73 research outputs found
Improving reconstruction of the baryon acoustic peak : the effect of local environment
Precise measurements of the baryon acoustic oscillation (BAO) scale as a
standard ruler in the clustering pattern of large-scale structure is a central
goal of current and future galaxy surveys. The BAO peak may be sharpened using
the technique of density-field reconstruction, in which the bulk displacements
of galaxies are estimated using a Zel'dovitch approximation. We use numerical
simulations to demonstrate how the accuracy of this approximation depends
strongly on local environment, and how this information may be used to
construct an improved BAO measurement through environmental re-weighting and
using higher-order perturbation theory. We outline further applications of the
displacement field for testing cosmological models.Comment: 13 pages, 14 figure
Excursion Set Halo Mass Function and Bias in a Stochastic Barrier Model of Ellipsoidal Collapse
We use the Excursion Set formalism to compute the properties of the halo mass
distribution for a stochastic barrier model which encapsulates the main
features of the ellipsoidal collapse of dark matter halos. Non-markovian
corrections due to the sharp filtering of the linear density field in real
space are computed with the path-integral technique introduced by Maggiore &
Riotto (2010). Here, we provide a detailed derivation of the results presented
in Corasaniti & Achitouv (2011) and extend the mass function analysis to higher
redshift. We also derive an analytical expression for the linear halo bias. We
find the analytically derived mass function to be in remarkable agreement with
N-body simulation data from Tinker et al. (2008) with differences smaller than
~5% over the range of mass probed by the simulations. The excursion set
solution from Monte Carlo generated random walks shows the same level of
agreement, thus confirming the validity of the path-integral approach for the
barrier model considered here. Similarly the analysis of the linear halo bias
shows deviations no greater than 20%. Overall these results indicate that the
Excursion Set formalism in combination with a realistic modeling of the
conditions of halo collapse can provide an accurate description of the halo
mass distribution.Comment: 16 pages, 9 figures; companion paper published in PRL 106 (2011)
241302. To appear on PR
Self-consistency of the Excursion Set Approach
The excursion set approach provides a framework for predicting how the
abundance of dark matter halos depends on the initial conditions. A key
ingredient of this formalism comes from the physics of halo formation: the
specification of a critical overdensity threshold (barrier) which protohalos
must exceed if they are to form bound virialized halos at a later time. Another
ingredient is statistical, as it requires the specification of the appropriate
statistical ensemble over which to average when making predictions. The
excursion set approach explicitly averages over all initial positions, thus
implicitly assuming that the appropriate ensemble is that associated with
randomly chosen positions in space, rather than special positions such as peaks
of the initial density field. Since halos are known to collapse around special
positions, it is not clear that the physical and statistical assumptions which
underlie the excursion set approach are self-consistent. We argue that they are
at least for low mass halos, and illustrate by comparing our excursion set
predictions with numerical data from the DEUS simulations.Comment: 5 pages, 2 figure
Computation of the Halo Mass Function Using Physical Collapse Parameters: Application to Non-Standard Cosmologies
In this article we compare the halo mass function predicted by the excursion
set theory with a drifting diffusive barrier against the results of N-body
simulations for several cosmological models. This includes the standard LCDM
case for a large range of halo masses, models with different types of
primordial non-Gaussianity, and the Ratra-Peebles quintessence model of Dark
Energy. We show that in all those cosmological scenarios, the abundance of dark
matter halos can be described by a drifting diffusive barrier, where the two
parameters describing the barrier have physical content. In the case of the
Gaussian LCDM, the statistics are precise enough to actually predict those
parameters at different redshifts from the initial conditions. Furthermore, we
found that the stochasticity in the barrier is nonnegligible making the simple
deterministic spherical collapse model a bad approximation even at very high
halo masses. We also show that using the standard excursion set approach with a
barrier inspired by peak patches leads to inconsistent predictions of the halo
mass function.Comment: 25 pages, 12 figure
Testing spherical evolution for modelling void abundances
We compare analytical predictions of void volume functions to those measured from N-body simulations, detecting voids with the zobov void finder. We push to very small, non-linear voids, below few Mpc radius, by considering the unsampled dark matter density field. We also study the case where voids are identified using haloes. We develop analytical formula for the void abundance of both the excursion set approach and the peaks formalism. These formulas are valid for random walks smoothed with a top-hat filter in real space, with a large class of realistic barrier models. We test the extent to which the spherical evolution approximation, which forms the basis of the analytical predictions, models the highly aspherical voids that occur in the cosmic web, and are found by a watershed-based algorithm such as zobov. We show that the volume function returned by zobov is quite sensitive to the choice of treatment of subvoids, a fact that has not been appreciated previously. For reasonable choices of subvoid exclusion, we find that the Lagrangian density δv of the zobov voids - which is predicted to be a constant δv≈−2.7 in the spherical evolution model - is different from the predicted value, showing substantial scatter and scale dependence. This result applies to voids identified at z=0 with effective radius between 1 and 10 h−1 Mpc. Our analytical approximations are flexible enough to give a good description of the resulting volume function; however, this happens for choices of parameter values that are different from those suggested by the spherical evolution assumption. We conclude that analytical models for voids must move away from the spherical approximation in order to be applied successfully to observations, and we discuss some possible ways forwar
Natural Language Processing for Financial Regulation
This article provides an understanding of Natural Language Processing
techniques in the framework of financial regulation, more specifically in order
to perform semantic matching search between rules and policy when no dataset is
available for supervised learning. We outline how to outperform simple
pre-trained sentences-transformer models using freely available resources and
explain the mathematical concepts behind the key building blocks of Natural
Language Processing.Comment: 20 pages, 3 figure
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