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Section I

Section I. Complexity-Entropy Planes for Full Datasets. The CH Plane. Figure 1: SSX points are averages over 12 channels, all 3 directions, and ~40 shots for two helicity settings . LAPD points are averages over 25 runs at two positions. The full CH Plane for SSX .

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Section I

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  1. Section I Complexity-Entropy Planes for Full Datasets

  2. The CH Plane Figure 1: SSX points are averages over 12 channels, all 3 directions, and ~40 shots for two helicity settings. LAPD points are averages over 25 runs at two positions.

  3. The full CH Plane for SSX Figure 2: As for all diagrams here presented, n=5 was used. 15456 SSX points are plotted, corresponding to time series from 3 directions, 16 channels, 8 helicity settings, and ~40 runs per helicity.

  4. The SSX CH Plane, first 12 channels only Figure 3: 11592 SSX points are plotted, corresponding to time series from 3 directions, 12 channels, 8 helicity settings, and ~40 runs per helicity.

  5. The Full CH Plane for LAPD Figure 4: 775 LAPD points are plotted, corresponding to time series from 25 runs and 31 positions.

  6. Section II Helicity Dependence of SSX Complexity-Entropy Plane

  7. All SSX data for each helicity setting: unstuffed 0.1 mWb 0.25 mWb 0.5 mWb

  8. All SSX data for each helicity cont. 0.75mWb 1.0 mWb 1.25 mWb 1.5 mWb

  9. SSX CH Plane, averaged over shots (channel 1 of 16) Figure 5: Note that points represent the radial direction, plus signs theta, and x-marks z. The color scale represents helicity.

  10. SSX CH Plane, averaged over shots and directions (channel 1 of 16) Figure 6: The color scale again represents helicity. Note the loop executed in the right side of the plane as helicity is varied. The least entropic helicity setting (pale blue) appears to be 0.5mWb.

  11. SSX CH Plane, averaged over shots and directions (channel 6 of 16) Figure 7: The same looping behavior as in Figure 6 seems to occur for channel 6 data, although the loop is angled a little higher in the plane

  12. SSX CH Plane, averaged over shots and directions (channel 12 of 16) Figure 8: Channel 12 data seems to loop through an even higher complexity region of the CH plane. Once again, 0.5mWb has the lowest entropy point.

  13. Section III Complexity-Entropy Planes for Varied Embedding Delay

  14. The following two slides show SSX data up to channel 12 for various embedding delays. • While τ denotes use of the embedding delay as described in most of the literature, which effectively reduces the length of the analyzed series by a factor of τ, τ’ indicates that a delay analysis like that used for the increments method was applied. • So τ ’ analyzed series are kept significantly longer, only losing (n-1) τ ’ or so values. • Figure 3 (τ ’ = τ = 1) has been reproduced above to provide comparison with the diagrams to follow. • I was surprised to see that keeping more of the series actually lowered the overall complexity of SSX data, according to these diagrams.

  15. τ = 2 τ = 4 τ = 6 τ = 8

  16. τ ’ = 2 τ ’ = 4 τ ’ = 6 τ ’ = 8

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