Patterns of Interactions in Complex Social Networks Based on Coloured Motifs Analysis

Coloured network motifs are small subgraphs that enable to discover and interpret the patterns of interaction within the complex networks. The analysis of three-nodes motifs where the colour of the node reflects its high – white node or low – black node centrality in the social network is presented in the paper. The importance of the vertices is assessed by utilizing two measures: degree prestige and degree centrality. The distribution of motifs in these two cases is compared to mine the interconnection patterns between nodes. The analysis is performed on the social network derived from email communication

The interaction of a gap with a free boundary in a two dimensional dimer system

Let $\ell$ be a fixed vertical lattice line of the unit triangular lattice in the plane, and let \Cal H be the half plane to the left of $\ell$. We consider lozenge tilings of \Cal H that have a triangular gap of side-length two and in which $\ell$ is a free boundary - i.e., tiles are allowed to protrude out half-way across $\ell$. We prove that the correlation function of this gap near the free boundary has asymptotics $\frac{1}{4\pi r}$, $r\to\infty$, where $r$ is the distance from the gap to the free boundary. This parallels the electrostatic phenomenon by which the field of an electric charge near a conductor can be obtained by the method of images.Comment: 34 pages, AmS-Te

The 6dF galaxy survey: fundamental plane data

We report the 6dFGS Fundamental Plane (6dFGSv) catalogue that is used to estimate distances and peculiar velocities for nearly 9000 early-type galaxies in the local (z < 0.055) universe. Velocity dispersions are derived by cross-correlation from 6dF V-band spectra with typical S/N of 12.9 Å−1 for a sample of 11 315 galaxies; the median velocity dispersion is 163 km s−1 and the median measurement error is 12.9 per cent. The photometric Fundamental Plane (FP) parameters (effective radii and surface brightnesses) are determined from the JHK 2MASS images for 11 102 galaxies. Comparison of the independent J- and K-band measurements implies that the average uncertainty in XFP, the combined photometric parameter that enters the FP, is 0.013 dex (3 per cent) for each band. Visual classification of morphologies was used to select a sample of nearly 9000 early-type galaxies that form 6dFGSv. This catalogue has been used to study the effects of stellar populations on galaxy scaling relations, to investigate the variation of the FP with environment and galaxy morphology, to explore trends in stellar populations through, along and across the FP, and to map and analyse the local peculiar velocity field

Current status of turbulent dynamo theory: From large-scale to small-scale dynamos

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.Comment: 36 pages, 11 figures, Spa. Sci. Rev., submitted to the special issue "Magnetism in the Universe" (ed. A. Balogh

The use of lichen growth rings in lichenometry : some preliminary findings

Certain species of crustose lichens have concentrically zoned margins which probably represent yearly growth rings. These marginal growth rings offer an alternative method of studying annual growth fluctuations, establishing growth rate–size curves, and determining the age of thalli for certain crustose species. Hence, marginal growth rings represent a potentially valuable, unexploited, tool in lichenometry. In a preliminary study, we measured the widths of the successive marginal rings in 25 thalli of Ochrolechia parella (L.) Massal., growing at a maritime site in north Wales. Mean ring widths of all thalli varied from a minimum of 1.02 mm (the outermost ring) to a maximum of 2.06 mm (the third ring from the margin). There is some suggestion that marginal ring width and thallus size are positively correlated; and hence that growth rates increase in larger thalli in this small population. In a further study on recently exposed bedrock adjacent to Breiðarlon, SE Iceland, we examined the potential for using marginal growth rings to estimate thallus age of a lichen tentatively identified as a Rhizocarpon (possibly R. concentricum (Davies) Beltram.) and thus confirm the timing of surface exposure (c. 50 years). Collectively, these results suggest: 1) the measurement of marginal rings is a possible alternative method of studying the growth of crustose lichens; 2) O. parella may grow differently to other crustose species, exhibiting a rapidly increasing radial growth rate in thalli >40 mm; 3) where lichens with marginal rings grow on recently exposed surfaces (<60 yrs), minimum age estimates can be made using growth rings as an in situ indication of lichen growth rate; 4) it is suggested that this phenomenon could provide a valuable, previously unexploited, in situ lichenometric-dating tool in areas lacking calibration control