transfer of substances, or monitoring of substances with short biological half-lives.

Polymer Percolation Threshold in Multi-Component HPMC Matrices Tablets

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Maryam Maghsoodi

2011-06-01

Full Text Available Introduction: The percolation theory studies the critical points or percolation thresholds of the system, where onecomponent of the system undergoes a geometrical phase transition, starting to connect the whole system. The application of this theory to study the release rate of hydrophilic matrices allows toexplain the changes in release kinetics of swellable matrix type system and results in a clear improvement of the design of controlled release dosage forms. Methods: In this study, the percolation theory has been applied to multi-component hydroxypropylmethylcellulose (HPMC hydrophilic matrices. Matrix tablets have been prepared using phenobarbital as drug,magnesium stearate as a lubricant employing different amount of lactose and HPMC K4M as a fillerandmatrix forming material, respectively. Ethylcelullose (EC as a polymeric excipient was also examined. Dissolution studies were carried out using the paddle method. In order to estimate the percolation threshold, the behaviour of the kinetic parameters with respect to the volumetric fraction of HPMC at time zero, was studied. Results: In both HPMC/lactose and HPMC/EC/lactose matrices, from the point of view of the percolation theory, the optimum concentration for HPMC, to obtain a hydrophilic matrix system for the controlled release of phenobarbital is higher than 18.1% (v/v HPMC. Above 18.1% (v/v HPMC, an infinite cluster of HPMC would be formed maintaining integrity of the system and controlling the drug release from the matrices. According to results, EC had no significant influence on the HPMC percolation threshold. Conclusion: This may be related to broad functionality of the swelling hydrophilic matrices.

Efficient linear algebra routines for symmetric matrices stored in packed form.

Science.gov (United States)

Ahlrichs, Reinhart; Tsereteli, Kakha

2002-01-30

Quantum chemistry methods require various linear algebra routines for symmetric matrices, for example, diagonalization or Cholesky decomposition for positive matrices. We present a small set of these basic routines that are efficient and minimize memory requirements.

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

OpenAIRE

Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan

2012-01-01

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the ...

Two-mode Gaussian density matrices and squeezing of photons

International Nuclear Information System (INIS)

Tucci, R.R.

1992-01-01

In this paper, the authors generalize to 2-mode states the 1-mode state results obtained in a previous paper. The authors study 2-mode Gaussian density matrices. The authors find a linear transformation which maps the two annihilation operators, one for each mode, into two new annihilation operators that are uncorrelated and unsqueezed. This allows the authors to express the density matrix as a product of two 1-mode density matrices. The authors find general conditions under which 2-mode Gaussian density matrices become pure states. Possible pure states include the 2-mode squeezed pure states commonly mentioned in the literature, plus other pure states never mentioned before. The authors discuss the entropy and thermodynamic laws (Second Law, Fundamental Equation, and Gibbs-Duhem Equation) for the 2-mode states being considered

Positive projections of symmetric matrices and Jordan algebras

DEFF Research Database (Denmark)

Fuglede, Bent; Jensen, Søren Tolver

2013-01-01

An elementary proof is given that the projection from the space of all symmetric p×p matrices onto a linear subspace is positive if and only if the subspace is a Jordan algebra. This solves a problem in a statistical model.......An elementary proof is given that the projection from the space of all symmetric p×p matrices onto a linear subspace is positive if and only if the subspace is a Jordan algebra. This solves a problem in a statistical model....

Statistical potential-based amino acid similarity matrices for aligning distantly related protein sequences.

Science.gov (United States)

Tan, Yen Hock; Huang, He; Kihara, Daisuke

2006-08-15

Aligning distantly related protein sequences is a long-standing problem in bioinformatics, and a key for successful protein structure prediction. Its importance is increasing recently in the context of structural genomics projects because more and more experimentally solved structures are available as templates for protein structure modeling. Toward this end, recent structure prediction methods employ profile-profile alignments, and various ways of aligning two profiles have been developed. More fundamentally, a better amino acid similarity matrix can improve a profile itself; thereby resulting in more accurate profile-profile alignments. Here we have developed novel amino acid similarity matrices from knowledge-based amino acid contact potentials. Contact potentials are used because the contact propensity to the other amino acids would be one of the most conserved features of each position of a protein structure. The derived amino acid similarity matrices are tested on benchmark alignments at three different levels, namely, the family, the superfamily, and the fold level. Compared to BLOSUM45 and the other existing matrices, the contact potential-based matrices perform comparably in the family level alignments, but clearly outperform in the fold level alignments. The contact potential-based matrices perform even better when suboptimal alignments are considered. Comparing the matrices themselves with each other revealed that the contact potential-based matrices are very different from BLOSUM45 and the other matrices, indicating that they are located in a different basin in the amino acid similarity matrix space.

Examination of solidified and stabilized matrices as a result of solidification and stabilization process of arseniccontaining sludge with portland cement and lime

Directory of Open Access Journals (Sweden)

Tanapon Phenrat

2004-02-01

Full Text Available By solidification and stabilization (S/S with Portland cement and lime, it is possible to reduce arsenic concentration in leachate of the arsenic-containing sludge from arsenic removal process by coagulation with ferric chloride. From the initial arsenic concentration in leachate of unsolidified /unstabilized sludge which was around 20.75 mg/L, the arsenic concentrations in leachate of solidified/stabilized waste were reduced to 0.3, 0.58, 1.09, and 1.85 mg/L for the waste-to-binder ratios of 0.15, 0.25, 0.5, and 1, respectively, due tothe formation of insoluble calcium-arsenic compounds. To be more cost effective for the future, alternative uses of these S/S products were also assessed by measurement of compressive strength of the mortar specimens. It was found that the compressive strengths of these matrices were from 28 ksc to 461 ksc. In conclusion, considering compressive strength and leachability of the solidified matrices, some of these solidified/ stabilized products have potential to serve as an interlocking concrete paving block.

The optimal version of Hua's fundamental theorem of geometry of rectangular matrices

CERN Document Server

Semrl, Peter

2014-01-01

Hua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m\\times n matrices over a division ring \\mathbb{D} which preserve adjacency in both directions. Motivated by several applications the author studies a long standing open problem of possible improvements. There are three natural questions. Can we replace the assumption of preserving adjacency in both directions by the weaker assumption of preserving adjacency in one direction only and still get the same conclusion? Can we relax the bijectivity assumption? Can we obtain an analogous result for maps acting between the spaces of rectangular matrices of different sizes? A division ring is said to be EAS if it is not isomorphic to any proper subring. For matrices over EAS division rings the author solves all three problems simultaneously, thus obtaining the optimal version of Hua's theorem. In the case of general division rings he gets such an optimal result only for square matrices and gives examples ...

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

Science.gov (United States)

2011-01-01

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

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

Directory of Open Access Journals (Sweden)

Lapointe François-Joseph

2011-03-01

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

Exploring Mixed Membership Stochastic Block Models via Non-negative Matrix Factorization

KAUST Repository

Peng, Chengbin

2014-12-01

Many real-world phenomena can be modeled by networks in which entities and connections are represented by nodes and edges respectively. When certain nodes are highly connected with each other, those nodes forms a cluster, which is called community in our context. It is usually assumed that each node belongs to one community only, but evidences in biology and social networks reveal that the communities often overlap with each other. In other words, one node can probably belong to multiple communities. In light of that, mixed membership stochastic block models (MMB) have been developed to model those networks with overlapping communities. Such a model contains three matrices: two incidence matrices indicating in and out connections and one probability matrix. When the probability of connections for nodes between communities are significantly small, the parameter inference problem to this model can be solved by a constrained non-negative matrix factorization (NMF) algorithm. In this paper, we explore the connection between the two models and propose an algorithm based on NMF to infer the parameters of MMB. The proposed algorithms can detect overlapping communities regardless of knowing or not the number of communities. Experiments show that our algorithm can achieve a better community detection performance than the traditional NMF algorithm. © 2014 IEEE.

On families of anticommuting matrices

Czech Academy of Sciences Publication Activity Database

Hrubeš, Pavel

2016-01-01

Roč. 493, March 15 (2016), s. 494-507 ISSN 0024-3795 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : anticommuting matrices * sum-of-squares formulas Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016 http://www.sciencedirect.com/science/article/pii/S0024379515007296

On families of anticommuting matrices

Czech Academy of Sciences Publication Activity Database

Hrubeš, Pavel

2016-01-01

Roč. 493, March 15 (2016), s. 494-507 ISSN 0024-3795 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : anticommuting matrices * sum -of-squares formulas Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016 http://www.sciencedirect.com/science/article/pii/S0024379515007296

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

Science.gov (United States)

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

2016-11-25

We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This allows us to prove general results on the monogamy of entanglement and steering quantifiers in continuous variable systems with an arbitrary number of modes per party. A powerful hierarchical relation for correlation measures based on the log-determinant of covariance matrices is further established for all Gaussian states, which has no counterpart among quantities based on the conventional von Neumann entropy.

Application of Parallel Hierarchical Matrices in Spatial Statistics and Parameter Identification

KAUST Repository

Litvinenko, Alexander

2018-04-20

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

A Conceptual Cost Benefit Analysis of Tailings Matrices Use in Construction Applications

OpenAIRE

Mahmood Ali A.; Elektorowicz Maria

2016-01-01

As part of a comprehensive research program, new tailings matrices are formulated of combinations of tailings and binder materials. The research program encompasses experimental and numerical analysis of the tailings matrices to investigate the feasibility of using them as construction materials in cold climates. This paper discusses a conceptual cost benefit analysis for the use of these new materials. It is shown here that the financial benefits of using the proposed new tailings matrices i...

Invertibility and Explicit Inverses of Circulant-Type Matrices with k-Fibonacci and k-Lucas Numbers

Directory of Open Access Journals (Sweden)

Zhaolin Jiang

2014-01-01

Full Text Available Circulant matrices have important applications in solving ordinary differential equations. In this paper, we consider circulant-type matrices with the k-Fibonacci and k-Lucas numbers. We discuss the invertibility of these circulant matrices and present the explicit determinant and inverse matrix by constructing the transformation matrices, which generalizes the results in Shen et al. (2011.

Asymptotic Distribution of Eigenvalues of Weakly Dilute Wishart Matrices

Energy Technology Data Exchange (ETDEWEB)

Khorunzhy, A. [Institute for Low Temperature Physics (Ukraine)], E-mail: khorunjy@ilt.kharkov.ua; Rodgers, G. J. [Brunel University, Uxbridge, Department of Mathematics and Statistics (United Kingdom)], E-mail: g.j.rodgers@brunel.ac.uk

2000-03-15

We study the eigenvalue distribution of large random matrices that are randomly diluted. We consider two random matrix ensembles that in the pure (nondilute) case have a limiting eigenvalue distribution with a singular component at the origin. These include the Wishart random matrix ensemble and Gaussian random matrices with correlated entries. Our results show that the singularity in the eigenvalue distribution is rather unstable under dilution and that even weak dilution destroys it.

Teaching Fourier optics through ray matrices

International Nuclear Information System (INIS)

Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F

2005-01-01

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics

Fabrication of chemically cross-linked porous gelatin matrices.

Science.gov (United States)

Bozzini, Sabrina; Petrini, Paola; Altomare, Lina; Tanzi, Maria Cristina

2009-01-01

The aim of this study was to chemically cross-link gelatin, by reacting its free amino groups with an aliphatic diisocyanate. To produce hydrogels with controllable properties, the number of reacting amino groups was carefully determined. Porosity was introduced into the gelatin-based hydrogels through the lyophilization process. Porous and non-porous matrices were characterized with respect to their chemical structure, morphology, water uptake and mechanical properties. The physical, chemical and mechanical properties of the porous matrices are related to the extent of their cross-linking, showing that they can be controlled by varying the reaction parameters. Water uptake values (24 hours) vary between 160% and 200% as the degree of cross-linking increases. The flexibility of the samples also decreases by changing the extent of cross-linking. Young's modulus shows values between 0.188 KPa, for the highest degree, and 0.142 KPa for the lowest degree. The matrices are potential candidates for use as tissue-engineering scaffolds by modulating their physical chemical properties according to the specific application.

Large-deviation theory for diluted Wishart random matrices

Science.gov (United States)

Castillo, Isaac Pérez; Metz, Fernando L.

2018-03-01

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

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

International Nuclear Information System (INIS)

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

2015-01-01

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

Multiple Regression Analysis of Unconfined Compression Strength of Mine Tailings Matrices

Directory of Open Access Journals (Sweden)

Mahmood Ali A.

2017-01-01

Full Text Available As part of a novel approach of sustainable development of mine tailings, experimental and numerical analysis is carried out on newly formulated tailings matrices. Several physical characteristic tests are carried out including the unconfined compression strength test to ascertain the integrity of these matrices when subjected to loading. The current paper attempts a multiple regression analysis of the unconfined compressive strength test results of these matrices to investigate the most pertinent factors affecting their strength. Results of this analysis showed that the suggested equation is reasonably applicable to the range of binder combinations used.

Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices

Directory of Open Access Journals (Sweden)

Juan Yang

2013-01-01

Full Text Available The Toeplitz Procrustes problems are the least squares problems for the matrix equation AX=B over some Toeplitz matrix sets. In this paper the necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions of the Toeplitz Procrustes problems when the unknown matrices are constrained to the general, the triangular, and the symmetric Toeplitz matrices, respectively. The algorithms are designed and the numerical examples show that these algorithms are feasible.

A Workshop on Algebraic Design Theory and Hadamard Matrices

CERN Document Server

2015-01-01

This volume develops the depth and breadth of the mathematics underlying the construction and analysis of Hadamard matrices and their use in the construction of combinatorial designs. At the same time, it pursues current research in their numerous applications in security and cryptography, quantum information, and communications. Bridges among diverse mathematical threads and extensive applications make this an invaluable source for understanding both the current state of the art and future directions. The existence of Hadamard matrices remains one of the most challenging open questions in combinatorics. Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, and combinatorics. Hadamard matrices arise in a very diverse set of applications. Starting with applications in experimental design theory and the theory of error-correcting codes, they have found unexpected and important ap...

A Technique for Controlling Matric Suction on Filter Papers . GroWth ...

African Journals Online (AJOL)

'Abstract. Moist filter papers are widely usedfor seed gennination tests but their water confent and matric suction are not usually controlled. A technique for controlling filter paper matric suction is described and usedfor germination studies involving fresh and aged sorghum seed (Sorghummcolor (L) Moench). Filter papers ...

ON MATRICES ARISING IN RETARDED DELAY DIFFERENTIAL SYSTEMS

Directory of Open Access Journals (Sweden)

S DJEZZAR

2002-12-01

Full Text Available Dans cet article, on considère une classe de système différentiels retardés et à laquelle on associe une matrice système sur R[s,z], l'anneau des polynômes à deux indéterminés s et z. Ensuite, en utilisant la notion de la matrice forme de Smith sur R[s,z], on étend un résultat de caractérisation obtenu précédemment [5] sur les formes canoniques, à un cas plus général.

On the Wigner law in dilute random matrices

Science.gov (United States)

Khorunzhy, A.; Rodgers, G. J.

1998-12-01

We consider ensembles of N × N symmetric matrices whose entries are weakly dependent random variables. We show that random dilution can change the limiting eigenvalue distribution of such matrices. We prove that under general and natural conditions the normalised eigenvalue counting function coincides with the semicircle (Wigner) distribution in the limit N → ∞. This can be explained by the observation that dilution (or more generally, random modulation) eliminates the weak dependence (or correlations) between random matrix entries. It also supports our earlier conjecture that the Wigner distribution is stable to random dilution and modulation.

Lectures on matrices

CERN Document Server

M Wedderburn, J H

1934-01-01

It is the organization and presentation of the material, however, which make the peculiar appeal of the book. This is no mere compendium of results-the subject has been completely reworked and the proofs recast with the skill and elegance which come only from years of devotion. -Bulletin of the American Mathematical Society The very clear and simple presentation gives the reader easy access to the more difficult parts of the theory. -Jahrbuch über die Fortschritte der Mathematik In 1937, the theory of matrices was seventy-five years old. However, many results had only recently evolved from sp

Theoretical origin of quark mass matrices

International Nuclear Information System (INIS)

Mohapatra, R.N.

1987-01-01

This paper presents the theoretical origin of specific quark mass matrices in the grand unified theories. The author discusses the first natural derivation of the Stech-type mass matrix in unified gauge theories. A solution to the strong CP-problem is provided

Regenerated cellulose micro-nano fiber matrices for transdermal drug release

International Nuclear Information System (INIS)

Liu, Yue; Nguyen, Andrew; Allen, Alicia; Zoldan, Janet; Huang, Yuxiang; Chen, Jonathan Y.

2017-01-01

In this work, biobased fibrous membranes with micro- and nano-fibers are fabricated for use as drug delivery carries because of their biocompatibility, eco-friendly approach, and potential for scale-up. The cellulose micro-/nano-fiber (CMF) matrices were prepared by electrospinning of pulp in an ionic liquid, 1-butyl-3-methylimidazolium chloride. A model drug, ibuprofen (IBU), was loaded on the CMF matrices by a simple immersing method. The amount of IBU loading was about 6% based on the weight of cellulose membrane. The IBU-loaded CMF matrices were characterized by Fourier-transform infrared spectroscopy, thermal gravimetric analysis, and scanning electron microscopy. The test of ibuprofen release was carried out in an acetate buffer solution of pH 5.5 and examined by UV–Vis spectroscopy. Release profiles from the CMF matrices indicated that the drug release rate could be determined by a Fickian diffusion mechanism. - Highlights: • Cellulose micro-nano fiber matrix was prepared by dry-wet electrospinning. • Ibuprofen was loaded on the matrix by a simple immersing method. • The drug loaded matrix showed a biphasic release profile. • The drug release was determined by a Fickian diffusion mechanism.

Regenerated cellulose micro-nano fiber matrices for transdermal drug release

Energy Technology Data Exchange (ETDEWEB)

Liu, Yue [School of Human Ecology, The University of Texas at Austin, Austin, TX (United States); Department of Chemistry, School of Science, Tianjin University, Tianjin (China); Nguyen, Andrew; Allen, Alicia; Zoldan, Janet [Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX (United States); Huang, Yuxiang [School of Human Ecology, The University of Texas at Austin, Austin, TX (United States); Chen, Jonathan Y., E-mail: jychen2@austin.utexas.edu [School of Human Ecology, The University of Texas at Austin, Austin, TX (United States)

2017-05-01

In this work, biobased fibrous membranes with micro- and nano-fibers are fabricated for use as drug delivery carries because of their biocompatibility, eco-friendly approach, and potential for scale-up. The cellulose micro-/nano-fiber (CMF) matrices were prepared by electrospinning of pulp in an ionic liquid, 1-butyl-3-methylimidazolium chloride. A model drug, ibuprofen (IBU), was loaded on the CMF matrices by a simple immersing method. The amount of IBU loading was about 6% based on the weight of cellulose membrane. The IBU-loaded CMF matrices were characterized by Fourier-transform infrared spectroscopy, thermal gravimetric analysis, and scanning electron microscopy. The test of ibuprofen release was carried out in an acetate buffer solution of pH 5.5 and examined by UV–Vis spectroscopy. Release profiles from the CMF matrices indicated that the drug release rate could be determined by a Fickian diffusion mechanism. - Highlights: • Cellulose micro-nano fiber matrix was prepared by dry-wet electrospinning. • Ibuprofen was loaded on the matrix by a simple immersing method. • The drug loaded matrix showed a biphasic release profile. • The drug release was determined by a Fickian diffusion mechanism.

A Technique for Controlling Matric Suction on Filter Papers Used in ...

African Journals Online (AJOL)

Moist filter papers are widely usedfor seed gennination tests but their water confent and matric suction are not usually controlled. A technique for controlling filter paper matric suction is described and usedfor germination studies involving fresh and aged sorghum seed (Sorghummcolor (L) Moench). Filter papers wetted to ...

Evolutionary Games with Randomly Changing Payoff Matrices

Science.gov (United States)

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

2015-06-01

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

Open vessel microwave digestion of food matrices (T6)

International Nuclear Information System (INIS)

Rhodes, L.; LeBlanc, G.

2002-01-01

Full text: Advancements in the field of open vessel microwave digestion continue to provide solutions for industries requiring acid digestion of large sample sizes. Those interesting in digesting food matrices are particularly interested in working with large amounts of sample and then diluting small final volumes. This paper will show the advantages of instantaneous regent addition and post-digestion evaporation when performing an open vessel digestion and evaporation methods for various food matrices will be presented along with analyte recovery data. (author)

Square matrices of order 2 theory, applications, and problems

CERN Document Server

Pop, Vasile

2017-01-01

This unique and innovative book presents an exciting and complete detail of all the important topics related to the theory of square matrices of order 2. The readers exploring every detailed aspect of matrix theory are gently led toward understanding advanced topics. They will follow every notion of matrix theory with ease, accumulating a thorough understanding of algebraic and geometric aspects of matrices of order 2. The prime jewel of this book is its offering of an unusual collection of problems, theoretically motivated, most of which are new, original, and seeing the light of publication for the first time in the literature. Nearly all of the exercises are presented with detailed solutions and vary in difficulty from easy to more advanced. Many problems are particularly challenging. These, and not only these, invite the reader to unleash their creativity and research capabilities and to discover their own methods of attacking a problem. Matrices have a vast practical importance to mathematics, science, a...

Preparation and characterization of porous crosslinked collagenous matrices containing bioavailable chondroitin sulphate

NARCIS (Netherlands)

Pieper, J.S.; Oosterhof, A.; Dijkstra, Pieter J.; Veerkamp, J.H.; van Kuppevelt, T.H.

1999-01-01

Porous collagen matrices with defined physical, chemical and biological characteristics are interesting materials for tissue engineering. Attachment of glycosaminoglycans (GAGs) may add to these characteristics and valorize collagen. In this study, porous type I collagen matrices were crosslinked

Efficiency of fly ash belite cement and zeolite matrices for immobilizing cesium

International Nuclear Information System (INIS)

Goni, S.; Guerrero, A.; Lorenzo, M.P.

