4,761 research outputs found
Weiqi games as a tree: Zipf's law of openings and beyond
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.Comment: 6 Latex pages including 6 figure
Polygonal vortex beams in quasi-frequency-degenerate states
We originally demonstrate the vortex beams with patterns of closed polygons
[namely polygonal vortex beams (PVBs)] generated by a
quasi-frequency-degenerate (QFD) Yb:CALGO laser resonator with astigmatic
transformation. The PVBs with peculiar patterns of triangular, square, and
parallelogram shapes carrying large orbital angular momentums (OAMs) are
theoretically investigated and experimentally obtained in the vicinity of the
SU(2) degenerate states of laser resonator. The PVBs in QFD states are compared
with the vortex beams with patterns of isolated spots arrays located on the
triangle-, square-, and parallelogram-shaped routes [namely
polygonalspots-array vortex beams (PSA-VBs)] under normal SU(2) degenerate
states. Beam profile shape of PVB or PSA-VB and OAM can be controlled by
adjusting the cavity length and the position of pump spot. The simulated and
experimental results validate the performance of our method to generate PVB,
which is of great potential for promoting novel technologies in particle
trapping and beam shaping
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