Entropy

17 pages, 372 KiB

Open AccessArticle

Can a Quantum Walk Tell Which Is Which?A Study of Quantum Walk-Based Graph Similarity

by Giorgia Minello, Luca Rossi and Andrea Torsello

Entropy 2019, 21(3), 328; https://doi.org/10.3390/e21030328 - 26 Mar 2019

Cited by 11 | Viewed by 4026

We consider the problem of measuring the similarity between two graphs using continuous-time quantum walks and comparing their time-evolution by means of the quantum Jensen-Shannon divergence. Contrary to previous works that focused solely on undirected graphs, here we consider the case of both [...] Read more.

We consider the problem of measuring the similarity between two graphs using continuous-time quantum walks and comparing their time-evolution by means of the quantum Jensen-Shannon divergence. Contrary to previous works that focused solely on undirected graphs, here we consider the case of both directed and undirected graphs. We also consider the use of alternative Hamiltonians as well as the possibility of integrating additional node-level topological information into the proposed framework. We set up a graph classification task and we provide empirical evidence that: (1) our similarity measure can effectively incorporate the edge directionality information, leading to a significant improvement in classification accuracy; (2) the choice of the quantum walk Hamiltonian does not have a significant effect on the classification accuracy; (3) the addition of node-level topological information improves the classification accuracy in some but not all cases. We also theoretically prove that under certain constraints, the proposed similarity measure is positive definite and thus a valid kernel measure. Finally, we describe a fully quantum procedure to compute the kernel. Full article

(This article belongs to the Special Issue Quantum Walks and Related Issues)

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22 pages, 554 KiB

Open AccessArticle

Unsupervised Indoor Positioning System Based on Environmental Signatures

by Pan Feng, Danyang Qin, Min Zhao, Ruolin Guo and Teklu Merhawit Berhane

Entropy 2019, 21(3), 327; https://doi.org/10.3390/e21030327 - 26 Mar 2019

Cited by 3 | Viewed by 3390

Abstract

Mobile sensors are widely used in indoor positioning in recent years, but most methods require cumbersome calibration for precise positioning results, thus the paper proposes a new unsupervised indoor positioning (UIP) without cumbersome calibration. UIP takes advantage of environment features in indoor environments, [...] Read more.

Mobile sensors are widely used in indoor positioning in recent years, but most methods require cumbersome calibration for precise positioning results, thus the paper proposes a new unsupervised indoor positioning (UIP) without cumbersome calibration. UIP takes advantage of environment features in indoor environments, as some indoor locations have their signatures. UIP considers these signatures as the landmarks, and combines dead reckoning with them in a simultaneous localization and mapping (SLAM) frame to reduce positioning errors and convergence time. The test results prove that the system can achieve accurate indoor positioning, which highlights its prospect as an unconventional method of indoor positioning. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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16 pages, 1639 KiB

Open AccessFeature PaperArticle

About Universality and Thermodynamics of Turbulence

by Damien Geneste, Hugues Faller, Florian Nguyen, Vishwanath Shukla, Jean-Philippe Laval, Francois Daviaud, Ewe-Wei Saw and Bérengère Dubrulle

Entropy 2019, 21(3), 326; https://doi.org/10.3390/e21030326 - 26 Mar 2019

Cited by 5 | Viewed by 4873

Abstract

This paper investigates the universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and direct numerical simulations (DNS) of the Navier-Stokes equations. It shows that the numerical and experimental velocity structure [...] Read more.

This paper investigates the universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and direct numerical simulations (DNS) of the Navier-Stokes equations. It shows that the numerical and experimental velocity structure functions up to order 9 follow a log-universality (Castaing et al. Phys. D Nonlinear Phenom. 1993); this leads to a collapse on a universal curve, when units including a logarithmic dependence on the Reynolds number are used. This paper then investigates the meaning and consequences of such log-universality, and shows that it is connected with the properties of a “multifractal free energy”, based on an analogy between multifractal and thermodynamics. It shows that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different Hölder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data. Full article

(This article belongs to the Special Issue Intermittency and Self-Organisation in Turbulence and Statistical Mechanics)

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12 pages, 320 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Entanglement 25 Years after Quantum Teleportation: Testing Joint Measurements in Quantum Networks

by Nicolas Gisin

Entropy 2019, 21(3), 325; https://doi.org/10.3390/e21030325 - 26 Mar 2019

Cited by 45 | Viewed by 6564

Abstract

Twenty-five years after the invention of quantum teleportation, the concept of entanglement gained enormous popularity. This is especially nice to those who remember that entanglement was not even taught at universities until the 1990s. Today, entanglement is often presented as a resource, the [...] Read more.

Twenty-five years after the invention of quantum teleportation, the concept of entanglement gained enormous popularity. This is especially nice to those who remember that entanglement was not even taught at universities until the 1990s. Today, entanglement is often presented as a resource, the resource of quantum information science and technology. However, entanglement is exploited twice in quantum teleportation. Firstly, entanglement is the “quantum teleportation channel”, i.e., entanglement between distant systems. Second, entanglement appears in the eigenvectors of the joint measurement that Alice, the sender, has to perform jointly on the quantum state to be teleported and her half of the “quantum teleportation channel”, i.e., entanglement enabling entirely new kinds of quantum measurements. I emphasize how poorly this second kind of entanglement is understood. In particular, I use quantum networks in which each party connected to several nodes performs a joint measurement to illustrate that the quantumness of such joint measurements remains elusive, escaping today’s available tools to detect and quantify it. Full article

(This article belongs to the Special Issue Quantum Communication—Celebrating the Silver Jubilee of Teleportation)

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32 pages, 1139 KiB

Open AccessArticle

Efficient Algorithms for Coded Multicasting in Heterogeneous Caching Networks

by Giuseppe Vettigli, Mingyue Ji, Karthikeyan Shanmugam, Jaime Llorca, Antonia M. Tulino and Giuseppe Caire

Entropy 2019, 21(3), 324; https://doi.org/10.3390/e21030324 - 25 Mar 2019

Cited by 6 | Viewed by 3724

Abstract

Coded multicasting has been shown to be a promising approach to significantly improve the performance of content delivery networks with multiple caches downstream of a common multicast link. However, the schemes that have been shown to achieve order-optimal performance require content items to [...] Read more.

Coded multicasting has been shown to be a promising approach to significantly improve the performance of content delivery networks with multiple caches downstream of a common multicast link. However, the schemes that have been shown to achieve order-optimal performance require content items to be partitioned into several packets that grows exponentially with the number of caches, leading to codes of exponential complexity that jeopardize their promising performance benefits. In this paper, we address this crucial performance-complexity tradeoff in a heterogeneous caching network setting, where edge caches with possibly different storage capacity collect multiple content requests that may follow distinct demand distributions. We extend the asymptotic (in the number of packets per file) analysis of shared link caching networks to heterogeneous network settings, and present novel coded multicast schemes, based on local graph coloring, that exhibit polynomial-time complexity in all the system parameters, while preserving the asymptotically proven multiplicative caching gain even for finite file packetization. We further demonstrate that the packetization order (the number of packets each file is split into) can be traded-off with the number of requests collected by each cache, while preserving the same multiplicative caching gain. Simulation results confirm the superiority of the proposed schemes and illustrate the interesting request aggregation vs. packetization order tradeoff within several practical settings. Our results provide a compelling step towards the practical achievability of the promising multiplicative caching gain in next generation access networks. Full article

(This article belongs to the Special Issue Information Theory for Data Communications and Processing)

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11 pages, 293 KiB

Open AccessArticle

On the Reality of Quantum Collapse and the Emergence of Space-Time

by Andreas Schlatter

Entropy 2019, 21(3), 323; https://doi.org/10.3390/e21030323 - 25 Mar 2019

Cited by 3 | Viewed by 4400

Abstract

We present a model, in which quantum-collapse is supposed to be real as a result of breaking unitary symmetry, and in which we can define a notion of “becoming”. We show how empirical space-time can emerge in this model, if duration is measured [...] Read more.

We present a model, in which quantum-collapse is supposed to be real as a result of breaking unitary symmetry, and in which we can define a notion of “becoming”. We show how empirical space-time can emerge in this model, if duration is measured by light-clocks. The model opens a possible bridge between Quantum Physics and Relativity Theory and offers a new perspective on some long-standing open questions, both within and between the two theories. Full article

13 pages, 3148 KiB

Open AccessArticle

Entropy-Based Method to Evaluate Contact-Pressure Distribution for Assembly-Accuracy Stability Prediction

by Xiao Chen, Xin Jin, Ke Shang and Zhijing Zhang

Entropy 2019, 21(3), 322; https://doi.org/10.3390/e21030322 - 25 Mar 2019

Cited by 14 | Viewed by 3003

Abstract

Assembly accuracy and accuracy stability prediction are significant research directions for improving the reliability and efficiency of precision assembly. In this study, an improved method for assembly accuracy stability prediction, based on the contact-pressure distribution entropy, is presented. By using the contact-pressure distribution [...] Read more.

Assembly accuracy and accuracy stability prediction are significant research directions for improving the reliability and efficiency of precision assembly. In this study, an improved method for assembly accuracy stability prediction, based on the contact-pressure distribution entropy, is presented. By using the contact-pressure distribution as the evaluation parameter instead of the strain-energy distribution, the improved method can not only predict the assembly accuracy of precision assembly more efficiently, but also predict the stability of the assembly accuracy with variations in the ambient temperature. The contact pressure has a clearer mechanical significance than strain energy density in the assembly process, which can be used to distinguish the actual contact area from the contact surface. Hence, the improved method is more efficient and accurate than the original. This study utilizes the same case used in the original method and an additional case from the actual production process to verify the improved method. The correctness and validity of the improved method are proved by these case studies. Full article

(This article belongs to the Section Multidisciplinary Applications)

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14 pages, 2863 KiB

Open AccessArticle

Exergy Analysis of Directional Solvent Extraction Desalination Process

by Sorour Alotaibi, Osama M. Ibrahim, Yu Wang and Tengfei Luo

Entropy 2019, 21(3), 321; https://doi.org/10.3390/e21030321 - 25 Mar 2019

Cited by 14 | Viewed by 4324

Abstract

This paper presents an exergy analysis to evaluate the performance of a continuous directional solvent extraction (DSE) desalination process using octanoic acid. The flow of exergy was calculated for each thermodynamic state and balanced for different components of the system to quantify the [...] Read more.

