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Register a new userA novel entropy recurrence quantification analysis
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The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on the concept of information entropy, in which the probabilities are associated to microstates defined from the recurrence phase space. Recurrence properties can properly be studied using recurrence plots, a methodology based on binary matrices where trajec- tories in phase space of dynamical systems are evaluated against other embedded trajectory. Our novel entropy methodology has several advantages compared to the traditional recurrence entropy defined in the literature, namely, the correct evaluation of the chaoticity level of the signal, the weak dependence on parameters, correct evaluation of periodic time series properties and more sensitivity to noise level of time series. Furthermore, the new entropy quantifier developed in this manuscript also fixes inconsistent results of the traditional recurrence entropy concept, reproducing classical results with novel insights.
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Solar activity affects the whole heliosphere and near-Earth space environment. It has been reported in the literature that the mechanism responsible for the solar activity modulation behaves like a low-dimensional chaotic system. Studying these kind of physical systems and, in particular, their temporal evolution requires non-linear analysis methods. To this regard, in this work we apply the recurrence quantification analysis (RQA) to the study of two of the most commonly used solar cycle indicators; i.e. the series of the sunspots number (SSN), and the radio flux 10.7 cm, with the aim of identifying possible dynamical transitions in the system. A task which is particularly suited to the RQA. The outcome of this analysis reveals the presence of large fluctuations of two RQA measures; namely the determinism and the laminarity. In addition, large differences are also seen between the evolution of the RQA measures of the SSN and the radio flux. That suggests the presence of transitions in the dynamics underlying the solar activity. Besides it also shows and quantifies the different nature of these two solar indices. Furthermore, in order to check whether our results are affected by data artifacts, we have also applied the RQA to both the recently recalibrated SSN series and the previous one, unveiling the main differences between the two data sets. The results are discussed in light of the recent literature on the subject.
Recurrence Quantification Analysis (RQA) can help to detect significant events and phase transitions of a dynamical system, but choosing a suitable set of parameters is crucial for the success. From recurrence plots different RQA variables can be obtained and analysed. Currently, most of the methods for RQA radius optimisation are focusing on a single RQA variable. In this work we are proposing two new methods for radius optimisation that look for an optimum in the higher dimensional space of the RQA variables, therefore synchronously optimising across several variables. We illustrate our approach using two case studies: a well known Lorenz dynamical system, and a time-series obtained from monitoring energy consumption of a small enterprise. Our case studies show that both methods result in plausible values and can be used to analyse energy data.
In this work we explore the possibility of using Recurrence Quantification Analysis (RQA) in astronomical high-contrast imaging to statistically discriminate the signal of faint objects from speckle noise. To this end, we tested RQA on a sequence of high frame rate (1 kHz) images acquired with the SHARK-VIS forerunner at the Large Binocular Telescope. Our tests show promising results in terms of detection contrasts at angular separations as small as $50$ mas, especially when RQA is applied to a very short sequence of data ($2$ s). These results are discussed in light of possible science applications and with respect to other techniques like, for example, Angular Differential Imaging and Speckle-Free Imaging.
We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function, and an Inverse-Wishart process prior for the covariance function. This model-based approach can borrow strength from all functional data to increase the smoothing accuracy, as well as estimate the mean-covariance functions simultaneously. An option of approximating the Bayesian inference process using cubic B-spline basis functions is integrated in BFDA, which allows for efficiently dealing with high-dimensional functional data. Examples of using BFDA in various scenarios and conducting follow-up functional regression are provided. The advantages of BFDA include: (1) Simultaneously smooths multiple functional data and estimates the mean-covariance functions in a nonparametric way; (2) flexibly deals with sparse and high-dimensional functional data with stationary and nonstationary covariance functions, and without the requirement of common observation grids; (3) provides accurately smoothed functional data for follow-up analysis.
We compare the two basic ordinal patterns, i.e., the original and amplitude permutations, used to characterize vector structures. The original permutation consists of the indexes of reorganized values in the original vector. By contrast, the amplitude permutation comprises the positions of values in the reordered vector, and it directly reflects the temporal structure. To accurately convey the structural characteristics of vectors, we modify indexes of equal values in permutations to be the same as, for example, the smallest or largest indexes in each group of equalities. Overall, we clarify the relationship between the original and amplitude permutations. And the results have implications for time- and amplitude-symmetric vectors and will lead to further theoretical and experimental studies.
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