Comparing two or more phylogenetic trees is a fundamental task in computational biology. The simplest outcome of such a comparison is a pairwise measure of similarity, dissimilarity, or distance. A large number of such measures have been proposed, but so far all suffer from problems varying from computational cost to lack of robustness; many can be shown to behave unexpectedly under certain plausible inputs. For instance, the widely used Robinson-Foulds distance is poorly distributed and thus affords little discrimination, while also lacking robustness in the face of very small changes--reattaching a single leaf elsewhere in a tree of any size can instantly maximize the distance. In this paper, we introduce a new pairwise distance measure, based on matching, for phylogenetic trees. We prove that our measure induces a metric on the space of trees, show how to compute it in low polynomial time, verify through statistical testing that it is robust, and finally note that it does not exhibit unexpected behavior under the same inputs that cause problems with other measures. We also illustrate its usefulness in clustering trees, demonstrating significant improvements in the quality of hierarchical clustering as compared to the same collections of trees clustered using the Robinson-Foulds distance.

Motivation Metagenomics studies have provided key insights into the composition and structure of microbial communities found in different environments. Among the techniques used to analyse metagenomic data, binning is considered a crucial step to characterize the different species of micro-organisms present. The use of short-read data in most binning tools poses several limitations, such as insufficient species-specific signal, and the emergence of long-read sequencing technologies offers us opportunities to surmount them. However, most current metagenomic binning tools have been developed for short reads. The few tools that can process long reads either do not scale with increasing input size or require a database with reference genomes that are often unknown. In this article, we present MetaBCC-LR, a scalable reference-free binning method which clusters long reads directly based on their k-mer coverage histograms and oligonucleotide composition. Results We evaluate MetaBCC-LR on multiple simulated and real metagenomic long-read datasets with varying coverages and error rates. Our experiments demonstrate that MetaBCC-LR substantially outperforms state-of-the-art reference-free binning tools, achieving ∼13% improvement in F1-score and ∼30% improvement in ARI compared to the best previous tools. Moreover, we show that using MetaBCC-LR before long-read assembly helps to enhance the assembly quality while significantly reducing the assembly cost in terms of time and memory usage. The efficiency and accuracy of MetaBCC-LR pave the way for more effective long-read-based metagenomics analyses to support a wide range of applications. Availability and implementation The source code is freely available at: https://github.com/anuradhawick/MetaBCC-LR. Supplementary information Supplementary data are available at Bioinformatics online.

The Internet has rich and rapidly increasing sources of high quality educational content. Inferring prerequisite relations between educational concepts is required for modern large-scale online educational technology applications such as personalized recommendations and automatic curriculum creation. We present PREREQ, a new supervised learning method for inferring concept prerequisite relations. PRE-REQ is designed using latent representations of concepts obtained from the Pairwise Latent Dirichlet Allocation model, and a neural network based on the Siamese network architecture. PREREQ can learn unknown concept prerequisites from course prerequisites and labeled concept prerequisite data. It outperforms state-of-the-art approaches on benchmark datasets and can effectively learn from very less training data. PREREQ can also use unlabeled video playlists, a steadily growing source of training data, to learn concept prerequisites, thus obviating the need for manual annotation of course prerequisites.

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Single cell data integration methods aim to integrate cells across data batches and modalities, and data integration tasks can be categorized into horizontal, vertical, diagonal, and mosaic integration, where mosaic integration is the most general and challenging case with few methods developed. We propose scMoMaT, a method that is able to integrate single cell multi-omics data under the mosaic integration scenario using matrix tri-factorization. During integration, scMoMaT is also able to uncover the cluster specific bio-markers across modalities. These multi-modal bio-markers are used to interpret and annotate the clusters to cell types. Moreover, scMoMaT can integrate cell batches with unequal cell type compositions. Applying scMoMaT to multiple real and simulated datasets demonstrated these features of scMoMaT and showed that scMoMaT has superior performance compared to existing methods. Specifically, we show that integrated cell embedding combined with learned bio-markers lead to cell type annotations of higher quality or resolution compared to their original annotations.