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

A Coverage Criterion for Spaced Seeds and its Applications to Support Vector Machine String Kernels and k-Mer Distances

Spaced seeds have been recently shown to not only detect more alignments, but also to give a more accurate measure of phylogenetic distances (Boden et al., 2013, Horwege et al., 2014, Leimeister et al., 2014), and to provide a lower misclassification rate when used with Support Vector Machines (SVMs) (On-odera and Shibuya, 2013), We confirm by independent experiments these two results, and propose in this article to use a coverage criterion (Benson and Mak, 2008, Martin, 2013, Martin and No{\'e}, 2014), to measure the seed efficiency in both cases in order to design better seed patterns. We show first how this coverage criterion can be directly measured by a full automaton-based approach. We then illustrate how this criterion performs when compared with two other criteria frequently used, namely the single-hit and multiple-hit criteria, through correlation coefficients with the correct classification/the true distance. At the end, for alignment-free distances, we propose an extension by adopting the coverage criterion, show how it performs, and indicate how it can be efficiently computed.Comment: http://online.liebertpub.com/doi/abs/10.1089/cmb.2014.017

SAN models of a benchmark on dynamic reliability

This report provides the detailed description of the Stochastic Activity Network (SAN) models appearing in [1] and concerning a benchmark on dynamic reliability taken from the literature