2006-01-01

The efficiency of innovative matrices for immobilizing cesium is presented in this work. The matrix formulation included the use of fly ash belite cement (FABC-2-W) and gismondine-type Na-P1 zeolite, both of which are synthesized from fly ash of coal combustion. The efficiency for immobilizing cesium is evaluated from the leaching test ANSI/ANS 16.1-1986 at the temperature of 40 deg. C, from which the apparent diffusion coefficient of cesium is obtained. Matrices with 100% of FABC-2-W are used as a reference. The integrity of matrices is evaluated by porosity and pore-size distribution from mercury intrusion porosimetry, X-ray diffraction and nitrogen adsorption analyses. Both matrices can be classified as good solidify systems for cesium, specially the FABC-2-W/zeolite matrix in which the replacement of 50% of belite cement by the gismondine-type Na-P1 zeolite caused a decrease of two orders of magnitude of cesium mean Effective Diffusion Coefficient (D e ) (2.8e-09 cm 2 /s versus 2.2e-07 cm 2 /s, for FABC-2-W/zeolite and FABC-2-W matrices, respectively)

Tumor cell invasion of collagen matrices requires coordinate lipid agonist-induced G-protein and membrane-type matrix metalloproteinase-1-dependent signaling

Directory of Open Access Journals (Sweden)

Anthis Nicholas J

2006-12-01

Full Text Available Abstract Background Lysophosphatidic acid (LPA and sphingosine 1-phosphate (S1P are bioactive lipid signaling molecules implicated in tumor dissemination. Membrane-type matrix metalloproteinase 1 (MT1-MMP is a membrane-tethered collagenase thought to be involved in tumor invasion via extracellular matrix degradation. In this study, we investigated the molecular requirements for LPA- and S1P-regulated tumor cell migration in two dimensions (2D and invasion of three-dimensional (3D collagen matrices and, in particular, evaluated the role of MT1-MMP in this process. Results LPA stimulated while S1P inhibited migration of most tumor lines in Boyden chamber assays. Conversely, HT1080 fibrosarcoma cells migrated in response to both lipids. HT1080 cells also markedly invaded 3D collagen matrices (~700 μm over 48 hours in response to either lipid. siRNA targeting of LPA1 and Rac1, or S1P1, Rac1, and Cdc42 specifically inhibited LPA- or S1P-induced HT1080 invasion, respectively. Analysis of LPA-induced HT1080 motility on 2D substrates vs. 3D matrices revealed that synthetic MMP inhibitors markedly reduced the distance (~125 μm vs. ~45 μm and velocity of invasion (~0.09 μm/min vs. ~0.03 μm/min only when cells navigated 3D matrices signifying a role for MMPs exclusively in invasion. Additionally, tissue inhibitors of metalloproteinases (TIMPs-2, -3, and -4, but not TIMP-1, blocked lipid agonist-induced invasion indicating a role for membrane-type (MT-MMPs. Furthermore, MT1-MMP expression in several tumor lines directly correlated with LPA-induced invasion. HEK293s, which neither express MT1-MMP nor invade in the presence of LPA, were transfected with MT1-MMP cDNA, and subsequently invaded in response to LPA. When HT1080 cells were seeded on top of or within collagen matrices, siRNA targeting of MT1-MMP, but not other MMPs, inhibited lipid agonist-induced invasion establishing a requisite role for MT1-MMP in this process. Conclusion LPA is a

Evaluation of the technical feasibility of new conditioning matrices for long-lived radionuclides

International Nuclear Information System (INIS)

Deschanels, X.

2004-01-01

Several matrices have been selected for the conditioning of long-lived radioactive wastes: a compound made of a iodo-apatite core coated with a densified matrice of vanadium-phosphorus-lead apatite for iodine; the hollandite ceramic for cesium; the britholite, zirconolite, thorium phosphate diphosphate, and the monazite-brabantite solid solution for minor actinides; and a Nb-based metal alloy and phosphate or titanate-type ceramics for technetium. This report presents the results of the researches carried out between 2002-2004 during the technical feasibility step. The main points described are: - the behaviour of matrices under irradiation. These studies were performed thanks to an approach combining the characterization of natural analogues, the doping of matrices with short-lived radionuclides and the use of external irradiations; - the behaviour of these matrices with respect to water alteration; - the sensibility of these structures with respect to the incorporation of chemical impurities; - a package-process approach including the optimization of the process and preliminary studies about the package concept retained. These studies show that important work remains to be done to develop conditioning matrices suitable for iodine and technetium, while for cesium and minor actinides, the first steps of the technical feasibility are made. However, it remains impossible today to determine the structure having the best global behaviour. (J.S.)

Matrices and society matrix algebra and its applications in the social sciences

CERN Document Server

Bradley, Ian

2014-01-01

Matrices offer some of the most powerful techniques in modem mathematics. In the social sciences they provide fresh insights into an astonishing variety of topics. Dominance matrices can show how power struggles in offices or committees develop; Markov chains predict how fast news or gossip will spread in a village; permutation matrices illuminate kinship structures in tribal societies. All these invaluable techniques and many more are explained clearly and simply in this wide-ranging book. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to

Theory of quark mixing matrix and invariant functions of mass matrices

International Nuclear Information System (INIS)

Jarlskog, C.

1987-10-01

The outline of this talk is as follows: The origin of the quark mixing matrix. Super elementary theory of flavour projection operators. Equivalences and invariances. The commutator formalism and CP violation. CP conditions for any number of families. The 'angle' between the quark mass matrices. Application to Fritzsch and Stech matrices. References. (author)

Geometry and arithmetic of factorized S-matrices

International Nuclear Information System (INIS)

Freund, P.G.O.

1995-01-01

In realistic four-dimensional quantum field theories integrability is elusive. Relativity, when combined with quantum theory does not permit an infinity of local conservation laws except for free fields, for which the S-matrix is trivial S = 1. In two space-time dimensions, where forward and backward scattering are the only possibilities, nontrivial S-matrices are possible even in integrable theories. Such S-matrices are known to factorize [1]. This means that there is no particle production, so that the 4-point amplitudes determine all higher n-point amplitudes. In our recent work [2, 3, 4, 5, 6] we found that in such integrable two-dimensional theories, even the input 4-point amplitudes are determined by a simple principle. Roughly speaking these amplitudes describe the S-wave scattering which one associates with free motion on certain quantum-symmetric spaces. The trivial S-matrix of free field theory describes the absence of scattering which one associates with free motion on a euclidean space, itself a symmetric space. As is well known [7, 8, 9], for curved symmetric spaces the S-matrices for S-wave scattering are no longer trivial, but rather they are determined by the Harish-Chandra c-functions of these spaces [10]. The quantum deformation of this situation is what appears when one considers excitation scattering in two-dimensional integrable models. (orig.)

Random Matrices for Information Processing – A Democratic Vision

DEFF Research Database (Denmark)

Cakmak, Burak

The thesis studies three important applications of random matrices to information processing. Our main contribution is that we consider probabilistic systems involving more general random matrix ensembles than the classical ensembles with iid entries, i.e. models that account for statistical...... dependence between the entries. Specifically, the involved matrices are invariant or fulfill a certain asymptotic freeness condition as their dimensions grow to infinity. Informally speaking, all latent variables contribute to the system model in a democratic fashion – there are no preferred latent variables...

Analysis of Block OMP using Block RIP

OpenAIRE

Wang, Jun; Li, Gang; Zhang, Hao; Wang, Xiqin

2011-01-01

Orthogonal matching pursuit (OMP) is a canonical greedy algorithm for sparse signal reconstruction. When the signal of interest is block sparse, i.e., it has nonzero coefficients occurring in clusters, the block version of OMP algorithm (i.e., Block OMP) outperforms the conventional OMP. In this paper, we demonstrate that a new notion of block restricted isometry property (Block RIP), which is less stringent than standard restricted isometry property (RIP), can be used for a very straightforw...

Studies of Catalytic Properties of Inorganic Rock Matrices in Redox Reactions

Directory of Open Access Journals (Sweden)

Nikolay M. Dobrynkin

2017-09-01

Full Text Available Intrinsic catalytic properties of mineral matrices of various kinds (basalts, clays, sandstones were studied, which are of interest for in-situ heavy oil upgrading (i.e., underground to create advanced technologies for enhanced oil recovery. The elemental, surface and phase composition and matrix particle morphology, surface and acidic properties were studied using elemental analysis, X-ray diffraction, adsorption and desorption of nitrogen and ammonia. The data on the catalytic activity of inorganic matrices in ammonium nitrate decomposition (reaction with a large gassing, oxidation of hydrocarbons and carbon monoxide, and hydrocracking of asphaltenes into maltenes (the conversion of heavy hydrocarbons into more valuable light hydrocarbons were discussed. In order to check their applicability for the asphaltenes hydrocracking catalytic systems development, basalt and clay matrices were used as supports for iron/basalt, nickel/basalt and iron/clay catalysts. The catalytic activity of the matrices in the reactions of the decomposition of ammonium nitrate, oxidation of hydrocarbons and carbon monoxide, and hydrocracking of asphaltens was observed for the first time.

Synthesis and controlled self-assembly of UV-responsive gold nanoparticles in block copolymer templates.

Science.gov (United States)

Song, Dong-Po; Wang, Xinyu; Lin, Ying; Watkins, James J

2014-11-06

We demonstrate the facile synthesis of gold nanoparticles (GNPs) functionalized by UV-responsive block copolymer ligands, poly(styrene)-b-poly(o-nitrobenzene acrylate)-SH (PS-b-PNBA-SH), followed by their targeted distribution within a lamellae-forming poly(styrene)-b-poly(2-vinylpyridine) (PS-b-P2VP) block copolymer. The multilayer, micelle-like structure of the GNPs consists of a gold core, an inner PNBA layer, and an outer PS layer. The UV-sensitive PNBA segment can be deprotected into a layer containing poly(acrylic acid) (PAA) when exposed to UV light at 365 nm, which enables the simple and precise tuning of GNP surface properties from hydrophobic to amphiphilic. The GNPs bearing ligands of different chemical compositions were successfully and selectively incorporated into the PS-b-P2VP block copolymer, and UV light showed a profound influence on the spatial distributions of GNPs. Prior to UV exposure, GNPs partition along the interfaces of PS and P2VP domains, while the UV-treated GNPs are incorporated into P2VP domains as a result of hydrogen bond interactions between PAA on the gold surface and P2VP domains. This provides an easy way of controlling the arrangement of nanoparticles in polymer matrices by tailoring the nanoparticle surface using UV light.

SUPERCRITICAL FLUID TREATMENT OF THREE-DIMENSIONAL HYDROGEL MATRICES, COMPOSED OF CHITOSAN DERIVATIVES

Directory of Open Access Journals (Sweden)

P. S. Timashev

2016-01-01

Full Text Available Aim. Controlled treatment of the physico-chemical and mechanical properties of a three-dimensional crosslinked matrix based on reactive chitosan. Materials and methods. The three-dimensional matrices were obtained using photosensitive composition based on allyl chitosan (5 wt%, poly(ethylene glycol diacrylate (8 wt% and the photoinitiator Irgacure 2959 (1 wt% by laser stereolithography setting. The kinetic swelling curves were constructed for structures in the base and salt forms of chitosan using gravimetric method and the contact angles were measured using droplet spreading. The supercritical fl uid setting (40 °C, 12 MPa was used to process matrices during 1.5 hours. Using nanohardness Piuma Nanoindenter we calculated values of Young’s modulus. The study of cytotoxicity was performed by direct contact with the culture of the NIH 3T3 mouse fi broblast cell line. Results. Architectonics of matrices fully repeats the program model. Matrices are uniform throughout and retain their shape after being transferred to the base form. Matrices compressed by 5% after treatment in supercritical carbon dioxide (scCO2 . The elastic modulus of matrices after scCO2 treatment is 4 times higher than the original matrix. The kinetic swelling curves have similar form. In this case the maximum degree of swelling for matrices in base form is 2–2.5 times greater than that of matrices in salt form. There was a surface hydrophobization after the material was transferred to the base form: the contact angle is 94°, and for the salt form it is 66°. The basic form absorbs liquid approximately 1.6 times faster. The fi lm thickness was increased in the area of contact with the liquid droplets after absorption by 133 and 87% for the base and the salt forms, respectively. Treatment of samples in scCO2 reduces their cytotoxicity from 2 degree of reaction (initial samples down to 1 degree of reaction. Conclusion. The use of supercritical carbon dioxide for scaffolds

31 CFR 595.301 - Blocked account; blocked property.

Science.gov (United States)

2010-07-01

... (Continued) OFFICE OF FOREIGN ASSETS CONTROL, DEPARTMENT OF THE TREASURY TERRORISM SANCTIONS REGULATIONS General Definitions § 595.301 Blocked account; blocked property. The terms blocked account and blocked...

The reflection of hierarchical cluster analysis of co-occurrence matrices in SPSS

NARCIS (Netherlands)

Zhou, Q.; Leng, F.; Leydesdorff, L.

2015-01-01

Purpose: To discuss the problems arising from hierarchical cluster analysis of co-occurrence matrices in SPSS, and the corresponding solutions. Design/methodology/approach: We design different methods of using the SPSS hierarchical clustering module for co-occurrence matrices in order to compare

Study on vulnerability matrices of masonry buildings of mainland China

Science.gov (United States)

Sun, Baitao; Zhang, Guixin

2018-04-01

The degree and distribution of damage to buildings subjected to earthquakes is a concern of the Chinese Government and the public. Seismic damage data indicates that seismic capacities of different types of building structures in various regions throughout mainland China are different. Furthermore, the seismic capacities of the same type of structure in different regions may vary. The contributions of this research are summarized as follows: 1) Vulnerability matrices and earthquake damage matrices of masonry structures in mainland China were chosen as research samples. The aim was to analyze the differences in seismic capacities of sample matrices and to present general rules for categorizing seismic resistance. 2) Curves relating the percentage of damaged masonry structures with different seismic resistances subjected to seismic demand in different regions of seismic intensity (VI to X) have been developed. 3) A method has been proposed to build vulnerability matrices of masonry structures. The damage ratio for masonry structures under high-intensity events such as the Ms 6.1 Panzhihua earthquake in Sichuan province on 30 August 2008, was calculated to verify the applicability of this method. This research offers a significant theoretical basis for predicting seismic damage and direct loss assessment of groups of buildings, as well as for earthquake disaster insurance.

Diagonalization of quark mass matrices and the Cabibbo-Kobayashi-Maskawa matrix

International Nuclear Information System (INIS)

Rasin, A.

1997-08-01

I discuss some general aspect of diagonalizing the quark mass matrices and list all possible parametrizations of the Cabibbo-Kobayashi-Maskawa matrix (CKM) in terms of three rotation angles and a phase. I systematically study the relation between the rotations needed to diagonalize the Yukawa matrices and various parametrizations of the CKM. (author). 17 refs, 1 tab

Concrete minimal 3 × 3 Hermitian matrices and some general cases

Directory of Open Access Journals (Sweden)

Klobouk Abel H.

2017-12-01

Full Text Available Given a Hermitian matrix M ∈ M3(ℂ we describe explicitly the real diagonal matrices DM such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ, where ║ · ║ denotes the operator norm. Moreover, we generalize our techniques to some n × n cases.

Preparation and characterization of chitosan-heparin composite matrices for blood contacting tissue engineering

International Nuclear Information System (INIS)

He Qing; Gong Kai; Gong Yandao; Zhang Xiufang; Ao Qiang; Zhang Lihai; Hu Min

2010-01-01

Chitosan has been widely used for biomaterial scaffolds in tissue engineering because of its good mechanical properties and cytocompatibility. However, the poor blood compatibility of chitosan has greatly limited its biomedical utilization, especially for blood contacting tissue engineering. In this study, we exploited a polymer blending procedure to heparinize the chitosan material under simple and mild conditions to improve its antithrombogenic property. By an optimized procedure, a macroscopically homogeneous chitosan-heparin (Chi-Hep) blended suspension was obtained, with which Chi-Hep composite films and porous scaffolds were fabricated. X-ray photoelectron spectroscopy and sulfur elemental analysis confirmed the successful immobilization of heparin in the composite matrices (i.e. films and porous scaffolds). Toluidine blue staining indicated that heparin was distributed homogeneously in the composite matrices. Only a small amount of heparin was released from the matrices during incubation in normal saline for 10 days. The composite matrices showed improved blood compatibility, as well as good mechanical properties and endothelial cell compatibility. These results suggest that the Chi-Hep composite matrices are promising candidates for blood contacting tissue engineering.

Nerve Blocks

Science.gov (United States)

... News Physician Resources Professions Site Index A-Z Nerve Blocks A nerve block is an injection to ... the limitations of Nerve Block? What is a Nerve Block? A nerve block is an anesthetic and/ ...

Calculation of controllability and observability matrices for special case of continuous-time multi-order fractional systems.

Science.gov (United States)

Hassanzadeh, Iman; Tabatabaei, Mohammad

2017-03-28

In this paper, controllability and observability matrices for pseudo upper or lower triangular multi-order fractional systems are derived. It is demonstrated that these systems are controllable and observable if and only if their controllability and observability matrices are full rank. In other words, the rank of these matrices should be equal to the inner dimension of their corresponding state space realizations. To reduce the computational complexities, these matrices are converted to simplified matrices with smaller dimensions. Numerical examples are provided to show the usefulness of the mentioned matrices for controllability and observability analysis of this case of multi-order fractional systems. These examples clarify that the duality concept is not necessarily true for these special systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Development and adjustment of programs for solving systems of linear equations

International Nuclear Information System (INIS)

Fujimura, Toichiro

1978-03-01

Programs for solving the systems of linear equations have been adjusted and developed in expanding the scientific subroutine library SSL. The principal programs adjusted are based on the congruent method, method of product form of the inverse, orthogonal method, Crout's method for sparse system, and acceleration of iterative methods. The programs developed are based on the escalator method, direct parallel residue method and block tridiagonal method for band system. Described are usage of the programs developed and their future improvement. FORTRAN lists with simple examples in tests of the programs are also given. (auth.)

Quick plasma equilibrium reconstruction based on GPU

International Nuclear Information System (INIS)

Xiao Bingjia; Huang, Y.; Luo, Z.P.; Yuan, Q.P.; Lao, L.

2014-01-01

A parallel code named P-EFIT which could complete an equilibrium reconstruction iteration in 250 μs is described. It is built with the CUDA TM architecture by using Graphical Processing Unit (GPU). It is described for the optimization of middle-scale matrix multiplication on GPU and an algorithm which could solve block tri-diagonal linear system efficiently in parallel. Benchmark test is conducted. Static test proves the accuracy of the P-EFIT and simulation-test proves the feasibility of using P-EFIT for real-time reconstruction on 65x65 computation grids. (author)

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

Science.gov (United States)

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

2016-10-01

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

Stabilization of chromium-bearing electroplating sludge with MSWI fly ash-based Friedel matrices.

Science.gov (United States)

Qian, Guangren; Yang, Xiaoyan; Dong, Shixiang; Zhou, Jizhi; Sun, Ying; Xu, Yunfeng; Liu, Qiang

2009-06-15

This work investigated the feasibility and effectiveness of MSWI fly ash-based Friedel matrices on stabilizing/solidifying industrial chromium-bearing electroplating sludge using MSWI fly ash as the main raw material with a small addition of active aluminum. The compressive strength, leaching behavior and chemical speciation of heavy metals and hydration phases of matrices were characterized by TCLP, XRD, FTIR and other experimental methods. The results revealed that MSWI fly ash-based Friedel matrices could effectively stabilize chromium-bearing electroplating sludge, the formed ettringite and Friedel phases played a significant role in the fixation of heavy metals in electroplating sludge. The co-disposal of chromium-bearing electroplating sludge and MSWI fly ash-based Friedel matrices with a small addition of active aluminum is promising to be an effective way of stabilizing chromium-bearing electroplating sludge.

Testing block subdivision algorithms on block designs

Science.gov (United States)

Wiseman, Natalie; Patterson, Zachary

2016-01-01

Integrated land use-transportation models predict future transportation demand taking into account how households and firms arrange themselves partly as a function of the transportation system. Recent integrated models require parcels as inputs and produce household and employment predictions at the parcel scale. Block subdivision algorithms automatically generate parcel patterns within blocks. Evaluating block subdivision algorithms is done by way of generating parcels and comparing them to those in a parcel database. Three block subdivision algorithms are evaluated on how closely they reproduce parcels of different block types found in a parcel database from Montreal, Canada. While the authors who developed each of the algorithms have evaluated them, they have used their own metrics and block types to evaluate their own algorithms. This makes it difficult to compare their strengths and weaknesses. The contribution of this paper is in resolving this difficulty with the aim of finding a better algorithm suited to subdividing each block type. The proposed hypothesis is that given the different approaches that block subdivision algorithms take, it's likely that different algorithms are better adapted to subdividing different block types. To test this, a standardized block type classification is used that consists of mutually exclusive and comprehensive categories. A statistical method is used for finding a better algorithm and the probability it will perform well for a given block type. Results suggest the oriented bounding box algorithm performs better for warped non-uniform sites, as well as gridiron and fragmented uniform sites. It also produces more similar parcel areas and widths. The Generalized Parcel Divider 1 algorithm performs better for gridiron non-uniform sites. The Straight Skeleton algorithm performs better for loop and lollipop networks as well as fragmented non-uniform and warped uniform sites. It also produces more similar parcel shapes and patterns.

In-situ crosslinkable and self-assembling elastin-like polypeptide block copolymers for cartilage tissue repair

Science.gov (United States)

Lim, Dong Woo

This work describes the development of genetically engineered elastin-like polypeptide (ELP) block copolymers as in-situ gelling scaffolds for cartilage tissue repair. The central hypothesis underlying this work is that ELP based biopolymers can be exploited as injectable biomaterials by rapid chemical crosslinking. To prove this, gene libraries encoding ELP having different molecular weights and amino acid sequences, and ELP block copolymers composed of various ELP blocks having diverse amino acid composition, length, and phase transition behavior were synthesized by recursive directional ligation, expressed in E. Coli and purified by inverse transition cycling. Mannich-type condensation of hydroxymethylphosphines (HMPs) with primary- and secondary-amines of amino acids was developed as a new crosslinking method of polypeptides. Chemically crosslinked ELP hydrogels were formed rapidly in an aqueous solution by reaction of ELPs containing periodic lysine residues with HMPs. The crosslinking density and mechanical property of the ELP hydrogels were controlled at the sequence level by varying the Lys density in ELPs composed of mono-block as well as by segregation of the Lys residues within specific blocks of tri-block architectures. Fibroblasts embedded in ELP hydrogels survived the crosslinking process and were viable after in vitro culture for at least 3 days. The DNA content of fibroblasts within the tri-block gels was significantly higher than that in the mono-block gels at day 3. These results suggest that the HMP crosslinked ELP block copolymer hydrogels show finely tuned mechanical properties and different microenvironments for cell viability as well as potential as in-situ crosslinkable biopolymers for tissue repair applications with load-bearing environments. As an alternative, rheological behavior of the ELP block copolymers and ELP-grafted hyaluronic acids (HAs) as artificial extracellular matrices (ECMs) showed that they were thermally aggregated into

Properties of Zero-Free Transfer Function Matrices

Science.gov (United States)

D. O. Anderson, Brian; Deistler, Manfred

Transfer functions of linear, time-invariant finite-dimensional systems with more outputs than inputs, as arise in factor analysis (for example in econometrics), have, for state-variable descriptions with generic entries in the relevant matrices, no finite zeros. This paper gives a number of characterizations of such systems (and indeed square discrete-time systems with no zeros), using state-variable, impulse response, and matrix-fraction descriptions. Key properties include the ability to recover the input values at any time from a bounded interval of output values, without any knowledge of an initial state, and an ability to verify the no-zero property in terms of a property of the impulse response coefficient matrices. Results are particularized to cases where the transfer function matrix in question may or may not have a zero at infinity or a zero at zero.

Sports drug testing using complementary matrices: Advantages and limitations.

Science.gov (United States)

Thevis, Mario; Geyer, Hans; Tretzel, Laura; Schänzer, Wilhelm

2016-10-25

Today, routine doping controls largely rely on testing whole blood, serum, and urine samples. These matrices allow comprehensively covering inorganic as well as low and high molecular mass organic analytes relevant to doping controls and are collecting and transferring from sampling sites to accredited anti-doping laboratories under standardized conditions. Various aspects including time and cost-effectiveness as well as intrusiveness and invasiveness of the sampling procedure but also analyte stability and breadth of the contained information have been motivation to consider and assess values potentially provided and added to modern sports drug testing programs by alternative matrices. Such alternatives could be dried blood spots (DBS), dried plasma spots (DPS), oral fluid (OF), exhaled breath (EB), and hair. In this review, recent developments and test methods concerning these alternative matrices and expected or proven contributions as well as limitations of these specimens in the context of the international anti-doping fight are presented and discussed, guided by current regulations for prohibited substances and methods of doping as established by the World Anti-Doping Agency (WADA). Focusing on literature published between 2011 and 2015, examples for doping control analytical assays concerning non-approved substances, anabolic agents, peptide hormones/growth factors/related substances and mimetics, β 2 -agonists, hormone and metabolic modulators, diuretics and masking agents, stimulants, narcotics, cannabinoids, glucocorticoids, and beta-blockers were selected to outline the advantages and limitations of the aforementioned alternative matrices as compared to conventional doping control samples (i.e. urine and blood/serum). Copyright © 2016 Elsevier B.V. All rights reserved.

The underexposed role of food matrices in probiotic products: reviewing the relationship between carrier matrices and product parameters

NARCIS (Netherlands)

Flach, J.; van der Waal, M.B.; van den Nieuwboer, M.; Claassen, H.J.H.M.; Larsen, O.F.A.

2017-01-01

 Full Article  Figures & data References  Supplemental  Citations Metrics  Reprints & Permissions  PDF ABSTRACT Probiotic microorganisms are increasingly incorporated into food matrices in order to confer proposed health benefits on the consumer. It is important that the health benefits,

Matrices and linear algebra

CERN Document Server

Schneider, Hans

1989-01-01

Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t

Inversion of General Cyclic Heptadiagonal Matrices

Directory of Open Access Journals (Sweden)

A. A. Karawia

2013-01-01

Full Text Available We describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The computational cost of it is operations. The algorithm is implementable to the Computer Algebra System (CAS such as MAPLE, MATLAB, and MATHEMATICA. Two examples are presented for the sake of illustration.

Critical statistics for non-Hermitian matrices

International Nuclear Information System (INIS)

Garcia-Garcia, A.M.; Verbaarschot, J.J.M.; Nishigaki, S.M.

2002-01-01

We introduce a generalized ensemble of non-Hermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble, and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an extension of the Itzykson-Zuber formula to general complex matrices. Its correlation functions are studied both in the case of weak non-Hermiticity and in the case of strong non-Hermiticity. In the weak non-Hermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics: the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing. To lowest order, its slope does not depend on the degree of non-Hermiticity. Close the edge, the spectral correlations are similar to the Hermitian case. In the strong non-Hermiticity limit the crossover behavior from the Ginibre ensemble to the Poisson ensemble first appears close to the surface of the spectrum. Our model may be relevant for the description of the spectral correlations of an open disordered system close to an Anderson transition

Quantification of iodine in porous hydroxyapatite matrices for application as radioactive sources in brachytherapy

OpenAIRE

Lacerda, Kássio André; Lameiras, Fernando Soares; Silva, Viviane Viana

2007-01-01

In this study, non-radioactive iodine was incorporated in two types of biodegradable hydroxyapatite-based porous matrices (HA and HACL) through impregnation process from sodium iodine aqueous solutions with varying concentrations (0.5 and 1.0 mol/L) . The results revealed that both systems presented a high capacity of incorporating iodine into their matrices. The quantity of incorporated iodine was measured through Neutron Activation Analysis (NAA). The porous ceramic matrices based on hydrox...

Classification of mass matrices and the calculability of the Cabibbo angle

International Nuclear Information System (INIS)

Rizzo, T.G.

1981-01-01

We have analyzed all possible 2 x 2 mass matrices with two nonzero elements in an attempt to find which matrices yield a reasonable value of the Cabibbo angle upon diagonalization. We do not concern ourselves with the origin of these mass matrices (spontaneous symmetry breaking, bare-mass term, etc.). We find that, in the limit m/sub u//m/sub c/→0, only four possible relationships exist between sin 2 theta/sub C/ and the quark mass ratio m/sub d//m/sub s/, only one of which is reasonable for the usual value of m/sub d//m/sub s/ (approx.1/20). This limits the possible forms of the quark mass matrix to be two in number, both of which have been discussed previously in the literature

Characterization and performance of monolithic detector blocks with a dedicated ASIC front-end readout for PET imaging of the human brain

International Nuclear Information System (INIS)

Rato Mendes, Pedro; Sarasola Martin, Iciar; Canadas, Mario; Garcia de Acilu, Paz; Cuypers, Robin; Perez, Jose Manuel; Willmott, Carlos

2011-01-01

We are developing a human brain PET scanner prototype compatible with MRI based on monolithic scintillator crystals, APD matrices and a dedicated ASIC front-end readout. In this work we report on the performance of individual detector modules and on the operation of such modules in PET coincidence. Results will be presented on the individual characterization of detector blocks and its ASIC front-end readout, with measured energy resolutions of 13% full-width half-maximum (FWHM) at 511 keV and spatial resolutions of the order of 2 mm FWHM. First results on PET coincidence performance indicate spatial resolutions as good as 2.1 mm FWHM for SSRB/FBP reconstruction of tomographic data obtained using a simple PET demonstrator based on a pair of monolithic detector blocks with ASIC readout.

Preconditioners for regularized saddle point matrices

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe

2011-01-01

Roč. 19, č. 2 (2011), s. 91-112 ISSN 1570-2820 Institutional research plan: CEZ:AV0Z30860518 Keywords : saddle point matrices * preconditioning * regularization * eigenvalue clustering Subject RIV: BA - General Mathematics Impact factor: 0.533, year: 2011 http://www.degruyter.com/view/j/jnma.2011.19.issue-2/jnum.2011.005/jnum.2011.005. xml

Cutaneous Sensory Block Area, Muscle-Relaxing Effect, and Block Duration of the Transversus Abdominis Plane Block

DEFF Research Database (Denmark)

Støving, Kion; Rothe, Christian; Rosenstock, Charlotte V

2015-01-01

BACKGROUND AND OBJECTIVES: The transversus abdominis plane (TAP) block is a widely used nerve block. However, basic block characteristics are poorly described. The purpose of this study was to assess the cutaneous sensory block area, muscle-relaxing effect, and block duration. METHODS: Sixteen...... healthy volunteers were randomized to receive an ultrasound-guided unilateral TAP block with 20 mL 7.5 mg/mL ropivacaine and placebo on the contralateral side. Measurements were performed at baseline and 90 minutes after performing the block. Cutaneous sensory block area was mapped and separated...... into a medial and lateral part by a vertical line through the anterior superior iliac spine. We measured muscle thickness of the 3 lateral abdominal muscle layers with ultrasound in the relaxed state and during maximal voluntary muscle contraction. The volunteers reported the duration of the sensory block...

Secure Multiple-Antenna Block-Fading Wiretap Channels with Limited CSI Feedback

KAUST Repository

Hyadi, Amal

2017-07-18

In this paper, we investigate the ergodic secrecy capacity of a block-fading wiretap channel with limited channel knowledge at the transmitter. We consider that the legitimate receiver, the eavesdropper and the transmitter are equipped with multiple antennas and that the receiving nodes are aware of their respective channel matrices. The transmitter, on the other hand, is only provided by a B-bit feedback of the main channel state information. The feedback bits are sent by the legitimate receiver, at the beginning of each fading block, over an error-free public link with limited capacity. The statistics of the main and the eavesdropper channel state information are known at all nodes. Assuming an average transmit power constraint, we establish upper and lower bounds on the ergodic secrecy capacity. Then, we present a framework to design the optimal codebooks for feedback and transmission. In addition, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback link becomes large, i.e. $B \\ ightarrow \\\\infty$ ; hence, fully characterizing the ergodic secrecy capacity in this case. Besides, we analyze the asymptotic behavior of the presented secrecy rates, at high Signal-to-Noise Ratio (SNR), and evaluate the gap between the bounds.

Secure Multiple-Antenna Block-Fading Wiretap Channels with Limited CSI Feedback

KAUST Repository

Hyadi, Amal; Rezki, Zouheir; Alouini, Mohamed-Slim

2017-01-01

In this paper, we investigate the ergodic secrecy capacity of a block-fading wiretap channel with limited channel knowledge at the transmitter. We consider that the legitimate receiver, the eavesdropper and the transmitter are equipped with multiple antennas and that the receiving nodes are aware of their respective channel matrices. The transmitter, on the other hand, is only provided by a B-bit feedback of the main channel state information. The feedback bits are sent by the legitimate receiver, at the beginning of each fading block, over an error-free public link with limited capacity. The statistics of the main and the eavesdropper channel state information are known at all nodes. Assuming an average transmit power constraint, we establish upper and lower bounds on the ergodic secrecy capacity. Then, we present a framework to design the optimal codebooks for feedback and transmission. In addition, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback link becomes large, i.e. $B \\rightarrow \\infty$ ; hence, fully characterizing the ergodic secrecy capacity in this case. Besides, we analyze the asymptotic behavior of the presented secrecy rates, at high Signal-to-Noise Ratio (SNR), and evaluate the gap between the bounds.

Characteristic Polynomials of Sample Covariance Matrices: The Non-Square Case

OpenAIRE

Kösters, Holger

2009-01-01

We consider the sample covariance matrices of large data matrices which have i.i.d. complex matrix entries and which are non-square in the sense that the difference between the number of rows and the number of columns tends to infinity. We show that the second-order correlation function of the characteristic polynomial of the sample covariance matrix is asymptotically given by the sine kernel in the bulk of the spectrum and by the Airy kernel at the edge of the spectrum. Similar results are g...

A block Hankel generalized confluent Vandermonde matrix

NARCIS (Netherlands)

Klein, A.; Spreij, P.

2014-01-01

Vandermonde matrices are well known. They have a number of interesting properties and play a role in (Lagrange) interpolation problems, partial fraction expansions, and finding solutions to linear ordinary differential equations, to mention just a few applications. Usually, one takes these matrices

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

Some algorithms for the solution of the symmetric eigenvalue problem on a multiprocessor electronic computer

International Nuclear Information System (INIS)

Molchanov, I.N.; Khimich, A.N.

1984-01-01

This article shows how a reflection method can be used to find the eigenvalues of a matrix by transforming the matrix to tridiagonal form. The method of conjugate gradients is used to find the smallest eigenvalue and the corresponding eigenvector of symmetric positive-definite band matrices. Topics considered include the computational scheme of the reflection method, the organization of parallel calculations by the reflection method, the computational scheme of the conjugate gradient method, the organization of parallel calculations by the conjugate gradient method, and the effectiveness of parallel algorithms. It is concluded that it is possible to increase the overall effectiveness of the multiprocessor electronic computers by either letting the newly available processors of a new problem operate in the multiprocessor mode, or by improving the coefficient of uniform partition of the original information

Reliability and Validity of Colored Progressive Matrices for 4-6 Age Children

Directory of Open Access Journals (Sweden)

Ahmet Bildiren

2017-06-01

Full Text Available In this research, it was aimed to test the reliability and validity of Colored Progressive Matrices for children between the ages of 4 to 6 from 15 schools. The sample of the study consisted of 640 kindergarten children. Test-retest and parallel form were used for reliability analyses. For the validity analysis, the relations between the Colored Progressive Matrices Test and Bender Gestalt Visual Motor Sensitivity Test, WISC-R and TONI-3 tests were examined. The results showed that there was a significant relation between the test-retest results and the parallel forms in all the age groups. Validity analyses showed strong correlations between the Colored Progressive Matrices and all the other measures.

Unified triminimal parametrizations of quark and lepton mixing matrices

International Nuclear Information System (INIS)

He Xiaogang; Li Shiwen; Ma Boqiang

2009-01-01

We present a detailed study on triminimal parametrizations of quark and lepton mixing matrices with different basis matrices. We start with a general discussion on the triminimal expansion of the mixing matrix and on possible unified quark and lepton parametrization using quark-lepton complementarity. We then consider several interesting basis matrices and compare the triminimal parametrizations with the Wolfenstein-like parametrizations. The usual Wolfenstein parametrization for quark mixing is a triminimal expansion around the unit matrix as the basis. The corresponding quark-lepton complementarity lepton mixing matrix is a triminimal expansion around the bimaximal basis. Current neutrino oscillation data show that the lepton mixing matrix is very well represented by the tribimaximal mixing. It is natural to take it as an expanding basis. The corresponding zeroth order basis for quark mixing in this case makes the triminimal expansion converge much faster than the usual Wolfenstein parametrization. The triminimal expansion based on tribimaximal mixing can be converted to the Wolfenstein-like parametrizations discussed in the literature. We thus have a unified description between different kinds of parametrizations for quark and lepton sectors: the standard parametrizations, the Wolfenstein-like parametrizations, and the triminimal parametrizations.

Raven's matrices and working memory: a dual-task approach.

Science.gov (United States)

Rao, K Venkata; Baddeley, Alan

2013-01-01

Raven's Matrices Test was developed as a "pure" measure of Spearman's concept of general intelligence, g. Subsequent research has attempted to specify the processes underpinning performance, some relating it to the concept of working memory and proposing a crucial role for the central executive, with the nature of other components currently unclear. Up to this point, virtually all work has been based on correlational analysis of number of correct solutions, sometimes related to possible strategies. We explore the application to this problem of the concurrent task methodology used widely in developing the concept of multicomponent working memory. Participants attempted to solve problems from the matrices under baseline conditions, or accompanied by backward counting or verbal repetition tasks, assumed to disrupt the central executive and phonological loop components of working memory, respectively. As in other uses of this method, number of items correct showed little effect, while solution time measures gave very clear evidence of an important role for the central executive, but no evidence for phonological loop involvement. We conclude that this and related concurrent task techniques hold considerable promise for the analysis of Raven's matrices and potentially for other established psychometric tests.

31 CFR 594.301 - Blocked account; blocked property.

Science.gov (United States)

2010-07-01

... (Continued) OFFICE OF FOREIGN ASSETS CONTROL, DEPARTMENT OF THE TREASURY GLOBAL TERRORISM SANCTIONS REGULATIONS General Definitions § 594.301 Blocked account; blocked property. The terms blocked account and...

Products of random matrices from fixed trace and induced Ginibre ensembles

Science.gov (United States)

Akemann, Gernot; Cikovic, Milan

2018-05-01

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

A basis independent formulation of the connection between quark mass matrices, CP violation and experiment

International Nuclear Information System (INIS)

Jarlskog, C.; Stockholm Univ.; Bergen Univ.

1985-01-01

In the standard electroweak model, with three families, a one-to-one correspondence between certain determinants involving quark mass matrices (m and m' for charge 2/3 and -1/3 quarks respectively) and the presence/absence of CP violation is given. In an arbitrary basis for mass matrices, the quantity Im det[mm + , m'm' + ] appropriately normalized is introduced as a measure of CP violation. By this measure, CP is not maximally violated in any transition in Nature. Finally, constraints on quark mass matrices are derived from experiment. Any model of mass matrices, with the ambition to explain Nature, must satisfy these conditions. (orig.)

Reduction of Under-Determined Linear Systems by Sparce Block Matrix Technique

DEFF Research Database (Denmark)

Tarp-Johansen, Niels Jacob; Poulsen, Peter Noe; Damkilde, Lars

1996-01-01

numerical stability of the aforementioned reduction. Moreover the coefficient matrix for the equilibrium equations is typically very sparse. The objective is to deal efficiently with the full pivoting reduction of sparse rectangular matrices using a dynamic storage scheme based on the block matrix concept.......Under-determined linear equation systems occur in different engineering applications. In structural engineering they typically appear when applying the force method. As an example one could mention limit load analysis based on The Lower Bound Theorem. In this application there is a set of under......-determined equilibrium equation restrictions in an LP-problem. A significant reduction of computer time spent on solving the LP-problem is achieved if the equilib rium equations are reduced before going into the optimization procedure. Experience has shown that for some structures one must apply full pivoting to ensure...

Dense tissue-like collagen matrices formed in cell-free conditions.

Science.gov (United States)

Mosser, Gervaise; Anglo, Anny; Helary, Christophe; Bouligand, Yves; Giraud-Guille, Marie-Madeleine

2006-01-01

A new protocol was developed to produce dense organized collagen matrices hierarchically ordered on a large scale. It consists of a two stage process: (1) the organization of a collagen solution and (2) the stabilization of the organizations by a sol-gel transition that leads to the formation of collagen fibrils. This new protocol relies on the continuous injection of an acid-soluble collagen solution into glass microchambers. It leads to extended concentration gradients of collagen, ranging from 5 to 1000 mg/ml. The self-organization of collagen solutions into a wide array of spatial organizations was investigated. The final matrices obtained by this procedure varied in concentration, structure and density. Changes in the liquid state of the samples were followed by polarized light microscopy, and the final stabilized gel states obtained after fibrillogenesis were analyzed by both light and electron microscopy. Typical organizations extended homogeneously by up to three centimetres in one direction and several hundreds of micrometers in other directions. Fibrillogenesis of collagen solutions of high and low concentrations led to fibrils spatially arranged as has been described in bone and derm, respectively. Moreover, a relationship was revealed between the collagen concentration and the aggregation of and rotational angles between lateral fibrils. These results constitute a strong base from which to further develop highly enriched collagen matrices that could lead to substitutes that mimic connective tissues. The matrices thus obtained may also be good candidates for the study of the three-dimensional migration of cells.

Classical r-matrices for the generalised Chern–Simons formulation of 3d gravity

Science.gov (United States)

Osei, Prince K.; Schroers, Bernd J.

2018-04-01

We study the conditions for classical r-matrices to be compatible with the generalised Chern–Simons action for 3d gravity. Compatibility means solving the classical Yang–Baxter equations with a prescribed symmetric part for each of the real Lie algebras and bilinear pairings arising in the generalised Chern–Simons action. We give a new construction of r-matrices via a generalised complexification and derive a non-linear set of matrix equations determining the most general compatible r-matrix. We exhibit new families of solutions and show that they contain some known r-matrices for special parameter values.

MGI-oriented High-throughput Measurement of Interdiffusion Coefficient Matrices in Ni-based Superalloys

Directory of Open Access Journals (Sweden)

TANG Ying

2017-01-01

Full Text Available One of the research hotspots in the field of high-temperature alloys was to search the substitutional elements for Re in order to prepare the single-crystal Ni-based superalloys with less or even no Re addition. To find the elements with similar or even lower diffusion coefficients in comparison with that of Re was one of the effective strategies. In multicomponent alloys, the interdiffusivity matrix were used to comprehensively characterize the diffusion ability of any alloying elements. Therefore, accurate determination of the composition-dependant and temperature-dependent interdiffusivities matrices of different elements in γ and γ' phases of Ni-based superalloys was high priority. The paper briefly introduces of the status of the interdiffusivity matrices determination in Ni-based superalloys, and the methods for determining the interdiffusivities in multicomponent alloys, including the traditional Matano-Kirkaldy method and recently proposed numerical inverse method. Because the traditional Matano-Kirkaldy method is of low efficiency, the experimental reports on interdiffusivity matrices in ternary and higher order sub-systems of the Ni-based superalloys were very scarce in the literature. While the numerical inverse method newly proposed in our research group based on Fick's second law can be utilized for high-throughput measurement of accurate interdiffusivity matrices in alloys with any number of components. After that, the successful application of the numerical inverse method in the high-throughput measurement of interdiffusivity matrices in alloys is demonstrated in fcc (γ phase of the ternary Ni-Al-Ta system. Moreover, the validation of the resulting composition-dependant and temperature-dependent interdiffusivity matrices is also comprehensively made. Then, this paper summarizes the recent progress in the measurement of interdiffusivity matrices in γ and γ' phases of a series of core ternary Ni-based superalloys achieved in

Characteristics of phosphorus adsorption by sediment mineral matrices with different particle sizes

Directory of Open Access Journals (Sweden)

Yang Xiao

2013-07-01

Full Text Available The particle size of sediment is one of the main factors that influence the phosphorus physical adsorption on sediment. In order to eliminate the effect of other components of sediment on the phosphorus physical adsorption the sediment mineral matrices were obtained by removing inorganic matter metal oxides, and organic matter from natural sediments, which were collected from the Nantong reach of the Yangtze River. The results show that an exponential relationship exists between the median particle size (D50 and specific surface area (Sg of the sediment mineral matrices, and the fine sediment mineral matrix sample has a larger specific surface area and pore volume than the coarse sediment particles. The kinetic equations were used to describe the phosphorus adsorption process of the sediment mineral matrices, including the Elovich equation, quasi-first-order adsorption kinetic equation, and quasi-second-order adsorption kinetic equation. The results show that the quasi-second-order adsorption kinetic equation has the best fitting effect. Using the mass conservation and Langmuir adsorption kinetic equations, a formula was deduced to calculate the equilibrium adsorption capacity of the sediment mineral matrices. The results of this study show that the phosphorus adsorption capacity decreases with the increase of D50, indicating that the specific surface area and pore volume are the main factors in determining the phosphorus adsorption capacity of the sediment mineral matrices. This study will help understand the important role of sediment in the transformation of phosphorus in aquatic environments.

Dimension from covariance matrices.

