  Symbolic methods of analysis are valuable tools for investigating complex
time-dependent signals. In particular, the ordinal method defines sequences of
symbols according to the ordering in which values appear in a time series. This
method has been shown to yield useful information, even when applied to signals
with large noise contamination. Here we use ordinal analysis to investigate the
transition between eyes closed (EC) and eyes open (EO) resting states. We
analyze two {EEG} datasets (with 71 and 109 healthy subjects) with different
recording conditions (sampling rates and the number of electrodes in the
scalp). Using as diagnostic tools the permutation entropy, the entropy computed
from symbolic transition probabilities, and an asymmetry coefficient (that
measures the asymmetry of the likelihood of the transitions between symbols) we
show that ordinal analysis applied to the raw data distinguishes the two brain
states. In both datasets, we find that the EO state is characterized by higher
entropies and lower asymmetry coefficient, as compared to the EC state. Our
results thus show that these diagnostic tools have the potential for detecting
and characterizing changes in time-evolving brain states.
