Zipf's frequency-rank distribution, however, does not bear any information about the way in which words are ordered in the linguistic sequence, and would be exactly the same for any random permutation of all the words of the sequence.
This result was exactly the same using fixed effect and random effects approaches.
First of all, since the baselines of each study were not exactly the same and the methods to generate random sequence were not clearly clarified in most trials, the selection biases cannot be controlled efficiently.
The essence of the LoC-approach is the use of all input parameters (treated as random variables) with exactly the same Probability of Exceedance (PoE).
It is important to remember that, in the present study, antlions in the Learning and Random treatments received exactly the same amount of food, at exactly the same time, each treatment day.
In all cases we observed that, besides the above principal component initialization, also different random initializations resulted in exactly the same prototypes up to a possibly reversed order.
In the random PPI network, all proteins had exactly the same connectivity as in the original PPI network and the choice of their interaction partners was random.
Thus, we would not expect the estimates for the GEE and the random-effects logistic regression to be exactly the same.
Since retrotransposition is thought to be more or less random with respect to the region of insertion, insertions at exactly the same location appear to be unlikely.
Shifting to a random choice of 100 genes (bottom left panel) we can observe exactly the same pattern displayed by the entire genome basis.
