Topological data analysis of the synchronization of a network of Rössler chaotic electronic oscillators.

Synchronization study allows a better understanding of the exchange of information among systems. In this work, we study experimental data recorded from a set of Rössler-like chaotic electronic oscillators arranged in a complex network, where the interactions between the oscillators are given in terms of a connectivity matrix, and their intensity is controlled by a global coupling parameter. We use the zero and one persistent homology groups to characterize the point clouds obtained from the signals recorded in pairs of oscillators. We show that the normalized persistent entropy (NPE) allows us to characterize the effective coupling between pairs of oscillators because it tends to increase with the coupling strength and to decrease with the distance between the oscillators. We also observed that pairs of oscillators that have similar degrees and are nearest neighbors tend to have higher NPE values than pairs with different degrees. However, large variability is found in the NPE values. Comparing the NPE behavior with that of the phase-locking value (PLV, commonly used to evaluate the synchronization of phase oscillators), we find that for large enough coupling, PLV only displays a monotonic increase, while NPE shows a richer behavior that captures variations in the behavior of the oscillators. This is due to the fact that PLV only captures coupling-induced phase changes, while NPE also captures amplitude changes. Moreover, when we consider the same network but with Kuramoto phase oscillators, we also find that NPE captures the transition to synchronization (as it increases with the coupling strength), and it also decreases with the distance between the oscillators. Therefore, we propose NPE as a data analysis technique to try to differentiate pairs of oscillators that have strong effective coupling because they are first or near neighbors, from those that have weaker coupling because they are distant neighbors.

On entropy research analysis: cross-disciplinary knowledge transfer.

Our aim is to illustrate how the thermodynamics-based concept of entropy has spread across different areas of knowledge by analyzing the distribution of papers, citations and the use of words related to entropy in the predefined Scopus categories. To achieve this, we analyze the Scopus papers database related to entropy research during the last 20 years, collecting 750 K research papers which directly contain or mention the word entropy. First, some well-recognized works which introduced novel entropy-related definitions are monitored. Then we compare the hierarchical structure which emerges for the different cases of association, which can be in terms of citations among papers, classification of papers in categories or key words in abstracts and titles. Our study allowed us to evaluate, to some extent, the utility and versatility of concepts such as entropy to permeate in different areas of science. Furthermore, the use of specific terms (key words) in titles and abstracts provided a useful way to account for the interaction between areas in the category research space.

Scaling differences of heartbeat excursions between wake and sleep periods.

We study the statistical properties of excursions in heart interbeat time series. An excursion is defined as the time employed by a walker to return to its mean value. We consider the homeostatic property of the heartbeat dynamics as a departing point to characterize the dynamics of excursions in beat-to-beat fluctuations. Scaling properties of excursions during wake and sleep periods from two groups are compared: 16 healthy subjects and 11 patients with congestive heart failure (CHF). We find that the cumulative distributions of excursions for both groups follow stretched exponential functions given by g(τ)~e(-aτ(b)) with different fitting parameters a and b, leading to different decaying rates. Our results show that the average characteristic scale associated with the excursion distributions is greater for healthy data compared to CHF patients whereas sleep-wake transitions are more significant for healthy data. Next, we explore changes in the distributions of excursions when considering (i) a shifted mean value to define an excursion and (ii) the sum of the kth excursion successor. Besides, the presence of temporal correlations in the excursions sequences is evaluated by means of the detrended fluctuation analysis. We observe the presence of long-range correlations for healthy subjects, whereas for the CHF group, correlations are described by two regimes; over short scales the fluctuations are close to uncorrelated noise, and for large scales the fluctuations reveal long-range correlations. Finally, we apply a stability analysis of excursions based on the Allan variance which reveals that healthy dynamics is more stable than heart failure excursions.

Simple model of the aging effect in heart interbeat time series.

In this work, we calculate the fractal dimension of heart interbeat time series of some healthy young and elderly individuals. As has been found by means of other methods (detrended fluctuation and spectral analyses), we also find that interbeat series of healthy young subjects can be characterized by only one scaling exponent and a crossover behavior in it is observed with aging. By means of a zoom over the hinges of the crossover region, interesting effects of aging are presented. Our results with real interbeat time series are reasonably reproduced by using a simple model based on combinations of noisy first-order autoregressive series.