A posteriori analysis of discontinuous galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator

A Bayesian Inverse Approach to Proton Therapy Dose Delivery Verification

This study presents a proof-of-concept for a novel Bayesian inverse method in a one-dimensional setting, aimed at proton beam therapy treatment verification. Our methodology is predicated on a hypothetical scenario wherein strategically positioned sensors detect prompt-{\gamma}'s emitted from a proton beam when it interacts with defined layers of tissue. Using this data, we employ a Bayesian framework to estimate the proton beam's energy deposition profile. We validate our Bayesian inverse estimations against a closed-form approximation of the Bragg Peak in a uniform medium and a layered lung tumour.Comment: 22 pages, 12 figure

Formation of Spaced Cleavage and Concurrent Mass Removal of Si02, Meguma Goup Metagreywackes, Goldenville, Nova Scotia

Increasing inequancy and decreasing fluctuation of long axes of quartz grains from lithons to cleavage zones in Heguna Group metagreywackes indicate an increase in strain. This strain increase is best ascribed to pervasive pressure solution in which quartz grains are trimmed to yield nearly rectangular sections in cleavage zones, as compared to their irregular outlines in lithons. Shortening calculated from a one-dimensional strain model reaches 60-7OZ in cleavage zones. Comparable values of shortening are calculated from modal analyses, and from chemical analyses of cleavages and lithons. The Implication of such shortening is that about ten percent of all the quartz in the original rock has been removed from the immediate system. This demands volumes of water about one order of magnitude greater than any likely content of connate water. The transport system was a dynamic one, involving most of the rock volume. RÉSUMÉ L'accroieseaent de l'inégalité et la baisse des fluctuations des longs axes des grains de quartz, des lithons jusqu'aux zones de clivage, dans les métagrauwackes du groupe Méguma, indique une haueae de tension. Cette hausse de tension est attribute à la solution de pression pénétrante dans laquelle les grains de quartz sont tallés et donnent des sections presque rectangulaires dans les zones de clivage, comparé à leur profile irrégulier dans les lithons. Le raccourcissement, calculi à partlr d'un modèle de pression unidimensionnel, atteint des valeurs entre 60 et 702 dans les zones de clivage. Des valeurs comparables du raccourcissement sont calculées à partlr d'analyses modales, et d'analyses chimiques des clivages et des lithons. L'implicatlon de ce raccourclssement est qu'environ dix pourcent de tout le quartz de la roche originaire, a été supérime du système immédiate Cela exige des volumes d'eau d'un ordre de grandeur plus important que n'importe quel système inné d'eau vraissembable. Ce système de transport était un système dynamique qui comprenait la majorité du volume des roches. [Traduit par le journal

NCP activates chloroplast transcription by controlling phytochrome-dependent dual nuclear and plastidial switches.

Phytochromes initiate chloroplast biogenesis by activating genes encoding the photosynthetic apparatus, including photosynthesis-associated plastid-encoded genes (PhAPGs). PhAPGs are transcribed by a bacterial-type RNA polymerase (PEP), but how phytochromes in the nucleus activate chloroplast gene expression remains enigmatic. We report here a forward genetic screen in Arabidopsis that identified NUCLEAR CONTROL OF PEP ACTIVITY (NCP) as a necessary component of phytochrome signaling for PhAPG activation. NCP is dual-targeted to plastids and the nucleus. While nuclear NCP mediates the degradation of two repressors of chloroplast biogenesis, PIF1 and PIF3, NCP in plastids promotes the assembly of the PEP complex for PhAPG transcription. NCP and its paralog RCB are non-catalytic thioredoxin-like proteins that diverged in seed plants to adopt nonredundant functions in phytochrome signaling. These results support a model in which phytochromes control PhAPG expression through light-dependent double nuclear and plastidial switches that are linked by evolutionarily conserved and dual-localized regulatory proteins

Cyanobacterial ribosomal RNA genes with multiple, endonuclease-encoding group I introns

