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Entropy
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Entropy and Its Applications across Disciplines III
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Entropy and Its Applications across Disciplines III

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

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 12750

Special Issue Editors

Dr. Francesco Villecco

E-Mail Website
Guest Editor
Department of Industrial Engineering, University of Salerno, Via Giovanni Paolo II 132, 84084 Fisciano, Italy
Interests: industrial design; entropy; fuzzy logic; computer-aided design (CAD); axiomatic design; MaxInf principle
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yusif S. Gasimov

E-Mail Website
Co-Guest Editor
Department of Mathematics and Information Technologies, Azerbaijan University, Jeyhun Hajibeyli str., 71, Baku AZ1007, Azerbaijan
Interests: spectral theory; inverse problems; variable domain eigenvalue problems; “shape” optimization
Prof. Dr. Nicola Cappetti

E-Mail Website
Co-Guest Editor
Department of Industrial Engineering, University of Salerno, Via Giovanni Paolo II 132, 84084 Fisciano, Italy
Interests: mechanical design and technical drawings

Special Issue Information

Dear Colleagues,

In modern research, many problems are characterized by complexity and dependence on multiple parameters. The entropy of a system is a direct measure of its complexity. Other complexity-related mathematical functions include the Hurst exponent, long-range correlation, fractals, stochastic processes, probability, and fuzzy probability. These models may be seen in various fields of science, such as physics, engineering, mechanics, biology, economics, and some more mathematical applications.

The aim of this Special Issue is to discuss, from both theoretical and applied points of view, the physical and engineering properties of the entropy- and complexity-based models arising in nature and applied sciences.

Topics of interest are given below, and papers related to these fields are welcome:

  • entropy and complexity of mathematical models with fractional and integer order;
  • new analytical and numerical methods in the analysis of problems where entropy and complexity are the main features;
  • entropy and complexity in computational methods for differential models;
  • entropy and complexity in engineering, fluid dynamics, and thermal engineering problems, as well as problems related to physics, applied sciences, and computer science;
  • deterministic and stochastic fractional order models;
  • entropy and complexity models in physics and engineering;
  • entropy and complexity in analytical and numerical solutions;
  • nonlinear dynamical complex systems;
  • entropic measure of epistemic uncertainties.

Dr. Francesco Villecco
Prof. Dr. Yusif S. Gasimov 
Prof. Dr. Nicola Cappetti
Guest Editors

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.

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Published Papers (6 papers)

