BackgroundRecent developments of high throughput sequencing technologies allow the characterization of the microbial communities inhabiting our world. Various metagenomic studies have suggested using microbial taxa as potential biomarkers for certain diseases. In practice, the number of available samples varies from experiment to experiment. Therefore, a robust biomarker detection algorithm is needed to provide a set of potential markers irrespective of the number of available samples. Consistent performance is essential to derive solid biological conclusions and to transfer these findings into clinical applications. Surprisingly, the consistency of a metagenomic biomarker detection algorithm with respect to the variation in the experiment size has not been addressed by the current state-of-art algorithms.ResultsWe propose a consistency-classification framework that enables the assessment of consistency and classification performance of a biomarker discovery algorithm. This evaluation protocol is based on random resampling to mimic the variation in the experiment size. Moreover, we model the metagenomic data matrix as a superposition of two matrices. The first matrix is a low-rank matrix that models the abundance levels of the irrelevant bacteria. The second matrix is a sparse matrix that captures the abundance levels of the bacteria that are differentially abundant between different phenotypes. Then, we propose a novel Robust Principal Component Analysis (RPCA) based biomarker discovery algorithm to recover the sparse matrix. RPCA belongs to the class of multivariate feature selection methods which treat the features collectively rather than individually. This provides the proposed algorithm with an inherent ability to handle the complex microbial interactions. Comprehensive comparisons of RPCA with the state-of-the-art algorithms on two realistic datasets are conducted. Results show that RPCA consistently outperforms the other algorithms in terms of classification accuracy and reproducibility performance.ConclusionsThe RPCA-based biomarker detection algorithm provides a high reproducibility performance irrespective of the complexity of the dataset or the number of selected biomarkers. Also, RPCA selects biomarkers with quite high discriminative accuracy. Thus, RPCA is a consistent and accurate tool for selecting taxanomical biomarkers for different microbial populations.ReviewersThis article was reviewed by Masanori Arita and Zoltan Gaspari.Electronic supplementary materialThe online version of this article (doi:10.1186/s13062-017-0175-4) contains supplementary material, which is available to authorized users.
BackgroundBiomarker detection presents itself as a major means of translating biological data into clinical applications. Due to the recent advances in high throughput sequencing technologies, an increased number of metagenomics studies have suggested the dysbiosis in microbial communities as potential biomarker for certain diseases. The reproducibility of the results drawn from metagenomic data is crucial for clinical applications and to prevent incorrect biological conclusions. The variability in the sample size and the subjects participating in the experiments induce diversity, which may drastically change the outcome of biomarker detection algorithms. Therefore, a robust biomarker detection algorithm that ensures the consistency of the results irrespective of the natural diversity present in the samples is needed.ResultsToward this end, this paper proposes a novel Regularized Low Rank-Sparse Decomposition (RegLRSD) algorithm. RegLRSD models the bacterial abundance data as a superposition between a sparse matrix and a low-rank matrix, which account for the differentially and non-differentially abundant microbes, respectively. Hence, the biomarker detection problem is cast as a matrix decomposition problem. In order to yield more consistent and solid biological conclusions, RegLRSD incorporates the prior knowledge that the irrelevant microbes do not exhibit significant variation between samples belonging to different phenotypes. Moreover, an efficient algorithm to extract the sparse matrix is proposed. Comprehensive comparisons of RegLRSD with the state-of-the-art algorithms on three realistic datasets are presented. The obtained results demonstrate that RegLRSD consistently outperforms the other algorithms in terms of reproducibility performance and provides a marker list with high classification accuracy.ConclusionsThe proposed RegLRSD algorithm for biomarker detection provides high reproducibility and classification accuracy performance regardless of the dataset complexity and the number of selected biomarkers. This renders RegLRSD as a reliable and powerful tool for identifying potential metagenomic biomarkers.
An increasing number of electric vehicles (EVs) are replacing gasoline vehicles in the automobile market due to the economic and environmental benefits. The high penetration of EVs is one of the main challenges in the future smart grid. As a result of EV charging, an excessive overloading is expected in different elements of the power system, especially at the distribution level. In this paper, we evaluate the impact of EVs on the distribution system under three loading conditions (light, intermediate, and full). For each case, we estimate the maximum number of EVs that can be charged simultaneously before reaching different system limitations, including the undervoltage, overcurrent, and transformer capacity limit. Finally, we use the 19-node distribution system to study these limitations under different loading conditions. The 19-node system is one of the typical distribution systems in Jordan. Our work estimates the upper limit of the possible EV penetration before reaching the system stability margins.
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