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Infinite Matrices

Description: This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.
Date: August 1957
Creator: Smallwood, James D.
Partner: UNT Libraries

The Use of the Power Method to Find Dominant Eigenvalues of Matrices

Description: This paper is the result of a study of the power method to find dominant eigenvalues of square matrices. It introduces ideas basic to the study and shows the development of the power method for the most well-behaved matrices possible, and it explores exactly which other types of matrices yield to the power method. The paper also discusses a type of matrix typically considered impossible for the power method, along with a modification of the power method which works for this type of matrix. It gives an overview of common extensions of the power method. The appendices contain BASIC versions of the power method and its modification.
Date: July 1992
Creator: Cavender, Terri A.
Partner: UNT Libraries

Lepton-flavor mixing and K --> pi nu nu bar decays

Description: The impact of possible sources of lepton-flavor mixing on K {yields} {pi}{nu}{bar {nu}} decays is analyzed. At the one-loop level lepton-flavor mixing originated from non-diagonal lepton mass matrices cannot generate a CP-conserving K{sub L} {yields} {pi}{sup 0}{nu}{bar {nu}} amplitude. The rates of these modes are sensitive to leptonic flavor violation when there are at least two different leptonic mixing matrices. New interactions that violate both quark and lepton universalities could enhance the CP-conserving component of {Lambda}(K{sub L} {yields} {pi}{sup 0}{nu}{bar {nu}}) and have a substantial impact. Explicit examples of these effects in the context of supersymmetric models, with and without R-parity conservation, are discussed.
Date: November 26, 2003
Creator: Grossman, Yuval; Isidori, Gino & Murayama, Hitoshi
Partner: UNT Libraries Government Documents Department

RegPredict: an integrated system for regulon inference in prokaryotes by comparative genomics approach

Description: RegPredict web server is designed to provide comparative genomics tools for reconstruction and analysis of microbial regulons using comparative genomics approach. The server allows the user to rapidly generate reference sets of regulons and regulatory motif profiles in a group of prokaryotic genomes. The new concept of a cluster of co-regulated orthologous operons allows the user to distribute the analysis of large regulons and to perform the comparative analysis of multiple clusters independently. Two major workflows currently implemented in RegPredict are: (i) regulon reconstruction for a known regulatory motif and (ii) ab initio inference of a novel regulon using several scenarios for the generation of starting gene sets. RegPredict provides a comprehensive collection of manually curated positional weight matrices of regulatory motifs. It is based on genomic sequences, ortholog and operon predictions from the MicrobesOnline. An interactive web interface of RegPredict integrates and presents diverse genomic and functional information about the candidate regulon members from several web resources. RegPredict is freely accessible at http://regpredict.lbl.gov.
Date: May 26, 2010
Creator: Novichkov, Pavel S.; Rodionov, Dmitry A.; Stavrovskaya, Elena D.; Novichkova, Elena S.; Kazakov, Alexey E.; Gelfand, Mikhail S. et al.
Partner: UNT Libraries Government Documents Department

Matrix membranes and integrability

Description: This is a pedagogical digest of results reported in Curtright, Fairlie, {ampersand} Zachos 1997, and an explicit implementation of Euler`s construction for the solution of the Poisson Bracket dual Nahm equation. But it does not cover 9 and 10-dimensional systems, and subsequent progress on them Fairlie 1997. Cubic interactions are considered in 3 and 7 space dimensions, respectively, for bosonic membranes in Poisson Bracket form. Their symmetries and vacuum configurations are explored. Their associated first order equations are transformed to Nahm`s equations, and are hence seen to be integrable, for the 3-dimensional case, by virtue of the explicit Lax pair provided. Most constructions introduced also apply to matrix commutator or Moyal Bracket analogs.
Date: June 1, 1997
Creator: Zachos, C.; Fairlie, D. & Curtright, T.
Partner: UNT Libraries Government Documents Department

Performance analysis of parallel supernodal sparse LU factorization

Description: We investigate performance characteristics for the LU factorization of large matrices with various sparsity patterns. We consider supernodal right-looking parallel factorization on a bi-dimensional grid of processors, making use of static pivoting. We develop a performance model and we validate it using the implementation in SuperLU-DIST, the real matrices and the IBM Power3 machine at NERSC. We use this model to obtain performance bounds on parallel computers, to perform scalability analysis and to identify performance bottlenecks. We also discuss the role of load balance and data distribution in this approach.
Date: February 5, 2004
Creator: Grigori, Laura & Li, Xiaoye S.
Partner: UNT Libraries Government Documents Department

