Small clique number graphs with three trivial critical ideals

The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. In this article we provide a set of minimal forbidden graphs for the set of graphs with at most three trivial critical ideals. Then we use these forbidden graphs to characterize the graphs with at most three trivial critical ideals and clique number equal to 2 and 3.Comment: 33 pages, 3 figure

An analysis of the Sargasso Sea resource and the consequences for database composition

Background: The environmental sequencing of the Sargasso Sea has introduced a huge new resource of genomic information. Unlike the protein sequences held in the current searchable databases, the Sargasso Sea sequences originate from a single marine environment and have been sequenced from species that are not easily obtainable by laboratory cultivation. The resource also contains very many fragments of whole protein sequences, a side effect of the shotgun sequencing method.These sequences form a significant addendum to the current searchable databases but also present us with some intrinsic difficulties. While it is important to know whether it is possible to assign function to these sequences with the current methods and whether they will increase our capacity to explore sequence space, it is also interesting to know how current bioinformatics techniques will deal with the new sequences in the resource.Results: The Sargasso Sea sequences seem to introduce a bias that decreases the potential of current methods to propose structure and function for new proteins. In particular the high proportion of sequence fragments in the resource seems to result in poor quality multiple alignments.Conclusion: These observations suggest that the new sequences should be used with care, especially if the information is to be used in large scale analyses. On a positive note, the results may just spark improvements in computational and experimental methods to take into account the fragments generated by environmental sequencing techniques