Weighted homological regularities

Varieties of Regularities in Weighted Sequences

A weighted sequence is a string in which a set of characters may appear at each position with respective probabilities of occurrence. A common task is to identify repetitive motifs in weighted sequences, with presence probability not less than a given threshold. We consider the problems of finding varieties of regularities in a weighted sequence. Based on the algorithms for computing all the re...

Searching for Regularities in Weighted Sequences

In this paper we describe algorithms for finding regularities in weighted sequences. A weighted sequence is a sequence of symbols drawn from an alphabet Σ that have a prespecified probability of occurrence. We show that known algorithms for finding repeats in solid sequences may fail to do so for weighted sequences. In particular, we show that Crochemore’s algorithm for finding repetitions cann...

Classification of weighted networks through mesoscale homological features

As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural method for both organizing this data and understanding deeper relationships between networks. Most existing metrics for network structure rely on classical graph...

Computation of Repetitions and Regularities of Biologically Weighted Sequences

Biological weighted sequences are used extensively in molecular biology as profiles for protein families, in the representation of binding sites and often for the representation of sequences produced by a shotgun sequencing strategy. In this paper, we address three fundamental problems in the area of biologically weighted sequences: (i) computation of repetitions, (ii) pattern matching, and (ii...

Homological Algebra