Catálogo de publicaciones - revistas

<jats:p>Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects, such as time series, networks, and images. Notably, not every divergence provides identical results when applied to the same problem. Therefore, it seems convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice, an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work, we choose the family of divergences known as the Burbea–Rao centroids (BRCs). For the mapping of the original time series into a symbolic sequence, we work with the ordinal pattern scheme. We apply our proposals to analyze simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen–Shannon divergence, besides the fact that it verifies some interesting formal properties.</jats:p>

<jats:p>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, that is, weighted differences of pattern frequencies. These contrasts are statistically independent and turn up as eigenvectors of a covariance matrix both in the independence model and the random walk model. The most important contrast is the turning rate. It can be used to evaluate sleep depth directly from EEG (electroencephalographic brain data). The paper discusses fluctuations of permutation entropy, statistical tests, and the need of new models for noises like EEG.</jats:p>

<jats:p>Discretizing a nonlinear time series enables us to calculate its statistics fast and rigorously. Before the turn of the century, the approach using partitions was dominant. In the last two decades, discretization via permutations has been developed to a powerful methodology, while recurrence plots have recently begun to be recognized as a method of discretization. In the meantime, horizontal visibility graphs have also been proposed to discretize time series. In this review, we summarize these methods and compare them from the viewpoint of symbolic dynamics, which is the right framework to study the symbolic representation of nonlinear time series and the inverse process: the symbolic reconstruction of dynamical systems. As we will show, symbolic dynamics is currently a very active research field with interesting applications.</jats:p>

<jats:p>Complex and networked dynamical systems characterize the time evolution of most of the natural and human-made world. The dimension of their state space, i.e., the number of (active) variables in such systems, arguably constitutes their most fundamental property yet is hard to access in general. Recent work [Haehne et al., Phys. Rev. Lett. 122, 158301 (2019)] introduced a method of inferring the state space dimension of a multi-dimensional networked system from repeatedly measuring time series of only some fraction of observed variables, while all other variables are hidden. Here, we show how time series observations of one single variable are mathematically sufficient for dimension inference. We reveal how successful inference in practice depends on numerical constraints of data evaluation and on experimental choices, in particular the sampling intervals and the total duration of observations. We illustrate robust inference for systems of up to N=10 to N=100 variables by evaluating time series observations of a single variable. We discuss how the faithfulness of the inference depends on the quality and quantity of collected data and formulate some general rules of thumb on how to approach the measurement of a given system.</jats:p>