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Entropy, Volume 20, Issue 5 (May 2018)

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Cover Story (view full-size image) The so-called quantum trajectories arising from the Bohm theory should not be called ``surreal'' as [...] Read more.
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Open AccessArticle Maxwell’s Demon and the Problem of Observers in General Relativity
Entropy 2018, 20(5), 391; https://doi.org/10.3390/e20050391
Received: 8 May 2018 / Revised: 18 May 2018 / Accepted: 22 May 2018 / Published: 22 May 2018
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Abstract
The fact that real dissipative (entropy producing) processes may be detected by non-comoving observers (tilted), in systems that appear to be isentropic for comoving observers, in general relativity, is explained in terms of the information theory, analogous with the explanation of the Maxwell’s
[...] Read more.
The fact that real dissipative (entropy producing) processes may be detected by non-comoving observers (tilted), in systems that appear to be isentropic for comoving observers, in general relativity, is explained in terms of the information theory, analogous with the explanation of the Maxwell’s demon paradox. Full article
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Open AccessArticle End-to-End Deep Neural Networks and Transfer Learning for Automatic Analysis of Nation-State Malware
Entropy 2018, 20(5), 390; https://doi.org/10.3390/e20050390
Received: 1 March 2018 / Revised: 10 May 2018 / Accepted: 11 May 2018 / Published: 22 May 2018
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Abstract
Malware allegedly developed by nation-states, also known as advanced persistent threats (APT), are becoming more common. The task of attributing an APT to a specific nation-state or classifying it to the correct APT family is challenging for several reasons. First, each nation-state has
[...] Read more.
Malware allegedly developed by nation-states, also known as advanced persistent threats (APT), are becoming more common. The task of attributing an APT to a specific nation-state or classifying it to the correct APT family is challenging for several reasons. First, each nation-state has more than a single cyber unit that develops such malware, rendering traditional authorship attribution algorithms useless. Furthermore, the dataset of such available APTs is still extremely small. Finally, those APTs use state-of-the-art evasion techniques, making feature extraction challenging. In this paper, we use a deep neural network (DNN) as a classifier for nation-state APT attribution. We record the dynamic behavior of the APT when run in a sandbox and use it as raw input for the neural network, allowing the DNN to learn high level feature abstractions of the APTs itself. We also use the same raw features for APT family classification. Finally, we use the feature abstractions learned by the APT family classifier to solve the attribution problem. Using a test set of 1000 Chinese and Russian developed APTs, we achieved an accuracy rate of 98.6% Full article
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Open AccessArticle Identification of Pulmonary Hypertension Using Entropy Measure Analysis of Heart Sound Signal
Entropy 2018, 20(5), 389; https://doi.org/10.3390/e20050389
Received: 3 April 2018 / Revised: 16 May 2018 / Accepted: 19 May 2018 / Published: 21 May 2018
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Abstract
This study introduced entropy measures to analyze the heart sound signals of people with and without pulmonary hypertension (PH). The lead II Electrocardiography (ECG) signal and heart sound signal were simultaneously collected from 104 subjects aged between 22 and 89. Fifty of them
[...] Read more.
This study introduced entropy measures to analyze the heart sound signals of people with and without pulmonary hypertension (PH). The lead II Electrocardiography (ECG) signal and heart sound signal were simultaneously collected from 104 subjects aged between 22 and 89. Fifty of them were PH patients and 54 were healthy. Eleven heart sound features were extracted and three entropy measures, namely sample entropy (SampEn), fuzzy entropy (FuzzyEn) and fuzzy measure entropy (FuzzyMEn) of the feature sequences were calculated. The Mann–Whitney U test was used to study the feature significance between the patient and health group. To reduce the age confounding factor, nine entropy measures were selected based on correlation analysis. Further, the probability density function (pdf) of a single selected entropy measure of both groups was constructed by kernel density estimation, as well as the joint pdf of any two and multiple selected entropy measures. Therefore, a patient or a healthy subject can be classified using his/her entropy measure probability based on Bayes’ decision rule. The results showed that the best identification performance by a single selected measure had sensitivity of 0.720 and specificity of 0.648. The identification performance was improved to 0.680, 0.796 by the joint pdf of two measures and 0.740, 0.870 by the joint pdf of multiple measures. This study showed that entropy measures could be a powerful tool for early screening of PH patients. Full article
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Open AccessArticle Teager Energy Entropy Ratio of Wavelet Packet Transform and Its Application in Bearing Fault Diagnosis
Entropy 2018, 20(5), 388; https://doi.org/10.3390/e20050388
Received: 27 April 2018 / Revised: 15 May 2018 / Accepted: 18 May 2018 / Published: 21 May 2018
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Abstract
Kurtogram can adaptively select the resonant frequency band, and then the characteristic fault frequency can be obtained by analyzing the selected band. However, the kurtogram is easily affected by random impulses and noise. In recent years, improvements to kurtogram have been concentrated on
[...] Read more.
Kurtogram can adaptively select the resonant frequency band, and then the characteristic fault frequency can be obtained by analyzing the selected band. However, the kurtogram is easily affected by random impulses and noise. In recent years, improvements to kurtogram have been concentrated on two aspects: (a) the decomposition method of the frequency band; and (b) the selection index of the optimal frequency band. In this article, a new method called Teager Energy Entropy Ratio Gram (TEERgram) is proposed. The TEER algorithm takes the wavelet packet transform (WPT) as the signal frequency band decomposition method, which can adaptively segment the frequency band and control the noise. At the same time, Teager Energy Entropy Ratio (TEER) is proposed as a computing index for wavelet packet subbands. WPT has better decomposition properties than traditional finite impulse response (FIR) filtering and Fourier decomposition in the kurtogram algorithm. At the same time, TEER has better performance than the envelope spectrum or even the square envelope spectrum. Therefore, the TEERgram method can accurately identify the resonant frequency band under strong background noise. The effectiveness of the proposed method is verified by simulation and experimental analysis. Full article
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Open AccessArticle Research on Weak Fault Extraction Method for Alleviating the Mode Mixing of LMD
Entropy 2018, 20(5), 387; https://doi.org/10.3390/e20050387
Received: 10 April 2018 / Revised: 16 May 2018 / Accepted: 16 May 2018 / Published: 21 May 2018
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Abstract
Compared with the strong background noise, the energy entropy of early fault signals of bearings are weak under actual working conditions. Therefore, extracting the bearings’ early fault features has always been a major difficulty in fault diagnosis of rotating machinery. Based on the
[...] Read more.
Compared with the strong background noise, the energy entropy of early fault signals of bearings are weak under actual working conditions. Therefore, extracting the bearings’ early fault features has always been a major difficulty in fault diagnosis of rotating machinery. Based on the above problems, the masking method is introduced into the Local Mean Decomposition (LMD) decomposition process, and a weak fault extraction method based on LMD and mask signal (MS) is proposed. Due to the mode mixing of the product function (PF) components decomposed by LMD in the noisy background, it is difficult to distinguish the authenticity of the fault frequency. Therefore, the MS method is introduced to deal with the PF components that are decomposed by the LMD and have strong correlation with the original signal, so as to suppress the modal aliasing phenomenon and extract the fault frequencies. In this paper, the actual fault signal of the rolling bearing is analyzed. By combining the MS method with the LMD method, the fault signal mixed with the noise is processed. The kurtosis value at the fault frequency is increased by eight-fold, and the signal-to-noise ratio (SNR) is increased by 19.1%. The fault signal is successfully extracted by the proposed composite method. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory III)
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Open AccessArticle Identification of Auditory Object-Specific Attention from Single-Trial Electroencephalogram Signals via Entropy Measures and Machine Learning
Entropy 2018, 20(5), 386; https://doi.org/10.3390/e20050386
Received: 17 April 2018 / Revised: 16 May 2018 / Accepted: 16 May 2018 / Published: 21 May 2018
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Abstract
Existing research has revealed that auditory attention can be tracked from ongoing electroencephalography (EEG) signals. The aim of this novel study was to investigate the identification of peoples’ attention to a specific auditory object from single-trial EEG signals via entropy measures and machine
[...] Read more.
Existing research has revealed that auditory attention can be tracked from ongoing electroencephalography (EEG) signals. The aim of this novel study was to investigate the identification of peoples’ attention to a specific auditory object from single-trial EEG signals via entropy measures and machine learning. Approximate entropy (ApEn), sample entropy (SampEn), composite multiscale entropy (CmpMSE) and fuzzy entropy (FuzzyEn) were used to extract the informative features of EEG signals under three kinds of auditory object-specific attention (Rest, Auditory Object1 Attention (AOA1) and Auditory Object2 Attention (AOA2)). The linear discriminant analysis and support vector machine (SVM), were used to construct two auditory attention classifiers. The statistical results of entropy measures indicated that there were significant differences in the values of ApEn, SampEn, CmpMSE and FuzzyEn between Rest, AOA1 and AOA2. For the SVM-based auditory attention classifier, the auditory object-specific attention of Rest, AOA1 and AOA2 could be identified from EEG signals using ApEn, SampEn, CmpMSE and FuzzyEn as features and the identification rates were significantly different from chance level. The optimal identification was achieved by the SVM-based auditory attention classifier using CmpMSE with the scale factor τ = 10. This study demonstrated a novel solution to identify the auditory object-specific attention from single-trial EEG signals without the need to access the auditory stimulus. Full article
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Open AccessArticle MOTiFS: Monte Carlo Tree Search Based Feature Selection
Entropy 2018, 20(5), 385; https://doi.org/10.3390/e20050385
Received: 13 April 2018 / Revised: 14 May 2018 / Accepted: 18 May 2018 / Published: 20 May 2018
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Abstract
Given the increasing size and complexity of datasets needed to train machine learning algorithms, it is necessary to reduce the number of features required to achieve high classification accuracy. This paper presents a novel and efficient approach based on the Monte Carlo Tree
[...] Read more.
