Science Advances

Supplementary Materials

This PDF file includes:

  • Data, context, and chronology of the events analyzed
  • Methods used in the analysis
  • Sensibility analysis of the parametrization
  • Validation of results (I): Time series randomization
  • Validation of results (II): Unfiltered Twitter stream
  • Validation of results (III): Synthetic time series generation
  • Table S1. List of keywords used to find tweets related to the Outono Brasileiro.
  • Fig. S1. Schematic representation of the algorithm used to gather geographical coordinates of the Hollywood movie release and the Google-Motorola acquisition data sets.
  • Fig. S2. Sample order pattern for m = 3.
  • Fig. S3. Schematic view of the sliding window scheme.
  • Fig. S4. Evolution of the order parameter θ for thresholded (green) and raw (red) T† matrices.
  • Fig. S5. Dependence of τ with the sliding window size ω, considering the Spanish 15M protest.
  • Fig. S6. Normalized directionality index for each geographical unit in the 15M data set for different ω.
  • Fig. S7. Fraction of false nearest neighbors as a function of m for the Spanish data set and the Madrid time series.
  • Fig. S8. Normalized directionality index for each geographical unit in the 15M data set for different m.
  • Fig. S9. Characteristic time scale t for four data sets at alternative geographical aggregation levels.
  • Fig. S10. Normalized directionality index for four data sets at alternative geographical aggregation levels.
  • Fig. S11. Behavior of θ as a function of time for four data sets at alternative geographical aggregation levels.
  • Fig. S12. Average total amount of STE for some Δt (top panel) and time scale profile τ (bottom panel) for 15M data set amplitude adjusted Fourier transform surrogates (50 randomizations).
  • Fig. S13. Behavior of θ as a function of time for 15M and Outono Brasileiro data sets randomized surrogates.
  • Fig. S14. Average total amount of STE for some Δt (top panel) and time scale profile τ (bottom panel) for 15M data set constrained surrogates (20 randomizations).
  • Fig. S15. Evolution of τ as a function of time.
  • Fig. S16. Thresholded T† matrices corresponding to different moments in the Twitter unfiltered data set.
  • Fig. S17. Raw time series for Twitter unfiltered stream for &Delat;t = 600 s and Δt = 45 s (left and right, respectively).
  • Fig. S18. Evolution of two nonlinear systems under four changing scenarios: from dynamic independence (β = 0) to strong asymmetric coupling (β = 20.0).
  • Part 1. Minimalist example: Disentangling volume and time scales (Δt).
  • Part 2. Nonlinear Lorentz oscillators: Time scales, volume, and dynamical coupling.
  • References (36–58)

Download PDF

Files in this Data Supplement: