Special Issue "Entropy: The Scientific Tool of the 21st Century"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 30 June 2021.

Special Issue Editor

Prof. Dr. José A. Tenreiro Machado
grade Website SciProfiles
Guest Editor
Department of Electrical Engineering, Institute of Engineering, Polytechnic Institute of Porto,4249-015 Porto, Portugal
Interests: nonlinear dynamics; fractional calculus; modeling; control; evolutionary computing; genomics; robotics; and intelligent transportation systems
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Special Issue Information

Dear Colleagues,

The concept of entropy emerges initially from the scope of physics, but it is now clear that entropy is deeply related to information theory and the process of inference. Today, entropic techniques have found a broad spectrum of applications in all branches of science.

This Special Issue will include the following main directions, which reflect the interdisciplinary nature of entropy and its applications:

Statistical physics
Information theory, probability, and statistics
Thermodynamics
Quantum information and foundations
Complex systems
Entropy in multidisciplinary applications

This Special Issue will publish, among other pieces, the extended versions of papers presented at the Entropy 2021 conference. It is, however, open to any other contributions related to the subjects of the Entropy 2021 conference.

Relevant special issue, https://www.mdpi.com/journal/entropy/special_issues/entropy2018

Prof. J. A. Tenreiro Machado
Guest Editor

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 papers will be 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 1600 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.

Published Papers (11 papers)

