Zhiyuan Xu

Zhiyuan Xu
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Zhiyuan Xu

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Mathematics - Differential Geometry (1)
Computer Science - Artificial Intelligence (1)
Computer Science - Distributed; Parallel; and Cluster Computing (1)

Publications Authored By Zhiyuan Xu

Automatic decision-making approaches, such as reinforcement learning (RL), have been applied to (partially) solve the resource allocation problem adaptively in the cloud computing system. However, a complete cloud resource allocation framework exhibits high dimensions in state and action spaces, which prohibit the usefulness of traditional RL techniques. In addition, high power consumption has become one of the critical concerns in design and control of cloud computing systems, which degrades system reliability and increases cooling cost. Read More

We verify that if $M$ is a compact minimal hypersurface in $\mathbb{S}^{n+1}$ whose squared length of the second fundamental form satisfying $0\leq |A|^2-n\leq\frac{n}{22}$, then $|A|^2\equiv n$ and $M$ is a Clifford torus. Moreover, we prove that if $M$ is a complete self-shrinker with polynomial volume growth in $\mathbb{R}^{n+1}$ whose equation is given by (\ref{selfshr}), and if the squared length of the second fundamental form of $M$ satisfies $0\leq|A|^2-1\leq\frac{1}{21}$, then $|A|^2\equiv1$ and $M$ is a round sphere or a cylinder. Our results improve the rigidity theorems due to Q. Read More