Density Matching for Bilingual Word Embedding

Recent approaches to cross-lingual word embedding have generally been based on linear transformations between the sets of embedding vectors in the two languages. In this paper, we propose an approach that instead expresses the two monolingual embedding spaces as probability densities defined by a Gaussian mixture model, and matches the two densities using a method called normalizing flow. The method requires no explicit supervision, and can be learned with only a seed dictionary of words that have identical strings. We argue that this formulation has several intuitively attractive properties, particularly with the respect to improving robustness and generalization to mappings between difficult language pairs or word pairs. On a benchmark data set of bilingual lexicon induction and cross-lingual word similarity, our approach can achieve competitive or superior performance compared to state-of-the-art published results, with particularly strong results being found on etymologically distant and/or morphologically rich languages.Comment: Accepted by NAACL-HLT 201

The Progenitors of Type Ia Supernovae: II. Are they Double-Degenerate Binaries? The Symbiotic Channel

In order for a white dwarf (WD) to achieve the Chandrasekhar mass, M_C, and explode as a Type Ia supernova (SNIa), it must interact with another star, either accreting matter from or merging with it. The failure to identify the types of binaries which produce SNeIa is the "progenitor problem". Its solution is required if we are to utilize the full potential of SNeIa to elucidate basic cosmological and physical principles. In single-degenerate models, a WD accretes and burns matter at high rates. Nuclear-burning WDs (NBWDs) with mass close to M_C are hot and luminous, potentially detectable as supersoft x-ray sources (SSSs). In previous work we showed that > 90-99% of the required number of progenitors do not appear as SSSs during most of the crucial phase of mass increase. The obvious implication is that double-degenerate (DD) binaries form the main class of progenitors. We show in this paper, however, that many binaries that later become DDs must pass through a long-lived NBWD phase during which they are potentially detectable as SSSs. The paucity of SSSs is therefore not a strong argument in favor of DD models. Those NBWDs that are the progenitors of DD binaries are likely to appear as symbiotic binaries for intervals > 10^6 years. In fact, symbiotic pre-DDs should be common, whether or not the WDs eventually produce SNeIa. The key to solving the progenitor problem lies in understanding the appearance of NBWDs. Most do not appear as SSSs most of the time. We therefore consider the evolution of NBWDs to address the question of what their appearance may be and how we can hope to detect them.Comment: 24 pages; 5 figures; submitted to Ap

The Progenitors of Type Ia Supernovae: Are They Supersoft Sources?

In a canonical model, the progenitors of Type Ia supernovae (SNe Ia) are accreting, nuclear-burning white dwarfs (NBWDs), which explode when the white dwarf reaches the Chandrasekhar mass, M_C. Such massive NBWDs are hot (kT ~100 eV), luminous (L ~ 10^{38} erg/s), and are potentially observable as luminous supersoft X-ray sources (SSSs). During the past several years, surveys for soft X-ray sources in external galaxies have been conducted. This paper shows that the results falsify the hypothesis that a large fraction of progenitors are NBWDs which are presently observable as SSSs. The data also place limits on sub-M_C models. While Type Ia supernova progenitors may pass through one or more phases of SSS activity, these phases are far shorter than the time needed to accrete most of the matter that brings them close to M_C.Comment: submitted to ApJ 18 November 2009; 17 pages, 2 figure

Optimizing egalitarian performance in the side-effects model of colocation for data center resource management

In data centers, up to dozens of tasks are colocated on a single physical machine. Machines are used more efficiently, but tasks' performance deteriorates, as colocated tasks compete for shared resources. As tasks are heterogeneous, the resulting performance dependencies are complex. In our previous work [18] we proposed a new combinatorial optimization model that uses two parameters of a task - its size and its type - to characterize how a task influences the performance of other tasks allocated to the same machine. In this paper, we study the egalitarian optimization goal: maximizing the worst-off performance. This problem generalizes the classic makespan minimization on multiple processors (P||Cmax). We prove that polynomially-solvable variants of multiprocessor scheduling are NP-hard and hard to approximate when the number of types is not constant. For a constant number of types, we propose a PTAS, a fast approximation algorithm, and a series of heuristics. We simulate the algorithms on instances derived from a trace of one of Google clusters. Algorithms aware of jobs' types lead to better performance compared with algorithms solving P||Cmax. The notion of type enables us to model degeneration of performance caused by using standard combinatorial optimization methods. Types add a layer of additional complexity. However, our results - approximation algorithms and good average-case performance - show that types can be handled efficiently.Comment: Author's version of a paper published in Euro-Par 2017 Proceedings, extends the published paper with addtional results and proof

