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