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30 pages, 21914 KiB

Open AccessArticle

Turbulent Flow in Street Canyons: A Complexity Approach

by Csanád Árpád Hubay, Bálint Papp and Tamás Kalmár-Nagy

Entropy 2025, 27(5), 488; https://doi.org/10.3390/e27050488 (registering DOI) - 30 Apr 2025

Velocity measurements and simulations in an idealized urban environment were studied, focusing on turbulent flow over street canyons. Time series of fluctuating velocities were considered as marked point processes, and the distribution of mean residence times was characterized using a lognormal fit. The [...] Read more.

Velocity measurements and simulations in an idealized urban environment were studied, focusing on turbulent flow over street canyons. Time series of fluctuating velocities were considered as marked point processes, and the distribution of mean residence times was characterized using a lognormal fit. The quadrant method was applied to transform time series into symbolic sequences, enabling the investigation of their information content. By analyzing word frequency and normalized entropy levels, we compared measured and simulated sequences with periodic symbol sequences with and without noise. Our results indicate that noisy periodic sequences exhibit entropy distributions qualitatively similar to those of the measured and simulated data. Surrogate sequences generated using first-, and higher-order Markov statistics also displayed similarity. Higher-order Markov chains provide a more accurate representation of the information content of velocity fluctuation series. These findings contribute to the comparison of experimental and simulation techniques in the investigation of turbulence. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

16 pages, 3473 KiB

Open AccessArticle

Information Theory Quantifiers in Cryptocurrency Time Series Analysis

by Micaela Suriano, Leonidas Facundo Caram, Cesar Caiafa, Hernán Daniel Merlino and Osvaldo Anibal Rosso

Entropy 2025, 27(4), 450; https://doi.org/10.3390/e27040450 - 21 Apr 2025

Viewed by 260

Abstract

This paper investigates the temporal evolution of cryptocurrency time series using information measures such as complexity, entropy, and Fisher information. The main objective is to differentiate between various levels of randomness and chaos. The methodology was applied to 176 daily closing price time [...] Read more.

This paper investigates the temporal evolution of cryptocurrency time series using information measures such as complexity, entropy, and Fisher information. The main objective is to differentiate between various levels of randomness and chaos. The methodology was applied to 176 daily closing price time series of different cryptocurrencies, from October 2015 to October 2024, with more than 30 days of data and not completely null. Complexity–entropy causality plane (CECP) analysis reveals that daily cryptocurrency series with lengths of two years or less exhibit chaotic behavior, while those longer than two years display stochastic behavior. Most longer series resemble colored noise, with the parameter k varying between 0 and 2. Additionally, Natural Language Processing (NLP) analysis identified the most relevant terms in each white paper, facilitating a clustering method that resulted in four distinct clusters. However, no significant characteristics were found across these clusters in terms of the dynamics of the time series. This finding challenges the assumption that project narratives dictate market behavior. For this reason, investment recommendations should prioritize real-time informational metrics over whitepaper content. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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31 pages, 12545 KiB

Open AccessArticle

Complexity Analysis of Environmental Time Series

by Holger Lange and Michael Hauhs

Entropy 2025, 27(4), 381; https://doi.org/10.3390/e27040381 - 3 Apr 2025

Viewed by 288

Abstract

Small, forested catchments are prototypes of terrestrial ecosystems and have been studied in several disciplines of environmental science over several decades. Time series of water and matter fluxes and nutrient concentrations from these systems exhibit a bewildering diversity of spatiotemporal patterns, indicating the [...] Read more.

Small, forested catchments are prototypes of terrestrial ecosystems and have been studied in several disciplines of environmental science over several decades. Time series of water and matter fluxes and nutrient concentrations from these systems exhibit a bewildering diversity of spatiotemporal patterns, indicating the intricate nature of processes acting on a large range of time scales. Nonlinear dynamics is an obvious framework to investigate catchment time series. We analyzed selected long-term data from three headwater catchments in the Bramke valley, Harz mountains, Lower Saxony in Germany at common biweekly resolution for the period 1991 to 2023. For every time series, we performed gap filling, detrending, and removal of the annual cycle using singular system analysis (SSA), and then calculated metrics based on ordinal pattern statistics: the permutation entropy, permutation complexity, and Fisher information, as well as their generalized versions (q-entropy and α-entropy). Further, the position of each variable in Tarnopolski diagrams is displayed and compared to reference stochastic processes, like fractional Brownian motion, fractional Gaussian noise, and β noise. Still another way of distinguishing deterministic chaos and structured noise, and quantifying the latter, is provided by the complexity from ordinal pattern positioned slopes (COPPS). We also constructed horizontal visibility graphs and estimated the exponent of the decay of the degree distribution. Taken together, the analyses create a characterization of the dynamics of these systems which can be scrutinized for universality, either across variables or between the three geographically very close catchments. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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14 pages, 8227 KiB

