PMC

Estimation of conditional entropy (left panel) and mutual information (right panel) for empirical codon substitution matrix P_ECM. A slower information loss for reading frames −2 is observed due to a protection of the protein-coding reading frame +1.

Estimated conditional entropy and effective measure complexity. The left six panels (A–G) shows the estimated conditional entropy for different movement types. Up to order 4 the conditional entropy is estimated from empirical frequencies (blue dots). The asymptote (black line) is estimated from LZ complexity. The red dots show a parametric interpolation of conditional entropies according to Equation 9. The gray areas indicate the integrated excess entropies that yield the effective measure complexity shown in the right panel (H). The different movement types included self-generated patterns (P), letter drawings (L), self-paced random motion (R1), random motion during pursuit (R2), and artificial rhythmic (AS) and random motions (AR with uniform distribution and AF with empirical first order frequency).

Conditional entropy for different movement types estimated from empirical frequencies depending on the length of the history. The different movement types included self-generated patterns (P), letter drawings (L), self-paced random motion (R1), random motion during pursuit (R2) and artificial rhythmic (AS) and random motions (AR with uniform distribution and AF with empirical first order frequency). The lines show means over subjects and the gray bands show standard errors.

ePE (a,b) and empirical conditional entropy of ordinal patterns (c,d) for the logistic map and its iterates in dependence on the pattern order d: Left side pictures (a,c) show results based on the naïve simulation and right side pictures (b,d) on the advanced simulation, each based on iterates. For comparison, in (a,b) the upper bound of the ePE () for d was added (blue curves).