Given the increasing size and complexity of datasets needed to train machine learning algorithms, it is necessary to reduce the number of features required to achieve high classification accuracy. This paper presents a novel and efficient approach based on the Monte Carlo Tree Search (MCTS) to find the optimal feature subset through the feature space. The algorithm searches for the best feature subset by combining the benefits of tree search with random sampling. Starting from an empty node, the tree is incrementally built by adding nodes representing the inclusion or exclusion of the features in the feature space. Every iteration leads to a feature subset following the tree and default policies. The accuracy of the classifier on the feature subset is used as the reward and propagated backwards to update the tree. Finally, the subset with the highest reward is chosen as the best feature subset. The efficiency and effectiveness of the proposed method is validated by experimenting on many benchmark datasets. The results are also compared with significant methods in the literature, which demonstrates the superiority of the proposed method. Full article
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Open AccessArticle Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors
Entropy 2018, 20(5), 384; https://doi.org/10.3390/e20050384
Received: 28 February 2018 / Revised: 27 April 2018 / Accepted: 8 May 2018 / Published: 20 May 2018
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Abstract
This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich–Fabrikant, Thomas’ cyclically symmetric attractor and Newton–Leipnik. Fractional conformable and β -conformable derivatives of Liouville–Caputo type are considered to solve the proposed systems. A numerical method based on the Adams–Moulton
[...] Read more.
This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich–Fabrikant, Thomas’ cyclically symmetric attractor and Newton–Leipnik. Fractional conformable and β -conformable derivatives of Liouville–Caputo type are considered to solve the proposed systems. A numerical method based on the Adams–Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and β -conformable attractors are provided to illustrate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory III)
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Open AccessArticle On f-Divergences: Integral Representations, Local Behavior, and Inequalities
Entropy 2018, 20(5), 383; https://doi.org/10.3390/e20050383
Received: 15 April 2018 / Revised: 7 May 2018 / Accepted: 15 May 2018 / Published: 19 May 2018
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Abstract
This paper is focused on f-divergences, consisting of three main contributions. The first one introduces integral representations of a general f-divergence by means of the relative information spectrum. The second part provides a new approach for the derivation of f-divergence
[...] Read more.
This paper is focused on f-divergences, consisting of three main contributions. The first one introduces integral representations of a general f-divergence by means of the relative information spectrum. The second part provides a new approach for the derivation of f-divergence inequalities, and it exemplifies their utility in the setup of Bayesian binary hypothesis testing. The last part of this paper further studies the local behavior of f-divergences. Full article
(This article belongs to the Special Issue Entropy and Information Inequalities)
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Open AccessArticle A Game-Theoretic Approach to Information-Flow Control via Protocol Composition
Entropy 2018, 20(5), 382; https://doi.org/10.3390/e20050382
Received: 24 March 2018 / Revised: 8 May 2018 / Accepted: 11 May 2018 / Published: 18 May 2018
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Abstract
In the inference attacks studied in Quantitative Information Flow (QIF), the attacker typically tries to interfere with the system in the attempt to increase its leakage of secret information. The defender, on the other hand, typically tries to decrease leakage by introducing some
[...] Read more.
In the inference attacks studied in Quantitative Information Flow (QIF), the attacker typically tries to interfere with the system in the attempt to increase its leakage of secret information. The defender, on the other hand, typically tries to decrease leakage by introducing some controlled noise. This noise introduction can be modeled as a type of protocol composition, i.e., a probabilistic choice among different protocols, and its effect on the amount of leakage depends heavily on whether or not this choice is visible to the attacker. In this work, we consider operators for modeling visible and hidden choice in protocol composition, and we study their algebraic properties. We then formalize the interplay between defender and attacker in a game-theoretic framework adapted to the specific issues of QIF, where the payoff is information leakage. We consider various kinds of leakage games, depending on whether players act simultaneously or sequentially, and on whether or not the choices of the defender are visible to the attacker. In the case of sequential games, the choice of the second player is generally a function of the choice of the first player, and his/her probabilistic choice can be either over the possible functions (mixed strategy) or it can be on the result of the function (behavioral strategy). We show that when the attacker moves first in a sequential game with a hidden choice, then behavioral strategies are more advantageous for the defender than mixed strategies. This contrasts with the standard game theory, where the two types of strategies are equivalent. Finally, we establish a hierarchy of these games in terms of their information leakage and provide methods for finding optimal strategies (at the points of equilibrium) for both attacker and defender in the various cases. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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Open AccessArticle Observables and Unobservables in Quantum Mechanics: How the No-Hidden-Variables Theorems Support the Bohmian Particle Ontology
Entropy 2018, 20(5), 381; https://doi.org/10.3390/e20050381
Received: 23 April 2018 / Revised: 5 May 2018 / Accepted: 17 May 2018 / Published: 18 May 2018
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Abstract
The paper argues that far from challenging—or even refuting—Bohm’s quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to position measurements; and (ii) Bohm’s theory provides a clear and
[...] Read more.
The paper argues that far from challenging—or even refuting—Bohm’s quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to position measurements; and (ii) Bohm’s theory provides a clear and coherent explanation of the measurement outcome statistics based on an ontology of particle positions, a law for their evolution and a probability measure linked with that law. What the no-hidden-variables theorems teach us is that (i) one cannot infer the properties that the physical systems possess from observables; and that (ii) measurements, being an interaction like other interactions, change the state of the measured system. Full article
(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)
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Open AccessArticle Adiabatic Quantum Computation Applied to Deep Learning Networks
Entropy 2018, 20(5), 380; https://doi.org/10.3390/e20050380
Received: 6 April 2018 / Revised: 15 May 2018 / Accepted: 16 May 2018 / Published: 18 May 2018
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Abstract
Training deep learning networks is a difficult task due to computational complexity, and this is traditionally handled by simplifying network topology to enable parallel computation on graphical processing units (GPUs). However, the emergence of quantum devices allows reconsideration of complex topologies. We illustrate
[...] Read more.
