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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

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

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

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

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

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

Estimates of frequency-dependent compressibility from a quasistatic double-porosity model

Description: Gassmann's relationship between the drained and undrained bulk modulus of a porous medium is often used to relate the dry bulk modulus to the saturated bulk modulus for elastic waves, because the compressibility of air is considered so high that the dry rock behaves in a drained fashion and the frequency of elastic waves is considered so high that the saturated rock behaves in an undrained fashion. The bulk modulus calculated from ultrasonic velocities, however, often does not match the Gassmann prediction. Mavko and Jizba examined how local flow effects and unequilibrated pore pressures can lead to greater stiffnesses. Their conceptual model consists of a distribution of porosities obtained from the strain-versus-confining-pressure behavior. Stiff pores that close at higher confining pressures are considered to remain undrained (unrelaxed) while soft pores drain even for high-frequency stress changes. If the pore shape distribution is bimodal, then the rock approximately satisfies the assumptions of a double-porosity, poroelastic material. Berryman and Wang [1995] established linear constitutive equations and identified four different time scales of ow behavior: (1) totally drained, (2) soft pores are drained but stiff pores are undrained, (3) soft and stiff pores are locally equilibrated, but undrained beyond the grain scale, and (4) both soft and stiff pores are undrained. The relative magnitudes of the four associated bulk moduli will be examined for all four moduli and illustrated for several sandstones.
Date: September 16, 1998
Creator: Berryman, J. G. & Wang, H. F.
Partner: UNT Libraries Government Documents Department

An insertion to eliminate horizontal temperature of high energy electron beam

Description: High energy electron cooling with a circulated electron bunch could significantly increase the luminosity of hadron colliders. One of the significant obstacles is high horizontal temperature of electron bunches, suppressing dramatically calculated cooling rates. Recently, a transformation of betatron coordinates and angles for elimination of the radial temperature was found. In our paper, we present a simple scheme to make up this transformation by thin quadruples, drifts and a solenoid.
Date: March 16, 1998
Creator: Burov, A.V. & Danilov, V.V.
Partner: UNT Libraries Government Documents Department

How to construct a second-order achromat with a 90 degree phase advance

Description: The author shows how to construct a second order achromatic (T{sub ij6} = 0, i, j {element_of} {l_brace}1,2{r_brace}) beamline with a total phase advance of 450{degree} (360{degree} + 90{degree}). The goal is to construct a 90{degree} cell which is achromatic to second order. One possible way to do this is to construct a 360{degree} sector followed by a 90{degree} cell; put dipoles and sextupoles in the 360{degree} sector; and throw the aberrations into the 90{degree} cell such that the final transformation is achromatic. The author expresses the aberrations in the 360{degree} sector in terms of the 90{degree} cell and determine whether any combination of sextupoles gives the correct cancellation.
Date: July 5, 2000
Creator: Kobilarcik, T.
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

Performance and Accuracy of LAPACK's Symmetric TridiagonalEigensolvers

Description: We compare four algorithms from the latest LAPACK 3.1 release for computing eigenpairs of a symmetric tridiagonal matrix. These include QR iteration, bisection and inverse iteration (BI), the Divide-and-Conquer method (DC), and the method of Multiple Relatively Robust Representations (MR). Our evaluation considers speed and accuracy when computing all eigenpairs, and additionally subset computations. Using a variety of carefully selected test problems, our study includes a variety of today's computer architectures. Our conclusions can be summarized as follows. (1) DC and MR are generally much faster than QR and BI on large matrices. (2) MR almost always does the fewest floating point operations, but at a lower MFlop rate than all the other algorithms. (3) The exact performance of MR and DC strongly depends on the matrix at hand. (4) DC and QR are the most accurate algorithms with observed accuracy O({radical}ne). The accuracy of BI and MR is generally O(ne). (5) MR is preferable to BI for subset computations.
Date: April 19, 2007
Creator: Demmel, Jim W.; Marques, Osni A.; Parlett, Beresford N. & Vomel,Christof
Partner: UNT Libraries Government Documents Department

