ALBERT

Description: Entropy, Vol. 20, Pages 550: Information Geometry of Nonlinear Stochastic Systems Entropy doi: 10.3390/e20080550 Authors: Rainer Hollerbach Donovan Dimanche Eun-jin Kim We elucidate the effect of different deterministic nonlinear forces on geometric structure of stochastic processes by investigating the transient relaxation of initial PDFs of a stochastic variable x under forces proportional to -xn (n=3,5,7) and different strength D of δ-correlated stochastic noise. We identify the three main stages consisting of nondiffusive evolution, quasi-linear Gaussian evolution and settling into stationary PDFs. The strength of stochastic noise is shown to play a crucial role in determining these timescales as well as the peak amplitude and width of PDFs. From time-evolution of PDFs, we compute the rate of information change for a given initial PDF and uniquely determine the information length L(t) as a function of time that represents the number of different statistical states that a system evolves through in time. We identify a robust geodesic (where the information changes at a constant rate) in the initial stage, and map out geometric structure of an attractor as L(t→∞)∝μm, where μ is the position of an initial Gaussian PDF. The scaling exponent m increases with n, and also varies with D (although to a lesser extent). Our results highlight ubiquitous power-laws and multi-scalings of information geometry due to nonlinear interaction.

Description: Entropy, Vol. 20, Pages 553: Hierarchical Structure of Generalized Thermodynamic and Informational Entropy Entropy doi: 10.3390/e20080553 Authors: Pierfrancesco Palazzo The present research aimed at discussing the thermodynamic and informational aspects of entropy concept to propose a unitary perspective of its definitions as an inherent property of any system in any state. The dualism and the relation between physical nature of information and the informational content of physical states of matter and phenomena play a fundamental role in the description of multi-scale systems characterized by hierarchical configurations. A method is proposed to generalize thermodynamic and informational entropy property and characterize the hierarchical structure of its canonical definition at macroscopic and microscopic levels of a system described in the domain of classical and quantum physics. The conceptual schema is based on dualisms and symmetries inherent to the geometric and kinematic configurations and interactions occurring in many-particle and few-particle thermodynamic systems. The hierarchical configuration of particles and sub-particles, representing the constitutive elements of physical systems, breaks down into levels characterized by particle masses subdivision, implying positions and velocities degrees of freedom multiplication. This hierarchy accommodates the allocation of phenomena and processes from higher to lower levels in the respect of the equipartition theorem of energy. However, the opposite and reversible process, from lower to higher level, is impossible by virtue of the Second Law, expressed as impossibility of Perpetual Motion Machine of the Second Kind (PMM2) remaining valid at all hierarchical levels, and the non-existence of Maxwell’s demon. Based on the generalized definition of entropy property, the hierarchical structure of entropy contribution and production balance, determined by degrees of freedom and constraints of systems configuration, is established. Moreover, as a consequence of the Second Law, the non-equipartition theorem of entropy is enunciated, which would be complementary to the equipartition theorem of energy derived from the First Law.

Description: Entropy, Vol. 20, Pages 552: The Gibbs Paradox Entropy doi: 10.3390/e20080552 Authors: Simon Saunders The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory (there is no classical solution), some to classical theory (the quantum case is different). The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability (in the classical case, Gibbs’ notion of ‘generic phase’). Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level of the tensor (or Cartesian) product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. ‘Distinguishability’, in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction.

Description: Entropy, Vol. 20, Pages 549: Entropy-Based Feature Extraction for Electromagnetic Discharges Classification in High-Voltage Power Generation Entropy doi: 10.3390/e20080549 Authors: Imene Mitiche Gordon Morison Alan Nesbitt Brian G. Stewart Philip Boreham This work exploits four entropy measures known as Sample, Permutation, Weighted Permutation, and Dispersion Entropy to extract relevant information from Electromagnetic Interference (EMI) discharge signals that are useful in fault diagnosis of High-Voltage (HV) equipment. Multi-class classification algorithms are used to classify or distinguish between various discharge sources such as Partial Discharges (PD), Exciter, Arcing, micro Sparking and Random Noise. The signals were measured and recorded on different sites followed by EMI expert’s data analysis in order to identify and label the discharge source type contained within the signal. The classification was performed both within each site and across all sites. The system performs well for both cases with extremely high classification accuracy within site. This work demonstrates the ability to extract relevant entropy-based features from EMI discharge sources from time-resolved signals requiring minimal computation making the system ideal for a potential application to online condition monitoring based on EMI.

Description: Entropy, Vol. 20, Pages 555: Quantum Games with Unawareness Entropy doi: 10.3390/e20080555 Authors: Piotr Frąckiewicz Games with unawareness model strategic situations in which players’ perceptions about the game are limited. They take into account the fact that the players may be unaware of some of the strategies available to them or their opponents as well as the players may have a restricted view about the number of players participating in the game. The aim of the paper is to introduce this notion into theory of quantum games. We focus on games in strategic form and Eisert–Wilkens–Lewenstein type quantum games. It is shown that limiting a player’s perception in the game enriches the structure of the quantum game substantially and allows the players to obtain results that are unattainable when the game is played in a quantum way by means of previously used methods.

Description: Entropy, Vol. 20, Pages 560: Ensemble Estimation of Information Divergence † Entropy doi: 10.3390/e20080560 Authors: Kevin R. Moon Kumar Sricharan Kristjan Greenewald Alfred O. Hero Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The theory of optimally weighted ensemble estimation is generalized to derive a divergence estimator that achieves the parametric rate when the densities are sufficiently smooth. Guidelines for the tuning parameter selection and the asymptotic distribution of this estimator are provided. Based on the theory, an empirical estimator of Rényi-α divergence is proposed that greatly outperforms the standard kernel density plug-in estimator in terms of mean squared error, especially in high dimensions. The estimator is shown to be robust to the choice of tuning parameters. We show extensive simulation results that verify the theoretical results of our paper. Finally, we apply the proposed estimator to estimate the bounds on the Bayes error rate of a cell classification problem.

Description: Entropy, Vol. 20, Pages 556: Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems Entropy doi: 10.3390/e20080556 Authors: Shaobo He Chunbiao Li Kehui Sun Sajad Jafari Designing a chaotic system with infinitely many attractors is a hot topic. In this paper, multiscale multivariate permutation entropy (MMPE) and multiscale multivariate Lempel–Ziv complexity (MMLZC) are employed to analyze the complexity of those self-reproducing chaotic systems with one-directional and two-directional infinitely many chaotic attractors. The analysis results show that complexity of this class of chaotic systems is determined by the initial conditions. Meanwhile, the values of MMPE are independent of the scale factor, which is different from the algorithm of MMLZC. The analysis proposed here is helpful as a reference for the application of the self-reproducing systems.

Description: Entropy, Vol. 20, Pages 564: A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors Entropy doi: 10.3390/e20080564 Authors: Jesus Munoz-Pacheco Ernesto Zambrano-Serrano Christos Volos Sajad Jafari Jacques Kengne Karthikeyan Rajagopal In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a `hurricane’-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.

Description: Entropy, Vol. 20, Pages 561: Statistical Significance of Earth’s Electric and Magnetic Field Variations Preceding Earthquakes in Greece and Japan Revisited Entropy doi: 10.3390/e20080561 Authors: Nicholas Sarlis By analyzing the seismicity in a new time domain, termed natural time, we recently found that the change of the entropy under time reversal (Physica A2018, 506, 625–634) and the relevant complexity measures (Entropy2018, 20, 477) exhibit pronounced variations before the occurrence of the M8.2 earthquake in Mexico on 7 September 2017. Here, the statistical significance of precursory phenomena associated with other physical properties and in particular the anomalous variations observed in the Earth’s electric and magnetic fields before earthquakes in different regions of the world and in particular in Greece since 1980s and Japan during 2001–2010 are revisited (the latter, i.e., the magnetic field variations are alternatively termed ultra low frequency (ULF) seismo-magnetic phenomena). Along these lines we employ modern statistical tools like the event coincidence analysis and the receiver operating characteristics technique. We find that these precursory variations are far beyond chance and in addition their lead times fully agree with the experimental findings in Greece since the 1980s.

Description: Entropy, Vol. 20, Pages 563: A New Underwater Acoustic Signal Denoising Technique Based on CEEMDAN, Mutual Information, Permutation Entropy, and Wavelet Threshold Denoising Entropy doi: 10.3390/e20080563 Authors: Yuxing Li Yaan Li Xiao Chen Jing Yu Hong Yang Long Wang Owing to the complexity of the ocean background noise, underwater acoustic signal denoising is one of the hotspot problems in the field of underwater acoustic signal processing. In this paper, we propose a new technique for underwater acoustic signal denoising based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), mutual information (MI), permutation entropy (PE), and wavelet threshold denoising. CEEMDAN is an improved algorithm of empirical mode decomposition (EMD) and ensemble EMD (EEMD). First, CEEMDAN is employed to decompose noisy signals into many intrinsic mode functions (IMFs). IMFs can be divided into three parts: noise IMFs, noise-dominant IMFs, and real IMFs. Then, the noise IMFs can be identified on the basis of MIs of adjacent IMFs; the other two parts of IMFs can be distinguished based on the values of PE. Finally, noise IMFs were removed, and wavelet threshold denoising is applied to noise-dominant IMFs; we can obtain the final denoised signal by combining real IMFs and denoised noise-dominant IMFs. Simulation experiments were conducted by using simulated data, chaotic signals, and real underwater acoustic signals; the proposed denoising technique performs better than other existing denoising techniques, which is beneficial to the feature extraction of underwater acoustic signal.

