Figure 2

The dependence of mobility statistical properties on the data temporal resolution. (a) Distribution \(P(t^{\mathrm{stay}})\) of the duration \(t^{\mathrm{stay}}\) of a stay at each location for all users. We then conduct the statistics below by removing the visited locations with \(t^{\mathrm{stay}}\) for all users. (b) The average number of visited locations as a function of T. In fact, the threshold T can be regarded as a parameter controlling the resolution of the data. A larger threshold T identifies less visited locations, and thus corresponds to a poorer data resolution. (c-f) The difference between the real data and the shuffled data in terms of (c) the total transited location pairs \(n_{\alpha }^{\mathrm{pairs}}\), (d) the variance \(Var_{\alpha }\) of the traveled frequency of location pairs, (e) the covered distance \(d_{\alpha }^{\mathrm{loop}}\) of the maximum loop, (f) the total traveled distance \(d_{\alpha }^{\mathrm{total}}\), as a function of threshold T. The insets in each figure show the mean values of the corresponding metric under different threshold. The power-law exponents γ of the distributions of (g) the number of neighboring locations from each location, and (h) population flux between each two locations, in the real data and the shuffled data as a function of threshold T. In both (g) and (h), there is large difference between the exponents of the real and the shuffled data when the threshold T is small, and the difference becomes negligible when the threshold is large