9,533 research outputs found
Robust Tracking of Multiple People Using Two Widely Separated Cameras
A thesis submitted for the degree of Doctor of Philosophy of the University of Londo
Modeling the Anisotropic Two-Point Galaxy Correlation Function on Small Scales and Improved Measurements of H(z), D_A(z), and f(z)sigma_8(z) from the Sloan Digital Sky Survey DR7 Luminous Red Galaxies
We present a simple and efficient phenomenological model for the
two-dimensional two-point galaxy correlation function that works well over a
wide range of scales, from large scales down to scales as small as 25Mpc/h. Our
model incorporates nonlinear effects, a scale-dependent galaxy bias on small
scales, and allows the redshift-space distortions to be scale and direction
dependent. We validate our model using LasDamas mock catalogs, and apply it to
the Sloan Digital Sky Survey (SDSS) DR7 Luminous Red Galaxies (LRGs). Using
only the monopole and quadrupole of the correlation function measured from the
SDSS DR7 LRGs, we obtain improved measurements H(z)r_s(z_d)/c=0.0433\pm 0.0042,
D_A(z)/r_s(z_d)=6.59\pm 0.46, and f(z)sigma_8(z)=0.429\pm 0.089 at z=0.35,
using the scale range of 25<s<120Mpc/h. We expect our results and model to be
useful in tightening dark energy and gravity constraints from the full analysis
of current and future galaxy clustering data.Comment: 9 pages, 5 figures, accepted by MNRAS, the last version matches
accepted one. arXiv admin note: substantial text overlap with
arXiv:1205.5573, arXiv:1102.225
Using Multipoles of the Correlation Function to Measure H(z), D_A(z), and \beta(z) from Sloan Digital Sky Survey Luminous Red Galaxies
Galaxy clustering data can be used to measure the cosmic expansion history
H(z), the angular-diameter distance D_A(z), and the linear redshift-space
distortion parameter beta(z). Here we present a method for using effective
multipoles of the galaxy two-point correlation function (\xi_0(s), \xi_2(s),
\xi}_4(s), and \xi_6(s), with s denoting the comoving separation) to measure
H(z), D_A(z)$, and beta(z), and validate it using LasDamas mock galaxy
catalogs. Our definition of effective multipoles explicitly incorporates the
discreteness of measurements, and treats the measured correlation function and
its theoretical model on the same footing. We find that for the mock data,
\xi_0+\xi_2+\xi_4 captures nearly all the information, and gives significantly
stronger constraints on H(z), D_A(z), and beta(z), compared to using only
\xi_0+\xi_2.
We apply our method to the sample of luminous red galaxies (LRGs) from the
Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) without assuming a dark
energy model or a flat Universe. We find that \xi}_4(s) deviates on scales of
s<60Mpc/h from the measurement from mock data (in contrast to \xi_0(s),
\xi_2(s), and \xi_6(s)), thus we only use \xi_0+\xi_2 for our fiducial
constraints. We obtain {H(0.35), D_A(0.35), Omega_mh^2, beta(z)} =
{79.6_{-8.7}^{+8.3} km/s/Mpc, 1057_{-87}^{+88}Mpc, 0.103\pm0.015, 0.44\pm0.15}
using \xi_0+\xi_2. We find that H(0.35)r_s(z_d)/c and D_A(0.35)/r_s(z_d) (where
r_s(z_d) is the sound horizon at the drag epoch) are more tightly constrained:
{H(0.35)r_s(z_d)/c, D_A(0.35)/r_s(z_d)} = {0.0437_{-0.0043}^{+0.0041},
6.48_{-0.43}^{+0.44}\} using \xi_0+\xi_2.Comment: 12 pages, 11 figures. arXiv admin note: substantial text overlap with
arXiv:1102.225
Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman
In Comm. Math. Physics 118 (1988), 651-701, A. Beilinson and V. Schechtman
define on the total space of a smooth family of curves a so-called trace
complex associated to a vector bundle, the 0-th relative cohomology of which is
the Atiyah algebra of the determinant bundle. Their proof reduces the general
case to the acyclic one. In particular, one needs a comparison of the image of
the trace complex for a bundle, and its twist by an \'etale multisection. We
analyse this and correct a point in the original proof.Comment: 6 pages, Latex 2
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