O(1) Computation of Legendre polynomials and Gauss-Legendre nodes and weights for parallel computing

A self-contained set of algorithms is proposed for the fast evaluation of Legendre polynomials of arbitrary degree and argument is an element of [-1, 1]. More specifically the time required to evaluate any Legendre polynomial, regardless of argument and degree, is bounded by a constant; i.e., the complexity is O(1). The proposed algorithm also immediately yields an O(1) algorithm for computing an arbitrary Gauss-Legendre quadrature node. Such a capability is crucial for efficiently performing certain parallel computations with high order Legendre polynomials, such as computing an integral in parallel by means of Gauss-Legendre quadrature and the parallel evaluation of Legendre series. In order to achieve the O(1) complexity, novel efficient asymptotic expansions are derived and used alongside known results. A C++ implementation is available from the authors that includes the evaluation routines of the Legendre polynomials and Gauss-Legendre quadrature rules

Weak scalability analysis of the distributed-memory parallel MLFMA

Distributed-memory parallelization of the multilevel fast multipole algorithm (MLFMA) relies on the partitioning of the internal data structures of the MLFMA among the local memories of networked machines. For three existing data partitioning schemes (spatial, hybrid and hierarchical partitioning), the weak scalability, i.e., the asymptotic behavior for proportionally increasing problem size and number of parallel processes, is analyzed. It is demonstrated that none of these schemes are weakly scalable. A nontrivial change to the hierarchical scheme is proposed, yielding a parallel MLFMA that does exhibit weak scalability. It is shown that, even for modest problem sizes and a modest number of parallel processes, the memory requirements of the proposed scheme are already significantly lower, compared to existing schemes. Additionally, the proposed scheme is used to perform full-wave simulations of a canonical example, where the number of unknowns and CPU cores are proportionally increased up to more than 200 millions of unknowns and 1024 CPU cores. The time per matrix-vector multiplication for an increasing number of unknowns and CPU cores corresponds very well to the theoretical time complexity

Performing large full-wave simulations by means of a parallel MLFMA implementation

In this paper large full-wave simulations are performed using a parallel Multilevel Fast Multipole Algorithm (MLFMA) implementation. The data structures of the MLFMA-tree are partitioned according to the so-called hierarchical partitioning scheme, while the radiation patterns are partitioned in a blockwise way. To test the implementation of the algorithm, a full-wave simulation of a canonical example with more than 50 millions of unknowns has been performed

Scalable parallel computation of the translation operator in three dimensions

We propose a novel algorithm for the parallel, distributed-memory computation of the translation operator in the three-dimensional multilevel fast multipole algorithm (MLFMA). Sequential algorithms can compute the translation operator with L multipoles and O(L-2) sampling points in O(L-2) time. State-of-the-art hierarchical parallelization schemes of the MLFMA rely on the distribution of radiation patterns and associated translation operators among P = O(L-2) parallel processes, necessitating the development of distributed-memory algorithms for the computation of the translation operator. Whereas a baseline parallel algorithm computes this translation operator in O(L) time, we propose an algorithm that achieves this in only O(log L) time. For large translation operators and a high number of parallel processes, our algorithm proves to be roughly ten times faster than the baseline algorithm

Prediction and overview of the RpoN-regulon in closely related species of the Rhizobiales

BACKGROUND: In the rhizobia, a group of symbiotic Gram-negative soil bacteria, RpoN (σ(54), σ(N), NtrA) is best known as the sigma factor enabling transcription of the nitrogen fixation genes. Recent reports, however, demonstrate the involvement of RpoN in other symbiotic functions, although no large-scale effort has yet been undertaken to unravel the RpoN-regulon in rhizobia. We screened two complete rhizobial genomes (Mesorhizobium loti, Sinorhizobium meliloti) and four symbiotic regions (Rhizobium etli, Rhizobium sp. NGR234, Bradyrhizobium japonicum, M. loti) for the presence of the highly conserved RpoN-binding sites. A comparison was also made with two closely related non-symbiotic members of the Rhizobiales (Agrobacterium tumefaciens, Brucella melitensis). RESULTS: A highly specific weight-matrix-based screening method was applied to predict members of the RpoN-regulon, which were stored in a highly annotated and manually curated dataset. Possible enhancer-binding proteins (EBPs) controlling the expression of RpoN-dependent genes were predicted with a profile hidden Markov model. CONCLUSIONS: The methodology used to predict RpoN-binding sites proved highly effective as nearly all known RpoN-controlled genes were identified. In addition, many new RpoN-dependent functions were found. The dependency of several of these diverse functions on RpoN seems species-specific. Around 30% of the identified genes are hypothetical. Rhizobia appear to have recruited RpoN for symbiotic processes, whereas the role of RpoN in A. tumefaciens and B. melitensis remains largely to be elucidated. All species screened possess at least one uncharacterized EBP as well as the usual ones. Lastly, RpoN could significantly broaden its working range by direct interfering with the binding of regulatory proteins to the promoter DNA

IAMBEE : a web-service for the identification of adaptive pathways from parallel evolved clonal populations

IAMBEE is a web server designed for the Identification of Adaptive Mutations in Bacterial Evolution Experiments (IAMBEE). Input data consist of genotype information obtained from independently evolved clonal populations or strains that show the same adapted behavior (phenotype). To distinguish adaptive from passenger mutations, IAMBEE searches for neighborhoods in an organism-specific interaction network that are recurrently mutated in the adapted populations. This search for recurrently mutated network neighborhoods, as proxies for pathways is driven by additional information on the functional impact of the observed genetic changes and their dynamics during adaptive evolution. In addition, the search explicitly accounts for the differences in mutation rate between the independently evolved populations. Using this approach, IAMBEE allows exploiting parallel evolution to identify adaptive pathways. The web-server is freely available at http://bioinformatics.intec.ugent.be/iambee/ with no login requirement