The superconvergence of the composite midpoint rule for the finite-part integral

AbstractThe composite midpoint rule is probably the simplest one among the Newton–Cotes rules for Riemann integral. However, this rule is divergent in general for Hadamard finite-part integral. In this paper, we turn this rule to a useful one and, apply it to evaluate Hadamard finite-part integral as well as to solve the relevant integral equation. The key point is based on the investigation of its pointwise superconvergence phenomenon, i.e., when the singular point coincides with some a priori known point, the convergence rate of the midpoint rule is higher than what is globally possible. We show that the superconvergence rate of the composite midpoint rule occurs at the midpoint of each subinterval and obtain the corresponding superconvergence error estimate. By applying the midpoint rule to approximate the finite-part integral and by choosing the superconvergence points as the collocation points, we obtain a collocation scheme for solving the finite-part integral equation. More interesting is that the inverse of the coefficient matrix of the resulting linear system has an explicit expression, by which an optimal error estimate is established. Some numerical examples are provided to validate the theoretical analysis

Naturally Occurring Core Protein Mutations Compensate for the Reduced Replication Fitness of a Lamivudine-Resistant HBV Isolate

Hepatitis B virus (HBV) replicates its DNA genome through reverse transcription of an RNA intermediate. The lack of proofreading capacity of the viral DNA polymerase results in a high mutation rate of HBV genome. Under the selective pressure created by the nucleos(t)ide analogue (NA) antiviral drugs, viruses with resistance mutations are selected. However, the replication fitness of NA-resistant mutants is markedly reduced compared to wild-type. Compensatory mutations in HBV polymerase, which restore the viral replication capacity, have been reported to arise under continuous treatment with lamivudine (LMV). We have previously identified a highly replicative LMV-resistant HBV isolate from a chronic hepatitis B patient experiencing acute disease exacerbation. Besides the common YMDD drug-resistant mutations, this isolate possesses multiple additional mutations in polymerase and core regions. The transcomplementation assay demonstrated that the enhanced viral replication is due to the mutations of core protein. Further mutagenesis study revealed that the P5T mutation of core protein plays an important role in the enhanced viral replication through increasing the levels of capsid formation and pregenomic RNA encapsidation. However, the LMV-resistant virus harboring compensatory core mutations remains sensitive to capsid assembly modulators (CpAMs). Taken together, our study suggests that the enhanced HBV nucleocapsid formation resulting from core mutations represents an important viral strategy to surmount the antiviral drug pressure and contribute to viral pathogenesis, and CpAMs hold promise for developing the combinational antiviral therapy for hepatitis B

A Tensor-Based Framework for Studying Eigenvector Multicentrality in Multilayer Networks

Centrality is widely recognized as one of the most critical measures to provide insight in the structure and function of complex networks. While various centrality measures have been proposed for single-layer networks, a general framework for studying centrality in multilayer networks (i.e., multicentrality) is still lacking. In this study, a tensor-based framework is introduced to study eigenvector multicentrality, which enables the quantification of the impact of interlayer influence on multicentrality, providing a systematic way to describe how multicentrality propagates across different layers. This framework can leverage prior knowledge about the interplay among layers to better characterize multicentrality for varying scenarios. Two interesting cases are presented to illustrate how to model multilayer influence by choosing appropriate functions of interlayer influence and design algorithms to calculate eigenvector multicentrality. This framework is applied to analyze several empirical multilayer networks, and the results corroborate that it can quantify the influence among layers and multicentrality of nodes effectively.Comment: 57 pages, 10 figure

Development and evaluation of a physically based multiscalar drought index: The Standardized Moisture Anomaly Index

In this study, a new physically based multiscalar drought index, the Standardized Moisture Anomaly Index (SZI), was developed and evaluated, which combines the advantages of the Palmer Drought Severity Index (PDSI) and the Standardized Precipitation Evapotranspiration Index (SPEI). The SZI is based on the water budget simulations produced with a sophisticated hydrological model, and it also includes a multiscalar feature to quantify drought events at different temporal scales taken from SPEI. The Chinese Loess Plateau was selected to evaluate the performance of the SZI. Our evaluation indicates that the SZI accurately captures the onset, duration, and ending of a multiyear drought event through its multiscalar feature, while the PDSI, which lacks this feature, is often unable to describe the evolution of a multiyear drought event. In addition, the variability of the SZI is more consistent with observed streamflow and the satellite normalized difference vegetation index than that of the Standardized Precipitation Index and the SPEI. Although the SPEI includes potential evapotranspiration (PE) as water demand, water demand is often unrealistically estimated based solely on PE, especially over arid and semiarid regions. The improved drought quantification with the SZI is the result of a more reasonable estimation of water demand by including evapotranspiration, runoff, and any change in soil moisture storage. In general, our newly developed SZI is physically based and includes a multiscalar feature, which enables it to provide better information for drought monitoring and identification at different temporal scales. © 2015. American Geophysical Union. All Rights Reserved

Genomic abundance is not predictive of tandem repeat localization in grass genomes.

Highly repetitive regions have historically posed a challenge when investigating sequence variation and content. High-throughput sequencing has enabled researchers to use whole-genome shotgun sequencing to estimate the abundance of repetitive sequence, and these methodologies have been recently applied to centromeres. Previous research has investigated variation in centromere repeats across eukaryotes, positing that the highest abundance tandem repeat in a genome is often the centromeric repeat. To test this assumption, we used shotgun sequencing and a bioinformatic pipeline to identify common tandem repeats across a number of grass species. We find that de novo assembly and subsequent abundance ranking of repeats can successfully identify tandem repeats with homology to known tandem repeats. Fluorescent in-situ hybridization shows that de novo assembly and ranking of repeats from non-model taxa identifies chromosome domains rich in tandem repeats both near pericentromeres and elsewhere in the genome

Amplification and adaptation of centromeric repeats in polyploid switchgrass species.

Centromeres in most higher eukaryotes are composed of long arrays of satellite repeats from a single satellite repeat family. Why centromeres are dominated by a single satellite repeat and how the satellite repeats originate and evolve are among the most intriguing and long-standing questions in centromere biology. We identified eight satellite repeats in the centromeres of tetraploid switchgrass (Panicum virgatum). Seven repeats showed characteristics associated with classical centromeric repeats with monomeric lengths ranging from 166 to 187 bp. Interestingly, these repeats share an 80-bp DNA motif. We demonstrate that this 80-bp motif may dictate translational and rotational phasing of the centromeric repeats with the cenH3 nucleosomes. The sequence of the last centromeric repeat, Pv156, is identical to the 5S ribosomal RNA genes. We demonstrate that a 5S ribosomal RNA gene array was recruited to be the functional centromere for one of the switchgrass chromosomes. Our findings reveal that certain types of satellite repeats, which are associated with unique sequence features and are composed of monomers in mono-nucleosomal length, are favorable for centromeres. Centromeric repeats may undergo dynamic amplification and adaptation before the centromeres in the same species become dominated by the best adapted satellite repeat