Interevent distribution.

<p>Log-log plot of the distribution of waiting times between communication events including both calls and text messages. Also shown is a power law with an exponent of <i>α</i> = −1.26, which fits the distribution all the way from one minute to one week. The power law nature of the distribution suggests that there is no natural time scale to separate initiatives from follow-up communication. The local peak at 3 hours is possibly the electronic response of an app and the oscillations at large inter event times correspond to circadian cycles.</p

Initiative dynamics.

<p>In (A) we show the probability of a relationship ending after a given initiative length. Here “initiative length” denotes the number of consecutive one sided initiatives. Note that relationships are more likely to end after several one-sided initiatives, although the probability drops back again for very large (13+) initiative lengths. In (B) we show the probability of the initiative changing direction as a function of the initiative length. We see that the probability drops exponentially as the number of one sided initiatives in a row is increased. This suggests that initiatives promotes the role of an initiator through a positive feedback.</p

Tweet rate signals.

<p>We show the number of tweets measured in a time window, Δ<i>T</i> = 10min, for a few brands. Note the regular daily variation and the irregular bursty behavior.</p

Application of the algorithm to a generic signal.

<p>A time series generated according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0123876#pone.0123876.e004" target="_blank">Eq (3)</a> is shown in (A) and below we show the analytic drift, (B), and diffusion, (C), along with the functional forms estimated by the algorithm.</p

Initiative statistics of individuals.

<p>In (A) we show the maximum-likelihood distribution of the personal initiative parameter <i>μ</i>_<i>p</i>, where <i>μ</i>_<i>p</i> is the probability that an initiative involving person A is attributed to him rather than to his friends. We note that <i>μ</i>_<i>p</i> varies a lot over the population; some people making only 25% of the initiatives themselves against 70% at the other end of the spectrum. This has social consequences. In (B) we have estimated <i>μ</i>_<i>p</i> and plotted it against the “friend abundance” for the full population. Friend abundance is estimated as the average number of unique friends among all consecutive combinations of 20 incoming initiatives. We find that people with large <i>μ</i>_<i>p</i> are rewarded by increased attention from their network.</p

Activity correlations.

<p>In (A)-(C) we show the probability of activity conditioned on respectively a call, movement, and social proximity at Δ<i>t</i> = 0. Also shown are reference activities (dashed), which takes into account the circadian correlations. The horizontal axis spans 24 hours backward and forward in time.</p