Training deep learning networks is a difficult task due to computational complexity, and this is traditionally handled by simplifying network topology to enable parallel computation on graphical processing units (GPUs). However, the emergence of quantum devices allows reconsideration of complex topologies. We illustrate a particular network topology that can be trained to classify MNIST data (an image dataset of handwritten digits) and neutrino detection data using a restricted form of adiabatic quantum computation known as quantum annealing performed by a D-Wave processor. We provide a brief description of the hardware and how it solves Ising models, how we translate our data into the corresponding Ising models, and how we use available expanded topology options to explore potential performance improvements. Although we focus on the application of quantum annealing in this article, the work discussed here is just one of three approaches we explored as part of a larger project that considers alternative means for training deep learning networks. The other approaches involve using a high performance computing (HPC) environment to automatically find network topologies with good performance and using neuromorphic computing to find a low-power solution for training deep learning networks. Our results show that our quantum approach can find good network parameters in a reasonable time despite increased network topology complexity; that HPC can find good parameters for traditional, simplified network topologies; and that neuromorphic computers can use low power memristive hardware to represent complex topologies and parameters derived from other architecture choices. Full article
(This article belongs to the Special Issue Quantum Foundations: 90 Years of Uncertainty)
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Open AccessArticle Flow and Heat Transfer in the Tree-Like Branching Microchannel with/without Dimples
Entropy 2018, 20(5), 379; https://doi.org/10.3390/e20050379
Received: 2 April 2018 / Revised: 10 May 2018 / Accepted: 16 May 2018 / Published: 18 May 2018
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Abstract
This work displays a numerical and experimental investigation on the flow and heat transfer in tree-like branching microchannels and studies the effects of dimples on the heat transfer enhancement. The numerical approach is certified by a smooth branching microchannel experiment. The verification result
[...] Read more.
This work displays a numerical and experimental investigation on the flow and heat transfer in tree-like branching microchannels and studies the effects of dimples on the heat transfer enhancement. The numerical approach is certified by a smooth branching microchannel experiment. The verification result shows that the SSG turbulence model can provide a reasonable prediction. Thus, further research on the convective heat transfer in dimpled branching microchannels is conducted with the SSG turbulence model. The results indicate that the dimples can significantly improve the averaged heat transfer performance of branching microchannels, and the heat transfer increment of the branch segment increases with the increase in the branching level. However, the flow dead zones in some dimples at bifurcations and bends suppress the turbulent flow and heat transfer. Furthermore, the Nu number ratio (Nua/Nus) and thermal enhancement factor (η) both monotonously decrease as the Re number increases, while the friction factor ratio (fa/fs) changes nonlinearly. The entropy generation rates of S ˙ t and S ˙ p in all dimpled cases are lower than those in the smooth case, and the dimpled case with the streamwise spacing to diameter ratio s/D = 3 obtains the lowest value of augmentation entropy generation (Ns) under the high Re number conditions. Nua/Nus, fa/fs, and η decline with the increase in the streamwise spacing to diameter ratio (s/D) from 3 to 9; therefore, the dimpled case with s/D = 3 shows the best overall thermal performance. Full article
(This article belongs to the Special Issue Non-Equilibrium Thermodynamics of Micro Technologies)
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Open AccessArticle Novel Bioinspired Approach Based on Chaotic Dynamics for Robot Patrolling Missions with Adversaries
Entropy 2018, 20(5), 378; https://doi.org/10.3390/e20050378
Received: 23 April 2018 / Revised: 15 May 2018 / Accepted: 16 May 2018 / Published: 18 May 2018
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Abstract
Living organisms have developed and optimized ingenious defense strategies based on positional entropy. One of the most significant examples in this respect is known as protean behavior, where a prey animal under threat performs unpredictable zig-zag movements in order to confuse, delay or
[...] Read more.
Living organisms have developed and optimized ingenious defense strategies based on positional entropy. One of the most significant examples in this respect is known as protean behavior, where a prey animal under threat performs unpredictable zig-zag movements in order to confuse, delay or escape the predator. This kind of defensive behavior can inspire efficient strategies for patrolling robots evolving in the presence of adversaries. The main goal of our proposed bioinspired method is to implement the protean behavior by altering the reference path of the robot with sudden and erratic direction changes without endangering the robot’s overall mission. By this, a foe intending to target and destroy the mobile robot from a distance has less time for acquiring and retaining the proper sight alignment. The method uses the chaotic dynamics of the 2D Arnold’s cat map as a primary source of positional entropy and transfers this feature to every reference path segment using the kinematic relative motion concept. The effectiveness of this novel biologically inspired method is validated through extensive and realistic simulation case studies. Full article
(This article belongs to the Section Complexity)
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Open AccessArticle Characterization of the Stroke-Induced Changes in the Variability and Complexity of Handgrip Force
Entropy 2018, 20(5), 377; https://doi.org/10.3390/e20050377
Received: 20 April 2018 / Revised: 14 May 2018 / Accepted: 14 May 2018 / Published: 17 May 2018
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Abstract
Introduction: The variability and complexity of handgrip forces in various modulations were investigated to identify post-stroke changes in force modulation, and extend our understanding of stroke-induced deficits. Methods: Eleven post-stroke subjects and ten age-matched controls performed voluntary grip force control tasks
[...] Read more.
