Languages of lossless seeds

Several algorithms for similarity search employ seeding techniques to quickly discard very dissimilar regions. In this paper, we study theoretical properties of lossless seeds, i.e., spaced seeds having full sensitivity. We prove that lossless seeds coincide with languages of certain sofic subshifts, hence they can be recognized by finite automata. Moreover, we show that these subshifts are fully given by the number of allowed errors k and the seed margin l. We also show that for a fixed k, optimal seeds must asymptotically satisfy l ~ m^(k/(k+1)).Comment: In Proceedings AFL 2014, arXiv:1405.527

RIME: Repeat Identification

We present an algorithm for detecting long similar fragments occurring at least twice in a set of biological sequences. The problem becomes computationally challenging when the frequency of a repeat is allowed to increase and when a non-negligible number of insertions, deletions and substitutions are allowed. We introduce in this paper an algorithm, Rime1 1 Rime is also a reference to Coleridge's poem "The Rime of an Ancient Mariner" which contains many repetitions as a poetic device. (for Repeat Identification: long, Multiple, and with Edits) that performs this task, and manages instances whose size and combination of parameters cannot be handled by other currently existing methods. This is achieved by using a filter as a preprocessing step, and by then exploiting the information gathered by the filter in the following actual repeat inference step. To the best of our knowledge, Rime is the first algorithm that can accurately deal with very long repeats (up to a few thousands), occurring possibly several times, and with a rate of differences (substitutions and indels) allowed among copies of a same repeat of 10-15% or even more

A Two-Phase Dynamic Programming Algorithm Tool for DNA Sequences

Sequence alignment has to do with the arrangement of DNA, RNA, and protein sequences to identify areas of similarity. Technic ally, it involves the arrangement of the primary sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural, or evolutionary relationships between the sequences. Similarity may be a consequence of functional, s tructural, or evolutionary relationships between the sequences. If two sequences in an alignment share a common ancestor, mismatches can be interpreted as mutations, and gaps as insertions. Such information becomes of great use in vital areas such as the study of d iseases, genomics and generally in the biological sciences. Thus, sequence alignment presents not just an exciting field of study, but a field of great importance to mankind. In this light, we extensively studied about seventy (70) existing sequence alignment tools available to us. Most of these tools are not user friendly and cannot be used by biologists. The few tools that attempted both Local and Global algorithms are not ready available freely. We therefore implemented a sequence alignment tool (CU-Aligner) in an understandable, user-friendly and portable way, with click-of-a-button simplicity. This is done utilizing the Needleman-Wunsh and Smith-Waterman algorithms for global and local alignments, respectively which focuses primarily on DNA sequences. Our aligner is implemented in the Java language in both application and applet mode and has been efficient on all windows operating systems

TRStalker: an Efficient Heuristic for Finding NP-Complete Tandem Repeats

Genomic sequences in higher eucaryotic organisms contain a substantial amount of (almost) repeated sequences. Tandem Repeats (TRs) constitute a large class of repetitive sequences that are originated via phenomena such as replication slippage, are characterized by close spatial contiguity, and play an important role in several molecular regulatory mechanisms. Certain types of tandem repeats are highly polymorphic and constitute a fingerprint feature of individuals. Abnormal TRs are known to be linked to several diseases. Researchers in bio-informatics in the last 20 years have proposed many formal definitions for the rather loose notion of a Tandem Repeat and have proposed exact or heuristic algorithms to detect TRs in genomic sequences. The general trend has been to use formal (implicit or explicit) definitions of TR for which verification of the solution was easy (with complexity linear, or polynomial in the TR\u27s length and substitution+indel rates) while the effort was directed towards identifying efficiently the sub-strings of the input to submit to the verification phase (either implicitly or explicitly). In this paper we take a step forward: we use a definition of TR for which also the verification step is difficult (in effect, NP-complete) and we develop new filtering techniques for coping with high error levels. The resulting heuristic algorithm, christened TRStalker, is approximate since it cannot guarantee that all NP-Complete Tandem Repeats satisfying the target definition in the input string will be found. However, in synthetic experiments with 30% of errors allowed, TRStalker has demonstrated a very high recall (ranging from 100% to 60%, depending on motif length and repetition number) for the NP-complete TRs. TRStalker has consistently better performance than some stateof- the-art methods for a large range of parameters on the class of NP-complete Tandem Repeats. TRStalker aims at improving the capability of TR detection for classes of TRs for which existing methods do not perform well

Compressed Spaced Suffix Arrays

Spaced seeds are important tools for similarity search in bioinformatics, and using several seeds together often significantly improves their performance. With existing approaches, however, for each seed we keep a separate linear-size data structure, either a hash table or a spaced suffix array (SSA). In this paper we show how to compress SSAs relative to normal suffix arrays (SAs) and still support fast random access to them. We first prove a theoretical upper bound on the space needed to store an SSA when we already have the SA. We then present experiments indicating that our approach works even better in practice

Longest property-preserved common factor

In this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here we consider two fundamental string properties: square-free factors and periodic factors under two different settings, one per property. In the first setting, we are given a string x and we are asked to construct a data structure over x answering the following type of on-line queries: given string y, find a longest square-free factor common to x and y. In the second setting, we are given k strings and an integer 1 < k’ ≤ k and we are asked to find a longest periodic factor common to at least k’ strings. We present linear-time solutions for both settings. We anticipate that our paradigm can be extended to other string properties

Circular sequence comparison: algorithms and applications

Background: Sequence comparison is a fundamental step in many important tasks in bioinformatics; from phylogenetic reconstruction to the reconstruction of genomes. Traditional algorithms for measuring approximation in sequence comparison are based on the notions of distance or similarity, and are generally computed through sequence alignment techniques. As circular molecular structure is a common phenomenon in nature, a caveat of the adaptation of alignment techniques for circular sequence comparison is that they are computationally expensive, requiring from super-quadratic to cubic time in the length of the sequences. Results: In this paper, we introduce a new distance measure based on q-grams, and show how it can be applied effectively and computed efficiently for circular sequence comparison. Experimental results, using real DNA, RNA, and protein sequences as well as synthetic data, demonstrate orders-of-magnitude superiority of our approach in terms of efficiency, while maintaining an accuracy very competitive to the state of the art

Clustering by compression

We present a new method for clustering based on compression. The method doesn't use subject-specific features or background knowledge, and works as follows: First, we determine a universal similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is universal in that it is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal but uses the non-computable notion of Kolmogorov complexity. We propose precise notions of similarity metric, normal compressor, and show that the NCD based on a normal compressor is a similarity metric that approximates universality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (binary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis.Comment: LaTeX, 27 pages, 20 figure