Figures and data
Task Description.
The large arrow at the top displays the course of the experiment. Both video blocks comprised 54 video clips (2-10 seconds), and after each video clip, participants had 30 seconds to rate their emotional experience based on five emotions. Both blocks also had a baseline emotion rating before the videos started. Participants underwent either a distancing (emotion regulation) or a relaxation (control) intervention between the two video blocks. After the second block of video clips, participants completed three standardized psychological questionnaires measuring symptoms of depression (PHQ-9) and anxiety (GAD-7) and emotion regulation difficulty (DERS-18). PHQ-9: Patient Health Questionnaire. GAD-7: Generalized Anxiety Disorder Assessment. DERS-18: Difficulties in Emotion Regulation Scale.
Conceptual mapping between formal control theory definitions and their psychological interpretations within this study.
Dynamical System and Controllability.
A) shows a graph visualization of the linear dynamical model, including external inputs (ut; emotional video clips). zt describes the latent (unobserved) emotion states evolving based on a Markov process and directly mapping onto the acquired emotion ratings xt. B) shows the trajectories of a two-dimensional system (ratings of “amused” and “anxious”) starting from a randomly chosen initial point without external inputs. Whereas anxiety decays independently of amusement, amusement is influenced by anxiety and thus, the trajectory of amusement is more complex and does not simply exponentially decay to zero. However, the more anxiety decays, the more the influence of anxiety on amusement decreases; and both variables converge towards zero. C) shows the trajectory of both emotion ratings plotted against each other. The blue x indicates the starting point. D) displays the independently evolving trajectories of the transformed variables 
Emotion Ratings.
A) The heatmap shows for each emotion eliciting video category the ratings from Cowen and Keltner (2017) averaged over the two emotion categories of interest (left y-axis). The coloured lines with dots report the emotion ratings from our experiment for each emotion after watching a video clip averaged over participants before the intervention occurred for the randomized and matched video sequences separately (right y-axis). B) shows the change between the rating (t) after a certain video and the previous rating (t - 1) averaged over participants and all trials, including videos from the same video category. Subplot B has the same emotion categories as subplot A (left label of A). The bar represents the mean of the change in ratings, the black line shows the standard deviation, and the * indicates a significant difference from zero. The black frame shows the dominant emotion for the specific emotion category (the emotion intended to be elicited by watching videos from that category). The unframed bars show that videos from a specific emotion category also affected non-dominant emotions. C) shows the autocorrelation coefficient averaged over participants for five lags for each emotion. The line indicates the mean and the shaded area standard deviation over participants. D) shows the mean and standard deviation of the cross-correlation coefficients between emotion time-series averaged over participants. Significance *≤ 0.5, **≤ 0.1, ***≤ 0.001, ****≤ 0.0001
Model Evaluation.
A) shows the differences in Bayesian Information Criterion (BIC) scores for all models tested compared to the most parsimonious model (blue star). All models were separately fitted to individuals’ emotion rating time-series over the whole experiment. The left y-axis shows the number of free parameters for each model. The most parsimonious model included a full dynamics matrix, full input weight matrix and diagonal noise covariances for observation and process noise. B) shows differences in BIC scores of models, allowing for parameters to change after the intervention. While in the control group, a model in which all parameters stayed the same best explained the data (grey star), in the distancing group dynamics matrix, input weights and noise covariances differed in the most parsimonious model (purple star). C) shows empirical (blue) and simulated data (orange) from two randomly selected participants. One of those was allocated to the control intervention and one to the distancing intervention. We simulated data from a linear state space model using the parameter estimates derived from fitting the Kalman Filter to individuals’ emotion rating time-series. The vertical grey dashed line indicates that a video was shown at that time-point which stems from the category aiming to elicit that specific emotion. Blue shading indicates the period before, and green shading after the intervention. Data was simulated based on different parameter sets before and after the intervention.
Intervention Effects.
