39,057 research outputs found
On Recovering the Nonlinear Bias Function from Counts in Cells Measurements
We present a simple and accurate method to constrain galaxy bias based on the
distribution of counts in cells. The most unique feature of our technique is
that it is applicable to non-linear scales, where both dark matter statistics
and the nature of galaxy bias are fairly complex. First, we estimate the
underlying continuous distribution function from precise counts-in-cells
measurements assuming local Poisson sampling. Then a robust, non-parametric
inversion of the bias function is recovered from the comparison of the
cumulative distributions in simulated dark matter and galaxy catalogs.
Obtaining continuous statistics from the discrete counts is the most delicate
novel part of our recipe. It corresponds to a deconvolution of a (Poisson)
kernel. For this we present two alternatives: a model independent algorithm
based on Richardson-Lucy iteration, and a solution using a parametric skewed
lognormal model. We find that the latter is an excellent approximation for the
dark matter distribution, but the model independent iterative procedure is more
suitable for galaxies. Tests based on high resolution dark matter simulations
and corresponding mock galaxy catalogs show that we can reconstruct the
non-linear bias function down to highly non-linear scales with high precision
in the range of . As far as the stochasticity of the bias,
we have found a remarkably simple and accurate formula based on Poisson noise,
which provides an excellent approximation for the scatter around the mean
non-linear bias function. In addition we have found that redshift distortions
have a negligible effect on our bias reconstruction, therefore our recipe can
be safely applied to redshift surveys.Comment: 32 pages, 18 figures; submitted to Ap
Magnification relations of quad lenses and applications on Einstein crosses
In this work, we mainly study the magnification relations of quad lens models
for cusp, fold and cross configurations. By dividing and ray-tracing in
different image regions, we numerically derive the positions and magnifications
of the four images for a point source lying inside of the astroid caustic.
Then, based on the magnifications, we calculate the signed cusp and fold
relations for the singular isothermal elliptical lenses. The signed fold
relation map has positive and negative regions, and the positive region is
usually larger than the negative region as has been confirmed before. It can
also explain that for many observed fold image pairs, the fluxes of the Fermat
minimum images are apt to be larger than those of the saddle images. We define
a new quantity cross relation which describes the magnification discrepancy
between two minimum images and two saddle images. Distance ratio is also
defined as the ratio of the distance of two saddle images to that of two
minimum images. We calculate the cross relations and distance ratios for nine
observed Einstein crosses. In theory, for most of the quad lens models, the
cross relations decrease as the distance ratios increase. In observation, the
cross relations of the nine samples do not agree with the quad lens models very
well, nevertheless, the cross relations of the nine samples do not give obvious
evidence for anomalous flux ratio as the cusp and fold types do. Then, we
discuss several reasons for the disagreement, and expect good consistencies for
more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA
Suppression of low-energy Andreev states by a supercurrent in YBa_2Cu_3O_7-delta
We report a coherence-length scale phenomenon related to how the high-Tc
order parameter (OP) evolves under a directly-applied supercurrent. Scanning
tunneling spectroscopy was performed on current-carrying YBa_2Cu_3O_7-delta
thin-film strips at 4.2K. At current levels well below the theoretical
depairing limit, the low-energy Andreev states are suppressed by the
supercurrent, while the gap-like structures remain unchanged. We rule out the
likelihood of various extrinsic effects, and propose instead a model based on
phase fluctuations in the d-wave BTK formalism to explain the suppression. Our
results suggest that a supercurrent could weaken the local phase coherence
while preserving the pairing amplitude. Other possible scenarios which may
cause the observed phenomenon are also discussed.Comment: 6 pages, 4 figures, to appear in Physical Review
Characteristics of Magnetoplasmas Semiannual Status Report No. 12, May 1 - Oct. 31, 1965
Magnetoplasma characteristics - anomalous diffusion across magnetic field, heat conduction in plasma, cesium plasma generator, and electron velocity distribution function in magnetoplasma
A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)
A new simple Young diagrammatic method for Kronecker products of O(n) and
Sp(2m) is proposed based on representation theory of Brauer algebras. A general
procedure for the decomposition of tensor products of representations for O(n)
and Sp(2m) is outlined, which is similar to that for U(n) known as the
Littlewood rules together with trace contractions from a Brauer algebra and
some modification rules given by King.Comment: Latex, 11 pages, no figure
Current Path Properties of the Transport Anisotropy at Filling Factor 9/2
To establish the presence and orientation of the proposed striped phase in
ultra-high mobility 2D electron systems at filling factor 9/2, current path
transport properties are determined by varying the separation and allignment of
current and voltage contacts. Contacts alligned orthogonal to the proposed
intrinsic striped phase produce voltages consistent with current spreading
along the stripes; current driven along the proposed stripe direction results
in voltages consistent with channeling along the stripes. Direct comparison is
made to current spreading/channeling properties of artificially induced 1D
charge modulated systems, which indicates the 9/2 direction.Comment: 10 pages, 4 figure
Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm
The primal-dual optimization algorithm developed in Chambolle and Pock (CP),
2011 is applied to various convex optimization problems of interest in computed
tomography (CT) image reconstruction. This algorithm allows for rapid
prototyping of optimization problems for the purpose of designing iterative
image reconstruction algorithms for CT. The primal-dual algorithm is briefly
summarized in the article, and its potential for prototyping is demonstrated by
explicitly deriving CP algorithm instances for many optimization problems
relevant to CT. An example application modeling breast CT with low-intensity
X-ray illumination is presented.Comment: Resubmitted to Physics in Medicine and Biology. Text has been
modified according to referee comments, and typos in the equations have been
correcte
Cosmological Three-Point Function: Testing The Halo Model Against Simulations
We perform detailed comparison of the semi-analytic halo model predictions
with measurements in numerical simulations of the two and three point
correlation functions (3PCF), as well as power spectrum and bispectrum. We
discuss the accuracy and self-consistency of the halo model description of
gravitational clustering in the non-linear regime and constrain halo model
parameters. We exploit the recently proposed multipole expansion of three point
statistics that expresses rotation invariance in the most natural way. This not
only offers technical advantages by reducing the integrals required for the
halo model predictions, but amounts to a convenient way of compressing the
information contained in the 3PCF. We find that, with an appropriate choice of
the halo boundary and mass function cut-off, halo model predictions are in good
agreement with the bispectrum measured in numerical simulations. However, the
halo model predicts less than the observed configuration dependence of the 3PCF
on ~ Mpc scales. This effect is mainly due to quadrupole moment deficit,
possibly related to the assumption of spherical halo geometry. Our analysis
shows that using its harmonic decomposition, the full configuration dependence
of the 3PCF in the non-linear regime can be compressed into just a few numbers,
the lowest multipoles. Moreover, these multipoles are closely related to the
highest signal to noise eigenmodes of the 3PCF. Therefore this estimator may
simplify future analyses aimed at constraining cosmological and halo model
parameters from observational data.Comment: Minor corrections. Accepted for publication by Ap
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