Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

In this paper three p-adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous Galerkin methods. The truncation error is approximated by means of a ? -estimation procedure and enables the identification of mesh regions that require adaptation. Three adaptation strategies are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. All strategies require fine solutions, which are obtained by enriching the polynomial order, but while the former needs time converged solutions, the last two rely on non-converged solutions, which lead to faster computations. In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier?Stokes equations. It is shown that the two quasi- a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively.

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

In this work a p-adaptation (modification of the polynomial order) strategy based on the minimization of the truncation error is developed for high order discontinuous Galerkin methods. The truncation error is approximated by means of a truncation error estimation procedure and enables the identification of mesh regions that require adaptation. Three truncation error estimation approaches are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. Fine solutions, which are obtained by enriching the polynomial order, are required to solve the numerical problem with adequate accuracy. For the three truncation error estimation methods the former needs time converged solutions, while the last two rely on non-converged solutions, which lead to faster computations. Based on these truncation error estimation methods, algorithms for mesh adaptation were designed and tested. Firstly, an isotropic adaptation approach is presented, which leads to equally distributed polynomial orders in different coordinate directions. This first implementation is improved by incorporating a method to extrapolate the truncation error. This results in a significant reduction of computational cost. Secondly, the employed high order method permits the spatial decoupling of the estimated errors and enables anisotropic p-adaptation. The incorporation of anisotropic features leads to meshes with different polynomial orders in the different coordinate directions such that flow-features related to the geometry are resolved in a better manner. These adaptations result in a significant reduction of degrees of freedom and computational cost, while the amount of improvement depends on the test-case. Finally, this anisotropic approach is extended by using error extrapolation which leads to an even higher reduction in computational cost. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. The main result is that the two quasi-a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of a factor of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively. RESUMEN En este trabajo se ha desarrollado una estrategia de adaptación-p (modificación del orden polinómico) para métodos Galerkin discontinuo de alto orden basada en la minimización del error de truncación. El error de truncación se estima utilizando el método tau-estimation. El estimador permite la identificación de zonas de la malla que requieren adaptación. Se distinguen tres técnicas de estimación: a posteriori, quasi a priori y quasi a priori con correción. Todas las estrategias requieren una solución obtenida en una malla fina, la cual es obtenida aumentando de manera uniforme el orden polinómico. Sin embargo, mientras que el primero requiere que esta solución esté convergida temporalmente, el resto utiliza soluciones no convergidas, lo que se traduce en un menor coste computacional. En este trabajo se han diseñado y probado algoritmos de adaptación de malla basados en métodos tau-estimation. En primer lugar, se presenta un algoritmo de adaptacin isótropo, que conduce a discretizaciones con el mismo orden polinómico en todas las direcciones espaciales. Esta primera implementación se mejora incluyendo un método para extrapolar el error de truncación. Esto resulta en una reducción significativa del coste computacional. En segundo lugar, el método de alto orden permite el desacoplamiento espacial de los errores estimados, permitiendo la adaptación anisotropica. Las mallas obtenidas mediante esta técnica tienen distintos órdenes polinómicos en cada una de las direcciones espaciales. La malla final tiene una distribución óptima de órdenes polinómicos, los cuales guardan relación con las características del flujo que, a su vez, depenen de la geometría. Estas técnicas de adaptación reducen de manera significativa los grados de libertad y el coste computacional. Por último, esta aproximación anisotropica se extiende usando extrapolación del error de truncación, lo que conlleva un coste computational aún menor. Las estrategias se verifican y se comparan en téminors de precisión y coste computacional utilizando las ecuaciones de Euler y Navier Stokes. Los dos métodos quasi a priori consiguen una reducción significativa del coste computacional en comparación con aumento uniforme del orden polinómico. En concreto, para una capa límite viscosa, obtenemos una mejora en tiempo de computación de 6.6 y 7.6 respectivamente, para las aproximaciones quasi-a priori y quasi-a priori con corrección.

