Wei Li

TL;DR: It is found that the excitation is most likely to be found at the initial nodes while the coherent transport to other nodes has a very low probability and in the long time limit the transition probabilities show characteristic patterns with identical values of limiting probabilities.

TL;DR: Wang et al. as discussed by the authors investigated the statistical properties of the empirical data taken from the Chinese stock market during the time period from January to July, 2007, and obtained evidence of strong correlations among different stock types, stock index, stock volume turnover, A share (B share) seat number and GDP per capita.

Abstract: ”Each individual will adopt a course of action that will involve the expenditure of the probably least average of his work.” This statement was named ”the principle of least effort”. The principle of least effort is often known as a ”deterministic description of human behavior”. In this paper, we present a brief introduction of this principle. Applications of the principle in different fields are also summarized. As the principle of least effort is proposed by Zipf, it is also called Zipf’s law. We then discuss the correlation between three widely considered distributions: Zipf distribution, Pareto distribution and probability distribution. With empirical investigations, it is often stated that, most social behaviors are controlled by the pure Zipf’s law that corresponds to the Zipf distribution of exponent -1. We summarily present the discovery of Zipf’s law in different social behaviors. Some empirical studies are also given as examples, verifying that, in most countries, the distribution of city size by population follows Zipf’s law, and the exponent of Zipf distribution of individual income is about -0.5, the same as Zipf predicted in theory.

TL;DR: In this paper, the authors show that using some simple techniques of ML, non-steady-state configurations of directed percolation (DP) suffice to capture its essential critical behaviors in both ($1+1$) and ($2+ 1$) dimensions.