Science.gov (United States)

Carroll, T L; Byers, J M

2017-02-01

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

Moment matrices, border bases and radical computation

NARCIS (Netherlands)

B. Mourrain; J.B. Lasserre; M. Laurent (Monique); P. Rostalski; P. Trebuchet (Philippe)

2013-01-01

htmlabstractIn this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and

Moment matrices, border bases and radical computation

NARCIS (Netherlands)

B. Mourrain; J.B. Lasserre; M. Laurent (Monique); P. Rostalski; P. Trebuchet (Philippe)

2011-01-01

htmlabstractIn this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and

Porcine skin as a source of biodegradable matrices: alkaline treatment and glutaraldehyde crosslinking

Directory of Open Access Journals (Sweden)

Fabiana T. Rodrigues

2010-06-01

Full Text Available In this work, the modifications promoted by alkaline hydrolysis and glutaraldehyde (GA crosslinking on type I collagen found in porcine skin have been studied. Collagen matrices were obtained from the alkaline hydrolysis of porcine skin, with subsequent GA crosslinking in different concentrations and reaction times. The elastin content determination showed that independent of the treatment, elastin was present in the matrices. Results obtained from in vitro trypsin degradation indicated that with the increase of GA concentration and reaction time, the degradation rate decreased. From thermogravimetry and differential scanning calorimetry analysis it can be observed that the collagen in the matrices becomes more resistant to thermal degradation as a consequence of the increasing crosslink degree. Scanning electron microscopy analysis indicated that after the GA crosslinking, collagen fibers become more organized and well-defined. Therefore, the preparations of porcine skin matrices with different degradation rates, which can be used in soft tissue reconstruction, are viable.

Introduction to random matrices theory and practice

CERN Document Server

Livan, Giacomo; Vivo, Pierpaolo

2018-01-01

Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum. The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques  (e.g., Coulomb gas approach, replica theory). Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.

["Habitual" left branch block alternating with 2 "disguised" bracnch block].

Science.gov (United States)

Lévy, S; Jullien, G; Mathieu, P; Mostefa, S; Gérard, R

1976-10-01

Two cases of alternating left bundle branch block and "masquerading block" (with left bundle branch morphology in the stnadard leads and right bundle branch block morphology in the precordial leads) were studied by serial tracings and his bundle electrocardiography. In case 1 "the masquerading" block was associated with a first degree AV block related to a prolongation of HV interval. This case is to our knowledge the first cas of alternating bundle branch block in which his bundle activity was recorded in man. In case 2, the patient had atrial fibrilation and His bundle recordings were performed while differents degrees of left bundle branch block were present: The mechanism of the alternation and the concept of "masquerading" block are discussed. It is suggested that this type of block represents a right bundle branch block associated with severe lesions of the "left system".

Amino acid "little Big Bang": representing amino acid substitution matrices as dot products of Euclidian vectors.

Science.gov (United States)

Zimmermann, Karel; Gibrat, Jean-François

2010-01-04

Sequence comparisons make use of a one-letter representation for amino acids, the necessary quantitative information being supplied by the substitution matrices. This paper deals with the problem of finding a representation that provides a comprehensive description of amino acid intrinsic properties consistent with the substitution matrices. We present a Euclidian vector representation of the amino acids, obtained by the singular value decomposition of the substitution matrices. The substitution matrix entries correspond to the dot product of amino acid vectors. We apply this vector encoding to the study of the relative importance of various amino acid physicochemical properties upon the substitution matrices. We also characterize and compare the PAM and BLOSUM series substitution matrices. This vector encoding introduces a Euclidian metric in the amino acid space, consistent with substitution matrices. Such a numerical description of the amino acid is useful when intrinsic properties of amino acids are necessary, for instance, building sequence profiles or finding consensus sequences, using machine learning algorithms such as Support Vector Machine and Neural Networks algorithms.

Amino acid "little Big Bang": Representing amino acid substitution matrices as dot products of Euclidian vectors

Directory of Open Access Journals (Sweden)

Zimmermann Karel

2010-01-01

Full Text Available Abstract Background Sequence comparisons make use of a one-letter representation for amino acids, the necessary quantitative information being supplied by the substitution matrices. This paper deals with the problem of finding a representation that provides a comprehensive description of amino acid intrinsic properties consistent with the substitution matrices. Results We present a Euclidian vector representation of the amino acids, obtained by the singular value decomposition of the substitution matrices. The substitution matrix entries correspond to the dot product of amino acid vectors. We apply this vector encoding to the study of the relative importance of various amino acid physicochemical properties upon the substitution matrices. We also characterize and compare the PAM and BLOSUM series substitution matrices. Conclusions This vector encoding introduces a Euclidian metric in the amino acid space, consistent with substitution matrices. Such a numerical description of the amino acid is useful when intrinsic properties of amino acids are necessary, for instance, building sequence profiles or finding consensus sequences, using machine learning algorithms such as Support Vector Machine and Neural Networks algorithms.

Quantification of iodine in porous hydroxyapatite matrices for application as radioactive sources in brachytherapy

Energy Technology Data Exchange (ETDEWEB)

Lacerda, Kassio Andre; Lameiras, Fernando Soares [Centro de Desenvolvimento da Tecnologia Nuclear, (CDTN/CNEN-MG), Belo Horizonte, MG (Brazil); Silva, Viviane Viana [Centro de Desenvolvimento da Tecnologia Nuclear, (CDTN/CNEN-MG), Belo Horizonte, MG (Brazil); Universidade Vale do Rio Verde de Tres Coracoes, MG (Brazil)

2007-07-15

In this study, non-radioactive iodine was incorporated in two types of biodegradable hydroxyapatite-based porous matrices (HA and HACL) through impregnation process from sodium iodine aqueous solutions with varying concentrations (0.5 and 1.0 mol/L) . The results revealed that both systems presented a high capacity of incorporating iodine into their matrices. The quantity of incorporated iodine was measured through Neutron Activation Analysis (NAA). The porous ceramic matrices based on hydroxyapatite demonstrated a great potential for uses in low dose rate (LDR) brachytherapy. (author)

Moment matrices, border bases and radical computation

NARCIS (Netherlands)

Lasserre, J.B.; Laurent, M.; Mourrain, B.; Rostalski, P.; Trébuchet, P.

2013-01-01

In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming its complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-definite

Generation speed in Raven's Progressive Matrices Test

NARCIS (Netherlands)

Verguts, T.; Boeck, P. De; Maris, E.G.G.

1999-01-01

In this paper, we investigate the role of response fluency on a well-known intelligence test, Raven's (1962) Advanced Progressive Matrices (APM) test. Critical in solving this test is finding rules that govern the items. Response fluency is conceptualized as generation speed or the speed at which a

A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms

Directory of Open Access Journals (Sweden)

Mingli Jing

2010-01-01

Full Text Available An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs, which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform.

Interactions between Food Additive Silica Nanoparticles and Food Matrices

Directory of Open Access Journals (Sweden)

Mi-Ran Go

2017-06-01

Full Text Available Nanoparticles (NPs have been widely utilized in the food industry as additives with their beneficial characteristics, such as improving sensory property and processing suitability, enhancing functional and nutritional values, and extending shelf-life of foods. Silica is used as an anti-caking agent to improve flow property of powered ingredients and as a carrier for flavors or active compounds in food. Along with the rapid development of nanotechnology, the sizes of silica fall into nanoscale, thereby raising concerns about the potential toxicity of nano-sized silica materials. There have been a number of studies carried out to investigate possible adverse effects of NPs on the gastrointestinal tract. The interactions between NPs and surrounding food matrices should be also taken into account since the interactions can affect their bioavailability, efficacy, and toxicity. In the present study, we investigated the interactions between food additive silica NPs and food matrices, such as saccharides, proteins, lipids, and minerals. Quantitative analysis was performed to determine food component-NP corona using HPLC, fluorescence quenching, GC-MS, and ICP-AES. The results demonstrate that zeta potential and hydrodynamic radius of silica NPs changed in the presence of all food matrices, but their solubility was not affected. However, quantitative analysis on the interactions revealed that a small portion of food matrices interacted with silica NPs and the interactions were highly dependent on the type of food component. Moreover, minor nutrients could also affect the interactions, as evidenced by higher NP interaction with honey rather than with a simple sugar mixture containing an equivalent amount of fructose, glucose, sucrose, and maltose. These findings provide fundamental information to extend our understanding about the interactions between silica NPs and food components and to predict the interaction effect on the safety aspects of food

Large deviations of the maximum eigenvalue in Wishart random matrices

International Nuclear Information System (INIS)

Vivo, Pierpaolo; Majumdar, Satya N; Bohigas, Oriol

2007-01-01

We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value (λ) = N/c decreases for large N as ∼exp[-β/2 N 2 Φ - (2√c + 1: c)], where β = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M ≤ 1 and Φ - (x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions

Large deviations of the maximum eigenvalue in Wishart random matrices

Energy Technology Data Exchange (ETDEWEB)

Vivo, Pierpaolo [School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH (United Kingdom) ; Majumdar, Satya N [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France)

2007-04-20

We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X{sup T}X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value ({lambda}) = N/c decreases for large N as {approx}exp[-{beta}/2 N{sup 2}{phi}{sub -} (2{radical}c + 1: c)], where {beta} = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M {<=} 1 and {phi}{sub -}(x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions.

E-Block: A Tangible Programming Tool with Graphical Blocks

Directory of Open Access Journals (Sweden)

Danli Wang

2013-01-01

Full Text Available This paper designs a tangible programming tool, E-Block, for children aged 5 to 9 to experience the preliminary understanding of programming by building blocks. With embedded artificial intelligence, the tool defines the programming blocks with the sensors as the input and enables children to write programs to complete the tasks in the computer. The symbol on the programming block's surface is used to help children understanding the function of each block. The sequence information is transferred to computer by microcomputers and then translated into semantic information. The system applies wireless and infrared technologies and provides user with feedbacks on both screen and programming blocks. Preliminary user studies using observation and user interview methods are shown for E-Block's prototype. The test results prove that E-Block is attractive to children and easy to learn and use. The project also highlights potential advantages of using single chip microcomputer (SCM technology to develop tangible programming tools for children.

Electrospun composite matrices of poly(ε-caprolactone)-montmorillonite made using tenside free Pickering emulsions

International Nuclear Information System (INIS)

Samanta, Archana; Takkar, Sonam; Kulshreshtha, Ritu; Nandan, Bhanu; Srivastava, Rajiv K.

2016-01-01

The production of composite electrospun matrices of poly(ε-caprolactone) (PCL) using an emulsifier-free emulsion, made with minimal organic solvent, as precursor is reported. Pickering emulsions of PCL were prepared using modified montmorillonite (MMT) clay as the stabilizer. Hydrophobic tallow group of the modified MMT clay resulted in analogous interaction of clay with oil and aqueous phase and its adsorption at the interface to provide stability to the resultant emulsion. Composite fibrous matrices of PCL and MMT were produced using electrospinning under controlled conditions. The fiber fineness was found to alter with PCL concentration and volume fraction of the aqueous and oil phases. A higher tensile strength and modulus was obtained with inclusion of MMT in PCL electrospun matrix in comparison to a matrix made using neat PCL. The presence of clay in the fibrous matrix did not change the cell proliferation efficiency in comparison to neat PCL matrix. Composite fibrous matrices of PCL/MMT bearing enhanced tensile properties may find applications in areas other than tissue engineering for example food packaging and filtration. - Highlights: • Tenside free, clay stabilized Pickering emulsion of PCL is made with minimal organic solvent. • Organic–inorganic composite fibrous matrices were produced via emulsion electrospinning. • Fiber fineness was efficiently controlled by variation in emulsion formulation. • Fibrous matrices of high tensile strength and modulus were obtained in comparison to neat PCL matrix. • PCL/clay matrices showed effective cell proliferation as a neat PCL matrix.

Electrospun composite matrices of poly(ε-caprolactone)-montmorillonite made using tenside free Pickering emulsions

Energy Technology Data Exchange (ETDEWEB)

Samanta, Archana [Department of Textile Technology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016 (India); Takkar, Sonam; Kulshreshtha, Ritu [Department of Biochemical Engineering and Biotechnology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016 (India); Nandan, Bhanu [Department of Textile Technology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016 (India); Srivastava, Rajiv K., E-mail: rajiv@textile.iitd.ac.in [Department of Textile Technology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016 (India)

2016-12-01

The production of composite electrospun matrices of poly(ε-caprolactone) (PCL) using an emulsifier-free emulsion, made with minimal organic solvent, as precursor is reported. Pickering emulsions of PCL were prepared using modified montmorillonite (MMT) clay as the stabilizer. Hydrophobic tallow group of the modified MMT clay resulted in analogous interaction of clay with oil and aqueous phase and its adsorption at the interface to provide stability to the resultant emulsion. Composite fibrous matrices of PCL and MMT were produced using electrospinning under controlled conditions. The fiber fineness was found to alter with PCL concentration and volume fraction of the aqueous and oil phases. A higher tensile strength and modulus was obtained with inclusion of MMT in PCL electrospun matrix in comparison to a matrix made using neat PCL. The presence of clay in the fibrous matrix did not change the cell proliferation efficiency in comparison to neat PCL matrix. Composite fibrous matrices of PCL/MMT bearing enhanced tensile properties may find applications in areas other than tissue engineering for example food packaging and filtration. - Highlights: • Tenside free, clay stabilized Pickering emulsion of PCL is made with minimal organic solvent. • Organic–inorganic composite fibrous matrices were produced via emulsion electrospinning. • Fiber fineness was efficiently controlled by variation in emulsion formulation. • Fibrous matrices of high tensile strength and modulus were obtained in comparison to neat PCL matrix. • PCL/clay matrices showed effective cell proliferation as a neat PCL matrix.

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

Science.gov (United States)

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

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

Marco Congedo

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

The Inverse of Banded Matrices

Science.gov (United States)

2013-01-01

indexed entries all zeros. In this paper, generalizing a method of Mallik (1999) [5], we give the LU factorization and the inverse of the matrix Br,n (if it...r ≤ i ≤ r, 1 ≤ j ≤ r, with the remaining un-indexed entries all zeros. In this paper generalizing a method of Mallik (1999) [5...matrices and applications to piecewise cubic approximation, J. Comput. Appl. Math. 8 (4) (1982) 285–288. [5] R.K. Mallik , The inverse of a lower

Transfer matrices for multilayer structures

International Nuclear Information System (INIS)

Baquero, R.

1988-08-01

We consider four of the transfer matrices defined to deal with multilayer structures. We deduce algorithms to calculate them numerically, in a simple and neat way. We illustrate their application to semi-infinite systems using SGFM formulae. These algorithms are of fast convergence and allow a calculation of bulk-, surface- and inner-layers band structure in good agreement with much more sophisticated calculations. Supermatrices, interfaces and multilayer structures can be calculated in this way with a small computational effort. (author). 10 refs

Synthesised standards in natural matrices

International Nuclear Information System (INIS)

Olsen, D.G.

1980-01-01

The problem of securing the most reliable standards for the accurate analysis of radionuclides is discussed in the paper and in the comment on the paper. It is contended in the paper that the best standards can be created by quantitative addition of accurately known spiking solutions into carefully selected natural matrices. On the other hand it is argued that many natural materials can be successfully standardized for numerous trace constituents. Both points of view are supported with examples. (U.K.)

NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES

Directory of Open Access Journals (Sweden)

Sachin Kumar

2017-12-01

Full Text Available We investigate spacing statistics for ensembles of various real random matrices where the matrix-elements have various Probability Distribution Function (PDF: f(x including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derive the spacing distributions p(s of adjacent energy eigenvalues. Nevertheless, they show the linear level repulsion near s = 0 as αs where α depends on the choice of the PDF. More interestingly when f(x = xe−x2 (f(0 = 0, we get cubic level repulsion near s = 0: p(s ~ s3e−s2.We also derive the distribution of eigenvalues D(ε for these matrices.

E-Block: A Tangible Programming Tool with Graphical Blocks

OpenAIRE

Danli Wang; Yang Zhang; Shengyong Chen

2013-01-01

This paper designs a tangible programming tool, E-Block, for children aged 5 to 9 to experience the preliminary understanding of programming by building blocks. With embedded artificial intelligence, the tool defines the programming blocks with the sensors as the input and enables children to write programs to complete the tasks in the computer. The symbol on the programming block's surface is used to help children understanding the function of each block. The sequence information is transfer...

The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers

Directory of Open Access Journals (Sweden)

Zhaolin Jiang

2014-01-01

Full Text Available Circulant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant and g-circulant matrices with any continuous Fibonacci and Lucas numbers are considered. Firstly, the invertibility of the circulant matrix is discussed and the explicit determinant and the inverse matrices by constructing the transformation matrices are presented. Furthermore, the invertibility of the left circulant and g-circulant matrices is also studied. We obtain the explicit determinants and the inverse matrices of the left circulant and g-circulant matrices by utilizing the relationship between left circulant, g-circulant matrices and circulant matrix, respectively.

Temperature dependence of electron spin-lattice relaxation of radiation-produced silver atoms in polycrystalline aqueous and glassy organic matrices. Importance of relaxation by tunneling modes in disordered matrices

International Nuclear Information System (INIS)

Michalik, J.; Kevan, L.

1978-01-01

The electron spin-lattice relaxation of trapped silver atoms in polycrystalline ice matrices and in methanol, ethanol, propylene carbonate, and 2-methyltetrahydrofuran organic glasses has been directly studied as a function of temperature by the saturation-recovery method. Below 40 K the dominant electron spin-lattice relaxation mechanism involves modulation of the electron nuclear dipolar interaction with nuclei in the radical's environment by tunneling of those nuclei between two nearly equal energy configurations. This relaxation mechanism occurs with high efficiency, has a characteristic linear temperature dependence, and is typically found in highly disordered matrices. The efficiency of this relaxation mechanism seems to decrease with decreasing polarity of the matrix. Deuteration experiments show that the tunneling nuclei are protons and in methanol it is shown that the methyl protons have more tunneling modes available than the hydroxyl protons. In polycrystalline ice matrices silver atoms can be stabilized with two different orientations of surrounding water molecules; the efficiency of the tunneling relaxation reflects this difference. From these and previous results on tunneling relaxation of trapped electrons in glassy matrices it appears that tunneling relaxation may be used to distinguish models with different geometrical configurations and to determine the relative rigidity of such configurations around trapped radicals in disordered solids. (author)

Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

OpenAIRE

Hillar, Christopher; Johnson, Charles R.

2005-01-01

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a long-standing problem in theoretical physics, and it was previously approached by the authors for words in two real positive definite matrices with positive integral exponents. A large class of words that do guarantee positive eig...

Intermittency and random matrices

Science.gov (United States)

Sokoloff, Dmitry; Illarionov, E. A.

2015-08-01

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

Finiteness properties of congruence classes of infinite matrices

NARCIS (Netherlands)

Eggermont, R.H.

2014-01-01

We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.

Multiplicative Structure and Hecke Rings of Generator Matrices for Codes over Quotient Rings of Euclidean Domains

Directory of Open Access Journals (Sweden)

Hajime Matsui

2017-12-01

Full Text Available In this study, we consider codes over Euclidean domains modulo their ideals. In the first half of the study, we deal with arbitrary Euclidean domains. We show that the product of generator matrices of codes over the rings mod a and mod b produces generator matrices of all codes over the ring mod a b , i.e., this correspondence is onto. Moreover, we show that if a and b are coprime, then this correspondence is one-to-one, i.e., there exist unique codes over the rings mod a and mod b that produce any given code over the ring mod a b through the product of their generator matrices. In the second half of the study, we focus on the typical Euclidean domains such as the rational integer ring, one-variable polynomial rings, rings of Gaussian and Eisenstein integers, p-adic integer rings and rings of one-variable formal power series. We define the reduced generator matrices of codes over Euclidean domains modulo their ideals and show their uniqueness. Finally, we apply our theory of reduced generator matrices to the Hecke rings of matrices over these Euclidean domains.

Solution of the Euler and Navier-Stokes equations on MIMD distributed memory multiprocessors using cyclic reduction

International Nuclear Information System (INIS)

Curchitser, E.N.; Pelz, R.B.; Marconi, F.

1992-01-01

The Euler and Navier-Stokes equations are solved for the steady, two-dimensional flow over a NACA 0012 airfoil using a 1024 node nCUBE/2 multiprocessor. Second-order, upwind-discretized difference equations are solved implicitly using ADI factorization. Parallel cyclic reduction is employed to solve the block tridiagonal systems. For realistic problems, communication times are negligible compared to calculation times. The processors are tightly synchronized, and their loads are well balanced. When the flux Jacobians flux are frozen, the wall-clock time for one implicit timestep is about equal to that of a multistage explicit scheme. 10 refs

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.

Study and optimization of positioning algorithms for monolithic PET detectors blocks

International Nuclear Information System (INIS)

Acilu, P Garcia de; Sarasola, I; Canadas, M; Cuerdo, R; Mendes, P Rato; Romero, L; Willmott, C

2012-01-01

We are developing a PET insert for existing MRI equipment to be used in clinical PET/MR studies of the human brain. The proposed scanner is based on annihilation gamma detection with monolithic blocks of cerium-doped lutetium yttrium orthosilicate (LYSO:Ce) coupled to magnetically-compatible avalanche photodiodes (APD) matrices. The light distribution generated on the LYSO:Ce block provides the impinging position of the 511 keV photons by means of a positioning algorithm. Several positioning methods, from the simplest Anger Logic to more sophisticate supervised-learning Neural Networks (NN), can be implemented to extract the incidence position of gammas directly from the APD signals. Finally, an optimal method based on a two-step Feed-Forward Neural Network has been selected. It allows us to reach a resolution at detector level of 2 mm, and acquire images of point sources using a first BrainPET prototype consisting of two monolithic blocks working in coincidence. Neural networks provide a straightforward positioning of the acquired data once they have been trained, however the training process is usually time-consuming. In order to obtain an efficient positioning method for the complete scanner it was necessary to find a training procedure that reduces the data acquisition and processing time without introducing a noticeable degradation of the spatial resolution. A grouping process and posterior selection of the training data have been done regarding the similitude of the light distribution of events which have one common incident coordinate (transversal or longitudinal). By doing this, the amount of training data can be reduced to about 5% of the initial number with a degradation of spatial resolution lower than 10%.

Equiangular tight frames and unistochastic matrices

Czech Academy of Sciences Publication Activity Database

Goyeneche, D.; Turek, Ondřej

2017-01-01

Roč. 50, č. 24 (2017), č. článku 245304. ISSN 1751-8113 R&D Projects: GA ČR GA17-01706S Institutional support: RVO:61389005 Keywords : equiangular tight frames * unistochastic matrices * SIC POVM Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.857, year: 2016

PHAGOCYTOSIS AND REMODELING OF COLLAGEN MATRICES

OpenAIRE

Abraham, Leah C.; Dice, J Fred.; Lee, Kyongbum; Kaplan, David L.

