MOTIVATION: Long tandem repeat expansions of more than 1000 nt have been suggested to be associated with diseases, but remain largely unexplored in individual human genomes because read lengths have been too short. However, new long-read sequencing technologies can produce single reads of 10 000 nt or more that can span such repeat expansions, although these long reads have high error rates, of 10-20%, which complicates the detection of repetitive elements. Moreover, most traditional algorithms for finding tandem repeats are designed to find short tandem repeats (<1000 nt) and cannot effectively handle the high error rate of long reads in a reasonable amount of time. RESULTS: Here, we report an efficient algorithm for solving this problem that takes advantage of the length of the repeat. Namely, a long tandem repeat has hundreds or thousands of approximate copies of the repeated unit, so despite the error rate, many short k-mers will be error-free in many copies of the unit. We exploited this characteristic to develop a method for first estimating regions that could contain a tandem repeat, by analyzing the k-mer frequency distributions of fixed-size windows across the target read, followed by an algorithm that assembles the k-mers of a putative region into the consensus repeat unit by greedily traversing a de Bruijn graph. Experimental results indicated that the proposed algorithm largely outperformed Tandem Repeats Finder, a widely used program for finding tandem repeats, in terms of sensitivity. AVAILABILITY AND IMPLEMENTATION: https://github.com/morisUtokyo/mTR.

MOTIVATION: Determining the methylation state of regions with high copy numbers is challenging for second-generation sequencing, because the read length is insufficient to map reads uniquely, especially when repetitive regions are long and nearly identical to each other. Single-molecule real-time (SMRT) sequencing is a promising method for observing such regions, because it is not vulnerable to GC bias, it produces long read lengths, and its kinetic information is sensitive to DNA modifications. RESULTS: We propose a novel linear-time algorithm that combines the kinetic information for neighboring CpG sites and increases the confidence in identifying the methylation states of those sites. Using a practical read coverage of ∼30-fold from an inbred strain medaka (Oryzias latipes), we observed that both the sensitivity and precision of our method on individual CpG sites were ∼93.7%. We also observed a high correlation coefficient (R = 0.884) between our method and bisulfite sequencing, and for 92.0% of CpG sites, methylation levels ranging over [0,1] were in concordance within an acceptable difference 0.25. Using this method, we characterized the landscape of the methylation status of repetitive elements, such as LINEs, in the human genome, thereby revealing the strong correlation between CpG density and hypomethylation and detecting hypomethylation hot spots of LTRs and LINEs. We uncovered the methylation states for nearly identical active transposons, two novel LINE insertions of identity ∼99% and length 6050 base pairs (bp) in the human genome, and 16 Tol2 elements of identity >99.8% and length 4682 bp in the medaka genome. AVAILABILITY AND IMPLEMENTATION: AgIn (Aggregate on Intervals) is available at: https://github.com/hacone/AgIn CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

K-means clustering has been widely used to gain insight into biological systems from large-scale life science data. To quantify the similarities among biological data sets, Pearson correlation distance and standardized Euclidean distance are used most frequently; however, optimization methods have been largely unexplored. These two distance measurements are equivalent in the sense that they yield the same k-means clustering result for identical sets of k initial centroids. Thus, an efficient algorithm used for one is applicable to the other. Several optimization methods are available for the Euclidean distance and can be used for processing the standardized Euclidean distance; however, they are not customized for this context. We instead approached the problem by studying the properties of the Pearson correlation distance, and we invented a simple but powerful heuristic method for markedly pruning unnecessary computation while retaining the final solution. Tests using real biological data sets with 50-60K vectors of dimensions 10-2001 (~400 MB in size) demonstrated marked reduction in computation time for k = 10-500 in comparison with other state-of-the-art pruning methods such as Elkan's and Hamerly's algorithms. The BoostKCP software is available at http://mlab.cb.k.u-tokyo.ac.jp/~ichikawa/boostKCP/.

We propose an in-parallel actuate mechanism that can simultaneously realize fine positioning resolution and a large working space, and we discuss its infinitesimal displacement characteristics. Based on a kinematic synthesis of this mechanism, an experimental manipulator has been developed and we discuss the results of experiments regarding its fine positioning characteristics.