We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power law with an exponent that increases linearly with the game depth, whereas the pooled distribution of all opening weights follows Zipf's law with universal exponent. We propose a simple stochastic process that is able to capture the observed playing ...

The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf's Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto's or Benford's, but contrary to po...

The lack of a large scale Chinese test collection is an obstacle to the Chinese information retrieval development. In order to address this issue, we built such a collection composed of millions of Chinese web pages, known as the Chinese Web Test collection with 100 gigabyte (CWT100g) in data volume, which is the largest Chinese web test collection as of this writing, and has been used by sever...

The rank–size distribution of cities follows Zipf’s law, and the Zipf scaling exponent often tends to a constant 1. This seems be general rule. However, recent numerical experiment shows that there exists contradiction between 1 high urbanization level in large population country. In this paper, mathematical modeling, computational analysis, method proof by are employed reveal relationships exp...

Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's...