2007-01-01

The biodegradation of collagen and the deposition of new collagen-based extracellular matrices are of central importance in tissue remodeling and function. Similarly, for collagen-based biomaterials used in tissue engineering, the degradation of collagen scaffolds with accompanying cellular infiltration and generation of new extracellular matrix is critical for integration of in vitro grown tissues in vivo. In earlier studies we observed significant impact of collagen structure on primary lun...

Identification of necessary and sufficient conditions for real non-negativeness of rational matrices

International Nuclear Information System (INIS)

Saeed, K.

1982-12-01

The necessary and sufficient conditions for real non-negativeness of rational matrices have been identified. A programmable algorithm is developed and is given with its computer flow chart. This algorithm can be used as a general solution to test the real non-negativeness of rational matrices. The computer program assures the feasibility of the suggested algorithm. (author)

Elements of Calculus Quaternionic Matrices And Some Applications In Vector Algebra And Kinematics

Directory of Open Access Journals (Sweden)

Pivnyak G.G.

2016-04-01

Full Text Available Quaternionic matrices are proposed to develop mathematical models and perform computational experiments. New formulae for complex vector and scalar products matrix notation, formulae of first curvature, second curvature and orientation of true trihedron tracing are demonstrated in this paper. Application of quaternionic matrices for a problem of airspace transport system trajectory selection is shown.

SAR matrices: automated extraction of information-rich SAR tables from large compound data sets.

Science.gov (United States)

Wassermann, Anne Mai; Haebel, Peter; Weskamp, Nils; Bajorath, Jürgen

2012-07-23

We introduce the SAR matrix data structure that is designed to elucidate SAR patterns produced by groups of structurally related active compounds, which are extracted from large data sets. SAR matrices are systematically generated and sorted on the basis of SAR information content. Matrix generation is computationally efficient and enables processing of large compound sets. The matrix format is reminiscent of SAR tables, and SAR patterns revealed by different categories of matrices are easily interpretable. The structural organization underlying matrix formation is more flexible than standard R-group decomposition schemes. Hence, the resulting matrices capture SAR information in a comprehensive manner.

Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113

Directory of Open Access Journals (Sweden)

Balonin N. A.

2018-01-01

Full Text Available We continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders 4v with odd v ≤ 41. In this paper we cover the cases v = 43, 45, 47, 49, 51. The odd integers v < 120 for which no symmetric Hadamard matrices of order 4v are known are the following: 47, 59, 65, 67, 73, 81, 89, 93, 101, 103, 107, 109, 113, 119. By using the propus construction, we found several symmetric Hadamard matrices of order 4v for v = 47, 73, 113.

Generalised Wigner surmise for (2 X 2) random matrices

International Nuclear Information System (INIS)

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

2001-01-01

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

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

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

2015-01-01

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

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander

2015-11-30

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

RGD peptide-displaying M13 bacteriophage/PLGA nanofibers as cell-adhesive matrices for smooth muscle cells

Energy Technology Data Exchange (ETDEWEB)

Shin, Yong Cheol; Lee, Jong Ho; Jin, Oh Seong; Lee, Eun Ji; Jin, Lin Hua; Kim, Chang Seok; Hong, Suck Won; Han, Dong Wook; Kim, Chun Tae; Oh, Jin Woo [Pusan National University, Busan (Korea, Republic of)

2015-01-15

Extracellular matrices (ECMs) are network structures that play an essential role in regulating cellular growth and differentiation. In this study, novel nanofibrous matrices were fabricated by electrospinning M13 bacteriophage and poly(lactic-co-glycolic acid) (PLGA) and were shown to be structurally and functionally similar to natural ECMs. A genetically-engineered M13 bacteriophage was constructed to display Arg-Gly-Asp (RGD) peptides on its surface. The physicochemical properties of RGD peptide-displaying M13 bacteriophage (RGD-M13 phage)/PLGA nanofibers were characterized by using scanning electron microscopy and Fourier-transform infrared spectroscopy. We used immunofluorescence staining to confirm that M13 bacteriophages were homogenously distributed in RGD-M13 phage/PLGA matrices. Furthermore, RGD-M13 phage/PLGA nanofibrous matrices, having excellent biocompatibility, can enhance the behaviors of vascular smooth muscle cells. This result suggests that RGD-M13 phage/PLGA nanofibrous matrices have potentials to serve as tissue engineering scaffolds.

On equations for the total suction and its matric and osmotic components

International Nuclear Information System (INIS)

Dao, Vinh N.T.; Morris, Peter H.; Dux, Peter F.

2008-01-01

A clear fundamental understanding of suctions is crucial for the study of the behaviour of plastic cement mortar and concrete, including plastic shrinkage cracking. In this paper, the expression relating the change in free energy of the pore water with an isothermal change in pressure is first derived. Based upon definitions of suctions, it is then shown that total, matric, and osmotic suctions can all be expressed in the same thermodynamic form. The widely accepted, but not yet satisfactorily validated, assumption that the total suction comprises matric and osmotic components is then confirmed theoretically. The well-known Kelvin equation for matric suction, and Morse and van't Hoff equations for osmotic suction are subsequently derived from the corresponding thermodynamic equations. The applicability of latter two equations in evaluating the osmotic suctions of cement mortar and concrete is highlighted

Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures

Directory of Open Access Journals (Sweden)

Nishchal K. Verma

2012-01-01

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

Sparse Matrices in Frame Theory

DEFF Research Database (Denmark)

Lemvig, Jakob; Krahmer, Felix; Kutyniok, Gitta

2014-01-01

Frame theory is closely intertwined with signal processing through a canon of methodologies for the analysis of signals using (redundant) linear measurements. The canonical dual frame associated with a frame provides a means for reconstruction by a least squares approach, but other dual frames...... yield alternative reconstruction procedures. The novel paradigm of sparsity has recently entered the area of frame theory in various ways. Of those different sparsity perspectives, we will focus on the situations where frames and (not necessarily canonical) dual frames can be written as sparse matrices...

Disaggregation of sectors in Social Accounting Matrices using a customized Wolsky method

OpenAIRE

BARRERA-LOZANO Margarita; MAINAR CAUSAPÉ ALFREDO; VALLÉS FERRER José

2014-01-01

The aim of this work is to enable the implementation of disaggregation processes for specific and homogeneous sectors in Social Accounting Matrices (SAMs), while taking into account the difficulties in data collection from these types of sectors. The method proposed is based on the Wolsky technique, customized for the disaggregation of Social Accounting Matrices, within the current-facilities framework. The Spanish Social Accounting Matrix for 2008 is used as a benchmark for the analysis, and...

Thermoresponsive microgels containing trehalose as soft matrices for 3D cell culture.

Science.gov (United States)

Burek, Małgorzata; Waśkiewicz, Sylwia; Lalik, Anna; Student, Sebastian; Bieg, Tadeusz; Wandzik, Ilona

2017-01-31

A series of thermoresponsive glycomicrogels with trehalose in the cross-links or with trehalose in the cross-links and as pending moieties was synthesized. These materials were obtained by surfactant-free precipitation copolymerization of N-isopropylacrylamide and various amounts of trehalose monomers. The resultant particles showed a spherical shape and a submicrometer hydrodynamic size with a narrow size distribution. At 25 °C, glycomicrogels in solutions with physiological ionic strength formed stable colloids, which further gelled upon heating to physiological temperature forming a macroscopic hydrogel with an interconnected porous structure. These extremely soft matrices with dynamic storage modulus in the range of 9-70 Pa were examined in 3D culture systems for HeLa cell culture in comparison to traditional 2D mode. They showed relatively low syneresis over time, especially when glycomicrogels with a high content of hydrophilic trehalose were used as building blocks. An incorporated pending trehalose composed of two α,α'-1,1'-linked d-glucose moieties was used with the intention of providing multivalent interactions with glucose transporters (GLUTs) expressed on the cell surface. A better cell viability was observed when a soft hydrogel with the highest content of trehalose and the lowest syneresis was used as a matrix compared to a 2D control assay.

An algebraic model for quark mass matrices with heavy top

International Nuclear Information System (INIS)

Krolikowski, W.; Warsaw Univ.

1991-01-01

In terms of an intergeneration U(3) algebra, a numerical model is constructed for quark mass matrices, predicting the top-quark mass around 170 GeV and the CP-violating phase around 75 deg. The CKM matrix is nonsymmetric in moduli with |V ub | being very small. All moduli are consistent with their experimental limits. The model is motivated by the author's previous work on three replicas of the Dirac particle, presumably resulting into three generations of leptons and quarks. The paper may be also viewed as an introduction to a new method of intrinsic dynamical description of lepton and quark mass matrices. (author)

Soft landing of size selected clusters in rare gas matrices

International Nuclear Information System (INIS)

Lau, J.T; Wurth, W.; Ehrke, H-U.; Achleitner, A.

2003-01-01

Soft landing of mass selected clusters in rare gas matrices is a technique used to preserve mass selection in cluster deposition. To prevent fragmentation upon deposition, the substrate is covered with rare gas matrices to dissipate the cluster kinetic energy upon impact. Theoretical and experimental studies demonstrate the power of this technique. Besides STM, optical absorption, excitation, and fluorescence experiments, x-ray absorption at core levels can be used as a tool to study soft landing conditions, as will be shown here. X-ray absorption spectroscopy is also well suited to follow diffusion and agglomeration of clusters on surfaces via energy shifts in core level absorption

Environmental assessment of waste matrices contaminated with arsenic.

Science.gov (United States)

Sanchez, F; Garrabrants, A C; Vandecasteele, C; Moszkowicz, P; Kosson, D S

2003-01-31

The use of equilibrium-based and mass transfer-based leaching tests has been proposed to provide an integrated assessment of leaching processes from solid wastes. The objectives of the research presented here are to (i) validate this assessment approach for contaminated soils and cement-based matrices, (ii) evaluate the use of diffusion and coupled dissolution-diffusion models for estimating constituent release, and (iii) evaluate model parameterization using results from batch equilibrium leaching tests and physical characterization. The test matrices consisted of (i) a soil contaminated with arsenic from a pesticide production facility, (ii) the same soil subsequently treated by a Portland cement stabilization/solidification (S/S) process, and (iii) a synthetic cement-based matrix spiked with arsenic(III) oxide. Results indicated that a good assessment of contaminant release from contaminated soils and cement-based S/S treated wastes can be obtained by the integrated use of equilibrium-based and mass transfer-based leaching tests in conjunction with the appropriate release model. During the time scale of laboratory testing, the release of arsenic from the contaminated soil matrix was governed by diffusion and the solubility of arsenic in the pore solution while the release of arsenic from the cement-based matrices was mainly controlled by solubilization at the interface between the matrix and the bulk leaching solution. In addition, results indicated that (i) estimation of the activity coefficient within the matrix pore water is necessary for accurate prediction of constituent release rates and (ii) inaccurate representation of the factors controlling release during laboratory testing can result in significant errors in release estimates.

Joint Matrices Decompositions and Blind Source Separation

Czech Academy of Sciences Publication Activity Database

Chabriel, G.; Kleinsteuber, M.; Moreau, E.; Shen, H.; Tichavský, Petr; Yeredor, A.

2014-01-01

Roč. 31, č. 3 (2014), s. 34-43 ISSN 1053-5888 R&D Projects: GA ČR GA102/09/1278 Institutional support: RVO:67985556 Keywords : joint matrices decomposition * tensor decomposition * blind source separation Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 5.852, year: 2014 http://library.utia.cas.cz/separaty/2014/SI/tichavsky-0427607.pdf

Model-independent analysis with BPM correlation matrices

International Nuclear Information System (INIS)

Irwin, J.; Wang, C.X.; Yan, Y.T.; Bane, K.; Cai, Y.; Decker, F.; Minty, M.; Stupakov, G.; Zimmermann, F.

1998-06-01

The authors discuss techniques for Model-Independent Analysis (MIA) of a beamline using correlation matrices of physical variables and Singular Value Decomposition (SVD) of a beamline BPM matrix. The beamline matrix is formed from BPM readings for a large number of pulses. The method has been applied to the Linear Accelerator of the SLAC Linear Collider (SLC)

Poly(ferrocenylsilane)-block-Polylactide Block Copolymers

NARCIS (Netherlands)

Roerdink, M.; van Zanten, Thomas S.; Hempenius, Mark A.; Zhong, Zhiyuan; Feijen, Jan; Vancso, Gyula J.

2007-01-01

A PFS/PLA block copolymer was studied to probe the effect of strong surface interactions on pattern formation in PFS block copolymer thin films. Successful synthesis of PFS-b-PLA was demonstrated. Thin films of these polymers show phase separation to form PFS microdomains in a PLA matrix, and

Spin theory of the density functional: reduced matrices and density functions

International Nuclear Information System (INIS)

Pavlov, R.; Delchev, Y.; Pavlova, K.; Maruani, J.

1993-01-01

Expressions for the reduced matrices and density functions of N-fermion systems of arbitrary order s (1<=s<=N) are derived within the frame of rigorous spin approach to the density functional theory (DFT). Using the local-scale transformation method and taking into account the particle spin it is shown that the reduced matrices and density functions are functionals of the total one-fermion density. Similar dependence is found for the distribution density of s-particle aggregates. Generalization and applicability of DFT to the case of s-particle ensembles and aggregates is discussed. 14 refs

Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices

KAUST Repository

Lan, Shiwei; Holbrook, Andrew; Fortin, Norbert J.; Ombao, Hernando; Shahbaba, Babak

2017-01-01

Modeling covariance (and correlation) matrices is a challenging problem due to the large dimensionality and positive-definiteness constraint. In this paper, we propose a novel Bayesian framework based on decomposing the covariance matrix

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

Science.gov (United States)

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

2017-02-01

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

Symmetry of anomalous dimension matrices for colour evolution of hard scattering processes

International Nuclear Information System (INIS)

Seymour, Michael H.

2005-01-01

In a recent paper, Dokshitzer and Marchesini rederived the anomalous dimension matrix for colour evolution of gg→gg scattering, first derived by Kidonakis, Oderda and Sterman. They noted a weird symmetry that it possesses under interchange of internal (colour group) and external (scattering angle) degrees of freedom and speculated that this may be related to an embedding into a context that correlates internal and external variables such as string theory. In this short note, I point out another symmetry possessed by all the colour evolution anomalous dimension matrices calculated to date. It is more prosaic, but equally unexpected, and may also point to the fact that colour evolution might be understood in some deeper theoretical framework. To my knowledge it has not been pointed out elsewhere, or anticipated by any of the authors calculating these matrices. It is simply that, in a suitably chosen colour basis, they are complex symmetric matrices

Quark mass matrices in left-right symmetric gauge theories

International Nuclear Information System (INIS)

Ecker, G.; Grimus, W.; Konetschny, W.

1981-01-01

The most general left-right symmetry for SU(2)sub(L) x SU(2)sub(R) x U(1) gauge theories with any number of flavours and with at most two scalar multiplets transforming as anti qq bilinears is analyzed. In order to get additional constraints on the structure of quark mass matrices all possible horizontal groups (continuous or discrete) are investigated. A complete classification of physically inequivalent quark mass matrices is given for four and six flavours. It is argued that the methods and results are also applicable in the case of dynamical symmetry breaking. Parity invariance and horizontal symmetry are shown to imply CP conservation on the Lagrangian level. For all non-trivial three-generation models there is spontaneous CP violation which in most cases turns out to be naturally small. (Auth.)

Schur complements of matrices with acyclic bipartite graphs

DEFF Research Database (Denmark)

Britz, Thomas Johann; Olesky, D.D.; van den Driessche, P.

2005-01-01

Bipartite graphs are used to describe the generalized Schur complements of real matrices having nos quare submatrix with two or more nonzero diagonals. For any matrix A with this property, including any nearly reducible matrix, the sign pattern of each generalized Schur complement is shown to be ...

Which matrices are immune against the transportation paradox

NARCIS (Netherlands)

Deineko, Vladimir G.; Klinz, Bettina; Woeginger, Gerhard

2003-01-01

We characterize the m×n cost matrices of the transportation problem for which there exist supplies and demands such that the transportation paradox arises. Our characterization is fairly simple and can be verified within O(mn) computational steps. Moreover, we discuss the corresponding question for

Block and sub-block boundary strengthening in lath martensite

NARCIS (Netherlands)

Du, C.; Hoefnagels, J.P.M.; Vaes, R.; Geers, M.G.D.

2016-01-01

Well-defined uniaxial micro-tensile tests were performed on lath martensite single block specimens and multi-block specimens with different number of block boundaries parallel to the loading direction. Detailed slip trace analyses consistently revealed that in the {110}<111> slip system with the

Fabrication of inert matrices for heterogeneous transmutation. EFTTRA-T2 (RAS 2) irradiation programme

International Nuclear Information System (INIS)

Boshoven, J.G.; Hein, H.; Konings, R.J.M.

1996-07-01

This report describes the fabrication of targets containing inert matrices for the heterogeneous transmutation of plutonium and minor actinides. These targets will be irradiated in the EFTTRA-T2 (RAS-2) irradiation programme. The selection, preparation and characterization of the inert matrices and fabrication and loading of the irradiation capsules are discussed. (orig.)

Powder wastes confinement block and manufacturing process of this block

International Nuclear Information System (INIS)

Dagot, L.; Brunel, G.

1996-01-01

This invention concerns a powder wastes containment block and a manufacturing process of this block. In this block, the waste powder is encapsulated in a thermo hardening polymer as for example an epoxy resin, the encapsulated resin being spread into cement. This block can contain between 45 and 55% in mass of wastes, between 18 and 36% in mass of polymer and between 14 and 32% in mass of cement. Such a containment block can be used for the radioactive wastes storage. (O.M.). 4 refs

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

Science.gov (United States)

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

2018-01-01

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

Wound care matrices for chronic leg ulcers: role in therapy

Directory of Open Access Journals (Sweden)

Sano H

2015-07-01

Full Text Available Hitomi Sano,1 Sachio Kouraba,2 Rei Ogawa11Department of Plastic, Reconstructive, and Aesthetic Surgery, Nippon Medical School, Tokyo, Japan; 2Sapporo Wound Care and Anti-Aging Laboratory, Sapporo, JapanAbstract: Chronic leg ulcers are a significant health care concern. Although deep wounds are usually treated by flap transfers, the operation is invasive and associates with serious complications. Skin grafts may be a less invasive means of covering wounds. However, skin grafts cannot survive on deep defects unless high-quality granulation tissue can first be generated in the defects. Technologies that generate high-quality granulation tissue are needed. One possibility is to use wound care matrices, which are bioengineered skin and soft tissue substitutes. Because they all support the healing process by providing a premade extracellular matrix material, these matrices can be termed “extracellular matrix replacement therapies”. The matrix promotes wound healing by acting as a scaffold for regeneration, attracting host cytokines to the wound, stimulating wound epithelialization and angiogenesis, and providing the wound bed with bioactive components. This therapy has lasting benefits as it not only helps large skin defects to be closed with thin skin grafts or patch grafts but also restores cosmetic appearance and proper function. In particular, since it acts as a layer that slides over the subcutaneous fascia, it provides skin elasticity, tear resistance, and texture. Several therapies and products employing wound care matrices for wound management have been developed recently. Some of these can be applied in combination with negative pressure wound therapy or beneficial materials that promote wound healing and can be incorporated into the matrix. To date, the clinical studies on these approaches suggest that wound care matrices promote spontaneous wound healing or can be used to facilitate skin grafting, thereby avoiding the need to use

Blocked Randomization with Randomly Selected Block Sizes

Directory of Open Access Journals (Sweden)

Jimmy Efird

2010-12-01

Full Text Available When planning a randomized clinical trial, careful consideration must be given to how participants are selected for various arms of a study. Selection and accidental bias may occur when participants are not assigned to study groups with equal probability. A simple random allocation scheme is a process by which each participant has equal likelihood of being assigned to treatment versus referent groups. However, by chance an unequal number of individuals may be assigned to each arm of the study and thus decrease the power to detect statistically significant differences between groups. Block randomization is a commonly used technique in clinical trial design to reduce bias and achieve balance in the allocation of participants to treatment arms, especially when the sample size is small. This method increases the probability that each arm will contain an equal number of individuals by sequencing participant assignments by block. Yet still, the allocation process may be predictable, for example, when the investigator is not blind and the block size is fixed. This paper provides an overview of blocked randomization and illustrates how to avoid selection bias by using random block sizes.

Population Blocks.

Science.gov (United States)

Smith, Martin H.

1992-01-01

Describes an educational game called "Population Blocks" that is designed to illustrate the concept of exponential growth of the human population and some potential effects of overpopulation. The game material consists of wooden blocks; 18 blocks are painted green (representing land), 7 are painted blue (representing water); and the remaining…

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander

2015-01-05

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

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

2015-01-01

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

Calibration of Ge gamma-ray spectrometers for complex sample geometries and matrices

Energy Technology Data Exchange (ETDEWEB)

Semkow, T.M., E-mail: thomas.semkow@health.ny.gov [Wadsworth Center, New York State Department of Health, Empire State Plaza, Albany, NY 12201 (United States); Department of Environmental Health Sciences, School of Public Health, University at Albany, State University of New York, Rensselaer, NY 12144 (United States); Bradt, C.J.; Beach, S.E.; Haines, D.K.; Khan, A.J.; Bari, A.; Torres, M.A.; Marrantino, J.C.; Syed, U.-F. [Wadsworth Center, New York State Department of Health, Empire State Plaza, Albany, NY 12201 (United States); Kitto, M.E. [Wadsworth Center, New York State Department of Health, Empire State Plaza, Albany, NY 12201 (United States); Department of Environmental Health Sciences, School of Public Health, University at Albany, State University of New York, Rensselaer, NY 12144 (United States); Hoffman, T.J. [Wadsworth Center, New York State Department of Health, Empire State Plaza, Albany, NY 12201 (United States); Curtis, P. [Kiltel Systems, Inc., Clyde Hill, WA 98004 (United States)

2015-11-01

A comprehensive study of the efficiency calibration and calibration verification of Ge gamma-ray spectrometers was performed using semi-empirical, computational Monte-Carlo (MC), and transfer methods. The aim of this study was to evaluate the accuracy of the quantification of gamma-emitting radionuclides in complex matrices normally encountered in environmental and food samples. A wide range of gamma energies from 59.5 to 1836.0 keV and geometries from a 10-mL jar to 1.4-L Marinelli beaker were studied on four Ge spectrometers with the relative efficiencies between 102% and 140%. Density and coincidence summing corrections were applied. Innovative techniques were developed for the preparation of artificial complex matrices from materials such as acidified water, polystyrene, ethanol, sugar, and sand, resulting in the densities ranging from 0.3655 to 2.164 g cm{sup −3}. They were spiked with gamma activity traceable to international standards and used for calibration verifications. A quantitative method of tuning MC calculations to experiment was developed based on a multidimensional chi-square paraboloid. - Highlights: • Preparation and spiking of traceable complex matrices in extended geometries. • Calibration of Ge gamma spectrometers for complex matrices. • Verification of gamma calibrations. • Comparison of semi-empirical, computational Monte Carlo, and transfer methods of Ge calibration. • Tuning of Monte Carlo calculations using a multidimensional paraboloid.