This paper presents an exergy analysis to evaluate the performance of a continuous directional solvent extraction (DSE) desalination process using octanoic acid. The flow of exergy was calculated for each thermodynamic state and balanced for different components of the system to quantify the inefficiencies in the process. A parametric study was performed to evaluate the impact of three critical design variables on exergy consumption. The parametric study reveals that the total exergy input decreases significantly with an increase in heat exchanger effectiveness. The results also indicate that the heat exchangers account for the highest exergy destruction. The total exergy consumption, however, has a slightly declining trend as the recovery-ratio increases. There is a small variation in the total exergy consumption, within the uncertainty of the calculation, as the highest process temperature increases. When compared to conventional desalination processes, the exergy consumption of the DSE, with heat recovery of 90%, is comparable to those of multi-stage flashing (MSF), but much higher than reverse osmosis (RO). Octanoic acid, which has low product water yield, is identified as the primary factor negatively impacting the exergy consumptions. To exploit the low-grade and low-temperature heat source feature of the DSE process, directional solvents with higher yield should be identified or designed to enable its full implementation. Full article

(This article belongs to the Special Issue Entropy and Thermodynamics in Desalination Systems)

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Graphical abstract

17 pages, 948 KiB

Open AccessArticle

Multifractal and Chaotic Properties of Solar Wind at MHD and Kinetic Domains: An Empirical Mode Decomposition Approach

by Tommaso Alberti, Giuseppe Consolini, Vincenzo Carbone, Emiliya Yordanova, Maria Federica Marcucci and Paola De Michelis

Entropy 2019, 21(3), 320; https://doi.org/10.3390/e21030320 - 25 Mar 2019

Cited by 37 | Viewed by 4211

Abstract

Turbulence, intermittency, and self-organized structures in space plasmas can be investigated by using a multifractal formalism mostly based on the canonical structure function analysis with fixed constraints about stationarity, linearity, and scales. Here, the Empirical Mode Decomposition (EMD) method is firstly used to [...] Read more.

Turbulence, intermittency, and self-organized structures in space plasmas can be investigated by using a multifractal formalism mostly based on the canonical structure function analysis with fixed constraints about stationarity, linearity, and scales. Here, the Empirical Mode Decomposition (EMD) method is firstly used to investigate timescale fluctuations of the solar wind magnetic field components; then, by exploiting the local properties of fluctuations, the structure function analysis is used to gain insights into the scaling properties of both inertial and kinetic/dissipative ranges. Results show that while the inertial range dynamics can be described in a multifractal framework, characterizing an unstable fixed point of the system, the kinetic/dissipative range dynamics is well described by using a monofractal approach, because it is a stable fixed point of the system, unless it has a higher degree of complexity and chaos. Full article

(This article belongs to the Special Issue Intermittency and Self-Organisation in Turbulence and Statistical Mechanics)

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21 pages, 13252 KiB

Open AccessEditor’s ChoiceArticle

Image Encryption Based on Pixel-Level Diffusion with Dynamic Filtering and DNA-Level Permutation with 3D Latin Cubes

by Taiyong Li, Jiayi Shi, Xinsheng Li, Jiang Wu and Fan Pan

Entropy 2019, 21(3), 319; https://doi.org/10.3390/e21030319 - 24 Mar 2019

Cited by 85 | Viewed by 5095

Abstract

Image encryption is one of the essential tasks in image security. In this paper, we propose a novel approach that integrates a hyperchaotic system, pixel-level Dynamic Filtering, DNA computing, and operations on 3D Latin Cubes, namely DFDLC, for image encryption. Specifically, the approach [...] Read more.

Image encryption is one of the essential tasks in image security. In this paper, we propose a novel approach that integrates a hyperchaotic system, pixel-level Dynamic Filtering, DNA computing, and operations on 3D Latin Cubes, namely DFDLC, for image encryption. Specifically, the approach consists of five stages: (1) a newly proposed 5D hyperchaotic system with two positive Lyapunov exponents is applied to generate a pseudorandom sequence; (2) for each pixel in an image, a filtering operation with different templates called dynamic filtering is conducted to diffuse the image; (3) DNA encoding is applied to the diffused image and then the DNA-level image is transformed into several 3D DNA-level cubes; (4) Latin cube is operated on each DNA-level cube; and (5) all the DNA cubes are integrated and decoded to a 2D cipher image. Extensive experiments are conducted on public testing images, and the results show that the proposed DFDLC can achieve state-of-the-art results in terms of several evaluation criteria. Full article

(This article belongs to the Special Issue Entropy in Image Analysis)

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28 pages, 96400 KiB

Open AccessArticle

Kapur’s Entropy for Color Image Segmentation Based on a Hybrid Whale Optimization Algorithm

by Chunbo Lang and Heming Jia

Entropy 2019, 21(3), 318; https://doi.org/10.3390/e21030318 - 23 Mar 2019

Cited by 45 | Viewed by 8950

Abstract

In this paper, a new hybrid whale optimization algorithm (WOA) called WOA-DE is proposed to better balance the exploitation and exploration phases of optimization. Differential evolution (DE) is adopted as a local search strategy with the purpose of enhancing exploitation capability. The WOA-DE [...] Read more.

In this paper, a new hybrid whale optimization algorithm (WOA) called WOA-DE is proposed to better balance the exploitation and exploration phases of optimization. Differential evolution (DE) is adopted as a local search strategy with the purpose of enhancing exploitation capability. The WOA-DE algorithm is then utilized to solve the problem of multilevel color image segmentation that can be considered as a challenging optimization task. Kapur’s entropy is used to obtain an efficient image segmentation method. In order to evaluate the performance of proposed algorithm, different images are selected for experiments, including natural images, satellite images and magnetic resonance (MR) images. The experimental results are compared with state-of-the-art meta-heuristic algorithms as well as conventional approaches. Several performance measures have been used such as average fitness values, standard deviation (STD), peak signal to noise ratio (PSNR), structural similarity index (SSIM), feature similarity index (FSIM), Wilcoxon’s rank sum test, and Friedman test. The experimental results indicate that the WOA-DE algorithm is superior to the other meta-heuristic algorithms. In addition, to show the effectiveness of the proposed technique, the Otsu method is used for comparison. Full article

