PMC4753305_01
(A) Evolution of the items "pressure," "perturbation," "hope," "suicide risk," "wish to live," and "wish to die." The numbers on the x-axis correspond to days of monitoring. (B) The evolution of the dynamic complexity corresponding to these items (calculated in a moving window of 7 data points [=days]). The two additional curves (light blue) represent a 95 and 99% confidence interval, calculation based on 21 data points. The numbers on the x-axis correspond to days of monitoring. (C) Recurrence Plots of the time series. Each of the items was embedded into a three-dimensional phase space with delay 1 (t-1, t-2, t-3). Radius: 20 (item 10/Perturbation), 18 (item 11/Hope), 13 (item 14/Suicide risk), 25 (item 15/Wish to live), 25 (item 16/Wish to die). Periods of instability or transients have reduced recurrence, i.e., very few dots, and correspond to increased dynamic complexity (middle column), and vice versa, periods with distinct recurrent signature correspond to a restricted dynamic complexity.
fpsyg-07-00130-g001.jpg
PMC4753305_01_fpsyg-07-00130-g001.jpg
F1
To identify statistical significance of the current dynamic complexity, a dynamic 95 and 99% confidence interval is applied, which is based on the distribution of the last 21 complexity values (see Figure 1). According to a selected threshold (radius of a hyper-cycle), neighbors which represent similar (recurring) patterns are marked by a dot in the time x time plot (Figure 1).
(A) Critical Incidents: the numbers on the x-axis correspond to days of monitoring. (B) Dynamic Complexity of item # 14 (blue line) and the confidence interval (light blue line). Increases of dynamic complexity indicate periods of critical instabilities in a change process. The dynamic complexity is calculated in a gliding window with window width of 7 points. The numbers on the x-axis correspond to days of monitoring. (C) Complexity Resonance Diagram: each row represents one item of the Salzburg Suicide Process Questionnaire. Light gray, dark gray, or black dots indicate three significance levels of the dynamic complexity (p < 0.050, p < 0.025, p < 0.010, respectively). The Complexity Resonance Diagram indicates periods of significantly increased complexities getting in resonance to each other, and by this, appear at the same time (vertical structures). Usually, those periods can be seen as the critical instabilities of a process. In this Complexity Resonance Diagram the two critical periods of the 3 months of monitoring are marked below. The top histogram summarizes dynamic complexities across items. (D) Synchronization: degree of intercorrelation between items. The numbers on the x-axis correspond to days of monitoring.
fpsyg-07-00130-g002.jpg
PMC4753305_01_fpsyg-07-00130-g002.jpg
F2
In addition, the evolving dynamic complexity of each item can be visualized by the Complexity Resonance Diagram (see Figure 2).