arXiv subjects
Publications and source records attributed to Zichao Dong.
Let $G$ be a graph on $n$ vertices of independence number $α(G)$ such that every induced subgraph of $G$ on $n-k$ vertices has an independent set of size at least $α(G) - \ell$. What is the largest possible $α(G)$ in terms of $n$ for fixed $k$ and $\ell$? We show that $α(G) \le n/2 + C_{k, \ell}$, which is sharp for $k-\ell \le 2$. We also use this result to determine new values of the Erdős--Rogers function.
We consider the expected length of the longest common subsequence between two random words of lengths $n$ and $(1-\varepsilon)kn$ over $k$-symbol alphabet. It is well-known that this quantity is asymptotic to $γ_{k,\varepsilon} n$ for some constant $γ_{k,\varepsilon}$. We show that $γ_{k,\varepsilon}$ is of the order $1-c\varepsilon^2$ uniformly in $k$ and $\varepsilon$. In addition, for large $k$, we give evidence that $γ_{k,\varepsilon}$ approaches $1-\tfrac{1}{4}\varepsilon^2$, and prove a matching lower bound.
Long-range and short-range temporal modeling are two complementary and crucial aspects of video recognition. Most of the state-of-the-arts focus on short-range spatio-temporal modeling and then average multiple snippet-level predictions to yield the final video-level prediction. Thus, their video-level prediction does not consider spatio-temporal features of how video evolves along the temporal dimension. In this paper, we introduce a novel Dynamic Segment Aggregation (DSA) module to capture relationship among snippets. To be more specific, we attempt to generate a dynamic kernel for a convolutional operation to aggregate long-range temporal information among adjacent snippets adaptively. The DSA module is an efficient plug-and-play module and can be combined with the off-the-shelf clip-based models (i.e., TSM, I3D) to perform powerful long-range modeling with minimal overhead. The final video architecture, coined as DSANet. We conduct extensive experiments on several video recognition benchmarks (i.e., Mini-Kinetics-200, Kinetics-400, Something-Something V1 and ActivityNet) to show its superiority. Our proposed DSA module is shown to benefit various video recognition models significantly. For example, equipped with DSA modules, the top-1 accuracy of I3D ResNet-50 is improved from 74.9% to 78.2% on Kinetics-400. Codes are available at https://github.com/whwu95/DSANet.