Evidence for protein X binding to a discontinuous epitope on the cellular prion protein during scrapie prion propagation

Studies on the transmission of human (Hu) prions to transgenic (Tg) mice suggested that another molecule provisionally designated protein X participates in the formation of nascent scrapie isoform of prion protein (PrPSc). We report the identification of the site at which protein X binds to the cellular isoform of PrP (PrPC) using scrapie-infected mouse (Mo) neuroblastoma cells transfected with chimeric Hu/MoPrP genes even though protein X has not yet been isolated. Substitution of a Hu residue at position 214 or 218 prevented PrPSc formation. The side chains of these residues protrude from the same surface of the C-terminal α-helix and form a discontinuous epitope with residues 167 and 171 in an adjacent loop. Substitution of a basic residue at positions 167, 171, or 218 also prevented PrPSc formation: at a mechanistic level, these mutant PrPs appear to act as “dominant negatives” by binding protein X and rendering it unavailable for prion propagation. Our findings seem to explain the protective effects of basic polymorphic residues in PrP of humans and sheep and suggest therapeutic and prophylactic approaches to prion diseases.

The heme oxygenase gene (pbsA) in the red alga Rhodella violacea is discontinuous and transcriptionally activated during iron limitation

Heme oxygenase (HO) catalyzes the opening of the heme ring with the release of iron in both plants and animals. In cyanobacteria, red algae, and cryptophyceae, HO is a key enzyme in the synthesis of the chromophoric part of the photosynthetic antennae. In an attempt to study the regulation of this key metabolic step, we cloned and sequenced the pbsA gene encoding this enzyme from the red alga Rhodella violacea. The gene is located on the chloroplast genome, split into three distant exons, and is presumably expressed by a trans-splicing mechanism. The deduced polypeptide sequence is homologous to other reported HOs from organisms containing phycobilisomes (Porphyra purpurea and Synechocystis sp. strain PCC 6803) and, to a lesser extent, to vertebrate enzymes. The expression is transcriptionally activated under iron deprivation, a stress condition frequently encountered by algae, suggesting a second role for HO as an iron-mobilizing agent in photosynthetic organisms.

OliI, a unique restriction endonuclease that recognizes the discontinuous sequence 5′-CACNN↓NNGTG-3′

A new type II restriction endonuclease designated OliI has been partially purified from the halophilic bacterium Oceanospirillum linum 4-5D. OliI recognizes the interrupted hexanucleotide palindrome 5′-CACNN↓NNGTG-3′ and cleaves it in the center generating blunt-ended DNA fragments.

Evaluation of the role of heterogeneous nuclear ribonucleoprotein A1 as a host factor in murine coronavirus discontinuous transcription and genome replication

Viruses with RNA genomes often capture and redirect host cell components to assist in mechanisms particular to RNA-dependent RNA synthesis. The nidoviruses are an order of positive-stranded RNA viruses, comprising coronaviruses and arteriviruses, that employ a unique strategy of discontinuous transcription, producing a series of subgenomic mRNAs linking a 5′ leader to distal portions of the genome. For the prototype coronavirus mouse hepatitis virus (MHV), heterogeneous nuclear ribonucleoprotein (hnRNP) A1 has been shown to be able to bind in vitro to the negative strand of the intergenic sequence, a cis-acting element found in the leader RNA and preceding each downstream ORF in the genome. hnRNP A1 thus has been proposed as a host factor in MHV transcription. To test this hypothesis genetically, we initially constructed MHV mutants with a very high-affinity hnRNP A1 binding site inserted in place of, or adjacent to, an intergenic sequence in the MHV genome. This inserted hnRNP A1 binding site was not able to functionally replace, or enhance transcription from, the intergenic sequence. This finding led us to test more directly the role of hnRNP A1 by analysis of MHV replication and RNA synthesis in a murine cell line that does not express this protein. The cellular absence of hnRNP A1 had no detectable effect on the production of infectious virus, the synthesis of genomic RNA, or the quantity or quality of subgenomic mRNAs. These results strongly suggest that hnRNP A1 is not a required host factor for MHV discontinuous transcription or genome replication.

Discontinuous epitopes of hepatitis B surface antigen derived from a filamentous phage peptide library.

