109,652 research outputs found
Faddeev-Skyrme Model and Rational Maps
The Faddeev-Skyrme model, a modified O(3) nonlinear sigma model in three
space dimensions, is known to admit topological solitons that are stabilized by
the Hopf charge. The Faddeev-Skyrme model is also related to the low-energy
limits of SU(2) Yang-Mills theory. Here, the model is reformulated into its
gauge-equivalent expression, which turns out to be Skyrme-like. The solitonic
solutions of this Skyrme-like model are analyzed by the rational map ansatz.
The energy function and the Bogomolny-type lower bound of the energy are
established. The generalized Faddeev-Skyrme model that originates from the
infrared limits of SU(N) Yang-Mills theory is presented.Comment: 12 pages, LaTex, minor typo correcte
STAR: A Concise Deep Learning Framework for Citywide Human Mobility Prediction
Human mobility forecasting in a city is of utmost importance to
transportation and public safety, but with the process of urbanization and the
generation of big data, intensive computing and determination of mobility
pattern have become challenging. This study focuses on how to improve the
accuracy and efficiency of predicting citywide human mobility via a simpler
solution. A spatio-temporal mobility event prediction framework based on a
single fully-convolutional residual network (STAR) is proposed. STAR is a
highly simple, general and effective method for learning a single tensor
representing the mobility event. Residual learning is utilized for training the
deep network to derive the detailed result for scenarios of citywide
prediction. Extensive benchmark evaluation results on real-world data
demonstrate that STAR outperforms state-of-the-art approaches in single- and
multi-step prediction while utilizing fewer parameters and achieving higher
efficiency.Comment: Accepted by MDM 201
Truncated Nuclear Norm Minimization for Image Restoration Based On Iterative Support Detection
Recovering a large matrix from limited measurements is a challenging task
arising in many real applications, such as image inpainting, compressive
sensing and medical imaging, and this kind of problems are mostly formulated as
low-rank matrix approximation problems. Due to the rank operator being
non-convex and discontinuous, most of the recent theoretical studies use the
nuclear norm as a convex relaxation and the low-rank matrix recovery problem is
solved through minimization of the nuclear norm regularized problem. However, a
major limitation of nuclear norm minimization is that all the singular values
are simultaneously minimized and the rank may not be well approximated
\cite{hu2012fast}. Correspondingly, in this paper, we propose a new multi-stage
algorithm, which makes use of the concept of Truncated Nuclear Norm
Regularization (TNNR) proposed in \citep{hu2012fast} and Iterative Support
Detection (ISD) proposed in \citep{wang2010sparse} to overcome the above
limitation. Besides matrix completion problems considered in
\citep{hu2012fast}, the proposed method can be also extended to the general
low-rank matrix recovery problems. Extensive experiments well validate the
superiority of our new algorithms over other state-of-the-art methods
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