28,690 research outputs found
The Milky Way Galaxy as a Strong Gravitational Lens
We study the gravitational lensing effects of spiral galaxies by taking a
model of the Milky Way and computing its lensing properties. The model is
composed of a spherical Hernquist bulge, a Miyamoto-Nagai disc and an
isothermal halo. As a strong lens, a spiral galaxy like the Milky Way can give
rise to four different imaging geometries. They are (i) three images on one
side of the galaxy centre (`disc triplets'), (ii) three images with one close
to the centre (`core triplets'), (iii) five images and (iv) seven images.
Neglecting magnification bias, we show that the core triplets, disc triplets
and fivefold imaging are roughly equally likely. Even though our models contain
edge-on discs, their image multiplicities are not dominated by disc triplets.
The halo has a small effect on the caustic structure, the time delays and
brightnesses of the images. The Milky Way model has a maximum disc (i.e., the
halo is not dynamically important in the inner parts). Strong lensing by nearly
edge-on disc galaxies breaks the degeneracy between the relative contribution
of the disc and halo to the overall rotation curve. If a spiral galaxy has a
sub-maximum disc, then the astroid caustic shrinks dramatically in size, whilst
the radial caustic shrinks more modestly. This causes changes in the relative
likelihood of the image geometries, specifically (i) core triplets are now 9/2
times more likely than disc triplets, (ii) the cross section for threefold
imaging is reduced by a factor of 2/3, whilst (iii) the cross section for
fivefold imaging is reduced by 1/2. Although multiple imaging is less likely
(the cross sections are smaller), the average total magnification is greater.Comment: MNRAS, in pres
Distributed Stochastic Optimization of the Regularized Risk
Many machine learning algorithms minimize a regularized risk, and stochastic
optimization is widely used for this task. When working with massive data, it
is desirable to perform stochastic optimization in parallel. Unfortunately,
many existing stochastic optimization algorithms cannot be parallelized
efficiently. In this paper we show that one can rewrite the regularized risk
minimization problem as an equivalent saddle-point problem, and propose an
efficient distributed stochastic optimization (DSO) algorithm. We prove the
algorithm's rate of convergence; remarkably, our analysis shows that the
algorithm scales almost linearly with the number of processors. We also verify
with empirical evaluations that the proposed algorithm is competitive with
other parallel, general purpose stochastic and batch optimization algorithms
for regularized risk minimization
Sigma Model BPS Lumps on Torus
We study doubly periodic Bogomol'nyi-Prasad-Sommerfield (BPS) lumps in
supersymmetric CP^{N-1} non-linear sigma models on a torus T^2. Following the
philosophy of the Harrington-Shepard construction of calorons in Yang-Mills
theory, we obtain the n-lump solutions on compact spaces by suitably arranging
the n-lumps on R^2 at equal intervals. We examine the modular invariance of the
solutions and find that there are no modular invariant solutions for n=1,2 in
this construction.Comment: 15 pages, 3 figures, published versio
WordRank: Learning Word Embeddings via Robust Ranking
Embedding words in a vector space has gained a lot of attention in recent
years. While state-of-the-art methods provide efficient computation of word
similarities via a low-dimensional matrix embedding, their motivation is often
left unclear. In this paper, we argue that word embedding can be naturally
viewed as a ranking problem due to the ranking nature of the evaluation
metrics. Then, based on this insight, we propose a novel framework WordRank
that efficiently estimates word representations via robust ranking, in which
the attention mechanism and robustness to noise are readily achieved via the
DCG-like ranking losses. The performance of WordRank is measured in word
similarity and word analogy benchmarks, and the results are compared to the
state-of-the-art word embedding techniques. Our algorithm is very competitive
to the state-of-the- arts on large corpora, while outperforms them by a
significant margin when the training set is limited (i.e., sparse and noisy).
With 17 million tokens, WordRank performs almost as well as existing methods
using 7.2 billion tokens on a popular word similarity benchmark. Our multi-node
distributed implementation of WordRank is publicly available for general usage.Comment: Conference on Empirical Methods in Natural Language Processing
(EMNLP), November 1-5, 2016, Austin, Texas, US
Sine-Gordon Soliton on a Cnoidal Wave Background
The method of Darboux transformation, which is applied on cnoidal wave
solutions of the sine-Gordon equation, gives solitons moving on a cnoidal wave
background. Interesting characteristics of the solution, i.e., the velocity of
solitons and the shift of crests of cnoidal waves along a soliton, are
calculated. Solutions are classified into three types (Type-1A, Type-1B,
Type-2) according to their apparent distinct properties.Comment: 11 pages, 5 figures, Contents change
Numerical simulation of super-square patterns in Faraday waves
We report the first simulations of the Faraday instability using the full
three-dimensional Navier-Stokes equations in domains much larger than the
characteristic wavelength of the pattern. We use a massively parallel code
based on a hybrid Front-Tracking/Level-set algorithm for Lagrangian tracking of
arbitrarily deformable phase interfaces. Simulations performed in rectangular
and cylindrical domains yield complex patterns. In particular, a
superlattice-like pattern similar to those of [Douady & Fauve, Europhys. Lett.
6, 221-226 (1988); Douady, J. Fluid Mech. 221, 383-409 (1990)] is observed. The
pattern consists of the superposition of two square superlattices. We
conjecture that such patterns are widespread if the square container is large
compared to the critical wavelength. In the cylinder, pentagonal cells near the
outer wall allow a square-wave pattern to be accommodated in the center
Dry Matter Production and Nutritive Value of Wild Alfalfa
Alfalfa grows wild in some parts of Korea, but specific information is lacking as to its agronomic characteristics, nutritive value and dry matter production potential. The objective of this study was to evaluate the usefulness of wild alfalfa (Medicago sativa L) as a forage. Wild alfalfa and Vernal were field sown at Keongsan, Keongbuk in the spring of 1995. Emergence for Vernal was better than for wild alfalfa. It was observed that the flowering date of the wild alfalfa was delayed by 8 days. Regrowth of Vernal was better than that of the wild alfalfa at each harvesting. After the last harvesting date, September 22, there was no regrowth of the wild alfalfa, but regrowth of Vernal measured 37cm. Weed infestation in the wild alfalfa plots was higher than in the Vernal plots. The dry matter yields per hectare were significantly(P\u3c0.05) higher for Vernal than for the wild alfalfa
Semiconducting-to-metallic photoconductivity crossover and temperature-dependent Drude weight in graphene
We investigated the transient photoconductivity of graphene at various
gate-tuned carrier densities by optical-pump terahertz-probe spectroscopy. We
demonstrated that graphene exhibits semiconducting positive photoconductivity
near zero carrier density, which crosses over to metallic negative
photoconductivity at high carrier density. Our observations are accounted for
by considering the interplay between photo-induced changes of both the Drude
weight and the carrier scattering rate. Notably, we observed multiple sign
changes in the temporal photoconductivity dynamics at low carrier density. This
behavior reflects the non-monotonic temperature dependence of the Drude weight,
a unique property of massless Dirac fermions
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