Permutation relative entropy is proposed to quantify time irreversibility in our nonlinear dynamics analysis of electroencephalogram (EEG). Ordinal patterns in multi-dimension phase space of time series are symbolized, and the probabilistic divergences of all symmetric ordinal pairs are measured by relative entropy as time irreversibility. Analyzing multi-channel EEG from 18 healthy volunteers ...

Forbidden ordinal patterns are ordinal patterns (or ‘rank blocks’) that cannot appear in the orbits generated by a map taking values on a linearly ordered space, in which case we say that the map has forbidden patterns. Once a map has a forbidden pattern of a given length L0, it has forbidden patterns of any length L ≥ L0 and their number grows superexponentially with L. Using recent results on...

In this work, we apply ordinal analysis of time series to the characterisation of neuronal activity. Automatic event detection is performed by means of the so-called permutation entropy, along with the quantification of the relative cardinality of forbidden patterns. In addition, multivariate time series are characterised using the joint permutation entropy. In order to illustrate the suitabili...

We study global climate networks constructed by means of ordinal time series analysis. Climate interdependencies among the nodes are quantified by the mutual information, computed from time series of monthly-averaged surface air temperature anomalies, and from their symbolic ordinal representation (OP). This analysis allows identifying topological changes in the network when varying the time-in...

Sequential learning (SL) refers to the ability to learn the temporal and ordinal patterns of one’s environment. Whereas research on the learning of ordinal patterns is common, the learning of temporal patterns within sequential events has been far less studied. The current study examines the effects of synchronous and asynchronous temporal patterns on visual sequential learning. We hypothesize ...

Ordinal time series analysis is a new approach to the qualitative investigation of long and complex time series. The idea behind it is to transform a given time series into a series of ordinal patterns each describing the order relations between the present and a fixed number of equidistant past values at a given time. Here we consider ordinal pattern distributions and some measures derived fro...

For equidistant discretizations of fractional Brownian motion (fBm), the probabilities of ordinal patterns of order d = 2 are monotonically related to the Hurst parameter H. By plugging the sample relative frequency of those patterns indicating changes between up and down into the monotonic relation to H, one obtains the Zero Crossing (ZC) estimator of the Hurst parameter which has found consid...

In order to develop fast and robust methods for extracting qualitative information from non-linear time series, Bandt and Pompe have proposed to consider time series from the pure ordinal viewpoint. On the base of counting ordinal patterns, which describe the up-and-down in a time series, they have introduced the concept of permutation entropy for quantifying the complexity of a system behind a...