Wavelet-Galerkin solution of boundary value problems

International audienceIn this paper we review the application of wavelets to the solution of partial differential equations. We consider in detail both the single scale and the multiscale Wavelet Galerkin method. The theory of wavelets is described here using the language and mathematics of signal processing. We show a method of adapting wavelets to an interval using an extrapolation technique called Wavelet Extrapolation. Wavelets on an interval allow boundary conditions to be enforced in partial differential equations and image boundary problems to be overcome in image processing. Finally, we discuss the fast inversion of matrices arising from differential operators by preconditioning the multiscale wavelet matrix. Wavelet preconditioning is shown to limit the growth of the matrix condition number, such that Krylov subspace iteration methods can accomplish fast inversion of large matrices

Introduction to wavelets in engineering

International audienceThe aim of this paper is to provide an introduction to the subject of wavelet analysis for engineering applications. The paper selects from the recent mathematical literature on wavelets the results necessary to develop wavelet-based numerical algorithms. In particular, we provide extensive details of the derivation of Mallat's transform and Daubechies' wavelet coefficients, since these are fundamental to gaining an insight into the properties of wavelets. The potential benefits of using wavelets are highlighted by presenting results of our research in one-and two-dimensional data analysis and in wavelet solutions of partial differential equations

Devitrite-based optical diffusers.

Devitrite is a novel material produced by heat treatment of commercial soda-lime-silica glass. It consists of fans of needle-like crystals which can extend up to several millimeters and have interspacings of up to a few hundred nanometers. To date, only the material properties of devitrite have been reported, and there has been a distinct lack of research on using it for optical applications. In this study, we demonstrate that randomly oriented fans of devitrite crystals can act as highly efficient diffusers for visible light. Devitrite crystals produce phase modulation of light because of their relatively high anisotropy. The nanoscale spacings between these needles enable light to be diffused to large scattering angles. Experimentally measured results suggest that light diffusion patterns with beam widths of up to 120° are produced. Since devitrite is an inexpensive material to produce, it has the potential to be used in a variety of commercial applications.HB would like to thank The Leverhulme Trust and Cambridge Philosophical Society for research funding.This is the author accepted manuscript. The final version can be found on the publisher's website at: http://pubs.acs.org/doi/abs/10.1021/nn500155e Copyright © 2014 American Chemical Societ

Population Genetic Analysis of Plasmodium falciparum Parasites Using a Customized Illumina GoldenGate Genotyping Assay

The diversity in the Plasmodium falciparum genome can be used to explore parasite population dynamics, with practical applications to malaria control. The ability to identify the geographic origin and trace the migratory patterns of parasites with clinically important phenotypes such as drug resistance is particularly relevant. With increasing single-nucleotide polymorphism (SNP) discovery from ongoing Plasmodium genome sequencing projects, a demand for high SNP and sample throughput genotyping platforms for large-scale population genetic studies is required. Low parasitaemias and multiple clone infections present a number of challenges to genotyping P. falciparum. We addressed some of these issues using a custom 384-SNP Illumina GoldenGate assay on P. falciparum DNA from laboratory clones (long-term cultured adapted parasite clones), short-term cultured parasite isolates and clinical (non-cultured isolates) samples from East and West Africa, Southeast Asia and Oceania. Eighty percent of the SNPs (n = 306) produced reliable genotype calls on samples containing as little as 2 ng of total genomic DNA and on whole genome amplified DNA. Analysis of artificial mixtures of laboratory clones demonstrated high genotype calling specificity and moderate sensitivity to call minor frequency alleles. Clear resolution of geographically distinct populations was demonstrated using Principal Components Analysis (PCA), and global patterns of population genetic diversity were consistent with previous reports. These results validate the utility of the platform in performing population genetic studies of P. falciparum

Pf7: an open dataset of Plasmodium falciparum genome variation in 20,000 worldwide samples

We describe the MalariaGEN Pf7 data resource, the seventh release of Plasmodium falciparum genome variation data from the MalariaGEN network. It comprises over 20,000 samples from 82 partner studies in 33 countries, including several malaria endemic regions that were previously underrepresented. For the first time we include dried blood spot samples that were sequenced after selective whole genome amplification, necessitating new methods to genotype copy number variations. We identify a large number of newly emerging crt mutations in parts of Southeast Asia, and show examples of heterogeneities in patterns of drug resistance within Africa and within the Indian subcontinent. We describe the profile of variations in the C-terminal of the csp gene and relate this to the sequence used in the RTS,S and R21 malaria vaccines. Pf7 provides high-quality data on genotype calls for 6 million SNPs and short indels, analysis of large deletions that cause failure of rapid diagnostic tests, and systematic characterisation of six major drug resistance loci, all of which can be freely downloaded from the MalariaGEN website

An open dataset of Plasmodium falciparum genome variation in 7,000 worldwide samples.

MalariaGEN is a data-sharing network that enables groups around the world to work together on the genomic epidemiology of malaria. Here we describe a new release of curated genome variation data on 7,000 Plasmodium falciparum samples from MalariaGEN partner studies in 28 malaria-endemic countries. High-quality genotype calls on 3 million single nucleotide polymorphisms (SNPs) and short indels were produced using a standardised analysis pipeline. Copy number variants associated with drug resistance and structural variants that cause failure of rapid diagnostic tests were also analysed.  Almost all samples showed genetic evidence of resistance to at least one antimalarial drug, and some samples from Southeast Asia carried markers of resistance to six commonly-used drugs. Genes expressed during the mosquito stage of the parasite life-cycle are prominent among loci that show strong geographic differentiation. By continuing to enlarge this open data resource we aim to facilitate research into the evolutionary processes affecting malaria control and to accelerate development of the surveillance toolkit required for malaria elimination

Pf7: an open dataset of Plasmodium falciparum genome variation in 20,000 worldwide samples

We describe the MalariaGEN Pf7 data resource, the seventh release of Plasmodium falciparum genome variation data from the MalariaGEN network.  It comprises over 20,000 samples from 82 partner studies in 33 countries, including several malaria endemic regions that were previously underrepresented.  For the first time we include dried blood spot samples that were sequenced after selective whole genome amplification, necessitating new methods to genotype copy number variations.  We identify a large number of newly emerging crt mutations in parts of Southeast Asia, and show examples of heterogeneities in patterns of drug resistance within Africa and within the Indian subcontinent.  We describe the profile of variations in the C-terminal of the csp gene and relate this to the sequence used in the RTS,S and R21 malaria vaccines.  Pf7 provides high-quality data on genotype calls for 6 million SNPs and short indels, analysis of large deletions that cause failure of rapid diagnostic tests, and systematic characterisation of six major drug resistance loci, all of which can be freely downloaded from the MalariaGEN website