1,368 research outputs found
A Model for Multi-property Galaxy Cluster Statistics
The massive dark matter halos that host groups and clusters of galaxies have
observable properties that appear to be log-normally distributed about
power-law mean scaling relations in halo mass. Coupling this assumption with
either quadratic or cubic approximations to the mass function in log space, we
derive closed-form expressions for the space density of halos as a function of
multiple observables as well as forms for the low-order moments of properties
of observable-selected samples. Using a Tinker mass function in a {\Lambda}CDM
cosmology, we show that the cubic analytic model reproduces results obtained
from direct, numerical convolution at the 10 percent level or better over
nearly the full range of observables covered by current observations and for
redshifts extending to z = 1.5. The model provides an efficient framework for
estimating effects arising from selection and covariance among observable
properties in survey samples.Comment: 9 pages, 4 figures, uses on-line mass function calculator
http://hmf.icrar.org/. Submitted to MNRA
Cosmology from supernova magnification maps
High-z Type Ia supernovae are expected to be gravitationally lensed by the
foreground distribution of large-scale structure. The resulting magnification
of supernovae is statistically measurable, and the angular correlation of the
magnification pattern directly probes the integrated mass density along the
line of sight. Measurements of cosmic magnification of supernovae therefore
complements galaxy shear measurements in providing a direct measure of
clustering of the dark matter. As the number of supernovae is typically much
smaller than the number of sheared galaxies, the two-point correlation function
of lensed Type Ia supernovae suffers from significantly increased shot noise.
Neverthless, we find that the magnification map of a large sample of
supernovae, such as that expected from next generation dedicated searches, will
be easily measurable and provide an important cosmological tool. For example, a
search over 20 sq. deg. over five years leading to a sample of ~ 10,000
supernovae would measure the angular power spectrum of cosmic magnification
with a cumulative signal-to-noise ratio of ~20. This detection can be further
improved once the supernova distance measurements are cross-correlated with
measurements of the foreground galaxy distribution. The magnification maps made
using supernovae can be used for important cross-checks with traditional
lensing shear statistics obtained in the same fields, as well as help to
control systematics. We discuss two applications of supernova magnification
maps: the breaking of the mass-sheet degeneracy when estimating masses of
shear-detected clusters, and constraining the second-order corrections to weak
lensing observables.Comment: 4 pages, 2 figures, ApJL submitted; "Signal" discussed here is the
extra covariance in astro-ph/050958
Problems with Pencils: Lensing Covariance of Supernova Distance Measurements
While luminosity distances from Type Ia supernovae (SNe) provide a powerful
probe of cosmological parameters, the accuracy with which these distances can
be measured is limited by cosmic magnification due to gravitational lensing by
the intervening large-scale structure. Spatial clustering of foreground mass
fluctuations leads to correlated errors in distance estimates from SNe. By
including the full covariance matrix of supernova distance measurements, we
show that a future survey covering more than a few square degrees on the sky,
and assuming a total of ~2000 SNe, will be largely unaffected by covariance
noise. ``Pencil beam'' surveys with small fields of view, however, will be
prone to the lensing covariance, leading to potentially significant
degradations in cosmological parameter estimates. For a survey with 30 arcmin
mean separation between SNe, lensing covariance leads to a ~45% increase in the
expected errors in dark energy parameters compared to fully neglecting lensing,
and a ~20% increase compared to including just the lensing variance. Given that
the lensing covariance is cosmology dependent and cannot be mapped out
sufficiently accurately with direct weak lensing observations, surveys with
small mean SN separation must incorporate the effects of lensing covariance,
including its dependence on the cosmological parameters.Comment: 4 pages, 2 figures, PRL submitted; "Noise" discussed here is the
"signal" in astro-ph/050957
Gravitational Lensing as a Probe of Quintessence
A large number of cosmological studies now suggest that roughly two-thirds of
the critical energy density of the Universe exists in a component with negative
pressure. If the equation of state of such an energy component varies with
time, it should in principle be possible to identify such a variation using