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Open AccessArticle
Robustness Analysis of the Estimators for the Nonlinear System Identification
Entropy 2020, 22(8), 834; https://doi.org/10.3390/e22080834 - 30 Jul 2020
Abstract
The main objective of the system identification is to deliver maximum information about the system dynamics, while still ensuring an acceptable cost of the identification experiment. The focus of such an idea is to design an appropriate experiment so that the departure from [...] Read more.
The main objective of the system identification is to deliver maximum information about the system dynamics, while still ensuring an acceptable cost of the identification experiment. The focus of such an idea is to design an appropriate experiment so that the departure from normal working conditions during the identification task is minimized. In this paper, the adaptive filtering (AF) scheme for plant model parameter estimation is proposed. The experimental results are obtained using the nonlinear interacting water tanks system. The adaptive filtering is expressed by minimizing the error between the system and the plant model outputs subject to the white noise signal affecting system output. This measurement error is quantified by the comparison of Minimum Error Entropy Renyi (MEER), Least Entropy Like (LEL), Least Squares (LS), and Least Absolute Deviation (LAD) estimators, respectively. The plant model parameters were obtained using sequential quadratic programming (SQP) algorithm. The robustness tests for the double-tank water system parameter estimators are performed using the ellipsoidal confidence regions. The effectiveness analysis for the above-mentioned estimators relies on the total number of iterations and the number of function evaluation comparisons. The main contribution of this paper is the evaluation of different estimation methods for the nonlinear system identification using various excitation signals. The proposed empirical study is illustrated by the numerical examples, and the simulation results are discussed. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessArticle
Susceptible-Infected-Susceptible Epidemic Discrete Dynamic System Based on Tsallis Entropy
Entropy 2020, 22(7), 769; https://doi.org/10.3390/e22070769 - 14 Jul 2020
Abstract
This investigation deals with a discrete dynamic system of susceptible-infected-susceptible epidemic (SISE) using the Tsallis entropy. We investigate the positive and maximal solutions of the system. Stability and equilibrium are studied. Moreover, based on the Tsallis entropy, we shall formulate a new design [...] Read more.
This investigation deals with a discrete dynamic system of susceptible-infected-susceptible epidemic (SISE) using the Tsallis entropy. We investigate the positive and maximal solutions of the system. Stability and equilibrium are studied. Moreover, based on the Tsallis entropy, we shall formulate a new design for the basic reproductive ratio. Finally, we apply the results on live data regarding COVID-19. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessArticle
Prognosis of Diabetic Peripheral Neuropathy via Decomposed Digital Volume Pulse from the Fingertip
Entropy 2020, 22(7), 754; https://doi.org/10.3390/e22070754 - 09 Jul 2020
Abstract
Diabetic peripheral neuropathy (DPN) is a very common neurological disorder in diabetic patients. This study presents a new percussion-based index for predicting DPN by decomposing digital volume pulse (DVP) signals from the fingertip. In this study, 130 subjects (50 individuals 44 to 89 [...] Read more.
Diabetic peripheral neuropathy (DPN) is a very common neurological disorder in diabetic patients. This study presents a new percussion-based index for predicting DPN by decomposing digital volume pulse (DVP) signals from the fingertip. In this study, 130 subjects (50 individuals 44 to 89 years of age without diabetes and 80 patients 37 to 86 years of age with type 2 diabetes) were enrolled. After baseline measurement and blood tests, 25 diabetic patients developed DPN within the following five years. After removing high-frequency noise in the original DVP signals, the decomposed DVP signals were used for percussion entropy index (PEIDVP) computation. Effects of risk factors on the incidence of DPN in diabetic patients within five years of follow-up were tested using binary logistic regression analysis, controlling for age, waist circumference, low-density lipoprotein cholesterol, and the new index. Multivariate analysis showed that patients who did not develop DPN in the five-year period had higher PEIDVP values than those with DPN, as determined by logistic regression model (PEIDVP: odds ratio 0.913, 95% CI 0.850 to 0.980). This study shows that PEIDVP can be a major protective factor in relation to the studied binary outcome (i.e., DPN or not in diabetic patients five years after baseline measurement). Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessArticle
A Novel Technique for Achieving the Approximated ISI at the Receiver for a 16QAM Signal Sent via a FIR Channel Based Only on the Received Information and Statistical Techniques
Entropy 2020, 22(6), 708; https://doi.org/10.3390/e22060708 - 26 Jun 2020
Abstract
A single-input-multiple-output (SIMO) channel is obtained from the use of an array of antennas in the receiver where the same information is transmitted through different sub-channels, and all received sequences are distinctly distorted versions of the same message. The inter-symbol-interference (ISI) level from [...] Read more.
A single-input-multiple-output (SIMO) channel is obtained from the use of an array of antennas in the receiver where the same information is transmitted through different sub-channels, and all received sequences are distinctly distorted versions of the same message. The inter-symbol-interference (ISI) level from each sub-channel is presently unknown to the receiver. Thus, even when one or more sub-channels cause heavy ISI, all the information from all the sub-channels was still considered in the receiver. Obviously, if we know the approximated ISI of each sub-channel, we will use in the receiver only those sub-channels with the lowest ISI level to get improved system performance. In this paper, we present a systematic way for obtaining the approximated ISI from each sub-channel modelled as a finite-impulse-response (FIR) channel with real-valued coefficients for a 16QAM (16 quadrature amplitude modulation) source signal transmission. The approximated ISI is based on the maximum entropy density approximation technique, on the Edgeworth expansion up to order six, on the Laplace integral method and on the generalized Gaussian distribution (GGD). Although the approximated ISI was derived for the noiseless case, it was successfully tested for signal to noise ratio (SNR) down to 20 dB. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessArticle
