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

Miniature High-Sensitivity High-Temperature Fiber Sensor with a Dispersion Compensation Fiber-Based Interferometer

A miniature high-sensitivity, high-temperature fiber sensor with an interferometer based on a bare small-core-diameter dispersion compensation fiber (DCF) is reported. The sensing head is a single-mode-fiber (SMF) DCF configuration formed by a 4 mm long bare DCF with one end connected to the SMF by a fusion splicing technique and the other end cleaved. Due to the large mode index difference and high thermo-optic coefficient induced by two dominative interference modes, a miniature high-temperature fiber sensor with a high sensitivity of 68.6 pm/°C is obtained by monitoring the wavelength shift of the interference spectrum. This type of sensor has the features of small size, high sensitivity, high stability, simple structure, and low cost

Optics of Wide Electron Beam Focusing

In the present paper, we have further studied an approach to the theoretical treatment of wide electron beam focusing, based on the application of the theory of focusing fields with arbitrary curved optical axis, considering the initial condition emitted from the cathode surface. It is assumed that the magnetic field vector B will be used instead of the magnetic scalar potential Ω and the electrostatic potential and the magnetic field vector B are known functions either by computation or experimentally in the laboratory system of coordinates. The new approach to the mathematical treatment appears to be a useful method for solving problems of wide electron beam focusing with arbitrary electrostatic and magnetic fields. The theoretical treatment presented here can be extended to solve problems of deflection defocusing in cathode ray tubes at large deflection angles