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Nonlinear dynamics play an important role in the analysis of signals. A popular, readily interpretable nonlinear measure is Permutation Entropy. It has recently been extended for the analysis of graph signals, thus providing a framework for…

Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…

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…

A transmitted, unknown radar signal is observed at the receiver through more than one path in additive noise. The aim is to recover the waveform of the intercepted signal and to simultaneously estimate the direction of arrival (DOA). We…

Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…

Since Bandt and Pompe's seminal work, permutation entropy has been used in several applications and is now an essential tool for time series analysis. Beyond becoming a popular and successful technique, permutation entropy inspired a…

In 2002, in a seminal article, Christoph Bandt and Bernd Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as…

Objective: To characterize the irregularity of the spectrum of a signal, spectral entropy is a widely adopted measure. However, such a metric is invariant under any permutation of the estimations of the powers of individual frequency…

Order patterns apply well to many fields, because of minimal stationarity assumptions. Here we fix the methodology of patterns of length 3 by introducing an orthogonal system of four pattern contrasts. These contrasts are statistically…

Orthogonal matching pursuit~(OMP) is a commonly used greedy algorithm for recovering sparse signals from compressed measurements. In this paper, we introduce a variant of the OMP algorithm to reduce the complexity of reconstructing a class…

We propose to use the ordinal pattern transition (OPT) entropy measured at sentinel central nodes as a potential predictor of explosive transitions to synchronization in networks of various dynamical systems with increasing complexity. Our…

Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to…

We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…

Permutation Entropy ($PE$) is a powerful nonlinear analysis technique for univariate time series. Recently, Permutation Entropy for Graph signals ($PEG$) has been proposed to extend PE to data residing on irregular domains. However, $PEG$…

We introduce Ordinal Synchronization ($OS$) as a new measure to quantify synchronization between dynamical systems. $OS$ is calculated from the extraction of the ordinal patterns related to two time series, their transformation into…

Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a…

Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand…

Neurons encode and transmit information in spike sequences. However, despite the effort devoted to quantify their information content, little progress has been made in this regard. Here we use a nonlinear method of time-series analysis…

Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice…

We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric, objective, and the required data processing is parsimonious. Main ingredients are a…