329,653 research outputs found
Non-negative matrix factorization for self-calibration of photometric redshift scatter in weak lensing surveys
Photo-z error is one of the major sources of systematics degrading the
accuracy of weak lensing cosmological inferences. Zhang et al. (2010) proposed
a self-calibration method combining galaxy-galaxy correlations and galaxy-shear
correlations between different photo-z bins. Fisher matrix analysis shows that
it can determine the rate of photo-z outliers at a level of 0.01-1% merely
using photometric data and do not rely on any prior knowledge. In this paper,
we develop a new algorithm to implement this method by solving a constrained
nonlinear optimization problem arising in the self-calibration process. Based
on the techniques of fixed-point iteration and non-negative matrix
factorization, the proposed algorithm can efficiently and robustly reconstruct
the scattering probabilities between the true-z and photo-z bins. The algorithm
has been tested extensively by applying it to mock data from simulated stage IV
weak lensing projects. We find that the algorithm provides a successful
recovery of the scatter rates at the level of 0.01-1%, and the true mean
redshifts of photo-z bins at the level of 0.001, which may satisfy the
requirements in future lensing surveys.Comment: 12 pages, 6 figures. Accepted for publication in ApJ. Updated to
match the published versio
Weak lensing power spectrum reconstruction by counting galaxies.-- I: the ABS method
We propose an Analytical method of Blind Separation (ABS) of cosmic
magnification from the intrinsic fluctuations of galaxy number density in the
observed galaxy number density distribution. The ABS method utilizes the
different dependences of the signal (cosmic magnification) and contamination
(galaxy intrinsic clustering) on galaxy flux, to separate the two. It works
directly on the measured cross galaxy angular power spectra between different
flux bins. It determines/reconstructs the lensing power spectrum analytically,
without assumptions of galaxy intrinsic clustering and cosmology. It is
unbiased in the limit of infinite number of galaxies. In reality the lensing
reconstruction accuracy depends on survey configurations, galaxy biases, and
other complexities, due to finite number of galaxies and the resulting shot
noise fluctuations in the cross galaxy power spectra. We estimate its
performance (systematic and statistical errors) in various cases. We find that,
stage IV dark energy surveys such as SKA and LSST are capable of reconstructing
the lensing power spectrum at and \ell\la 5000 accurately. This
lensing reconstruction only requires counting galaxies, and is therefore highly
complementary to the cosmic shear measurement by the same surveys.Comment: v1: 13 pages, 10 figures. v2: minor revisions. ApJ in pres
Large deviations in the reinforced random walk model on trees
In this paper, we consider the linearly reinforced and the once-reinforced
random walk models in the transient phase on trees. We show the large
deviations for the upper tails for both models. We also show the exponential
decay for the lower tail in the once-reinforced random walk model. On the other
hand, the lower tail is in polynomial decay for the linearly reinforced random
walk model.Comment: 20 page
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