Figure 1.
An illustration of the concept of recurrence plots, using the Lorenz system (a well-known 3-dimensional non-linear system - reproduced here from [68]).
a) The Lorenz attractor: an example trajectory of the Lorenz system represented in 3-dimensional phase space. b) The recurrence plot for this trajectory. Both axes represent time. Looking along the x axis, we can follow the system's evolution. If the system's position in phase space at is closely approached at
, we place a dot at coordinates
. The positions at
and
need not be exactly the same, but they must be close to within a tolerance
which we set to be very small. The recurrence plot thus shows all time points when the system returns very close to a previous state; each dot in the graph represents a revisit, and we can read the two visiting times from the x and y axes. Note that recurrence plots are symmetric. Code for reproducing these figures can be found at http://people.physik.hu-berlin.de/schinkel/timely/html/index.html.
Figure 2.
Quiet stance sway path for a single representative subject.
The figure shows sway with eyes open (red) and eyes closed (blue) over a 60 second period. It should be pointed out that, according to traditional conventions, negative y values represent forwards postural sway.
Table 1.
Means and standard deviations for seated vection.
Figure 3.
Ellipse fits for eyes open compared to eyes closed conditions for another representative subject.
The figure shows sway with eyes open (red) and eyes closed (blue) over a 60 second period. The area ratio was calculated as the ratio of eyes-open to eyes-closed ellipse areas. Code for these calculations can be found at http://dx.doi.org/10.6084/m9.figshare.1126648.
Figure 4.
Correlations between vection measures and sway area ratios (log transformed).
(a–c) Expanding vection; (d–f) Contracting vection. (a, d) Verbal ratings. (b, e) Throttle maximum values. (c,f) Latency.
Table 2.
Correlations between VEPRs and vection.
Figure 5.
Correlations between vection measures and visually-evoked postural responses.
The VEPR was measured as the mean position difference (forward or backward) between a period of optic flow (expanding or contracting) and the preceding period. Top: verbal ratings. Middle: Throttle maximum values. Bottom: Latency. Vection for expanding stimuli is plotted on the right, and for contracting on the left.
Figure 6.
Representative recurrence plots for eyes-open and eyes-closed conditions for two individuals.
a) Eyes-open for an individual who experienced strong vection. b) Eyes-closed for the same individual c) Eyes-open for an individual who experienced weak vection d) Eyes-closed for the same individual.
Figure 7.
Correlations between vection measures and the difference between % recurrence for the quiet-stance eyes open and eyes closed, as measured by RQA.
The percentage of recurrence was measured using the recurrence quantification Maltab toolbox, downloaded from http:/nuweb.neu.edu/cjhasson. This means that individuals who experienced stronger vection showed a greater percentage of recurrences with eyes closed than with eyes open, while the reverse was true for those who experienced weaker vection.
Table 3.
Correlations between percent recurrence (RQA) and vection.