Ordinal methods: Concepts, applications, new developments, and challenges—In memory of Karsten Keller (1961–2022)

Amigó, José M.; Rosso, Osvaldo A.

doi:10.1063/5.0167263

Cited by 18 publications

(4 citation statements)

References 97 publications

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“…This method is based on the construction of a histogram of ordinal patterns. A brief description is given here, as it has been studied extensively, but the reader is referred to the following references for a formal explanation, simple examples, and similar applications (Bandt and Pompe, 2002 ; Jauregui et al, 2018 ; Pessa and Ribeiro, 2021 ; Zanin and Olivares, 2021 ; Amigó and Rosso, 2023 ; Guisande et al, 2023 ).…”

Section: Methodsmentioning

confidence: 99%

Rényi entropy-complexity causality space: a novel neurocomputational tool for detecting scale-free features in EEG/iEEG data

Guisande,

Montani

2024

Front. Comput. Neurosci.

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Scale-free brain activity, linked with learning, the integration of different time scales, and the formation of mental models, is correlated with a metastable cognitive basis. The spectral slope, a key aspect of scale-free dynamics, was proposed as a potential indicator to distinguish between different sleep stages. Studies suggest that brain networks maintain a consistent scale-free structure across wakefulness, anesthesia, and recovery. Although differences in anesthetic sensitivity between the sexes are recognized, these variations are not evident in clinical electroencephalographic recordings of the cortex. Recently, changes in the slope of the power law exponent of neural activity were found to correlate with changes in Rényi entropy, an extended concept of Shannon's information entropy. These findings establish quantifiers as a promising tool for the study of scale-free dynamics in the brain. Our study presents a novel visual representation called the Rényi entropy-complexity causality space, which encapsulates complexity, permutation entropy, and the Rényi parameter q. The main goal of this study is to define this space for classical dynamical systems within theoretical bounds. In addition, the study aims to investigate how well different time series mimicking scale-free activity can be discriminated. Finally, this tool is used to detect dynamic features in intracranial electroencephalography (iEEG) signals. To achieve these goals, the study implementse the Bandt and Pompe method for ordinal patterns. In this process, each signal is associated with a probability distribution, and the causal measures of Rényi entropy and complexity are computed based on the parameter q. This method is a valuable tool for analyzing simulated time series. It effectively distinguishes elements of correlated noise and provides a straightforward means of examining differences in behaviors, characteristics, and classifications. For the iEEG experimental data, the REM state showed a greater number of significant sex-based differences, while the supramarginal gyrus region showed the most variation across different modes and analyzes. Exploring scale-free brain activity with this framework could provide valuable insights into cognition and neurological disorders. The results may have implications for understanding differences in brain function between the sexes and their possible relevance to neurological disorders.

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Section: Methodsmentioning

confidence: 99%

Rényi entropy-complexity causality space: a novel neurocomputational tool for detecting scale-free features in EEG/iEEG data

Guisande,

Montani

2024

Front. Comput. Neurosci.

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“…The main reasons behind this success are its wide applicability and the fact that the BP discretization method is naturally able to capture the presence of underlying temporal correlations in the dynamics of the process that generates the time series. Interested readers are referred to the reviews [35][36][37][38][39][40] for further details. The BP recipe for symbolizing a time series can be briefly summarized as follows.…”

Section: Permutation Jensen-shannon Distancementioning

confidence: 99%

Revisiting the Characterization of Resting Brain Dynamics with the Permutation Jensen–Shannon Distance

Zunino

2024

Entropy

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Taking into account the complexity of the human brain dynamics, the appropriate characterization of any brain state is a challenge not easily met. Actually, even the discrimination of simple behavioral tasks, such as resting with eyes closed or eyes open, represents an intricate problem and many efforts have been and are being made to overcome it. In this work, the aforementioned issue is carefully addressed by performing multiscale analyses of electroencephalogram records with the permutation Jensen–Shannon distance. The influence that linear and nonlinear temporal correlations have on the discrimination is unveiled. Results obtained lead to significant conclusions that help to achieve an improved distinction between these resting brain states.

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“…Such robustness is one of the reasons why the Bandt & Pompe symbolization approach has become a trendy and successful way of analyzing time series 1 . The marginal 3 analysis of ordinal patterns proceeds by computing the histogram of proportions q of the patterns observed in π:…”

Section: Introductionmentioning

confidence: 99%

“…The conditional probabilities are: (1,6), (2,4), (2,6), (5, 1), (5, 3), (6, 1), (6, 3)}, 0.20 if (i, j) ∈ {(3, 2), (3,4), (4, 2), (4, 5)}, 0.15 if (i, j) ∈ {(1, 2), (1, 5), (2, 2), (2, 5), (3, 1), (3,3), (3,4), (3,6), (4, 1), (4, 3), (4, 4), (4, 6), (5, 1), (5, 5), (6, 1), (6, 5)}, 0.05 if (i, j) ∈ {(1, 1), (1, 3), (2, 1), (2, 3), (5,4), (5,6), (6,4), (6,6)}.…”

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confidence: 99%

The asymptotic distribution of the permutation entropy

Rey,

Frery,

Gambini

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Ordinal patterns serve as a robust symbolic transformation technique, enabling the unveiling of latent dynamics within time series data. This methodology involves constructing histograms of patterns, followed by the calculation of both entropy and statistical complexity—an avenue yet to be fully understood in terms of its statistical properties. While asymptotic results can be derived by assuming a multinomial distribution for histogram proportions, the challenge emerges from the non-independence present in the sequence of ordinal patterns. Consequently, the direct application of the multinomial assumption is questionable. This study focuses on the computation of the asymptotic distribution of permutation entropy, considering the inherent patterns’ correlation structure. Furthermore, the research delves into a comparative analysis, pitting this distribution against the entropy derived from a multinomial law. We present simulation algorithms for sampling time series with prescribed histograms of patterns and transition probabilities between them. Through this analysis, we better understand the intricacies of ordinal patterns and their statistical attributes.

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Ordinal methods: Concepts, applications, new developments, and challenges—In memory of Karsten Keller (1961–2022)

Cited by 18 publications

References 97 publications

Rényi entropy-complexity causality space: a novel neurocomputational tool for detecting scale-free features in EEG/iEEG data

Rényi entropy-complexity causality space: a novel neurocomputational tool for detecting scale-free features in EEG/iEEG data

Revisiting the Characterization of Resting Brain Dynamics with the Permutation Jensen–Shannon Distance

The asymptotic distribution of the permutation entropy

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