Book Review Geostatistical Analysis of Compositional Data

Description: Compositional data are represented as vector variables with individual vector components ranging between zero and a positive maximum value representing a constant sum constraint, usually unity (or 100 percent). The earth sciences are flooded with spatial distributions of compositional data, such as concentrations of major ion constituents in natural waters (e.g. mole, mass, or volume fractions), mineral percentages, ore grades, or proportions of mutually exclusive categories (e.g. a water-oil-rock system). While geostatistical techniques have become popular in earth science applications since the 1970s, very little attention has been paid to the unique mathematical properties of geostatistical formulations involving compositional variables. The book 'Geostatistical Analysis of Compositional Data' by Vera Pawlowsky-Glahn and Ricardo Olea (Oxford University Press, 2004), unlike any previous book on geostatistics, directly confronts the mathematical difficulties inherent to applying geostatistics to compositional variables. The book righteously justifies itself with prodigious referencing to previous work addressing nonsensical ranges of estimated values and error, spurious correlation, and singular cross-covariance matrices.
Date: March 26, 2007
Creator: Carle, S F
Partner: UNT Libraries Government Documents Department

Accelerated Gibbs Sampling for Infinite Sparse Factor Analysis

Description: The Indian Buffet Process (IBP) gives a probabilistic model of sparse binary matrices with an unbounded number of columns. This construct can be used, for example, to model a fixed numer of observed data points (rows) associated with an unknown number of latent features (columns). Markov Chain Monte Carlo (MCMC) methods are often used for IBP inference, and in this technical note, we provide a detailed review of the derivations of collapsed and accelerated Gibbs samplers for the linear-Gaussian infinite latent feature model. We also discuss and explain update equations for hyperparameter resampling in a 'full Bayesian' treatment and present a novel slice sampler capable of extending the accelerated Gibbs sampler to the case of infinite sparse factor analysis by allowing the use of real-valued latent features.
Date: September 12, 2011
Creator: Andrzejewski, D M
Partner: UNT Libraries Government Documents Department

Direction-preserving and Schur-monotonic Semi-separable Approximations of Symmetric Positive Definite Matrices

Description: For a given symmetric positive definite matrix A {element_of} R{sup nxn}, we develop a fast and backward stable algorithm to approximate A by a symmetric positive-definite semi-separable matrix, accurate to any prescribed tolerance. In addition, this algorithm preserves the product, AZ, for a given matrix Z {element_of} R{sup nxd}, where d << n. Our algorithm guarantees the positive-definiteness of the semi-separable matrix by embedding an approximation strategy inside a Cholesky factorization procedure to ensure that the Schur complements during the Cholesky factorization all remain positive definite after approximation. It uses a robust direction-preserving approximation scheme to ensure the preservation of AZ. We present numerical experiments and discuss potential implications of our work.
Date: October 20, 2009
Creator: Gu, Ming; Li, Xiaoye Sherry & Vassilevski, Panayot S.
Partner: UNT Libraries Government Documents Department

Variable Metric Method for Minimization

Description: A method for determining numerically local minima of differentiable functions of several variables is presented. In the process of locating each minimum, a matrix which characterizes the behavior of the iunction about the minimum is determined. For a region in which the function depends quadratically on the variables, no more than N iterations are required, where N is the number of variables. By suitable choice of starting values and without modification of the procedure, linear constraints can be imposed upon the variables. (auth)
Date: November 1, 1959
Creator: Davidon, W. C.
Partner: UNT Libraries Government Documents Department

Variable Metric Method for Minimization

Description: A method is presented for numerically determining local minima of differentiable functions of several variables. In the proeess of locating each minimum, a matrix is determined which characterizes the behavior of the function about the minimum. For a region in which thc function depends quadratically on the variables, no more than N iterations are required, where N is the number of variables. By suitable choice of starting values and without modification of the procedure, linear constraints can be imposed upon the variables. (auth)
Date: May 1, 1959
Creator: Davidon, W. C.
Partner: UNT Libraries Government Documents Department

