Abstract. Given a set of sequences, S, and degeneracy parameter, d, the Consensus Sequence problem asks whether there exists a sequence that has Hamming distance at most d from each sequence in S. A valid motif set is a set of sequences for which such a consensus sequence exists, while a decoy set is a set of sequences that does not have a consensus sequence but whose pairwise Hamming distances...

The words “spectral sequence” strike fear into the hearts of many hardened mathematicians. These notes will attempt to demonstrate that spectral sequences are not so scary, and also very powerful. This is an unfinished handout for my algebraic topology class. In particular I did not have time to reproduce here the little spectral sequence diagrams showing where all the arrows go. For a comprehe...

A new method for realizing the first and second order cohomology groups of an internal abelian group in a Barr-exact category was introduced in [6] and [10]. The main role, in each level, is played by a direction functor. This approach can be generalized to any level n and produces a long exact cohomology sequence. By applying this method to Moore categories we show that they represent a good c...