Predicting Session Length in Media Streaming

Session length is a very important aspect in determining a user's satisfaction with a media streaming service. Being able to predict how long a session will last can be of great use for various downstream tasks, such as recommendations and ad scheduling. Most of the related literature on user interaction duration has focused on dwell time for websites, usually in the context of approximating post-click satisfaction either in search results, or display ads. In this work we present the first analysis of session length in a mobile-focused online service, using a real world data-set from a major music streaming service. We use survival analysis techniques to show that the characteristics of the length distributions can differ significantly between users, and use gradient boosted trees with appropriate objectives to predict the length of a session using only information available at its beginning. Our evaluation on real world data illustrates that our proposed technique outperforms the considered baseline.Comment: 4 pages, 3 figure

Insight Into the Formation of the Milky Way Through Cold Halo Substructure. III. Statistical Chemical Tagging in the Smooth Halo

We find that the relative contribution of satellite galaxies accreted at high redshift to the stellar population of the Milky Way's smooth halo increases with distance, becoming observable relative to the classical smooth halo about 15 kpc from the Galactic center. In particular, we determine line-of-sight-averaged [Fe/H] and [alpha/Fe] in the metal-poor main-sequence turnoff (MPMSTO) population along every Sloan Extension for Galactic Understanding and Exploration (SEGUE) spectroscopic line of sight. Restricting our sample to those lines of sight along which we do not detect elements of cold halo substructure (ECHOS), we compile the largest spectroscopic sample of stars in the smooth component of the halo ever observed in situ beyond 10 kpc. We find significant spatial autocorrelation in [Fe/H] in the MPMSTO population in the distant half of our sample beyond about 15 kpc from the Galactic center. Inside of 15 kpc however, we find no significant spatial autocorrelation in [Fe/H]. At the same time, we perform SEGUE-like observations of N-body simulations of Milky Way analog formation. While we find that halos formed entirely by accreted satellite galaxies provide a poor match to our observations of the halo within 15 kpc of the Galactic center, we do observe spatial autocorrelation in [Fe/H] in the simulations at larger distances. This observation is an example of statistical chemical tagging and indicates that spatial autocorrelation in metallicity is a generic feature of stellar halos formed from accreted satellite galaxies.Comment: 27 pages, 8 figures, and 7 tables in emulateapj format; accepted for publication in ApJ. Full tables can be extracted from LaTeX sourc

On the assembly of the Milky Way dwarf satellites and their common mass scale

We use a particle tagging technique to dynamically populate the N-body Via Lactea II high-resolution simulation with stars. The method is calibrated using the observed luminosity function of Milky Way satellites and the concentration of their stellar populations, and self-consistently follows the accretion and disruption of progenitor dwarfs and the build-up of the stellar halo in a cosmological "live host". Simple prescriptions for assigning stellar populations to collisionless particles are able to reproduce many properties of the observed Milky Way halo and its surviving dwarf satellites, like velocity dispersions, sizes, brightness profiles, metallicities, and spatial distribution. Our model predicts the existence of approximately 1,850 subhalos harboring "extremely faint" satellites (with mass-to-light ratios >5,000) lying beyond the Sloan Digital Sky Survey detection threshold. Of these, about 20 are "first galaxies", i.e. satellites that formed a stellar mass above 10 Msun before redshift 9. The ten most luminous satellites (L> 1e6 Lsun) in the simulation are hosted by subhalos with peak circular velocities today in the range V_max=10-40 km/s that have shed between 80% and 99% of their dark mass after being accreted at redshifts 1.7< z <4.6. The satellite maximum circular velocity and stellar line-of-sight velocity dispersion today follow the relation V_max=2.2 sigma_los. We apply a standard mass estimation algorithm based on Jeans modelling of the line-of-sight velocity dispersion profiles to the simulated dwarf spheroidals, and test the accuracy of this technique. The inner (within 300 pc) mass-luminosity relation for currently detectable satellites is nearly flat in our model, in qualitative agreement with the "common mass scale" found in Milky Way dwarfs. We do, however, predict a weak, but significant positive correlation for these objects: M_300 ~L^{0.088 \pm 0.024}.Comment: 14 pages, 9 figures, accepted for publication in The Astrophysical Journa