Introduction: The variability and complexity of handgrip forces in various modulations were investigated to identify post-stroke changes in force modulation, and extend our understanding of stroke-induced deficits. Methods: Eleven post-stroke subjects and ten age-matched controls performed voluntary grip force control tasks (power-grip tasks) at three contraction levels, and stationary dynamometer holding tasks (stationary holding tasks). Variability and complexity were described with root mean square jerk (RMS-jerk) and fuzzy approximate entropy (fApEn), respectively. Force magnitude, Fugl-Meyer upper extremity assessment and Wolf motor function test were also evaluated. Results: Comparing the affected side with the controls, fApEn was significantly decreased and RMS-jerk increased across the three levels in power-grip tasks, and fApEn was significantly decreased in stationary holding tasks. There were significant strong correlations between RMS-jerk and clinical scales in power-grip tasks. Discussion: Abnormal neuromuscular control, altered mechanical properties, and atrophic motoneurons could be the main causes of the differences in complexity and variability in post-stroke subjects. Full article
(This article belongs to the Section Complexity)
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Open AccessArticle Dynamics Analysis of a Nonlinear Stochastic SEIR Epidemic System with Varying Population Size
Entropy 2018, 20(5), 376; https://doi.org/10.3390/e20050376
Received: 16 April 2018 / Revised: 14 May 2018 / Accepted: 16 May 2018 / Published: 17 May 2018
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Abstract
This paper considers a stochastic susceptible exposed infectious recovered (SEIR) epidemic model with varying population size and vaccination. We aim to study the global dynamics of the reduced nonlinear stochastic proportional differential system. We first investigate the existence and uniqueness of global positive
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This paper considers a stochastic susceptible exposed infectious recovered (SEIR) epidemic model with varying population size and vaccination. We aim to study the global dynamics of the reduced nonlinear stochastic proportional differential system. We first investigate the existence and uniqueness of global positive solution of the stochastic system. Then the sufficient conditions for the extinction and permanence in mean of the infectious disease are obtained. Furthermore, we prove that the solution of the stochastic system has a unique ergodic stationary distribution under appropriate conditions. Finally, the discussion and numerical simulation are given to demonstrate the obtained results. Full article
(This article belongs to the Special Issue Information Theory and Stochastics for Multiscale Nonlinear Systems)
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Open AccessArticle Transition of Transient Channel Flow with High Reynolds Number Ratios
Entropy 2018, 20(5), 375; https://doi.org/10.3390/e20050375
Received: 24 March 2018 / Revised: 14 May 2018 / Accepted: 15 May 2018 / Published: 17 May 2018
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Abstract
Large-eddy simulations of turbulent channel flow subjected to a step-like acceleration have been performed to investigate the effect of high Reynolds number ratios on the transient behaviour of turbulence. It is shown that the response of the flow exhibits the same fundamental characteristics
[...] Read more.
Large-eddy simulations of turbulent channel flow subjected to a step-like acceleration have been performed to investigate the effect of high Reynolds number ratios on the transient behaviour of turbulence. It is shown that the response of the flow exhibits the same fundamental characteristics described in He & Seddighi (J. Fluid Mech., vol. 715, 2013, pp. 60–102 and vol. 764, 2015, pp. 395–427)—a three-stage response resembling that of the bypass transition of boundary layer flows. The features of transition are seen to become more striking as the Re-ratio increases—the elongated streaks become stronger and longer, and the initial turbulent spot sites at the onset of transition become increasingly sparse. The critical Reynolds number of transition and the transition period Reynolds number for those cases are shown to deviate from the trends of He & Seddighi (2015). The high Re-ratio cases show double peaks in the transient response of streamwise fluctuation profiles shortly after the onset of transition. Conditionally-averaged turbulent statistics based on a λ_2-criterion are used to show that the two peaks in the fluctuation profiles are due to separate contributions of the active and inactive regions of turbulence generation. The peak closer to the wall is attributed to the generation of “new” turbulence in the active region, whereas the peak farther away from the wall is attributed to the elongated streaks in the inactive region. In the low Re-ratio cases, the peaks of these two regions are close to each other during the entire transient, resulting in a single peak in the domain-averaged profile. Full article
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Open AccessArticle Robust Estimation for the Single Index Model Using Pseudodistances
Entropy 2018, 20(5), 374; https://doi.org/10.3390/e20050374
Received: 31 March 2018 / Revised: 11 May 2018 / Accepted: 14 May 2018 / Published: 17 May 2018
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Abstract
For portfolios with a large number of assets, the single index model allows for expressing the large number of covariances between individual asset returns through a significantly smaller number of parameters. This avoids the constraint of having very large samples to estimate the
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For portfolios with a large number of assets, the single index model allows for expressing the large number of covariances between individual asset returns through a significantly smaller number of parameters. This avoids the constraint of having very large samples to estimate the mean and the covariance matrix of the asset returns, which practically would be unrealistic given the dynamic of market conditions. The traditional way to estimate the regression parameters in the single index model is the maximum likelihood method. Although the maximum likelihood estimators have desirable theoretical properties when the model is exactly satisfied, they may give completely erroneous results when outliers are present in the data set. In this paper, we define minimum pseudodistance estimators for the parameters of the single index model and using them we construct new robust optimal portfolios. We prove theoretical properties of the estimators, such as consistency, asymptotic normality, equivariance, robustness, and illustrate the benefits of the new portfolio optimization method for real financial data. Full article
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Open AccessArticle An Efficient Big Data Anonymization Algorithm Based on Chaos and Perturbation Techniques
Entropy 2018, 20(5), 373; https://doi.org/10.3390/e20050373
Received: 21 April 2018 / Revised: 12 May 2018 / Accepted: 15 May 2018 / Published: 17 May 2018
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Abstract
The topic of big data has attracted increasing interest in recent years. The emergence of big data leads to new difficulties in terms of protection models used for data privacy, which is of necessity for sharing and processing data. Protecting individuals’ sensitive information
[...] Read more.
