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

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

Deadline for manuscript submissions: 30 September 2021.

Special Issue Editor

Prof. Dr. José A. Tenreiro Machado
grade E-Mail Website
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, complex systems
Special Issues and Collections in MDPI journals

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 1800 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 (23 papers)

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Article
Entropy and Entropic Forces to Model Biological Fluids
Entropy 2021, 23(9), 1166; https://doi.org/10.3390/e23091166 - 04 Sep 2021
Viewed by 351
Abstract
Living cells are complex systems characterized by fluids crowded by hundreds of different elements, including, in particular, a high density of polymers. They are an excellent and challenging laboratory to study exotic emerging physical phenomena, where entropic forces emerge from the organization processes [...] Read more.
Living cells are complex systems characterized by fluids crowded by hundreds of different elements, including, in particular, a high density of polymers. They are an excellent and challenging laboratory to study exotic emerging physical phenomena, where entropic forces emerge from the organization processes of many-body interactions. The competition between microscopic and entropic forces may generate complex behaviors, such as phase transitions, which living cells may use to accomplish their functions. In the era of big data, where biological information abounds, but general principles and precise understanding of the microscopic interactions is scarce, entropy methods may offer significant information. In this work, we developed a model where a complex thermodynamic equilibrium resulted from the competition between an effective electrostatic short-range interaction and the entropic forces emerging in a fluid crowded by different sized polymers. The target audience for this article are interdisciplinary researchers in complex systems, particularly in thermodynamics and biophysics modeling. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Effects of Cardiac Resynchronization Therapy on Cardio-Respiratory Coupling
Entropy 2021, 23(9), 1126; https://doi.org/10.3390/e23091126 - 30 Aug 2021
Viewed by 376
Abstract
In this study, the effect of cardiac resynchronization therapy (CRT) on the relationship between the cardiovascular and respiratory systems in heart failure subjects was examined for the first time. We hypothesized that alterations in cardio-respiratory interactions, after CRT implantation, quantified by signal complexity, [...] Read more.
In this study, the effect of cardiac resynchronization therapy (CRT) on the relationship between the cardiovascular and respiratory systems in heart failure subjects was examined for the first time. We hypothesized that alterations in cardio-respiratory interactions, after CRT implantation, quantified by signal complexity, could be a marker of a favorable CRT response. Sample entropy and scaling exponents were calculated from synchronously recorded cardiac and respiratory signals 20 min in duration, collected in 47 heart failure patients at rest, before and 9 months after CRT implantation. Further, cross-sample entropy between these signals was calculated. After CRT, all patients had lower heart rate and CRT responders had reduced breathing frequency. Results revealed that higher cardiac rhythm complexity in CRT non-responders was associated with weak correlations of cardiac rhythm at baseline measurement over long scales and over short scales at follow-up recording. Unlike CRT responders, in non-responders, a significant difference in respiratory rhythm complexity between measurements could be consequence of divergent changes in correlation properties of the respiratory signal over short and long scales. Asynchrony between cardiac and respiratory rhythm increased significantly in CRT non-responders during follow-up. Quantification of complexity and synchrony between cardiac and respiratory signals shows significant associations between CRT success and stability of cardio-respiratory coupling. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties
Entropy 2021, 23(8), 1056; https://doi.org/10.3390/e23081056 - 16 Aug 2021
Viewed by 529
Abstract
Our intention is to provide easy methods for estimating entropy and chemical potentials for gas phase reactions. Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role [...] Read more.
Our intention is to provide easy methods for estimating entropy and chemical potentials for gas phase reactions. Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. Based on this partitioning of thermal energy as sensible heat and also as a latent heat or field potential energy, in action mechanics we express the entropy of ideal gases as a capacity factor for enthalpy plus the configurational work to sustain the relative translational, rotational, and vibrational action. This yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies, and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia, and vibrational frequencies. We conclude that the large molecular size of many enzymes may catalyze reaction rates because of their large radial inertia as colloidal particles, maximising action states by impulsive collisions. Understanding how Clausius’ virial theorem justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the second law’s evolutionary nature and the principle of maximum entropy. The ease of performing these operations is illustrated with three important chemical gas phase reactions: the reversible dissociation of hydrogen molecules, lysis of water to hydrogen and oxygen, and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work overcoming molecular interactions plus the configurational work of change in Gibbs energy, often neglected; this may provide a practical guide for managing industrial processes and risk in climate change at the global scale. The concepts developed should also have value as novel methods for the instruction of senior students. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model
Entropy 2021, 23(8), 1019; https://doi.org/10.3390/e23081019 - 07 Aug 2021
Viewed by 347
Abstract
Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give [...] Read more.
Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit q. Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
A Stepwise Assessment of Parsimony and Fuzzy Entropy in Species Distribution Modelling
Entropy 2021, 23(8), 1014; https://doi.org/10.3390/e23081014 - 05 Aug 2021
Cited by 1 | Viewed by 558
Abstract
Entropy is intrinsic to the geographical distribution of a biological species. A species distribution with higher entropy involves more uncertainty, i.e., is more gradually constrained by the environment. Species distribution modelling tries to yield models with low uncertainty but normally has to reduce [...] Read more.