Accuracy and Stability of Virtual Source Method for Numerical Simulations of Nonlinear Water Waves

The virtual source method (VSM) developed by Langfeld et al., (2016) is based upon the integral equations derived by using Green’s identity with Laplace’s equation for the velocity potential. These authors presented preliminary results using the method to simulate standing waves. In this paper, we numerically model a non-linear standing wave by using the VSM to illustrate the energy and volume conservation. Analytical formulas are derived to compute the volume and potential energy while the kinetic energy is computed by numerical integration. Results are compared with both theory and boundary element method (BEM)

Exploring the (Efficient) Frontiers of Portfolio Optimization

The cardinality-constrained portfolio optimization problem is NP-hard. Its Pareto front (or the Efficient Frontier - EF) is usually calculated by stochastic algorithms, including EAs. However, in certain cases the EF may be decomposed into a union of sub-EFs. In this work we propose a systematic process of excluding sub-EFs dominated by others, enabling us to calculate non-dominated sub-EFs. We then calculate whole EFs to a high degree of accuracy for small cardinalities, providing an alternative to EAs in those cases. We can use also this to provide insight into EAs on the problem

The Millennium Galaxy Catalogue: The MbhM_{bh}--LspheroidL_{spheroid} derived supermassive black hole mass function

Supermassive black hole mass estimates are derived for 1743 galaxies from the Millennium Galaxy Catalogue using the recently revised empirical relation between supermassive black hole mass and the luminosity of the host spheroid. The MGC spheroid luminosities are based on $R^{1/n}$-bulge plus exponential-disc decompositions. The majority of black hole masses reside between $10^6 M_{\odot}$ and an upper limit of $2\times10^9 M_{\odot}$. Using previously determined space density weights, we derive the SMBH mass function which we fit with a Schechter-like function. Integrating the black hole mass function over $10^6< M_{bh}/ M_{\odot} < 10^{10}$ gives a supermassive black hole mass density of ($3.8 \pm 0.6) \times 10^5 h^{3}_{70} M_{\odot}$ Mpc$^{-3}$ for early-type galaxies and ($0.96 \pm 0.2) \times10^5 h^{3}_{70} M_{\odot}$ Mpc$^{-3}$ for late-type galaxies. The errors are estimated from Monte Carlo simulations which include the uncertainties in the $M_{bh}$--$L$ relation, the luminosity of the host spheroid and the intrinsic scatter of the $M_{bh}$--$L$ relation. Assuming supermassive black holes form via baryonic accretion we find that ($0.008\pm0.002) h_{70}^{3}$ per cent of the Universe's baryons are currently locked up in supermassive black holes. This result is consistent with our previous estimate based on the $M_{bh}$--$n$ (S{\'e}rsic index) relation.Comment: 10 pages, 6 figures, accepted to MNRA

A Relationship between Supermassive Black Hole Mass and the Total Gravitational Mass of the Host Galaxy

We investigate the correlation between the mass of a central supermassive black hole and the total gravitational mass of the host galaxy (M_tot). The results are based on 43 galaxy-scale strong gravitational lenses from the Sloan Lens ACS (SLACS) Survey whose black hole masses were estimated through two scaling relations: the relation between black hole mass and Sersic index (M_bh - n) and the relation between black hole mass and stellar velocity dispersion (M_bh - sigma). We use the enclosed mass within R_200, the radius within which the density profile of the early type galaxy exceeds the critical density of the Universe by a factor of 200, determined by gravitational lens models fitted to HST imaging data, as a tracer of the total gravitational mass. The best fit correlation, where M_bh is determined from M_bh - sigma relation, is log(M_bh) = (8.18 +/- 0.11) + (1.55 +/- 0.31) (log(M_tot) - 13.0) over 2 orders of magnitude in M_bh. From a variety of tests, we find that we cannot reliably infer a connection between M_bh and M_tot from the M_bh - n relation. The M_bh - M_tot relation provides some of the first, direct observational evidence to test the prediction that supermassive black hole properties are determined by the halo properties of the host galaxy.Comment: 29 pages, 10 figures, Accepted for publication in Ap