(This article belongs to the Special Issue Entropy in Image Analysis)

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12 pages, 2884 KiB

Open AccessArticle

Intra- and Inter-Modular Connectivity Alterations in the Brain Structural Network of Spinocerebellar Ataxia Type 3

by Chi-Wen Jao, Bing-Wen Soong, Tzu-Yun Wang, Hsiu-Mei Wu, Chia-Feng Lu, Po-Shan Wang and Yu-Te Wu

Entropy 2019, 21(3), 317; https://doi.org/10.3390/e21030317 - 23 Mar 2019

Cited by 9 | Viewed by 3254

Abstract

In addition to cerebellar degeneration symptoms, patients with spinocerebellar ataxia type 3 (SCA3) exhibit extensive involvements with damage in the prefrontal cortex. A network model has been proposed for investigating the structural organization and functional mechanisms of clinical brain disorders. For neural degenerative [...] Read more.

In addition to cerebellar degeneration symptoms, patients with spinocerebellar ataxia type 3 (SCA3) exhibit extensive involvements with damage in the prefrontal cortex. A network model has been proposed for investigating the structural organization and functional mechanisms of clinical brain disorders. For neural degenerative diseases, a cortical feature-based structural connectivity network can locate cortical atrophied regions and indicate how their connectivity and functions may change. The brain network of SCA3 has been minimally explored. In this study, we investigated this network by enrolling 48 patients with SCA3 and 48 healthy subjects. A novel three-dimensional fractal dimension-based network was proposed to detect differences in network parameters between the groups. Copula correlations and modular analysis were then employed to categorize and construct the structural networks. Patients with SCA3 exhibited significant lateralized atrophy in the left supratentorial regions and significantly lower modularity values. Their cerebellar regions were dissociated from higher-level brain networks, and demonstrated decreased intra-modular connectivity in all lobes, but increased inter-modular connectivity in the frontal and parietal lobes. Our results suggest that the brain networks of patients with SCA3 may be reorganized in these regions, with the introduction of certain compensatory mechanisms in the cerebral cortex to minimize their cognitive impairment syndrome. Full article

(This article belongs to the Special Issue Application of Information Theory in Biomedical Data Mining)

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14 pages, 546 KiB

Open AccessArticle

The Impact of Financial and Macroeconomic Shocks on the Entropy of Financial Markets

by Sorin Anagnoste and Petre Caraiani

Entropy 2019, 21(3), 316; https://doi.org/10.3390/e21030316 - 23 Mar 2019

Cited by 6 | Viewed by 3256

Abstract

We propose here a method to analyze whether financial and macroeconomic shocks influence the entropy of financial networks. We derive a measure of entropy using the correlation matrix of the stock market components of the DOW Jones Industrial Average (DJIA) index. Using VAR [...] Read more.

We propose here a method to analyze whether financial and macroeconomic shocks influence the entropy of financial networks. We derive a measure of entropy using the correlation matrix of the stock market components of the DOW Jones Industrial Average (DJIA) index. Using VAR models in different specifications, we show that shocks in production or the DJIA index lead to an increase in the entropy of the financial markets. Full article

(This article belongs to the Collection Advances in Applied Statistical Mechanics)

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18 pages, 286 KiB

Open AccessArticle

Confidence Interval Estimation for Precipitation Quantiles Based on Principle of Maximum Entropy

by Ting Wei and Songbai Song

Entropy 2019, 21(3), 315; https://doi.org/10.3390/e21030315 - 22 Mar 2019

Cited by 5 | Viewed by 3177

Abstract

The principle of maximum entropy (POME) has been used for a variety of applications in hydrology, however it has not been used in confidence interval estimation. Therefore, the POME was employed for confidence interval estimation for precipitation quantiles in this study. The gamma, [...] Read more.

The principle of maximum entropy (POME) has been used for a variety of applications in hydrology, however it has not been used in confidence interval estimation. Therefore, the POME was employed for confidence interval estimation for precipitation quantiles in this study. The gamma, Pearson type 3 (P3), and extreme value type 1 (EV1) distributions were used to fit the observation series. The asymptotic variances and confidence intervals of gamma, P3, and EV1 quantiles were then calculated based on POME. Monte Carlo simulation experiments were performed to evaluate the performance of the POME method and to compare with widely used methods of moments (MOM) and the maximum likelihood (ML) method. Finally, the confidence intervals T-year design precipitations were calculated using the POME for the three distributions and compared with those of MOM and ML. Results show that the POME is superior to MOM and ML in reducing the uncertainty of quantile estimators. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

16 pages, 575 KiB

Open AccessArticle

Development of Postural Stability Index to Distinguish Different Stability States

by Nurul Retno Nurwulan, Bernard C. Jiang and Vera Novak

Entropy 2019, 21(3), 314; https://doi.org/10.3390/e21030314 - 22 Mar 2019

Cited by 9 | Viewed by 3398

Abstract

A key factor for fall prevention involves understanding the pathophysiology of stability. This study proposes the postural stability index (PSI), which is a novel measure to quantify different stability states on healthy subjects. The results of the x-, y-, and z-axes of the [...] Read more.