Open AccessArticle

Exploring Word-Adjacency Networks with Multifractal Time Series Analysis Techniques

by Jakub Dec, Michał Dolina, Stanisław Drożdż, Robert Kluszczyński, Jarosław Kwapień and Tomasz Stanisz

Entropy 2025, 27(4), 356; https://doi.org/10.3390/e27040356 - 28 Mar 2025

Viewed by 248

Abstract

A novel method of exploring linguistic networks is introduced by mapping word-adjacency networks to time series and applying multifractal analysis techniques. This approach captures the complex structural patterns of language by encoding network properties—such as clustering coefficients and node degrees—into temporal sequences. Using [...] Read more.

A novel method of exploring linguistic networks is introduced by mapping word-adjacency networks to time series and applying multifractal analysis techniques. This approach captures the complex structural patterns of language by encoding network properties—such as clustering coefficients and node degrees—into temporal sequences. Using Alice’s Adventures in Wonderland by Lewis Carroll as a case study, both traditional word-adjacency networks and extended versions that incorporate punctuation are examined. The results indicate that the time series derived from clustering coefficients, when following the natural reading order, exhibits multifractal characteristics, revealing inherent complexity in textual organization. Statistical validation confirms that observed multifractal properties arise from genuine correlations rather than from spurious effects. Extending this analysis by taking into account punctuation equally with words, however, changes the nature of the global scaling to a more convolved form that is not describable by a uniform multifractal. An analogous analysis based on the node degrees does not show such rich behaviors, however. These findings reveal a new perspective for quantitative linguistics and network science, providing a deeper understanding of the interplay between text structure and complex systems. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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14 pages, 678 KiB

Open AccessArticle

Sustainability of a Three-Species Predator–Prey Model in Tumor-Immune Dynamics with Periodic Treatment

by Avan Al-Saffar and Eun-jin Kim

Entropy 2025, 27(3), 264; https://doi.org/10.3390/e27030264 - 3 Mar 2025

Viewed by 586

Abstract

Using a tumor-immune growth model, we investigate how immunotherapy affects its dynamical characteristics. Specifically, we extend the prey–predator model of tumor cells and immune cells by including periodic immunotherapy, the nonlinear damping of cancer cells, and the dynamics of a healthy cell population, [...] Read more.

Using a tumor-immune growth model, we investigate how immunotherapy affects its dynamical characteristics. Specifically, we extend the prey–predator model of tumor cells and immune cells by including periodic immunotherapy, the nonlinear damping of cancer cells, and the dynamics of a healthy cell population, and investigate the effects of the model parameters. The ideal value of immunotherapy, which promotes the growth of immune (and healthy) cells while contributing to the elimination or control of the cancer cells, is determined by using Fisher information as a measure of variability throughout our study. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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18 pages, 921 KiB

Open AccessArticle

Irreversibility and Energy Transfer at Non-MHD Scales in a Magnetospheric Current Disruption Event

by Giuseppe Consolini and Paola De Michelis

Entropy 2025, 27(3), 260; https://doi.org/10.3390/e27030260 - 1 Mar 2025

Viewed by 499

Abstract

Irreversibility and the processes occurring at ion and sub-ion scales are key challenges in understanding energy dissipation in non-collisional space plasmas. Recent advances have significantly improved the characterization of irreversibility and energy transfer across scales in turbulent fluid-like media, using high-order correlation functions [...] Read more.