Calibration of Ge gamma-ray spectrometers for complex sample geometries and matrices

International Nuclear Information System (INIS)

Semkow, T.M.; Bradt, C.J.; Beach, S.E.; Haines, D.K.; Khan, A.J.; Bari, A.; Torres, M.A.; Marrantino, J.C.; Syed, U.-F.; Kitto, M.E.; Hoffman, T.J.; Curtis, P.

2015-01-01

A comprehensive study of the efficiency calibration and calibration verification of Ge gamma-ray spectrometers was performed using semi-empirical, computational Monte-Carlo (MC), and transfer methods. The aim of this study was to evaluate the accuracy of the quantification of gamma-emitting radionuclides in complex matrices normally encountered in environmental and food samples. A wide range of gamma energies from 59.5 to 1836.0 keV and geometries from a 10-mL jar to 1.4-L Marinelli beaker were studied on four Ge spectrometers with the relative efficiencies between 102% and 140%. Density and coincidence summing corrections were applied. Innovative techniques were developed for the preparation of artificial complex matrices from materials such as acidified water, polystyrene, ethanol, sugar, and sand, resulting in the densities ranging from 0.3655 to 2.164 g cm −3 . They were spiked with gamma activity traceable to international standards and used for calibration verifications. A quantitative method of tuning MC calculations to experiment was developed based on a multidimensional chi-square paraboloid. - Highlights: • Preparation and spiking of traceable complex matrices in extended geometries. • Calibration of Ge gamma spectrometers for complex matrices. • Verification of gamma calibrations. • Comparison of semi-empirical, computational Monte Carlo, and transfer methods of Ge calibration. • Tuning of Monte Carlo calculations using a multidimensional paraboloid

Report on the scientific feasibility of new matrices for the conditioning of long lived radionuclides; Rapport sur la faisabilite scientifique des matrices nouvelles de conditionnement des radionucleides a vie longue

Energy Technology Data Exchange (ETDEWEB)

NONE

2001-07-01

New specific matrices for the conditioning of long lived radionuclides (I, Cs, Tc, minor actinides) have been developed. This report presents the conditions of their synthesis by sintering or melting and the quantifying of their crystallographic, physical and thermal properties. A 7% mass insertion of iodine can be reached with a phosphorus-vanadium-lead iodo-apatite. A 5% mass insertion of cesium is reached with the hollandite-type crystal structure (barium aluminate-titanate). An insertion level of at least 10% mass of rare earth oxides (simulating the presence of actinides) is reached for britholite, zirconolite, thorium phosphate, monazite, and zirconolite glass/ceramic materials. The chemical durability has been also determined. Enhanced aqueous corrosion resistance, 100 times better than for the glasses used today, are obtained for iodo-apatite (I), hollandite (Cs), britholite (actinides 3+/4+), thorium phosphate (actinides 4+) and monazite (3+/4+). The first elements of stability with respect to irradiation are reported for the minor actinide conditioning matrices. External post-irradiation examinations by heavy ion bombardment coupled to atomistic modeling have been performed. The characterization of self-irradiated natural analogues of britholite, zirconolite and monazite with more than 10{sup 20} {alpha}/g disintegrations confirms the very long time stability of these mineral structures (>10{sup 8} years). On the basis of the obtained results, it appears that the iodo-apatite, britholite, zirconolite, and thorium phosphate conditioning matrices have reached the stage of scientifical feasibility. The monazite matrice is on the way to reach the feasibility too. Other specific matrices for technetium (metal alloys) and cesium (hollandite) are also under development, but their long-term properties remain to be determined. (J.S.)

Multigroup P8 - elastic scattering matrices of main reactor elements

International Nuclear Information System (INIS)

Garg, S.B.; Shukla, V.K.

1979-01-01

To study the effect of anisotropic scattering phenomenon on shielding and neutronics of nuclear reactors multigroup P8-elastic scattering matrices have been generated for H, D, He, 6 Li, 7 Li, 10 B, C, N, O, Na, Cr, Fe, Ni, 233 U, 235 U, 238 U, 239 Pu, 240 Pu, 241 Pu and 242 Pu using their angular distribution, Legendre coefficient and elastic scattering cross-section data from the basic ENDF/B library. Two computer codes HSCAT and TRANS have been developed to complete this task for BESM-6 and CDC-3600 computers. These scattering matrices can be directly used as input to the transport theory codes ANISN and DOT. (auth.)

Completely X-symmetric S-matrices corresponding to theta functions and models of statistical mechanics

International Nuclear Information System (INIS)

Chudnovsky, D.V.; Chudnovsky, G.V.

1981-01-01

We consider general expressions of factorized S-matrices with Abelian symmetry expressed in terms of theta-functions. These expressions arise from representations of the Heisenberg group. New examples of factorized S-matrices lead to a large class of completely integrable models of statistical mechanics which generalize the XYZ-model of the eight-vertex model. (orig.)

A definition of column reduced proper rational matrices

Czech Academy of Sciences Publication Activity Database

Ruiz-León, J. J.; Castellanos, A.; Ramos-Velasco, Luis Enrique

2002-01-01

Roč. 75, č. 3 (2002), s. 195-203 ISSN 0020-7179 R&D Projects: GA AV ČR KSK1019101 Institutional research plan: CEZ:AV0Z1075907 Keywords : linear systems * columm reduced polynomial matrices * decoupling Subject RIV: BC - Control Systems Theory Impact factor: 0.861, year: 2002

Behavior of sulfur mustard in sand, concrete, and asphalt matrices: Evaporation, degradation, and decontamination.

Science.gov (United States)

Jung, Hyunsook; Choi, Seungki

2017-10-15

The evaporation, degradation, and decontamination of sulfur mustard on environmental matrices including sand, concrete, and asphalt are described. A specially designed wind tunnel and thermal desorber in combination with gas chromatograph (GC) produced profiles of vapor concentration obtained from samples of the chemical agent deposited as a drop on the surfaces of the matrices. The matrices were exposed to the chemical agent at room temperature, and the degradation reactions were monitored and characterized. A vapor emission test was also performed after a decontamination process. The results showed that on sand, the drop of agent spread laterally while evaporating. On concrete, the drop of the agent was absorbed immediately into the matrix while spreading and evaporating. However, the asphalt surface conserved the agent and slowly released parts of the agent over an extended period of time. The degradation reactions of the agent followed pseudo first order behavior on the matrices. Trace amounts of the residual agent present at the surface were also released as vapor after decontamination, posing a threat to the exposed individual and environment.

Numerically Stable Evaluation of Moments of Random Gram Matrices With Applications

KAUST Repository

Elkhalil, Khalil; Kammoun, Abla; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim

2017-01-01

This paper focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.

Numerically Stable Evaluation of Moments of Random Gram Matrices With Applications

KAUST Repository

Elkhalil, Khalil

2017-07-31

This paper focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.

Optimization of the determinant of the Vandermonde matrix and related matrices

Energy Technology Data Exchange (ETDEWEB)

Lundengård, Karl; Österberg, Jonas; Silvestrov, Sergei [Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Box 883, SE-721 23 Västerås (Sweden)

2014-12-10

Various techniques for interpolation of data, moment matching in stochastic applications and various methods in numerical analysis can be described using Vandermonde matrices. For this reason the properties of the determinant of the Vandermonde matrix and related matrices are interesting. Here the extreme points of the Vandermonde determinant, and related determinants, on some simple surfaces such as the unit sphere are analyzed, both numerically and analytically. Some results are also visualized in various dimensions. The extreme points of the Vandermonde determinant are also related to the roots of certain orthogonal polynomials such as the Hermite polynomials.

Consolidity analysis for fully fuzzy functions, matrices, probability and statistics

Directory of Open Access Journals (Sweden)

Walaa Ibrahim Gabr

2015-03-01

Full Text Available The paper presents a comprehensive review of the know-how for developing the systems consolidity theory for modeling, analysis, optimization and design in fully fuzzy environment. The solving of systems consolidity theory included its development for handling new functions of different dimensionalities, fuzzy analytic geometry, fuzzy vector analysis, functions of fuzzy complex variables, ordinary differentiation of fuzzy functions and partial fraction of fuzzy polynomials. On the other hand, the handling of fuzzy matrices covered determinants of fuzzy matrices, the eigenvalues of fuzzy matrices, and solving least-squares fuzzy linear equations. The approach demonstrated to be also applicable in a systematic way in handling new fuzzy probabilistic and statistical problems. This included extending the conventional probabilistic and statistical analysis for handling fuzzy random data. Application also covered the consolidity of fuzzy optimization problems. Various numerical examples solved have demonstrated that the new consolidity concept is highly effective in solving in a compact form the propagation of fuzziness in linear, nonlinear, multivariable and dynamic problems with different types of complexities. Finally, it is demonstrated that the implementation of the suggested fuzzy mathematics can be easily embedded within normal mathematics through building special fuzzy functions library inside the computational Matlab Toolbox or using other similar software languages.

Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

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

2017-01-01

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

Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander

2017-11-01

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

PRIMITIVE MATRICES AND GENERATORS OF PSEUDO RANDOM SEQUENCES OF GALOIS

Directory of Open Access Journals (Sweden)

A. Beletsky

2014-04-01

Full Text Available In theory and practice of information cryptographic protection one of the key problems is the forming a binary pseudo-random sequences (PRS with a maximum length with acceptable statistical characteristics. PRS generators are usually implemented by linear shift register (LSR of maximum period with linear feedback [1]. In this paper we extend the concept of LSR, assuming that each of its rank (memory cell can be in one of the following condition. Let’s call such registers “generalized linear shift register.” The research goal is to develop algorithms for constructing Galois and Fibonacci generalized matrix of n-order over the field , which uniquely determined both the structure of corresponding generalized of n-order LSR maximal period, and formed on their basis Galois PRS generators of maximum length. Thus the article presents the questions of formation the primitive generalized Fibonacci and Galois arbitrary order matrix over the prime field . The synthesis of matrices is based on the use of irreducible polynomials of degree and primitive elements of the extended field generated by polynomial. The constructing methods of Galois and Fibonacci conjugated primitive matrices are suggested. The using possibilities of such matrices in solving the problem of constructing generalized generators of Galois pseudo-random sequences are discussed.

ReplacementMatrix: a web server for maximum-likelihood estimation of amino acid replacement rate matrices.

Science.gov (United States)

Dang, Cuong Cao; Lefort, Vincent; Le, Vinh Sy; Le, Quang Si; Gascuel, Olivier

2011-10-01

Amino acid replacement rate matrices are an essential basis of protein studies (e.g. in phylogenetics and alignment). A number of general purpose matrices have been proposed (e.g. JTT, WAG, LG) since the seminal work of Margaret Dayhoff and co-workers. However, it has been shown that matrices specific to certain protein groups (e.g. mitochondrial) or life domains (e.g. viruses) differ significantly from general average matrices, and thus perform better when applied to the data to which they are dedicated. This Web server implements the maximum-likelihood estimation procedure that was used to estimate LG, and provides a number of tools and facilities. Users upload a set of multiple protein alignments from their domain of interest and receive the resulting matrix by email, along with statistics and comparisons with other matrices. A non-parametric bootstrap is performed optionally to assess the variability of replacement rate estimates. Maximum-likelihood trees, inferred using the estimated rate matrix, are also computed optionally for each input alignment. Finely tuned procedures and up-to-date ML software (PhyML 3.0, XRATE) are combined to perform all these heavy calculations on our clusters. http://www.atgc-montpellier.fr/ReplacementMatrix/ olivier.gascuel@lirmm.fr Supplementary data are available at http://www.atgc-montpellier.fr/ReplacementMatrix/

Tensor Dictionary Learning for Positive Definite Matrices.

Science.gov (United States)

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

2015-11-01

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

Virial expansion for almost diagonal random matrices

International Nuclear Information System (INIS)

Yevtushenko, Oleg; Kravtsov, Vladimir E

2003-01-01

Energy level statistics of Hermitian random matrices H-circumflex with Gaussian independent random entries H i≥j is studied for a generic ensemble of almost diagonal random matrices with (vertical bar H ii vertical bar 2 ) ∼ 1 and (vertical bar H i≠j vertical bar 2 ) bF(vertical bar i - j vertical bar) parallel 1. We perform a regular expansion of the spectral form-factor K(τ) = 1 + bK 1 (τ) + b 2 K 2 (τ) + c in powers of b parallel 1 with the coefficients K m (τ) that take into account interaction of (m + 1) energy levels. To calculate K m (τ), we develop a diagrammatic technique which is based on the Trotter formula and on the combinatorial problem of graph edges colouring with (m + 1) colours. Expressions for K 1 (τ) and K 2 (τ) in terms of infinite series are found for a generic function F(vertical bar i - j vertical bar ) in the Gaussian orthogonal ensemble (GOE), the Gaussian unitary ensemble (GUE) and in the crossover between them (the almost unitary Gaussian ensemble). The Rosenzweig-Porter and power-law banded matrix ensembles are considered as examples

Explicit Determinants of the RFPrLrR Circulant and RLPrFrL Circulant Matrices Involving Some Famous Numbers

Directory of Open Access Journals (Sweden)

Tingting Xu

2014-01-01

Full Text Available Circulant matrices may play a crucial role in solving various differential equations. In this paper, the techniques used herein are based on the inverse factorization of polynomial. We give the explicit determinants of the RFPrLrR circulant matrices and RLPrFrL circulant matrices involving Fibonacci, Lucas, Pell, and Pell-Lucas number, respectively.

Corpus Linguistics, Network Analysis and Co-occurrence Matrices Corpus Linguistics, Network Analysis and Co-occurrence Matrices

Directory of Open Access Journals (Sweden)

Keith Stuart

2009-12-01

Full Text Available This article describes research undertaken in order to design a methodology for the reticular representation of knowledge of a specific discourse community. To achieve this goal, a representative corpus of the scientific production of the members of this discourse community (Universidad Politécnica de Valencia, UPV was created. The article presents the practical analysis (frequency, keyword, collocation and cluster analysis that was carried out in the initial phases of the study aimed at establishing the theoretical and practical background and framework for our matrix and network analysis of the scientific discourse of the UPV. In the methodology section, the processes that have allowed us to extract from the corpus the linguistic elements needed to develop co-occurrence matrices, as well as the computer tools used in the research, are described. From these co-occurrence matrices, semantic networks of subject and discipline knowledge were generated. Finally, based on the results obtained, we suggest that it may be viable to extract and to represent the intellectual capital of an academic institution using corpus linguistics methods in combination with the formulations of network theory.En este artículo describimos la investigación que se ha desarrollado en el diseño de una metodología para la representación reticular del conocimiento que se genera en el seno de una institución a partir de un corpus representativo de la producción científica de los integrantes de dicha comunidad discursiva, la Universidad Politécnica de Valencia.. Para ello, presentamos las acciones que se realizaron en las fases iniciales del estudio encaminadas a establecer el marco teórico y práctico en el que se inscribe nuestro análisis. En la sección de metodología se describen las herramientas informáticas utilizadas, así como los procesos que nos permitieron disponer de aquellos elementos presentes en el corpus, que nos llevarían al desarrollo de

Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices

Science.gov (United States)

Glaister, P.

2008-01-01

The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander

2015-01-07

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design

Photoluminescence of nanocrystals embedded in oxide matrices

International Nuclear Information System (INIS)

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

2006-12-01

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

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

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

2015-01-01

We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design

Tensor Permutation Matrices in Finite Dimensions

OpenAIRE

Christian, Rakotonirina

2005-01-01

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...

BMP-silk composite matrices heal critically sized femoral defects

NARCIS (Netherlands)

Kirker-Head, C.; Karageorgiou, V.; Hofmann, S.; Fajardo, R.; Betz, O.; Merkle, H.P.; Hilbe, M.; Rechenberg, von B.; McCool, J.; Abrahamsen, L.; Nazarian, A.; Cory, E.; Curtis, M.; Kaplan, D.L.; Meinel, L.

2007-01-01

Clinical drawbacks of bone grafting prompt the search for alternative bone augmentation technologies such as use of growth and differentiation factors, gene therapy, and cell therapy. Osteopromotive matrices are frequently employed for the local delivery and controlled release of these augmentation

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

KAUST Repository

Litvinenko, Alexander

2018-03-12

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

Minimum description length block finder, a method to identify haplotype blocks and to compare the strength of block boundaries.

Science.gov (United States)

Mannila, H; Koivisto, M; Perola, M; Varilo, T; Hennah, W; Ekelund, J; Lukk, M; Peltonen, L; Ukkonen, E

2003-07-01

We describe a new probabilistic method for finding haplotype blocks that is based on the use of the minimum description length (MDL) principle. We give a rigorous definition of the quality of a segmentation of a genomic region into blocks and describe a dynamic programming algorithm for finding the optimal segmentation with respect to this measure. We also describe a method for finding the probability of a block boundary for each pair of adjacent markers: this gives a tool for evaluating the significance of each block boundary. We have applied the method to the published data of Daly and colleagues. The results expose some problems that exist in the current methods for the evaluation of the significance of predicted block boundaries. Our method, MDL block finder, can be used to compare block borders in different sample sets, and we demonstrate this by applying the MDL-based method to define the block structure in chromosomes from population isolates.

Breast cancer cell behaviors on staged tumorigenesis-mimicking matrices derived from tumor cells at various malignant stages

International Nuclear Information System (INIS)

Hoshiba, Takashi; Tanaka, Masaru

2013-01-01

Highlights: •Models mimicking ECM in tumor with different malignancy were prepared. •Cancer cell proliferation was suppressed on benign tumor ECM. •Benign tumor cell proliferation was suppressed on cancerous ECM. •Chemoresistance of cancer cell was enhanced on cancerous ECM. -- Abstract: Extracellular matrix (ECM) has been focused to understand tumor progression in addition to the genetic mutation of cancer cells. Here, we prepared “staged tumorigenesis-mimicking matrices” which mimic in vivo ECM in tumor tissue at each malignant stage to understand the roles of ECM in tumor progression. Breast tumor cells, MDA-MB-231 (invasive), MCF-7 (non-invasive), and MCF-10A (benign) cells, were cultured to form their own ECM beneath the cells and formed ECM was prepared as staged tumorigenesis-mimicking matrices by decellularization treatment. Cells showed weak attachment on the matrices derived from MDA-MB-231 cancer cells. The proliferations of MDA-MB-231 and MCF-7 was promoted on the matrices derived from MDA-MB-231 cancer cells whereas MCF-10A cell proliferation was not promoted. MCF-10A cell proliferation was promoted on the matrices derived from MCF-10A cells. Chemoresistance of MDA-MB-231 cells against 5-fluorouracil increased on only matrices derived from MDA-MB-231 cells. Our results showed that the cells showed different behaviors on staged tumorigenesis-mimicking matrices according to the malignancy of cell sources for ECM preparation. Therefore, staged tumorigenesis-mimicking matrices might be a useful in vitro ECM models to investigate the roles of ECM in tumor progression

Breast cancer cell behaviors on staged tumorigenesis-mimicking matrices derived from tumor cells at various malignant stages

Energy Technology Data Exchange (ETDEWEB)

Hoshiba, Takashi [Graduate School of Science and Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata 992-8510 (Japan); International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044 (Japan); Tanaka, Masaru, E-mail: tanaka@yz.yamagata-u.ac.jp [Graduate School of Science and Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata 992-8510 (Japan)

2013-09-20

Highlights: •Models mimicking ECM in tumor with different malignancy were prepared. •Cancer cell proliferation was suppressed on benign tumor ECM. •Benign tumor cell proliferation was suppressed on cancerous ECM. •Chemoresistance of cancer cell was enhanced on cancerous ECM. -- Abstract: Extracellular matrix (ECM) has been focused to understand tumor progression in addition to the genetic mutation of cancer cells. Here, we prepared “staged tumorigenesis-mimicking matrices” which mimic in vivo ECM in tumor tissue at each malignant stage to understand the roles of ECM in tumor progression. Breast tumor cells, MDA-MB-231 (invasive), MCF-7 (non-invasive), and MCF-10A (benign) cells, were cultured to form their own ECM beneath the cells and formed ECM was prepared as staged tumorigenesis-mimicking matrices by decellularization treatment. Cells showed weak attachment on the matrices derived from MDA-MB-231 cancer cells. The proliferations of MDA-MB-231 and MCF-7 was promoted on the matrices derived from MDA-MB-231 cancer cells whereas MCF-10A cell proliferation was not promoted. MCF-10A cell proliferation was promoted on the matrices derived from MCF-10A cells. Chemoresistance of MDA-MB-231 cells against 5-fluorouracil increased on only matrices derived from MDA-MB-231 cells. Our results showed that the cells showed different behaviors on staged tumorigenesis-mimicking matrices according to the malignancy of cell sources for ECM preparation. Therefore, staged tumorigenesis-mimicking matrices might be a useful in vitro ECM models to investigate the roles of ECM in tumor progression.

Evaluation of hydrophobic materials as matrices for controlled-release drug delivery.

Science.gov (United States)

Quadir, Mohiuddin Abdul; Rahman, M Sharifur; Karim, M Ziaul; Akter, Sanjida; Awkat, M Talat Bin; Reza, Md Selim

2003-07-01

The present study was undertaken to evaluate the effect of different insoluble and erodable wax-lipid based materials and their content level on the release profile of drug from matrix systems. Matrix tablets of theophylline were prepared using carnauba wax, bees wax, stearic acid, cetyl alcohol, cetostearyl alcohol and glyceryl monostearate as rate-retarding agents by direct compression process. The release of theophylline from these hydrophobic matrices was studied over 8-hours in buffer media of pH 6.8. Statistically significant difference was found among the drug release profile from different matrices. The release kinetics was found to be governed by the type and content of hydrophobic materials in the matrix. At lower level of wax matrices (25%), a potential burst release was observed with all the materials being studied. Bees wax could not exert any sustaining action while an extensive burst release was found with carnauba wax at this hydrophobic load. Increasing the concentration of fat-wax materials significantly decreased the burst effect of drug from the matrix. At higher hydrophobic level (50% of the matrix), the rate and extent of drug release was significantly reduced due to increased tortuosity and reduced porosity of the matrix. Cetostearyl alcohol imparted the strongest retardation of drug release irrespective of fat-wax level. Numerical fits indicate that the Higuchi square root of time model was the most appropriate one for describing the release profile of theophylline from hydrophobic matrices. The release mechanism was also explored and explained with biexponential equation. Application of this model indicates that Fickian or case I kinetics is the predominant mechanism of drug release from these wax-lipid matrices. The mean dissolution time (MDT) was calculated for all the formulations and the highest MDT value was obtained with cetostearyl matrix. The greater sustaining activity of cetostearyl alcohol can be attributed to some level of

Melting Behavior of Organic Nanocrystals Grown in Sol-gel Matrices

International Nuclear Information System (INIS)

Sanz, N.; Boudet, A.; Ibanez, A.