Description: Entropy, Vol. 20, Pages 567: Nonlocality in Bell’s Theorem, in Bohm’s Theory, and in Many Interacting Worlds Theorising Entropy doi: 10.3390/e20080567 Authors: Mojtaba Ghadimi Michael J. W. Hall Howard M. Wiseman “Locality” is a fraught word, even within the restricted context of Bell’s theorem. As one of us has argued elsewhere, that is partly because Bell himself used the word with different meanings at different stages in his career. The original, weaker, meaning for locality was in his 1964 theorem: that the choice of setting by one party could never affect the outcome of a measurement performed by a distant second party. The epitome of a quantum theory violating this weak notion of locality (and hence exhibiting a strong form of nonlocality) is Bohmian mechanics. Recently, a new approach to quantum mechanics, inspired by Bohmian mechanics, has been proposed: Many Interacting Worlds. While it is conceptually clear how the interaction between worlds can enable this strong nonlocality, technical problems in the theory have thus far prevented a proof by simulation. Here we report significant progress in tackling one of the most basic difficulties that needs to be overcome: correctly modelling wavefunctions with nodes.

Description: Entropy, Vol. 20, Pages 455: A Novel Fault Diagnosis Method of Rolling Bearings Based on AFEWT-KDEMI Entropy doi: 10.3390/e20060455 Authors: Mingtao Ge Jie Wang Fangfang Zhang Ke Bai Xiangyang Ren According to the dynamic characteristics of the rolling bearing vibration signal and the distribution characteristics of its noise, a fault identification method based on the adaptive filtering empirical wavelet transform (AFEWT) and kernel density estimation mutual information (KDEMI) classifier is proposed. First, we use AFEWT to extract the feature of the rolling bearing vibration signal. The hypothesis test of the Gaussian distribution is carried out for the sub-modes that are obtained by the twice decomposition of EWT, and Gaussian noise is filtered out according to the test results. In this way, we can overcome the noise interference and avoid the mode selection problem when we extract the feature of the signal. Then we combine the advantages of kernel density estimation (KDE) and mutual information (MI) and put forward a KDEMI classifier. The mutual information of the probability density combining the unknown signal feature vector and the probability density of the known type signal is calculated. The type of the unknown signal is determined via the value of the mutual information, so as to achieve the purpose of fault identification of the rolling bearing. In order to verify the effectiveness of AFEWT in feature extraction, we extract signal features using three methods, AFEWT, EWT, and EMD, and then use the same classifier to identify fault signals. Experimental results show that the fault signal has the highest recognition rate by using AFEWT for feature extraction. At the same time, in order to verify the performance of the AFEWT-KDEMI method, we compare two classical fault signal identification methods, SVM and BP neural network, with the AFEWT-KDEMI method. Through experimental analysis, we found that the AFEWT-KDEMI method is more stable and effective.

Description: Entropy, Vol. 20, Pages 458: Vacuum Landscaping: Cause of Nonlocal Influences without Signaling Entropy doi: 10.3390/e20060458 Authors: Gerhard Grössing Siegfried Fussy Johannes Mesa Pascasio Herbert Schwabl In the quest for an understanding of nonlocality with respect to an appropriate ontology, we propose a “cosmological solution”. We assume that from the beginning of the universe each point in space has been the location of a scalar field representing a zero-point vacuum energy that nonlocally vibrates at a vast range of different frequencies across the whole universe. A quantum, then, is a nonequilibrium steady state in the form of a “bouncer” coupled resonantly to one of those (particle type dependent) frequencies, in remote analogy to the bouncing oil drops on an oscillating oil bath as in Couder’s experiments. A major difference to the latter analogy is given by the nonlocal nature of the vacuum oscillations. We show with the examples of double- and n-slit interference that the assumed nonlocality of the distribution functions alone suffices to derive the de Broglie–Bohm guiding equation for N particles with otherwise purely classical means. In our model, no influences from configuration space are required, as everything can be described in 3-space. Importantly, the setting up of an experimental arrangement limits and shapes the forward and osmotic contributions and is described as vacuum landscaping.

Description: Entropy, Vol. 20, Pages 436: Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures Entropy doi: 10.3390/e20060436 Authors: Antonio M. Scarfone Hiroshi Matsuzoe Tatsuaki Wada In this paper, we present a review of recent developments on the κ -deformed statistical mechanics in the framework of the information geometry. Three different geometric structures are introduced in the κ -formalism which are obtained starting from three, not equivalent, divergence functions, corresponding to the κ -deformed version of Kullback–Leibler, “Kerridge” and Brègman divergences. The first statistical manifold derived from the κ -Kullback–Leibler divergence form an invariant geometry with a positive curvature that vanishes in the κ → 0 limit. The other two statistical manifolds are related to each other by means of a scaling transform and are both dually-flat. They have a dualistic Hessian structure endowed by a deformed Fisher metric and an affine connection that are consistent with a statistical scalar product based on the κ -escort expectation. These flat geometries admit dual potentials corresponding to the thermodynamic Massieu and entropy functions that induce a Legendre structure of κ -thermodynamics in the picture of the information geometry.

Description: Entropy, Vol. 20, Pages 440: On a Common Misconception Regarding the de Broglie–Bohm Theory Entropy doi: 10.3390/e20060440 Authors: Oliver Passon We discuss a common misconception regarding the de Broglie–Bohm (dBB) theory; namely, that it not only assigns a position to each quantum object but also contains the momenta as “hidden variables”. Sometimes this alleged property of the theory is even used to argue that the dBB theory is inconsistent with quantum theory. We explain why this claim is unfounded and show in particular how this misconception veils the true novelty of the dBB theory.

Description: Entropy, Vol. 20, Pages 438: Analysis of Cell Signal Transduction Based on Kullback–Leibler Divergence: Channel Capacity and Conservation of Its Production Rate during Cascade Entropy doi: 10.3390/e20060438 Authors: Tatsuaki Tsuruyama Kullback–Leibler divergence (KLD) is a type of extended mutual entropy, which is used as a measure of information gain when transferring from a prior distribution to a posterior distribution. In this study, KLD is applied to the thermodynamic analysis of cell signal transduction cascade and serves an alternative to mutual entropy. When KLD is minimized, the divergence is given by the ratio of the prior selection probability of the signaling molecule to the posterior selection probability. Moreover, the information gain during the entire channel is shown to be adequately described by average KLD production rate. Thus, this approach provides a framework for the quantitative analysis of signal transduction. Moreover, the proposed approach can identify an effective cascade for a signaling network.

Description: Entropy, Vol. 20, Pages 437: Complexity Analysis of Global Temperature Time Series Entropy doi: 10.3390/e20060437 Authors: António M. Lopes J. A. Tenreiro Machado Climate has complex dynamics due to the plethora of phenomena underlying its evolution. These characteristics pose challenges to conducting solid quantitative analysis and reaching assertive conclusions. In this paper, the global temperature time series (TTS) is viewed as a manifestation of the climate evolution, and its complexity is calculated by means of four different indices, namely the Lempel–Ziv complexity, sample entropy, signal harmonics power ratio, and fractal dimension. In the first phase, the monthly mean TTS is pre-processed by means of empirical mode decomposition, and the TTS trend is calculated. In the second phase, the complexity of the detrended signals is estimated. The four indices capture distinct features of the TTS dynamics in a 4-dim space. Hierarchical clustering is adopted for dimensional reduction and visualization in the 2-dim space. The results show that TTS complexity exhibits space-time variability, suggesting the presence of distinct climate forcing processes in both dimensions. Numerical examples with real-world data demonstrate the effectiveness of the approach.

Description: Entropy, Vol. 20, Pages 439: Factoid Question Answering with Distant Supervision Entropy doi: 10.3390/e20060439 Authors: Hongzhi Zhang Xiao Liang Guangluan Xu Kun Fu Feng Li Tinglei Huang Automatic question answering (QA), which can greatly facilitate the access to information, is an important task in artificial intelligence. Recent years have witnessed the development of QA methods based on deep learning. However, a great amount of data is needed to train deep neural networks, and it is laborious to annotate training data for factoid QA of new domains or languages. In this paper, a distantly supervised method is proposed to automatically generate QA pairs. Additional efforts are paid to let the generated questions reflect the query interests and expression styles of users by exploring the community QA. Specifically, the generated questions are selected according to the estimated probabilities they are asked. Diverse paraphrases of questions are mined from community QA data, considering that the model trained on monotonous synthetic questions is very sensitive to variants of question expressions. Experimental results show that the model solely trained on generated data via the distant supervision and mined paraphrases could answer real-world questions with the accuracy of 49.34%. When limited annotated training data is available, significant improvements could be achieved by incorporating the generated data. An improvement of 1.35 absolute points is still observed on WebQA, a dataset with large-scale annotated training samples.