A) shows the average ratings separated in before and after the intervention and for both intervention groups. Purple shades refer to the distancing group and grey shades to the control group. The boxes show the quartiles of the ratings, while the whiskers extend to show the rest of the distribution. The horizontal bars in the boxes indicate the median, and the green triangles the mean across participants. B) shows mean and standard deviation for the elements of the input weight matrix (C matrix) averaged across participants before the intervention occurred. C) shows the effect of distancing on the input weight matrix (C matrix), which is computed as the mean change (after minus before intervention) divided by its standard deviation for each matrix element only in participants allocated to the distancing intervention. D) The boxplot presents the quartiles of the dominant eigenvalues of the dynamics matrix, while the whiskers display the rest of the distribution. E) The boxplot illustrates the quartiles of the dominant singular values of the controllability matrix, with the whiskers showing the rest of the distribution. F) The polar plots show the left singular vector direction of the dominant singular value separated between participants in the distancing (purple shades) and the control (grey shades) group before (left) and after (right) intervention. Significance *≤ 0.05, **≤ 0.01, ***≤ 0.001, ****≤ 0.0001. We report the significance after Bonferroni correction for testing five different emotions. Interaction effects (time × group) were significant for mean emotion ratings (F(5,208) = 2.6,p = 0.026) and the most controllable direction (F(5,200) = 2.5,p = 0.03), panels A) and F) respectively.
The mean rating (blue bars) and standard deviations (black line) of 20 video clips in each category.
Video clips were chosen based on the highest ratings and lowest entropies. A specific emotion-eliciting video category predominantly affected a focused cluster of related emotions.
Heatmap showing the intensity of ratings extracted from Cowen and Keltner (2017) for the chosen video sequences.
Video clips elicited the intended emotions in a relatively specific manner. The table located on the right displays the category to which each video belongs.
A) shows the recoverability of the dynamics matrix based on the correlation between entries of the known and estimated dynamics matrix. B) shows the absolute dot product of the known and estimated first eigenvector of the dynamics matrix. C) demonstrates the recoverability of the input weights by computing the average correlation between entries of the known and estimated input weight matrix. D) shows the absolute dot product of the known and estimated first unit vector of the controllability matrix. Blue bars indicate the mean averaged across 100 simulated datasets and the black errorbars indicate the standard deviation.
Parameter recovery quality with variance decomposition.
Values shown as mean (across-subject SD) [within-subject mean SD]. Mean represents average recovery quality across subjects (each subject averaged over 100 simulations). Across-subject SD captures between-subject heterogeneity. Within-subject mean SD captures average within-subject variability across simulations. N = 104 subjects per period.
Parameter recovery analysis for Kalman filter model across 104 subjects and 2 time periods.
A) Per-subject recovery quality showing mean Pearson correlation ± SD across subjects for each parameter (100 simulations per subject). Dashed lines indicate minimum acceptable (0.5, green) and target (0.7, orange) correlation thresholds. B) Scatter plot of true versus recovered dominant eigenvalue magnitudes (N=20’800 observations). C) Distribution of eigenvector recovery quality using Pearson correlation for dominant eigenvector (blue) and dominant left singular vector (red). D) Variance decomposition showing across-subject variability (red) and within-subject variability (blue, across simulations) separately. E) Scatter plot of true versus recovered dominant singular values (N=20’800 observations). F) Eigenvector recovery using dot product metric.
Recovery of group differences via Hotelling T2 tests across 100 parameter recovery simulations.
Values report mean T2± SD, percentage of simulations reaching significance thresholds, and median p-value.
A) The bar chart displays estimated model frequencies across the participant cohort for the concatenated time-series. The results indicate a competitiveness between the model featuring full input weights and the comprehensive model incorporating both full dynamics and full input weights. B) A detailed view of the expected frequencies for models allowed to change after the intervention. Asterisks indicate significant differences in model preference between the distancing (purple) and control (grey) interventions. C) The difference in expected frequencies (distancing – control) with 95% bootstrap confidence intervals. The distancing intervention significantly decreased the frequency of the ‘same parameters’ model (−0.33) and increased the preference for complex models where noise, dynamics, and input weights differ (+0.20).