Toward the M(F)-theory embedding of realistic free-fermion models

Description: We construct a Landau-Ginzburg model with the same data and symmetries as a Z{sub 2} x Z{sub 2} orbifold that corresponds to a class of realistic free-fermion models. Within the class of interest, we show that this orbifolding connects between different Z{sub 2} x Z{sub 2} orbifold models and connects with the mirror symmetry. Our work suggests that duality symmetries previously discussed in the context of specific M and F theory compactifications may be extended to the special Z{sub 2} x Z{sub 2} orbifold that characterizes realistic free-fermion models.
Date: March 1, 1998
Creator: Berglund, P.; Ellis, J. & Faraggi, A.E.
Partner: UNT Libraries Government Documents Department

Sodium Removal from Hanford Waste Simulants Using Hydrated Antimony Pentoxide

Description: Sodium has been removed from each of the three Hanford waste simulants with Hydrated Antimony Pentoxide (HAP) to facilitate technetium measurement by ICP-MS. Technetium was successfully measured in simulants A and B with small dilutions of the simulants (10x). Matrix interference, probably due to organic components, prevented the accurate measurement of Tc in simulant C. HAP has been used for the selective removal of sodium from samples prior to radiochemical analysis.1-4 The analytical development section of SRTC has successfully used HAP to remove sodium from a simulated sample matrix of a SRS waste tank.5 This sample pretreatment method eliminated signal suppression caused by the 5 molar sodium matrix without affecting the concentration of Pt, Ru, and Re as measured by Inductively Coupled Plasma-Mass Spectrometry (ICP-MS). With this initial success, we decided to investigate the use of HAP to remove sodium from the three Hanford waste matrices prior to ICP-MS analysis of technetium. The results of this investigation are summarized in this report.
Date: November 18, 1999
Creator: Tovo, L.L.
Partner: UNT Libraries Government Documents Department

Results on the effect of orderings on SSOR and ILU preconditionings

Description: It is known that for SSOR and ILU preconditionings for solving systems of linear equations, orderings can have an enormous impact on robustness, convergence rate and parallelism. Unfortunately, it has been observed that there is an inverse relation between the convergence rate and the parallelism of typical orderings used in practice. This paper presents some numerical experiments with simple matrices to illustrate this behavior as well as a new theoretical result which sheds some light on this phenomenon and also gives an upper bound on the convergence rate of a number of preconditioners in popular use.
Date: December 31, 1998
Creator: Joubert, W. & Knill, E.
Partner: UNT Libraries Government Documents Department

ATGC: a database of orthologous genes from closely related prokaryotic genomes and a research platform for microevolution of prokaryotes

Description: The database of Alignable Tight Genomic Clusters (ATGCs) consists of closely related genomes of archaea and bacteria, and is a resource for research into prokaryotic microevolution. Construction of a data set with appropriate characteristics is a major hurdle for this type of studies. With the current rate of genome sequencing, it is difficult to follow the progress of the field and to determine which of the available genome sets meet the requirements of a given research project, in particular, with respect to the minimum and maximum levels of similarity between the included genomes. Additionally, extraction of specific content, such as genomic alignments or families of orthologs, from a selected set of genomes is a complicated and time-consuming process. The database addresses these problems by providing an intuitive and efficient web interface to browse precomputed ATGCs, select appropriate ones and access ATGC-derived data such as multiple alignments of orthologous proteins, matrices of pairwise intergenomic distances based on genome-wide analysis of synonymous and nonsynonymous substitution rates and others. The ATGC database will be regularly updated following new releases of the NCBI RefSeq. The database is hosted by the Genomics Division at Lawrence Berkeley National laboratory and is publicly available at http://atgc.lbl.gov.
Date: July 23, 2009
Creator: Novichkov, Pavel S.; Ratnere, Igor; Wolf, Yuri I.; Koonin, Eugene V. & Dubchak, Inna
Partner: UNT Libraries Government Documents Department

Methodology for the relative risk assessment in the LDF safety analysis report

Description: This document provides the methodology used for the relative risk assessment performed in the LDF Safety Analysis Report. The safety analysis for a facility of the hazard level of the LDF Complex (Buildings 490L, 492 are low hazard) should be mostly qualitative. This was the approach taken for the LDF risk assessment, where qualitative descriptors were assigned to event consequences and frequencies. The event consequences and frequencies were then combined using a risk matrix to obtain an assessment of the relative risk presented by each event to LDF workers and to the public. The development of the risk matrices is the main subject of this report. The matrices have been applied in the LDF SAR (LLNL, 1997).
Date: September 3, 1997
Creator: Brereton, S.J.
Partner: UNT Libraries Government Documents Department