Irreversibility and the processes occurring at ion and sub-ion scales are key challenges in understanding energy dissipation in non-collisional space plasmas. Recent advances have significantly improved the characterization of irreversibility and energy transfer across scales in turbulent fluid-like media, using high-order correlation functions and testing the validity of certain fluctuation relations. In this study, we explore irreversibility at non-MHD scales during a magnetospheric current disruption event. Our approach involves analyzing the asymmetric correlation function, assessing the validity of a fluctuation relation, and investigating delayed coupling between different scales to reveal evidence of a cascading mechanism. The results clearly demonstrate the irreversible nature of fluctuations at ion and sub-ion scales. Additionally, we provide potential evidence for an energy cascading mechanism occurring over short time delays. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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18 pages, 1508 KiB

Open AccessArticle

Evaluating Methods for Detrending Time Series Using Ordinal Patterns, with an Application to Air Transport Delays

by Felipe Olivares, F. Javier Marín-Rodríguez, Kishor Acharya and Massimiliano Zanin

Entropy 2025, 27(3), 230; https://doi.org/10.3390/e27030230 - 23 Feb 2025

Viewed by 524

Abstract

Functional networks have become a standard tool for the analysis of complex systems, allowing the unveiling of their internal connectivity structure while only requiring the observation of the system’s constituent dynamics. To obtain reliable results, one (often overlooked) prerequisite involves the stationarity of [...] Read more.

Functional networks have become a standard tool for the analysis of complex systems, allowing the unveiling of their internal connectivity structure while only requiring the observation of the system’s constituent dynamics. To obtain reliable results, one (often overlooked) prerequisite involves the stationarity of an analyzed time series, without which spurious functional connections may emerge. Here, we show how ordinal patterns and metrics derived from them can be used to assess the effectiveness of detrending methods. We apply this approach to data representing the evolution of delays in major European and US airports, and to synthetic versions of the same, obtaining operational conclusions about how these propagate in the two systems. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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17 pages, 784 KiB

Open AccessArticle

Effects of Multiplicative Noise in Bistable Dynamical Systems

by Sara C. Quintanilha Valente, Rodrigo da Costa Lima Bruni, Zochil González Arenas and Daniel G. Barci

Entropy 2025, 27(2), 155; https://doi.org/10.3390/e27020155 - 2 Feb 2025

Viewed by 709

Abstract

This study explores the escape dynamics of bistable systems influenced by multiplicative noise, extending the classical Kramers rate formula to scenarios involving state-dependent diffusion in asymmetric potentials. Using a generalized stochastic calculus framework, we derive an analytical expression for the escape rate and [...] Read more.

This study explores the escape dynamics of bistable systems influenced by multiplicative noise, extending the classical Kramers rate formula to scenarios involving state-dependent diffusion in asymmetric potentials. Using a generalized stochastic calculus framework, we derive an analytical expression for the escape rate and corroborate it with numerical simulations. The results highlight the critical role of the equilibrium potential

U_{eq} (x)

, which incorporates noise intensity, stochastic prescription, and diffusion properties. We show how asymmetries and stochastic calculus prescriptions influence transition rates and equilibrium configurations. Using path integral techniques and weak noise approximations, we analyze the interplay between noise and potential asymmetry, uncovering phenomena such as barrier suppression and metastable state decay. The agreement between numerical and analytical results underscores the robustness of the proposed framework. This work provides a comprehensive foundation for studying noise-induced transitions in stochastic systems, offering insights into a broad range of applications in physics, chemistry, and biology. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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14 pages, 661 KiB

Open AccessArticle

Local Predictors of Explosive Synchronization with Ordinal Methods

by I. Leyva, Juan A. Almendral, Christophe Letellier and Irene Sendiña-Nadal

Entropy 2025, 27(2), 113; https://doi.org/10.3390/e27020113 - 24 Jan 2025

Viewed by 659

Abstract

We propose using the ordinal pattern transition (OPT) entropy measured at sentinel central nodes as a potential predictor of explosive transitions to synchronization in networks of various dynamical systems with increasing complexity. Our results demonstrate that the OPT entropic measure surpasses traditional early [...] Read more.

We propose using the ordinal pattern transition (OPT) entropy measured at sentinel central nodes as a potential predictor of explosive transitions to synchronization in networks of various dynamical systems with increasing complexity. Our results demonstrate that the OPT entropic measure surpasses traditional early warning signal (EWS) measures and could be valuable to the tools available for predicting critical transitions. In particular, we investigate networks of diffusively coupled phase oscillators and chaotic Rössler systems. As maps, we consider a neural network of Chialvo maps coupled in star and scale-free configurations. Furthermore, we apply this measure to time series data obtained from a network of electronic circuits operating in the chaotic regime. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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14 pages, 2466 KiB

Open AccessArticle

Statistical Complexity Analysis of Sleep Stages

by Cristina D. Duarte, Marianela Pacheco, Francisco R. Iaconis, Osvaldo A. Rosso, Gustavo Gasaneo and Claudio A. Delrieux

Entropy 2025, 27(1), 76; https://doi.org/10.3390/e27010076 - 16 Jan 2025

Viewed by 823

Abstract

Studying sleep stages is crucial for understanding sleep architecture, which can help identify various health conditions, including insomnia, sleep apnea, and neurodegenerative diseases, allowing for better diagnosis and treatment interventions. In this paper, we explore the effectiveness of generalized weighted permutation entropy (GWPE) [...] Read more.

