Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings.

Genome-wide mapping of 5-hydroxymethylcytosine in three rice cultivars reveals its preferential localization in transcriptionally silent transposable element genes

5-Hydroxymethylcytosine (5hmC), a modified form of cytosine that is considered the sixth nucleobase in DNA, has been detected in mammals and is believed to play an important role in gene regulation. In this study, 5hmC modification was detected in rice by employing a dot-blot assay, and its levels was further quantified in DNA from different rice tissues using liquid chromatography-multistage mass spectrometry (LC-MS/MS/MS). The results showed large intertissue variation in 5hmC levels. The genome-wide profiles of 5hmC modification in three different rice cultivars were also obtained using a sensitive chemical labelling followed by a next-generation sequencing method. Thousands of 5hmC peaks were identified, and a comparison of the distributions of 5hmC among different rice cultivars revealed the specificity and conservation of 5hmC modification. The identified 5hmC peaks were significantly enriched in heterochromatin regions,and mainly located in transposable element (TE) genes, especially around retrotransposons. The correlation analysis of 5hmC and gene expression data revealed a close association between 5hmC and silent TEs. These findings provide a resource for plant DNA 5hmC epigenetic studies and expand our knowledge of 5hmC modification.

Sparse space-time boundary element methods for the heat equation

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(h

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Thyroid hormone can increase estrogen-mediated transcription from a consensus estrogen response element in neuroblastoma cells

Thyroid hormones (T) and estrogens (E) are nuclear receptor ligands with at least two molecular mechanisms of action: (i) relatively slow genomic effects, such as the regulation of transcription by cognate T receptors (TR) and E receptors (ER); and (ii) relatively rapid nongenomic effects, such as kinase activation and calcium release initiated at the membrane by putative membrane receptors. Genomic and nongenomic effects were thought to be disparate and independent. However, in a previous study using a two-pulse paradigm in neuroblastoma cells, we showed that E acting at the membrane could potentiate transcription from an E-driven reporter gene in the nucleus. Because both T and E can have important effects on mood and cognition, it is possible that the two hormones can act synergistically. In this study, we demonstrate that early actions of T via TRalpha1 and TRbeta1 can potentiate E-mediated transcription (genomic effects) from a consensus E response element (ERE)-driven reporter gene in transiently transfected neuroblastoma cells. Such potentiation was reduced by inhibition of mitogen-activated protein kinase. Using phosphomutants of ERalpha, we also show that probable mitogen-activated protein kinase phosphorylation sites on the ERalpha, the serines at position 167 and 118, are important in TRbeta1-mediated potentiation of ERalpha-induced transactivation. We suggest that crosstalk between T and E includes potential interactions through both nuclear and membrane-initiated molecular mechanisms of hormone signaling.