Superlinear convergence for PCG using band plus algebra preconditioners for Toeplitz systems

AbstractThe paper studies fast and efficient solution algorithms for n×n symmetric ill conditioned Toeplitz systems Tn(f)x=b where the generating function f is known a priori, real valued, nonnegative, and has isolated roots of even order. The preconditioner that we propose is a product of a band Toeplitz matrix and matrices that belong to a certain trigonometric algebra. The basic idea behind the proposed scheme is to combine the advantages of all components of the product that are well known when every component is used as a stand-alone preconditioner. As a result we obtain a flexible preconditioner which can be applied to the system Tn(f)x=b infusing superlinear convergence to the PCG method. The important feature of the proposed technique is that it can be extended to cover the 2D case, i.e. ill-conditioned block Toeplitz matrices with Toeplitz blocks. We perform many numerical experiments, whose results confirm the theoretical analysis and effectiveness of the proposed strategy

Trilogy on Computing Maximal Eigenpair

The eigenpair here means the twins consist of eigenvalue and its eigenvector. This paper introduces the three steps of our study on computing the maximal eigenpair. In the first two steps, we construct efficient initials for a known but dangerous algorithm, first for tridiagonal matrices and then for irreducible matrices, having nonnegative off-diagonal elements. In the third step, we present two global algorithms which are still efficient and work well for a quite large class of matrices, even complex for instance.Comment: Updated versio

The relationship between the Jacobi and the successive overrelaxation (SOR) matrices of a k-cyclic matrix

AbstractLet A be a (k−l, l)-generalized consistently ordered matrix with T and Lω its associated Jacobi and SOR matrices whose eigenvalues μ and λ satisfy the well-known relationship (λ+ω−1)k=ωkμkλk−1. For a subclass of the above matrices A we prove that the matrix analogue of the previous relationship holds. Exploiting the matrix relationship we show that the SOR method is equivalent to a certain monoparametric k-step iterative one when used for the solution of the fixed-point problem x=Tx+c

Comprehensive data infrastructure for plant bioinformatics

The iPlant Collaborative is a 5-year, National Science Foundation-funded effort to develop cyberinfrastructure to address a series of grand challenges in plant science. The second of these grand challenges is the Genotype-to- Phenotype project, which seeks to provide tools, in the form of a web-based Discovery Environment, for understanding the developmental process from DNA to a full-grown plant. Addressing this challenge requires the integration of multiple data types that may be stored in multiple formats, with varying levels of standardization. Providing for reproducibility requires that detailed information documenting the experimental provenance of data, and the computational transformations applied to data once it is brought into the iPlant environment. Handling the large quantities of data involved in high-throughput sequencing and other experimental sources of bioinformatics data requires a robust infrastructure for storing and reusing large data objects. We describe the currently planned workflows to be developed for the Genotype-to-Phenotype discovery environment, the data types and formats that must be imported and manipulated within the environment, and we describe the data model that has been developed to express and exchange data within the Discovery Environment, along with the provenance model defined for capturing experimental source and digital transformation descriptions. Capabilities for interaction with reference databases are addressed, focusing not just on the ability to retrieve data from such data sources, but on the ability to use the iPlant Discovery Environment to further populate these important resources. Future activities and the challenges they will present to the data infrastructure of the iPlant Collaborative are also described. © 2010 IEEE

Analysis of 101 nuclear transcriptomes reveals 23 distinct regulons and their relationship to metabolism, chromosomal gene distribution and co-ordination of nuclear and plastid gene expression

