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Ziyu Liu

Publications and source records attributed to Ziyu Liu.

94 records · Page 6Linked to original sources

Towards Understanding Chinese Checkers with Heuristics, Monte Carlo Tree Search, and Deep Reinforcement Learning

The game of Chinese Checkers is a challenging traditional board game of perfect information that differs from other traditional games in two main aspects: first, unlike Chess, all checkers remain indefinitely in the game and hence the branching factor of the search tree does not decrease as the game progresses; second, unlike Go, there are also no upper bounds on the depth of the search tree since repetitions and backward movements are allowed. Therefore, even in a restricted game instance, the state-space of the game can still be unbounded, making it challenging for a computer program to excel. In this work, we present an approach that effectively combines the use of heuristics, Monte Carlo tree search, and deep reinforcement learning for building a Chinese Checkers agent without the use of any human game-play data. Experiment results show that our agent is competent under different scenarios and reaches the level of experienced human players.

cs.LG↗

An Investigation on Partitions with Equal Products

An ordered triple $(s,p,n)$ is called admissible if there exist two different multisets $X=\{x_1,x_2,\dotsc,x_n\}$ and $Y=\{y_1,y_2,\dotsc,y_n\}$ such that $X$ and $Y$ share the same sum $s$, the same product $p$, and the same size $n$. We first count the number of $n$ such that $(s,p,n)$ are admissible for a fixed $s$. We also fully characterize the values $p$ such that $(s,p,n)$ is admissible. Finally, we consider the situation where $r$ different multisets are needed, instead of just two. This project is also related to John Conway's wizard puzzle from the 1960s.

math.NT↗

Decomposition of noncommutative U(1) gauge potential

We investigate the decomposition of noncommutative gauge potential $\hat{A_{i}}$, and find it has inner structure, namely, $\hat{A_{i}}$ can be decomposed in two parts $\hat{b_{i}}$ and $\hat{a_{i}}$, here $\hat{b_{i}}$ satisfies gauge transformations while $\hat{a_{i}}$ satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U(1) gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tenser can be expressed in terms of the unit vector field. When the unit vector field has non singularity point, noncommutative gauge potential and gauge field tenser will equal to ordinary gauge potential and gauge field tenser.

hep-th↗

Topological structure of the vortex solution in Jackiw-Pi model

By using $ϕ$ -mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortices solution and topological number which is determined by Hopf index and and Brouwer degree. We also give the quantization of flux in the case. Then, we study the angular momentum of the vortex, it can be expressed in terms of the flux.

hep-th↗