10,560 research outputs found
Non-monogamy of quantum discord and upper bounds for quantum correlation
We consider a monogamy inequality of quantum discord in a pure tripartite
state and show that it is equivalent to an inequality between quantum mutual
information and entanglement of formation of two parties. Since this inequality
does not hold for arbitrary bipartite states, quantum discord can generally be
both monogamous and polygamous. We also carry out numerical calculations for
some special states. The upper bounds of quantum discord and classical
correlation are also discussed and we give physical analysis on the invalidness
of a previous conjectured upper bound of quantum correlation. Our results
provide new insights for further understanding of distributions of quantum
correlations.Comment: Title changed, abstract and introduction revised, references adde
Spectral Learning for Supervised Topic Models
Supervised topic models simultaneously model the latent topic structure of
large collections of documents and a response variable associated with each
document. Existing inference methods are based on variational approximation or
Monte Carlo sampling, which often suffers from the local minimum defect.
Spectral methods have been applied to learn unsupervised topic models, such as
latent Dirichlet allocation (LDA), with provable guarantees. This paper
investigates the possibility of applying spectral methods to recover the
parameters of supervised LDA (sLDA). We first present a two-stage spectral
method, which recovers the parameters of LDA followed by a power update method
to recover the regression model parameters. Then, we further present a
single-phase spectral algorithm to jointly recover the topic distribution
matrix as well as the regression weights. Our spectral algorithms are provably
correct and computationally efficient. We prove a sample complexity bound for
each algorithm and subsequently derive a sufficient condition for the
identifiability of sLDA. Thorough experiments on synthetic and real-world
datasets verify the theory and demonstrate the practical effectiveness of the
spectral algorithms. In fact, our results on a large-scale review rating
dataset demonstrate that our single-phase spectral algorithm alone gets
comparable or even better performance than state-of-the-art methods, while
previous work on spectral methods has rarely reported such promising
performance
Multifrequency multi-qubit entanglement based on plasmonic hot spots
The theoretical method to study strong coupling between an ensemble of
quantum emitters (QEs) and surface plasmons excited by the nanoparticle cluster
has been presented by using a rigorous first-principles electromagnetic Green's
tensor technique. We have demonstrated that multi-qubit entanglement for
two-level QEs can be produced at different frequencies simultaneously, when
they locate in hot spots of metallic nanoparticle clusters. The duration of
quantum beats for such an entanglement can reach two orders longer than that
for the entanglement in a photonic cavity. The phenomenon originates from
collective coupling resonance excitation of the cluster. At the frequency of
single scattering resonance, the entanglement cannot be produced although the
single QE spontaneous decay rate is very bi
Optimal Real-Time Bidding Frameworks Discussion
This note is a complementary material for the solution of optimal real-time
bidding function in paper "Optimal Real-Time Bidding for Display Advertising,
KDD 2014", where the estimated cost is taken as the bid price, i.e., the upper
bound of the true cost. Here we discuss a more general bid optimisation
framework with various utility and cost functions.Comment: 4 page
Kernel Bayesian Inference with Posterior Regularization
We propose a vector-valued regression problem whose solution is equivalent to
the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior
distribution. This equivalence provides a new understanding of kernel Bayesian
inference. Moreover, the optimization problem induces a new regularization for
the posterior embedding estimator, which is faster and has comparable
performance to the squared regularization in kernel Bayes' rule. This
regularization coincides with a former thresholding approach used in kernel
POMDPs whose consistency remains to be established. Our theoretical work solves
this open problem and provides consistency analysis in regression settings.
Based on our optimizational formulation, we propose a flexible Bayesian
posterior regularization framework which for the first time enables us to put
regularization at the distribution level. We apply this method to nonparametric
state-space filtering tasks with extremely nonlinear dynamics and show
performance gains over all other baselines.Comment: NIPS 201
A CNN Based Scene Chinese Text Recognition Algorithm With Synthetic Data Engine
Scene text recognition plays an important role in many computer vision
applications. The small size of available public available scene text datasets
is the main challenge when training a text recognition CNN model. In this
paper, we propose a CNN based Chinese text recognition algorithm. To enlarge
the dataset for training the CNN model, we design a synthetic data engine for
Chinese scene character generation, which generates representative character
images according to the fonts use frequency of Chinese texts. As the Chinese
text is more complex, the English text recognition CNN architecture is modified
for Chinese text. To ensure the small size nature character dataset and the
large size artificial character dataset are comparable in training, the CNN
model are trained progressively. The proposed Chinese text recognition
algorithm is evaluated with two Chinese text datasets. The algorithm achieves
better recognize accuracy compared to the baseline methods.Comment: 2 pages, DAS 2016 short pape
Backlund transformations for Burgers Equation via localization of residual symmetries
In this paper, we obtained the non-local residual symmetry related to
truncated Painlev\'e expansion of Burgers equation. In order to localize the
residual symmetry, we introduced new variables to prolong the original Burgers
equation into a new system. By using Lie's first theorem, we got the finite
transformation for the localized residual symmetry. More importantly, we also
localized the linear superposition of multiple residual symmetries to find the
corresponding finite transformations. It is interesting to find that the nth
Backlund transformation for Burgers equation can be expressed by determinants
in a compact way
New interaction solutions of Kadomtsev-Petviashvili equation
The residual symmetry coming from truncated Painleve expansion of KP equation
is nonlocal, which is localized in this paper by introducing multiple new
dependent variables. By using the standard Lie group approach, the symmetry
reduction solutions for KP equation is obtained based on the general form of
Lie point symmetry for the prolonged system. In this way, the interaction
solutions between solitons and background waves is obtained, which is hard to
study by other traditional methods
New symmetry reductions related with the residual symmetry of Boussinesq equation
The Backlund transformation related symmetry is nonlocal, which is hardly to
apply in constructing solutions for nonlinear equations. In this paper, we
first localize nonlocal residual symmetry to Lie point symmetry by introducing
multiple new variables and obtain new Baaklund transformation. Then, by solving
out the general form of localized the residual symmetry, we reduce the enlarged
system by classical symmetry approach and obtain the corresponding reduction
solutions as well as related reduction equations. The localization procedure
provides a new way to investigate interaction solutions between different
waves
Residual Symmetry Reductions and Interaction Solutions of (2+1)-Dimensional Burgers Equation
The (2+1)-dimensional Burgers equation has been investigated first from
prospective of symmetry by localizing the nonlocal residual symmetries and then
studied by a simple generalized tanh expansion method. New symmetry reduction
solutions has been obtained by using the standard Lie point symmetry group
approach. A new B\"{a}klund transformation for Burgers equation has been given
with the generalized tanh expansion method . From this BT, interactive
solutions among different nonlinear excitations which is hard to obtain by
other methods has also been obtained easily
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