Post-endosymbiotic evolution of the proto-chloroplast was characterized by gene transfer to the nucleus. Hence, most chloroplast proteins are nuclear-encoded and the regulation of chloroplast functions includes nuclear transcriptional control. The expression profiles of 3292 nuclear Arabidopsis genes, most of them encoding chloroplast proteins, were determined from 101 different conditions and have been deposited at the GEO database (http://www.ncbi.nlm.nih.gov/geo/) under GSE1160-GSE1260. The 1590 most-regulated genes fell into 23 distinct groups of co-regulated genes (regulons). Genes of some regulons are not evenly distributed among the five Arabidopsis chromosomes and pairs of adjacent, co-expressed genes exist. Except regulons 1 and 2, regulons are heterogeneous and consist of genes coding for proteins with different subcellular locations or contributing to several biochemical functions. This implies that different organelles and/or metabolic pathways are co-ordinated at the nuclear transcriptional level, and a prototype for this is regulon 12 which contains genes with functions in amino acid and carbohydrate metabolism, as well as genes associated with transport or transcription. The co-expression of nuclear genes coding for subunits of the photosystems or encoding proteins involved in the transcription/translation of plastome genes (particularly ribosome polypeptides) (regulons 1 and 2, respectively) implies the existence of a novel mechanism that co-ordinates plastid and nuclear gene expression and involves nuclear control of plastid ribosome abundance. The co-regulation of genes for photosystem and plastid ribosome proteins escapes a previously described general control of nuclear chloroplast proteins imposed by a transcriptional master switch, highlighting a mode of transcriptional regulation of photosynthesis which is different compared to other chloroplast functions. From the evolutionary standpoint, the results provided indicate that functional integration of the proto-chloroplast into the eukaryotic cell was associated with the establishment of different layers of nuclear transcriptional control

Modelling the Galactic distribution of free electrons

In this paper we test 8 models of the free electron distribution in the Milky Way that have been published previously, and we introduce 4 additional models that explore the parameter space of possible models further. These new models consist of a simple exponential thick disk model, and updated versions of the models by Taylor & Cordes and Cordes & Lazio with more extended thick disks. The final model we introduce uses the observed H-alpha intensity as a proxy for the total electron column density, also known as the dispersion measure (DM). We use the latest available data sets of pulsars with accurate distances (through parallax measurements or association with globular clusters) to optimise the parameters in these models. In the process of fitting a new scale height for the thick disk in the model by Cordes & Lazio we discuss why this thick disk cannot be replaced by the thick disk that Gaensler et al. advocated in a recent paper. In the second part of our paper we test how well the different models can predict the DMs of these pulsars at known distances. Almost all models perform well, in that they predict DMs within a factor of 1.5-2 of the observed DMs for about 75% of the lines of sight. This is somewhat surprising since the models we tested range from very simple models that only contain a single exponential thick disk to very complex models like the model by Cordes & Lazio. We show that the model by Taylor & Cordes that we updated with a more extended thick disk consistently performs better than the other models we tested. Finally, we analyse which sightlines have DMs that prove difficult to predict by most models, which indicates the presence of local features in the ISM between us and the pulsar. (abridged)Comment: 16 pages, 10 figures, 5 tables. Accepted for publication in the Monthly Notices of the RAS by the Royal Astronomical Society and Blackwell Publishin

The High Time Resolution Universe Pulsar Survey IV: Discovery and polarimetry of millisecond pulsars

We present the discovery of six millisecond pulsars (MSPs) in the High Time Resolution Universe (HTRU) survey for pulsars and fast transients carried out with the Parkes radio telescope. All six are in binary systems with approximately circular orbits and are likely to have white dwarf companions. PSR J1017-7156 has a high flux density and a narrow pulse width, making it ideal for precision timing experiments. PSRs J1446-4701 and J1125-5825 are coincident with gamma-ray sources, and folding the high-energy photons with the radio timing ephemeris shows evidence of pulsed gamma-ray emission. PSR J1502-6752 has a spin period of 26.7 ms, and its low period derivative implies that it is a recycled pulsar. The orbital parameters indicate it has a very low mass function, and therefore a companion mass much lower than usually expected for such a mildly recycled pulsar. In addition we present polarisation profiles for all 12 MSPs discovered in the HTRU survey to date. Similar to previous observations of MSPs, we find that many have large widths and a wide range of linear and circular polarisation fractions. Their polarisation profiles can be highly complex, and although the observed position angles often do not obey the rotating vector model, we present several examples of those that do. We speculate that the emission heights of MSPs are a substantial fraction of the light cylinder radius in order to explain broad emission profiles, which then naturally leads to a large number of cases where emission from both poles is observed.Comment: Update to correct affiliation for CAASTRO. 16 pages, 18 figures. Accepted for publication in MNRA