A key factor for fall prevention involves understanding the pathophysiology of stability. This study proposes the postural stability index (PSI), which is a novel measure to quantify different stability states on healthy subjects. The results of the x-, y-, and z-axes of the acceleration signals were analyzed from 10 healthy young adults and 10 healthy older adults under three conditions as follows: Normal walking, walking with obstacles, and fall-like motions. The ensemble empirical mode decomposition (EEMD) was used to reconstruct the acceleration signal data. Wearable accelerometers were located on the ankles and knees of the subjects. The PSI indicated a decreasing trend of its values from normal walking to the fall-like motions. Free-walking data were used to determine the stability based on the PSI. The segmented free-walking data indicated changes in the stability states that suggested that the PSI is potentially helpful in quantifying gait stability. Full article

(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications)

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17 pages, 14072 KiB

Open AccessArticle

A New Phylogenetic Inference Based on Genetic Attribute Reduction for Morphological Data

by Jun Feng, Zeyun Liu, Hongwei Feng, Richard F. E. Sutcliffe, Jianni Liu and Jian Han

Entropy 2019, 21(3), 313; https://doi.org/10.3390/e21030313 - 22 Mar 2019

Viewed by 3679

Abstract

To address the instability of phylogenetic trees in morphological datasets caused by missing values, we present a phylogenetic inference method based on a concept decision tree (CDT) in conjunction with attribute reduction. First, a reliable initial phylogenetic seed tree is created using [...] Read more.

To address the instability of phylogenetic trees in morphological datasets caused by missing values, we present a phylogenetic inference method based on a concept decision tree (CDT) in conjunction with attribute reduction. First, a reliable initial phylogenetic seed tree is created using a few species with relatively complete morphological information by using biologists’ prior knowledge or by applying existing tools such as MrBayes. Second, using a top-down data processing approach, we construct concept-sample templates by performing attribute reduction at each node in the initial phylogenetic seed tree. In this way, each node is turned into a decision point with multiple concept-sample templates, providing decision-making functions for grafting. Third, we apply a novel matching algorithm to evaluate the degree of similarity between the species’ attributes and their concept-sample templates and to determine the location of the species in the initial phylogenetic seed tree. In this manner, the phylogenetic tree is established step by step. We apply our algorithm to several datasets and compare it with the maximum parsimony, maximum likelihood, and Bayesian inference methods using the two evaluation criteria of accuracy and stability. The experimental results indicate that as the proportion of missing data increases, the accuracy of the CDT method remains at 86.5%, outperforming all other methods and producing a reliable phylogenetic tree. Full article

(This article belongs to the Special Issue Application of Information Theory in Biomedical Data Mining)

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19 pages, 1090 KiB

Open AccessEditor’s ChoiceArticle

Probability Distributions with Singularities

by Federico Corberi and Alessandro Sarracino

Entropy 2019, 21(3), 312; https://doi.org/10.3390/e21030312 - 21 Mar 2019

Cited by 10 | Viewed by 3575

Abstract

In this paper we review some general properties of probability distributions which exhibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such paradigms, the underlying mathematical mechanism producing [...] Read more.

In this paper we review some general properties of probability distributions which exhibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such paradigms, the underlying mathematical mechanism producing the singularity and other topics such as the condensation of fluctuations, the relationships with ordinary phase-transitions, the giant response associated to anomalous fluctuations, and the interplay with fluctuation relations. Full article

(This article belongs to the Special Issue Fluctuation Relations and Nonequilibrium Thermodynamics in Classical and Quantum Systems)

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19 pages, 3078 KiB

Open AccessArticle

Combination of Global Features for the Automatic Quality Assessment of Retinal Images

by Jorge Jiménez-García, Roberto Romero-Oraá, María García, María I. López-Gálvez and Roberto Hornero

Entropy 2019, 21(3), 311; https://doi.org/10.3390/e21030311 - 21 Mar 2019

Cited by 7 | Viewed by 3583

Abstract

Diabetic retinopathy (DR) is one of the most common causes of visual loss in developed countries. Computer-aided diagnosis systems aimed at detecting DR can reduce the workload of ophthalmologists in screening programs. Nevertheless, a large number of retinal images cannot be analyzed by [...] Read more.

Diabetic retinopathy (DR) is one of the most common causes of visual loss in developed countries. Computer-aided diagnosis systems aimed at detecting DR can reduce the workload of ophthalmologists in screening programs. Nevertheless, a large number of retinal images cannot be analyzed by physicians and automatic methods due to poor quality. Automatic retinal image quality assessment (RIQA) is needed before image analysis. The purpose of this study was to combine novel generic quality features to develop a RIQA method. Several features were calculated from retinal images to achieve this goal. Features derived from the spatial and spectral entropy-based quality (SSEQ) and the natural images quality evaluator (NIQE) methods were extracted. They were combined with novel sharpness and luminosity measures based on the continuous wavelet transform (CWT) and the hue saturation value (HSV) color model, respectively. A subset of non-redundant features was selected using the fast correlation-based filter (FCBF) method. Subsequently, a multilayer perceptron (MLP) neural network was used to obtain the quality of images from the selected features. Classification results achieved 91.46% accuracy, 92.04% sensitivity, and 87.92% specificity. Results suggest that the proposed RIQA method could be applied in a more general computer-aided diagnosis system aimed at detecting a variety of retinal pathologies such as DR and age-related macular degeneration. Full article

(This article belongs to the Special Issue Selected Papers from 36th Annual Conference of Spanish Society of Biomedical Engineering)

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20 pages, 2855 KiB

Open AccessReview

The Observable Representation

by L. S. Schulman

Entropy 2019, 21(3), 310; https://doi.org/10.3390/e21030310 - 21 Mar 2019

Viewed by 2644

Abstract

The observable representation (OR) is an embedding of the space on which a stochastic dynamics is taking place into a low dimensional Euclidean space. The most significant feature of the OR is that it respects the dynamics. Examples are given in several areas: [...] Read more.