Hottelling T2-test comparing the mean and variance of simulated ratings between the distancing and control intervention group.
A) shows that by solely altering A before and after the intervention while keeping C constant, we could reproduce the difference in mean ratings. B) illustrates that altering only the C while maintaining the same A before and after the intervention also allowed us to replicate the difference in mean ratings.
PHQ-9=Patient Health Questionnaire, 9-item version total score (possible range 0–27).
PHQ-9 scores of 5, 10, 15, and 20 represented mild, moderate, moderately severe, and severe depression, respectively. GAD-7=Generalised Anxiety Disorder Assessment, 7-item version total score (possible range 0–21). GAD-7 scores of 5, 10, and 15 are taken as the cut-off points for mild, moderate and severe anxiety, respectively. DERS-18=Difficulties in Emotion Regulation Scale, 18-item version total score (possible range 0–72).
The change of emotion ratings from t – 1 to t (where t indicates the rating time after the video from a specific video category was shown) was greater for the video’s target emotion than other emotions, but all videos have broad, complex effects.
One-sided two-sample t-tests were conducted to test whether the dominant emotion was higher than non-dominant emotions and two-sided one-sample t-tests were performed to test whether the dominant emotion was different from zero.
Mean (M) and standard deviation (SD) of the autocorrelation coefficients of emotion time series averaged over participants and their statistical difference from zero is reported.
Comparison of dynamics matrices (A) across groups and time.
The figure illustrates the estimated emotional dynamics pre (Row 1) and post (Row 2) intervention, and the difference (post - pre; Row 3) for both the distancing (Column 1) and control (Column 2) group.
Comparison of input matrices (C) across groups and time.
The figure illustrates the estimated emotional dynamics pre (Row 1) and post (Row 2) intervention, and the difference (post - pre; Row 3) for both the distancing (Column 1) and control (Column 2) group.
This table reports mean (M) and standard deviation (SD) of the cross-correlation coefficients between emotion time series averaged over participants and their statistical difference from zero.
Statistical comparisons of emotion ratings before and after intervention.
For group comparisons, Mann-Whitney U tests were used; for within-group comparisons (before vs. after), Wilcoxon Signed-Rank tests were used.
statistical comparisons of the 1st eigenvector of dynamics and the 1st unit vector of controllability, group comparisons (t = 0, t = 1) used Mann-Whitney U tests; within-group comparisons (before vs. after) used Wilcoxon Signed-Rank tests.
This table reports the outcomes of GLMs used to deduce connections between symptoms (PHQ-9, GAD-7, and DERS-18 total scores) and emotion ratings at baseline (t0), as well as emotion ratings averaged (M) and variation (VAR) over the first video block (t1) and the second video block (t2).
We ran separate GLMs to infer i) the associations between emotion summary statistics (DV) and symptoms (IV) controlling for the intervention group, and ii) an interaction effect between symptoms (IV) and intervention group. All variables are z-scored, except for the group variable which is coded 0 for the control group and 1 for the distancing group. Bonferroni correction: 
This table reports links between single first loadings derived from the dynamics and the controllability matrix and the DERS-18 total score.
We ran separate GLMs to infer i) the associations between first eigen-/singular value loadings (DV) and symptoms (IV) controlling for the intervention group, and ii) an interaction effect between symptoms (IV) and intervention group. All variables are z-scored, except for the group variable which is coded 0 for the control group and 1 for the distancing group. Bonferroni correction: 
This table reports the relationships between the dominant eigenvalue of the dynamics and the dominant singular value controllability matrix and the DERS-18 total score.
We ran separate GLMs to infer i) the associations between first eigen-/singular values (DV) and symptoms (IV) controlling for the intervention group, and ii) an interaction effect between symptoms (IV) and intervention group. All variables are z-scored, except for the group variable which is coded 0 for the control group and 1 for the distancing group.
