Searching for local sequence patterns is one of the basic tasks in bioinformatics. Sequence patterns might have structural, functional or some other relevance, and numerous methods have been developed to detect and analyze them. These methods often depend on the wealth of information already collected. The explosion in the number of newly available sequences calls for novel methods to explore local sequence similarity. We have developed a high sensitivity web-based iterative local similarity scanner, that finds sequence patterns similar to a submitted query. Availability: The IGLOSS web server is available at http://compbioserv.math.hr/igloss/

We consider a generalized one-dimensional chain in a periodic potential (the Frenkel-Kontorova model), with dissipative, pulsating (or ratchet) dynamics as a model of transport when the average force on the system is zero. We find lower bounds on the transport speed under mild assumptions on the asymmetry and steepness of the site potential. Physically relevant applications include explicit estimates of the pulse frequencies and mean spacings for which the transport is non-zero, and more specifically the pulse frequencies which maximize work. The bounds explicitly depend on the pulse period and subtle number-theoretical properties of the mean spacing. The main tool is the study of time evolution of spatially invariant measures in the space of measures equipped with the L 1 -Wasserstein metric.

We prove an analogue to the well-known equivalence of intersective sets and Poincaré recurrent sets, in a stronger setting. We show that a set D is van der Corput, if and only if for each Hilbert space H, unitary operator U, and x ∈ H such that the projection of x to the kernel of (U − I) is nonvanishing, there exists d ∈ D such that (U d x, x) = 0. We also characterize the smallest such d.Mathematics Subject Classification. 37A45, 11P99, 37B20.

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BackgroundMotif scanning is a very common method in bioinformatics. Its objective is to detect motifs of sufficient similarity to the query, which is then used to determine familiy membership, or structural or functional features or assignments. Considering a variety of uses, accuracy of motif scanning procedures is of great importance. ResultsWe present a new approach for improving motif scanning accuracy, based on analysis of in-between similarity. Given a set of motifs obtained from a scanning process, we construct an associated weighted graph. We also compute the expected weight of an edge in such a graph. It turns out that restricting results to the maximal clique in the graph, computed with respect to the expected weight, greatly increases precision, hence improves accuracy of the scan. We tested the method on an ungapped motif-characterized protein family from five plant proteomes. The method was applied to three iterative motif scanners -PSI-BLAST, JackHMMer and IGLOSS -with very good results. ConclusionsWe presented a method for improving protein motif scanning accuracy, and have successfully applied it in several situations. The method has wider implications, for general pattern recognition and feature extraction strategies, as long as one can determine the expected similarity between objects under consideration.