78,211 research outputs found
Gravitational Lensing and Anisotropies of CBR on the Small Angular Scales
We investigate the effect of gravitational lensing, produced by linear
density perturbations, for anisotropies of the Cosmic Background Radiation
(CBR) on scales of arcminutes. In calculations, a flat universe ()
and the Harrison-Zel'dovich spectrum () are assumed. The numerical results
show that on scales of a few arcminutes, gravitational lensing produces only
negligible anisotropies in the temperature of the CBR. Our conclusion disagrees
with that of Cay\'{o}n {\it et al.} who argue that the amplification of on scales may even be larger than 100\%.Comment: Accepted by MNRAS. 16 pages, 2 figures, tarred, compressed and
uuencoded Postscript file
Independence Test for High Dimensional Random Vectors
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The asymptotic distributions of the test statistic under the null and local alternative hypotheses are established as dimensionality and the sample size of the data are comparable. We apply this test to examine multiple MA(1) and AR(1) models, panel data models with some spatial cross-sectional structures. In addition, in a flexible applied fashion, the proposed test can capture some dependent but uncorrelated structures, for example, nonlinear MA(1) models, multiple ARCH(1) models and vandermonde matrices. Simulation results are provided for detecting these dependent structures. An empirical study of dependence between closed stock prices of several companies from New York Stock Exchange (NYSE) demonstrates that the feature of cross-sectional dependence is popular in stock marketsIndependence test, cross-sectional dependence, empirical spectral distribution, characteristic function, Marcenko-Pastur Law
The Effects of Halo Assembly Bias on Self-Calibration in Galaxy Cluster Surveys
Self-calibration techniques for analyzing galaxy cluster counts utilize the
abundance and the clustering amplitude of dark matter halos. These properties
simultaneously constrain cosmological parameters and the cluster
observable-mass relation. It was recently discovered that the clustering
amplitude of halos depends not only on the halo mass, but also on various
secondary variables, such as the halo formation time and the concentration;
these dependences are collectively termed assembly bias. Applying modified
Fisher matrix formalism, we explore whether these secondary variables have a
significant impact on the study of dark energy properties using the
self-calibration technique in current (SDSS) and the near future (DES, SPT, and
LSST) cluster surveys. The impact of the secondary dependence is determined by
(1) the scatter in the observable-mass relation and (2) the correlation between
observable and secondary variables. We find that for optical surveys, the
secondary dependence does not significantly influence an SDSS-like survey;
however, it may affect a DES-like survey (given the high scatter currently
expected from optical clusters) and an LSST-like survey (even for low scatter
values and low correlations). For an SZ survey such as SPT, the impact of
secondary dependence is insignificant if the scatter is 20% or lower but can be
enhanced by the potential high scatter values introduced by a highly correlated
background. Accurate modeling of the assembly bias is necessary for cluster
self-calibration in the era of precision cosmology.Comment: 13 pages, 5 figures, replaced to match published versio
Generation of N-qubit W state with rf-SQUID qubits by adiabatic passage
A simple scheme is presented to generate n-qubit W state with
rf-superconducting quantum interference devices (rf-SQUIDs) in cavity QED
through adiabatic passage. Because of the achievable strong coupling for
rf-SQUID qubits embedded in cavity QED, we can get the desired state with high
success probability. Furthermore, the scheme is insensitive to position
inaccuracy of the rf-SQUIDs. The numerical simulation shows that, by using
present experimental techniques, we can achieve our scheme with very high
success probability, and the fidelity could be eventually unity with the help
of dissipation.Comment: to appear in Phys. Rev.
From Electrons to Finite Elements: A Concurrent Multiscale Approach for Metals
We present a multiscale modeling approach that concurrently couples quantum
mechanical, classical atomistic and continuum mechanics simulations in a
unified fashion for metals. This approach is particular useful for systems
where chemical interactions in a small region can affect the macroscopic
properties of a material. We discuss how the coupling across different scales
can be accomplished efficiently, and we apply the method to multiscale
simulations of an edge dislocation in aluminum in the absence and presence of H
impurities.Comment: 4 page
Probabilistic teleportation of unknown two-particle state via POVM
We propose a scheme for probabilistic teleportation of unknown two-particle
state with partly entangled four-particle state via POVM. In this scheme the
teleportation of unknown two-particle state can be realized with certain
probability by performing two Bell state measurements, a proper POVM and a
unitary transformation.Comment: 5 pages, no figur
SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
In this paper, we introduce a new class of nonsmooth convex functions called
SOS-convex semialgebraic functions extending the recently proposed notion of
SOS-convex polynomials. This class of nonsmooth convex functions covers many
common nonsmooth functions arising in the applications such as the Euclidean
norm, the maximum eigenvalue function and the least squares functions with
-regularization or elastic net regularization used in statistics and
compressed sensing. We show that, under commonly used strict feasibility
conditions, the optimal value and an optimal solution of SOS-convex
semi-algebraic programs can be found by solving a single semi-definite
programming problem (SDP). We achieve the results by using tools from
semi-algebraic geometry, convex-concave minimax theorem and a recently
established Jensen inequality type result for SOS-convex polynomials. As an
application, we outline how the derived results can be applied to show that
robust SOS-convex optimization problems under restricted spectrahedron data
uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP
relaxation result for restricted ellipsoidal data uncertainty and answers the
open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a
robust solution from the semi-definite programming relaxation in this broader
setting
An Agent-based Modelling Framework for Driving Policy Learning in Connected and Autonomous Vehicles
Due to the complexity of the natural world, a programmer cannot foresee all
possible situations, a connected and autonomous vehicle (CAV) will face during
its operation, and hence, CAVs will need to learn to make decisions
autonomously. Due to the sensing of its surroundings and information exchanged
with other vehicles and road infrastructure, a CAV will have access to large
amounts of useful data. While different control algorithms have been proposed
for CAVs, the benefits brought about by connectedness of autonomous vehicles to
other vehicles and to the infrastructure, and its implications on policy
learning has not been investigated in literature. This paper investigates a
data driven driving policy learning framework through an agent-based modelling
approaches. The contributions of the paper are two-fold. A dynamic programming
framework is proposed for in-vehicle policy learning with and without
connectivity to neighboring vehicles. The simulation results indicate that
while a CAV can learn to make autonomous decisions, vehicle-to-vehicle (V2V)
communication of information improves this capability. Furthermore, to overcome
the limitations of sensing in a CAV, the paper proposes a novel concept for
infrastructure-led policy learning and communication with autonomous vehicles.
In infrastructure-led policy learning, road-side infrastructure senses and
captures successful vehicle maneuvers and learns an optimal policy from those
temporal sequences, and when a vehicle approaches the road-side unit, the
policy is communicated to the CAV. Deep-imitation learning methodology is
proposed to develop such an infrastructure-led policy learning framework
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