cosmological probes over a wide range in redshift. Proper detection of any time
variation, however, requires cosmological probes beyond the currently studied
range in redshift of 0.1 to 1. We extend our analysis to gravitational
lensing statistics at high redshift and suggest that a reliable sample of
lensed sources, out to a redshift of 5, can be used to constrain the
variation of the equation of state, provided that both the redshift
distribution of lensed sources and the selection function involved with the
lensed source discovery process are known. An exciting opportunity to catalog
an adequate sample of lensed sources (quasars) to probe quintessence is now
available with the ongoing Sloan Digital Sky Survey. Writing , we study the expected accuracy to which the equation of state
today and its rate of change can simultaneously be
constrained. Such a determination can rule out some missing-energy candidates,
such as classes of quintessence models or a cosmological constant.Comment: Accepted for publication in ApJ Letters (4 pages, including 4
figures
Fast approximation of centrality and distances in hyperbolic graphs
We show that the eccentricities (and thus the centrality indices) of all
vertices of a -hyperbolic graph can be computed in linear
time with an additive one-sided error of at most , i.e., after a
linear time preprocessing, for every vertex of one can compute in
time an estimate of its eccentricity such that
for a small constant . We
prove that every -hyperbolic graph has a shortest path tree,
constructible in linear time, such that for every vertex of ,
. These results are based on an
interesting monotonicity property of the eccentricity function of hyperbolic
graphs: the closer a vertex is to the center of , the smaller its
eccentricity is. We also show that the distance matrix of with an additive
one-sided error of at most can be computed in
time, where is a small constant. Recent empirical studies show that
many real-world graphs (including Internet application networks, web networks,
collaboration networks, social networks, biological networks, and others) have
small hyperbolicity. So, we analyze the performance of our algorithms for
approximating centrality and distance matrix on a number of real-world
networks. Our experimental results show that the obtained estimates are even
better than the theoretical bounds.Comment: arXiv admin note: text overlap with arXiv:1506.01799 by other author
Localised projective measurement of a relativistic quantum field in non-inertial frames
We propose a scheme to study the effect of motion on measurements of a
quantum field carried out by a finite-size detector. We introduce a model of
projective detection of a localised field mode in an arbitrary reference frame.
We apply it to extract vacuum entanglement by a pair of counter-accelerating
detectors and to estimate the Unruh temperature of a single accelerated
detector. The introduced method allows us to directly relate the observed
effects with the instantaneous proper acceleration of the detector.Comment: 5 pages, 2 figures. v2 Significant increase in the detail level
regarding the motivation of the detector mode
Application of a D Number based LBWA Model and an Interval MABAC Model in Selection of an Automatic Cannon for Integration into Combat Vehicles
A decision making procedure for selection of a weapon system involves different, often contradictory criteriaand reaching decisions under conditions of uncertainty. This paper proposes a novel multi-criteria methodology based on D numbers which enables efficient analysis of the information used for decision making. The proposed methodology has been developed in order to enable selection of an efficient weapon system under conditions when a large number of hierarchically structured evaluation criteria has to be processed. A novel D number based Level Based Weight Assessment – Multi Attributive Border Approximation area Comparison (D LBWA-MABAC) model is used for selection of an automatic cannon for integration into combat vehicles. Criteria weights are determined based on the improved LBWA-D model. The traditional MABAC method has been further developed by integration of interval numbers. A hybrid D LBWA-MABAC framework is used for evaluation of an automatic cannon for integration into combat vehicles. Nine weapon systems used worldwide have been ranked in this paper. This multicriteria approach allows decision makers to assess options objectively and reach a rational decision regarding the selection of an optimal weapon system. Validation of the proposed methodology is performed through sensitivity analysis which studies how changes in the weights of the best criterion and the elasticity coefficient affect the ranking results
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