Comparative genomics is a powerful means to gain insight into the evolutionary processes that shape the genomes of related species. As the number of sequenced genomes increases, the development of software to perform accurate cross-species analyses becomes indispensable. However, many implementations that have the ability to compare multiple genomes exhibit unfavorable computational and memory requirements, limiting the number of genomes that can be analyzed in one run. Here, we present a software package to unveil genomic homology based on the identification of conservation of gene content and gene order (collinearity), i-ADHoRe 3.0, and its application to eukaryotic genomes. The use of efficient algorithms and support for parallel computing enable the analysis of large-scale data sets. Unlike other tools, i-ADHoRe can process the Ensembl data set, containing 49 species, in 1 h. Furthermore, the profile search is more sensitive to detect degenerate genomic homology than chaining pairwise collinearity information based on transitive homology. From ultra-conserved collinear regions between mammals and birds, by integrating coexpression information and protein–protein interactions, we identified more than 400 regions in the human genome showing significant functional coherence. The different algorithmical improvements ensure that i-ADHoRe 3.0 will remain a powerful tool to study genome evolution.

Abstract. A self-contained set of algorithms is proposed for the fast evaluation of Legendre polynomials of arbitrary degree and argument ∈ [−1, 1]. More specifically the time required to evaluate any Legendre polynomial, regardless of argument and degree, is bounded by a constant, i.e. the complexity is O (1). The proposed algorithm also immediately yields an O (1) algorithm for computing an arbitrary Gauss-Legendre quadrature node. Such a capability is crucial for efficiently performing certain parallel computations with high order Legendre polynomials, such as computing an integral in parallel by means of Gauss-Legendre quadrature and the parallel evaluation of Legendre series. In order to achieve the O (1) complexity, novel efficient asymptotic expansions are derived and used alongside known results. A C++ implementation is available from the authors that includes the evaluation routines of the Legendre polynomials and Gauss-Legendre quadrature rules.

BackgroundThird generation sequencing platforms produce longer reads with higher error rates than second generation technologies. While the improved read length can provide useful information for downstream analysis, underlying algorithms are challenged by the high error rate. Error correction methods in which accurate short reads are used to correct noisy long reads appear to be attractive to generate high-quality long reads. Methods that align short reads to long reads do not optimally use the information contained in the second generation data, and suffer from large runtimes. Recently, a new hybrid error correcting method has been proposed, where the second generation data is first assembled into a de Bruijn graph, on which the long reads are then aligned.ResultsIn this context we present Jabba, a hybrid method to correct long third generation reads by mapping them on a corrected de Bruijn graph that was constructed from second generation data. Unique to our method is the use of a pseudo alignment approach with a seed-and-extend methodology, using maximal exact matches (MEMs) as seeds. In addition to benchmark results, certain theoretical results concerning the possibilities and limitations of the use of MEMs in the context of third generation reads are presented.ConclusionJabba produces highly reliable corrected reads: almost all corrected reads align to the reference, and these alignments have a very high identity. Many of the aligned reads are error-free. Additionally, Jabba corrects reads using a very low amount of CPU time. From this we conclude that pseudo alignment with MEMs is a fast and reliable method to map long highly erroneous sequences on a de Bruijn graph.