Quantitative understanding of human behaviors provides elementary comprehension of the complexity of many human-initiated systems. In this paper, we investigate the behavior of people on the $BBS$ forum by the statistical analysis of the amounts of view and reply of posts. According to our statistics, we find that the amounts of view and reply of posts follow the power law distributions with different power exponent. Furthermore, we discover that the amounts of view and reply of posts have nonlinear relationship. They are related by power function and show us straight line in log-log plot. Based on the estimation of slope and intercept of the line, we can characterize the behaviors quantitatively and know that people of Chinese forum and those of foreign forum have different preference towards replying to and viewing the posts. At last, we analyze the burstiness and memory in replying time series. They show some universal properties among different forum. All of them locate themselves in the high-$B$, low-$M$ region.

A way to fight your traffic tickets. The paper was awarded a special prize of $400 that the author did not have to pay to the state of California. <br />In view of enormous, extremely surprising and completely unexpected public interest to this work, we have added an appendix answering the two most common questions.

This Chapter is written for the Festschrift celebrating the 70th birthday of the distinguished economist Duncan Foley from the New School for Social Research in New York. This Chapter reviews applications of statistical physics methods, such as the principle of entropy maximization, to the probability distributions of money, income, and global energy consumption per capita. The exponential probability distribution of wages, predicted by the statistical equilibrium theory of a labor market developed by Foley in 1996, is supported by empirical data on income distribution in the USA for the majority (about 97%) of population. In addition, the upper tail of income distribution (about 3% of population) follows a power law and expands dramatically during financial bubbles, which results in a significant increase of the overall income inequality. A mathematical analysis of the empirical data clearly demonstrates the two-class structure of a society, as pointed out Karl Marx and recently highlighted by the Occupy Movement. Empirical data for the energy consumption per capita around the world are close to an exponential distribution, which can be also explained by the entropy maximization principle.

Prediction markets show considerable promise for developing flexible mechanisms for machine learning. Here, machine learning markets for multivariate systems are defined, and a utility-based framework is established for their analysis. This differs from the usual approach of defining static betting functions. It is shown that such markets can implement model combination methods used in machine learning, such as product of expert and mixture of expert approaches as equilibrium pricing models, by varying agent utility functions. They can also implement models composed of local potentials, and message passing methods. Prediction markets also allow for more flexible combinations, by combining multiple different utility functions. Conversely, the market mechanisms implement inference in the relevant probabilistic models. This means that market mechanism can be utilized for implementing parallelized model building and inference for probabilistic modelling.

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized 9c5 by only two variables, p and q. Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.