31,614 research outputs found
Determining Gravitational Masses of Galaxy Clusters With (1)Virial Equilibrium And (2)Arc-like Images
The mass derived from gravitational lensing reflects the total mass contained
in the lensing system, independent of the specific matter contents and states.
A comparison of the dynamical masses from hydrostatic equilibrium with the
gravitational masses from arc-like images of background galaxies is made for
four clusters of galaxies at intermediate redshits. It is found that virial
analysis has underestimated the total cluster masses (from lensing) by a factor
of within a radius of Mpc around the cluster
centers, indicating that clusters of galaxies might not be regarded as the well
relaxed virialized systems. The increase of the total cluster masses obtained
from lensing leads to the decrease of the baryon fractions of clusters of
galaxies, which provides a crue for solving the `` disprepancy
puzzle" in cosmology.Comment: 11 pages plus 1 Table. LATEX style, submitted to ApJ, BAO-BGGC-940
Gravitational Microlensing by the MACHOs of the LMC
The expected microlensing events of the LMC by the MACHOs of the LMC itself
are calculated and compared with analogue events by objects in the Galactic
halo. The LMC matter distribution is modelled by a spherical halo and an
exponential disk while a face-on exponential disk is used for the stellar
distribution of the LMC. Among the microlensing events discovered by the MACHOs
and EROS projects, a fraction of could be caused by the lenses near the
center of the LMC or from lenses at from the LMC center.
Therefore, any statistical study of these microlensing events must take the LMC
lenses into account.Comment: 12 pages, 6 figures (not included) by fax, ApJ submitted, DAEC-OPM-9
Optimal Design of Multiple Description Lattice Vector Quantizers
In the design of multiple description lattice vector quantizers (MDLVQ),
index assignment plays a critical role. In addition, one also needs to choose
the Voronoi cell size of the central lattice v, the sublattice index N, and the
number of side descriptions K to minimize the expected MDLVQ distortion, given
the total entropy rate of all side descriptions Rt and description loss
probability p. In this paper we propose a linear-time MDLVQ index assignment
algorithm for any K >= 2 balanced descriptions in any dimensions, based on a
new construction of so-called K-fraction lattice. The algorithm is greedy in
nature but is proven to be asymptotically (N -> infinity) optimal for any K >=
2 balanced descriptions in any dimensions, given Rt and p. The result is
stronger when K = 2: the optimality holds for finite N as well, under some mild
conditions. For K > 2, a local adjustment algorithm is developed to augment the
greedy index assignment, and conjectured to be optimal for finite N.
Our algorithmic study also leads to better understanding of v, N and K in
optimal MDLVQ design. For K = 2 we derive, for the first time, a
non-asymptotical closed form expression of the expected distortion of optimal
MDLVQ in p, Rt, N. For K > 2, we tighten the current asymptotic formula of the
expected distortion, relating the optimal values of N and K to p and Rt more
precisely.Comment: Submitted to IEEE Trans. on Information Theory, Sep 2006 (30 pages, 7
figures
- …