Electronic structure near an impurity and terrace on the surface of a 3-dimensional topological insulator

Motivated by recent scanning tunneling microscopy experiments on surfaces of Bi$_{1-x}$Sb$_{x'}$\cite{yazdanistm,gomesstm} and Bi$_2$Te$_3$,\cite{kaptunikstm,xuestm} we theoretically study the electronic structure of a 3-dimensional (3D) topological insulator in the presence of a local impurity or a domain wall on its surface using a 3D lattice model. While the local density of states (LDOS) oscillates significantly in space at energies above the bulk gap, the oscillation due to the in-gap surface Dirac fermions are very weak. The extracted modulation wave number as a function of energy satisfies the Dirac dispersion for in-gap energies and follows the border of the bulk continuum above the bulk gap. We have also examined analytically the effects of the defects by using a pure Dirac fermion model for the surface states and found that the LDOS decays asymptotically faster at least by a factor of 1/r than that in normal metals, consistent with the results obtained from our lattice model.Comment: 7 pages, 5 figure

DesnowNet: Context-Aware Deep Network for Snow Removal

Existing learning-based atmospheric particle-removal approaches such as those used for rainy and hazy images are designed with strong assumptions regarding spatial frequency, trajectory, and translucency. However, the removal of snow particles is more complicated because it possess the additional attributes of particle size and shape, and these attributes may vary within a single image. Currently, hand-crafted features are still the mainstream for snow removal, making significant generalization difficult to achieve. In response, we have designed a multistage network codenamed DesnowNet to in turn deal with the removal of translucent and opaque snow particles. We also differentiate snow into attributes of translucency and chromatic aberration for accurate estimation. Moreover, our approach individually estimates residual complements of the snow-free images to recover details obscured by opaque snow. Additionally, a multi-scale design is utilized throughout the entire network to model the diversity of snow. As demonstrated in experimental results, our approach outperforms state-of-the-art learning-based atmospheric phenomena removal methods and one semantic segmentation baseline on the proposed Snow100K dataset in both qualitative and quantitative comparisons. The results indicate our network would benefit applications involving computer vision and graphics

Information Filtering on Coupled Social Networks

In this paper, based on the coupled social networks (CSN), we propose a hybrid algorithm to nonlinearly integrate both social and behavior information of online users. Filtering algorithm based on the coupled social networks, which considers the effects of both social influence and personalized preference. Experimental results on two real datasets, \emph{Epinions} and \emph{Friendfeed}, show that hybrid pattern can not only provide more accurate recommendations, but also can enlarge the recommendation coverage while adopting global metric. Further empirical analyses demonstrate that the mutual reinforcement and rich-club phenomenon can also be found in coupled social networks where the identical individuals occupy the core position of the online system. This work may shed some light on the in-depth understanding structure and function of coupled social networks

A new quasi-exactly solvable problem and its connection with an anharmonic oscillator

The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator had been investigated by methods of KS transformation