The topic of big data has attracted increasing interest in recent years. The emergence of big data leads to new difficulties in terms of protection models used for data privacy, which is of necessity for sharing and processing data. Protecting individuals’ sensitive information while maintaining the usability of the data set published is the most important challenge in privacy preserving. In this regard, data anonymization methods are utilized in order to protect data against identity disclosure and linking attacks. In this study, a novel data anonymization algorithm based on chaos and perturbation has been proposed for privacy and utility preserving in big data. The performance of the proposed algorithm is evaluated in terms of Kullback–Leibler divergence, probabilistic anonymity, classification accuracy, F-measure and execution time. The experimental results have shown that the proposed algorithm is efficient and performs better in terms of Kullback–Leibler divergence, classification accuracy and F-measure compared to most of the existing algorithms using the same data set. Resulting from applying chaos to perturb data, such successful algorithm is promising to be used in privacy preserving data mining and data publishing. Full article
(This article belongs to the Section Information Theory)
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Open AccessArticle Software Code Smell Prediction Model Using Shannon, Rényi and Tsallis Entropies
Entropy 2018, 20(5), 372; https://doi.org/10.3390/e20050372
Received: 27 January 2018 / Revised: 22 April 2018 / Accepted: 1 May 2018 / Published: 17 May 2018
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Abstract
The current era demands high quality software in a limited time period to achieve new goals and heights. To meet user requirements, the source codes undergo frequent modifications which can generate the bad smells in software that deteriorate the quality and reliability of
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The current era demands high quality software in a limited time period to achieve new goals and heights. To meet user requirements, the source codes undergo frequent modifications which can generate the bad smells in software that deteriorate the quality and reliability of software. Source code of the open source software is easily accessible by any developer, thus frequently modifiable. In this paper, we have proposed a mathematical model to predict the bad smells using the concept of entropy as defined by the Information Theory. Open-source software Apache Abdera is taken into consideration for calculating the bad smells. Bad smells are collected using a detection tool from sub components of the Apache Abdera project, and different measures of entropy (Shannon, Rényi and Tsallis entropy). By applying non-linear regression techniques, the bad smells that can arise in the future versions of software are predicted based on the observed bad smells and entropy measures. The proposed model has been validated using goodness of fit parameters (prediction error, bias, variation, and Root Mean Squared Prediction Error (RMSPE)). The values of model performance statistics ( R 2 , adjusted R 2 , Mean Square Error (MSE) and standard error) also justify the proposed model. We have compared the results of the prediction model with the observed results on real data. The results of the model might be helpful for software development industries and future researchers. Full article
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Open AccessArticle Normal Laws for Two Entropy Estimators on Infinite Alphabets
Entropy 2018, 20(5), 371; https://doi.org/10.3390/e20050371
Received: 3 April 2018 / Revised: 9 May 2018 / Accepted: 10 May 2018 / Published: 17 May 2018
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Abstract
This paper offers sufficient conditions for the Miller–Madow estimator and the jackknife estimator of entropy to have respective asymptotic normalities on countably infinite alphabets. Full article
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Open AccessArticle A Survey of Viewpoint Selection Methods for Polygonal Models
Entropy 2018, 20(5), 370; https://doi.org/10.3390/e20050370
Received: 24 March 2018 / Revised: 11 May 2018 / Accepted: 11 May 2018 / Published: 16 May 2018
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Abstract
Viewpoint selection has been an emerging area in computer graphics for some years, and it is now getting maturity with applications in fields such as scene navigation, scientific visualization, object recognition, mesh simplification, and camera placement. In this survey, we review and compare
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Viewpoint selection has been an emerging area in computer graphics for some years, and it is now getting maturity with applications in fields such as scene navigation, scientific visualization, object recognition, mesh simplification, and camera placement. In this survey, we review and compare twenty-two measures to select good views of a polygonal 3D model, classify them using an extension of the categories defined by Secord et al., and evaluate them against the Dutagaci et al. benchmark. Eleven of these measures have not been reviewed in previous surveys. Three out of the five short-listed best viewpoint measures are directly related to information. We also present in which fields the different viewpoint measures have been applied. Finally, we provide a publicly available framework where all the viewpoint selection measures are implemented and can be compared against each other. Full article
(This article belongs to the Special Issue Information Theory Application in Visualization)
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Open AccessArticle The Role of Entropy in Estimating Financial Network Default Impact
Entropy 2018, 20(5), 369; https://doi.org/10.3390/e20050369
Received: 25 April 2018 / Revised: 10 May 2018 / Accepted: 15 May 2018 / Published: 16 May 2018
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Abstract
Agents in financial networks can simultaneously be both creditors and debtors, creating the possibility that a default may cause a subsequent default cascade. Resolution of unpayable debts in these situations will have a distributional impact. Using a relative entropy-based measure of the distributional
