28,496 research outputs found
Generation of maximally entangled mixed states of two atoms via on-resonance asymmetric atom-cavity couplings
A scheme for generating the maximally entangled mixed state of two atoms
on-resonance asymmetrically coupled to a single mode optical cavity field is
presented. The part frontier of both maximally entangled mixed states and
maximal Bell violating mixed states can be approximately reached by the
evolving reduced density matrix of two atoms if the ratio of coupling strengths
of two atoms is appropriately controlled. It is also shown that exchange
symmetry of global maximal concurrence is broken if and only if coupling
strength ratio lies between and for the case of
one-particle excitation and asymmetric coupling, while this partial
symmetry-breaking can not be verified by detecting maximal Bell violation.Comment: 5 pages, 5 figure
Squeezing induced transition of long-time decay rate
We investigate the nonclassicality of several kinds of nonclassical optical
fields such as the pure or mixed single photon-added coherent states and the
cat states in the photon-loss or the dephasing channels by exploring the
entanglement potential as the measure. It is shown that the long-time decay of
entanglement potentials of these states in photon loss channel is dependent of
their initial quadrature squeezing properties. In the case of photon-loss,
transition of long-time decay rate emerges at the boundary between the
squeezing and non-squeezing initial non-gaussian states if log-negativity is
adopted as the measure of entanglement potential. However, the transition
behavior disappears if the concurrence is adopted as the measure of
entanglement potential. For the case of the dephasing, distinct decay behaviors
of the nonclassicality are also revealed.Comment: 7 pages, 7 figures, RevTex
Competition of different evaluation schemes in the continuous variable game
An asymmetric generalization of classical Cournot's duopoly game was
introduced and the simulation scheme of its quantized version was analyzed. In
this scheme, the player assigned by a 'classical' measurement scheme always
wins the player assigned by a quantum measurement scheme. It was shown that the
fluctuation causes the disadvantage game rule of the 'quantum' player.Comment: 5 pages, 4 figures, RevTex4, some references are adde
High-Dimensional Bayesian Inference in Nonparametric Additive Models
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric
additive models in which the number of additive components may be larger than
the sample size, though ideally the true model is believed to include only a
small number of components. Bayesian approaches can conduct stochastic model
search and fulfill flexible parameter estimation by stochastic draws. The
theory shows that the proposed model selection method has satisfactory
properties. For instance, when the hyperparameter associated with the model
prior is correctly specified, the true model has posterior probability
approaching one as the sample size goes to infinity; when this hyperparameter
is incorrectly specified, the selected model is still acceptable since
asymptotically it is proved to be nested in the true model. To enhance model
flexibility, two new -priors are proposed and their theoretical performance
is examined. We also propose an efficient MCMC algorithm to handle the
computational issues. Several simulation examples are provided to demonstrate
the computational advantages of our method
Bayesian Ultrahigh-Dimensional Screening Via MCMC
We explore the theoretical and numerical property of a fully Bayesian model
selection method in sparse ultrahigh-dimensional settings, i.e., ,
where is the number of covariates and is the sample size. Our method
consists of (1) a hierarchical Bayesian model with a novel prior placed over
the model space which includes a hyperparameter controlling the model
size, and (2) an efficient MCMC algorithm for automatic and stochastic search
of the models. Our theory shows that, when specifying correctly, the
proposed method yields selection consistency, i.e., the posterior probability
of the true model asymptotically approaches one; when is misspecified,
the selected model is still asymptotically nested in the true model. The theory
also reveals insensitivity of the selection result with respect to the choice
of . In implementations, a reasonable prior is further assumed on
which allows us to draw its samples stochastically. Our approach conducts
selection, estimation and even inference in a unified framework. No additional
prescreening or dimension reduction step is needed. Two novel -priors are
proposed to make our approach more flexible. A simulation study is given to
display the numerical advantage of our method
Quasi-periodic solutions for differential equations with an elliptic-type degenerate equilibrium point under small perturbations
This work focuses on the existence of quasi-periodic solutions for ordinary
and delay differential equations (ODEs and DDEs for short) with an
elliptic-type degenerate equilibrium point under quasi-periodic perturbations.