Description: Entropy, Vol. 20, Pages 434: Complexity Analysis of Carbon Market Using the Modified Multi-Scale Entropy Entropy doi: 10.3390/e20060434 Authors: Jiuli Yin Cui Su Yongfen Zhang Xinghua Fan Carbon markets provide a market-based way to reduce climate pollution. Subject to general market regulations, the major existing emission trading markets present complex characteristics. This paper analyzes the complexity of carbon market by using the multi-scale entropy. Pilot carbon markets in China are taken as the example. Moving average is adopted to extract the scales due to the short length of the data set. Results show a low-level complexity inferring that China’s pilot carbon markets are quite immature in lack of market efficiency. However, the complexity varies in different time scales. China’s carbon markets (except for the Chongqing pilot) are more complex in the short period than in the long term. Furthermore, complexity level in most pilot markets increases as the markets developed, showing an improvement in market efficiency. All these results demonstrate that an effective carbon market is required for the full function of emission trading.

Description: Entropy, Vol. 20, Pages 462: On Bohmian Mechanics, Particle Creation, and Relativistic Space-Time: Happy 100th Birthday, David Bohm! Entropy doi: 10.3390/e20060462 Authors: Roderich Tumulka The biggest and most lasting among David Bohm’s (1917–1992) many achievements is to have proposed a picture of reality that explains the empirical rules of quantum mechanics. This picture, known as pilot wave theory or Bohmian mechanics among other names, is still the simplest and most convincing explanation available. According to this theory, electrons are point particles in the literal sense and move along trajectories governed by Bohm’s equation of motion. In this paper, I describe some more recent developments and extensions of Bohmian mechanics, concerning in particular relativistic space-time and particle creation and annihilation.

Description: Entropy, Vol. 20, Pages 465: Ontological Clarity via Canonical Presentation: Electromagnetism and the Aharonov–Bohm Effect Entropy doi: 10.3390/e20060465 Authors: Tim Maudlin Quantum physics demands some radical revision of our fundamental beliefs about physical reality. We know that because there are certain verified physical phenomena—two-slit interference, the disappearance of interference upon monitoring, violations of Bell’s inequality—that have no classical analogs. But the exact nature of that revision has been under dispute since the foundation of quantum theory. I offer a method of clarifying what the commitments of a clearly formulated physical theory are, and apply it to a discussion of some options available to account for another non-classical phenomenon: the Aharonov–Bohm effect.

Description: Entropy, Vol. 20, Pages 464: Non-Quadratic Distances in Model Assessment Entropy doi: 10.3390/e20060464 Authors: Marianthi Markatou Yang Chen One natural way to measure model adequacy is by using statistical distances as loss functions. A related fundamental question is how to construct loss functions that are scientifically and statistically meaningful. In this paper, we investigate non-quadratic distances and their role in assessing the adequacy of a model and/or ability to perform model selection. We first present the definition of a statistical distance and its associated properties. Three popular distances, total variation, the mixture index of fit and the Kullback-Leibler distance, are studied in detail, with the aim of understanding their properties and potential interpretations that can offer insight into their performance as measures of model misspecification. A small simulation study exemplifies the performance of these measures and their application to different scientific fields is briefly discussed.

Description: Entropy, Vol. 20, Pages 466: The Gibbs Paradox and Particle Individuality Entropy doi: 10.3390/e20060466 Authors: Dennis Dieks A consensus seems to have developed that the Gibbs paradox in classical thermodynamics (the discontinuous drop in the entropy of mixing when the mixed gases become equal to each other) is unmysterious: in any actual situation, two gases can be separated or not, and the associated harmless discontinuity from “yes” to “no” is responsible for the discontinuity. By contrast, the Gibbs paradox in statistical physics continues to attract attention. Here, the problem is that standard calculations in statistical mechanics predict a non-vanishing value of the entropy of mixing even when two gases of the same kind are mixed, in conflict with thermodynamic predictions. This version of the Gibbs paradox is often seen as a sign that there is something fundamentally wrong with either the traditional expression S=klnW or with the way W is calculated. It is the aim of this article to review the situation from the orthodox (as opposed to information theoretic) standpoint. We demonstrate how the standard formalism is not only fully capable of dealing with the paradox, but also provides an intuitively clear picture of the relevant physical mechanisms. In particular, we pay attention to the explanatory relevance of the existence of particle trajectories in the classical context. We also discuss how the paradox survives the transition to quantum mechanics, in spite of the symmetrization postulates.

Description: Entropy, Vol. 20, Pages 470: Noise Enhanced Signal Detection of Variable Detectors under Certain Constraints Entropy doi: 10.3390/e20060470 Authors: Ting Yang Shujun Liu Wenguo Liu Jishun Guo Pin Wang In this paper, a noise enhanced binary hypothesis-testing problem was studied for a variable detector under certain constraints in which the detection probability can be increased and the false-alarm probability can be decreased simultaneously. According to the constraints, three alternative cases are proposed, the first two cases concerned minimization of the false-alarm probability and maximization of the detection probability without deterioration of one by the other, respectively, and the third case was achieved by a randomization of two optimal noise enhanced solutions obtained in the first two limit cases. Furthermore, the noise enhanced solutions that satisfy the three cases were determined whether randomization between different detectors was allowed or not. In addition, the practicality of the third case was proven from the perspective of Bayes risk. Finally, numerous examples and conclusions are presented.

Description: Entropy, Vol. 20, Pages 483: Non-Commutative Worlds and Classical Constraints Entropy doi: 10.3390/e20070483 Authors: Louis Kauffman This paper reviews results about discrete physics and non-commutative worlds and explores further the structure and consequences of constraints linking classical calculus and discrete calculus formulated via commutators. In particular, we review how the formalism of generalized non-commutative electromagnetism follows from a first order constraint and how, via the Kilmister equation, relationships with general relativity follow from a second order constraint. It is remarkable that a second order constraint, based on interlacing the commutative and non-commutative worlds, leads to an equivalent tensor equation at the pole of geodesic coordinates for general relativity.

Description: Entropy, Vol. 20, Pages 481: Relating Vertex and Global Graph Entropy in Randomly Generated Graphs Entropy doi: 10.3390/e20070481 Authors: Philip Tee George Parisis Luc Berthouze Ian Wakeman Combinatoric measures of entropy capture the complexity of a graph but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of vertex level measures that do not suffer from this pathological computational complexity, but that can be shown to be effective at quantifying graph complexity. In this paper, we consider whether these local measures are fundamentally equivalent to global entropy measures. Specifically, we investigate the existence of a correlation between vertex level and global measures of entropy for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate strong correlation for this subset of graphs and outline how this may arise theoretically.

Description: Entropy, Vol. 20, Pages 485: Symmetric Logarithmic Derivative of Fermionic Gaussian States Entropy doi: 10.3390/e20070485 Authors: Angelo Carollo Bernardo Spagnolo Davide Valenti In this article, we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.

Description: Entropy, Vol. 20, Pages 489: A Moment-Based Maximum Entropy Model for Fitting Higher-Order Interactions in Neural Data Entropy doi: 10.3390/e20070489 Authors: N. Alex Cayco-Gajic Joel Zylberberg Eric Shea-Brown Correlations in neural activity have been demonstrated to have profound consequences for sensory encoding. To understand how neural populations represent stimulus information, it is therefore necessary to model how pairwise and higher-order spiking correlations between neurons contribute to the collective structure of population-wide spiking patterns. Maximum entropy models are an increasingly popular method for capturing collective neural activity by including successively higher-order interaction terms. However, incorporating higher-order interactions in these models is difficult in practice due to two factors. First, the number of parameters exponentially increases as higher orders are added. Second, because triplet (and higher) spiking events occur infrequently, estimates of higher-order statistics may be contaminated by sampling noise. To address this, we extend previous work on the Reliable Interaction class of models to develop a normalized variant that adaptively identifies the specific pairwise and higher-order moments that can be estimated from a given dataset for a specified confidence level. The resulting “Reliable Moment” model is able to capture cortical-like distributions of population spiking patterns. Finally, we show that, compared with the Reliable Interaction model, the Reliable Moment model infers fewer strong spurious higher-order interactions and is better able to predict the frequencies of previously unobserved spiking patterns.

Description: Entropy, Vol. 20, Pages 498: Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle Entropy doi: 10.3390/e20070498 Authors: Francisco J. Valverde-Albacete Carmen Peláez-Moreno Data transformation, e.g., feature transformation and selection, is an integral part of any machine learning procedure. In this paper, we introduce an information-theoretic model and tools to assess the quality of data transformations in machine learning tasks. In an unsupervised fashion, we analyze the transformation of a discrete, multivariate source of information X¯ into a discrete, multivariate sink of information Y¯ related by a distribution PX¯Y¯. The first contribution is a decomposition of the maximal potential entropy of (X¯,Y¯), which we call a balance equation, into its (a) non-transferable, (b) transferable, but not transferred, and (c) transferred parts. Such balance equations can be represented in (de Finetti) entropy diagrams, our second set of contributions. The most important of these, the aggregate channel multivariate entropy triangle, is a visual exploratory tool to assess the effectiveness of multivariate data transformations in transferring information from input to output variables. We also show how these decomposition and balance equations also apply to the entropies of X¯ and Y¯, respectively, and generate entropy triangles for them. As an example, we present the application of these tools to the assessment of information transfer efficiency for Principal Component Analysis and Independent Component Analysis as unsupervised feature transformation and selection procedures in supervised classification tasks.

