An HMM--ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media

We design a numerical approximation of a system of partial differential equations modelling the miscible displacement of a fluid by another in a porous medium. The advective part of the system is discretised using a characteristic method, and the diffusive parts by a finite volume method. The scheme is applicable on generic (possibly non-conforming) meshes as encountered in applications. The main features of our work are the reconstruction of a Darcy velocity, from the discrete pressure fluxes, that enjoys a local consistency property, an analysis of implementation issues faced when tracking, via the characteristic method, distorted cells, and a new treatment of cells near the injection well that accounts better for the conservativity of the injected fluid

Some Properties of the Exchange Operator with respect to Structured Matrices defined by Indefinite Scalar Product Spaces

The properties of the exchange operator on some types of matrices are explored in this paper. In particular, the properties of exc(A,p,q), where A is a given structured matrix of size (p+q)Ã(p+q) and exc : M ÃNÃN â M is the exchange operator are studied. This paper is a generalization of one of the results in [N.J. Higham. J-orthogonal matrices: Properties and generation. SIAM Review, 45:504â519, 2003.]

MicroRNA networks direct neuronal development and plasticity

MicroRNAs (miRNAs) constitute a class of small, non-coding RNAs that act as post-transcriptional regulators of gene expression. In neurons, the functions of individual miRNAs are just beginning to emerge, and recent studies have elucidated roles for neural miRNAs at various stages of neuronal development and maturation, including neurite outgrowth, dendritogenesis, and spine formation. Notably, miRNAs regulate mRNA translation locally in the axosomal and synaptodendritic compartments, and thereby contribute to the dynamic spatial organization of axonal and dendritic structures and their function. Given the critical role for miRNAs in regulating early brain development and in mediating synaptic plasticity later in life, it is tempting to speculate that the pathology of neurological disorders is affected by altered expression or functioning of miRNAs. Here we provide an overview of recently identified mechanisms of neuronal development and plasticity involving miRNAs, and the consequences of miRNA dysregulation

An efficient implementation of mass conserving characteristic-based schemes in two and three dimensions

In this paper, we develop the ball-approximated characteristics (B-char) method, which is an algorithm for efficiently implementing characteristic-based schemes in two and three dimensions. Core to the implementation of numerical schemes is the evaluation of integrals, which in the context of characteristic-based schemes with piecewise constant approximations boils down to computing the intersections between two regions. In the literature, these regions are approximated by polytopes (polygons in two dimensions and polyhedra in three dimensions) and, due to this, the implementation in three dimensions is nontrivial. The main novelty in this paper is the approximation of the regions by balls, whose intersections are much cheaper to compute than those of polytopes. Of course, balls cannot fully tessellate a region, and hence some mass may be lost. We perform some adjustments, and also solve an optimization problem, in order to yield a scheme that is both locally and globally mass conserving. This algorithm can achieve results that are similar to those obtained from an implementation which uses polytopal intersections, with a much cheaper computational cost

Methyltransferase-Directed Labeling of Biomolecules and its Applications

Methyltransferases (MTases) form a large family of enzymes that methylate a diverse set of targets, ranging from the three major biopolymers to small molecules. Most of these MTases use the cofactor S-adenosyl-l-Methionine (AdoMet) as a methyl source. In recent years, there have been significant efforts toward the development of AdoMet analogues with the aim of transferring moieties other than simple methyl groups. Two major classes of AdoMet analogues currently exist: doubly-activated molecules and aziridine based molecules, each of which employs a different approach to achieve transalkylation rather than transmethylation. In this review, we discuss the various strategies for labelling and functionalizing biomolecules using AdoMet-dependent MTases and AdoMet analogues. We cover the synthetic routes to AdoMet analogues, their stability in biological environments and their application in transalkylation reactions. Finally, some perspectives are presented for the potential use of AdoMet analogues in biology research, (epi)genetics and nanotechnology