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.

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.

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.

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.

Is Bach's brain a Markov chain? Recurrence quantification to assess Markov order for short, symbolic, musical compositions.

It is rarely possible to precisely characterise the system underlying a series of observations. Hypothesis testing, which involves assessing simple assumptions about driving mechanisms, provides hope that we can at least rule out certain possibilities regarding the nature of the system. Unfortunately, the brevity, nonstationarity, and symbolic nature of certain time series of interest undermines traditional hypothesis tests.

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.