An observation of circular RNAs in bacterial RNA-seq data

Circular RNAs (circRNAs) are a class of RNA with an important role in micro RNA (miRNA) regulation recently discovered in Human and various other eukaryotes as well as in archaea. Here, we have analyzed RNA-seq data obtained from {\it Enterococcus faecalis} and {\it Escherichia coli} in a way similar to previous studies performed on eukaryotes. We report observations of circRNAs in RNA-seq data that are reproducible across multiple experiments performed with different protocols or growth conditions

Some results related to dense families of database relations

The dense families of database relations were introduced by Järvinen [7]. The aim of this paper is to investigate some new properties of dense families of database relations, and their applications. That is, we characterize functional dependencies and minimal keys in terms of dense families. We give a necessary and sufficient condition for an abitrary family to be R— dense family. We prove that with a given relation R the equality set ER is an R—dense family whose size is at most m(m-1)/2, where m is the number of tuples in R. We also prove that the set of all minimal keys of relation R is the transversal hypergraph of the complement of the equality set ER. We give an effective algorithm finding all minimal keys of a given relation R. We also give an algorithm which from a given relation R finds a cover of functional dependencies that holds in R. The complexity of these algorithms is also esimated