Estimation of entropies and dimensions by nonlinear symbolic time series analysis

CEPS: An Open Access MATLAB Graphical User Interface (GUI) for the Analysis of Complexity and Entropy in Physiological Signals

BACKGROUND

We developed CEPS as an open access MATLAB^® GUI (graphical user interface) for the analysis of Complexity and Entropy in Physiological Signals (CEPS), and demonstrate its use with an example data set that shows the effects of paced breathing (PB) on variability of heart, pulse and respiration rates. CEPS is also sufficiently adaptable to be used for other time series physiological data such as EEG (electroencephalography), postural sway or temperature measurements.

METHODS

Data were collected from a convenience sample of nine healthy adults in a pilot for a larger study investigating the effects on vagal tone of breathing paced at various different rates, part of a development programme for a home training stress reduction system.

RESULTS

The current version of CEPS focuses on those complexity and entropy measures that appear most frequently in the literature, together with some recently introduced entropy measures which may have advantages over those that are more established. Ten methods of estimating data complexity are currently included, and some 28 entropy measures. The GUI also includes a section for data pre-processing and standard ancillary methods to enable parameter estimation of embedding dimension m and time delay τ ('tau') where required. The software is freely available under version 3 of the GNU Lesser General Public License (LGPLv3) for non-commercial users. CEPS can be downloaded from Bitbucket. In our illustration on PB, most complexity and entropy measures decreased significantly in response to breathing at 7 breaths per minute, differentiating more clearly than conventional linear, time- and frequency-domain measures between breathing states. In contrast, Higuchi fractal dimension increased during paced breathing.

CONCLUSIONS

We have developed CEPS software as a physiological data visualiser able to integrate state of the art techniques. The interface is designed for clinical research and has a structure designed for integrating new tools. The aim is to strengthen collaboration between clinicians and the biomedical community, as demonstrated here by using CEPS to analyse various physiological responses to paced breathing.

Ordinal partition transition network based complexity measures for inferring coupling direction and delay from time series

It has been demonstrated that the construction of ordinal partition transition networks (OPTNs) from time series provides a prospective approach to improve our understanding of the underlying dynamical system. In this work, we introduce a suite of OPTN based complexity measures to infer the coupling direction between two dynamical systems from pairs of time series. For several examples of coupled stochastic processes, we demonstrate that our approach is able to successfully identify interaction delays of both unidirectional and bidirectional coupling configurations. Moreover, we show that the causal interaction between two coupled chaotic Hénon maps can be captured by the OPTN based complexity measures for a broad range of coupling strengths before the onset of synchronization. Finally, we apply our method to two real-world observational climate time series, disclosing the interaction delays underlying the temperature records from two distinct stations in Oxford and Vienna. Our results suggest that ordinal partition transition networks can be used as complementary tools for causal inference tasks and provide insights into the potentials and theoretical foundations of time series networks.

An analysis of high-frequency cryptocurrencies prices dynamics using permutation-information-theory quantifiers

This paper discusses the dynamics of intraday prices of 12 cryptocurrencies during the past months' boom and bust. The importance of this study lies in the extended coverage of the cryptoworld, accounting for more than 90% of the total daily turnover. By using the complexity-entropy causality plane, we could discriminate three different dynamics in the data set. Whereas most of the cryptocurrencies follow a similar pattern, there are two currencies (ETC and ETH) that exhibit a more persistent stochastic dynamics, and two other currencies (DASH and XEM) whose behavior is closer to a random walk. Consequently, similar financial assets, using blockchain technology, are differentiated by market participants.

Permutation entropy and statistical complexity quantifier of nonstationarity effect in the vertical velocity records

How the nonstationarity in the atmosphere turbulent vertical velocity series affects its organization degree of multiscale structures is quantified by permutation entropy (PE) and complexity-entropy causality plane (CECP), and marked PE and CECP differences are detected between the nonstationary and stationary series. We find that the value of PE is lower in the nonstationary vertical velocity series than the stationary counterparts. Both types of series locate near the region of the higher complexity value in the CECP as chaotic systems, but the PE is smaller and the complexity degree is larger in the nonstationary series than the stationary with smaller time delays. Due to the close relationship between PE and the multiscale Shannon entropy, we show that the PE and CECP can be also taken as an indicator to quantify the different organization degrees of the multiscale structures existing between the stationary and nonstationary surface vertical velocity records.

Permutation-information-theory approach to unveil delay dynamics from time-series analysis

In this paper an approach to identify delay phenomena from time series is developed. We show that it is possible to perform a reliable time delay identification by using quantifiers derived from information theory, more precisely, permutation entropy and permutation statistical complexity. These quantifiers show clear extrema when the embedding delay τ of the symbolic reconstruction matches the characteristic time delay τ(S) of the system. Numerical data originating from a time delay system based on the well-known Mackey-Glass equations operating in the chaotic regime were used as test beds. We show that our method is straightforward to apply and robust to additive observational and dynamical noise. Moreover, we find that the identification of the time delay is even more efficient in a noise environment. Our permutation approach is also able to recover the time delay in systems with low feedback rate or high nonlinearity.

Electrophysiological changes of cardiac function during antidepressant treatment

Some antidepressant agents can cause electrophysiological changes of cardiac function leading to ventricular arrhythmias and sudden death. However, antidepressants have also protective effects on the heart through their capacity to modulate cardiac autonomic-mediated physiological responses. Heart rate variability and QTc length are two strictly linked parameters that allow us to appreciate the effects of different drugs on cardiac physiology. Heart rate variability reflects functioning of the autonomic nervous system and possibly also regulation by the limbic system. Autonomic regulation of cardiac activity influences also cardiac repolarization and QT length, both directly and via its effects on heart rate. In this review we present the methodologies adopted to study the effect of antidepressant drugs on QT length and heart rate variability and we summarize data on electrophysiological changes related to antidepressant treatment. Clinical implications for the choice of different antidepressants in different clinical populations are discussed.

On the control of chaotic systems via symbolic time series analysis

Symbolic analysis of time series is extended to systems with inputs, in order to obtain input/output symbolic models to be used for control policy design. For that, the notion of symbolic word is broadened to possibly include past input values. Then, a model is derived in the form of a controlled Markov chain, i.e., transition probabilities are conditioned on the control value. The quality of alternative models with different word length and alphabet size is assessed by means of an indicator based on Shannon entropy. A control problem is formulated, with the goal of confining the system output in a smaller domain with respect to that of the uncontrolled case. Solving this problem (by means of a suitable numerical method) yields the relevant control policy, as well as an estimate of the probability distribution of the output of the controlled system. Three examples of application (based on the analysis of time series synthetically generated by the logistic map, the Lorenz system, and an epidemiological model) are presented and used to discuss the features and limitations of the method.