The bounds of heavy-tailed return distributions in evolving complex networks

We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an agent model, presented in the context of economic networks of trades, which shows the emergence of critical behavior. Starting from a brief discussion about the main features of the evolving network of trades, we show that the logarithmic return distributions have bounded heavy-tails, and the corresponding bounding exponent values can be derived. Finally, we discuss these findings in the context of model risk

A new hierarchy for automaton semigroups

We define a new strict and computable hierarchy for the family of automaton semigroups, which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy extends that given by Sidki for automaton groups, and also gives new insights into the latter. Its exponential part coincides with a notion of entropy for some associated automata. We prove that the Order Problem is decidable when the state-activity is bounded. The Order Problem remains open for the next level of this hierarchy, that is, when the state-activity is linear. Gillibert showed that it is undecidable in the whole family. The former results are implemented and will be available in the GAP package FR developed by the first author.Comment: 12 pages, accepted and presented at CIAA 201

Spreading gossip in social networks

We study a simple model of information propagation in social networks, where two quantities are introduced: the spread factor, which measures the average maximal fraction of neighbors of a given node that interchange information among each other, and the spreading time needed for the information to reach such fraction of nodes. When the information refers to a particular node at which both quantities are measured, the model can be taken as a model for gossip propagation. In this context, we apply the model to real empirical networks of social acquaintances and compare the underlying spreading dynamics with different types of scale-free and small-world networks. We find that the number of friendship connections strongly influences the probability of being gossiped. Finally, we discuss how the spread factor is able to be applied to other situations.Comment: 10 pages, 16 figures, Revtex; Virt.J. of Biol. Phys., Oct.1 200

Iron and s-elements abundance variations in NGC5286: comparison with anomalous globular clusters and Milky Way satellites

We present a high resolution spectroscopic analysis of 62 red giants in the Milky Way globular cluster NGC5286. We have determined abundances of representative light proton-capture, alpha, Fe-peak and neutron-capture element groups, and combined them with photometry of multiple sequences observed along the colour-magnitude diagram. Our principal results are: (i) a broad, bimodal distribution in s-process element abundance ratios, with two main groups, the s-poor and s-rich groups; (ii) substantial star-to-star Fe variations, with the s-rich stars having higher Fe, e.g. _s-rich - _s-poor ~ 0.2~dex; and (iii) the presence of O-Na-Al (anti-)correlations in both stellar groups. We have defined a new photometric index, c_{BVI}=(B-V)-(V-I), to maximise the separation in the colour-magnitude diagram between the two stellar groups with different Fe and s-element content, and this index is not significantly affected by variations in light elements (such as the O-Na anticorrelation). The variations in the overall metallicity present in NGC5286 add this object to the class of "anomalous" GCs. Furthermore, the chemical abundance pattern of NGC5286 resembles that observed in some of the anomalous GCs, e.g. M22, NGC1851, M2, and the more extreme Omega Centauri, that also show internal variations in s-elements, and in light elements within stars with different Fe and s-elements content. In view of the common variations in s-elements, we propose the term s-Fe-anomalous GCs to describe this sub-class of objects. The similarities in chemical abundance ratios between these objects strongly suggest similar formation and evolution histories, possibly associated with an origin in tidally disrupted dwarf satellites.Comment: 28 pages, 21 figures, accepted for publication in MNRA

Photometric signatures of multiple stellar populations in Galactic globular clusters

