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Entropy
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Complexity and Synchronization in Time Series
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Complexity and Synchronization in Time Series

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: 10 December 2025 | Viewed by 924

Special Issue Editors

Dr. Lev Guzmán-Vargas

E-Mail Website
Guest Editor
Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Mexico City 07340, Mexico
Interests: time-series analysis; complexity; sychronization; complex networks
Dr. Daniel Aguilar-Velázquez

E-Mail Website
Guest Editor Assistant
Centro de Investigación y de Estudios Avanzados, Laboratorio de Neurogénesis y Neuroplasticidad, Departamento de Fisiología, Biofísica y Neurociencia, Ciudad de Mexico 07360, Mexico
Interests: complex systems; deep learning; critical phenomena; computational neuroscience; network science

Special Issue Information

Dear Colleagues,

A wide variety of complex systems exhibit behaviors that can be characterized by means of nonlinear dynamics, including methodologies such as fractality, multifractality, entropy, complex networks, etc. On the other hand, synchronization phenomena in coupled systems usually manifest themselves in collective coherent regimes that exhibit features such as the presence of avalanches, temporal correlations, and information theory processes. The study of the complexity displayed by the systems and their synchronization levels has become highly relevant, both from the point of view of dynamical models and experimentally in signals. Both complexity and synchrony also represent robust mechanisms that enhance communication in complex systems. This has led to a number of advances in the understanding of synchrony phenomena in complex systems, including coupling analyses in spatial and temporal records, as well as in signal models based on complex networks.

This Special Issue aims to bring together and disseminate recent research on new and improved techniques for modeling, analysis, and synchronization studies of complex systems. In particular, the analysis and interpretation of complex systems and applications in engineering based on information processing fall within the scope of this Special Issue.

Dr. Lev Guzmán-Vargas
Guest Editor

Dr. Daniel Aguilar-Velázquez
Guest Editor Assistant

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • time series synchronization
  • entropy analysis
  • fractal analysis
  • signaling networks

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Published Papers (2 papers)

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Research

23 pages, 321 KB  
Article
Nonlinear Shrinkage Estimation of Higher-Order Moments for Portfolio Optimization Under Uncertainty in Complex Financial Systems
by Wanbo Lu and Zhenzhong Tian
Entropy 2025, 27(10), 1083; https://doi.org/10.3390/e27101083 - 20 Oct 2025
Viewed by 211
Abstract
This paper develops a nonlinear shrinkage estimation method for higher-order moment matrices within a multifactor model framework and establishes its asymptotic consistency under high-dimensional settings. The approach extends the nonlinear shrinkage methodology from covariance to higher-order moments, thereby mitigating the “curse of dimensionality” [...] Read more.
This paper develops a nonlinear shrinkage estimation method for higher-order moment matrices within a multifactor model framework and establishes its asymptotic consistency under high-dimensional settings. The approach extends the nonlinear shrinkage methodology from covariance to higher-order moments, thereby mitigating the “curse of dimensionality” and alleviating estimation uncertainty in high-dimensional settings. Monte Carlo simulations demonstrate that, compared with linear shrinkage estimation, the proposed method substantially reduces mean squared errors (MSEs) and achieves greater Percentage Relative Improvement in Average Loss (PRIAL) for covariance and cokurtosis estimates; relative to sample estimation, it delivers significant gains in mitigating uncertainty for covariance, coskewness, and cokurtosis. An empirical portfolio analysis incorporating higher-order moments shows that, when the asset universe is large, portfolios based on the nonlinear shrinkage estimator outperform those constructed using linear shrinkage and sample estimators, achieving higher annualized return and Sharpe ratio with lower kurtosis and maximum drawdown, thus providing stronger resilience against uncertainty in complex financial systems. In smaller asset universes, nonlinear shrinkage portfolios perform on par with their linear shrinkage counterparts. These findings highlight the potential of nonlinear shrinkage techniques to reduce uncertainty in higher-order moment estimation and to improve portfolio performance across diverse and complex investment environments. Full article
(This article belongs to the Special Issue Complexity and Synchronization in Time Series)
18 pages, 9355 KB  
Article
Two-Dimensional Image Lempel–Ziv Complexity Calculation Method and Its Application in Defect Detection
by Jiancheng Yin, Wentao Sui, Xuye Zhuang, Yunlong Sheng and Yongbo Li
Entropy 2025, 27(10), 1014; https://doi.org/10.3390/e27101014 - 27 Sep 2025
Viewed by 374
Abstract
Although Lempel–Ziv complexity (LZC) can reflect changes in object characteristics by measuring changes in independent patterns in the signal, it can only be applied to one-dimensional time series and cannot be directly applied to two-dimensional images. To address this issue, this paper proposed [...] Read more.
Although Lempel–Ziv complexity (LZC) can reflect changes in object characteristics by measuring changes in independent patterns in the signal, it can only be applied to one-dimensional time series and cannot be directly applied to two-dimensional images. To address this issue, this paper proposed a two-dimensional Lempel–Ziv complexity by combining the concept of local receptive field in convolutional neural networks. This extends the application scenario of LZC from one-dimensional time series to two-dimensional images, further broadening the scope of application of LZC. First, the pixels and size of the image were normalized. Then, the image was encoded according to the sorting of normalized values within the 4 × 4 region. Next, the encoding result of the image was rearranged into a vector by row. Finally, the Lempel–Ziv complexity of the image could be obtained based on the rearranged vector. The proposed method was further used for defect detection in conjunction with the dilation operator and Sobel operator, and validated by two practical cases. The results showed that the proposed method can effectively identify independent pattern changes in images and can be used for defect detection. The accuracy rate of defect detection can reach 100%. Full article
(This article belongs to the Special Issue Complexity and Synchronization in Time Series)
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