Description: Entropy, Vol. 20, Pages 568: Symbolic Entropy Analysis and Its Applications Entropy doi: 10.3390/e20080568 Authors: Raúl Alcaraz This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers.

Description: Entropy, Vol. 20, Pages 569: Random Finite Set Based Parameter Estimation Algorithm for Identifying Stochastic Systems Entropy doi: 10.3390/e20080569 Authors: Peng Wang Ge Li Yong Peng Rusheng Ju Parameter estimation is one of the key technologies for system identification. The Bayesian parameter estimation algorithms are very important for identifying stochastic systems. In this paper, a random finite set based algorithm is proposed to overcome the disadvantages of the existing Bayesian parameter estimation algorithms. It can estimate the unknown parameters of the stochastic system which consists of a varying number of constituent elements by using the measurements disturbed by false detections, missed detections and noises. The models used for parameter estimation are constructed by using random finite set. Based on the proposed system model and measurement model, the key principles and formula derivation of the proposed algorithm are detailed. Then, the implementation of the algorithm is presented by using sequential Monte Carlo based Probability Hypothesis Density (PHD) filter and simulated tempering based importance sampling. Finally, the experiments of systematic errors estimation of multiple sensors are provided to prove the main advantages of the proposed algorithm. The sensitivity analysis is carried out to further study the mechanism of the algorithm. The experimental results verify the superiority of the proposed algorithm.

Description: Entropy, Vol. 20, Pages 570: Analysis of Solar Irradiation Time Series Complexity and Predictability by Combining Kolmogorov Measures and Hamming Distance for La Reunion (France) Entropy doi: 10.3390/e20080570 Authors: Dragutin T. Mihailović Miloud Bessafi Sara Marković Ilija Arsenić Slavica Malinović-Milićević Patrick Jeanty Mathieu Delsaut Jean-Pierre Chabriat Nusret Drešković Anja Mihailović Analysis of daily solar irradiation variability and predictability in space and time is important for energy resources planning, development, and management. The natural variability of solar irradiation is being complicated by atmospheric conditions (in particular cloudiness) and orography, which introduce additional complexity into the phenomenological records. To address this question for daily solar irradiation data recorded during the years 2013, 2014 and 2015 at 11 stations measuring solar irradiance on La Reunion French tropical Indian Ocean Island, we use a set of novel quantitative tools: Kolmogorov complexity (KC) with its derivative associated measures and Hamming distance (HAM) and their combination to assess complexity and corresponding predictability. We find that all half-day (from sunrise to sunset) solar irradiation series exhibit high complexity. However, all of them can be classified into three groups strongly influenced by trade winds that circulate in a “flow around” regime: the windward side (trade winds slow down), the leeward side (diurnal thermally-induced circulations dominate) and the coast parallel to trade winds (winds are accelerated due to Venturi effect). We introduce Kolmogorov time (KT) that quantifies the time span beyond which randomness significantly influences predictability.

Description: Entropy, Vol. 20, Pages 583: Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines Entropy doi: 10.3390/e20080583 Authors: Song Cheng Jing Chen Lei Wang We compare and contrast the statistical physics and quantum physics inspired approaches for unsupervised generative modeling of classical data. The two approaches represent probabilities of observed data using energy-based models and quantum states, respectively. Classical and quantum information patterns of the target datasets therefore provide principled guidelines for structural design and learning in these two approaches. Taking the Restricted Boltzmann Machines (RBM) as an example, we analyze the information theoretical bounds of the two approaches. We also estimate the classical mutual information of the standard MNIST datasets and the quantum Rényi entropy of corresponding Matrix Product States (MPS) representations. Both information measures are much smaller compared to their theoretical upper bound and exhibit similar patterns, which imply a common inductive bias of low information complexity. By comparing the performance of RBM with various architectures on the standard MNIST datasets, we found that the RBM with local sparse connection exhibit high learning efficiency, which supports the application of tensor network states in machine learning problems.

Description: Entropy, Vol. 20, Pages 588: On a Matrix Inequality Related to the Distillability Problem Entropy doi: 10.3390/e20080588 Authors: Yi Shen Lin Chen We investigate the distillability problem in quantum information in Cd⊗Cd. One case of the problem has been reduced to proving a matrix inequality when d=4. We investigate the inequality for three families of non-normal matrices. We prove the inequality for the first two families with d=4 and for the third family with d≥5. We also present a sufficient condition for the fulfillment of the inequality with d=4.

Description: Entropy, Vol. 20, Pages 597: Work Availability and Exergy Analysis Entropy doi: 10.3390/e20080597 Authors: Pouria Ahmadi Behnaz Rezaie n/a

Description: Entropy, Vol. 20, Pages 598: Entropy Applications in Environmental and Water Engineering Entropy doi: 10.3390/e20080598 Authors: Huijuan Cui Bellie Sivakumar Vijay P. Singh n/a

Description: Entropy, Vol. 20, Pages 613: Time-Dependent Probability Density Functions and Attractor Structure in Self-Organised Shear Flows Entropy doi: 10.3390/e20080613 Authors: Quentin Jacquet Eun-jin Kim Rainer Hollerbach We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal PDF with the two peaks representing non-zero mean values of a shear flow. Using theoretical analyses of limiting cases, as well as numerical solutions of the full Fokker–Planck equation, we present a thorough parameter study of PDFs for different values of the correlation time and amplitude of stochastic forcing. From time-dependent PDFs, we calculate the information length ( L ), which is the total number of statistically different states that a system passes through in time and utilise it to understand the information geometry associated with the formation of bimodal or unimodal PDFs. We identify the difference between the relaxation and build-up of the shear gradient in view of information change and discuss the total information length ( L ∞ = L ( t → ∞ ) ) which maps out the underlying attractor structures, highlighting a unique property of L ∞ which depends on the trajectory/history of a PDF’s evolution.

Description: Entropy, Vol. 20, Pages 612: Permutation Entropy Based on Non-Uniform Embedding Entropy doi: 10.3390/e20080612 Authors: Mei Tao Kristina Poskuviene Nizar Faisal Alkayem Maosen Cao Minvydas Ragulskis A novel visualization scheme for permutation entropy is presented in this paper. The proposed scheme is based on non-uniform attractor embedding of the investigated time series. A single digital image of permutation entropy is produced by averaging all possible plain projections of the permutation entropy measure in the multi-dimensional delay coordinate space. Computational experiments with artificially-generated and real-world time series are used to demonstrate the advantages of the proposed visualization scheme.

Description: Entropy, Vol. 20, Pages 611: Multi-Fault Diagnosis of Gearbox Based on Improved Multipoint Optimal Minimum Entropy Deconvolution Entropy doi: 10.3390/e20080611 Authors: Fuhe Yang Xingquan Shen Zhijian Wang Under complicated conditions, the extraction of a multi-fault in gearboxes is difficult to achieve. Due to improper selection of methods, leakage diagnosis or misdiagnosis will usually occur. Ensemble Empirical Mode Decomposition (EEMD) often causes energy leakage due to improper selection of white noise during signal decomposition. Considering that only a single fault cycle can be extracted when MOMED (Multipoint Optimal Minimum Entropy Deconvolution) is used, it is necessary to perform the sub-band processing of the compound fault signal. This paper presents an adaptive gearbox multi-fault-feature extraction method based on Improved MOMED (IMOMED). Firstly, EEMD decomposes the signal adaptively and selects the intrinsic mode functions with strong correlation with the original signal to perform FFT (Fast Fourier transform); considering the mode-mixing phenomenon of EEMD, reconstruct the intrinsic mode functions with the same timescale, and obtain several intrinsic mode functions of the same scale to improve the entropy of fault features. There is a lot of white noise in the original signal, and EEMD can improve the signal-to-noise ratio of the original signal. Finally, through the setting of different noise-reduction intervals to extract fault features through MOMED. The proposed method is compared with EEMD and VMD (Variational Mode Decomposition) to verify its feasibility.

