Erratum: Collective behavior in the North Rhine-Westphalia motorway network (2021 J. Stat. Mech. 123401)

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We found a programming error that affected our numerical computations.The rows of the data matrix G were wrongly reordered in a particular step.Luckily, this error only has an impact on the details, but has neither an effect on the main results nor on the conclusions.A closer look even reveals that the collective behavior that we identified comes out clearer now, particular for the central and the parallel regions.In this erratum, we present new figures 2-11 that replace the corresponding ones in our original publication, with the same numbering.* Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Figure 2 .
Figure 2. Empirical eigenvalue density ρ(λ) in the bulk region for the six cases, compared with the eigenvalue density of a purely random correlation matrix, ρ rm (λ) simulated and Marchenko-Pastur distribution ρ MP (λ).

Figure 3 .
Figure 3. Full empirical eigenvalue densities ρ(λ) for the six cases, where the left and right red dash lines correspond to the minimal and maximal eigenvalues Λ ± in the Marchenko-Pastur distribution ρ MP (λ), respectively.

Figure 4 .
Figure 4. Dependence of the ratio 1/(I n N) of significant participants to all participants for the eigenvalues Λ n in the six cases.The markers filled with red color indicate the ratios of significant participants for the fifth eigenvalues.The gray areas correspond to the ranges of random eigenvalues.

Figure 5 .
Figure 5. Geographic distributions of the significant sections for the largest eigenvalues in the three workday cases.For the information and the data source of the base map, refer to figure 1.

Figure 6 .
Figure 6.Geographic distributions of the significant sections for the largest eigenvalues in the three holiday cases.For the information and the data source of the base map, refer to figure 1.

Figure 7 .
Figure7.The distributions of components of eigenvectors corresponding to the bulks of small eigenvalues between Λ − and Λ + , the fifth eigenvalues Λ 5th max , the second eigenvalues Λ 2nd max and the largest eigenvalues Λ max (shown in each column) in six cases (shown in each row).The empirical distributions of the significant participants are highlighted with black color.In each case, the empirical distribution of the bulk eigenvalues is fitted by a random distribution N (μ bulk , σ bulk ) with a red line.The other distributions in the same case are all compared with this distribution N (μ bulk , σ bulk ).The histograms are all normalized to one.

Figure 8 .
Figure 8.The distributions of components of eigenvectors corresponding to the largest eigenvalues during different time periods (shown in each column) in one day.The empirical distributions of the significant participants are highlighted with black color.In each case (shown in each row), the empirical distribution are all compared with the random distribution N (μ bulk , σ bulk ).The histograms are all normalized to one.

Figure 9 .Figure 10 .Figure 11 .
Figure 9.The distributions of correlation components C max,kl corresponding to the largest eigenvalues for six cases (shown in each row) during three time periods (shown in each column) in one day.

Table 1 .
Parameters for the first and the fifth largest eigenvalues in each case. in the text are also required, which we list in the following table.Erratum: Collective behavior in the North Rhine-Westphalia motorway network(2021 J. Stat.Mech.123401) https://doi.org/10.1088/1742-5468/ac8c90