Entropy is intrinsic to the geographical distribution of a biological species. A species distribution with higher entropy involves more uncertainty, i.e., is more gradually constrained by the environment. Species distribution modelling tries to yield models with low uncertainty but normally has to reduce uncertainty by increasing their complexity, which is detrimental for another desirable property of the models, parsimony. By modelling the distribution of 18 vertebrate species in mainland Spain, we show that entropy may be computed along the forward-backwards stepwise selection of variables in Logistic Regression Models to check whether uncertainty is reduced at each step. In general, a reduction of entropy was produced asymptotically at each step of the model. This asymptote could be used to distinguish the entropy attributable to the species distribution from that attributable to model misspecification. We discussed the use of fuzzy entropy for this end because it produces results that are commensurable between species and study areas. Using a stepwise approach and fuzzy entropy may be helpful to counterbalance the uncertainty and the complexity of the models. The model yielded at the step with the lowest fuzzy entropy combines the reduction of uncertainty with parsimony, which results in high efficiency. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Action and Entropy in Heat Engines: An Action Revision of the Carnot Cycle
Entropy 2021, 23(7), 860; https://doi.org/10.3390/e23070860 - 05 Jul 2021
Cited by 1 | Viewed by 572
Abstract
Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct [...] Read more.
Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv = mr2ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@ = mr2ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational, and translational action ratios with Planck’s quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink: the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, which Carnot identified as reversible temperature-dependent but unequal caloric exchanges. Importantly, the engine’s inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, which is a point strongly emphasized by Carnot. Our action revision equates Carnot’s calorique, or the non-sensible heat later described by Clausius as ‘work-heat’, exclusively to negative Gibbs energy (−G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion, and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth’s climates. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Entropic Dynamics on Gibbs Statistical Manifolds
Entropy 2021, 23(5), 494; https://doi.org/10.3390/e23050494 - 21 Apr 2021
Cited by 4 | Viewed by 607
Abstract
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of [...] Read more.
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution. Thus, the dynamics unfolds on a statistical manifold that is automatically endowed by a metric structure provided by information geometry. The curvature of the manifold has a significant influence. We focus our dynamics on the statistical manifold of Gibbs distributions (also known as canonical distributions or the exponential family). The model includes an “entropic” notion of time that is tailored to the system under study; the system is its own clock. As one might expect that entropic time is intrinsically directional; there is a natural arrow of time that is led by entropic considerations. As illustrative examples, we discuss dynamics on a space of Gaussians and the discrete three-state system. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Associations between Neurocardiovascular Signal Entropy and Physical Frailty
Entropy 2021, 23(1), 4; https://doi.org/10.3390/e23010004 - 22 Dec 2020
Viewed by 1409
Abstract
In this cross-sectional study, the relationship between noninvasively measured neurocardiovascular signal entropy and physical frailty was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA). The hypothesis under investigation was that dysfunction in the neurovascular and [...] Read more.
In this cross-sectional study, the relationship between noninvasively measured neurocardiovascular signal entropy and physical frailty was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA). The hypothesis under investigation was that dysfunction in the neurovascular and cardiovascular systems, as quantified by short-length signal complexity during a lying-to-stand test (active stand), could provide a marker for frailty. Frailty status (i.e., “non-frail”, “pre-frail”, and “frail”) was based on Fried’s criteria (i.e., exhaustion, unexplained weight loss, weakness, slowness, and low physical activity). Approximate entropy (ApEn) and sample entropy (SampEn) were calculated during resting (lying down), active standing, and recovery phases. There was continuously measured blood pressure/heart rate data from 2645 individuals (53.0% female) and frontal lobe tissue oxygenation data from 2225 participants (52.3% female); both samples had a mean (SD) age of 64.3 (7.7) years. Results revealed statistically significant associations between neurocardiovascular signal entropy and frailty status. Entropy differences between non-frail and pre-frail/frail were greater during resting state compared with standing and recovery phases. Compared with ApEn, SampEn seemed to have better discriminating power between non-frail and pre-frail/frail individuals. The quantification of entropy in short length neurocardiovascular signals could provide a clinically useful marker of the multiple physiological dysregulations that underlie physical frailty. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Interpreting Social Accounting Matrix (SAM) as an Information Channel
Entropy 2020, 22(12), 1346; https://doi.org/10.3390/e22121346 - 28 Nov 2020
Viewed by 753
Abstract
Information theory, and the concept of information channel, allows us to calculate the mutual information between the source (input) and the receiver (output), both represented by probability distributions over their possible states. In this paper, we use the theory behind the information channel [...] Read more.
Information theory, and the concept of information channel, allows us to calculate the mutual information between the source (input) and the receiver (output), both represented by probability distributions over their possible states. In this paper, we use the theory behind the information channel to provide an enhanced interpretation to a Social Accounting Matrix (SAM), a square matrix whose columns and rows present the expenditure and receipt accounts of economic actors. Under our interpretation, the SAM’s coefficients, which, conceptually, can be viewed as a Markov chain, can be interpreted as an information channel, allowing us to optimize the desired level of aggregation within the SAM. In addition, the developed information measures can describe accurately the evolution of a SAM over time. Interpreting the SAM matrix as an ergodic chain could show the effect of a shock on the economy after several periods or economic cycles. Under our new framework, finding the power limit of the matrix allows one to check (and confirm) whether the matrix is well-constructed (irreducible and aperiodic), and obtain new optimization functions to balance the SAM matrix. In addition to the theory, we also provide two empirical examples that support our channel concept and help to understand the associated measures. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Kullback–Leibler Divergence of a Freely Cooling Granular Gas