Description: Entropy, Vol. 20, Pages 610: SU(2) Decomposition for the Quantum Information Dynamics in 2d-Partite Two-Level Quantum Systems Entropy doi: 10.3390/e20080610 Authors: Francisco Delgado The gate array version of quantum computation uses logical gates adopting convenient forms for computational algorithms based on the algorithms classical computation. Two-level quantum systems are the basic elements connecting the binary nature of classical computation with the settlement of quantum processing. Despite this, their design depends on specific quantum systems and the physical interactions involved, thus complicating the dynamics analysis. Predictable and controllable manipulation should be addressed in order to control the quantum states in terms of the physical control parameters. Resources are restricted to limitations imposed by the physical settlement. This work presents a formalism to decompose the quantum information dynamics in S U ( 2 2 d ) for 2 d -partite two-level systems into 2 2 d − 1 S U ( 2 ) quantum subsystems. It generates an easier and more direct physical implementation of quantum processing developments for qubits. Easy and traditional operations proposed by quantum computation are recovered for larger and more complex systems. Alternating the parameters of local and non-local interactions, the procedure states a universal exchange semantics on the basis of generalized Bell states. Although the main procedure could still be settled on other interaction architectures by the proper selection of the basis as natural grammar, the procedure can be understood as a momentary splitting of the 2 d information channels into 2 2 d − 1 pairs of 2 level quantum information subsystems. Additionally, it is a settlement of the quantum information manipulation that is free of the restrictions imposed by the underlying physical system. Thus, the motivation of decomposition is to set control procedures easily in order to generate large entangled states and to design specialized dedicated quantum gates. They are potential applications that properly bypass the general induced superposition generated by physical dynamics.

Description: Entropy, Vol. 20, Pages 616: Dynamic Clustering and Coordinated User Scheduling for Cooperative Interference Cancellation on Ultra-High Density Distributed Antenna Systems Entropy doi: 10.3390/e20080616 Authors: Kazuki Maruta This paper proposes dynamic clustering and user scheduling for previously conceived inter-cluster interference cancellation scheme on ultra-high density distributed antenna system (UHD-DAS). UHD-DAS is composed of one central unit (CU) and densely deployed remote radio units (RUs) serving as small cell access points. It can enhance spatial spectral efficiency by alleviating traffic load imposed per radio unit; however, intenser small cell deployment revives the inter-cell interference (ICI) problem. Cell clustering, cooperation of multiple RUs, can mitigate ICI partially, whereas inter-cluster interference (ICLI) still limits its possible capacity. Simplified ICLI cancellation based on localized RU cooperation was previously proposed to mitigate interference globally. The resolved issue is that it required frequency reuse distance to fully obtain its interference cancellation ability. This paper introduces dynamic clustering with coordinated user scheduling to ensure reuse distance without extra frequency reuse. Joint dynamic clustering and ICLI cancellation can effectively work and almost reaches ideal performance as full cooperative spatial multiplexing transmission.

Description: Entropy, Vol. 20, Pages 621: The Maximum Entropy Method in Ultrasonic Non-Destructive Testing—Increasing the Resolution, Image Noise Reduction and Echo Acquisition Rate Entropy doi: 10.3390/e20080621 Authors: Evgeny Gennadievich Bazulin The use of linear methods, for example, the Combined Synthetic Aperture Focusing Technique (C–SAFT), does not allow one to obtain images with high resolution and low noise, especially structural noise in all cases. Non-linear methods should improve the quality of the reconstructed image. Several examples of the application of the maximum entropy (ME) method for ultrasonic echo processing in order to reconstruct the image of reflectors with Rayleigh super-resolution and a high signal-to-noise ratio are considered in the article. The use of the complex phase-shifted Barker code signal as a probe pulse and the compression of measured echoes by the ME method made it possible to increase the signal-to-noise ratio by more than 20 dB for the image of a flat-bottom hole with a diameter of 1 mm in a model experiment. A modification of the ME method for restoring the reflector image by the time-of-flight diffraction (TOFD) method is considered, taking into account the change of the echo signal shape, depending on the depth of the reflector. Using the ME method, 2.5D-images of models of dangling cracks in a pipeline with a diameter of 800 mm were obtained, which make it possible to determine their dimensions. In the object with structural noise, using the ME method, it was possible to increase the signal-to-noise ratio of the reflector image by more than 12 dB. To accelerate the acquisition of echoes in the dual scan mode, it is proposed to use code division multiple access (CDMA) technology based on simultaneous emission by all elements of the array of pseudo-orthogonal signals. The model experiment showed the effectiveness of applying the ME method.

Description: Entropy, Vol. 20, Pages 619: A Classical Interpretation of the Scrooge Distribution Entropy doi: 10.3390/e20080619 Authors: William K. Wootters The Scrooge distribution is a probability distribution over the set of pure states of a quantum system. Specifically, it is the distribution that, upon measurement, gives up the least information about the identity of the pure state compared with all other distributions that have the same density matrix. The Scrooge distribution has normally been regarded as a purely quantum mechanical concept with no natural classical interpretation. In this paper, we offer a classical interpretation of the Scrooge distribution viewed as a probability distribution over the probability simplex. We begin by considering a real-amplitude version of the Scrooge distribution for which we find that there is a non-trivial but natural classical interpretation. The transition to the complex-amplitude case requires a step that is not particularly natural but that may shed light on the relation between quantum mechanics and classical probability theory.

Description: Entropy, Vol. 20, Pages 633: Fractal Structure and Non-Extensive Statistics Entropy doi: 10.3390/e20090633 Authors: Airton Deppman Tobias Frederico Eugenio Megías Debora P. Menezes The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics have been discussed in detail in many works and triggered an interesting discussion on the most deep meaning of entropy and its role in complex systems. Some possible mechanisms that could give rise to non-extensive statistics have been formulated over the last several years, in particular a fractal structure in thermodynamic functions was recently proposed as a possible origin for non-extensive statistics in physical systems. In the present work, we investigate the properties of such fractal thermodynamical system and propose a diagrammatic method for calculations of relevant quantities related to such a system. It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that provided evidence of the connections between those fluctuations and Tsallis statistics. Finally, the scale invariance of the fractal thermodynamical system is discussed in terms of the Callan–Symanzik equation.

Description: Entropy, Vol. 20, Pages 634: An Entropy-Based Approach for Measuring Factor Contributions in Factor Analysis Models Entropy doi: 10.3390/e20090634 Authors: Nobuoki Eshima Minoru Tabata Claudio Giovanni Borroni In factor analysis, factor contributions of latent variables are assessed conventionally by the sums of the squared factor loadings related to the variables. First, the present paper considers issues in the conventional method. Second, an alternative entropy-based approach for measuring factor contributions is proposed. The method measures the contribution of the common factor vector to the manifest variable vector and decomposes it into contributions of factors. A numerical example is also provided to demonstrate the present approach.

Description: Entropy, Vol. 20, Pages 631: Entropic Equilibria Selection of Stationary Extrema in Finite Populations Entropy doi: 10.3390/e20090631 Authors: Marc Harper Dashiell Fryer We propose the entropy of random Markov trajectories originating and terminating at the same state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary distributions of Markov processes. We apply this definition of stability to local maxima and minima of the stationary distribution of the Moran process with mutation and show that variations in population size, mutation rate, and strength of selection all affect the stability of the stationary extrema.

Description: Entropy, Vol. 20, Pages 635: Detailed Fluctuation Theorems: A Unifying Perspective Entropy doi: 10.3390/e20090635 Authors: Riccardo Rao Massimiliano Esposito We present a general method to identify an arbitrary number of fluctuating quantities which satisfy a detailed fluctuation theorem for all times within the framework of time-inhomogeneous Markovian jump processes. In doing so, we provide a unified perspective on many fluctuation theorems derived in the literature. By complementing the stochastic dynamics with a thermodynamic structure (i.e., using stochastic thermodynamics), we also express these fluctuating quantities in terms of physical observables.

Description: Entropy, Vol. 20, Pages 644: Model Error, Information Barriers, State Estimation and Prediction in Complex Multiscale Systems Entropy doi: 10.3390/e20090644 Authors: Andrew Majda Nan Chen Complex multiscale systems are ubiquitous in many areas. This research expository article discusses the development and applications of a recent information-theoretic framework as well as novel reduced-order nonlinear modeling strategies for understanding and predicting complex multiscale systems. The topics include the basic mathematical properties and qualitative features of complex multiscale systems, statistical prediction and uncertainty quantification, state estimation or data assimilation, and coping with the inevitable model errors in approximating such complex systems. Here, the information-theoretic framework is applied to rigorously quantify the model fidelity, model sensitivity and information barriers arising from different approximation strategies. It also succeeds in assessing the skill of filtering and predicting complex dynamical systems and overcomes the shortcomings in traditional path-wise measurements such as the failure in measuring extreme events. In addition, information theory is incorporated into a systematic data-driven nonlinear stochastic modeling framework that allows effective predictions of nonlinear intermittent time series. Finally, new efficient reduced-order nonlinear modeling strategies combined with information theory for model calibration provide skillful predictions of intermittent extreme events in spatially-extended complex dynamical systems. The contents here include the general mathematical theories, effective numerical procedures, instructive qualitative models, and concrete models from climate, atmosphere and ocean science.

Description: Entropy, Vol. 20, Pages 643: Random Spacing between Metal Tree Electrodeposits in Linear DLA Arrays Entropy doi: 10.3390/e20090643 Authors: Jaad Tannous Lina Anouti Rabih Sultan When we examine the random growth of trees along a linear alley in a rural area, we wonder what governs the location of those trees, and hence the distance between adjacent ones. The same question arises when we observe the growth of metal electro-deposition trees along a linear cathode in a rectangular film of solution. We carry out different sets of experiments wherein zinc trees are grown by electrolysis from a linear graphite cathode in a 2D film of zinc sulfate solution toward a thick zinc metal anode. We measure the distance between adjacent trees, calculate the average for each set, and correlate the latter with probability and entropy. We also obtain a computational image of the grown trees as a function of parameters such as the cell size, number of particles, and sticking probability. The dependence of average distance on concentration is studied and assessed.

