Weighted first moments of some special quadratic Dirichlet LL-functions

In this paper, we obtain asymptotic formulas for weighted first moments of central values of families of primitive quadratic Dirichlet $L$-functions whose conductors comprise only primes that split in a given quadratic number field. We then deduce a non-vanishing result of these $L$-functions at the point $s=1/2$.Comment: 7 page

First Moment of Hecke LL-functions with quartic characters at the central point

In this paper, we study the first moment of central values of Hecke $L$-functions associated with quartic characters.Comment: 11 page

One level density of low-lying zeros of quadratic and quartic Hecke LL-functions

In this paper, we prove some one level density results for the low-lying zeros of famliies of quadratic and quartic Hecke $L$-functions of the Gaussian field. As corollaries, we deduce that, respectively, at least $94.27 \%$ and $5\%$ of the members of the quadratic family and the quartic family do not vanish at the central point.Comment: 25 pages. arXiv admin note: text overlap with arXiv:0910.506

Saliency-guided video classification via adaptively weighted learning

Video classification is productive in many practical applications, and the recent deep learning has greatly improved its accuracy. However, existing works often model video frames indiscriminately, but from the view of motion, video frames can be decomposed into salient and non-salient areas naturally. Salient and non-salient areas should be modeled with different networks, for the former present both appearance and motion information, and the latter present static background information. To address this problem, in this paper, video saliency is predicted by optical flow without supervision firstly. Then two streams of 3D CNN are trained individually for raw frames and optical flow on salient areas, and another 2D CNN is trained for raw frames on non-salient areas. For the reason that these three streams play different roles for each class, the weights of each stream are adaptively learned for each class. Experimental results show that saliency-guided modeling and adaptively weighted learning can reinforce each other, and we achieve the state-of-the-art results.Comment: 6 pages, 1 figure, accepted by ICME 201