Homologous Recombination in Q-Beta Rna Bacteriophage

Description: Q-Beta phage RNAs with inactivating insertion (8 base) or deletion (17 base) mutations within their replicase genes were transfected into Escherichia coli spheroplasts containing QB replicase provided in trans by a resident plasmid. Replicase-defective (Rep~) Q3 phage produced by these spheroplasts were unable to form plaques on cells lacking this plasmid. When individual Rep~ phage were isolated and grown to high titer in cells containing plasmid derived Q3 replicase, revertant Q3 phage (Rep'), with the original mutation (insertion or deletion) repaired, were obtained at a frequency of ca. 1 x 108. RNA recombination via a "template switching" mechanism involving Q3 replicase, the mutant phage genome, and the plasmid-derived replicase mRNA was shown to be the primary means by which these mutant phages reverted to wild type.
Date: May 1992
Creator: Palasingam, Kampan
Partner: UNT Libraries

Updating the Symmetric Indefinite Factorization with Applications in a Modified Newton's Method

Description: In recent years the use of quasi-Newton methods in optimization algorithms has inspired much of the research in an area of numerical linear algebra called updating matrix factorizations. Previous research in this area has been concerned with updating the factorization of a symmetric positive definite matrix. Here, a numerical algorithm is presented for updating the Symmetric Indefinite Factorization of Bunch and Parlett. The algorithm requires only O(n/sup 2/) arithmetic operations to update the factorization of an n x n symmetric matrix when modified by a rank-one matrix. An error analysis of this algorithm is given. Computational results are presented that investigate the timing and accuracy of this algorithm. Another algorithm is presented for the unconstrained minimization of a nonlinear functional. The algorithm is a modification of Newton's method. At points where the Hessian is indefinite the search for the next iterate is conducted along a quadratic curve in the plane spanned by a direction of negative curvature and a gradient-related descent direction. The stopping criteria for this search take into account the second-order derivative information. The result is that the iterates are shown to converge globally to a critical point at which the Hessian is positive semi-definite. Computational results are presented which indicate that the method is promising.
Date: June 1977
Creator: Sorensen, Danny C.
Partner: UNT Libraries Government Documents Department

Combinatorial Algorithms for Computing Column Space Bases ThatHave Sparse Inverses

Description: This paper presents a combinatorial study on the problem ofconstructing a sparse basis forthe null-space of a sparse, underdetermined, full rank matrix, A. Such a null-space is suitable forsolving solving many saddle point problems. Our approach is to form acolumn space basis of A that has a sparse inverse, by selecting suitablecolumns of A. This basis is then used to form a sparse null-space basisin fundamental form. We investigate three different algorithms forcomputing the column space basis: Two greedy approaches that rely onmatching, and a third employing a divide and conquer strategy implementedwith hypergraph partitioning followed by the greedy approach. We alsodiscuss the complexity of selecting a column basis when it is known thata block diagonal basis exists with a small given block size.
Date: March 18, 2005
Creator: Pinar, Ali; Chow, Edmond & Pothen, Alex
Partner: UNT Libraries Government Documents Department

Anarchy and hierarchy

Description: We advocate a new approach to study models of fermion massesand mixings, namely anarchy proposed in hep-ph/9911341. In this approach,we scan the O(1) coefficients randomly. We argue that this is the correctapproach when the fundamental theory is sufficiently complicated.Assuming there is no physical distinction among three generations ofneutrinos, the probability distributions in MNS mixing angles can bepredicted independent of the choice of the measure. This is because themixing angles are distributed according to the Haar measure of the Liegroups whose elements diagonalize the mass matrices. The near-maximalmixings, as observed in the atmospheric neutrino data and as required inthe LMA solution to the solar neutrino problem, are highly probable. Asmall hierarchy between the Delta m2 for the atmospheric and the solarneutrinos is obtained very easily; the complex seesaw case gives ahierarchy of a factor of 20 as the most probable one, even though thisconclusion is more measure-dependent. U_e3 has to be just below thecurrent limit from the CHOOZ experiment. The CP-violating parameter sindelta is preferred to be maximal. We present a simple SU(5)-likeextension of anarchy to the charged-lepton and quark sectors which workswell phenomenologically.
Date: September 14, 2000
Creator: Haba, Naoyuki & Murayama, Hitoshi
Partner: UNT Libraries Government Documents Department