Abstract Motivation Microbial communities have been proved to have close relationship with many diseases. The identification of differentially abundant microbial species is clinically meaningful for finding disease-related pathogenic or probiotic bacteria. However, certain characteristics of microbiome data have hurdled the accuracy and effectiveness of differential abundance analysis. The abundances or counts of microbiome species are usually on different scales and exhibit zero-inflation and over-dispersion. Normalization is a crucial step before the differential abundance test. However, existing normalization methods typically try to adjust counts on different scales to a common scale by constructing size factors with the assumption that count distributions across samples are equivalent up to a certain percentile. These methods often yield undesirable results when differentially abundant species are of low to medium abundance level. For differential abundance analysis, existing methods often use a single distribution to model the dispersion of species which lacks flexibility to catch a single species’ distinctiveness. These methods tend to detect a lot of false positives and often lack of power when the effect size is small. Results We develop a novel framework for differential abundance analysis on sparse high-dimensional marker gene microbiome data. Our methodology relies on a novel network-based normalization technique and a two-stage zero-inflated mixture count regression model (RioNorm2). Our normalization method aims to find a group of relatively invariant microbiome species across samples and conditions in order to construct the size factor. Another contribution of the paper is that our testing approach can take under-sampling and over-dispersion into consideration by separating microbiome species into two groups and model them separately. Through comprehensive simulation studies, the performance of our method is consistently powerful and robust across different settings with different sample size, library size and effect size. We also demonstrate the effectiveness of our novel framework using a published dataset of metastatic melanoma and find biological insights from the results. Availability and implementation The R package ‘RioNorm2’ can be installed from Github athttps://github.com/yuanjing-ma/RioNorm2. Supplementary information Supplementary data are available at Bioinformatics online.

NEW SURFACE PATCHES FOR MINIMAL BALANCE SURFACES. II b ]/ 2, [ a + b ]/ 2, c/2).These four surfaces are mapped onto another, for example, by the symmetry operations listed in Table 1. The genus is 9 for MC6 as well as for MC7 surfaces. Minimal surfaces oMC5 (double catenoids)Rectangular nets 44 of twofold axes (case 26) are defined by orthorhombic group-subgroup pairs of 33 types. Only 12 of them are compatible with catenoidlike surface patches and with the respective minimal balance surfaces oP, a family of orthorhombically distorted P surfaces. Common properties of MC surfacesFor all minimal balance surfaces built up from multiple catenoids two layers of such catenoids exist per c-translation period. AbstractThe Bloch-wave method for reflection diffraction problems, primarily electron diffraction as in reflection high-energy electron diffraction (RHEED) and reflection electron microscopy (REM), is developed.0108-7673/89/020174-09503.00The basic Bloch-wave approach for surfaces is reviewed, introducing the current flow concept which plays a major role both in understanding reflection diffraction and determining the allowed Bloch waves. This is followed by a brief description of the numeri- A number of other Bloch-wave phenomena are also discussed, namely resonance diffraction and its relationship to internal and external reflection and variations in the boundary conditions and Blochwave character, splitting of diffraction spots due to stepped surfaces, which can be completely explained, and the reflection equivalent of thickness fringes.

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Application of simple Bloch-wave theory to reflection electron microscopy and diffraction leads to inconsistent results -there are not enough boundary conditions to generate a unique solution. To overcome this problem in the past the solution for a thick slab has been used instead of that for a single surface. It is shown that a simpler method valid for a single surface is to insist that only Bloch waves with current flow into or parallel to the crystal surface are allowed. Because of the equations of continuity, this is identical to insisting that only decaying waves are excited in the crystal. An additional feature of this simpler method is that the allowed Bloch waves can be readily represented on a dispersion-surface construction.