Description: Entropy, Vol. 20, Pages 656: “The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory Entropy doi: 10.3390/e20090656 Authors: Arkady Plotnitsky The article reconsiders quantum theory in terms of the following principle, which can be symbolically represented as QUANTUMNESS → PROBABILITY → ALGEBRA and will be referred to as the QPA principle. The principle states that the quantumness of physical phenomena, that is, the specific character of physical phenomena known as quantum, implies that our predictions concerning them are irreducibly probabilistic, even in dealing with quantum phenomena resulting from the elementary individual quantum behavior (such as that of elementary particles), which in turn implies that our theories concerning these phenomena are fundamentally algebraic, in contrast to more geometrical classical or relativistic theories, although these theories, too, have an algebraic component to them. It follows that one needs to find an algebraic scheme able make these predictions in a given quantum regime. Heisenberg was first to accomplish this in the case of quantum mechanics, as matrix mechanics, whose matrix character testified to his algebraic method, as Einstein characterized it. The article explores the implications of the Heisenberg method and of the QPA principle for quantum theory, and for the relationships between mathematics and physics there, from a nonrealist or, in terms of this article, “reality-without-realism” or RWR perspective, defining the RWR principle, thus joined to the QPA principle.

Description: Entropy, Vol. 20, Pages 648: The Effects of Mo and Nb on the Microstructures and Properties of CrFeCoNi(Nb,Mo) Alloys Entropy doi: 10.3390/e20090648 Authors: Chun-Huei Tsau Meng-Chi Tsai The effects of niobium and molybdenum additions on the microstructures, hardness and corrosion behaviors of CrFeCoNi(Nb,Mo) alloys were investigated. All of the CrFeCoNi(Nb,Mo) alloys displayed dendritic microstructures. The dendrites of CrFeCoNiNb and CrFeCoNiNb0.5Mo0.5 alloys were a hexagonal close packing (HCP) phase and the interdendrites were a eutectic structure of HCP and face-centered cubic (FCC) phases. Additionally, the dendrites of CrFeCoNiMo alloys were a simple cubic (SC) phase and the interdendrites were a eutectic structure of SC and FCC phases. The volume fraction of dendrites and interdendrites in these alloys were calculated. The influences of the volume fraction of dendrite in the alloys on the overall hardness were also discussed. The CrFeCoNiNb alloy had the larger volume fraction of dendrite and thus had the highest hardness among these alloys. The CrFeCoNi(Nb,Mo) alloys also showed better corrosion resistances in 1 M H2SO4 and 1 M NaCl solutions by comparing with commercial 304 stainless steel. The CrFeCoNiNb0.5Mo0.5 alloy possessed the best corrosion resistances in these solutions among the CrFeCoNi(Nb,Mo) alloys.

Description: Entropy, Vol. 20, Pages 646: Tensile Behavior and Evolution of the Phases in the Al10Co25Cr8Fe15Ni36Ti6 Compositionally Complex/High Entropy Alloy Entropy doi: 10.3390/e20090646 Authors: Anna Maria Manzoni Sebastian Haas Haneen Daoud Uwe Glatzel Christiane Förster Nelia Wanderka Compositionally complex alloys, or high entropy alloys, are good candidates for applications at higher temperatures in gas turbines. After their introduction, the equiatomic Al17Co17Cr17Cu17Fe17Ni17 (at.%) served as a starting material and a long optimization road finally led to the recently optimized Al10Co25Cr8Fe15Ni36Ti6 (at.%) alloy, which shows promising mechanical properties. Investigations of the as-cast state and after different heat treatments focus on the evolution of the microstructure and provide an overview of some mechanical properties. The dendritic solidification provides two phases in the dendritic cores and two different ones in the interdendritic regions. Three of the four phases remain after heat treatments. Homogenization and subsequent annealing produce a γ-γ’ based microstructure, similar to Ni-based superalloys. The γ phase is Co-Cr-Fe rich and the γ’ phase is Al-Ni-Ti rich. The understanding of the mechanical behavior of the investigated alloy is supported and enhanced by the study of the different phases and their nanohardness measurements. The observations are compared with mechanical and microstructural data from commercial Ni-based superalloys, Co-based alloys, and Co-Ni-based alloys at the desired application temperature of ~800 °C.

Description: Entropy, Vol. 20, Pages 667: Application of Mutual Information-Sample Entropy Based MED-ICEEMDAN De-Noising Scheme for Weak Fault Diagnosis of Hoist Bearing Entropy doi: 10.3390/e20090667 Authors: Fen Yang Ziming Kou Juan Wu Tengyu Li In this paper, a novel weak fault features extraction scheme is proposed to extract weak fault features in head sheave bearings of floor-type multi-rope friction mine hoists in strong noise environments. A mutual information-based sample entropy (MI-SE) is proposed to select the effective intrinsic mode function (IMF). The numerical simulation presented in this paper has demonstrated that the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) has a poor performance on weak signals processing under a strong noise background, and fault features cannot be identified clearly. The de-noised signal is decomposed into several IMFs by the ICEEMDAN method, with the help of the minimum entropy deconvolution (MED), which works as a pre-filter to increase the kurtosis value by about 3.2 times. The envelope spectrum of the effective IMF selected by the MI-SE method shows almost all fault features clearly. An analogous experiment system was built to verify the feasibility of the proposed scheme, whose results have also shown that the proposed hybrid scheme has better performance compared with ICEEMDAN or MED on the weak fault features extraction under a strong noise background. This paper provides a novel method to diagnose the weak faults of the slow speed and heavy load rolling bearings in a strong noise environment.

Description: Entropy, Vol. 20, Pages 661: Non-Orthogonal eMBB-URLLC Radio Access for Cloud Radio Access Networks with Analog Fronthauling Entropy doi: 10.3390/e20090661 Authors: Andrea Matera Rahif Kassab Osvaldo Simeone Umberto Spagnolini This paper considers the coexistence of Ultra Reliable Low Latency Communications (URLLC) and enhanced Mobile BroadBand (eMBB) services in the uplink of Cloud Radio Access Network (C-RAN) architecture based on the relaying of radio signals over analog fronthaul links. While Orthogonal Multiple Access (OMA) to the radio resources enables the isolation and the separate design of different 5G services, Non-Orthogonal Multiple Access (NOMA) can enhance the system performance by sharing wireless and fronthaul resources. This paper provides an information-theoretic perspective in the performance of URLLC and eMBB traffic under both OMA and NOMA. The analysis focuses on standard cellular models with additive Gaussian noise links and a finite inter-cell interference span, and it accounts for different decoding strategies such as puncturing, Treating Interference as Noise (TIN) and Successive Interference Cancellation (SIC). Numerical results demonstrate that, for the considered analog fronthauling C-RAN architecture, NOMA achieves higher eMBB rates with respect to OMA, while guaranteeing reliable low-rate URLLC communication with minimal access latency. Moreover, NOMA under SIC is seen to achieve the best performance, while, unlike the case with digital capacity-constrained fronthaul links, TIN always outperforms puncturing.

Description: Entropy, Vol. 20, Pages 665: Assessing Time Series Reversibility through Permutation Patterns Entropy doi: 10.3390/e20090665 Authors: Massimiliano Zanin Alejandro Rodríguez-González Ernestina Ruiz David Papo Time irreversibility, i.e., the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here, we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.

Description: Entropy, Vol. 20, Pages 666: Chart for Thermoelectric Systems Operation Based on a Ternary Diagram for Bithermal Systems Entropy doi: 10.3390/e20090666 Authors: Julien Ramousse Christophe Goupil Thermoelectric system’s operation needs careful attention to ensure optimal power conversion depending on the application aims. As a ternary diagram of bithermal systems allows a synthetic graphical analysis of the performance attainable by any work-heat conversion system, thermoelectric systems operation is plotted as a parametric curve function of the operating conditions (electric current and reservoirs’ temperature), based on the standard model of Ioffe. The threshold of each operating mode (heat engine, heat pump, thermal dissipation, and forced thermal transfer), along with the optimal efficiencies and powers of the heat pump and heat engine modes, are characterized graphically and analytically as a function of the material properties and the operating conditions. The sensibility of the performance aims (maximum efficiency vs. maximum power) with the operating conditions is, thus, highlighted. In addition, the specific contributions of each phenomenon involved in the semiconductor (reversible Seebeck effect, irreversible heat leakage by conduction and irreversible thermal dissipation by Joule effect) are discussed in terms of entropy generation. Finally, the impact of the exo-irreversibilities on the performance is analyzed by taking the external thermal resistances into account.