High Resolution Numerical Studies of the Milky Way Halo

The halo of the MilkyWay (MW) contains residual evidence of its hierarchical accretion history, such as stellar streams, dwarf satellite galaxies and possibly even intermediate-mass black holes the latter carried as they fell into the larger Galaxy. The discovery and study of these objects have the potential to answer elusive questions about our Galaxy, such as the accurate determination of its total mass, a fundamental quantity that determines the properties and fate of galaxies in the Universe.I use a particle tagging technique to dynamically populate the N-body Via Lactea II high-resolution simulation with stars. The method is calibrated using the observed luminosity function of Milky Way satellites and the concentration of their stellar populations, and self-consistently follows the accretion and disruption of progenitor dwarfs and the build-up of the stellar halo in a cosmological "live host". Simple prescriptions for assigning stellar populations to collisionless particles are able to reproduce many properties of the observed Milky Way halo and its surviving dwarf satellites, like velocity dispersions, sizes, brightness profiles, metallicities, and spatial distribution. I apply a standard mass estimation algorithm based on Jeans modelling of the line-of-sight velocity dispersion profiles to the simulated dwarf spheroidals, and test the accuracy of this technique. The inner mass-luminosity relation for currently detectable satellites is nearly flat in this model, in qualitative agreement with the "common mass scale" found in Milky Way dwarfs.I extend the tagging approach to the study of intermediate-mass black holes (IMBHs), and assess the size, properties, and detectability of the leftover accreted halo population. The method assigns a black hole to the most tightly bound central particle of each subhalo at infall according to an extrapolation of the MBH-sigma star relation, and self-consistently follows the accretion and disruption of Milky Way progenitor dwarfs and their holes in a cosmological "live" host from high redshift to today. I show that, depending on the minimum stellar velocity dispersion, below which central black holes are assumed to be increasingly rare, as many as two thousand or as few as seventy IMBHs may be left wandering in the halo of the Milky Way today. I identify two main Galactic subpopulations, "naked" IMBHs, whose host subhalos were totally destroyed after infall, and "clothed" IMBHs residing in dark matter satellites that survived tidal stripping. Naked IMBHs typically constitute about half of the total and are more centrally concentrated. Their detection may provide an observational tool to constrain the formation history of massiveblack holes in the early Universe.I use the results from the stellar halo tagging in combination with the state-of-the-art hydrodynamical cosmological simulation Eris to address the question of the poorly known Milky Way halo mass. Taking advantage of the two simulated galaxies' very different masses, I explore the full range of estimates for the Galaxy from observational data. I establish that the simulated halos reproduce many of the properties of the MW stellar halo, including its density profile slope, velocity anisotropy and, in the case of the lighter galaxy, its radial velocity dispersion profile. There is a striking link between discontinuities in these quantities where significant pileup of stars in the orbital apocenters of their progenitors exists in phase space. I carry out controlled experiments using numerical integration of the Jeans equation to conclude that the lighter halo, Eris, indeed provides a much better fit to the data than the more massive halo of Via Lactea II

Direct gravitational imaging of intermediate mass black holes in extragalactic haloes

International audienceA galaxy halo may contain a large number of intermediate mass black holes (IMBHs) with masses in the range of 102 M⊙ ≲ MBH ≲ 106 M⊙. We propose to directly detect these IMBHs by observing multiply imaged QSO-galaxy or galaxy-galaxy strong lens systems in the submillimetre bands with high angular resolution. The silhouette of an IMBH in the lensing galaxy halo would appear as either a monopole-like or a dipole-like variation at the scale of the Einstein radius against the Einstein ring of the dust-emitting region surrounding the QSO. We use a particle tagging technique to dynamically populate a Milky Way-sized dark matter halo with black holes (BHs), and show that the surface mass density and number density of IMBHs have power-law dependences on the distance from the centre of the host halo if smoothed on a scale of ∼ 1 kpc. Most of the BHs orbiting close to the centre are freely roaming as they have lost their dark matter hosts during infall due to tidal stripping. Next generation submillimetre telescopes with high angular resolution (≲0.3 mas) will be capable of directly mapping such off-nuclear freely roaming BHs with a mass of ≲106 M⊙ in a lensing galaxy that harbours an O(109) M⊙ supermassive black hole in its nucleus