Physics of games and sports PACS 89.20.-a -Interdisciplinary applications of physics PACS 89.75.Da -Systems obeying scaling laws PACS 89.75.Hc -Networks and genealogical treesAbstract -Weiqi is one of the most complex board games played by two persons. The placement strategies adopted by Weiqi players are often used to analog the philosophy of human wars. Contrary to the western chess, Weiqi games are less studied by academics partially because Weiqi is popular only in East Asia, especially in China, Japan and Korea. Here, we propose to construct a directed tree using a database of extensive Weiqi games and perform a quantitative analysis of the Weiqi tree. We find that the popularity distribution of Weiqi openings with a same number of moves is distributed according to a power law and the tail exponent increases with the number of moves. Intriguingly, the superposition of the popularity distributions of Weiqi openings with the number of moves no more than a given number also has a power-law tail in which the tail exponent increases with the number of moves, and the superposed distribution approaches to the Zipf law. These findings are the same as for chess and support the conjecture that the popularity distribution of board game openings follows the Zipf law with a universal exponent. We also find that the distribution of out-degrees has a power-law form, the distribution of branching ratios has a very complicated pattern, and the distribution of uniqueness scores defined by the path lengths from the root vertex to the leaf vertices exhibits a unimodal shape. Our work provides a promising direction for the study of the decision making process of Weiqi playing from the angle of directed branching tree.

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Graphene oxide (GO) and its functionalized derivatives have attracted increasing attention in medical treatment. Herein, a reduction sensitive PEI‐GO‐SS‐TPP was synthesized for photodynamic therapy. More than 80% porphyrin release was observed in the presence of 10 mmol•L−1 DTT in one day. The confocal laser scanning microscopy confirmed that the cell uptake efficiency of PEI‐GO‐SS‐TPP was remarkably enhanced as compared to free porphyrin which was significantly dependent on incubation time. For photodynamic therapy, GSH‐OEt could effectively increase the photodynamic therapy efficiency of PEI‐GO‐SS‐TPP. Compared with free porphyrin, the toxicity from PEI‐GO‐SS‐TPP is much higher with a low IC50 (2.1 µg/mL) value. All results indicate that the PEI‐GO‐SS‐TPP PSs are promising for photodynamic therapy.

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