We prove that under appropriate hypotheses there exist quasi-periodic solutions
for perturbed ODEs and DDEs near the equilibrium point for most parameter
values, then apply these results to the delayed van der Pol's oscillator with
zero-Hopf singularity.Comment: 32page
Order-2 Asymptotic Optimality of the Fully Distributed Sequential Hypothesis Test
This work analyzes the asymptotic performances of fully distributed
sequential hypothesis testing procedures as the type-I and type-II error rates
approach zero, in the context of a sensor network without a fusion center. In
particular, the sensor network is defined by an undirected graph, where each
sensor can observe samples over time, access the information from the adjacent
sensors, and perform the sequential test based on its own decision statistic.
Different from most literature, the sampling process and the information
exchange process in our framework take place simultaneously (or, at least in
comparable time-scales), thus cannot be decoupled from one another. Two
message-passing schemes are considered, based on which the distributed
sequential probability ratio test (DSPRT) is carried out respectively. The
first scheme features the dissemination of the raw samples. Although the sample
propagation based DSPRT is shown to yield the asymptotically optimal
performance at each sensor, it incurs excessive inter-sensor communication
overhead due to the exchange of raw samples with index information. The second
scheme adopts the consensus algorithm, where the local decision statistic is
exchanged between sensors instead of the raw samples, thus significantly
lowering the communication requirement compared to the first scheme. In
particular, the decision statistic for DSPRT at each sensor is updated by the
weighted average of the decision statistics in the neighbourhood at every
message-passing step. We show that, under certain regularity conditions, the
consensus algorithm based DSPRT also yields the order-2 asymptotically optimal
performance at all sensors.Comment: 36 page
Cooperative Change Detection for Online Power Quality Monitoring
This paper considers the real-time power quality monitoring in power grid
systems. The goal is to detect the occurrence of disturbances in the nominal
sinusoidal voltage/current signal as quickly as possible such that protection
measures can be taken in time. Based on an autoregressive (AR) model for the
disturbance, we propose a generalized local likelihood ratio (GLLR) detector
which processes meter readings sequentially and alarms as soon as the test
statistic exceeds a prescribed threshold. The proposed detector not only reacts
to a wide range of disturbances, but also achieves lower detection delay
compared to the conventional block processing method. Then we further propose
to deploy multiple meters to monitor the power signal cooperatively. The
distributed meters communicate wirelessly to a central meter, where the data
fusion and detection are performed. In light of the limited bandwidth of
wireless channels, we develop a level-triggered sampling scheme, where each
meter transmits only one-bit each time asynchronously. The proposed multi-meter
scheme features substantially low communication overhead, while its performance
is close to that of the ideal case where distributed meter readings are
perfectly available at the central meter
Signature candidate of quantum chaos far from the semiclassical regime
We numerically investigated the entanglement product in the simplest coupled
kicked top model with the spin . Different from the dynamical pattern of
entanglement in the semiclassical regime, two similar initial states may have
discordant entanglement oscillations. A candidate of the quantum signature of
this classical chaotic system was proposed. The potential antimonotonic
relation between the rank correlation coefficient qualifying the concordant of
two entanglement evolutions and the stationary entanglement was preliminarily
revealed.Comment: 6 pages, 8 figures, RevTex4, The calculation of the scaled rank
correlation coefficient was added. Accepted by Chao
Sequential Hypothesis Test with Online Usage-Constrained Sensor Selection
This work investigates the sequential hypothesis testing problem with online
sensor selection and sensor usage constraints. That is, in a sensor network,
the fusion center sequentially acquires samples by selecting one "most
informative" sensor at each time until a reliable decision can be made. In
particular, the sensor selection is carried out in the online fashion since it
depends on all the previous samples at each time. Our goal is to develop the
sequential test (i.e., stopping rule and decision function) and sensor
selection strategy that minimize the expected sample size subject to the
constraints on the error probabilities and sensor usages. To this end, we first
recast the usage-constrained formulation into a Bayesian optimal stopping
problem with different sampling costs for the usage-contrained sensors. The
Bayesian problem is then studied under both finite- and infinite-horizon
setups, based on which, the optimal solution to the original usage-constrained
problem can be readily established. Moreover, by capitalizing on the structures
of the optimal solution, a lower bound is obtained for the optimal expected
sample size. In addition, we also propose algorithms to approximately evaluate
the parameters in the optimal sequential test so that the sensor usage and
error probability constraints are satisfied. Finally, numerical experiments are
provided to illustrate the theoretical findings, and compare with the existing
methods.Comment: 33 page
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