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Using joint permutation entropy we address the issue of minimizing the cost of monitoring, while minimizing redundancy of the information content, of daily streamflow data recorded during the period 1989–2016 at twelve gauging stations on Brazos River, Texas, USA. While the conventional entropy measures take into account only the probability of occurrence of a given set of events, permutation entropy also takes into account local ordering of the sequential values, thus enriching the analysis. We find that the best cost efficiency is achieved by performing weekly measurements, in comparison with which daily measurements exhibit information redundancy, and monthly measurements imply information loss. We also find that the cumulative information redundancy of the twelve considered stations is over 10% for the observed period, and that the number of monitoring stations can be reduced by half bringing the cumulative redundancy level to less than 1%. [ABSTRACT FROM AUTHOR]

In this paper we investigated the influence of the construction of Sobradinho dam on daily streamflow of São Francisco river, Brazil, using permutation entropy method. We analyzed a long daily streamflow time series recorded during the period 1929–2010 encompassing the construction of Sobradinho dam between 1973 and 1979. We found that the original and deseasonalized streamflow time series are characterized by clear different complexity and entropy patterns before the construction of the dam; while, after it, their degree of randomness and complexity are nearly identical. Furthermore, investigating the oscillatory behavior of the entropy and complexity time variation, the periodicity of 3.67 years was identified, identical to one of the main periodicities revealed in the Multivariate ENSO Index (MEI). Such finding confirms the close relationship between streamflow dynamics and ENSO phenomenon. After the construction of the dam, the time variation of entropy and complexity changes almost abruptly toward stochastic regime characterized by higher entropy and lower complexity. Although the dam operations could be considered responsible for such abrupt dynamical change in the streamflow, we cannot exclude the presence of a co-induced ENSO effect; in fact, the analysis of MEI shows a strikingly similar and concomitant change in the long-term trend, identified by using the singular spectrum analysis. [ABSTRACT FROM AUTHOR]

Agricultural commodities are considered perhaps the most important commodities, as any abrupt increase in food prices has serious consequences on food security and welfare, especially in developing countries. In this work, we analyze predictability of Brazilian agricultural commodity prices during the period after 2007/2008 food crisis. We use information theory based method Complexity/Entropy causality plane (CECP) that was shown to be successful in the analysis of market efficiency and predictability. By estimating information quantifiers permutation entropy and statistical complexity, we associate to each commodity the position in CECP and compare their efficiency (lack of predictability) using the deviation from a random process. Coffee market shows highest efficiency (lowest predictability) while pork market shows lowest efficiency (highest predictability). By analyzing temporal evolution of commodities in the complexity–entropy causality plane, we observe that during the analyzed period (after 2007/2008 crisis) the efficiency of cotton, rice, and cattle markets increases, the soybeans market shows the decrease in efficiency until 2012, followed by the lower predictability and the increase of efficiency, while most commodities (8 out of total 12) exhibit relatively stable efficiency, indicating increased market integration in post-crisis period. [ABSTRACT FROM AUTHOR]

Digital assets termed cryptocurrencies are creating new paradigms for financial transactions as well as alternative means of capital. Despite their increasing relevance in financial situations, a complete understanding of the entire system remains lacking. Here the cryptocurrency market is treated as a complex system and analyzed using methods from statistical physics. The complexity–entropy causality plane (or CH plane) is employed in order to explore disorder and complexity in the space of cryptocurrencies. They are found to exist on distinct planar locations in the representation space, ranging from structured to stochastic-like behavior. The temporal trajectories of entropy and statistical complexity of prices vary drastically with position along the plane. Lastly cryptocurrencies appear to be characterized by ordinal patterns that represent strictly decreasing or increasing trends in price. The present analysis expands the understanding of and helps to quantify varying degrees of complexity in cryptocurrencies. • We map cryptocurrencies to the complexity–entropy causality plane. • We discover rather distinct degrees of complexity in the cryptocurrency space. • Their price behavior ranges from deterministic chaos to stochastic-like processes. • Most cryptocurrencies are characterized by downward or upward trends. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the performance of the 12 entropy-based features for the monitoring and detection of bearing faults. These entropy measures were proposed both in time, frequency and time–frequency domain. Probability mass function (PMF) was extracted from the time waveforms using four different methods: (i) via power spectral density, (ii) via ordinal pattern distribution, (iii) via wavelet packet tree and iv) ensemble empirical mode decomposition. Three different entropy measures were used in the article: (i) Shannon entropy, (ii) Rényi entropy and (iii) Jensen–Rényi divergence. A new bearing produces a vibration time series characterised by random noise without prominent periodic content. As soon as a fault develops, impulses are produced, what excites structural resonances generating a train of impulse responses. As defect grows, it becomes a distributed fault, and then no sharp impulses are generated but rather an amplitude modulated random noise signal. The proposed methodology has been applied to detect bearing faults by the analysis of two real bearing datasets, from run-to-failure experiments. Three bearings that presented different defects in the test (inner race fault, rolling elements fault and outer race fault) were analysed to validate the performance of the entropy-based features. The modified Z-score has been implemented and used as an index to detect changes of the entropy features. The results clearly demonstrate that the proposed approach represents a valuable non-parametric tool for early detection of anomalies in bearings vibration signals. Highlights • We study 12 entropy-based features for monitoring and detection of bearing faults. • The proposed methodology is tested on two real bearing vibration signal datasets. • Entropy is shown to be a valuable tool for early detection of anomalies in bearings. [ABSTRACT FROM AUTHOR]