Example of an experiment that requires a t-1 random walk (E = 23).

<p>A) Improvement of the modeling by going from t-3 via t-2 to t-1 random walks. B) for each experiment and its surrogate set. Red dots: experiments. Blue: dots: mean values of t-3 random walks; bars: one standard deviation. Green: mean values of t-3, t-2, t-1 random walks; bars: one standard deviation. Some blue dots and bars are obscured by red and green dots and green bars. One can clearly see that the green dots approximate the experimental red dots much better than the blue dots.</p

Effect of random-walk grammar on closed cycles.

<p>A) Histogram of the cumulative number of closed cycles across all data files from a) in a t-3 random walk model of the data, b) in t-3, t-2, t-1 random walk model according to the data’s classification,. The experimental data (“exp”) with 468 cycles fits well only into the t-3, t-2, t-1 model. Histograms are based on 100 simulations for each experimental file. B) Distribution of t-3, of t-2, of t-1 classifications a) across all experiments, b) across all experiments with females, c) across all experiments with normal males, where the absolute numbers are exhibited.</p

Comparison of experimental files to grammar-generated files.

<p>A) For each experimental symbol string, strings with the identical symbol probabilities are generated using a t-3 random walk. B) For each string (observed and simulated), is calculated. Thick red lines: experiments, thin lines: t-3 random walks. numbers the experiment. C) Red dots: for the experimental files. Blue dots: Mean values of from t-3 random walks. Bars: One standard deviation. For two thirds of all files, the t-3 model fails.</p