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Agents in financial networks can simultaneously be both creditors and debtors, creating the possibility that a default may cause a subsequent default cascade. Resolution of unpayable debts in these situations will have a distributional impact. Using a relative entropy-based measure of the distributional impact of the subsequent default resolution process, it is argued that minimum mutual information estimation of unknown cells in the matrix of funds originally owed by the network participants to each other does not introduce systematic biases when estimating that impact. Full article
(This article belongs to the Section Information Theory)
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Open AccessArticle Writing, Proofreading and Editing in Information Theory
Entropy 2018, 20(5), 368; https://doi.org/10.3390/e20050368
Received: 5 April 2018 / Revised: 4 May 2018 / Accepted: 12 May 2018 / Published: 15 May 2018
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Abstract
Information is a physical entity amenable to be described by an abstract theory. The concepts associated with the creation and post-processing of the information have not, however, been mathematically established, despite being broadly used in many fields of knowledge. Here, inspired by how
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Information is a physical entity amenable to be described by an abstract theory. The concepts associated with the creation and post-processing of the information have not, however, been mathematically established, despite being broadly used in many fields of knowledge. Here, inspired by how information is managed in biomolecular systems, we introduce writing, entailing any bit string generation, and revision, as comprising proofreading and editing, in information chains. Our formalism expands the thermodynamic analysis of stochastic chains made up of material subunits to abstract strings of symbols. We introduce a non-Markovian treatment of operational rules over the symbols of the chain that parallels the physical interactions responsible for memory effects in material chains. Our theory underlies any communication system, ranging from human languages and computer science to gene evolution. Full article
(This article belongs to the Special Issue Thermodynamics of Information Processing)
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Open AccessArticle Feynman Paths and Weak Values
Entropy 2018, 20(5), 367; https://doi.org/10.3390/e20050367
Received: 16 April 2018 / Revised: 4 May 2018 / Accepted: 9 May 2018 / Published: 14 May 2018
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Abstract
There has been a recent revival of interest in the notion of a ‘trajectory’ of a quantum particle. In this paper, we detail the relationship between Dirac’s ideas, Feynman paths and the Bohm approach. The key to the relationship is the weak value
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There has been a recent revival of interest in the notion of a ‘trajectory’ of a quantum particle. In this paper, we detail the relationship between Dirac’s ideas, Feynman paths and the Bohm approach. The key to the relationship is the weak value of the momentum which Feynman calls a transition probability amplitude. With this identification we are able to conclude that a Bohm ‘trajectory’ is the average of an ensemble of actual individual stochastic Feynman paths. This implies that they can be interpreted as the mean momentum flow of a set of individual quantum processes and not the path of an individual particle. This enables us to give a clearer account of the experimental two-slit results of Kocsis et al. Full article
(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)
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Open AccessArticle Thermoelectric Efficiency of a Topological Nano-Junction
Entropy 2018, 20(5), 366; https://doi.org/10.3390/e20050366
Received: 24 March 2018 / Revised: 10 May 2018 / Accepted: 11 May 2018 / Published: 14 May 2018
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Abstract
We studied the non-equilibrium current, transport coefficients and thermoelectric performance of a nano-junction, composed by a quantum dot connected to a normal superconductor and a topological superconductor leads, respectively. We considered a one-dimensional topological superconductor, which hosts two Majorana fermion states at its
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We studied the non-equilibrium current, transport coefficients and thermoelectric performance of a nano-junction, composed by a quantum dot connected to a normal superconductor and a topological superconductor leads, respectively. We considered a one-dimensional topological superconductor, which hosts two Majorana fermion states at its edges. Our results show that the electric and thermal currents across the junction are highly mediated by multiple Andreev reflections between the quantum dot and the leads, thus leading to a strong nonlinear dependence of the current on the applied bias voltage. Remarkably, we find that our system reaches a sharp maximum of its thermoelectric efficiency at a finite bias, when an external magnetic field is imposed upon the junction. We propose that this feature can be used for accurate temperature sensing at the nanoscale. Full article
(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)
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Open AccessArticle Analysis of Chaotic Behavior in a Novel Extended Love Model Considering Positive and Negative External Environment
Entropy 2018, 20(5), 365; https://doi.org/10.3390/e20050365
Received: 27 March 2018 / Revised: 8 May 2018 / Accepted: 12 May 2018 / Published: 14 May 2018
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Abstract
The aim of this study was to describe a novel extended dynamical love model with the external environments of the love story of Romeo and Juliet. We used the sinusoidal function as external environments as it could represent the positive and negative characteristics