The structure of the small hepatitis B virus surface antigen (HBsAg) was investigated by epitope mapping of four anti-HBsAg monoclonal antibodies (mAbs). Amino acid sequences of epitopes were derived from affinity-enrichment experiments (biopanning) using a filamentous phage peptide library. The library consists of 10(9) different clones bearing a 30-residue peptide fused to gene III. Sequence homologies between peptides obtained from panning the library against the antibodies and the native HBsAg sequence allowed for precise description of the binding regions. Three of four mAbs were found to bind to distinct discontinuous epitopes between amino acid residues 101 and 207 of HBsAg. The fourth mAb was demonstrated to bind to residues 121-124. The sequence data are supported by ELISA assays demonstrating the binding of the HBsAg-specific peptides on filamentous phage to mAbs. The sequence data were used to map the surface of HBsAg and to derive a topological model for the alpha-carbon trace of the 101-207 region of HBsAg. The approach should be useful for other proteins for which the crystal structure is not available but a representative set of mAbs can be obtained.

Modeling collisional processes in plasmas using discontinuous numerical methods

Thesis (Ph.D.)--University of Washington, 2016-06

A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

Thesis (Ph.D.)--University of Washington, 2016-03

Timing continuous or discontinuous movements across effectors specified by different pacing modalities and intervals

Sensorimotor synchronization is hypothesized to arise through two different processes, associated with continuous or discontinuous rhythmic movements. This study investigated synchronization of continuous and discontinuous movements to different pacing signals (auditory or visual), pacing interval (500, 650, 800, 950 ms) and across effectors (non-dominant vs. non-dominant hand). The results showed that mean and variability of asynchronization errors were consistently smaller for discontinuous movements compared to continuous movements. Furthermore, both movement types were timed more accurately with auditory pacing compared to visual pacing and were more accurate with the dominant hand. Shortening the pacing interval also improved sensorimotor synchronization accuracy in both continuous and discontinuous movements. These results show the dependency of temporal control of movements on the nature of the motor task, the type and rate of extrinsic sensory information as well as the efficiency of the motor actuators for sensory integration.

Racing for radical innovation:how motorsport companies harness network diversity for discontinuous innovation

The motorsport industry is a significant part of the UK economy. According to industry estimates approximately 4,500 companies are involved in the UK Motorsport and Performance Engineering Industry and its wide-ranging support activities. The industry has an annual turnover of £6.0 billion, and contributes £3.6 billion worth of exports. The Motorsport Industry Association estimates that the support side of the sector alone "involving events management, public relations, marketing, sponsorship and a host of other support functions" accounts for approximately £1.7 billion of the yearly industry total. And in terms of employment, UK Motorsport supports 38,500 full and part-time jobs, including 25,000 engineers.

Discontinuous control of multi-variable processes

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Stream dissolved organic matter bioavailability and composition in watersheds underlain with discontinuous permafrost

We examined the impact of permafrost on dissolved organic matter (DOM) composition in Caribou-Poker Creeks Research Watershed (CPCRW), a watershed underlain with discontinuous permafrost, in interior Alaska. We analyzed long term data from watersheds underlain with varying degrees of permafrost, sampled springs and thermokarsts, used fluorescence spectroscopy, and measured the bioavailabity of dissolved organic carbon (DOC). Permafrost driven patterns in hydrology and vegetation influenced DOM patterns in streams, with the stream draining the high permafrost watershed having higher DOC and dissolved organic nitrogen (DON) concentrations, higher DOC:- DON and greater specific ultraviolet absorbance (SUVA) than the streams draining the low and medium permafrost watersheds. Streams, springs and thermokarsts exhibited a wide range of DOC and DON concentrations (1.5–37.5 mgC/L and 0.14–1.26 mgN/L, respectively), DOC:DON (7.1–42.8) and SUVA (1.5–4.7 L mgC-1 m-1). All sites had a high proportion of humic components, a low proportion of protein components, and a low fluorescence index value (1.3–1.4), generally consistent with terrestrially derivedDOM. Principal component analysis revealed distinct groups in our fluorescence data determined by diagenetic processing and DOM source. The proportion of bioavailable DOC ranged from 2 to 35%, with the proportion of tyrosine- and tryptophan-like fluorophores in the DOM being a major predictor of DOC loss (p\0.05, R2 = 0.99). Our results indicate that the degradation of permafrost in CPCRW will result in a decrease in DOC and DON concentrations, a decline in DOC:DON, and a reduction in SUVA, possibly accompanied by

A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

We develop the a posteriori error estimation of interior penalty discontinuous Galerkin discretizations for H(curl)-elliptic problems that arise in eddy current models. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The proposed a posteriori error estimator is validated by numerical experiments, illustrating its reliability and efficiency for a range of test problems.