2002-01-01

We have characterized the thermal stability of organic nanocrystals grown in the pores of sol-gel matrices. The structure has been measured with transmission electron microscopy (TEM) analysis. Depending on the nature of organic molecules and sol-gel matrices, we have modified the dye-matrix interactions and the interfacial structure between nanocrystals and gel-glasses. When the dye-matrix interactions are weak (Van der Waals' bonds), the corresponding interfacial structure observed by TEM is sharp and the nanocrystals melt below the bulk melting point. On the other hand, when the dye-matrix interactions are strong (hydrogen bonds), the interfacial structure is fuzzy and a great superheating of organic nanocrystals is observed in comparison to the bulk melting point of the dye

The influence of inorganic matrices on the decomposition of Eucalyptus litter

International Nuclear Information System (INIS)

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

1997-01-01

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

On the representation matrices of the spin permutation group. [for atomic and molecular electronic structures

Science.gov (United States)

Wilson, S.

1977-01-01

A method is presented for the determination of the representation matrices of the spin permutation group (symmetric group), a detailed knowledge of these matrices being required in the study of the electronic structure of atoms and molecules. The method is characterized by the use of two different coupling schemes. Unlike the Yamanouchi spin algebraic scheme, the method is not recursive. The matrices for the fundamental transpositions can be written down directly in one of the two bases. The method results in a computationally significant reduction in the number of matrix elements that have to be stored when compared with, say, the standard Young tableaux group theoretical approach.

Completely X-symmetric S-matrices corresponding to theta functions

International Nuclear Information System (INIS)

Chudnovsky, D.V.

1981-01-01

We consider the realization of the classical Weyl commutation relations using THETA-functions. The representations of the Heisenberg group enable us to realize completely symmetric factorized S-matrices in terms of THETA-functions corresponding to the torsion subgroup of an abelian variety. (orig.)

Designer matrices for intestinal stem cell and organoid culture

NARCIS (Netherlands)

Gjorevski, Nikolce; Sachs, Norman; Manfrin, Andrea; Giger, Sonja; Bragina, Maiia E.; Ordóñez-Morán, Paloma; Clevers, Hans; Lutolf, Matthias P.

2016-01-01

Epithelial organoids recapitulate multiple aspects of real organs, making them promising models of organ development, function and disease. However, the full potential of organoids in research and therapy has remained unrealized, owing to the poorly defined animal-derived matrices in which they are

High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices

Science.gov (United States)

Dunham, Benjamin Z.

This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions--most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series--without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed "stencils," each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the "forward mode" is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N--i.e., O(1)--the N x N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive--e.g., a N x N x N rank-three tensor can be found in O(N2). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of

Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander

2017-09-03

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

Fast Approximate Joint Diagonalization Incorporating Weight Matrices

Czech Academy of Sciences Publication Activity Database

Tichavský, Petr; Yeredor, A.

2009-01-01

Roč. 57, č. 3 (2009), s. 878-891 ISSN 1053-587X R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : autoregressive processes * blind source separation * nonstationary random processes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.212, year: 2009 http://library.utia.cas.cz/separaty/2009/SI/tichavsky-fast approximate joint diagonalization incorporating weight matrices.pdf

Gaussian density matrices: Quantum analogs of classical states

International Nuclear Information System (INIS)

Mann, A.; Revzen, M.

1993-01-01

We study quantum analogs of clasical situations, i.e. quantum states possessing some specific classical attribute(s). These states seem quite generally, to have the form of gaussian density matrices. Such states can always be parametrized as thermal squeezed states (TSS). We consider the following specific cases: (a) Two beams that are built from initial beams which passed through a beam splitter cannot, classically, be distinguished from (appropriately prepared) two independent beams that did not go through a splitter. The only quantum states possessing this classical attribute are TSS. (b) The classical Cramer's theorem was shown to have a quantum version (Hegerfeldt). Again, the states here are Gaussian density matrices. (c) The special case in the study of the quantum version of Cramer's theorem, viz. when the state obtained after partial tracing is a pure state, leads to the conclusion that all states involved are zero temperature limit TSS. The classical analog here are gaussians of zero width, i.e. all distributions are δ functions in phase space. (orig.)

The structure of completely positive matrices according to their CP-rank and CP-plus-rank

NARCIS (Netherlands)

Dickinson, Peter James Clair; Bomze, Immanuel M.; Still, Georg J.

2015-01-01

We study the topological properties of the cp-rank operator $\\mathrm{cp}(A)$ and the related cp-plus-rank operator $\\mathrm{cp}^+(A)$ (which is introduced in this paper) in the set $\\mathcal{S}^n$ of symmetric $n\\times n$-matrices. For the set of completely positive matrices, $\\mathcal{CP}^n$, we

Generalisations of Fisher Matrices

Directory of Open Access Journals (Sweden)

Alan Heavens

2016-06-01

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

Polyphosphazene functionalized polyester fiber matrices for tendon tissue engineering: in vitro evaluation with human mesenchymal stem cells

International Nuclear Information System (INIS)

Peach, M Sean; James, Roshan; Toti, Udaya S; Deng, Meng; Laurencin, Cato T; Kumbar, Sangamesh G; Morozowich, Nicole L; Allcock, Harry R

2012-01-01

Poly[(ethyl alanato) 1 (p-methyl phenoxy) 1 ] phosphazene (PNEA-mPh) was used to modify the surface of electrospun poly(ε-caprolactone) (PCL) nanofiber matrices having an average fiber diameter of 3000 ± 1700 nm for the purpose of tendon tissue engineering and augmentation. This study reports the effect of polyphosphazene surface functionalization on human mesenchymal stem cell (hMSC) adhesion, cell-construct infiltration, proliferation and tendon differentiation, as well as long term cellular construct mechanical properties. PCL fiber matrices functionalized with PNEA-mPh acquired a rougher surface morphology and led to enhanced cell adhesion as well as superior cell-construct infiltration when compared to smooth PCL fiber matrices. Long-term in vitro hMSC cultures on both fiber matrices were able to produce clinically relevant moduli. Both fibrous constructs expressed scleraxis, an early tendon differentiation marker, and a bimodal peak in expression of the late tendon differentiation marker tenomodulin, a pattern that was not observed in PCL thin film controls. Functionalized matrices achieved a more prominent tenogenic differentiation, possessing greater tenomodulin expression and superior phenotypic maturity according to the ratio of collagen I to collagen III expression. These findings indicate that PNEA-mPh functionalization is an efficient method for improving cell interactions with electrospun PCL matrices for the purpose of tendon repair. (paper)

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

KAUST Repository

Litvinenko, Alexander

2017-01-01

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

Matrices funcionales e integración morfológica

Directory of Open Access Journals (Sweden)

Barbeito Andrés, Jimena

2012-01-01

Full Text Available Los estudios ontogénicos permiten conocer cómo se generan las diferencias morfológicas que encontramos en adultos. Éstas resultan de la asociación diferencial entre rasgos morfológicos, lo que puede deberse tanto a factores del desarrollo como funcionales. De acuerdo a la hipótesis funcional, los cambios en las estructuras óseas son consecuencia de la influencia de tejidos blandos, cavidades y órganos (matriz funcional. En este trabajo se analizaron dos estructuras craneofaciales: la bóveda, formada por varios huesos y una matriz funcional homogénea y el maxilar, un hueso único afectado por diversas matrices, para poner a prueba la hipótesis que postula que durante la ontogenia cambian los patrones de covariación. Se relevaron puntos craneofaciales sobre 267 cráneos de adultos y subadultos, se aplicó Análisis de Componentes Principales para establecer la variación en forma a lo largo de la ontogenia y se realizó un análisis de correlación entre las matrices de covarianza de las sucesivas edades para evaluar el cambio en los patrones de integración morfológica. Los resultados indicaron que mientras en la bóveda los patrones de covariación no cambian durante la ontogenia, esto sí ocurre en el maxilar. Los patrones de covariación de estas estructuras se comportarían en relación a la cantidad y características de las matrices asociadas.

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

Directory of Open Access Journals (Sweden)

Sunita Nayak

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

The algebraic structure of lax equations for infinite matrices

NARCIS (Netherlands)

Helminck, G.F.

2002-01-01

In this paper we discuss the algebraic structure of the tower of differential difference equations that one can associate with any commutative subalgebra of $M_k(\\mathbb{C})$. These equations can be formulated conveniently in so-called Lax equations for infinite upper- resp. lowertriangular matrices

Mechanical behaviour and diffusion of gas during neutron irradiation of actinides in ceramic inert matrices

NARCIS (Netherlands)

Neeft, E.A.C.

2004-01-01

Fission of actinides from nuclear waste in inert matrices (materials without uranium) can reduce the period in time that nuclear waste is more radiotoxic than uranium ore that is the rock from which ordinary reactor fuel is made. A pioneering study is performed with the inert matrices: MgO, MgAl2O4,

Determinants of (–1,1-matrices of the skew-symmetric type: a cocyclic approach

Directory of Open Access Journals (Sweden)

Álvarez Víctor

2015-01-01

Full Text Available An n by n skew-symmetric type (-1; 1-matrix K =[ki;j ] has 1’s on the main diagonal and ±1’s elsewhere with ki;j =-kj;i . The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n ≡ 0 mod 4 (skew-Hadamard matrices, but for n ≡ 2 mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (-1; 1-matrices of skew type. Some explicit calculations have been done up to t =11. To our knowledge, the upper bounds on the maximal determinant in orders 18 and 22 have been improved.

Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems

Directory of Open Access Journals (Sweden)

Emran Tohidi

2013-01-01

Full Text Available The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.

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

Science.gov (United States)

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

2017-08-01

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

Minimally Adhesive, Advanced Non-toxic Coatings of Dendrimeric Catalysts in Sol-Gel Matrices

Science.gov (United States)

2015-10-19

Catalysts in Sol -Gel Matrices 5a. CONTRACT NUMBER 5b. GRANT NUMBER N00014-09-1-0217 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Detty, Michael R. 5d...Technical Report for ONR N00014-09-1-0217 Minimally Adhesive, Advanced Non-toxic Coatings of Dendrimeric Catalysts in Sol -Gel Matrices Michael R. Detty, PI...Environmentally benign sol -gel antifouling and foul-releasing coatings. Ace. Chem. Res. 2014, 47, 678-687. 11) Alberto, E. E.; Müller, L. M

Nanocomposites from Stable Dispersions of Carbon Nanotubes in Polymeric Matrices Using Dispersion Interaction

Science.gov (United States)

Wise, Kristopher Eric (Inventor); Park, Cheol (Inventor); Kang, Jin Ho (Inventor); Siochi, Emilie J. (Inventor); Harrison, Joycelyn S. (Inventor)

2016-01-01

Stable dispersions of carbon nanotubes (CNTs) in polymeric matrices include CNTs dispersed in a host polymer or copolymer whose monomers have delocalized electron orbitals, so that a dispersion interaction results between the host polymer or copolymer and the CNTs dispersed therein. Nanocomposite products, which are presented in bulk, or when fabricated as a film, fiber, foam, coating, adhesive, paste, or molding, are prepared by standard means from the present stable dispersions of CNTs in polymeric matrices, employing dispersion interactions, as presented hereinabove.

Coherence and extensions of stochastic matrices

Directory of Open Access Journals (Sweden)

Angelo Gilio

1995-11-01

Full Text Available In this paper a review of some general results on coherence of conditional probability assessments is given. Then, a necessary and sufficient condition on coherence of two finite families of discrete conditianal probability distributions, represented by two stochastic matrices P and Q, is obtained. Moreover, the possible extensions of the assessment (P,Q to the marginal distributions are examined and explicit formulas for them are given in some special case. Finally, a general algorithm to check coherence of (P,Q and to derive its extensions is proposed.

Generalized Block Failure

DEFF Research Database (Denmark)

Jönsson, Jeppe

2015-01-01

Block tearing is considered in several codes as a pure block tension or a pure block shear failure mechanism. However in many situations the load acts eccentrically and involves the transfer of a substantial moment in combination with the shear force and perhaps a normal force. A literature study...... shows that no readily available tests with a well-defined substantial eccentricity have been performed. This paper presents theoretical and experimental work leading towards generalized block failure capacity methods. Simple combination of normal force, shear force and moment stress distributions along...... yield lines around the block leads to simple interaction formulas similar to other interaction formulas in the codes....

A Comparison of Teacher Stress and School Climate across Schools with Different Matric Success Rates

Science.gov (United States)

Milner, Karen; Khoza, Harriet

2008-01-01

Our aim was to investigate differences in teacher stress and perceptions of school climate among teachers from schools with differing matriculation success rates in the Limpopo province of South Africa. Two schools with matric pass rates of 100% and two schools with matric pass rates of less than 25% were selected from a list of schools provided…

Numerical stability in problems of linear algebra.

Science.gov (United States)

Babuska, I.

1972-01-01

Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

Resistant lower rank approximation of matrices by iterative majorization

NARCIS (Netherlands)

Verboon, Peter; Heiser, Willem

2011-01-01

It is commonly known that many techniques for data analysis based on the least squares criterion are very sensitive to outliers in the data. Gabriel and Odoroff (1984) suggested a resistant approach for lower rank approximation of matrices. In this approach, weights are used to diminish the

Data for constructing insect genome content matrices for phylogenetic analysis and functional annotation

Directory of Open Access Journals (Sweden)

Jeffrey Rosenfeld

2016-03-01

Full Text Available Twenty one fully sequenced and well annotated insect genomes were used to construct genome content matrices for phylogenetic analysis and functional annotation of insect genomes. To examine the role of e-value cutoff in ortholog determination we used scaled e-value cutoffs and a single linkage clustering approach.. The present communication includes (1 a list of the genomes used to construct the genome content phylogenetic matrices, (2 a nexus file with the data matrices used in phylogenetic analysis, (3 a nexus file with the Newick trees generated by phylogenetic analysis, (4 an excel file listing the Core (CORE genes and Unique (UNI genes found in five insect groups, and (5 a figure showing a plot of consistency index (CI versus percent of unannotated genes that are apomorphies in the data set for gene losses and gains and bar plots of gains and losses for four consistency index (CI cutoffs.

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

Science.gov (United States)

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

2010-02-01

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

Large-Capacity Three-Party Quantum Digital Secret Sharing Using Three Particular Matrices Coding

International Nuclear Information System (INIS)

Lai Hong; Tao Li; Liu Zhi-Ming; Luo Ming-Xing; Pieprzyk, Josef; Orgun, Mehmet A.

2016-01-01

In this paper, we develop a large-capacity quantum digital secret sharing (QDSS) scheme, combined the Fibonacci- and Lucas-valued orbital angular momentum (OAM) entanglement with the recursive Fibonacci and Lucas matrices. To be exact, Alice prepares pairs of photons in the Fibonacci- and Lucas-valued OAM entangled states, and then allocates them to two participants, say, Bob and Charlie, to establish the secret key. Moreover, the available Fibonacci and Lucas values from the matching entangled states are used as the seed for generating the Fibonacci and Lucas matrices. This is achieved because the entries of the Fibonacci and Lucas matrices are recursive. The secret key can only be obtained jointly by Bob and Charlie, who can further recover the secret. Its security is based on the facts that nonorthogonal states are indistinguishable, and Bob or Charlie detects a Fibonacci number, there is still a twofold uncertainty for Charlie' (Bob') detected value. (paper)

Diclofenac sodium sustained release hot melt extruded lipid matrices.

Science.gov (United States)

Vithani, K; Cuppok, Y; Mostafa, S; Slipper, I J; Snowden, M J; Douroumis, D

2014-08-01

Sustained release diclofenac sodium (Df-Na) solid lipid matrices with Compritol® 888 ATO were developed in this study. The drug/lipid powders were processed via cold and hot melt extrusion at various drug loadings. The influence of the processing temperatures, drug loading and the addition of excipients on the obtained dissolution rates was investigated. The physicochemical characterization of the extruded batches showed the existence of crystalline drug in the extrudates with a small amount being solubilized in the lipid matrix. The drug content and uniformity on the tablet surface were also investigated by using energy dispersive X-ray microanalysis. The dissolution rates were found to depend on the actual Df-Na loading and the nature of the added excipients, while the effect of the processing temperatures was negligible. The dissolution mechanism of all extruded formulations followed Peppas-Korsemeyer law, based on the estimated determination coefficients and the dissolution constant rates, indicating drug diffusion from the lipid matrices.

Determination of chromium in biological matrices by neutron activation

International Nuclear Information System (INIS)

McClendon, L.T.

1978-01-01

Chromium is recognized to be an essential trace element in several biological systems. It exists in many biological materials in a variety of chemical forms and very low concentration levels which cause problems for many analytical techniques. Both instrumental and destructive neutron activation analysis were used to determine the chromium concentration in Orchard Leaves, SRM 1571, Brewers Yeast, SRM 1569, and Bovine Liver, SRM 1577. Some of the problems inherent with determining chromium in certain biological matrices and the data obtained here at the National Bureau of Standards using this technique are discussed. The results obtained from dissolution of brewers yeast in a closed system as described in the DNAA procedure are in good agreement with the INAA results. The same phenomenon existed in the determination of chromium in bovine liver. The radiochemical procedure described for chromium (DNAA) provides the analyst with a simple, rapid and selective technique for chromium determination in a variety of matrices. (T.G.)

Epidural block

Science.gov (United States)

... page: //medlineplus.gov/ency/patientinstructions/000484.htm Epidural block - pregnancy To use the sharing features on this page, please enable JavaScript. An epidural block is a numbing medicine given by injection (shot) ...

Random volumes from matrices

Energy Technology Data Exchange (ETDEWEB)

Fukuma, Masafumi; Sugishita, Sotaro; Umeda, Naoya [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)

2015-07-17

We propose a class of models which generate three-dimensional random volumes, where each configuration consists of triangles glued together along multiple hinges. The models have matrices as the dynamical variables and are characterized by semisimple associative algebras A. Although most of the diagrams represent configurations which are not manifolds, we show that the set of possible diagrams can be drastically reduced such that only (and all of the) three-dimensional manifolds with tetrahedral decompositions appear, by introducing a color structure and taking an appropriate large N limit. We examine the analytic properties when A is a matrix ring or a group ring, and show that the models with matrix ring have a novel strong-weak duality which interchanges the roles of triangles and hinges. We also give a brief comment on the relationship of our models with the colored tensor models.

Factoring symmetric indefinite matrices on high-performance architectures

Science.gov (United States)

Jones, Mark T.; Patrick, Merrell L.

1990-01-01

The Bunch-Kaufman algorithm is the method of choice for factoring symmetric indefinite matrices in many applications. However, the Bunch-Kaufman algorithm does not take advantage of high-performance architectures such as the Cray Y-MP. Three new algorithms, based on Bunch-Kaufman factorization, that take advantage of such architectures are described. Results from an implementation of the third algorithm are presented.

New sample treatment strategies for the determination of organic contaminants in environmental matrices.

OpenAIRE

Casas Ferreira, Ana María

2011-01-01

[ES] El objeto general de esta memoria consiste en proponer y desarrollar nuevas estrategias de tratamiento de muestra para la determinación de contaminantes orgánicos en matrices medioambientales. En muchos casos, cuando se trabaja con diferentes matrices, tales como aguas o suelos, es necesaria la utilización de técnicas de pretratamiento de muestra previas al análisis instrumental, cuyo objetivo principal es aislar los analitos de interés del resto de componentes presentes en la matriz...

Recent advances in sample preparation methods for analysis of endocrine disruptors from various matrices.

Science.gov (United States)

Singh, Baljinder; Kumar, Ashwini; Malik, Ashok Kumar

2014-01-01

Due to the high toxicity of endocrine disruptors (EDs), studies are being undertaken to design effective techniques for separation and detection of EDs in various matrices. Recently, research activities in this area have shown that a diverse range of chromatographic techniques are available for the quantification and analysis of EDs. Therefore, on the basis of significant, recent original publications, we aimed at providing an overview of different separation and detection methods for the determination of trace-level concentrations of selected EDs. The biological effects of EDs and current pretreatment techniques applied to EDs are also discussed. Various types of chromatographic techniques are presented for quantification, highlighting time- and cost-effective techniques that separate and quantify trace levels of multiple EDs from various environmental matrices. Reports related to methods for the quantification of EDs from various matrices primarily published since 2008 have been cited.

Modelling the Long Term Leaching Behaviour of 137CS from Different Stabilized Waste Matrices

International Nuclear Information System (INIS)

El-Kamash, A.M.

2013-01-01

Leaching characteristics of ''1''3''7Cs from immobilized waste matrices in different cement-based grouts have been assessed to investigate the influence of the additives on the leaching behavior of the solid waste matrices. The International Atomic Energy's Agency (IAEA) standard leach method has been employed to study the leach pattern of 137 Cs radionuclide from the immobilized waste form. The examination of the leaching data revealed that clay additives reduces the leach rate for the studied radionuclide. The controlling leaching mechanism has been studied and the transport parameters were calculated for all studied waste matrices. Simplified analytical models have been derived to predict the Cumulative Leach Fraction (CLF) of radionuclides over the studied experimental period. These simplified research models could be used as a screening tool to assess the performance of the waste matrix under repository conditions. (author)

Predictability of blocking

International Nuclear Information System (INIS)

Tosi, E.; Ruti, P.; Tibaldi, S.; D'Andrea, F.