Shannon Entropy as an Indicator for Sorting Processes in Hydrothermal Systems
Entropy 2020, 22(6), 656; https://doi.org/10.3390/e22060656 - 13 Jun 2020
Abstract
Hydrothermal processes modify the chemical and mineralogical composition of rock. We studied and quantified the effects of hydrothermal processes on the composition of volcanic rocks by a novel application of the Shannon entropy, which is a measure of uncertainty and commonly applied in [...] Read more.
Hydrothermal processes modify the chemical and mineralogical composition of rock. We studied and quantified the effects of hydrothermal processes on the composition of volcanic rocks by a novel application of the Shannon entropy, which is a measure of uncertainty and commonly applied in information theory. We show here that the Shannon entropies calculated on major elemental chemical composition data and short-wave infrared (SWIR) reflectance spectra of hydrothermally altered rocks are lower than unaltered rocks with a comparable primary composition. The lowering of the Shannon entropy indicates chemical and spectral sorting during hydrothermal alteration of rocks. The hydrothermal processes described in this study present a natural mechanism for transforming energy from heat to increased order in rock. The increased order is manifest as the increased sorting of chemical elements and SWIR absorption features of the rock, and can be measured and quantified by the Shannon entropy. The results are useful for the study of hydrothermal mineral deposits, early life environments and the effects of hydrothermal processes on rocks. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessArticle
Cascaded Thermodynamic and Environmental Analyses of Energy Generation Modalities of a High-Performance Building Based on Real-Time Measurements
Entropy 2020, 22(4), 445; https://doi.org/10.3390/e22040445 - 14 Apr 2020
Abstract
This study presents cascaded thermodynamic and environmental analyses of a high-performance academic building. Five different energy efficiency measures and operation scenarios are evaluated based on the actual measurements starting from the initial design concept. The study is to emphasize that by performing dynamical [...] Read more.
This study presents cascaded thermodynamic and environmental analyses of a high-performance academic building. Five different energy efficiency measures and operation scenarios are evaluated based on the actual measurements starting from the initial design concept. The study is to emphasize that by performing dynamical energy, exergy, exergoeconomic, and environmental analyses with increasing complexity, a better picture of building performance indicators can be obtained for both the building owners and users, helping them to decide on different investment strategies. As the first improvement, the original design is modified by the addition of a ground-air heat exchanger for pre-conditioning the incoming air to heat the ground floors. The installation of roof-top PV panels to use solar energy is considered as the third case, and the use of a trigeneration system as an energy source instead of traditional boiler systems is considered as the fourth case. The last case is the integration of all these three alternative energy modalities for the building. It is determined that the use of a trigeneration system provides a better outcome than the other scenarios for decreased energy demand, for cost reduction, and for the improved exergy efficiency and sustainability index values relative to the original baseline design scenario. Yet, an integrated approach combining all these energy generation modalities provide the best return of investment. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessArticle
Analyzing the Influence of Hyper-parameters and Regularizers of Topic Modeling in Terms of Renyi Entropy
Entropy 2020, 22(4), 394; https://doi.org/10.3390/e22040394 - 30 Mar 2020
Cited by 1
Abstract
Topic modeling is a popular technique for clustering large collections of text documents. A variety of different types of regularization is implemented in topic modeling. In this paper, we propose a novel approach for analyzing the influence of different regularization types on results [...] Read more.
Topic modeling is a popular technique for clustering large collections of text documents. A variety of different types of regularization is implemented in topic modeling. In this paper, we propose a novel approach for analyzing the influence of different regularization types on results of topic modeling. Based on Renyi entropy, this approach is inspired by the concepts from statistical physics, where an inferred topical structure of a collection can be considered an information statistical system residing in a non-equilibrium state. By testing our approach on four models—Probabilistic Latent Semantic Analysis (pLSA), Additive Regularization of Topic Models (BigARTM), Latent Dirichlet Allocation (LDA) with Gibbs sampling, LDA with variational inference (VLDA)—we, first of all, show that the minimum of Renyi entropy coincides with the “true” number of topics, as determined in two labelled collections. Simultaneously, we find that Hierarchical Dirichlet Process (HDP) model as a well-known approach for topic number optimization fails to detect such optimum. Next, we demonstrate that large values of the regularization coefficient in BigARTM significantly shift the minimum of entropy from the topic number optimum, which effect is not observed for hyper-parameters in LDA with Gibbs sampling. We conclude that regularization may introduce unpredictable distortions into topic models that need further research. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessArticle
Segmentation Method for Ship-Radiated Noise Using the Generalized Likelihood Ratio Test on an Ordinal Pattern Distribution
Entropy 2020, 22(4), 374; https://doi.org/10.3390/e22040374 - 25 Mar 2020
Abstract
Due to the diversity of ship-radiated noise (SRN), audio segmentation is an essential procedure in the ship statuses/categories identification. However, the existing segmentation methods are not suitable for the SRN because of the lack of prior knowledge. In this paper, by a generalized [...] Read more.
