Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact count is strictly lowered for all N > 4. These results are derived by considering the DCT to be a special case of a DFT of length 8N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV.Comment: 11 page

A methodology for determining amino-acid substitution matrices from set covers

We introduce a new methodology for the determination of amino-acid substitution matrices for use in the alignment of proteins. The new methodology is based on a pre-existing set cover on the set of residues and on the undirected graph that describes residue exchangeability given the set cover. For fixed functional forms indicating how to obtain edge weights from the set cover and, after that, substitution-matrix elements from weighted distances on the graph, the resulting substitution matrix can be checked for performance against some known set of reference alignments and for given gap costs. Finding the appropriate functional forms and gap costs can then be formulated as an optimization problem that seeks to maximize the performance of the substitution matrix on the reference alignment set. We give computational results on the BAliBASE suite using a genetic algorithm for optimization. Our results indicate that it is possible to obtain substitution matrices whose performance is either comparable to or surpasses that of several others, depending on the particular scenario under consideration

Linking de novo assembly results with long DNA reads by dnaasm-link application

Currently, third-generation sequencing techniques, which allow to obtain much longer DNA reads compared to the next-generation sequencing technologies, are becoming more and more popular. There are many possibilities to combine data from next-generation and third-generation sequencing. Herein, we present a new application called dnaasm-link for linking contigs, a result of \textit{de novo} assembly of second-generation sequencing data, with long DNA reads. Our tool includes an integrated module to fill gaps with a suitable fragment of appropriate long DNA read, which improves the consistency of the resulting DNA sequences. This feature is very important, in particular for complex DNA regions, as presented in the paper. Finally, our implementation outperforms other state-of-the-art tools in terms of speed and memory requirements, which may enable the usage of the presented application for organisms with a large genome, which is not possible in~existing applications. The presented application has many advantages as (i) significant memory optimization and reduction of computation time (ii) filling the gaps through the appropriate fragment of a specified long DNA read (iii) reducing number of spanned and unspanned gaps in the existing genome drafts. The application is freely available to all users under GNU Library or Lesser General Public License version 3.0 (LGPLv3). The demo application, docker image and source code are available at http://dnaasm.sourceforge.net.Comment: 16 pages, 5 figure