Analytic solution of a static scale-free network model

We present a detailed analytical study of a paradigmatic scale-free network model, the Static Model. Analytical expressions for its main properties are derived by using the hidden variables formalism. We map the model into a canonic hidden variables one, and solve the latter. The good agreement between our predictions and extensive simulations of the original model suggests that the mapping is exact in the infinite network size limit. One of the most remarkable findings of this study is the presence of relevant disassortative correlations, which are induced by the physical condition of absence of self and multiple connections.Comment: 8 pages, 4 figure

Na-O anticorrelation and HB. IX. Kinematics of the program clusters. A link between systemic rotation and HB morphology?

We use accurate radial velocities for 1981 member stars in 20 Galactic globular clusters, collected within our large survey aimed at the analysis of the Na-O anti-correlation, to study the internal kinematics of the clusters. We performed the first systematic exploration of the possible connections between cluster kinematics and the multiple populations phenomenon in GCs. We did not find any significant correlation between Na abundance and either velocity dispersion or systemic rotation. We searched for systemic rotation in the eight clusters of our sample that lack such analysis from previous works in the literature (NGC2808, NGC5904, NGC6171, NGC6254, NGC6397, NGC6388, NGC6441, and NGC6838). These clusters are found to span a large range of rotational amplitudes, from ~0.0 km/s (NGC6397) to ~13.0 km/s (NGC6441). We found a significant correlation between the ratio of rotational velocity to central velocity dispersion (V_{rot}/sigma_0) and the Horizontal Branch Morphology parameter (B-R)/(B+R+V). V_{rot}/sigma_0 is found to correlate also with metallicity, possibly hinting to a significant role of dissipation in the process of formation of globular clusters. V_{rot} is found to correlate well with (B-R)/(B+R+V), M_V, sigma_0 and [Fe/H]. All these correlations strongly suggest that systemic rotation may be intimately linked with the processes that led to the formation of globular clusters and the stellar populations they host.Comment: Accepted for publication on Astronomy & Astrophysics. Pdflatex, 16 pages, 16 pdf figures. The position angles of the rotation axes have been corrected, since the values reported in the previous version were erroneous. The results of the analysis are unchanged. The manuscript has also been processed by a language edito

Random walks on complex trees

We study the properties of random walks on complex trees. We observe that the absence of loops is reflected in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and the mean topological displacement from the origin present a considerable slowing down in the tree case. Second, the mean first passage time (MFPT) displays a logarithmic degree dependence, in contrast to the inverse degree shape exhibited in looped networks. This deviation can be ascribed to the dominance of source-target topological distance in trees. To show this, we study the distance dependence of a symmetrized MFPT and derive its logarithmic profile, obtaining good agreement with simulation results. These unique properties shed light on the recently reported anomalies observed in diffusive dynamical systems on trees

Remarks on some tardigrades of the African fauna with the description of three new species of Macrobiotus Schultze 1834

Ten species of tardigrades are recorded. Three of them, Macrobiotus radiatus, Macrobiotus vanescens, and Macrobiotus iharosi are new for science; two species, Macrobiotus sapiens Binda & Pilato 1984 and Isohypsibius kristenseni Pilato et al. 1989, are new for the African fauna. Macrobiotus radiatus n. sp. differs from the other species of the harmsioorthi group in the characters of the eggs and in other characters regarding various structures (buccal armature, or placoids length, or the insertion point of the stylet supports, or the claws length). Macrobiotus vanescens n. sp. is similar to Macrobiotus richtersi Murray 1911 and to Macrobiotus peteri Pilato et al. 1989 but differs from them in some characters regarding the bucco-pharyngeal apparatus, the claws and the eggs. Macrobiotus iharosi n. sp. differs from Macrobiotus echinogenitus Richters 1904 in the characters of the eggs, and from Macrobiotus sapiens Binda & Pilato 1984 in some characters of the bucco-pharyngeal apparatus and of the claws

The normal chemistry of multiple stellar populations in the dense globular cluster NGC 6093 (M 80)

We present the abundance analysis of 82 red giant branch stars in the dense, metal-poor globular cluster NGC 6093 (M 80), the largest sample of stars analyzed in this way for this cluster. From high resolution UVES spectra of 14 stars and intermediate resolution GIRAFFE spectra for the other stars we derived abundances of O, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Ba, La, Ce, Pr, Nd, Sm, Eu. On our UVES metallicity scale the mean metal abundance of M 80 is [Fe/H]=-1.791+/-0.006+/-0.076 (+/-statistical +/-systematic error) with rms=0.023 (14 stars). M 80 shows star to star variations in proton-capture elements, and the extension of the Na-O anticorrelation perfectly fit the relations with (i) total cluster mass, (ii) horizontal branch morphology, and (iii) cluster concentration previously found by our group. The chemistry of multiple stellar populations in M 80 does not look extreme. The cluster is also a typical representative of halo globular clusters for what concerns the pattern of alpha-capture and Fe-group elements. However we found that a significant contribution from the s-process is required to account for the distribution of neutron-capture elements. A minority of stars in M 80 seem to exhibit slightly enhanced abundances of s-process species, compatible with those observed in M 22 and NGC 1851, although further confirmation from larger samples is required.Comment: 18 pages, 21 figures, 10 tables; accepted for publication on Astronomy and Astrophysic