The observable representation (OR) is an embedding of the space on which a stochastic dynamics is taking place into a low dimensional Euclidean space. The most significant feature of the OR is that it respects the dynamics. Examples are given in several areas: the definition of a phase transition (including metastable phases), random walks in which the OR recovers the original space, complex systems, systems in which the number of extrema exceed convenient viewing capacity, and systems in which successful features are displayed, but without the support of known theorems. Full article

(This article belongs to the Special Issue 20th Anniversary of Entropy—Review Papers Collection)

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24 pages, 9580 KiB

Open AccessArticle

A Fractional-Order Partially Non-Linear Model of a Laboratory Prototype of Hydraulic Canal System

by Saddam Gharab, Vicente Feliu-Batlle and Raul Rivas-Perez

Entropy 2019, 21(3), 309; https://doi.org/10.3390/e21030309 - 21 Mar 2019

Cited by 6 | Viewed by 2980

Abstract

This article addresses the identification of the nonlinear dynamics of the main pool of a laboratory hydraulic canal installed in the University of Castilla La Mancha. A new dynamic model has been developed by taking into account the measurement errors caused by the [...] Read more.

This article addresses the identification of the nonlinear dynamics of the main pool of a laboratory hydraulic canal installed in the University of Castilla La Mancha. A new dynamic model has been developed by taking into account the measurement errors caused by the different parts of our experimental setup: (a) the nonlinearity associated to the input signal, which is caused by the movements of the upstream gate, is avoided by using a nonlinear equivalent upstream gate model, (b) the nonlinearity associated to the output signal, caused by the sensor’s resolution, is avoided by using a quantization model in the identification process, and (c) the nonlinear behaviour of the canal, which is related to the working flow regime, is taken into account considering two completely different models in function of the operating regime: the free and the submerged flows. The proposed technique of identification is based on the time-domain data. An input pseudo-random binary signal (PRBS) is designed depending on the parameters of an initially estimated linear model that was obtained by using a fundamental technique of identification. Fractional and integer order plus time delay models are used to approximate the responses of the main pool of the canal in its different flow regimes. An accurate model has been obtained, which is composed of two submodels: a first order plus time delay submodel that accurately describes the dynamics of the free flow and a fractional-order plus time delay submodel that properly describes the dynamics of the submerged flow. Full article

(This article belongs to the Special Issue The Fractional View of Complexity)

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38 pages, 3517 KiB

Open AccessArticle

The Understanding Capacity and Information Dynamics in the Human Brain

by Yan M. Yufik

Entropy 2019, 21(3), 308; https://doi.org/10.3390/e21030308 - 21 Mar 2019

Cited by 14 | Viewed by 5002

Abstract

This article proposes a theory of neuronal processes underlying cognition, focusing on the mechanisms of understanding in the human brain. Understanding is a product of mental modeling. The paper argues that mental modeling is a form of information production inside the neuronal system [...] Read more.

This article proposes a theory of neuronal processes underlying cognition, focusing on the mechanisms of understanding in the human brain. Understanding is a product of mental modeling. The paper argues that mental modeling is a form of information production inside the neuronal system extending the reach of human cognition “beyond the information given” (Bruner, J.S., Beyond the Information Given, 1973). Mental modeling enables forms of learning and prediction (learning with understanding and prediction via explanation) that are unique to humans, allowing robust performance under unfamiliar conditions having no precedents in the past history. The proposed theory centers on the notions of self-organization and emergent properties of collective behavior in the neuronal substrate. The theory motivates new approaches in the design of intelligent artifacts (machine understanding) that are complementary to those underlying the technology of machine learning. Full article

(This article belongs to the Special Issue Information Dynamics in Brain and Physiological Networks)

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3 pages, 199 KiB

Open AccessCorrection

Correction: Veen, D.; Stoel, D.; Schalken, N.; Mulder, K.; Van de Schoot, R. Using the Data Agreement Criterion to Rank Experts’ Beliefs. Entropy 2018, 20, 592

by Duco Veen, Diederick Stoel, Naomi Schalken, Kees Mulder and Rens van de Schoot

Entropy 2019, 21(3), 307; https://doi.org/10.3390/e21030307 - 21 Mar 2019

Cited by 1 | Viewed by 2895

Abstract

Due to a coding error the marginal likelihoods have not been correctly calculated for the empirical example and thus the Bayes Factors following from these marginal likelihoods are incorrect. The corrections required occur in Section 3.2 and in two paragraphs of the discussion [...] Read more.

Due to a coding error the marginal likelihoods have not been correctly calculated for the empirical example and thus the Bayes Factors following from these marginal likelihoods are incorrect. The corrections required occur in Section 3.2 and in two paragraphs of the discussion in which the results are referred to. The corrections have limited consequences for the paper and the main conclusions hold. Additionally typos in Equations, and, an error in the numbering of the Equations are remedied. Full article

(This article belongs to the Special Issue Bayesian Inference and Information Theory)

14 pages, 446 KiB

Open AccessEditor’s ChoiceArticle

Using Permutations for Hierarchical Clustering of Time Series

by Jose S. Cánovas, Antonio Guillamón and María Carmen Ruiz-Abellón

Entropy 2019, 21(3), 306; https://doi.org/10.3390/e21030306 - 21 Mar 2019

Cited by 3 | Viewed by 3583

Abstract

Two distances based on permutations are considered to measure the similarity of two time series according to their strength of dependency. The distance measures are used together with different linkages to get hierarchical clustering methods of time series by dependency. We apply these [...] Read more.

