Scaling behavior of online human activity

The rapid development of Internet technology enables human explore the web and record the traces of online activities. From the analysis of these large-scale data sets (i.e. traces), we can get insights about dynamic behavior of human activity. In this letter, the scaling behavior and complexity of human activity in the e-commerce, such as music, book, and movie rating, are comprehensively investigated by using detrended fluctuation analysis technique and multiscale entropy method. Firstly, the interevent time series of rating behaviors of these three type medias show the similar scaling property with exponents ranging from 0.53 to 0.58, which implies that the collective behaviors of rating media follow a process embodying self-similarity and long-range correlation. Meanwhile, by dividing the users into three groups based their activities (i.e., rating per unit time), we find that the scaling exponents of interevent time series in three groups are different. Hence, these results suggest the stronger long-range correlations exist in these collective behaviors. Furthermore, their information complexities vary from three groups. To explain the differences of the collective behaviors restricted to three groups, we study the dynamic behavior of human activity at individual level, and find that the dynamic behaviors of a few users have extremely small scaling exponents associating with long-range anticorrelations. By comparing with the interevent time distributions of four representative users, we can find that the bimodal distributions may bring the extraordinary scaling behaviors. These results of analyzing the online human activity in the e-commerce may not only provide insights to understand its dynamic behaviors but also be applied to acquire the potential economic interest

Experimental Realization of Entanglement Concentration and A Quantum Repeater

We report an experimental realization of entanglement concentration using two polarization-entangled photon pairs produced by pulsed parametric down-conversion. In the meantime, our setup also provides a proof-in-principle demonstration of a quantum repeater. The quality of our procedure is verified by observing a violation of Bell's inequality by more than 5 standard deviations. The high experimental accuracy achieved in the experiment implies that the requirement of tolerable error rate in multi-stage realization of quantum repeaters can be fulfilled, hence providing a practical toolbox for quantum communication over large distances.Comment: 15 pages, 4 figures, submitte

Relative clock demonstrates the endogenous heterogeneity of human dynamics

The heavy-tailed inter-event time distributions are widely observed in many human-activated systems, which may result from both endogenous mechanisms like the highest-priority-first protocol and exogenous factors like the varying global activity versus time. To distinguish the effects on temporal statistics from different mechanisms is this of theoretical significance. In this Letter, we propose a new timing method by using a relative clock, where the time length between two consecutive events of an individual is counted as the number of other individuals' events appeared during this interval. We propose a model, in which agents act either in a constant rate or with a power-law inter-event time distribution, and the global activity either keeps unchanged or varies periodically versus time. Our analysis shows that the heavy tails caused by the heterogeneity of global activity can be eliminated by setting the relative clock, yet the heterogeneity due to real individual behaviors still exists. We perform extensive experiments on four large-scale systems, the search engine by AOL, a social bookmarking system--Delicious, a short-message communication network, and a microblogging system--Twitter. Strong heterogeneity and clear seasonality of global activity are observed, but the heavy tails cannot be eliminated by using the relative clock. Our results suggest the existence of endogenous heterogeneity of human dynamics.Comment: 6 pages 7 figures 2 Table