Accelerating Dynamics of Collective Attention

The colored lines are the ensemble average values of all sub-trajectories L (t  ± t) from each trajectory L (t) around all its M local maxima, at respective times \(t_1 \ldots t_{M_i}\) for each year: \(\langle L(t_m \pm t)\rangle = \mathop {\sum}

olimits_{i = 1}^N (\mathop {\sum}

olimits_{{\mathrm{m}} = 1}^{M_i} L_i(t_m \pm t)/M_i)/N\). In order to avoid trivial effects such as system size dependence, we do not consider the total changes ΔL for measuring the velocity of attention allocation, but the relative gains ΔL /L in positive direction: \([\Delta L_i^{{\mathrm{(g)}}}/L_i](t) = (L_i(t) – L_i(t – 1))/L_i(t – 1) > 0\) at every instance t. The normalized empirical distribution of relative losses \(P(\Delta L_i^{{\mathrm{(l)}}}/L_i)\) is plotted in Figs. 1d and 3g with an inverted x-axis to visually clarify their negative character (in Supplementary Figure 4 for the other datasets without that visualization).

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