Spectral clustering algorithms for the detection of clusters in block-cyclic and block-acyclic graphs

We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes, referred to as blocks. Our methods are based on the computation of extremal eigenvalues of the transition matrix associated to the directed graph. The two algorithms outperform state-of-the-art methods for the detection of node clusters in synthetic block-cyclic or block-acyclic graphs, including methods based on blockmodels, bibliometric symmetrization and random walks. In particular, we demonstrate the ability of our algorithms to focus on the cyclic or the acyclic patterns of connection in directed graphs, even in the presence of edges that perturb these patterns. Our algorithms have the same space complexity as classical spectral clustering algorithms for undirected graphs and their time complexity is also linear in the number of edges in the graph. One of our methods is applied to a trophic network based on predator–prey relationships. It successfully extracts common categories of preys and predators encountered in food chains. The same method is also applied to highlight the hierarchical structure of a worldwide network of autonomous systems depicting business agreements between Internet Service Provider

Clonal analysis and identification of epidemic strains of methicillin-resistant Staphylococcus aureus by antibiotyping and determination of protein A gene and coagulase gene polymorphisms.

Forty-three methicillin-resistant Staphylococcus aureus (MRSA) isolates with known genetic and epidemiological relatedness and different degrees of transmission were analyzed by antibiotyping, protein A gene polymorphism analysis, and coagulase gene polymorphism analysis. The three typing systems were evaluated for their performance and convenience to define clones and to discriminate between epidemic MRSA (EMRSA) and sporadic MRSA (SMRSA). Antibiotyping and AluI restriction fragment length polymorphism analysis of the coagulase gene were able to define clones in the same way as DNA macrorestriction analysis (SmaI). However, both techniques presented disadvantages, making neither of them useful as a single typing method. Protein A gene polymorphism analysis appeared to be of no value for clonal analysis. None of the three typing methods was able to differentiate between EMRSA and SMRSA

Neutron diffraction studies of U₄O₉ : Comparison with EXAFS results

Conradson et al.1 have analyzed X-ray absorption fine-structure spectra of the UO$_2$-U$_4$O$_9$ system and concluded that oxygen atoms are incorporated in U$_4$O$_9$ as oxo groups with U-O distances in the range 1.72-1.76 Å. They also found that the uranium sublattice consists of an ordered portion and an additional 'spectroscopically silent' glassy portion. We have carried out studies of powdered U$_4$O$_9$ by neutron diffraction which contradict these conclusions from EXAFS measurements. Our analysis shows that there are no U-O bonds shorter than 2.2 Å and that U4O9 is crystallographically ordered with no evidence of a glassy structure