We have calculated synthetic spectra for typical chemical element mixtures (i.e., a standard alpha-enhanced distribution, and distributions displaying CN and ONa anticorrelations) found in the various subpopulations harboured by Galactic globular clusters. From the spectra we have determined bolometric corrections to the standard Johnson-Cousins and Stroemgren filters, and finally predicted colours. These bolometric corrections and colour-transformations, coupled to our theoretical isochrones with the appropriate chemical composition, provide a complete and self-consistent set of theoretical predictions for the effect of abundance variations on the observed cluster CMD. CNO abundance variations affect mainly wavelengths shorter than 400 nm, due to the arise of molecular absorption bands in cooler atmospheres. As a consequence, colour and magnitude changes are largest in the blue filters, independently of using broad or intermediate bandpasses. Colour-magnitude diagrams involving uvy and UB filters (and their various possible colour combinations) are thus the ones best suited to infer photometrically the presence of multiple stellar generations in individual clusters. They are particularly sensitive to variations in the N abundance, with the largest variations affecting the Red Giant Branch (RGB) and lower Main Sequence (MS). BVI diagrams are expected to display multiple sequences only if the different populations are characterized by variations of the C+N+O sum and helium abundance, that lead to changes in luminosity and effective temperature, but leave the flux distribution above 400 nm practically unaffected. A variation of just the helium abundance, up to the level we investigate here, affects exclusively the interior structure of stars, and is largely irrelevant for the atmospheric structure and the resulting flux distribution in the whole wavelength range spanned by our analysis.Comment: 15 pages, 15 figures, submitted to A&A, referee comments addresse

High-Resolution Spectroscopic Study of Extremely Metal-Poor Star Candidates from the SkyMapper Survey

The SkyMapper Southern Sky Survey is carrying out a search for the most metal-poor stars in the Galaxy. It identifies candidates by way of its unique filter set that allows for estimation of stellar atmospheric parameters. The set includes a narrow filter centered on the Ca II K 3933A line, enabling a robust estimate of stellar metallicity. Promising candidates are then confirmed with spectroscopy. We present the analysis of Magellan-MIKE high-resolution spectroscopy of 122 metal-poor stars found by SkyMapper in the first two years of commissioning observations. 41 stars have [Fe/H] <= -3.0. Nine have [Fe/H] <= -3.5, with three at [Fe/H] ~ -4. A 1D LTE abundance analysis of the elements Li, C, Na, Mg, Al, Si, Ca, Sc, Ti, Cr, Mn, Co, Ni, Zn, Sr, Ba and Eu shows these stars have [X/Fe] ratios typical of other halo stars. One star with low [X/Fe] [X/Fe values appears to be "Fe-enhanced," while another star has an extremely large [Sr/Ba] ratio: >2. Only one other star is known to have a comparable value. Seven stars are "CEMP-no" stars ([C/Fe] > 0.7, [Ba/Fe] < 0). 21 stars exhibit mild r-process element enhancements (0.3 <=[Eu/Fe] < 1.0), while four stars have [Eu/Fe] >= 1.0. These results demonstrate the ability to identify extremely metal-poor stars from SkyMapper photometry, pointing to increased sample sizes and a better characterization of the metal-poor tail of the halo metallicity distribution function in the future.Comment: Minor corrections to text, missing data added to Tables 3 and 4; updated to match published version. Complete tables included in sourc

The halo+cluster system of the Galactic globular cluster NGC1851

NGC1851 is surrounded by a stellar component that extends more than ten times beyond the tidal radius. Although the nature of this stellar structure is not known, it has been suggested to be a sparse halo of stars or associated with a stellar stream. We analyse the nature of this intriguing stellar component surrounding NGC1851 by investigating its radial velocities and chemical composition, in particular in comparison with those of the central cluster analysed in a homogeneous manner. In total we observed 23 stars in the halo with radial velocities consistent with NGC1851, and for 15 of them we infer [Fe/H] abundances. Our results show that: (i) stars dynamically linked to NGC1851 are present at least up to ~2.5 tidal radii, supporting the presence of a halo of stars surrounding the cluster; (ii) apart from the NGC1851 radial velocity-like stars, our observed velocity distribution agrees with that expected from Galactic models, suggesting that no other sub-structure (such as a stream) at different radial velocities is present in our field; (iii) the chemical abundances for the s-process elements Sr and Ba are consistent with the s-normal stars observed in NGC1851; (iv) all halo stars have metallicities, and abundances for the other studied elements Ca, Mg and Cr, consistent with those exhibited by the cluster. The complexity of the whole NGC1851 cluster+halo system may agree with the scenario of a tidally-disrupted dwarf galaxy in which NGC1851 was originally embedded.Comment: 21 pages, 16 figures, accepted for publication in MNRA