Two distances based on permutations are considered to measure the similarity of two time series according to their strength of dependency. The distance measures are used together with different linkages to get hierarchical clustering methods of time series by dependency. We apply these distances to both simulated theoretical and real data series. For simulated time series the distances show good clustering results, both in the case of linear and non-linear dependencies. The effect of the embedding dimension and the linkage method are also analyzed. Finally, several real data series are properly clustered using the proposed method. Full article

(This article belongs to the Special Issue Theoretical Developments and Applications of Entropy and Ordinal Patterns)

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20 pages, 1078 KiB

Open AccessArticle

Deep Neural Networks for ECG-Based Pulse Detection during Out-of-Hospital Cardiac Arrest

by Andoni Elola, Elisabete Aramendi, Unai Irusta, Artzai Picón, Erik Alonso, Pamela Owens and Ahamed Idris

Entropy 2019, 21(3), 305; https://doi.org/10.3390/e21030305 - 21 Mar 2019

Cited by 56 | Viewed by 9419

Abstract

The automatic detection of pulse during out-of-hospital cardiac arrest (OHCA) is necessary for the early recognition of the arrest and the detection of return of spontaneous circulation (end of the arrest). The only signal available in every single defibrillator and valid for the [...] Read more.

The automatic detection of pulse during out-of-hospital cardiac arrest (OHCA) is necessary for the early recognition of the arrest and the detection of return of spontaneous circulation (end of the arrest). The only signal available in every single defibrillator and valid for the detection of pulse is the electrocardiogram (ECG). In this study we propose two deep neural network (DNN) architectures to detect pulse using short ECG segments (5 s), i.e., to classify the rhythm into pulseless electrical activity (PEA) or pulse-generating rhythm (PR). A total of 3914 5-s ECG segments, 2372 PR and 1542 PEA, were extracted from 279 OHCA episodes. Data were partitioned patient-wise into training (80%) and test (20%) sets. The first DNN architecture was a fully convolutional neural network, and the second architecture added a recurrent layer to learn temporal dependencies. Both DNN architectures were tuned using Bayesian optimization, and the results for the test set were compared to state-of-the art PR/PEA discrimination algorithms based on machine learning and hand crafted features. The PR/PEA classifiers were evaluated in terms of sensitivity (Se) for PR, specificity (Sp) for PEA, and the balanced accuracy (BAC), the average of Se and Sp. The Se/Sp/BAC of the DNN architectures were 94.1%/92.9%/93.5% for the first one, and 95.5%/91.6%/93.5% for the second one. Both architectures improved the performance of state of the art methods by more than 1.5 points in BAC. Full article

(This article belongs to the Special Issue Selected Papers from 36th Annual Conference of Spanish Society of Biomedical Engineering)

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12 pages, 735 KiB

Open AccessArticle

Primality, Fractality, and Image Analysis

by Emanuel Guariglia

Entropy 2019, 21(3), 304; https://doi.org/10.3390/e21030304 - 21 Mar 2019

Cited by 112 | Viewed by 4960

Abstract

This paper deals with the hidden structure of prime numbers. Previous numerical studies have already indicated a fractal-like behavior of prime-indexed primes. The construction of binary images enables us to generalize this result. In fact, two-integer sequences can easily be converted into a [...] Read more.

This paper deals with the hidden structure of prime numbers. Previous numerical studies have already indicated a fractal-like behavior of prime-indexed primes. The construction of binary images enables us to generalize this result. In fact, two-integer sequences can easily be converted into a two-color image. In particular, the resulting method shows that both the coprimality condition and Ramanujan primes resemble the Minkowski island and Cantor set, respectively. Furthermore, the comparison between prime-indexed primes and Ramanujan primes is introduced and discussed. Thus the Cantor set covers a relevant role in the fractal-like description of prime numbers. The results confirm the feasibility of the method based on binary images. The link between fractal sets and chaotic dynamical systems may allow the characterization of the Hénon map only in terms of prime numbers. Full article

(This article belongs to the Special Issue Entropy in Image Analysis)

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32 pages, 937 KiB

Open AccessArticle

Dynamics of Ebola Disease in the Framework of Different Fractional Derivatives

by Khan Muhammad Altaf and Abdon Atangana

Entropy 2019, 21(3), 303; https://doi.org/10.3390/e21030303 - 21 Mar 2019

Cited by 73 | Viewed by 4469

Abstract

In recent years the world has witnessed the arrival of deadly infectious diseases that have taken many lives across the globe. To fight back these diseases or control their spread, mankind relies on modeling and medicine to control, cure, and predict the behavior [...] Read more.

In recent years the world has witnessed the arrival of deadly infectious diseases that have taken many lives across the globe. To fight back these diseases or control their spread, mankind relies on modeling and medicine to control, cure, and predict the behavior of such problems. In the case of Ebola, we observe spread that follows a fading memory process and also shows crossover behavior. Therefore, to capture this kind of spread one needs to use differential operators that posses crossover properties and fading memory. We analyze the Ebola disease model by considering three differential operators, that is the Caputo, Caputo–Fabrizio, and the Atangana–Baleanu operators. We present brief detail and some mathematical analysis for each operator applied to the Ebola model. We present a numerical approach for the solution of each operator. Further, numerical results for each operator with various values of the fractional order parameter

α

are presented. A comparison of the suggested operators on the Ebola disease model in the form of graphics is presented. We show that by decreasing the value of the fractional order parameter

α

, the number of individuals infected by Ebola decreases efficiently and conclude that for disease elimination, the Atangana–Baleanu operator is more useful than the other two. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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11 pages, 261 KiB

Open AccessDiscussion

Category Theory for Autonomous and Networked Dynamical Systems

by Jean-Charles Delvenne

Entropy 2019, 21(3), 302; https://doi.org/10.3390/e21030302 - 20 Mar 2019

Cited by 8 | Viewed by 4564

Abstract

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological [...] Read more.

