Fine gradings of complex simple Lie algebras and Finite Root Systems

A $G$-grading on a complex semisimple Lie algebra $L$, where $G$ is a finite abelian group, is called quasi-good if each homogeneous component is 1-dimensional and 0 is not in the support of the grading. Analogous to classical root systems, we define a finite root system $R$ to be some subset of a finite symplectic abelian group satisfying certain axioms. There always corresponds to $R$ a semisimple Lie algebra $L(R)$ together with a quasi-good grading on it. Thus one can construct nice basis of $L(R)$ by means of finite root systems. We classify finite maximal abelian subgroups $T$ in \Aut(L) for complex simple Lie algebras $L$ such that the grading induced by the action of $T$ on $L$ is quasi-good, and show that the set of roots of $T$ in $L$ is always a finite root system. There are five series of such finite maximal abelian subgroups, which occur only if $L$ is a classical simple Lie algebra

Coherent Online Video Style Transfer

Training a feed-forward network for fast neural style transfer of images is proven to be successful. However, the naive extension to process video frame by frame is prone to producing flickering results. We propose the first end-to-end network for online video style transfer, which generates temporally coherent stylized video sequences in near real-time. Two key ideas include an efficient network by incorporating short-term coherence, and propagating short-term coherence to long-term, which ensures the consistency over larger period of time. Our network can incorporate different image stylization networks. We show that the proposed method clearly outperforms the per-frame baseline both qualitatively and quantitatively. Moreover, it can achieve visually comparable coherence to optimization-based video style transfer, but is three orders of magnitudes faster in runtime.Comment: Corrected typo

CPCP violation induced by the double resonance for pure annihilation decay process in Perturbative QCD

In Perturbative QCD (PQCD) approach we study the direct $CP$ violation in the pure annihilation decay process of $\bar{B}^0_{s}\rightarrow\pi^+\pi^-\pi^+\pi^-$ induced by the $\rho$ and $\omega$ double resonance effect. Generally, the $CP$ violation is small in the pure annihilation type decay process. However, we find that the $CP$ violation can be enhanced by double $\rho-\omega$ interference when the invariant masses of the $\pi^+\pi^-$ pairs are in the vicinity of the $\omega$ resonance. For the decay process of $\bar{B}^0_{s}\rightarrow\pi^+\pi^-\pi^+\pi^-$, the maximum $CP$ violation can reach 28.64{\%}

Dual Skipping Networks

Inspired by the recent neuroscience studies on the left-right asymmetry of the human brain in processing low and high spatial frequency information, this paper introduces a dual skipping network which carries out coarse-to-fine object categorization. Such a network has two branches to simultaneously deal with both coarse and fine-grained classification tasks. Specifically, we propose a layer-skipping mechanism that learns a gating network to predict which layers to skip in the testing stage. This layer-skipping mechanism endows the network with good flexibility and capability in practice. Evaluations are conducted on several widely used coarse-to-fine object categorization benchmarks, and promising results are achieved by our proposed network model.Comment: CVPR 2018 (poster); fix typ