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Research

19 pages, 3665 KiB  
Article
Multivariate Multiscale Cosine Similarity Entropy and Its Application to Examine Circularity Properties in Division Algebras
by Hongjian Xiao, Theerasak Chanwimalueang and Danilo P. Mandic
Entropy 2022, 24(9), 1287; https://doi.org/10.3390/e24091287 - 13 Sep 2022
Cited by 4 | Viewed by 1577
Abstract
The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding [...] Read more.
The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding multivariate methods, multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), were developed to explore the structural richness within signals at high scales. However, the requirement of high scale limits the selection of embedding dimension and thus, the performance is unavoidably restricted by the trade-off between the data size and the required high scale. More importantly, the scale of interest in different situations is varying, yet little is known about the optimal setting of the scale range in MMSE and MMFE. To this end, we extend the univariate cosine similarity entropy (CSE) method to the multivariate case, and show that the resulting multivariate multiscale cosine similarity entropy (MMCSE) is capable of quantifying structural complexity through the degree of self-correlation within signals. The proposed approach relaxes the prohibitive constraints between the embedding dimension and data length, and aims to quantify the structural complexity based on the degree of self-correlation at low scales. The proposed MMCSE is applied to the examination of the complex and quaternion circularity properties of signals with varying correlation behaviors, and simulations show the MMCSE outperforming the standard methods, MMSE and MMFE. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines III)
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14 pages, 2510 KiB  
Article
Brain Tumor Segmentation Based on Bendlet Transform and Improved Chan-Vese Model
by Kexin Meng, Piercarlo Cattani and Francesco Villecco
Entropy 2022, 24(9), 1199; https://doi.org/10.3390/e24091199 - 27 Aug 2022
Cited by 6 | Viewed by 1745
Abstract
Automated segmentation of brain tumors is a difficult procedure due to the variability and blurred boundary of the lesions. In this study, we propose an automated model based on Bendlet transform and improved Chan-Vese (CV) model for brain tumor segmentation. Since the Bendlet [...] Read more.
Automated segmentation of brain tumors is a difficult procedure due to the variability and blurred boundary of the lesions. In this study, we propose an automated model based on Bendlet transform and improved Chan-Vese (CV) model for brain tumor segmentation. Since the Bendlet system is based on the principle of sparse approximation, Bendlet transform is applied to describe the images and map images to the feature space and, thereby, first obtain the feature set. This can help in effectively exploring the mapping relationship between brain lesions and normal tissues, and achieving multi-scale and multi-directional registration. Secondly, the SSIM region detection method is proposed to preliminarily locate the tumor region from three aspects of brightness, structure, and contrast. Finally, the CV model is solved by the Hermite-Shannon-Cosine wavelet homotopy method, and the boundary of the tumor region is more accurately delineated by the wavelet transform coefficient. We randomly selected some cross-sectional images to verify the effectiveness of the proposed algorithm and compared with CV, Ostu, K-FCM, and region growing segmentation methods. The experimental results showed that the proposed algorithm had higher segmentation accuracy and better stability. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines III)
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16 pages, 471 KiB  
Article
Essential Conditions for the Full Synergy of Probability of Occurrence Distributions
by Rubem P. Mondaini and Simão C. de Albuquerque Neto
Entropy 2022, 24(7), 993; https://doi.org/10.3390/e24070993 - 18 Jul 2022
Cited by 3 | Viewed by 1463
Abstract
In this contribution, we specify the conditions for assuring the validity of the synergy of the distribution of probabilities of occurrence. We also study the subsequent restriction on the maximal extension of the strict concavity region on the parameter space of Sharma–Mittal entropy [...] Read more.
In this contribution, we specify the conditions for assuring the validity of the synergy of the distribution of probabilities of occurrence. We also study the subsequent restriction on the maximal extension of the strict concavity region on the parameter space of Sharma–Mittal entropy measures, which has been derived in a previous paper in this journal. The present paper is then a necessary complement to that publication. Some applications of the techniques introduced here are applied to protein domain families (Pfam databases, versions 27.0 and 35.0). The results will show evidence of their usefulness for testing the classification work performed with methods of alignment that are used by expert biologists. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines III)
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13 pages, 11248 KiB  
Article
Bendlet Transform Based Adaptive Denoising Method for Microsection Images
by Shuli Mei, Meng Liu, Aleksey Kudreyko, Piercarlo Cattani, Denis Baikov and Francesco Villecco
Entropy 2022, 24(7), 869; https://doi.org/10.3390/e24070869 - 24 Jun 2022
Cited by 18 | Viewed by 1853
Abstract
Magnetic resonance imaging (MRI) plays an important role in disease diagnosis. The noise that appears in MRI images is commonly governed by a Rician distribution. The bendlets system is a second-order shearlet transform with bent elements. Thus, the bendlets system is a powerful [...] Read more.
Magnetic resonance imaging (MRI) plays an important role in disease diagnosis. The noise that appears in MRI images is commonly governed by a Rician distribution. The bendlets system is a second-order shearlet transform with bent elements. Thus, the bendlets system is a powerful tool with which to represent images with curve contours, such as the brain MRI images, sparsely. By means of the characteristic of bendlets, an adaptive denoising method for microsection images with Rician noise is proposed. In this method, the curve contour and texture can be identified as low-frequency components, which is not the case with other methods, such as the wavelet, shearlet, and so on. It is well known that the Rician noise belongs to a high-frequency channel, so it can be easily removed without blurring the clarity of the contour. Compared with other algorithms, such as the shearlet transform, block matching 3D, bilateral filtering, and Wiener filtering, the values of Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) obtained by the proposed method are better than those of other methods. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines III)
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10 pages, 5716 KiB  
Article
Entropy and Turbulence Structure
by T.-W. Lee and J. E. Park
Entropy 2022, 24(1), 11; https://doi.org/10.3390/e24010011 - 22 Dec 2021
Cited by 3 | Viewed by 3002
Abstract
Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement [...] Read more.
Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement with experimental data across the entire wavenumber range. Dissipation can also be attributed to the Reynolds number effect in wall-bounded turbulent flows. Within the global energy and dissipation constraints, the gradients (d/dy+ or d2/dy+2) of the Reynolds stress components neatly fold onto respective curves, so that function prescriptions (dissipation structure functions) can serve as a template to expand to other Reynolds numbers. The Reynolds stresses are fairly well prescribed by the current scaling and dynamical formalism so that the origins of the turbulence structure can be understood and quantified from the entropy perspective. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines III)
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19 pages, 6919 KiB  
Article
Complexity Evaluation of an Environmental Control and Life-Support System Based on Directed and Undirected Structural Entropy Methods
by Kaichun Yang, Chunxin Yang, Han Yang and Chenglong Zhou
Entropy 2021, 23(9), 1173; https://doi.org/10.3390/e23091173 - 7 Sep 2021
Cited by 3 | Viewed by 1909
Abstract
During manned space missions, an environmental control and life-support system (ECLSS) is employed to meet the life-supporting requirements of astronauts. The ECLSS is a type of hierarchical system, with subsystem—component—single machines, forming a complex structure. Therefore, system-level conceptual designing and performance evaluation of [...] Read more.
During manned space missions, an environmental control and life-support system (ECLSS) is employed to meet the life-supporting requirements of astronauts. The ECLSS is a type of hierarchical system, with subsystem—component—single machines, forming a complex structure. Therefore, system-level conceptual designing and performance evaluation of the ECLSS must be conducted. This study reports the top-level scheme of ECLSS, including the subsystems of atmosphere revitalization, water management, and waste management. We propose two schemes based on the design criteria of improving closure and reducing power consumption. In this study, we use the structural entropy method (SEM) to calculate the system order degree to quantitatively evaluate the ECLSS complexity at the top level. The complexity of the system evaluated by directed SEM and undirected SEM presents different rules. The results show that the change in the system structure caused by the replacement of some single technologies will not have great impact on the overall system complexity. The top-level scheme design and complexity evaluation presented in this study may provide technical support for the development of ECLSS in future manned spaceflights. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines III)
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