QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included

Does the Sun shrink with increasing magnetic activity?

It has been demonstrated that frequencies of f-modes can be used to estimate the solar radius to a good accuracy. These frequencies have been used to study temporal variations in the solar radius with conflicting results. The variation in f-mode frequencies is more complicated than what is assumed in these studies. If a careful analysis is performed then it turns out that there is no evidence for any variation in the solar radius.Comment: To appear in Astrophys.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead

Genetic Locus and Structural Characterization of the Biochemical Defect in the O-Antigenic Polysaccharide of the Symbiotically Deficient \u3cem\u3eRhizobium etli\u3c/em\u3e Mutant, CE166

The O-antigen polysaccharide (OPS) of Rhizobium etli CE3 lipopolysaccharide (LPS) is linked to the core oligosaccharide via an N-acetylquinovosaminosyl (QuiNAc) residue. A mutant of CE3, CE166, produces LPS with reduced amounts of OPS, and a suppressed mutant, CE166α, produces LPS with nearly normal OPS levels. Both mutants are deficient in QuiNAc production. Characterization of OPS from CE166 and CE166α showed that QuiNAc was replaced by its 4-keto derivative, 2-acetamido-2,6-dideoxyhexosyl-4-ulose. The identity of this residue was determined by NMR and mass spectrometry, and by gas chromatography-mass spectrometry analysis of its 2-acetamido-4-deutero-2,6-dideoxyhexosyl derivatives produced by reduction of the 4-keto group using borodeuteride. Mass spectrometric and methylation analyses showed that the 2-acetamido-2,6-dideoxyhexosyl-4-ulosyl residue was 3-linked and attached to the core-region external Kdo III residue of the LPS, the same position as that of QuiNAc in the CE3 LPS. DNA sequencing revealed that the transposon insertion in strain CE166 was located in an open reading frame whose predicted translation product, LpsQ, falls within a large family of predicted open reading frames, which includes biochemically characterized members that are sugar epimerases and/or reductases. A hypothesis to be tested in future work is that lpsQ encodes UDP-2-acetamido-2,6-dideoxyhexosyl-4-ulose reductase, the second step in the synthesis of UDP-QuiNAc from UDP-GlcNAc

Situational reasoning for road driving in an urban environment

Robot navigation in urban environments requires situational reasoning. Given the complexity of the environment and the behavior specified by traffic rules, it is necessary to recognize the current situation to impose the correct traffic rules. In an attempt to manage the complexity of the situational reasoning subsystem, this paper describes a finite state machine model to govern the situational reasoning process. The logic state machine and its interaction with the planning system are discussed. The approach was implemented on Alice, Team Caltech’s entry into the 2007 DARPA Urban Challenge. Results from the qualifying rounds are discussed. The approach is validated and the shortcomings of the implementation are identified

Genetic Locus Required for Antigenic Maturation of \u3cem\u3eRhizobium etli\u3c/em\u3e CE3 Lipopolysaccharide

Rhizobium etli modifies lipopolysaccharide (LPS) structure in response to environmental signals, such as low pH and anthocyanins. These LPS modifications result in the loss of reactivity with certain monoclonal antibodies. The same antibodies fail to recognize previously isolated R. etli mutant strain CE367, even in the absence of such environmental cues. Chemical analysis of the LPS in strain CE367 demonstrated that it lacked the terminal sugar of the wild-type O antigen, 2,3,4-tri-O-methylfucose. A 3-kb stretch of DNA, designated as lpe3, restored wild-type antigenicity when transferred into CE367. From the sequence of this DNA, five open reading frames were postulated. Site-directed mutagenesis and complementation analysis suggested that the genes were organized in at least two transcriptional units, both of which were required for the production of LPS reactive with the diagnostic antibodies. Growth in anthocyanins or at low pH did not alter the specific expression of gusA from the transposon insertion of mutant CE367, nor did the presence of multiple copies of lpe3 situated behind a strong, constitutive promoter prevent epitope changes induced by these environmental cues. Mutations of the lpe genes did not prevent normal nodule development on Phaseolus vulgaris and had very little effect on the occupation of nodules in competition with the wild-type strain

Phase and Risetime Dependence Using RF Pulses in Multiphoton Processes

With this experiment we demonstrate that excitation of a two-state system with radio-frequency fields differing in phase by 90° produces nonintuitively different results, even for very long pulses. In addition, we show how the phase dependence of the transition probability of long pulses can be easily understood by using the single cycle time propagator. Finally, we have found surprising results for real pulses in the strong-field regime, i.e., pulses having appreciable rise and fall times

Population Trapping in Extremely Highly Excited States in Microwave Ionization

When a lithium atom in a Rydberg state (n 80) is exposed to a short, intense microwave pulse we find that substantial population is left in extremely highly excited states (n . 120), in spite of the fact that the microwave field amplitude is more than 40 times larger than required to classically ionize these states

Phase and Risetime Dependence Using RF Pulses in Multiphoton Processes

With this experiment we demonstrate that excitation of a two-state system with radio-frequency fields differing in phase by 90° produces nonintuitively different results, even for very long pulses. In addition, we show how the phase dependence of the transition probability of long pulses can be easily understood by using the single cycle time propagator. Finally, we have found surprising results for real pulses in the strong-field regime, i.e., pulses having appreciable rise and fall times