On detecting dynamical regime change using a transformation cost metric between persistent homology diagrams.

This work outlines a pipeline for time series analysis that incorporates a measure of similarity not previously applied between homological summaries. Specifically, the well-established, but disparate, methods of persistent homology and TrAnsformation Cost Time Series (TACTS) are combined to provide a metric for tracking dynamics via changing homological features. TACTS allows subtle changes in dynamics to be accounted for, gives a quantitative output that can be directly interpreted, and is tunable to provide several complementary perspectives simultaneously. Our method is demonstrated first with known dynamical systems and then with a real-world electrocardiogram dataset. This paper highlights inadequacies in existing persistent homology metrics and describes circumstances where TACTS can be more sensitive and better suited to detecting a variety of regime changes.

The reliability of recurrence network analysis is influenced by the observability properties of the recorded time series.

Recurrence network analysis (RNA) is a remarkable technique for the detection of dynamical transitions in experimental applications. However, in practical experiments, often only a scalar time series is recorded. This requires the state-space reconstruction from this single time series which, as established by embedding and observability theory, is shown to be hampered if the recorded variable conveys poor observability. In this work, we investigate how RNA metrics are impacted by the observability properties of the recorded time series. Following the framework of Zou et al. [Chaos 20, 043130 (2010)], we use the Rössler and Duffing-Ueda systems as benchmark models for our study. It is shown that usually RNA metrics perform badly with variables of poor observability as for recurrence quantification analysis. An exception is the clustering coefficient, which is rather robust to observability issues. Along with its efficacy to detect dynamical transitions, it is shown to be an efficient tool for RNA-especially when no prior information of the variable observability is available.

Consistency in echo-state networks.

Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency of a driven nonlinear system to its input. We apply this concept to echo-state networks, which are an artificial-neural network version of reservoir computing. Through a replica test, we measure the consistency levels of the high-dimensional response, yielding a comprehensive portrait of the echo-state property.

On system behaviour using complex networks of a compression algorithm.

We construct complex networks of scalar time series using a data compression algorithm. The structure and statistics of the resulting networks can be used to help characterize complex systems, and one property, in particular, appears to be a useful discriminating statistic in surrogate data hypothesis tests. We demonstrate these ideas on systems with known dynamical behaviour and also show that our approach is capable of identifying behavioural transitions within electroencephalogram recordings as well as changes due to a bifurcation parameter of a chaotic system. The technique we propose is dependent on a coarse grained quantization of the original time series and therefore provides potential for a spatial scale-dependent characterization of the data. Finally the method is as computationally efficient as the underlying compression algorithm and provides a compression of the salient features of long time series.

Characterisation of neonatal cardiac dynamics using ordinal partition network.

The maturation of the autonomic nervous system (ANS) starts in the gestation period and it is completed after birth in a variable time, reaching its peak in adulthood. However, the development of ANS maturation is not entirely understood in newborns. Clinically, the ANS condition is evaluated with monitoring of gestational age, Apgar score, heart rate, and by quantification of heart rate variability using linear methods. Few researchers have addressed this problem from the perspective nonlinear data analysis. This paper proposes a new data-driven methodology using nonlinear time series analysis, based on complex networks, to classify ANS conditions in newborns. We map 74 time series given by RR intervals from premature and full-term newborns to ordinal partition networks and use complexity quantifiers to discriminate the dynamical process present in both conditions. We obtain three complexity quantifiers (permutation, conditional, and global node entropies) using network mappings from forward and reverse directions, and considering different time lags and embedding dimensions. The results indicate that time asymmetry is present in the data of both groups and the complexity quantifiers can differentiate the groups analysed. We show that the conditional and global node entropies are sensitive for detecting subtle differences between the neonates, particularly for small embedding dimensions (m < 7). This study reinforces the assessment of nonlinear techniques for RR interval time series analysis. Graphical Abstract.