339,963 research outputs found
Time evolution of Wigner function in laser process derived by entangled state representation
Evaluating the Wigner function of quantum states in the entangled state
representation is introduced, based on which we present a new approach for
deriving time evolution formula of Wigner function in laser process.
Application of this fomula to calculating time evolution of photon number is
also presented, as an example, the case when the initial state is photon-added
coherent state is discussed.Comment: 6 pages, revtex
High-dimensional classification using features annealed independence rules
Classification using high-dimensional features arises frequently in many
contemporary statistical studies such as tumor classification using microarray
or other high-throughput data. The impact of dimensionality on classifications
is poorly understood. In a seminal paper, Bickel and Levina [Bernoulli 10
(2004) 989--1010] show that the Fisher discriminant performs poorly due to
diverging spectra and they propose to use the independence rule to overcome the
problem. We first demonstrate that even for the independence classification
rule, classification using all the features can be as poor as the random
guessing due to noise accumulation in estimating population centroids in
high-dimensional feature space. In fact, we demonstrate further that almost all
linear discriminants can perform as poorly as the random guessing. Thus, it is
important to select a subset of important features for high-dimensional
classification, resulting in Features Annealed Independence Rules (FAIR). The
conditions under which all the important features can be selected by the
two-sample -statistic are established. The choice of the optimal number of
features, or equivalently, the threshold value of the test statistics are
proposed based on an upper bound of the classification error. Simulation
studies and real data analysis support our theoretical results and demonstrate
convincingly the advantage of our new classification procedure.Comment: Published in at http://dx.doi.org/10.1214/07-AOS504 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Entanglement and nonlocality of one- and two-mode combination squeezed state
We investigate the entanglement and nonlocality properties of one- and
two-mode combination squeezed vacuum state (OTCSS, with two-parameter lamda and
gamma) by analyzing the logarithmic negativity and the Bell's inequality. It is
found that this state exhibits larger entanglement than that of the usual
two-mode squeezed vacuum state (TSVS), and that in a certain regime of lamda,
the violation of Bell's inequality becomes more obvious, which indicates that
the nonlocality of OTCSS can be stronger than that of TSVS. As an application
of OTCSS, the quantum teleportaion is examined, which shows that there is a
region spanned by lamda and gamma in which the fidelity of OTCSS channel is
larger than that of TSVS.Comment: 15 pages, 7 figures, accepted by Optics communication
Adaptive robust variable selection
Heavy-tailed high-dimensional data are commonly encountered in various
scientific fields and pose great challenges to modern statistical analysis. A
natural procedure to address this problem is to use penalized quantile
regression with weighted -penalty, called weighted robust Lasso
(WR-Lasso), in which weights are introduced to ameliorate the bias problem
induced by the -penalty. In the ultra-high dimensional setting, where the
dimensionality can grow exponentially with the sample size, we investigate the
model selection oracle property and establish the asymptotic normality of the
WR-Lasso. We show that only mild conditions on the model error distribution are
needed. Our theoretical results also reveal that adaptive choice of the weight
vector is essential for the WR-Lasso to enjoy these nice asymptotic properties.
To make the WR-Lasso practically feasible, we propose a two-step procedure,
called adaptive robust Lasso (AR-Lasso), in which the weight vector in the
second step is constructed based on the -penalized quantile regression
estimate from the first step. This two-step procedure is justified
theoretically to possess the oracle property and the asymptotic normality.
Numerical studies demonstrate the favorable finite-sample performance of the
AR-Lasso.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1191 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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