The third dredge-up and the carbon star luminosity functions in the Magellanic Clouds

We investigate the formation of carbon stars as a function of the stellar mass and parent metallicity. Theoretical modelling is based on an improved scheme for treating the third dredge-up in synthetic calculations of thermally pulsing asymptotic giant branch (TP-AGB) stars. In this approach, the usual criterion (based on a constant minimum core mass for the occurrence of dredge-up, M_c^min) is replaced by one on the minimum temperature at the base of the convective envelope, T_b^dred, at the stage of the post-flash luminosity maximum. Envelope integrations then allow determination of M_c^min as a function of stellar mass, metallicity, and pulse strength (see Wood 1981), thus inferring if and when dredge-up first occurs. Moreover, the final possible shut down of the process is predicted. Extensive grids of TP-AGB models were computed using this scheme. We present and discuss the calibration of the two dredge-up parameters (lambda and T_b^dred) aimed at reproducing the carbon star luminosity function (CSLF) in the LMC. It turns out that the faint tail is almost insensitive to the history of star formation rate (SFR) in the parent galaxy (it is essentially determined by T_b^dred), in contrast to the bright wing which may be more affected by the details of the recent SFR. Once the faint end is reproduced, the peak location is a stringent calibrator of lambda. The best fit to the observed CSLF in the LMC is obtained with Z=0.008, lambda=0.50, log(T_b^dred)=6.4, and a constant SFR up to 5x10^8 yr ago. A good fit to the CSLF in the SMC is then easily derived from the Z=0.004 models, with a single choice of parameters, and a constant SFR over the entire significant age interval. The results are consistent with the theoretical expectation that the third dredge-up is more efficient at lower Zs.Comment: 22 pages with 15 figures, to appear in A&

Motif counting beyond five nodes

Counting graphlets is a well-studied problem in graph mining and social network analysis. Recently, several papers explored very simple and natural algorithms based on Monte Carlo sampling of Markov Chains (MC), and reported encouraging results. We show, perhaps surprisingly, that such algorithms are outperformed by color coding (CC) [2], a sophisticated algorithmic technique that we extend to the case of graphlet sampling and for which we prove strong statistical guarantees. Our computational experiments on graphs with millions of nodes show CC to be more accurate than MC; furthermore, we formally show that the mixing time of the MC approach is too high in general, even when the input graph has high conductance. All this comes at a price however. While MC is very efficient in terms of space, CC’s memory requirements become demanding when the size of the input graph and that of the graphlets grow. And yet, our experiments show that CC can push the limits of the state-of-the-art, both in terms of the size of the input graph and of that of the graphlets

The Limits of Popularity-Based Recommendations, and the Role of Social Ties

In this paper we introduce a mathematical model that captures some of the salient features of recommender systems that are based on popularity and that try to exploit social ties among the users. We show that, under very general conditions, the market always converges to a steady state, for which we are able to give an explicit form. Thanks to this we can tell rather precisely how much a market is altered by a recommendation system, and determine the power of users to influence others. Our theoretical results are complemented by experiments with real world social networks showing that social graphs prevent large market distortions in spite of the presence of highly influential users.Comment: 10 pages, 9 figures, KDD 201

Dust and Nebular Emission in Star Forming Galaxies

Star forming galaxies exhibit a variety of physical conditions, from quiescent normal spirals to the most powerful dusty starbursts. In order to study these complex systems, we need a suitable tool to analyze the information coming from observations at all wavelengths. We present a new spectro-photometric model which considers in a consistent way starlight as reprocessed by gas and dust. We discuss preliminary results to interpret some observed properties of VLIRGs.Comment: 8 pages, to be published in "The link between stars and cosmology", 26-30 March, 2001, Puerto Vallarta, Mexico, by Kluwer, eds. M. Chavez, A. Bressan, A. Buzzoni, and D. Mayy

Formation of black holes in the pair-instability mass gap: evolution of a post-collision star

The detection of GW190521 by the LIGO-Virgo collaboration revealed the existence of black holes (BHs) in the pair-instability (PI) mass gap. Here, we investigate the formation of BHs in the PI mass gap via star -- star collisions in young stellar clusters. To avoid PI, the stellar-collision product must have a relatively small core and a massive envelope. We generate our initial conditions from the outputs of a hydro-dynamical simulation of the collision between a core helium burning star ($\sim 58$ M$_\odot$) and a main-sequence star ($\sim 42$ M$_\odot$). The hydro-dynamical simulation allows us to take into account the mass lost during the collision ($\sim 12$ M$_\odot$) and to build the chemical composition profile of the post-collision star. We then evolve the collision product with the stellar evolution codes PARSEC and MESA. We find that the post-collision star evolves through all the stellar burning phases until core collapse, avoiding PI. At the onset of core collapse, the post-collision product is a blue super-giant star. We estimate a total mass loss of about 1 M$_\odot$ during the post-collision evolution, due to stellar winds and shocks induced by neutrino emission in a failed supernova. The final BH mass is $\approx{87}$ M$_\odot$. Therefore, we confirm that the collision scenario is a suitable formation channel to populate the PI mass gap.Comment: 9 pages, 6 figures, comments welcome