10,633 research outputs found
Exact solutions to the three-dimensional Gross-Pitaevskii equation with modulated radial nonlinearity
We study the Bose-Einstein condensate trapped in a three-dimensional
spherically symmetrical potential. Exact solutions to the stationary
Gross-Pitaevskii equation are obtained for properly modulated radial
nonlinearity. The solutions contain vortices with different winding numbers and
exhibit the shell-soliton feature in the radial distributions.Comment: 5 figure
Transition of defect patterns from 2D to 3D in liquid crystals
Defects arise when nematic liquid crystals are under topological constraints
at the boundary. Recently the study of defects has drawn a lot of attention. In
this paper, we investigate the relationship between two-dimensional defects and
three-dimensional defects within nematic liquid crystals confined in a shell
under the Landau-de Gennes model. We use a highly accurate spectral method to
numerically solve the Landau- de Gennes model to get the detailed static
structures of defects. Interestingly, the solution is radial-invariant when the
thickness of the shell is sufficiently small. As the shell thickness increase,
the solution undergo symmetry break to reconfigure the disclination lines. We
study this three-dimensional reconfiguration of disclination lines in detail
under different boundary conditions. We also discuss the topological charge of
defects in two- and three-dimensional spaces within the tensor model
Learning to Transfer
Transfer learning borrows knowledge from a source domain to facilitate
learning in a target domain. Two primary issues to be addressed in transfer
learning are what and how to transfer. For a pair of domains, adopting
different transfer learning algorithms results in different knowledge
transferred between them. To discover the optimal transfer learning algorithm
that maximally improves the learning performance in the target domain,
researchers have to exhaustively explore all existing transfer learning
algorithms, which is computationally intractable. As a trade-off, a sub-optimal
algorithm is selected, which requires considerable expertise in an ad-hoc way.
Meanwhile, it is widely accepted in educational psychology that human beings
improve transfer learning skills of deciding what to transfer through
meta-cognitive reflection on inductive transfer learning practices. Motivated
by this, we propose a novel transfer learning framework known as Learning to
Transfer (L2T) to automatically determine what and how to transfer are the best
by leveraging previous transfer learning experiences. We establish the L2T
framework in two stages: 1) we first learn a reflection function encrypting
transfer learning skills from experiences; and 2) we infer what and how to
transfer for a newly arrived pair of domains by optimizing the reflection
function. Extensive experiments demonstrate the L2T's superiority over several
state-of-the-art transfer learning algorithms and its effectiveness on
discovering more transferable knowledge.Comment: 12 pages, 8 figures, conferenc
Learning to Multitask
Multitask learning has shown promising performance in many applications and
many multitask models have been proposed. In order to identify an effective
multitask model for a given multitask problem, we propose a learning framework
called learning to multitask (L2MT). To achieve the goal, L2MT exploits
historical multitask experience which is organized as a training set consists
of several tuples, each of which contains a multitask problem with multiple
tasks, a multitask model, and the relative test error. Based on such training
set, L2MT first uses a proposed layerwise graph neural network to learn task
embeddings for all the tasks in a multitask problem and then learns an
estimation function to estimate the relative test error based on task
embeddings and the representation of the multitask model based on a unified
formulation. Given a new multitask problem, the estimation function is used to
identify a suitable multitask model. Experiments on benchmark datasets show the
effectiveness of the proposed L2MT framework
Parallel energy-stable phase field crystal simulations based on domain decomposition methods
In this paper, we present a parallel numerical algorithm for solving the
phase field crystal equation. In the algorithm, a semi-implicit finite
difference scheme is derived based on the discrete variational derivative
method. Theoretical analysis is provided to show that the scheme is
unconditionally energy stable and can achieve second-order accuracy in both
space and time. An adaptive time step strategy is adopted such that the time
step size can be flexibly controlled based on the dynamical evolution of the
problem. At each time step, a nonlinear algebraic system is constructed from
the discretization of the phase field crystal equation and solved by a domain
decomposition based, parallel Newton--Krylov--Schwarz method with improved
boundary conditions for subdomain problems. Numerical experiments with several
two and three dimensional test cases show that the proposed algorithm is
second-order accurate in both space and time, energy stable with large time
steps, and highly scalable to over ten thousands processor cores on the Sunway
TaihuLight supercomputer
Stability and Optimization Error of Stochastic Gradient Descent for Pairwise Learning
In this paper we study the stability and its trade-off with optimization
error for stochastic gradient descent (SGD) algorithms in the pairwise learning
setting. Pairwise learning refers to a learning task which involves a loss
function depending on pairs of instances among which notable examples are
bipartite ranking, metric learning, area under ROC (AUC) maximization and
minimum error entropy (MEE) principle. Our contribution is twofold. Firstly, we
establish the stability results of SGD for pairwise learning in the convex,
strongly convex and non-convex settings, from which generalization bounds can
be naturally derived. Secondly, we establish the trade-off between stability
and optimization error of SGD algorithms for pairwise learning. This is
achieved by lower-bounding the sum of stability and optimization error by the
minimax statistical error over a prescribed class of pairwise loss functions.