Studying sleep stages is crucial for understanding sleep architecture, which can help identify various health conditions, including insomnia, sleep apnea, and neurodegenerative diseases, allowing for better diagnosis and treatment interventions. In this paper, we explore the effectiveness of generalized weighted permutation entropy (GWPE) in distinguishing between different sleep stages from EEG signals. Using classification algorithms, we evaluate feature sets derived from both standard permutation entropy (PE) and GWPE to determine which set performs better in classifying sleep stages, demonstrating that GWPE significantly enhances sleep stage differentiation, particularly in identifying the transition between N1 and REM sleep. The results highlight the potential of GWPE as a valuable tool for understanding sleep neurophysiology and improving the diagnosis of sleep disorders. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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13 pages, 603 KiB

Open AccessArticle

The Structure of Bit-String Similarity Networks

by David M. Schneider and Damián H. Zanette

Entropy 2025, 27(1), 57; https://doi.org/10.3390/e27010057 - 10 Jan 2025

Viewed by 628

Abstract

We study the structural properties of networks formed by random sets of bit strings—namely the ordered arrays of binary variables representing, for instance, genetic information or cultural profiles. Two bit strings are connected by a network link when they are sufficiently similar to [...] Read more.

We study the structural properties of networks formed by random sets of bit strings—namely the ordered arrays of binary variables representing, for instance, genetic information or cultural profiles. Two bit strings are connected by a network link when they are sufficiently similar to each other, i.e., when their Hamming distance is below a certain threshold. Using both analytical and numerical techniques, we determine the degree distribution and the conditions for the existence of a giant component in this kind of network. In addition, we analyze their clustering, assortativity, and mean geodesic distance. We show that these properties combine features specific to random networks with characteristics that derive from the Hamming metrics implicit in the definition of similarity between bit strings. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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13 pages, 1876 KiB

Open AccessArticle

Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions

by Diana Monteoliva, Angelo Plastino and Angel Ricardo Plastino

Entropy 2025, 27(1), 37; https://doi.org/10.3390/e27010037 - 6 Jan 2025

Viewed by 612

Abstract

In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (

C_{f}

) in a finite model of N interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its [...] Read more.

In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (

C_{f}

) in a finite model of N interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its essential features in a more manageable form compared to a realistic nuclear model, which would require the diagonalization of matrices with millions of elements, making the extraction of qualitative features a significant challenge. Specifically, we aim to correlate

C_{f}

with particle number fluctuations and temperature, using the paradigmatic Lipkin model. Our analysis reveals intriguing dependencies of

C_{f}

on the total fermion number, showcasing distinct behaviors at different temperatures. Notably, we find that the degree of quantum mixedness exhibits a strong dependence on the total fermion number, with varying trends across different temperature regimes. Remarkably, this dependence remains unaffected by the strength of the fermion–fermion interaction (as long as it is non-zero), underscoring the robustness of the observed phenomena. Through comprehensive numerical simulations, we provide illustrative graphs depicting these dependencies, offering valuable insights into the fundamental characteristics of quantum many-body fermion systems. Our findings illuminate the intricate dynamics of the degree of mixedness, a crucial quantum property, with potential implications for diverse fields ranging from condensed matter physics to quantum information science. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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14 pages, 1056 KiB

Open AccessArticle

Spatio-Temporal Analysis of Acute Myocardial Ischaemia Based on Entropy–Complexity Plane

by Esteban R. Valverde, Victoria Vampa, Osvaldo A. Rosso and Pedro D. Arini

Entropy 2025, 27(1), 8; https://doi.org/10.3390/e27010008 - 26 Dec 2024

Viewed by 588

Abstract

Myocardial ischaemia is a decompensation of the oxygen supply and demand ratio, often caused by coronary atherosclerosis. During the initial stage of ischaemia, the electrical activity of the heart is disrupted, increasing the risk of malignant arrhythmias. The aim of this study is [...] Read more.

