Equivalence between Hypergraph Convexities

Let G be a connected graph on V. A subset X of V is all-paths convex (or ap -convex) if X contains each vertex on every path joining two vertices in X and is monophonically convex (or m-convex) if X contains each vertex on every chordless path joining two vertices in X. First of all, we prove that ap -convexity and m-convexity coincide in G if and only if G is a tree. Next, in order to generalize this result to a connected hypergraph H, in addition to the hypergraph versions of ap -convexity and m-convexity, we consider canonical convexity (or c-convexity) and simple-path convexity (or sp -convexity) for which it is well known that m-convexity is finer than both c-convexity and sp -convexity and sp -convexity is finer than ap -convexity. After proving sp -convexity is coarser than c-convexity, we characterize the hypergraphs in which each pair of the four convexities above is equivalent. As a result, we obtain a convexity-theoretic characterization of Berge-acyclic hypergraphs and of γ-acyclic hypergraphs

Genome profiling of ovarian adenocarcinomas using pangenomic BACs microarray comparative genomic hybridization

<p>Abstract</p> <p>Background</p> <p>Routine cytogenetic investigations for ovarian cancers are limited by culture failure and poor growth of cancer cells compared to normal cells. Fluorescence <it>in situ </it>Hybridization (FISH) application or classical comparative genome hybridization techniques are also have their own limitations in detecting genome imbalance especially for small changes that are not known ahead of time and for which FISH probes could not be thus designed.</p> <p>Methods</p> <p>We applied microarray comparative genomic hybridization (A-CGH) using one mega base BAC arrays to investigate chromosomal disorders in ovarian adenocarcinoma in patients with familial history.</p> <p>Results</p> <p>Our data on 10 cases of ovarian cancer revealed losses of 6q (4 cases mainly mosaic loss), 9p (4 cases), 10q (3 cases), 21q (3 cases), 22q (4 cases) with association to a monosomy X and gains of 8q and 9q (occurring together in 8 cases) and gain of 12p. There were other abnormalities such as loss of 17p that were noted in two profiles of the studied cases. Total or mosaic segmental gain of 2p, 3q, 4q, 7q and 13q were also observed. Seven of 10 patients were investigated by FISH to control array CGH results. The FISH data showed a concordance between the 2 methods.</p> <p>Conclusion</p> <p>The data suggest that A-CGH detects unique and common abnormalities with certain exceptions such as tetraploidy and balanced translocation, which may lead to understanding progression of genetic changes as well as aid in early diagnosis and have an impact on therapy and prognosis.</p

Recognition Algorithms and Design Methodologies for Acyclic Database Schemes

2special issue on “The Theory of Databases”, P.Kannellakis and F.Preparata ed., JAI Press Inc.,nonenoneA. D'ATRI; M.MOSCARINID'Atri, Alessandro; M., Moscarin