From this fundamental trade-off, we obtain lower bounds for the optimization
error of SGD algorithms and the excess expected risk over a class of pairwise
losses. In addition, we illustrate our stability results by giving some
specific examples of AUC maximization, metric learning and MEE.Comment: 35 page
Learning High-level Image Representation for Image Retrieval via Multi-Task DNN using Clickthrough Data
Image retrieval refers to finding relevant images from an image database for
a query, which is considered difficult for the gap between low-level
representation of images and high-level representation of queries. Recently
further developed Deep Neural Network sheds light on automatically learning
high-level image representation from raw pixels. In this paper, we proposed a
multi-task DNN learned for image retrieval, which contains two parts, i.e.,
query-sharing layers for image representation computation and query-specific
layers for relevance estimation. The weights of multi-task DNN are learned on
clickthrough data by Ring Training. Experimental results on both simulated and
real dataset show the effectiveness of the proposed method
Cryptanalysis and improvement of a quantum-communication-based online shopping mechanism
Recently, Chou et al. [Electron Commer Res, DOI 10.1007/s10660-014-9143-6]
presented a novel controlled quantum secure direct communication protocol which
can be used for online shopping. The authors claimed that their protocol was
immune to the attacks from both external eavesdropper and internal betrayer.
However, we find that this protocol is vulnerable to the attack from internal
betrayer. In this paper, we analyze the security of this protocol to show that
the controller in this protocol is able to eavesdrop the secret information of
the sender (i.e., the customer's shopping information), which indicates that it
cannot be used for secure online shopping as the authors expected. Moreover, an
improvement to resist the controller's attack is proposed.Comment: 9 page
Breather induced quantized superfluid vortex filaments and their characterization
We study and characterize the breather-induced quantized superfluid vortex
filaments which correspond to the Kuznetsov-Ma breather and super-regular
breather excitations developing from localised perturbations. Such vortex
filaments, emerging from an otherwise perturbed helical vortex, exhibit
intriguing loop structures corresponding to the large amplitude of breathers
due to the dual action of bending and twisting of the vortex. The loop induced
by Kuznetsov-Ma breather emerges periodically as time increases, while the loop
structure triggered by super-regular breather---the loop pair---exhibits
striking symmetry breaking due to the broken reflection symmetry of the group
velocities of super-regular breather. In particular, we identify explicitly the
generation conditions of these loop excitations by introducing a physical
quantity---the integral of the relative quadratic curvature---which corresponds
to the effective energy of breathers. Although the nature of nonlinearity, it
is demonstrated that this physical quantity shows a linear correlation with the
loop size. These results will deepen our understanding of breather-induced
vortex filaments and be helpful for controllable ring-like excitations on the
vortices.Comment: 9 pages, 9 figure
Joint Uplink and Downlink Relay Selection in Cooperative Cellular Networks
We consider relay selection technique in a cooperative cellular network where
user terminals act as mobile relays to help the communications between base
station (BS) and mobile station (MS). A novel relay selection scheme, called
Joint Uplink and Downlink Relay Selection (JUDRS), is proposed in this paper.
Specifically, we generalize JUDRS in two key aspects: (i) relay is selected
jointly for uplink and downlink, so that the relay selection overhead can be
reduced, and (ii) we consider to minimize the weighted total energy consumption
of MS, relay and BS by taking into account channel quality and traffic load
condition of uplink and downlink. Information theoretic analysis of the
diversity-multiplexing tradeoff demonstrates that the proposed scheme achieves
full spatial diversity in the quantity of cooperating terminals in this
network. And numerical results are provided to further confirm a significant
energy efficiency gain of the proposed algorithm comparing to the previous best
worse channel selection and best harmonic mean selection algorithms.Comment: Accepted by VTC-2010FAL
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