160,735 research outputs found
Some recent developments in quantization of fractal measures
We give an overview on the quantization problem for fractal measures,
including some related results and methods which have been developed in the
last decades. Based on the work of Graf and Luschgy, we propose a three-step
procedure to estimate the quantization errors. We survey some recent progress,
which makes use of this procedure, including the quantization for self-affine
measures, Markov-type measures on graph-directed fractals, and product measures
on multiscale Moran sets. Several open problems are mentioned.Comment: 13 page
Accelerating universe from gravitational leakage into extra dimensions: confrontation with SNeIa
There is mounting observational evidence that the expansion of our universe
is undergoing an acceleration. A dark energy component has usually been invoked
as the most feasible mechanism for the acceleration. However, it is desirable
to explore alternative possibilities motivated by particle physics before
adopting such an untested entity. In this work, we focus our attention on an
acceleration mechanism: one arising from gravitational leakage into extra
dimensions. We confront this scenario with high- type Ia supernovae compiled
by Tonry et al. (2003) and recent measurements of the X-ray gas mass fractions
in clusters of galaxies published by Allen et al. (2002,2003). A combination of
the two databases gives at a 99% confidence level that
, , and
, indicating a closed universe. We then
constrain the model using the test of the turnaround redshift, , at
which the universe switches from deceleration to acceleration. We show that, in
order to explain that acceleration happened earlier than within
the framework of gravitational leakage into extra dimensions, a low matter
density, , or a closed universe is necessary.Comment: 16 pages, 4 figures, accepted for publication in Ap
Thermal Entanglement between Alternate Qubits of a Four-qubit Heisenberg XX Chain in a Magnetic Field
The concurrence of two alternate qubits in a four-qubit Heisenberg XX chain
is investigated when a uniform magnetic field B is included. It is found that
there is no thermal entanglement between alternate qubits if B is close to
zero. Magnetic field can induce entanglement in a certain range both for the
antiferromagnetic and ferromagnetic cases. Near zero temperature, the
entanglement undergoes two sudden changes with increasing value of the magnetic
field B. This is due to the changes in the ground state. This novel property
may be used as quantum entanglement switch. The anisotropy in the system can
also induce the entanglement between two alternate qubits.Comment: 10 pages, 3 figure
Resampling methods for spatial regression models under a class of stochastic designs
In this paper we consider the problem of bootstrapping a class of spatial
regression models when the sampling sites are generated by a (possibly
nonuniform) stochastic design and are irregularly spaced. It is shown that the
natural extension of the existing block bootstrap methods for grid spatial data
does not work for irregularly spaced spatial data under nonuniform stochastic
designs. A variant of the blocking mechanism is proposed. It is shown that the
proposed block bootstrap method provides a valid approximation to the
distribution of a class of M-estimators of the spatial regression parameters.
Finite sample properties of the method are investigated through a moderately
large simulation study and a real data example is given to illustrate the
methodology.Comment: Published at http://dx.doi.org/10.1214/009053606000000551 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Cooperative Localization under Limited Connectivity
We report two decentralized multi-agent cooperative localization algorithms
in which, to reduce the communication cost, inter-agent state estimate
correlations are not maintained but accounted for implicitly. In our first
algorithm, to guarantee filter consistency, we account for unknown inter-agent
correlations via an upper bound on the joint covariance matrix of the agents.
In the second method, we use an optimization framework to estimate the unknown
inter-agent cross-covariance matrix. In our algorithms, each agent localizes
itself in a global coordinate frame using a local filter driven by local dead
reckoning and occasional absolute measurement updates, and opportunistically
corrects its pose estimate whenever it can obtain relative measurements with
respect to other mobile agents. To process any relative measurement, only the
agent taken the measurement and the agent the measurement is taken from need to
communicate with each other. Consequently, our algorithms are decentralized
algorithms that do not impose restrictive network-wide connectivity condition.
Moreover, we make no assumptions about the type of agents or relative
measurements. We demonstrate our algorithms in simulation and a
robotic~experiment.Comment: 9 pages, 5 figure
- …