Heterogenous Human Dynamics in Intra and Inter-day Time Scale

In this paper, we study two large data sets containing the information of two different human behaviors: blog-posting and wiki-revising. In both cases, the interevent time distributions decay as power-laws at both individual and population level. As different from previous studies, we put emphasis on time scales and obtain heterogeneous decay exponents in intraand interday range for the same dataset. Moreover, we observe opposite trend of exponents in relation to individual Activity. Further investigations show that the presence of intra-day activities mask the correlation between consecutive inter-day activities and lead to an underestimate of Memory, which explain the contradicting results in recent empirical studies. Removal of data in intra-day range reveals the high values of Memory and lead us to convergent results between wiki-revising and blog-posting. Introduction. – Thanks to the development of the information technology, comprehensive data available from the internet give us valuable insights into the pattern of human behaviors. Many recent studies of human behavior focus on the distributions of inter-event time or waiting time and report a heavy-tail both at the individual and population level. Examples of empirical studies including communication patterns of electronic mails [2–4, 17] and surface mail [4,5], web surfing [6,7],short message [8], movie rating [9]. In all the above systems, the observed distributions of interevent time goes as τ with exponents ranging from 1 to 3. Various mechanisms were suggested to explain the underlying dynamics. One main class of mechanism is the priority-queue model [2,17], which yields power-law waiting-time distributions p(τ) = τ with universal exponents a=1.0 and 1.5. Other mechanisms include the adaptive interesting model [11], the memory model [12] and the interaction model [13]. A crucial assumption of all these models and empirical studies is that the mechanisms driving human behaviors are identical in all time scales. According to this assumption, interevent time with length in minutes and in days are generated by the same mechanism (a)[email protected] (b)[email protected] and follow the same scaling law. Even in the cascading nonhomogeneous Poisson process [3, 4] which emphasizes external factors such as circadian and weekly cycles, the distributions still follow power-laws with identical exponent over the whole range. Table 1 shows a collection of recent empirical results, including the exponents and the unit of interevent time and the time range where the power-laws were observed. In this table, we simply classify the results into intraand inter-day behaviors. As we can see, for those data with unit in second or minute, the studies are often focused on the intra-day interevent time distribution; for those with unit in hour or day, only the inter-day range was studied. None of these studies investigated both the intra and inter-day behavior, though some noticed a hump in the interevent time distribution caused by the circadian rhythm [14]. One case that had been studied intensively is email and letter based communications, where some studies suggested that mechanisms of the two activities are different, based on the different exponents observed [2]; others suggested that the two are essentially the same based on the data collapse of interevent time distributions [4]. Limited attention has been paid on the different time range in the two activities, as the timestamp of email and letters communications are respectively in the unit of second and day, and exponents are thus extracted from different