End-to-end Flow Correlation Tracking with Spatial-temporal Attention

Discriminative correlation filters (DCF) with deep convolutional features have achieved favorable performance in recent tracking benchmarks. However, most of existing DCF trackers only consider appearance features of current frame, and hardly benefit from motion and inter-frame information. The lack of temporal information degrades the tracking performance during challenges such as partial occlusion and deformation. In this work, we focus on making use of the rich flow information in consecutive frames to improve the feature representation and the tracking accuracy. Firstly, individual components, including optical flow estimation, feature extraction, aggregation and correlation filter tracking are formulated as special layers in network. To the best of our knowledge, this is the first work to jointly train flow and tracking task in a deep learning framework. Then the historical feature maps at predefined intervals are warped and aggregated with current ones by the guiding of flow. For adaptive aggregation, we propose a novel spatial-temporal attention mechanism. Extensive experiments are performed on four challenging tracking datasets: OTB2013, OTB2015, VOT2015 and VOT2016, and the proposed method achieves superior results on these benchmarks.Comment: Accepted in CVPR 201

Entanglement and chaos in warped conformal field theories

Various aspects of warped conformal field theories (WCFTs) are studied including entanglement entropy on excited states, the Renyi entropy after a local quench, and out-of-time-order four-point functions. Assuming a large central charge and dominance of the vacuum block in the conformal block expansion, (i) we calculate the single-interval entanglement entropy on an excited state, matching previous finite temperature results by changing the ensemble; and (ii) we show that WCFTs are maximally chaotic, a result that is compatible with the existence of black holes in the holographic duals. Finally, we relax the aforementioned assumptions and study the time evolution of the Renyi entropy after a local quench. We find that the change in the Renyi entropy is topological, vanishing at early and late times, and nonvanishing in between only for charged states in spectrally-flowed WCFTs.Comment: 31 pages; v2: corrected typos, matches published versio

Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions of fully nonlinear elliptic equations

We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation $F(D^{2}u,x)=f(x)$ defined in a bounded $C^{1,1}$ domain. The oscillation of nonlinearity $F$ with respect to $x$ is assumed to be small in the $L^{n}$-sense. Here, we employ the Lorentz boundedness of the Hardy-Littlewood maximal operators and an equivalent representation of weighted Lorentz norm

Market Stability Switches in a Continuous-Time Financial Market with Heterogeneous Beliefs

By considering a financial market of fundamentalists and trend followers in which the price trend of the trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examines the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. This interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, suffcient conditions on the stability and global existence of the periodic solution are obtained.asset price; fundamentalists; trend followers; delay differential equations; stability; bifurcations

Spectral radius conditions for fractional [a,b][a,b]-covered graphs

A graph $G$ is called fractional $[a,b]$-covered if for every edge $e$ of $G$ there is a fractional $[a,b]$-factor with the indicator function $h$ such that $h(e)=1$. In this paper, we provide tight spectral radius conditions for graphs being fractional $[a,b]$-covered.Comment: 9 page