Myocardial ischaemia is a decompensation of the oxygen supply and demand ratio, often caused by coronary atherosclerosis. During the initial stage of ischaemia, the electrical activity of the heart is disrupted, increasing the risk of malignant arrhythmias. The aim of this study is to understand the differential behaviour of the ECG during occlusion of both the left anterior descending (LAD) and right anterior coronary artery (RCA), respectively, using spatio-temporal quantifiers from information theory. A standard 12-lead ECG was recorded for each patient in the database. The control condition was obtained initially. Then, a percutaneous transluminal coronary angioplasty procedure (PTCA), which encompassed the occlusion/reperfusion period, was performed. To evaluate information quantifiers, the Bandt and Pompe permutation method was used to estimate the probability distribution associated with the electrocardiographic vector modulus. Subsequently, we analysed the positioning in the

H \times C

causal plane for the control and ischaemia. In LAD occlusion, decreased entropy and increased complexity can be seen, i.e., the behaviour is more predictable with an increase in the degree of complexity of the system. RCA occlusion had the opposite effects, i.e., the phenomenon is less predictable and exhibits a lower degree of organisation. Finally, both entropy and complexity decrease during the reperfusion phase in LAD and RCA cases. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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17 pages, 13222 KiB

Open AccessArticle

A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC)

by Zhe Lin and Arjendu K. Pattanayak

Entropy 2024, 26(12), 1085; https://doi.org/10.3390/e26121085 - 12 Dec 2024

Viewed by 793

Abstract

Chaotic systems can exhibit completely different behaviors given only slightly different initial conditions, yet it is possible to synchronize them through appropriate coupling. A wide variety of behaviors—complete chaos, complete synchronization, phase synchronization, etc.—across a variety of systems have been identified but rely [...] Read more.

Chaotic systems can exhibit completely different behaviors given only slightly different initial conditions, yet it is possible to synchronize them through appropriate coupling. A wide variety of behaviors—complete chaos, complete synchronization, phase synchronization, etc.—across a variety of systems have been identified but rely on systems’ phase space trajectories, which suppress important distinctions between very different behaviors and require access to the differential equations. In this paper, we introduce the Difference Time Series Peak Complexity (DTSPC) algorithm, a technique using entropy as a tool to quantitatively measure synchronization. Specifically, this uses peak pattern complexity created from sampled time series, focusing on the behavior of ringing patterns in the difference time series to distinguish a variety of synchronization behaviors based on the entropic complexity of the populations of various patterns. We present results from the paradigmatic case of coupled Lorenz systems, both identical and non-identical, and across a range of parameters and show that this technique captures the diversity of possible synchronization, including non-monotonicity as a function of parameter as well as complicated boundaries between different regimes. Thus, this peak pattern entropic analysis algorithm reveals and quantifies the complexity of chaos synchronization dynamics, and in particular captures transitional behaviors between different regimes. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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15 pages, 714 KiB

Open AccessArticle

Identifying Ordinal Similarities at Different Temporal Scales

by Luciano Zunino, Xavier Porte and Miguel C. Soriano

Entropy 2024, 26(12), 1016; https://doi.org/10.3390/e26121016 - 24 Nov 2024

Cited by 1 | Viewed by 688

Abstract

This study implements the permutation Jensen–Shannon distance as a metric for discerning ordinal patterns and similarities across multiple temporal scales in time series data. Initially, we present a numerically controlled analysis to validate the multiscale capabilities of this method. Subsequently, we apply our [...] Read more.

This study implements the permutation Jensen–Shannon distance as a metric for discerning ordinal patterns and similarities across multiple temporal scales in time series data. Initially, we present a numerically controlled analysis to validate the multiscale capabilities of this method. Subsequently, we apply our methodology to a complex photonic system, showcasing its practical utility in a real-world scenario. Our findings suggest that this approach is a powerful tool for identifying the precise temporal scales at which two distinct time series exhibit ordinal similarity. Given its robustness, we anticipate that this method could be widely applicable across various scientific disciplines, offering a new lens through which to analyze time series data. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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15 pages, 1727 KiB

Open AccessArticle

Quantum-Like Approaches Unveil the Intrinsic Limits of Predictability in Compartmental Models

by José Alejandro Rojas-Venegas, Pablo Gallarta-Sáenz, Rafael G. Hurtado, Jesús Gómez-Gardeñes and David Soriano-Paños

Entropy 2024, 26(10), 888; https://doi.org/10.3390/e26100888 - 21 Oct 2024

Cited by 1 | Viewed by 1132

Abstract

Obtaining accurate forecasts for the evolution of epidemic outbreaks from deterministic compartmental models represents a major theoretical challenge. Recently, it has been shown that these models typically exhibit trajectory degeneracy, as different sets of epidemiological parameters yield comparable predictions at early stages of [...] Read more.

