Clustering in complex networks. I. General formalism

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in that it involves the properties of two --and not just one-- vertices. The formalism is completed with the definition of a three-vertex correlation function, which is the fundamental quantity describing the properties of clustered networks. The formalism suggests new metrics that are able to thoroughly characterize transitive relations. A rigorous analysis of several real networks, which makes use of the new formalism and the new metrics, is also provided. It is also found that clustered networks can be classified into two main groups: the {\it weak} and the {\it strong transitivity} classes. In the first class, edge multiplicity is small, with triangles being disjoint. In the second class, edge multiplicity is high and so triangles share many edges. As we shall see in the following paper, the class a network belongs to has strong implications in its percolation properties

Transcriptomic resources for an endemic Neotropical plant lineage (Gesneriaceae).

Despite the extensive phenotypic variation that characterizes the Gesneriaceae family, there is a lack of genomic resources to investigate the molecular basis of their diversity. We developed and compared the transcriptomes for two species of the Neotropical lineage of the Gesneriaceae. Illumina sequencing and de novo assembly of floral and leaf samples were used to generate multigene sequence data for Sinningia eumorpha and S. magnifica, two species endemic to the Brazilian Atlantic Forest. A total of 300 million reads were used to assemble the transcriptomes, with an average of 92,038 transcripts and 43,506 genes per species. The transcriptomes showed good quality metrics, with the presence of all eukaryotic core genes, and an equal representation of clusters of orthologous groups (COG) classifications between species. The orthologous search produced 8602 groups, with 15-20% of them annotated using BLAST tools. This study provides the first step toward a comprehensive multispecies transcriptome characterization of the Gesneriaceae family. These resources are the basis for comparative analyses in this species-rich Neotropical plant group; they will also allow the investigation of the evolutionary importance of multiple metabolic pathways and phenotypic diversity, as well as developmental programs in these nonmodel species

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions

R-Band Imaging of Fields Around 1<z<2 Radiogalaxies

We have taken deep $R$-band images of fields around five radiogalaxies: 0956+47, 1217+36, 3C256, 3C324 and 3C294 with $1<z<2$ . 0956+47 is found to show a double nucleus. Our data on 1217+36 suggest the revision of its classification as a radiogalaxy. We found a statistically significant excess of bright ($19.5<R<22$) galaxies on scales of 2 arcmin around the radiogalaxies (which have $R \approx 21.4$) in our sample. The excess has been determined empirically to be at $\gtrsim 99.5\%$ level. It is remarkable that this excess is not present for $22<R<23.75$ galaxies within the same area, suggesting that the excess is not physically associated to the galaxies but due to intervening groups and then related to gravitational lensing.Comment: 20 pages, uuencoded compressed PostScript including tables. Figures available upon request. To appear in the March 1995 issue of The Astronomical Journa

Atmospheric mixing ratios of methyl ethyl ketone (2-butanone) in tropical, boreal, temperate and marine environments

Methyl ethyl ketone (MEK) enters the atmosphere following direct emission from vegetation and anthropogenic activities, as well as being produced by the gas-phase oxidation of volatile organic compounds (VOCs) such as n-butane. This study presents the first overview of ambient MEK measurements at six different locations, characteristic of forested, urban and marine environments. In order to understand better the occurrence and behaviour of MEK in the atmosphere, we analyse diel cycles of MEK mixing ratios, vertical profiles, ecosystem flux data, and HYSPLIT back trajectories, and compare with co-measured VOCs. MEK measurements were primarily conducted with proton transfer reaction–mass spectrometer (PTR-MS) instruments. Results from the sites under biogenic influence demonstrate that vegetation is an important source of MEK. The diel cycle of MEK follows that of ambient temperature and the forest structure plays an important role in air mixing. At such sites a high correlation of MEK with acetone was observed (e.g. r2 = 0.96 for the SMEAR-Estonia site in a remote hemi-boreal forest in Tartumaa, Estonia, and r2 = 0.89 at the ATTO pristine tropical rainforest site in central Amazonia). Under polluted conditions, we observed strongly enhanced MEK mixing ratios. Overall, the MEK mixing ratios and flux data presented here indicate that both biogenic and anthropogenic sources contribute to its occurrence in the global atmosphere