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way. Full article

(This article belongs to the Special Issue Entropy in Networked Control)

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16 pages, 1003 KiB

Open AccessArticle

Identifying the Occurrence Time of the Deadly Mexico M8.2 Earthquake on 7 September 2017

by Nicholas V. Sarlis, Efthimios S. Skordas, Panayiotis A. Varotsos, Alejandro Ramírez-Rojas and Elsa Leticia Flores-Márquez

Entropy 2019, 21(3), 301; https://doi.org/10.3390/e21030301 - 20 Mar 2019

Cited by 11 | Viewed by 3270

Abstract

It has been shown that some dynamic features hidden in the time series of complex systems can be unveiled if we analyze them in a time domain termed natural time. In this analysis, we can identify when a system approaches a critical point [...] Read more.

It has been shown that some dynamic features hidden in the time series of complex systems can be unveiled if we analyze them in a time domain termed natural time. In this analysis, we can identify when a system approaches a critical point (dynamic phase transition). Here, based on natural time analysis, which enables the introduction of an order parameter for seismicity, we discuss a procedure through which we could achieve the identification of the occurrence time of the M8.2 earthquake that occurred on 7 September 2017 in Mexico in Chiapas region, which is the largest magnitude event recorded in Mexico in more than a century. In particular, we first investigated the order parameter fluctuations of seismicity in the entire Mexico and found that, during an almost 30-year period, i.e., from 1 January 1988 until the M8.2 earthquake occurrence, they were minimized around 27 July 2017. From this date, we started computing the variance of seismicity in Chiapas region and found that it approached the critical value 0.070 on 6 September 2017, almost one day before this M8.2 earthquake occurrence. Full article

(This article belongs to the Special Issue Entropy, Nonlinear Dynamics, and Methods of Complex Systems in Earthquake Physics including Precursory Phenomena)

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19 pages, 1191 KiB

Open AccessArticle

Brain Network Modeling Based on Mutual Information and Graph Theory for Predicting the Connection Mechanism in the Progression of Alzheimer’s Disease

by Shuaizong Si, Bin Wang, Xiao Liu, Chong Yu, Chao Ding and Hai Zhao

Entropy 2019, 21(3), 300; https://doi.org/10.3390/e21030300 - 20 Mar 2019

Cited by 15 | Viewed by 4471

Abstract

Alzheimer’s disease (AD) is a progressive disease that causes problems of cognitive and memory functions decline. Patients with AD usually lose their ability to manage their daily life. Exploring the progression of the brain from normal controls (NC) to AD is an essential [...] Read more.

Alzheimer’s disease (AD) is a progressive disease that causes problems of cognitive and memory functions decline. Patients with AD usually lose their ability to manage their daily life. Exploring the progression of the brain from normal controls (NC) to AD is an essential part of human research. Although connection changes have been found in the progression, the connection mechanism that drives these changes remains incompletely understood. The purpose of this study is to explore the connection changes in brain networks in the process from NC to AD, and uncovers the underlying connection mechanism that shapes the topologies of AD brain networks. In particular, we propose a mutual information brain network model (MINM) from the perspective of graph theory to achieve our aim. MINM concerns the question of estimating the connection probability between two cortical regions with the consideration of both the mutual information of their observed network topologies and their Euclidean distance in anatomical space. In addition, MINM considers establishing and deleting connections, simultaneously, during the networks modeling from the stage of NC to AD. Experiments show that MINM is sufficient to capture an impressive range of topological properties of real brain networks such as characteristic path length, network efficiency, and transitivity, and it also provides an excellent fit to the real brain networks in degree distribution compared to experiential models. Thus, we anticipate that MINM may explain the connection mechanism for the formation of the brain network organization in AD patients. Full article

(This article belongs to the Special Issue Information Theory and Complexity Science Approaches to Health Conditions and Cognitive Decline)

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18 pages, 541 KiB

Open AccessArticle

Goal Identification Control Using an Information Entropy-Based Goal Uncertainty Metric

by Kai Xu and Quanjun Yin

Entropy 2019, 21(3), 299; https://doi.org/10.3390/e21030299 - 20 Mar 2019

Cited by 3 | Viewed by 2965

Abstract

Recent research has found situations where the identification of agent goals could be purposefully controlled, either by changing the underlying environment to make it easier, or exploiting it during agent planning to delay the opponent’s goal recognition. The paper tries to answer the [...] Read more.

Recent research has found situations where the identification of agent goals could be purposefully controlled, either by changing the underlying environment to make it easier, or exploiting it during agent planning to delay the opponent’s goal recognition. The paper tries to answer the following questions: what kinds of actions contain less information and more uncertainty about the agent’s real goal, and how to describe this uncertainty; what is the best way to control the process of goal identification. Our contribution is the introduction of a new measure we call relative goal uncertainty (rgu) with which we assess the goal-related information that each action contains. The rgu is a relative value associated with each action and represents the goal uncertainty quantified by information entropy after the action is taken compared to other executable ones in each state. After that, we show how goal vagueness could be controlled either for one side or for both confronting sides, and formulate this goal identification control problem as a mixed-integer programming problem. Empirical evaluation shows the effectiveness of the proposed solution in controlling goal identification process. Full article

(This article belongs to the Special Issue Entropy Production and Its Applications: From Cosmology to Biology)

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Entropy, Volume 21, Issue 3 (March 2019) – 110 articles

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