<p>Abstract</p> <p>Background</p> <p>Group I introns are one of the four major classes of introns as defined by their distinct splicing mechanisms. Because they catalyze their own removal from precursor transcripts, group I introns are referred to as autocatalytic introns. Group I introns are common in fungal and protist nuclear ribosomal RNA genes and in organellar genomes. In contrast, they are rare in all other organisms and genomes, including bacteria.</p> <p>Results</p> <p>Here we report five group I introns, each containing a LAGLIDADG homing endonuclease gene (HEG), in large subunit (LSU) rRNA genes of cyanobacteria. Three of the introns are located in the LSU gene of <it>Synechococcus </it>sp. C9, and the other two are in the LSU gene of <it>Synechococcus lividus </it>strain C1. Phylogenetic analyses show that these introns and their HEGs are closely related to introns and HEGs located at homologous insertion sites in organellar and bacterial rDNA genes. We also present a compilation of group I introns with homing endonuclease genes in bacteria.</p> <p>Conclusion</p> <p>We have discovered multiple HEG-containing group I introns in a single bacterial gene. To our knowledge, these are the first cases of multiple group I introns in the same <it>bacterial </it>gene (multiple group I introns have been reported in at least one phage gene and one prophage gene). The HEGs each contain one copy of the LAGLIDADG motif and presumably function as homodimers. Phylogenetic analysis, in conjunction with their patchy taxonomic distribution, suggests that these intron-HEG elements have been transferred horizontally among organelles and bacteria. However, the mode of transfer and the nature of the biological connections among the intron-containing organisms are unknown.</p

rbcL and matK Earn Two Thumbs Up as the Core DNA Barcode for Ferns

BACKGROUND: DNA barcoding will revolutionize our understanding of fern ecology, most especially because the accurate identification of the independent but cryptic gametophyte phase of the fern's life history--an endeavor previously impossible--will finally be feasible. In this study, we assess the discriminatory power of the core plant DNA barcode (rbcL and matK), as well as alternatively proposed fern barcodes (trnH-psbA and trnL-F), across all major fern lineages. We also present plastid barcode data for two genera in the hyperdiverse polypod clade--Deparia (Woodsiaceae) and the Cheilanthes marginata group (currently being segregated as a new genus of Pteridaceae)--to further evaluate the resolving power of these loci. PRINCIPAL FINDINGS: Our results clearly demonstrate the value of matK data, previously unavailable in ferns because of difficulties in amplification due to a major rearrangement of the plastid genome. With its high sequence variation, matK complements rbcL to provide a two-locus barcode with strong resolving power. With sequence variation comparable to matK, trnL-F appears to be a suitable alternative barcode region in ferns, and perhaps should be added to the core barcode region if universal primer development for matK fails. In contrast, trnH-psbA shows dramatically reduced sequence variation for the majority of ferns. This is likely due to the translocation of this segment of the plastid genome into the inverted repeat regions, which are known to have a highly constrained substitution rate. CONCLUSIONS: Our study provides the first endorsement of the two-locus barcode (rbcL+matK) in ferns, and favors trnL-F over trnH-psbA as a potential back-up locus. Future work should focus on gathering more fern matK sequence data to facilitate universal primer development

Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data

We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these norms. As an application we examine some problems with rough source term where the solution can not be characterised as a weak solution and show quasi-optimal error control

Brain microtubule-associated proteins modulate microtubule dynamic instability in vitro : real-time-observations using video microscopy

We used video assays to study the dynamic instability behavior of individual microtubules assembled in vitro with purified tau, purified MAP2 or a preparation of unfractionated heat-stable MAPs. Axoneme-nucleated microtubules were assembled from pure tubulin at concentrations between 4 and 9 microM in the presence of MAPs, and observed by video-differential interference contrast microscopy. Microtubules co-assembled with each MAP preparation exhibited the elongation and rapid shortening phases and the abrupt transitions (catastrophe and rescue) characteristic of dynamic instability. Each MAP preparation increased the microtubule elongation rate above that for purified tubulin alone by decreasing the tubulin subunit dissociation rate during elongation. The brain MAPs used in this study reduced the rate of microtubule rapid shortening, but allowed significant loss of polymer during the shortening phase. Purified tau and MAP2 decreased the frequency of catastrophe and increased the frequency of rescue, while the heat-stable MAPs suppressed catastrophe at all but the lowest tubulin concentrations. Thus, each of these MAPs modulates, but does not abolish, dynamic instability behavior of microtubules. We propose a model to explain how MAP2 and tau bind to the microtubule lattice at sites along protofilaments so that the MAPs promote polymerization, but do not significantly block the mechanism of rapid shortening inherent in the tubulin lattice. Rapid shortening, when it occurs, proceeds primarily by the dissociation of short fragments of protofilaments, which contain the bound MAPs