Due to the diversity of ship-radiated noise (SRN), audio segmentation is an essential procedure in the ship statuses/categories identification. However, the existing segmentation methods are not suitable for the SRN because of the lack of prior knowledge. In this paper, by a generalized likelihood ratio (GLR) test on the ordinal pattern distribution (OPD), we proposed a segmentation criterion and introduce it into single change-point detection (SCPD) and multiple change-points detection (MCPD) for SRN. The proposed method is free from the acoustic feature extraction and the corresponding probability distribution estimation. In addition, according to the sequential structure of ordinal patterns, the OPD is efficiently estimated on a series of analysis windows. By comparison with the Bayesian Information Criterion (BIC) based segmentation method, we evaluate the performance of the proposed method on both synthetic signals and real-world SRN. The segmentation results on synthetic signals show that the proposed method estimates the number and location of the change-points more accurately. The classification results on real-world SRN show that our method obtains more distinguishable segments, which verifies its effectiveness in SRN segmentation. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessArticle
Deng Entropy Weighted Risk Priority Number Model for Failure Mode and Effects Analysis
Entropy 2020, 22(3), 280; https://doi.org/10.3390/e22030280 - 28 Feb 2020
Cited by 2
Abstract
Failure mode and effects analysis (FMEA), as a commonly used risk management method, has been extensively applied to the engineering domain. A vital parameter in FMEA is the risk priority number (RPN), which is the product of occurrence (O), severity (S), and detection [...] Read more.
Failure mode and effects analysis (FMEA), as a commonly used risk management method, has been extensively applied to the engineering domain. A vital parameter in FMEA is the risk priority number (RPN), which is the product of occurrence (O), severity (S), and detection (D) of a failure mode. To deal with the uncertainty in the assessments given by domain experts, a novel Deng entropy weighted risk priority number (DEWRPN) for FMEA is proposed in the framework of Dempster–Shafer evidence theory (DST). DEWRPN takes into consideration the relative importance in both risk factors and FMEA experts. The uncertain degree of objective assessments coming from experts are measured by the Deng entropy. An expert’s weight is comprised of the three risk factors’ weights obtained independently from expert’s assessments. In DEWRPN, the strategy of assigning weight for each expert is flexible and compatible to the real decision-making situation. The entropy-based relative weight symbolizes the relative importance. In detail, the higher the uncertain degree of a risk factor from an expert is, the lower the weight of the corresponding risk factor will be and vice versa. We utilize Deng entropy to construct the exponential weight of each risk factor as well as an expert’s relative importance on an FMEA item in a state-of-the-art way. A case study is adopted to verify the practicability and effectiveness of the proposed model. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessArticle
Entropy of the Multi-Channel EEG Recordings Identifies the Distributed Signatures of Negative, Neutral and Positive Affect in Whole-Brain Variability
Entropy 2019, 21(12), 1228; https://doi.org/10.3390/e21121228 - 16 Dec 2019
Cited by 2
Abstract
Individuals’ ability to express their subjective experiences in terms of such attributes as pleasant/unpleasant or positive/negative feelings forms a fundamental property of their affect and emotion. However, neuroscientific findings on the underlying neural substrates of the affect appear to be inconclusive with some [...] Read more.
Individuals’ ability to express their subjective experiences in terms of such attributes as pleasant/unpleasant or positive/negative feelings forms a fundamental property of their affect and emotion. However, neuroscientific findings on the underlying neural substrates of the affect appear to be inconclusive with some reporting the presence of distinct and independent brain systems and others identifying flexible and distributed brain regions. A common theme among these studies is the focus on the change in brain activation. As a result, they do not take into account the findings that indicate the brain activation and its information content does not necessarily modulate and that the stimuli with equivalent sensory and behavioural processing demands may not necessarily result in differential brain activation. In this article, we take a different stance on the analysis of the differential effect of the negative, neutral and positive affect on the brain functioning in which we look into the whole-brain variability: that is the change in the brain information processing measured in multiple distributed regions. For this purpose, we compute the entropy of individuals’ muti-channel EEG recordings who watched movie clips with differing affect. Our results suggest that the whole-brain variability significantly differentiates between the negative, neutral and positive affect. They also indicate that although some brain regions contribute more to such differences, it is the whole-brain variational pattern that results in their significantly above chance level prediction. These results imply that although the underlying brain substrates for negative, neutral and positive affect exhibit quantitatively differing degrees of variability, their differences are rather subtly encoded in the whole-brain variational patterns that are distributed across its entire activity. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Open AccessDiscussion
Pearle’s Hidden-Variable Model Revisited
Entropy 2020, 22(1), 1; https://doi.org/10.3390/e22010001 - 18 Dec 2019
Cited by 1
Abstract
Pearle (1970) gave an example of a local hidden variables model which exactly reproduced the singlet correlations of quantum theory, through the device of data-rejection: particles can fail to be detected in a way which depends on the hidden variables carried by the [...] Read more.
Pearle (1970) gave an example of a local hidden variables model which exactly reproduced the singlet correlations of quantum theory, through the device of data-rejection: particles can fail to be detected in a way which depends on the hidden variables carried by the particles and on the measurement settings. If the experimenter computes correlations between measurement outcomes of particle pairs for which both particles are detected, he or she is actually looking at a subsample of particle pairs, determined by interaction involving both measurement settings and the hidden variables carried in the particles. We correct a mistake in Pearle’s formulas (a normalization error) and more importantly show that the model is simpler than first appears. We illustrate with visualizations of the model and with a small simulation experiment, with code in the statistical programming language R included in the paper. Open problems are discussed. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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