Entropy 2020, 22(11), 1308; https://doi.org/10.3390/e22111308 - 17 Nov 2020
Cited by 2 | Viewed by 617
Abstract
Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original H-theorem hypotheses do not fit here and the H-functional presents some additional measure problems that [...] Read more.
Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original H-theorem hypotheses do not fit here and the H-functional presents some additional measure problems that are solved by the Kullback–Leibler divergence (KLD) of a reference velocity distribution function from the actual distribution. The right choice of the reference distribution in the KLD is crucial for the latter to qualify or not as a Lyapunov functional, the asymptotic “homogeneous cooling state” (HCS) distribution being a potential candidate. Due to the lack of a formal proof far from the quasielastic limit, the aim of this work is to support this conjecture aided by molecular dynamics simulations of inelastic hard disks and spheres in a wide range of values for the coefficient of restitution (α) and for different initial conditions. Our results reject the Maxwellian distribution as a possible reference, whereas they reinforce the HCS one. Moreover, the KLD is used to measure the amount of information lost on using the former rather than the latter, revealing a non-monotonic dependence with α. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Complexity as Causal Information Integration
Entropy 2020, 22(10), 1107; https://doi.org/10.3390/e22101107 - 30 Sep 2020
Cited by 1 | Viewed by 1029
Abstract
Complexity measures in the context of the Integrated Information Theory of consciousness try to quantify the strength of the causal connections between different neurons. This is done by minimizing the KL-divergence between a full system and one without causal cross-connections. Various measures have [...] Read more.
Complexity measures in the context of the Integrated Information Theory of consciousness try to quantify the strength of the causal connections between different neurons. This is done by minimizing the KL-divergence between a full system and one without causal cross-connections. Various measures have been proposed and compared in this setting. We will discuss a class of information geometric measures that aim at assessing the intrinsic causal cross-influences in a system. One promising candidate of these measures, denoted by ΦCIS, is based on conditional independence statements and does satisfy all of the properties that have been postulated as desirable. Unfortunately it does not have a graphical representation, which makes it less intuitive and difficult to analyze. We propose an alternative approach using a latent variable, which models a common exterior influence. This leads to a measure ΦCII, Causal Information Integration, that satisfies all of the required conditions. Our measure can be calculated using an iterative information geometric algorithm, the em-algorithm. Therefore we are able to compare its behavior to existing integrated information measures. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Entropy Analysis of a Flexible Markovian Queue with Server Breakdowns
Entropy 2020, 22(9), 979; https://doi.org/10.3390/e22090979 - 03 Sep 2020
Viewed by 743
Abstract
In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold level c, the server serves customers one a time when the queue length is less than c, and in batches of fixed size c when the queue [...] Read more.
In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold level c, the server serves customers one a time when the queue length is less than c, and in batches of fixed size c when the queue length is greater than or equal to c. The server is subject to failure when serving either a single or a batch of customers. Service rates, failure rates, and repair rates, depend on whether the server is serving a single customer or a batch of customers. While the analytical method provides the initial probability vector, we use the entropy principle to obtain both the initial probability vector (for comparison) and the tail probability vector. The comparison shows the results obtained analytically and approximately are in good agreement, especially when the first two moments are used in the entropy approach. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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Article
Robustness Analysis of the Estimators for the Nonlinear System Identification
Entropy 2020, 22(8), 834; https://doi.org/10.3390/e22080834 - 30 Jul 2020
Viewed by 799
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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Article
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
Cited by 4 | Viewed by 987
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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Article
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
Cited by 1 | Viewed by 860
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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Article
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
Cited by 1 | Viewed by 871
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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Article
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
Viewed by 1694
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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Article
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
Cited by 3 | Viewed by 926
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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Article
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 2 | Viewed by 1484
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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Article
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
Viewed by 932
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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Article
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 12 | Viewed by 1467
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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Article
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 4 | Viewed by 1182
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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Pearle’s Hidden-Variable Model Revisited
Entropy 2020, 22(1), 1; https://doi.org/10.3390/e22010001 - 18 Dec 2019
Cited by 4 | Viewed by 1062
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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