457 research outputs found
Embedded Lensing Time Delays, the Fermat Potential, and the Integrated Sachs-Wolfe Effect
We derive the Fermat potential for a spherically symmetric lens embedded in
an FLRW cosmology and use it to investigate the late-time integrated
Sachs-Wolfe (ISW) effect, i.e., secondary temperature fluctuations in the
cosmic microwave background (CMB) caused by individual large scale clusters and
voids. We present a simple analytical expression for the temperature
fluctuation in the CMB across such a lens as a derivative of the lens' Fermat
potential. This formalism is applicable to both linear and nonlinear density
evolution scenarios, to arbitrarily large density contrasts, and to all open
and closed background cosmologies. It is much simpler to use and makes the same
predictions as conventional approaches. In this approach the total temperature
fluctuation can be split into a time-delay part and an evolutionary part. Both
parts must be included for cosmic structures that evolve and both can be
equally important. We present very simple ISW models for cosmic voids and
galaxy clusters to illustrate the ease of use of our formalism. We use the
Fermat potentials of simple cosmic void models to compare predicted ISW effects
with those recently extracted from WMAP and \emph{Planck} data by stacking
large cosmic voids using the aperture photometry method. If voids in the local
universe with large density contrasts are no longer evolving we find that the
time delay contribution alone predicts values consistent with the measurements.
However, we find that for voids still evolving linearly, the evolutionary
contribution cancels a significant part of the time delay contribution and
results in predicted signals that are much smaller than recently observed.Comment: 25 pages, 4 figures, ApJ in pres
A Simple Gravitational Lens Model For Cosmic Voids
We present a simple gravitational lens model to illustrate the ease of using
the embedded lensing theory when studying cosmic voids. It confirms the
previously used repulsive lensing models for deep voids. We start by estimating
magnitude fluctuations and weak lensing shears of background sources lensed by
large voids. We find that sources behind large () and deep
voids (density contrast about ) can be magnified or demagnified with
magnitude fluctuations of up to and that the weak-lensing
shear can be up to the level in the outer regions of large
voids. Smaller or shallower voids produce proportionally smaller effects. We
investigate the "wiggling" of the primary cosmic microwave background (CMB)
temperature anisotropies caused by intervening cosmic voids. The void-wiggling
of primary CMB temperature gradients is of the opposite sign to that caused by
galaxy clusters. Only extremely large and deep voids can produce wiggling
amplitudes similar to galaxy clusters, by a large void of
radius and central density contrast at redshift 0.5
assuming a CMB background gradient of . The
dipole signal is spread over the entire void area, and not concentrated at the
lens' center as it is for clusters. Finally we use our model to simulate CMB
sky maps lensed by large cosmic voids. Our embedded theory can easily be
applied to more complicated void models and used to study gravitational lensing
of the CMB, to probe dark-matter profiles, to reduce the lensing-induced
systematics in supernova Hubble diagrams, as well as study the integrated
Sachs-Wolfe effect.Comment: 25 pages, 4 figures, ApJ accepte
On the Structure of Quasi-Universal Jets for Gamma-Ray Bursts
The idea that GRBs originate from uniform jets has been used to explain
numerous observations of breaks in the GRB afterglow lightcurves. We explore
the possibility that GRBs instead originate from a structured jet that may be
quasi-universal, where the variation in the observed properties of GRBs is due
to the variation in the observer viewing angle. We test how various models
reproduce the jet data of Bloom, Frail, & Kulkarni (2003), which show a
negative correlation between the isotropic energy output and the inferred jet
opening angle (in a uniform jet configuration). We find, consistent with
previous studies, that a power-law structure for the jet energy as a function
of angle gives a good description. However, a Gaussian jet structure can also
reproduce the data well, particularly if the parameters of the Gaussian are
allowed some scatter. We place limits on the scatter of the parameters in both
the Gaussian and power-law models needed to reproduce the data, and discuss how
future observations will better distinguish between these models for the GRB
jet structure. In particular, the Gaussian model predicts a turnover at small
opening angles and in some cases a sharp cutoff at large angles, the former of
which may already have been observed. We also discuss the predictions each
model makes for the observed luminosity function of GRBs and compare these
predictions with the existing data.Comment: 13 pages, including 10 figures; To appear in Ap
Non-linear Learning for Statistical Machine Translation
Modern statistical machine translation (SMT) systems usually use a linear
combination of features to model the quality of each translation hypothesis.
The linear combination assumes that all the features are in a linear
relationship and constrains that each feature interacts with the rest features
in an linear manner, which might limit the expressive power of the model and
lead to a under-fit model on the current data. In this paper, we propose a
non-linear modeling for the quality of translation hypotheses based on neural
networks, which allows more complex interaction between features. A learning
framework is presented for training the non-linear models. We also discuss
possible heuristics in designing the network structure which may improve the
non-linear learning performance. Experimental results show that with the basic
features of a hierarchical phrase-based machine translation system, our method
produce translations that are better than a linear model.Comment: submitted to a conferenc
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