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25 pages, 2800 KiB

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Algorithmic Approaches for Assessing Multiscale Irreversibility in Time Series: Review and Comparison

by Massimiliano Zanin and David Papo

Entropy 2025, 27(2), 126; https://doi.org/10.3390/e27020126 - 25 Jan 2025

Cited by 1 | Viewed by 830

Many physical and biological phenomena are characterized by time asymmetry, and are referred to as irreversible. Time-reversal symmetry breaking is in fact the hallmark of systems operating away from equilibrium and reflects the power dissipated by driving the system away from it. Time asymmetry may manifest in a wide range of time scales; quantifying irreversibility in such systems thus requires methods capable of detecting time asymmetry in a multiscale fashion. In this contribution we review the main algorithmic solutions that have been proposed to detect time irreversibility, and evaluate their performance and limitations when used in a multiscale context using several well-known synthetic dynamical systems. While a few of them have a general applicability, most tests yield conflicting results on the same data, stressing that a “one size fits all” solution is still to be achieved. We conclude presenting some guidelines for the interested practitioner, as well as general considerations on the meaning of multiscale time irreversibility. Full article

(This article belongs to the Section Entropy Reviews)

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33 pages, 1495 KiB

Open AccessEditor’s ChoiceArticle

Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison

by Massimiliano Zanin and David Papo

Entropy 2021, 23(11), 1474; https://doi.org/10.3390/e23111474 - 8 Nov 2021

Cited by 27 | Viewed by 4375

Abstract

The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that “one size does not fit all”, as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues. Full article

(This article belongs to the Special Issue Entropy and Irreversibility in Biological Systems)

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12 pages, 1060 KiB

Open AccessArticle

Endoscopist’s Judgment Is as Useful as Risk Scores for Predicting Outcome in Peptic Ulcer Bleeding: A Multicenter Study

by Enric Brullet, Pilar Garcia-Iglesias, Xavier Calvet, Michel Papo, Montserrat Planella, Albert Pardo, Félix Junquera, Silvia Montoliu, Raquel Ballester, Eva Martinez-Bauer, David Suarez and Rafel Campo

J. Clin. Med. 2020, 9(2), 408; https://doi.org/10.3390/jcm9020408 - 3 Feb 2020

Cited by 10 | Viewed by 2684

Abstract

Background: Guidelines recommend using prognostic scales for risk stratification in patients with non-variceal upper gastrointestinal bleeding. It remains unclear whether risk scores offer greater accuracy than clinical evaluation. Objective: Compare the diagnostic accuracy of the endoscopist’s judgment against different risk-scoring systems (Rockall, Glasgow–Blatchford, Baylor and the Cedars–Sinai scores) for predicting outcomes in peptic ulcer bleeding (PUB). Methods: Between February 2006 and April 2010 we prospectively recruited 401 patients with peptic ulcer bleeding; 225 received endoscopic treatment. The endoscopist recorded his/her subjective assessment (“endoscopist judgment”) of the risk of rebleeding and death immediately after endoscopy for each patient. Independent evaluators calculated the different scores. Area under the receiver-operating-characteristics (ROC) curve, sensitivity, specificity, positive and negative predictive values were calculated for rebleeding and mortality. Results: The areas under ROC curve of the endoscopist’s clinical judgment for rebleeding (0.67–0.75) and mortality (0.84–0.9) were similar or even superior to the different risk scores in both the whole group and in patients receiving endoscopic therapy. Conclusions: The accuracy of the currently available risk scores for predicting rebleeding and mortality in PUB patients was moderate and not superior to the endoscopist’s judgment. More precise prognostic scales are needed. Full article

(This article belongs to the Special Issue New Trends and Advances in Non-Variceal Gastrointestinal Bleeding)

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15 pages, 534 KiB

Open AccessArticle

Assessing Time Series Reversibility through Permutation Patterns

by Massimiliano Zanin, Alejandro Rodríguez-González, Ernestina Menasalvas Ruiz and David Papo

Entropy 2018, 20(9), 665; https://doi.org/10.3390/e20090665 - 3 Sep 2018

Cited by 40 | Viewed by 6003

Abstract

Time irreversibility, i.e., the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here, we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation. Full article

(This article belongs to the Section Statistical Physics)

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14 pages, 21583 KiB

Open AccessArticle

Characterizing Motif Dynamics of Electric Brain Activity Using Symbolic Analysis

by Massimiliano Zanin and David Papo

Entropy 2014, 16(11), 5654-5667; https://doi.org/10.3390/e16115654 - 27 Oct 2014

Cited by 1 | Viewed by 5874

Abstract

Motifs are small recurring circuits of interactions which constitute the backbone of networked systems. Characterizing motif dynamics is therefore key to understanding the functioning of such systems. Here we propose a method to define and quantify the temporal variability and time scales of electroencephalogram (EEG) motifs of resting brain activity. Given a triplet of EEG sensors, links between them are calculated by means of linear correlation; each pattern of links (i.e., each motif) is then associated to a symbol, and its appearance frequency is analyzed by means of Shannon entropy. Our results show that each motif becomes observable with different coupling thresholds and evolves at its own time scale, with fronto-temporal sensors emerging at high thresholds and changing at fast time scales, and parietal ones at low thresholds and changing at slower rates. Finally, while motif dynamics differed across individuals, for each subject, it showed robustness across experimental conditions, indicating that it could represent an individual dynamical signature. Full article

(This article belongs to the Special Issue Entropy and Electroencephalography)

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13 pages, 556 KiB

Open AccessArticle

Knowledge Discovery in Spectral Data by Means of Complex Networks

by Massimiliano Zanin, David Papo, José Luis González Solís, Juan Carlos Martínez Espinosa, Claudio Frausto-Reyes, Pascual Palomares Anda, Ricardo Sevilla-Escoboza, Rider Jaimes-Reategui, Stefano Boccaletti, Ernestina Menasalvas and Pedro Sousa

Metabolites 2013, 3(1), 155-167; https://doi.org/10.3390/metabo3010155 - 11 Mar 2013

Cited by 7 | Viewed by 6562

Abstract

In the last decade, complex networks have widely been applied to the study of many natural and man-made systems, and to the extraction of meaningful information from the interaction structures created by genes and proteins. Nevertheless, less attention has been devoted to metabonomics, due to the lack of a natural network representation of spectral data. Here we define a technique for reconstructing networks from spectral data sets, where nodes represent spectral bins, and pairs of them are connected when their intensities follow a pattern associated with a disease. The structural analysis of the resulting network can then be used to feed standard data-mining algorithms, for instance for the classification of new (unlabeled) subjects. Furthermore, we show how the structure of the network is resilient to the presence of external additive noise, and how it can be used to extract relevant knowledge about the development of the disease. Full article

(This article belongs to the Special Issue Data Processing in Metabolomics)

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25 pages, 365 KiB

Open AccessArticle

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

by Massimiliano Zanin, Luciano Zunino, Osvaldo A. Rosso and David Papo

Entropy 2012, 14(8), 1553-1577; https://doi.org/10.3390/e14081553 - 23 Aug 2012

Cited by 538 | Viewed by 28542

Abstract

Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems. Full article

(This article belongs to the Special Issue Concepts of Entropy and Their Applications)

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