Obtaining accurate forecasts for the evolution of epidemic outbreaks from deterministic compartmental models represents a major theoretical challenge. Recently, it has been shown that these models typically exhibit trajectory degeneracy, as different sets of epidemiological parameters yield comparable predictions at early stages of the outbreak but disparate future epidemic scenarios. In this study, we use the Doi–Peliti approach and extend the classical deterministic compartmental models to a quantum-like formalism to explore whether the uncertainty of epidemic forecasts is also shaped by the stochastic nature of epidemic processes. This approach allows us to obtain a probabilistic ensemble of trajectories, revealing that epidemic uncertainty is not uniform across time, being maximal around the epidemic peak and vanishing at both early and very late stages of the outbreak. Therefore, our results show that, independently of the models’ complexity, the stochasticity of contagion and recovery processes poses a natural constraint for the uncertainty of epidemic forecasts. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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23 pages, 6755 KiB

Open AccessArticle

Neural Dynamics Associated with Biological Variation in Normal Human Brain Regions

by Natalí Guisande, Osvaldo A. Rosso and Fernando Montani

Entropy 2024, 26(10), 828; https://doi.org/10.3390/e26100828 - 29 Sep 2024

Viewed by 1344

Abstract

The processes involved in encoding and decoding signals in the human brain are a continually studied topic, as neuronal information flow involves complex nonlinear dynamics. This study examines awake human intracranial electroencephalography (iEEG) data from normal brain regions to explore how biological sex [...] Read more.

The processes involved in encoding and decoding signals in the human brain are a continually studied topic, as neuronal information flow involves complex nonlinear dynamics. This study examines awake human intracranial electroencephalography (iEEG) data from normal brain regions to explore how biological sex influences these dynamics. The iEEG data were analyzed using permutation entropy and statistical complexity in the time domain and power spectrum calculations in the frequency domain. The Bandt and Pompe method was used to assess time series causality by associating probability distributions based on ordinal patterns with the signals. Due to the invasive nature of data acquisition, the study encountered limitations such as small sample sizes and potential sources of error. Nevertheless, the high spatial resolution of iEEG allows detailed analysis and comparison of specific brain regions. The results reveal differences between sexes in brain regions, observed through power spectrum, entropy, and complexity analyses. Significant differences were found in the left supramarginal gyrus, posterior cingulate, supplementary motor cortex, middle temporal gyrus, and right superior temporal gyrus. This study emphasizes the importance of considering sex as a biological variable in brain dynamics research, which is essential for improving the diagnosis and treatment of neurological and psychiatric disorders. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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Review

Jump to: Research

42 pages, 984 KiB

Open AccessReview

Applications of Entropy in Data Analysis and Machine Learning: A Review

by Salomé A. Sepúlveda-Fontaine and José M. Amigó

Entropy 2024, 26(12), 1126; https://doi.org/10.3390/e26121126 - 23 Dec 2024

Cited by 1 | Viewed by 3565

Abstract

Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and the Theory of Dynamical Systems. Specifically, [...] Read more.

Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and the Theory of Dynamical Systems. Specifically, we are referring to the classical entropies: the Boltzmann–Gibbs, von Neumann, Shannon, Kolmogorov–Sinai and topological entropies. In addition to their common name, which is historically justified (as we briefly describe in this review), another commonality of the classical entropies is the important role that they have played and are still playing in the theory and applications of their respective fields and beyond. Therefore, it is not surprising that, in the course of time, many other instances of the overarching concept of entropy have been proposed, most of them tailored to specific purposes. Following the current usage, we will refer to all of them, whether classical or new, simply as entropies. In particular, the subject of this review is their applications in data analysis and machine learning. The reason for these particular applications is that entropies are very well suited to characterize probability mass distributions, typically generated by finite-state processes or symbolized signals. Therefore, we will focus on entropies defined as positive functionals on probability mass distributions and provide an axiomatic characterization that goes back to Shannon and Khinchin. Given the plethora of entropies in the literature, we have selected a representative group, including the classical ones. The applications summarized in this review nicely illustrate the power and versatility of entropy in data analysis and machine learning. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

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