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The aim of this study was to describe a novel extended dynamical love model with the external environments of the love story of Romeo and Juliet. We used the sinusoidal function as external environments as it could represent the positive and negative characteristics of humans. We considered positive and negative advice from a third person. First, we applied the same amount of positive and negative advice. Second, the amount of positive advice was greater than that of negative advice. Third, the amount of positive advice was smaller than that of negative advice in an external environment. To verify the chaotic phenomena in the proposed extended dynamic love affair with external environments, we used time series, phase portraits, power spectrum, Poincare map, bifurcation diagram, and the maximal Lyapunov exponent. With a variation of parameter “a”, we recognized that the novel extended dynamic love affairs with different three situations of external environments had chaotic behaviors. We showed 1, 2, 4 periodic motion, Rössler type attractor, and chaotic attractor when parameter “a” varied under the following conditions: the amount of positive advice = the amount of negative advice, the amount of positive advice > the amount of negative advice, and the amount of positive advice < the amount of negative advice. Full article
(This article belongs to the Special Issue Theoretical Aspect of Nonlinear Statistical Physics)
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Open AccessArticle Fault Diagnosis of Gearboxes Using Nonlinearity and Determinism by Generalized Hurst Exponents of Shuffle and Surrogate Data
Entropy 2018, 20(5), 364; https://doi.org/10.3390/e20050364
Received: 14 April 2018 / Revised: 10 May 2018 / Accepted: 11 May 2018 / Published: 14 May 2018
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Abstract
Vibrations of defective gearboxes show great complexities. Therefore, dynamics and noise levels of vibrations of gearboxes vary with operation of gearboxes. As a result, nonlinearity and determinism of data can serve to describe running conditions of gearboxes. However, measuring of nonlinearity and determinism
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Vibrations of defective gearboxes show great complexities. Therefore, dynamics and noise levels of vibrations of gearboxes vary with operation of gearboxes. As a result, nonlinearity and determinism of data can serve to describe running conditions of gearboxes. However, measuring of nonlinearity and determinism of data is challenging. This paper defines a two-dimensional measure for simultaneously quantifying nonlinearity and determinism of data by comparing generalized Hurst exponents of original, shuffle and surrogate data. Afterwards, this paper proposes a novel method for fault diagnosis of gearboxes using the two-dimensional measure. Robustness of the proposed method was validated numerically by analyzing simulative signals with different noise levels. Moreover, the performance of the proposed method was benchmarked against Approximate Entropy, Sample Entropy, Permutation Entropy and Delay Vector Variance by conducting two independent gearbox experiments. The results show that the proposed method achieves superiority over the others in fault diagnosis of gearboxes. Full article
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Open AccessArticle Quantifying the Effects of Topology and Weight for Link Prediction in Weighted Complex Networks
Entropy 2018, 20(5), 363; https://doi.org/10.3390/e20050363
Received: 6 April 2018 / Revised: 10 May 2018 / Accepted: 10 May 2018 / Published: 13 May 2018
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Abstract
In weighted networks, both link weight and topological structure are significant characteristics for link prediction. In this study, a general framework combining null models is proposed to quantify the impact of the topology, weight correlation and statistics on link prediction in weighted networks.
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In weighted networks, both link weight and topological structure are significant characteristics for link prediction. In this study, a general framework combining null models is proposed to quantify the impact of the topology, weight correlation and statistics on link prediction in weighted networks. Three null models for topology and weight distribution of weighted networks are presented. All the links of the original network can be divided into strong and weak ties. We can use null models to verify the strong effect of weak or strong ties. For two important statistics, we construct two null models to measure their impacts on link prediction. In our experiments, the proposed method is applied to seven empirical networks, which demonstrates that this model is universal and the impact of the topology and weight distribution of these networks in link prediction can be quantified by it. We find that in the USAir, the Celegans, the Gemo, the Lesmis and the CatCortex, the strong ties are easier to predict, but there are a few networks whose weak edges can be predicted more easily, such as the Netscience and the CScientists. It is also found that the weak ties contribute more to link prediction in the USAir, the NetScience and the CScientists, that is, the strong effect of weak ties exists in these networks. The framework we proposed is versatile, which is not only used to link prediction but also applicable to other directions in complex networks. Full article
(This article belongs to the Special Issue Research Frontier in Chaos Theory and Complex Networks)
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Open AccessArticle Thermodynamics at Solid–Liquid Interfaces
Entropy 2018, 20(5), 362; https://doi.org/10.3390/e20050362
Received: 3 April 2018 / Revised: 26 April 2018 / Accepted: 9 May 2018 / Published: 12 May 2018
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Abstract
The variation of the liquid properties in the vicinity of a solid surface complicates the description of heat transfer along solid–liquid interfaces. Using Molecular Dynamics simulations, this investigation aims to understand how the material properties, particularly the strength of the solid–liquid interaction, affect
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The variation of the liquid properties in the vicinity of a solid surface complicates the description of heat transfer along solid–liquid interfaces. Using Molecular Dynamics simulations, this investigation aims to understand how the material properties, particularly the strength of the solid–liquid interaction, affect the thermal conductivity of the liquid at the interface. The molecular model consists of liquid argon confined by two parallel, smooth, solid walls, separated by a distance of 6.58 σ. We find that the component of the thermal conductivity parallel to the surface increases with the affinity of the solid and liquid. Full article
(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)
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