We study the impact of human activity patterns on information diffusion. To this end we ran a viral email experiment involving 31 183 individuals in which we were able to track a specific piece of information through the social network. We found that, contrary to traditional models, information travels at an unexpectedly slow pace. By using a branching model which accurately describes the experiment, we show that the large heterogeneity found in the response time is responsible for the slow dynamics of information at the collective level. Given the generality of our result, we discuss the important implications of this finding while modeling human dynamical collective phenomena. All of them are determined by the way humans spread or share information and thus depend on the rhythms and activity patterns of humans [6] [7] [8] [9] . Despite its importance, detailed empirical data on how humans disseminate a specific piece of information are scarce or indirect [10] [11] [12] [13] . Most understanding comes from epidemiological models run on empirical or synthetic social networks [2] [3] [4] 14] . These models usually neglect human activity patterns, assuming that the response time R , i.e., the time it takes for an individual to resend the information, is homogeneous or described by an exponential distribution which leads to a Poissonian description for human activity patterns. The main justification for this approximation is that it allows theoretical and computational descriptions through simpler Markovian (nonmemory) models. However, recent research shows that human activity is much more heterogeneous than considered in stark contradiction with the Poissonian approximation. For example, email activity [6-8], market trading frequencies, Web page visits [9] , or activity in online social spaces [13, 15] are all described by heavy-tailed or power-law distributions. We show how the large heterogeneity of human activity rhythms controls the information diffusion dynamics and question the validity of current models to describe it. The same issue was considered in Ref. [16] , where the authors investigate the effect of heavy-tailed distributions observed for E , the time between consecutive emails (the interevent time), in email communication [6] [7] [8] 17] . The authors proposed a relationship between R and E : The response time can be approximated (from below) by the time elapsed between receiving and sending emails RS . If incoming emails arrive at random times, average R is given by the solution of the waiting time paradox in renewal processes . The database [17] used in Ref. [16] gives E ' 1 day and E ' 3:3 days, and then R ' 6 days. Thus while the average interevent time is around one day, its heterogeneity makes the response time much bigger and information travels slower than expected. However, this is a poor approximation for R since receiving an email may trigger action on it which correlates the reception and forwarding events. In fact, the same database [17] used in Ref. [16] contains data on incoming and outgoing emails from whence one can obtain that RS ' 2:5 hours, and then the approximation R ' RS used in Ref. [16] yields the opposite conclusion: Information should travel much faster than expected. This example highlights an important shortcoming of currently available data: the inability to resolve the dynamics of a specific content item at the individuals' level (see, however, [10]). This forces one to make inferences about the dynamics from online communication data [12, 13] , or without knowledge of the nature of information transmitted [16, 17] , or from population averaged results [11] . In order to overcome this limitation, we conducted a large scale experiment to measure the influence of human activity on the diffusion of a specific piece of information. Subscribers to an online newsletter in 11 European countries were rewarded for recommending it. The offering email spread through viral propagation [19] tracked at every step. Web advertising spurred 7154 individuals to start recommendation cascades (Fig. 1) that, driven by 2111 secondary spreaders, grew until a total of 31 183 people received the message, 77% of them through recommendation emails. The propagation graph contains 7188 cascades of sizes between 2 and 146 nodes and diameters of up to 8 propagation steps [20] .
Iribarren and Moro REF have conducted an experiment, involving e-mails with "viral" content, that allows them to track the diffusion of information in a social network.
Impact of Human Activity Patterns on the Dynamics of Information Diffusion
Physical review letters
Physical review letters
Physics Medicine