Description: Entropy, Vol. 20, Pages 663: Cross-Sectoral Information Transfer in the Chinese Stock Market around Its Crash in 2015 Entropy doi: 10.3390/e20090663 Authors: Xudong Wang Xiaofeng Hui This paper applies effective transfer entropy to research the information transfer in the Chinese stock market around its crash in 2015. According to the market states, the entire period is divided into four sub-phases: the tranquil, bull, crash, and post-crash periods. Kernel density estimation is used to calculate the effective transfer entropy. Then, the information transfer network is constructed. Nodes’ centralities and the directed maximum spanning trees of the networks are analyzed. The results show that, in the tranquil period, the information transfer is weak in the market. In the bull period, the strength and scope of the information transfer increases. The utility sector outputs a great deal of information and is the hub node for the information flow. In the crash period, the information transfer grows further. The market efficiency in this period is worse than that in the other three sub-periods. The information technology sector is the biggest information source, while the consumer staples sector receives the most information. The interactions of the sectors become more direct. In the post-crash period, information transfer declines but is still stronger than the tranquil time. The financial sector receives the largest amount of information and is the pivot node.

Description: Entropy, Vol. 20, Pages 676: Trailing-Edge Flap Control for Mitigating Rotor Power Fluctuations of a Large-Scale Offshore Floating Wind Turbine under the Turbulent Wind Condition Entropy doi: 10.3390/e20090676 Authors: Bofeng Xu Junheng Feng Tongguang Wang Yue Yuan Zhenzhou Zhao Wei Zhong A trailing-edge flap control strategy for mitigating rotor power fluctuations of a 5 MW offshore floating wind turbine is developed under turbulent wind inflow. The wind shear must be considered because of the large rotor diameter. The trailing-edge flap control strategy is based on the turbulent wind speed, the blade azimuth angle, and the platform motions. The rotor power is predicted using the free vortex wake method, coupled with the control strategy. The effect of the trailing-edge flap control on the rotor power is determined by a comparison with the rotor power of a turbine without a trailing-edge flap control. The optimal values of the three control factors are obtained. The results show that the trailing-edge flap control strategy is effective for improving the stability of the output rotor power of the floating wind turbine under the turbulent wind condition.

Description: Entropy, Vol. 20, Pages 672: Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications Entropy doi: 10.3390/e20090672 Authors: Majdoleen Abu Qamar Nasruddin Hassan The idea of the Q-neutrosophic soft set emerges from the neutrosophic soft set by upgrading the membership functions to a two-dimensional entity which indicate uncertainty, indeterminacy and falsity. Hence, it is able to deal with two-dimensional inconsistent, imprecise, and indeterminate information appearing in real life situations. In this study, the tools that measure the similarity, distance and the degree of fuzziness of Q-neutrosophic soft sets are presented. The definitions of distance, similarity and measures of entropy are introduced. Some formulas for Q-neutrosophic soft entropy were presented. The known Hamming, Euclidean and their normalized distances are generalized to make them well matched with the idea of Q-neutrosophic soft set. The distance measure is subsequently used to define the measure of similarity. Lastly, we expound three applications of the measures of Q-neutrosophic soft sets by applying entropy and the similarity measure to a medical diagnosis and decision making problems.

Description: Entropy, Vol. 20, Pages 686: Gaussian Multiple Access Channels with One-Bit Quantizer at the Receiver Entropy doi: 10.3390/e20090686 Authors: Borzoo Rassouli Morteza Varasteh Deniz Gündüz The capacity region of a two-transmitter Gaussian multiple access channel (MAC) under average input power constraints is studied, when the receiver employs a zero-threshold one-bit analogue-to-digital converter (ADC). It is proven that the input distributions of the two transmitters that achieve the boundary points of the capacity region are discrete. Based on the position of a boundary point, upper bounds on the number of the mass points of the corresponding distributions are derived. Furthermore, a lower bound on the sum capacity is proposed that can be achieved by time division with power control. Finally, inspired by the numerical results, the proposed lower bound is conjectured to be tight.

Description: Entropy, Vol. 20, Pages 694: Overview of the 37th MaxEnt Entropy doi: 10.3390/e20090694 Authors: Teresa C. M. Dias Marcio A. Diniz Carlos A. de B. Pereira Adriano Polpo The 37th edition of MaxEnt was held in Brazil, hosting several distinguished researchers and students. The workshop offered four tutorials, nine invited talks, twenty four oral presentations and twenty seven poster presentations. All submissions received their first choice between oral and poster presentations. The event held a celebration to Julio Stern’s 60th anniversary and awarded two prizes to young researchers. As customary, the workshop had one free afternoon, in which participants visited the city’s surroundings and experienced Brazilian food and traditions.

Description: Entropy, Vol. 20, Pages 693: Dynamic Rounds Chaotic Block Cipher Based on Keyword Abstract Extraction Entropy doi: 10.3390/e20090693 Authors: Juan Wang Qun Ding According to the keyword abstract extraction function in the Natural Language Processing and Information Retrieval Sharing Platform (NLPIR), the design method of a dynamic rounds chaotic block cipher is presented in this paper, which takes into account both the security and efficiency. The cipher combines chaotic theory with the Feistel structure block cipher, and uses the randomness of chaotic sequence and the nonlinearity of chaotic S-box to dynamically generate encrypted rounds, realizing more numbers of dynamic rounds encryption for the important information marked by NLPIR, while less numbers of dynamic rounds encryption for the non-important information that is not marked. Through linear and differential cryptographic analysis, ciphertext information entropy, “0–1” balance and National Institute of Science and Technology (NIST) tests and the comparison with other traditional and lightweight block ciphers, the results indicate that the dynamic variety of encrypted rounds can achieve different levels of encryption for different information, which can achieve the purpose of enhancing the anti-attack ability and reducing the number of encrypted rounds. Therefore, the dynamic rounds chaotic block cipher can guarantee the security of information transmission and realize the lightweight of the cryptographic algorithm.

Description: Entropy, Vol. 20, Pages 691: The Behavior of VLF/LF Variations Associated with Geomagnetic Activity, Earthquakes, and the Quiet Condition Using a Neural Network Approach Entropy doi: 10.3390/e20090691 Authors: Irina Popova Alexandr Rozhnoi Maria Solovieva Danila Chebrov Masashi Hayakawa The neural network approach is proposed for studying very-low- and low-frequency (VLF and LF) subionospheric radio wave variations in the time vicinities of magnetic storms and earthquakes, with the purpose of recognizing anomalies of different types. We also examined the days with quiet geomagnetic conditions in the absence of seismic activity, in order to distinguish between the disturbed signals and the quiet ones. To this end, we trained the neural network (NN) on the examples of the representative database. The database included both the VLF/LF data that was measured during four-year monitoring at the station in Petropavlovsk-Kamchatsky, and the parameters of seismicity in the Kuril-Kamchatka and Japan regions. It was shown that the neural network can distinguish between the disturbed and undisturbed signals. Furthermore, the prognostic behavior of the VLF/LF variations indicative of magnetic and seismic activity has a different appearance in the time vicinity of the earthquakes and magnetic storms.

Description: Entropy, Vol. 20, Pages 690: Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms Entropy doi: 10.3390/e20090690 Authors: Ali H. Alkhaldi Mohd. Aquib Aliya Naaz Siddiqui Mohammad Hasan Shahid In this paper, we obtain the upper bounds for the normalized δ -Casorati curvatures and generalized normalized δ -Casorati curvatures for statistical submanifolds in Sasaki-like statistical manifolds with constant curvature. Further, we discuss the equality case of the inequalities. Moreover, we give the necessary and sufficient condition for a Sasaki-like statistical manifold to be η -Einstein. Finally, we provide the condition under which the metric of Sasaki-like statistical manifolds with constant curvature is a solution of vacuum Einstein field equations.

Description: Entropy, Vol. 20, Pages 695: Optimization of Thurston’s Core Entropy Algorithm for Polynomials with a Critical Point of Maximal Order Entropy doi: 10.3390/e20090695 Authors: Gamaliel Blé Domingo González This paper discusses some properties of the topological entropy systems generated by polynomials of degree d in their Hubbard tree. An optimization of Thurston’s core entropy algorithm is developed for a family of polynomials of degree d.

Description: Entropy, Vol. 20, Pages 692: New Entropic Inequalities and Hidden Correlations in Quantum Suprematism Picture of Qudit States Entropy doi: 10.3390/e20090692 Authors: Margarita A. Man’ko Vladimir I. Man’ko We study an analog of Bayes’ formula and the nonnegativity property of mutual information for systems with one random variable. For single-qudit states, we present new entropic inequalities in the form of the subadditivity and condition corresponding to hidden correlations in quantum systems. We present qubit states in the quantum suprematism picture, where these states are identified with three probability distributions, describing the states of three classical coins, and illustrate the states by Triada of Malevich’s squares with areas satisfying the quantum constraints. We consider arbitrary quantum states belonging to N-dimensional Hilbert space as ( N 2 − 1 ) fair probability distributions describing the states of ( N 2 − 1 ) classical coins. We illustrate the geometrical properties of the qudit states by a set of Triadas of Malevich’s squares. We obtain new entropic inequalities for matrix elements of an arbitrary density N×N-matrix of qudit systems using the constructed maps of the density matrix on a set of the probability distributions. In addition, to construct the bijective map of the qudit state onto the set of probabilities describing the positions of classical coins, we show that there exists a bijective map of any quantum observable onto the set of dihotomic classical random variables with statistics determined by the above classical probabilities. Finally, we discuss the physical meaning and possibility to check derived inequalities in the experiments with superconducting circuits based on Josephson junction devices.

