Breaking Sticks and Ambiguities with Adaptive Skip-gram

Recently proposed Skip-gram model is a powerful method for learning high-dimensional word representations that capture rich semantic relationships between words. However, Skip-gram as well as most prior work on learning word representations does not take into account word ambiguity and maintain only single representation per word. Although a number of Skip-gram modifications were proposed to overcome this limitation and learn multi-prototype word representations, they either require a known number of word meanings or learn them using greedy heuristic approaches. In this paper we propose the Adaptive Skip-gram model which is a nonparametric Bayesian extension of Skip-gram capable to automatically learn the required number of representations for all words at desired semantic resolution. We derive efficient online variational learning algorithm for the model and empirically demonstrate its efficiency on word-sense induction task

SN1993J VLBI (I): The Center of the Explosion and a Limit on Anisotropic Expansion

Phase-referenced VLBI observations of supernova 1993J at 24 epochs, from 50 days after shock breakout to the present, allowed us to determine the coordinates of the explosion center relative to the quasi-stationary core of the host galaxy M81 with an accuracy of 45 micro-arcsec, and to determine the nominal proper motion of the geometric center of the radio shell with an accuracy of 9micro-arcsec/yr. The uncertainties correspond to 160 AU for the position and 160 km/s for the proper motion at the distance of the source of 3.63 Mpc. After correcting for the expected galactic proper motion of the supernova around the core of M81 using HI rotation curves, we obtain a peculiar proper motion of the radio shell center of only 320 +/- 160 km/s to the south, which limits any possible one-sided expansion of the shell. We also find that the shell is highly circular, the outer contours in fact being circular to within 3%. Combining our proper motion values with the degree of circular symmetry, we find that the expansion of the shockfront from the explosion center is isotropic to within 5.5% in the plane of the sky. This is a more fundamental result on isotropic expansion than can be derived from the circularity of the images alone. The brightness of the radio shell, however, varies along the ridge and systematically changes with time. The degree of isotropy in the expansion of the shockfront contrasts with the asymmetries and polarization found in optical spectral lines. Asymmetric density distributions in the ejecta or more likely in the circumstellar medium, are favored to reconcile the radio and optical results. We see no sign of any disk-like density distribution of the circumstellar material, with the average axis ratio of the radio shell of SN1993J being less than 1.04.Comment: 21 pages, LaTex + 5 Figures (encapulsated PostScript), Accepted for Publication in the Astrophysical Journa

The Distribution of High and Low Redshift Type Ia Supernovae

The distribution of high redshift Type Ia supernovae (SNe Ia) with respect to projected distance from the center of the host galaxy is studied and compared to the distribution of local SNe. The distribution of high-z SNe Ia is found to be similar to the local sample of SNe Ia discovered with CCDs, but different than the sample discovered photographically. This is shown to be due to the Shaw effect. These results have implications for the use of SNe Ia to determine cosmological parameters if the local sample of supernovae used to calibrate the light curve decline relationships is drawn from a sample discovered photographically. A K-S test shows that the probability that the high redshift SNe of the Supernova Cosmology Project are drawn from the same distribution as the low redshift calibrators of Riess et al. is 0.1%. This is a potential problem because photographically discovered SNe are preferentially discovered farther away from the galaxy nucleus, where SNe show a lower scatter in absolute magnitude, and are on average 0.3 magnitudes fainter than SNe located closer to the center of their host galaxy. This raises questions about whether or not the calibration SNe sample the full range of parameters potentially present in high redshift SNe Ia. The limited data available suggest that the calibration process is adequate; however, it would be preferable if high redshift SNe and the low redshift SNe used to calibrate them were drawn from the same sample, as subtle differences may be important. Data are also presented which suggest that the seeming anti-Malmquist trend noticed by Tammann et al.(1996, 1998) for SNe Ia in galaxies with Cepheid distances may be due to the location of the SNe in their host galaxies.Comment: 16 pages, 2 figures Accepted for publication in the Astrophysical Journa

Supernovae in isolated galaxies, in pairs and in groups of galaxies

In order to investigate the influence of the environment on the supernova (SN) production we have performed a statistical investigation of the SNe discovered in isolated galaxies, in pairs and in groups of galaxies. 22 SNe in 18 isolated galaxies, 48 SNe in 40 galaxies members of 37 pairs and 211 SNe in 170 galaxies members of 116 groups have been selected and studied. We found that the radial distributions of core-collapse SNe in galaxies located in different environments are similar, and consistent with that reported by Bartunov, Makarova & Tsvetkov (1992). SNe discovered in pairs do not privilege a particular direction with respect to the companion galaxy. Also the azimuthal distributions inside the hosts members of galaxy groups are consistent with being isotropics. The fact that SNe are more frequent in the brighter components of the pairs and groups is expected from the dependence of the SN rates on the galaxy luminosity. There is an indication that the SN rate is higher in galaxy pairs compared with that in groups. This can be related to the enhanced star formation rate in strongly interacting systems. It is concluded that, with the possible exception of strongly interacting system, the parent galaxy environment has no direct influence on the SN productionComment: 10 pages, accepted for publication to MNRA

Type Ibc supernovae in disturbed galaxies: evidence for a top-heavy IMF

We compare the radial locations of 178 core-collapse supernovae to the R-band and H alpha light distributions of their host galaxies. When the galaxies are split into `disturbed' and `undisturbed' categories, a striking difference emerges. The disturbed galaxies have a central excess of core-collapse supernovae, and this excess is almost completely dominated by supernovae of types Ib, Ic and Ib/c, whereas type II supernovae dominate in all other environments. The difference cannot easily be explained by metallicity or extinction effects, and thus we propose that this is direct evidence for a stellar initial mass function that is strongly weighted towards high mass stars, specifically in the central regions of disturbed galaxies.Comment: 22 pages, 5 figures, accepted for publication in Ap