1994-01-01

Tibaldi and Molteni (1990, hereafter referred to as TM) had previously investigated operational blocking predictability by the ECMWF model and the possible relationships between model systematic error and blocking in the winter season of the Northern Hemisphere, using seven years of ECMWF operational archives of analyses and day 1 to 10 forecasts. They showed that fewer blocking episodes than in the real atmosphere were generally simulated by the model, and that this deficiency increased with increasing forecast time. As a consequence of this, a major contribution to the systematic error in the winter season was shown to derive from the inability of the model to properly forecast blocking. In this study, the analysis performed in TM for the first seven winter seasons of the ECMWF operational model is extended to the subsequent five winters, during which model development, reflecting both resolution increases and parametrisation modifications, continued unabated. In addition the objective blocking index developed by TM has been applied to the observed data to study the natural low frequency variability of blocking. The ability to simulate blocking of some climate models has also been tested

Immobilization of plutonium from solutions on porous matrices by the method of high temperature sorption

Energy Technology Data Exchange (ETDEWEB)

Nardova, A.K.; Filippov, E.A. [All Research Institute of Chemical Technologies, Moscow (Russian Federation); Glagolenko, Y.B. [and others

1996-05-01

This report presents the results of investigations of plutonium immobilization from solutions on inorganic matrices with the purpose of producing a solid waste form. High-temperature sorption is described which entails the adsorption of radionuclides from solutions on porous, inorganic matrices, as for example silica gel. The solution is brought to a boil with additional thermal process (calcination) of the saturated granules.

Diagonal K-matrices and transfer matrix eigenspectra associated with the G(1)2 R-matrix

International Nuclear Information System (INIS)

Yung, C.M.; Batchelor, M.T.

1995-01-01

We find all the diagonal K-matrices for the R-matrix associated with the minimal representation of the exceptional affine algebra G (1) 2 . The corresponding transfer matrices are diagonalized with a variation of the analytic Bethe ansatz. We find many similarities with the case of the Izergin-Korepin R-matrix associated with the affine algebra A (2) 2 . ((orig.))

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

International Nuclear Information System (INIS)

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

1980-01-01

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

Noisy covariance matrices and portfolio optimization II

Science.gov (United States)

Pafka, Szilárd; Kondor, Imre

2003-03-01

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

Study of remobilization polycyclic aromatic hydrocarbons (PAHs) in contaminated matrices

International Nuclear Information System (INIS)

Belkessam, L.; Vessigaud, S.; Laboudigue, A.; Vessigaud, S.; Perrin-Ganier, C.; Schiavon, M.; Denys, S.

2005-01-01

Polycyclic aromatic hydrocarbons (PAHs) originate from many pyrolysis processes. They are widespread environmental pollutants because some of them present toxic and genotoxic properties. In coal pyrolysis sites such as former manufactured gas plants and coke production plants, coal tar is a major source of PAHs. The management of such sites requires better understanding of the mechanisms that control release of PAHs to the biosphere. Determining total PAH concentrations is not sufficient since it does not inform about the pollutants availability to environmental processes. The fate and transport of PAHs in soil are governed by sorption and microbial processes which are well documented. Globally, enhancing retention of the compounds by a solid matrix reduces the risk of pollutant dispersion, but decreases their accessibility to microbial microflora. Conversely, the remobilization of organics from contaminated solid matrices represents a potential hazard since these pollutants can reach groundwater resources. However the available data are often obtained from laboratory experiments in which many field parameters can not be taken into account (long term, temperature, co-pollution, ageing phenomenon, heterogenous distribution of pollution). The present work focuses on the influence assessment and understanding of some of these parameters on PAHs remobilization from heavily polluted matrices in near-field conditions (industrial contaminated matrices, high contact time, ..). Results concerning effects of temperature and physical state of pollution (dispersed among the soil or condensed in small clusters or in coal tar) are presented. (authors)

Simplifications of rational matrices by using UML

OpenAIRE

Tasić, Milan B.; Stanimirović, Ivan P.

2013-01-01

The simplification process on rational matrices consists of simplifying each entry represented by a rational function. We follow the classic approach of dividing the numerator and denominator polynomials by their common GCD polynomial, and provide the activity diagram in UML for this process. A rational matrix representation as the quotient of a polynomial matrix and a polynomial is also discussed here and illustrated via activity diagrams. Also, a class diagram giving the links between the c...

Growing Pereskia aculeata under intermittent irrigation according to levels of matric potential reduction

Directory of Open Access Journals (Sweden)

Carla Regina Amorim dos Anjos Queiroz

2015-03-01

Full Text Available Pereskia aculeata Mill., popularly known in Brazil as “Ora-pro-nobis”, is an unconventional edible vegetable. Taking into account its potential for agronomic cultivation, this study aimed to evaluate the growth response of this plant under intermittent drought through controlled reductions in the substrate matric potential, in a greenhouse. Treatments consisted of adding to the pots a volume of water to raise the matric potential to -5 kPa, according to the water retention curve in the substrate, whenever the mean substrate matric potential reached values between -10 kPa and -70 kPa, depending on the treatment. At 140 days after transplanting, leaf area and dry mass of leaves, stems and roots were determined. The intermittent reduction of the matric potential in the root zone of “Ora-pro-nobis” affected less the dry mass accumulation in leaves (reduction of 21.4% than in stems (reduction of 48.1% and roots (reduction of 63.7%, and that is interesting because leaves are the main commercial product of this plant. The treatment also modified the proportionality of dry mass allocation among plant parts and reduced the photosynthetic efficiency of leaves, fact evidenced by the linear increase of the specific leaf area (0.63 cm2 g-1kPa-1 and leaf area ratio (0.39 cm-2 g-1kPa-1, although not affecting directly the leaf area.

Human elastin polypeptides improve the biomechanical properties of three-dimensional matrices through the regulation of elastogenesis.

Science.gov (United States)

Boccafoschi, Francesca; Ramella, Martina; Sibillano, Teresa; De Caro, Liberato; Giannini, Cinzia; Comparelli, Roberto; Bandiera, Antonella; Cannas, Mario

2015-03-01

The replacement of diseased tissues with biological substitutes with suitable biomechanical properties is one of the most important goal in tissue engineering. Collagen represents a satisfactory choice for scaffolds. Unfortunately, the lack of elasticity represents a restriction to a wide use of collagen for several applications. In this work, we studied the effect of human elastin-like polypeptide (HELP) as hybrid collagen-elastin matrices. In particular, we studied the biomechanical properties of collagen/HELP scaffolds considering several components involved in ECM remodeling (elastin, collagen, fibrillin, lectin-like receptor, metalloproteinases) and cell phenotype (myogenin, myosin heavy chain) with particular awareness for vascular tissue engineering applications. Elastin and collagen content resulted upregulated in collagen-HELP matrices, even showing an improved structural remodeling through the involvement of proteins to a ECM remodeling activity. Moreover, the hybrid matrices enhanced the contractile activity of C2C12 cells concurring to improve the mechanical properties of the scaffold. Finally, small-angle X-ray scattering analyses were performed to enable a very detailed analysis of the matrices at the nanoscale, comparing the scaffolds with native blood vessels. In conclusion, our work shows the use of recombinant HELP, as a very promising complement able to significantly improve the biomechanical properties of three-dimensional collagen matrices in terms of tensile stress and elastic modulus. © 2014 Wiley Periodicals, Inc.

Homogeneous bilateral block shifts

Indian Academy of Sciences (India)

Douglas class were classified in [3]; they are unilateral block shifts of arbitrary block size (i.e. dim H(n) can be anything). However, no examples of irreducible homogeneous bilateral block shifts of block size larger than 1 were known until now.

Construction of MDS self-dual codes from orthogonal matrices

OpenAIRE

Shi, Minjia; Sok, Lin; Solé, Patrick

2016-01-01

In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.

Computing the sparse matrix vector product using block-based kernels without zero padding on processors with AVX-512 instructions

Directory of Open Access Journals (Sweden)

Bérenger Bramas

2018-04-01

Full Text Available The sparse matrix-vector product (SpMV is a fundamental operation in many scientific applications from various fields. The High Performance Computing (HPC community has therefore continuously invested a lot of effort to provide an efficient SpMV kernel on modern CPU architectures. Although it has been shown that block-based kernels help to achieve high performance, they are difficult to use in practice because of the zero padding they require. In the current paper, we propose new kernels using the AVX-512 instruction set, which makes it possible to use a blocking scheme without any zero padding in the matrix memory storage. We describe mask-based sparse matrix formats and their corresponding SpMV kernels highly optimized in assembly language. Considering that the optimal blocking size depends on the matrix, we also provide a method to predict the best kernel to be used utilizing a simple interpolation of results from previous executions. We compare the performance of our approach to that of the Intel MKL CSR kernel and the CSR5 open-source package on a set of standard benchmark matrices. We show that we can achieve significant improvements in many cases, both for sequential and for parallel executions. Finally, we provide the corresponding code in an open source library, called SPC5.

A structural analysis of a regional economy using social accounting matrices 1990-1999

OpenAIRE

Lima, M. Carmen; Cardenete Flores, Manuel Alejandro; Hewings, Geoffrey J.D.; Vallés Ferrer, José

2004-01-01

Las matrices de contabilidad social (MCS) son un instrumento que permite ampliar la información proporcionada por el análisis imput-output al recoger además de las relaciones intersectoriales de una economía, el comportamiento de los consumidores, el sector público o el sector exterior, logrando así completar el flujo circular de la renta. En este trabajo utilizamos las matrices de contabilidad social para Andalucía correspondientes a los años 1990, 1995 y 1999 elaboradas en trabajos previos....

The Golden mean, Fibonacci matrices and partial weakly super-increasing sources

International Nuclear Information System (INIS)

Esmaeili, M.; Gulliver, T.A.; Kakhbod, A.

2009-01-01

A source S={s 1 ,s 2 ,...}, with at least i+1 source symbols, having a binary Huffman code with codeword lengths satisfying l 1 =1,l 2 =2,...,l i =i, is called an i-level partial weakly super-increasing (PWSI) source. Connections between these sources, Fibonacci matrices and the Golden mean are studied. It is shown that the Euclidean projection of the distributions associated with these sources is given by Fibonacci-Hessenberg matrices. While there is no upper bound on the expected codeword length of Huffman codes representing PWSI sources (and hence no upper bound on their entropy), the Fibonacci sequence and the Golden mean (1+√(5))/2 provide a lower bound on the maximum expected codeword length of these codes.

Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice

NARCIS (Netherlands)

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

2017-01-01

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

EFFECT OF GALACTO-OLIGOSACCHARIDES:MALTODEXTRIN MATRICES ON THE RECOVERY OF LACTOBACILLUS PLANTARUM AFTER SPRAY-DRYING

Directory of Open Access Journals (Sweden)

Natalia eSosa

2016-05-01

Full Text Available In this work maltodextrins were added to commercial GOS in a 1:1 ratio and their thermophysical characteristics were analyzed. GOS:MD solutions were then used as matrices during spray-drying of L. plantarum CIDCA 83114. The obtained powders were equilibrated at different relative humidities (RH and stored at 5 and 20ºC for 12 weeks, or at 30ºC for 6 weeks.The Tgs of GOS:MD matrices were about 20-30oC higher than those of GOS at RH within 11 and 52%. A linear relation between the spin-spin relaxation time (T2 and T-Tg parameter was observed for GOS:MD matrices equilibrated at 11, 22, 33 and 44% RH at 5, 20 and 30ºC.Spray-drying of L. plantarum CIDCA 83114 in GOS:MD matrices allowed the recovery of 93% microorganisms. In contrast, only 64% microorganisms were recovered when no MD were included in the dehydration medium. Survival of L. plantarum CIDCA 83114 during storage showed the best performance for bacteria stored at 5oC. In a further step, the slopes of the linear regressions provided information about the rate of microbial inactivation for each storage condition (k values. This information can be useful to calculate the shelf-life of spray-dried starters stored at different temperatures and RH. Using GOS:MD matrices as a dehydration medium enhanced the recovery of L. plantarum CIDCA 83114 after spray-drying. This strategy allowed for the first time the spray-drying stabilization of a potentially probiotic strain in the presence of GOS.

Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification

Directory of Open Access Journals (Sweden)

Jonas Maziero

2016-01-01

Full Text Available Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a reasonable option. Notwithstanding, as we demonstrate in this paper, some algebraic manipulations before programming can reduce considerably their computational complexity. Besides, we provide Fortran code to generate generalized Gell-Mann matrices and to compute the optimized and unoptimized versions of associated Bloch’s vectors and correlation matrix in the case of bipartite quantum systems. As a code test and application example, we consider the calculation of Hilbert-Schmidt quantum discords.

Comparison of Individual Performance in Intelligence Tests WAIS III and RPM (Raven's Progressive Matrices)

OpenAIRE

Petrů, Vít

2017-01-01

This thesis deals with replacement of performative scale of Wechsler Adult Intelligence Scale (3rd revision) through Raven's Standard Progressive Matrices and Advanced Progressive Matrices. In the theoretical part introduces the concepts of intelligence, approaches to its exploration and intelligence tests. The theoretical part is also devoted to the description of the used methods and presents an overview of the research on a similar theme as this work. In the empirical part of the thesis is...

Constructing valid density matrices on an NMR quantum information processor via maximum likelihood estimation

Energy Technology Data Exchange (ETDEWEB)

Singh, Harpreet; Arvind; Dorai, Kavita, E-mail: kavita@iisermohali.ac.in

2016-09-07

Estimation of quantum states is an important step in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not positive, and hence not physically acceptable. How do we ensure that at all stages of reconstruction, we keep the density matrix positive? Recently a method has been suggested based on maximum likelihood estimation, wherein the density matrix is guaranteed to be positive definite. We experimentally implement this protocol on an NMR quantum information processor. We discuss several examples and compare with the standard method of state estimation. - Highlights: • State estimation using maximum likelihood method was performed on an NMR quantum information processor. • Physically valid density matrices were obtained every time in contrast to standard quantum state tomography. • Density matrices of several different entangled and separable states were reconstructed for two and three qubits.

Multivariate analysis of nutritional information of foodstuff of plant origin for the selection of representative matrices for the analysis of pesticide residues

International Nuclear Information System (INIS)

Neves Bettencourt da Silva, Ricardo Jorge; Gomes Ferreira Crujo Camoes, Maria Filomena

2010-01-01

Testing safety of foodstuffs of plant origin involves the analysis of hundreds of pesticide residues. This control is only cost-effective through the use of methods validated for the analysis of many thousands of analyte/matrix combinations. Several documents propose representative matrices of groups of matrices from which the validity of the analytical method can be extrapolated to the represented matrices after summarised experimental check of within group method performance homogeneity. Those groups are based on an evolved expert consensus based on the empirical knowledge on the current analytical procedures; they are not exhaustive, they are not objectively defined and they propose a large list of representative matrices which makes their application difficult. This work proposes grouping 240 matrices, based on the nutritional composition pattern equivalence of the analytical portion right after hydration and before solvent extraction, aiming at defining groups that observe method performance homogeneity. This grouping was based on the combined outcome of three multivariate tools, namely: Principal Component Analysis, Hierarchical Cluster Analysis and K-Mean Cluster Analysis. These tools allowed the selection of eight groups for which representative matrices with average characteristics and objective criteria to test inclusion of new matrices were established. The proposed matrices groups are homogeneous to nutritional data not considered in their definition but correlated with the studied multivariate nutritional pattern. The developed grouping that must be checked with experimental test before use was tested against small deviations in food composition and for the integration of new matrices.

Detection block

International Nuclear Information System (INIS)

Bezak, A.

1987-01-01

A diagram is given of a detection block used for monitoring burnup of nuclear reactor fuel. A shielding block is an important part of the detection block. It stabilizes the fuel assembly in the fixing hole in front of a collimator where a suitable gamma beam is defined for gamma spectrometry determination of fuel burnup. The detector case and a neutron source case are placed on opposite sides of the fixing hole. For neutron measurement for which the water in the tank is used as a moderator, the neutron detector-fuel assembly configuration is selected such that neutrons from spontaneous fission and neutrons induced with the neutron source can both be measured. The patented design of the detection block permits longitudinal travel and rotation of the fuel assembly to any position, and thus more reliable determination of nuclear fuel burnup. (E.S.). 1 fig

Multimodal approach to characterization of hydrophilic matrices manufactured by wet and dry granulation or direct compression methods.

Science.gov (United States)

Kulinowski, Piotr; Woyna-Orlewicz, Krzysztof; Obrał, Jadwiga; Rappen, Gerd-Martin; Haznar-Garbacz, Dorota; Węglarz, Władysław P; Jachowicz, Renata; Wyszogrodzka, Gabriela; Klaja, Jolanta; Dorożyński, Przemysław P

2016-02-29

The purpose of the research was to investigate the effect of the manufacturing process of the controlled release hydrophilic matrix tablets on their hydration behavior, internal structure and drug release. Direct compression (DC) quetiapine hemifumarate matrices and matrices made of powders obtained by dry granulation (DG) and high shear wet granulation (HS) were prepared. They had the same quantitative composition and they were evaluated using X-ray microtomography, magnetic resonance imaging and biorelevant stress test dissolution. Principal results concerned matrices after 2 h of hydration: (i) layered structure of the DC and DG hydrated tablets with magnetic resonance image intensity decreasing towards the center of the matrix was observed, while in HS matrices layer of lower intensity appeared in the middle of hydrated part; (ii) the DC and DG tablets retained their core and consequently exhibited higher resistance to the physiological stresses during simulation of small intestinal passage than HS formulation. Comparing to DC, HS granulation changed properties of the matrix in terms of hydration pattern and resistance to stress in biorelevant dissolution apparatus. Dry granulation did not change these properties-similar hydration pattern and dissolution in biorelevant conditions were observed for DC and DG matrices. Copyright © 2015 Elsevier B.V. All rights reserved.

Performance of population specific job exposure matrices (JEMs) : European collaborative analyses on occupational risk factors for chronic obstructive pulmonary disease with job exposure matrices (ECOJEM)

NARCIS (Netherlands)

Le Moual, N; Bakke, P; Orlowski, E; Heederik, D; Kromhout, H; Kennedy, SM; Rijcken, B; Kauffmann, F

Objectives-To compare the performance of population specific job exposure matrices (JEMs) sand self reported occupational exposure with data on exposure and lung function from three European general populations. Methods-Self reported occupational exposure (yes or no) and present occupation were

DOWNER (version 79-1): group collapse cross section and transfer matrices

International Nuclear Information System (INIS)

Cullen, D.E.

1979-01-01

FORTRAN-callable subroutines are provided to allow a user to group-collapse cross sections and/or transfer matrices from any arbitrary initial group structure to any arbitrary final group structure. 3 figures

Off-shell T-matrices from inverse scattering

International Nuclear Information System (INIS)

Von Geramb, H.V.; Amos, K.A.

1989-01-01

Inverse scattering theory is used to determine local, energy independent, coordinate space nucleon-nucleon potentials. Inversions are made of phase shifts obtained by analyzes of data and from meson exchange theory, in particular the Paris and the Bonn parametrizations. Half off-shell T-matrices are generated to compare the exact meson theoretical results with those of inversion and it is found that phase equivalent interactions have essentially the same off-shell behaviour for any physically significant range of momenta. 8 refs., 8 figs

Morphological changes in cotton roots in relation to soil mechanical impedance and matric potential

International Nuclear Information System (INIS)

Nabi, G.; Mullins, C.E.

2006-01-01

Soil mechanical impedance (M1) and matric potential can both root growth rate, modify rooting pattern and root diameter. Cotton seedlings are sensitive to the soil physical environment, particularly during early stages of growth. Soil matric potential and M1 effect on root biomass, axial root length and diameter, and the number and length of lateral roots in soil packed to penetration resistances (PR) of 0.1, 1.0, 1.1 and 1.2 Mpa (mega Pascal 10/sup 6/ Pascal), each at three matric potentials of-10,-100 and -500 kpa (kilopascal ) = 10/sup 3/ Pascal), were determined. Total root length were reduced by 29, 50 and 53% at impedance of 1.0, 1.1 and 1.2 Mpa, respectively, as compared to the control, whereas M1 of 1.2 Mpa resulted in 60% reduction in axial root length. A similar increase in diameter was caused by increasing mechanical impedance, while decreasing matric potential had little effect. Roots that were water stressed did not change their diameter but had a shorter axis and longer lateral length. In contrast, the impeded roots (PR=1.0, 1.1 and 1.2 MPa) had both a shorter axis and a smaller total length, but had increased diameter. These results not only illustrate the plasticity of root response to stress but also demonstrate how the response differs between different types of stresses. (author)

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

Science.gov (United States)

Yang, Yang; DeGruttola, Victor

2012-06-22

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

Fully constrained Majorana neutrino mass matrices using Σ(72 x 3)

Energy Technology Data Exchange (ETDEWEB)

Krishnan, R.; Harrison, P.F. [Warwick Univ., Coventry (United Kingdom); Scott, W.G. [Rutherford Appleton Laboratory, Chilton, Didcot (United Kingdom)

2018-01-15

In 2002, two neutrino mixing ansatze having trimaximally mixed middle (ν{sub 2}) columns, namely tri-chi-maximal mixing (TχM) and tri-phi-maximal mixing (TφM), were proposed. In 2012, it was shown that TχM with χ = ± (π)/(16) as well as TφM with φ = ± (π)/(16) leads to the solution, sin{sup 2} θ{sub 13} = (2)/(3) sin{sup 2} (π)/(16), consistent with the latest measurements of the reactor mixing angle, θ{sub 13}. To obtain TχM{sub (χ=±(π)/(16))} and TφM{sub (φ=±(π)/(16))}, the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, m{sub 1}: m{sub 2}: m{sub 3} = ((2+√2))/(1+√(2(2+√2))): 1: ((2+√2))/(-1+√(2(2+√2))). In this paper we construct a flavour model based on the discrete group Σ(72 x 3) and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric 3 x 3 matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of Σ(72 x 3). Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices. (orig.)

Calculations of light scattering matrices for stochastic ensembles of nanosphere clusters

International Nuclear Information System (INIS)

Bunkin, N.F.; Shkirin, A.V.; Suyazov, N.V.; Starosvetskiy, A.V.

2013-01-01

Results of the calculation of the light scattering matrices for systems of stochastic nanosphere clusters are presented. A mathematical model of spherical particle clustering with allowance for cluster–cluster aggregation is used. The fractal properties of cluster structures are explored at different values of the model parameter that governs cluster–cluster interaction. General properties of the light scattering matrices of nanosphere-cluster ensembles as dependent on their mean fractal dimension have been found. The scattering-matrix calculations were performed for finite samples of 10 3 random clusters, made up of polydisperse spherical nanoparticles, having lognormal size distribution with the effective radius 50 nm and effective variance 0.02; the mean number of monomers in a cluster and its standard deviation were set to 500 and 70, respectively. The implemented computation environment, modeling the scattering matrices for overall sequences of clusters, is based upon T-matrix program code for a given single cluster of spheres, which was developed in [1]. The ensemble-averaged results have been compared with orientation-averaged ones calculated for individual clusters. -- Highlights: ► We suggested a hierarchical model of cluster growth allowing for cluster–cluster aggregation. ► We analyzed the light scattering by whole ensembles of nanosphere clusters. ► We studied the evolution of the light scattering matrix when changing the fractal dimension