Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion

This is the published version, also available here: http://dx.doi.org/10.1137/100807156.We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean's caricature of the cubic, we construct front solutions which correspond, in the case of homogeneous diffusion, to monotone traveling front solutions or, in the case of propagation failure, to stationary front solutions. A general form for these fronts is given for essentially arbitrary inhomogeneous discrete diffusion, and conditions are given for the existence of solutions to the original discrete Nagumo equation. The specific case of one defect is considered in depth, giving a complete understanding of propagation failure and a grasp on changes in wave speed. Insight into the dynamic behavior of these front solutions as a function of the magnitude and relative position of the defects is obtained with the assistance of numerical results

Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion

We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean\u27s caricature of the cubic, we construct front solutions which correspond, in the case of homogeneous diffusion, to monotone traveling front solutions or, in the case of propagation failure, to stationary front solutions. A general form for these fronts is given for essentially arbitrary inhomogeneous discrete diffusion, and conditions are given for the existence of solutions to the original discrete Nagumo equation. The specific case of one defect is considered in depth, giving a complete understanding of propagation failure and a grasp on changes in wave speed. Insight into the dynamic behavior of these front solutions as a function of the magnitude and relative position of the defects is obtained with the assistance of numerical results

Analysis of mutations causing familial hypercholesterolaemia in black South African patients of different ancestry

Background. Familial hypercholesterolaemia (FH) is usually caused by mutations in three genes (LDLR, APOB and PCSK9).Objective. To identify the spectrum of FH-causing mutations in black South African (SA) patients.Methods. DNA samples of 16 unrelated South African FH patients with elevated low-density lipoprotein cholesterol levels, tendon xanthomas and corneal arcus (3 clinically homozygous FH and 13 heterozygous FH) of ethnic African origin were screened for mutations in the LDLR (coding region, promoter and intron/exon boundaries), APOB (part of exon 26) and PCSK9 genes (exon 7), using high-resolution melting.Results. Eight LDLR mutations were identified, for an overall detection rate of 8/19 predicted FH-causing alleles (42.1%). The previously reported six base pair deletion p.(D47_G48del) was found in two patients, and two novel variants (c.1187-25T>C and c.1664T>G p.(L555R)) were found, both predicted to be pathogenic using in silico web-based predictive algorithms. No pathogenic variants in APOB or PCSK9 were found.Conclusions. These findings contribute to the knowledge of allelic heterogeneity in the spectrum of FH-causing mutations in black SA patients, signifying their ancestral diversity. The relatively low overall detection rate may reflect locus heterogeneity of the FH phenotype in black SA FH patients

Report from the Expert Panel on the evaluation of the VRZs during the 2018/19 fishing season

In July 2018 ARK (the Association of Responsible Krill harvesting companies) launched a set of voluntary measures, known as ARK’s Commitment, which were proposed to improve the long-term sustainability of the krill fishery. The Commitment was initiated with support from Greenpeace, WWF and The Pew Charitable Trusts as a precautionary action whilst CCAMLR developed spatial management of the krill fishery in Area 48. The Commitment, which took the form of Voluntary Restriction Zones (VRZs), was implemented for the 2018-19 fishing season. The krill fishing fleet associated with ARK agreed to avoid fishing in an area of up to 40 km from penguin colonies in Subarea 48.1 during the penguin breeding season

Computation of Mixed Type Functional Differential Boundary Value Problems

This is the published version, also available here: http://dx.doi.org/10.1137/040603425.We study boundary value differential-difference equations where the difference terms may contain both advances and delays. Special attention is paid to connecting orbits, in particular to the modeling of the tails after truncation to a finite interval, and we reformulate these problems as functional differential equations over a bounded domain. Connecting orbits are computed for several such problems including discrete Nagumo equations, an Ising model, and Frenkel--Kontorova type equations. We describe the collocation boundary value problem code used to compute these solutions, and the numerical analysis issues which arise, including linear algebra, boundary functions and conditions, and convergence theory for the collocation approximation on finite intervals

A Comparison of Multivariate and Pre-Processing Methods for Quantitative Laser-Induced Breakdown Spectroscopy of Geologic Samples

The ChemCam instrument selected for the Curiosity rover is capable of remote laser-induced breakdown spectroscopy (LIBS).[1] We used a remote LIBS instrument similar to ChemCam to analyze 197 geologic slab samples and 32 pressed-powder geostandards. The slab samples are well-characterized and have been used to validate the calibration of previous instruments on Mars missions, including CRISM [2], OMEGA [3], the MER Pancam [4], Mini-TES [5], and Moessbauer [6] instruments and the Phoenix SSI [7]. The resulting dataset was used to compare multivariate methods for quantitative LIBS and to determine the effect of grain size on calculations. Three multivariate methods - partial least squares (PLS), multilayer perceptron artificial neural networks (MLP ANNs) and cascade correlation (CC) ANNs - were used to generate models and extract the quantitative composition of unknown samples. PLS can be used to predict one element (PLS1) or multiple elements (PLS2) at a time, as can the neural network methods. Although MLP and CC ANNs were successful in some cases, PLS generally produced the most accurate and precise results

On the Complex Network Structure of Musical Pieces: Analysis of Some Use Cases from Different Music Genres

This paper focuses on the modeling of musical melodies as networks. Notes of a melody can be treated as nodes of a network. Connections are created whenever notes are played in sequence. We analyze some main tracks coming from different music genres, with melodies played using different musical instruments. We find out that the considered networks are, in general, scale free networks and exhibit the small world property. We measure the main metrics and assess whether these networks can be considered as formed by sub-communities. Outcomes confirm that peculiar features of the tracks can be extracted from this analysis methodology. This approach can have an impact in several multimedia applications such as music didactics, multimedia entertainment, and digital music generation.Comment: accepted to Multimedia Tools and Applications, Springe

Index

The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Jüttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.Original Publication: Antoine Bret, Laurent Gremillet and Mark Eric Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, 2010, Physics of Plasmas, (17), 12, 120501-1-120501-36. http://dx.doi.org/10.1063/1.3514586 Copyright: American Institute of Physics http://www.aip.org/</p