ordinal patterns
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Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1655
Author(s):  
Philippe Ravier ◽  
Antonio Dávalos ◽  
Meryem Jabloun ◽  
Olivier Buttelli

Surface electromyography (sEMG) is a valuable technique that helps provide functional and structural information about the electric activity of muscles. As sEMG measures output of complex living systems characterized by multiscale and nonlinear behaviors, Multiscale Permutation Entropy (MPE) is a suitable tool for capturing useful information from the ordinal patterns of sEMG time series. In a previous work, a theoretical comparison in terms of bias and variance of two MPE variants—namely, the refined composite MPE (rcMPE) and the refined composite downsampling (rcDPE), was addressed. In the current paper, we assess the superiority of rcDPE over MPE and rcMPE, when applied to real sEMG signals. Moreover, we demonstrate the capacity of rcDPE in quantifying fatigue levels by using sEMG data recorded during a fatiguing exercise. The processing of four consecutive temporal segments, during biceps brachii exercise maintained at 70% of maximal voluntary contraction until exhaustion, shows that the 10th-scale of rcDPE was capable of better differentiation of the fatigue segments. This scale actually brings the raw sEMG data, initially sampled at 10 kHz, to the specific 0–500 Hz sEMG spectral band of interest, which finally reveals the inner complexity of the data. This study promotes good practices in the use of MPE complexity measures on real data.


Author(s):  
Isadora Cardoso-Pereira ◽  
João B. Borges ◽  
Pedro H. Barros ◽  
Antonio F. Loureiro ◽  
Osvaldo A. Rosso ◽  
...  

Author(s):  
Christian H. Weiß ◽  
Manuel Ruiz Marín ◽  
Karsten Keller ◽  
Mariano Matilla-García

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1097
Author(s):  
Tim Gutjahr ◽  
Karsten Keller

Ordinal patterns classifying real vectors according to the order relations between their components are an interesting basic concept for determining the complexity of a measure-preserving dynamical system. In particular, as shown by C. Bandt, G. Keller and B. Pompe, the permutation entropy based on the probability distributions of such patterns is equal to Kolmogorov–Sinai entropy in simple one-dimensional systems. The general reason for this is that, roughly speaking, the system of ordinal patterns obtained for a real-valued “measuring arrangement” has high potential for separating orbits. Starting from a slightly different approach of A. Antoniouk, K. Keller and S. Maksymenko, we discuss the generalizations of ordinal patterns providing enough separation to determine the Kolmogorov–Sinai entropy. For defining these generalized ordinal patterns, the idea is to substitute the basic binary relation ≤ on the real numbers by another binary relation. Generalizing the former results of I. Stolz and K. Keller, we establish conditions that the binary relation and the dynamical system have to fulfill so that the obtained generalized ordinal patterns can be used for estimating the Kolmogorov–Sinai entropy.


2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Massimiliano Zanin ◽  
Felipe Olivares

AbstractOne of the most important aspects of time series is their degree of stochasticity vs. chaoticity. Since the discovery of chaotic maps, many algorithms have been proposed to discriminate between these two alternatives and assess their prevalence in real-world time series. Approaches based on the combination of “permutation patterns” with different metrics provide a more complete picture of a time series’ nature, and are especially useful to tackle pathological chaotic maps. Here, we provide a review of such approaches, their theoretical foundations, and their application to discrete time series and real-world problems. We compare their performance using a set of representative noisy chaotic maps, evaluate their applicability through their respective computational cost, and discuss their limitations.


2021 ◽  
Author(s):  
Isadora Cardoso P. Silva ◽  
Joao B. Borges ◽  
Pedro H. Barros ◽  
Antonio F. Loureiro ◽  
Osvaldo A. Rosso ◽  
...  

Abstract Analyzing people mobility and identifying the transportation mode used by them is essential for cities that want to reduce traffic jams and travel time between their points, thus helping to improve the quality of life of citizens. Mining this type of data, however, faces several complexities due to its unique properties. In this work, we propose the use of Information Theory quantifiers retained from the Ordinal Patterns (OP) transformation, for transportation mode identification. As an initial exploration, our results show that OP satisfactorily characterizes the trajectories. Moreover, in this scenario, the characteristics of OP transformation can be advantageous, such as its simplicity, robustness, and speed.


AIP Advances ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 045122
Author(s):  
Zelin Zhang ◽  
Mingbo Zhang ◽  
Yufeng Chen ◽  
Zhengtao Xiang ◽  
Jinyu Xu ◽  
...  

2021 ◽  
Vol 31 (2) ◽  
pp. 023104
Author(s):  
Ivan Gunther ◽  
Arjendu K. Pattanayak ◽  
Andrés Aragoneses

2021 ◽  
Vol 8 (1) ◽  
pp. 201011
Author(s):  
Yair Neuman ◽  
Yochai Cohen ◽  
Boaz Tamir

Prediction in natural environments is a challenging task, and there is a lack of clarity around how a myopic organism can make short-term predictions given limited data availability and cognitive resources. In this context, we may ask what kind of resources are available to the organism to help it address the challenge of short-term prediction within its own cognitive limits. We point to one potentially important resource: ordinal patterns , which are extensively used in physics but not in the study of cognitive processes. We explain the potential importance of ordinal patterns for short-term prediction, and how natural constraints imposed through (i) ordinal pattern types, (ii) their transition probabilities and (iii) their irreversibility signature may support short-term prediction. Having tested these ideas on a massive dataset of Bitcoin prices representing a highly fluctuating environment, we provide preliminary empirical support showing how organisms characterized by bounded rationality may generate short-term predictions by relying on ordinal patterns.


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