Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes

This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of the condition numbers that is logarithmic in the polynomial degrees when all degrees are equal and quadratic otherwise, our main objective is to realize full robustness with respect to arbitrarily large locally varying polynomial degrees degrees, i.e., under mild grading constraints condition numbers stay uniformly bounded with respect to the mesh size and variable degrees. The conceptual foundation of the envisaged preconditioners is the auxiliary space method. The main conceptual ingredients that will be shown in this framework to yield "optimal" preconditioners in the above sense are Legendre-Gauss-Lobatto grids in connection with certain associated anisotropic nested dyadic grids as well as specially adapted wavelet preconditioners for the resulting low order auxiliary problems. Moreover, the preconditioners have a modular form that facilitates somewhat simplified partial realizations. One of the components can, for instance, be conveniently combined with domain decomposition, at the expense though of a logarithmic growth of condition numbers. Our analysis is complemented by quantitative experimental studies of the main components.Comment: 41 pages, 11 figures; Major revision: rearrangement of the contents for better readability, part on wavelet preconditioner adde

A 1/29 chromosome translocation in Southern African Nguni cattle. The identification, occurrence and origin of the translocation

International audienc

Methodologies for the analysis of pesticides and pharmaceuticals in sediments and plant tissue

Eco-technologies that utilize natural processes involving wetland vegetation, soil and their associated microbial assemblages are increasingly used for the removal of contaminants of emerging concern (CECs) from polluted water. However, information on removal processes in these systems is not always available, possibly due to the lack of simple and robust methodologies for analysis of CECs in complex matrices such as sediment and plant tissue. The aim of the present study was to use a simple and fast procedure based on ultrasonic extraction (USE) and reduced clean-up procedures to analyse 8 pesticides and 9 pharmaceuticals by high-performance liquid chromatography (HPLC) coupled with diode array detector. The established methods demonstrated suitable sensitivity and reliability, and proved fit-for-purpose in quantifying multiple classes of pesticides and pharmaceuticals. For sediments, extraction with methanol/acetone (95:5, v/v) followed by a simple evaporation to dryness and redissolution (water:methanol 50:50) provided acceptable recovery (50 - 101%) and RSD 64%) with RSD < 22% determined using different types of wetland plants. The methodology has been successfully applied in different studies on the fate of emerging contaminants in water treatment eco-technology systems

Unsupervised denoising for sparse multi-spectral computed tomography

Multi-energy computed tomography (CT) with photon counting detectors (PCDs) enables spectral imaging as PCDs can assign the incoming photons to specific energy channels. However, PCDs with many spectral channels drastically increase the computational complexity of the CT reconstruction, and bespoke reconstruction algorithms need fine-tuning to varying noise statistics. \rev{Especially if many projections are taken, a large amount of data has to be collected and stored. Sparse view CT is one solution for data reduction. However, these issues are especially exacerbated when sparse imaging scenarios are encountered due to a significant reduction in photon counts.} In this work, we investigate the suitability of learning-based improvements to the challenging task of obtaining high-quality reconstructions from sparse measurements for a 64-channel PCD-CT. In particular, to overcome missing reference data for the training procedure, we propose an unsupervised denoising and artefact removal approach by exploiting different filter functions in the reconstruction and an explicit coupling of spectral channels with the nuclear norm. Performance is assessed on both simulated synthetic data and the openly available experimental Multi-Spectral Imaging via Computed Tomography (MUSIC) dataset. We compared the quality of our unsupervised method to iterative total nuclear variation regularized reconstructions and a supervised denoiser trained with reference data. We show that improved reconstruction quality can be achieved with flexibility on noise statistics and effective suppression of streaking artefacts when using unsupervised denoising with spectral coupling

Genetic diversity in three invasive clonal aquatic species in New Zealand

<p>Abstract</p> <p>Background</p> <p><it>Elodea canadensis, Egeria densa </it>and <it>Lagarosiphon major </it>are dioecious clonal species which are invasive in New Zealand and other regions. Unlike many other invasive species, the genetic variation in New Zealand is very limited. Clonal reproduction is often considered an evolutionary dead end, even though a certain amount of genetic divergence may arise due to somatic mutations. The successful growth and establishment of invasive clonal species may be explained not by adaptability but by pre-existing ecological traits that prove advantageous in the new environment. We studied the genetic diversity and population structure in the North Island of New Zealand using AFLPs and related the findings to the number of introductions and the evolution that has occurred in the introduced area.</p> <p>Results</p> <p>Low levels of genetic diversity were found in all three species and appeared to be due to highly homogeneous founding gene pools. <it>Elodea canadensis </it>was introduced in 1868, and its populations showed more genetic structure than those of the more recently introduced of <it>E. densa </it>(1946) and <it>L. major </it>(1950). <it>Elodea canadensis </it>and <it>L. major</it>, however, had similar phylogeographic patterns, in spite of the difference in time since introduction.</p> <p>Conclusions</p> <p>The presence of a certain level of geographically correlated genetic structure in the absence of sexual reproduction, and in spite of random human dispersal of vegetative propagules, can be reasonably attributed to post-dispersal somatic mutations. Direct evidence of such evolutionary events is, however, still insufficient.</p

Intrinsic quadrupole moment of the nucleon

We address the question of the intrinsic quadrupole moment Q_0 of the nucleon in various models. All models give a positive intrinsic quadrupole moment for the proton. This corresponds to a prolate deformation. We also calculate the intrinsic quadrupole moment of the Delta(1232). All our models lead to a negative intrinsic quadrupole moment of the Delta corresponding to an oblate deformation.Comment: 17 pages, 5 figure

Temporal Variability of Organic C and Nitrate in a Shallow Aquifer

The loading of organic substrates into shallow aquifers may follow seasonal cycles, which will impact the transport and fate of agrichemicals. The objective of this research was to measure temporal changes in the groundwater dissolved organic C (DOC) and nitrate concentrations. Groundwater monitoring wells were installed and sediment samples from the aquifer were collected in 1991. Sediment samples were used to evaluate denitrification potentials, while water samples were collected at periodic intervals in 1992 and 1993 from the surface of the aquifer. Water samples were analyzed for nitrate-N and DOC-C. Denitrification was observed in sediment amended with nitrate and incubated under anaerobic conditions at 10°C. Addition of algae lazed biomass increased denitrification, establishing that denitrification was substrate limited. In the aquifer, DOC concentrations followed seasonal patterns. DOC concentrations were highest following spring recharge and then decreased. Peak timing indicates that freezing and thawing were responsible for seasonal DOC patterns. These findings show that seasonally driven physical processes, such as freezing and thawing, influence organic substrate transport from surface to subsurface environments, and that this process should be taken into account when assessing agrichemical detoxification rates in shallow aquifers