We present constraints on the stellar initial mass function (IMF) in two ultra-faint dwarf (UFD) galaxies, Hercules and Leo IV, based on deep Hubble Space Telescope Advanced Camera for Surveys imaging. The Hercules and Leo IV galaxies are extremely low luminosity (M V = −6.2, −5.5), metal-poor ( [Fe/H] = −2.4, −2.5) systems that have old stellar populations (>11 Gyr). Because they have long relaxation times, we can directly measure the low-mass stellar IMF by counting stars below the main-sequence turnoff without correcting for dynamical evolution. Over the stellar mass range probed by our data, 0.52-0.77 M , the IMF is best fit by a power-law slope of α = 1.2 +0.4 −0.5 for Hercules and α = 1.3 ± 0.8 for Leo IV. For Hercules, the IMF slope is more shallow than a Salpeter (α = 2.35) IMF at the 5.8σ level, and a Kroupa (α = 2.3 above 0.5 M ) IMF slope at 5.4σ level. We simultaneously fit for the binary fraction, f binary , finding f binary = 0.47 +0.16 −0.14 for Hercules, and 0.47 +0.37 −0.17 for Leo IV. The UFD binary fractions are consistent with that inferred for Milky Way stars in the same mass range, despite very different metallicities. In contrast, the IMF slopes in the UFDs are shallower than other galactic environments. In the mass range 0.5-0.8 M , we see a trend across the handful of galaxies with directly measured IMFs such that the power-law slopes become shallower (more bottom-light) with decreasing galactic velocity dispersion and metallicity. This trend is qualitatively consistent with results in elliptical galaxies inferred via indirect methods and is direct evidence for IMF variations with galactic environment.

No abstract

No abstract

Understanding the underlying community structure is an important challenge in social network analysis. Most state-of-the-art algorithms only consider structural properties to detect disjoint subcommunities and do not include the fact that people can belong to more than one community and also ignore the information contained in posts that users have made. To tackle this problem, we developed a novel methodology to detect overlapping subcommunities in online social networks and a method to analyze the content patterns for each subcommunities using topic models. This paper presents our main contribution, a hybrid algorithm which combines two different overlapping sub-community detection approaches: the first one considers the graph structure of the network (topology-based subcommunities detection approach) and the second one takes the textual information of the network nodes into consideration (topic-based subcommunities detection approach). Additionally we provide a method to analyze and compare the content generated. Tests on real-world virtual communities show that our algorithm outperforms other methods.