Description: Entropy, Vol. 20, Pages 687: Classical and Quantum Causal Interventions Entropy doi: 10.3390/e20090687 Authors: Gerard Milburn Sally Shrapnel Characterising causal structure is an activity that is ubiquitous across the sciences. Causal models are representational devices that can be used as oracles for future interventions, to predict how values of some variables will change in response to interventions on others. Recent work has generalised concepts from this field to situations involving quantum systems, resulting in a new notion of quantum causal structure. A key concept in both the classical and quantum context is that of an intervention. Interventions are the controlled operations required to identify causal structure and ultimately the feature that endows causal models with empirical meaning. Although interventions are a crucial feature of both the classical and quantum causal modelling frameworks, to date there has been no discussion of their physical basis. In this paper, we consider interventions from a physical perspective and show that, in both the classical and quantum case, they are constrained by the thermodynamics of measurement and feedback in open systems. We demonstrate that the perfect “atomic” or “surgical” interventions characterised by Pearl’s famous do-calculus are physically impossible, and this is the case for both classical and quantum systems.

Description: Entropy, Vol. 20, Pages 700: Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers Entropy doi: 10.3390/e20090700 Authors: Michail Vlysidis Yiannis Kaznessis The time evolution of stochastic reaction networks can be modeled with the chemical master equation of the probability distribution. Alternatively, the numerical problem can be reformulated in terms of probability moment equations. Herein we present a new alternative method for numerically solving the time evolution of stochastic reaction networks. Based on the assumption that the entropy of the reaction network is maximum, Lagrange multipliers are introduced. The proposed method derives equations that model the time derivatives of these Lagrange multipliers. We present detailed steps to transform moment equations to Lagrange multiplier equations. In order to demonstrate the method, we present examples of non-linear stochastic reaction networks of varying degrees of complexity, including multistable and oscillatory systems. We find that the new approach is as accurate and significantly more efficient than Gillespie’s original exact algorithm for systems with small number of interacting species. This work is a step towards solving stochastic reaction networks accurately and efficiently.

Description: Entropy, Vol. 20, Pages 698: Combining Entropy Measures for Anomaly Detection Entropy doi: 10.3390/e20090698 Authors: Alberto Muñoz Nicolás Hernández Javier M. Moguerza Gabriel Martos The combination of different sources of information is a problem that arises in several situations, for instance, when data are analysed using different similarity measures. Often, each source of information is given as a similarity, distance, or a kernel matrix. In this paper, we propose a new class of methods which consists of producing, for anomaly detection purposes, a single Mercer kernel (that acts as a similarity measure) from a set of local entropy kernels and, at the same time, avoids the task of model selection. This kernel is used to build an embedding of data in a variety that will allow the use of a (modified) one-class Support Vector Machine to detect outliers. We study several information combination schemes and their limiting behaviour when the data sample size increases within an Information Geometry context. In particular, we study the variety of the given positive definite kernel matrices to obtain the desired kernel combination as belonging to that variety. The proposed methodology has been evaluated on several real and artificial problems.

Description: Entropy, Vol. 20, Pages 699: Two Novel Information Entropy Indices for Analysis of the Eddy Current Distribution Entropy doi: 10.3390/e20090699 Authors: Guolong Chen The Koch curve exciting coil eddy current sensor is a kind of novel flexible planar eddy current probe. In this study, an intersection angle spectrum entropy index and a radial direction energy spectrum entropy were proposed to evaluate the eddy current distribution. Eddy current distributions induced by one turn of a circular coil and one turn of a second order Koch curve coil feed with different exciting frequency alternative currents and at different lift-off distances, were simulated and the eddy current distributions varying with lift-off distance in different exciting frequencies were compared by the two proposed indices. With the increase of the lift-off distance or the decrease of exciting frequency, the similarity between the shape of the Koch curve and the eddy current distribution became weakened and the degree of the concentration of the eddy current distribution in the specimen under the exciting coil was loosened.

Description: Entropy, Vol. 20, Pages 689: Evaluation of Sustainability Information Disclosure Based on Entropy Entropy doi: 10.3390/e20090689 Authors: Ming Li Jialin Wang Ying Li Yingcheng Xu Disclosure of sustainability information is important for stockholders and governments. In order to evaluate the quality of sustainability information disclosure in heavily polluting industries, the quality of the disclosure is proposed to be evaluated from completeness, adequacy, relevance, reliability, normativeness and clarity aspects. The corresponding evaluation indicator system is constructed. Due to the ambiguity and complexity of the evaluation information, the intuitionistic fuzzy sets are applied to model the linguistic ratings. Entropy is used to derive the weight of experts, the object weight and the subject weight of the indicators. which are integrated when dealing with the evaluation information. The quality of sustainability information disclosure of seven representative companies in heavily polluting industries is evaluated. The importance of indicators and ranking of the companies are derived. Based on the evaluation results, the discussion and suggestions are also provided.

Description: Entropy, Vol. 20, Pages 701: Research on Recognition Method of Driving Fatigue State Based on Sample Entropy and Kernel Principal Component Analysis Entropy doi: 10.3390/e20090701 Authors: Beige Ye Taorong Qiu Xiaoming Bai Ping Liu In view of the nonlinear characteristics of electroencephalography (EEG) signals collected in the driving fatigue state recognition research and the issue that the recognition accuracy of the driving fatigue state recognition method based on EEG is still unsatisfactory, this paper proposes a driving fatigue recognition method based on sample entropy (SE) and kernel principal component analysis (KPCA), which combines the advantage of the high recognition accuracy of sample entropy and the advantages of KPCA in dimensionality reduction for nonlinear principal components and the strong non-linear processing capability. By using support vector machine (SVM) classifier, the proposed method (called SE_KPCA) is tested on the EEG data, and compared with those based on fuzzy entropy (FE), combination entropy (CE), three kinds of entropies including SE, FE and CE that merged with KPCA. Experiment results show that the method is effective.

Description: Entropy, Vol. 20, Pages 710: The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders Entropy doi: 10.3390/e20090710 Authors: Samir Bendoukha Adel Ouannas Xiong Wang Amina-Aicha Khennaoui Viet-Thanh Pham Giuseppe Grassi Van Huynh This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings.

Description: Entropy, Vol. 20, Pages 709: Change-Point Detection Using the Conditional Entropy of Ordinal Patterns Entropy doi: 10.3390/e20090709 Authors: Anton Unakafov Karsten Keller This paper is devoted to change-point detection using only the ordinal structure of a time series. A statistic based on the conditional entropy of ordinal patterns characterizing the local up and down in a time series is introduced and investigated. The statistic requires only minimal a priori information on given data and shows good performance in numerical experiments. By the nature of ordinal patterns, the proposed method does not detect pure level changes but changes in the intrinsic pattern structure of a time series and so it could be interesting in combination with other methods.

Description: Entropy, Vol. 20, Pages 707: Energy Dissipation and Information Flow in Coupled Markovian Systems Entropy doi: 10.3390/e20090707 Authors: Matthew E. Quenneville David A. Sivak A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental states. The non-predictive model complexity has been shown to lower-bound the thermodynamic dissipation. Here we explore these statistical and physical quantities at steady state in simple models. We show that under quasi-static driving this model complexity saturates the dissipation. Beyond the quasi-static limit, we demonstrate a lower bound on the ratio of this model complexity to total dissipation, that is realized in the limit of weak driving.

Description: Entropy, Vol. 20, Pages 705: Spatial Organization of Five-Fold Morphology as a Source of Geometrical Constraint in Biology Entropy doi: 10.3390/e20090705 Authors: Juan López-Sauceda Jorge López-Ortega Gerardo Abel Laguna Sánchez Jacobo Sandoval Gutiérrez Ana Paola Rojas Meza José Luis Aragón A basic pattern in the body plan architecture of many animals, plants and some molecular and cellular systems is five-part units. This pattern has been understood as a result of genetic blueprints in development and as a widely conserved evolutionary character. Despite some efforts, a definitive explanation of the abundance of pentagonal symmetry at so many levels of complexity is still missing. Based on both, a computational platform and a statistical spatial organization argument, we show that five-fold morphology is substantially different from other abundant symmetries like three-fold, four-fold and six-fold symmetries in terms of spatial interacting elements. We develop a measuring system to determine levels of spatial organization in 2D polygons (homogeneous or heterogeneous partition of defined areas) based on principles of regularity in a morphospace. We found that spatial organization of five-fold symmetry is statistically higher than all other symmetries studied here (3 to 10-fold symmetries) in terms of spatial homogeneity. The significance of our findings is based on the statistical constancy of geometrical constraints derived from spatial organization of shapes, beyond the material or complexity level of the many different systems where pentagonal symmetry occurs.

Description: Entropy, Vol. 20, Pages 708: Morphogenesis of Urban Water Distribution Networks: A Spatiotemporal Planning Approach for Cost-Efficient and Reliable Supply Entropy doi: 10.3390/e20090708 Authors: Jonatan Zischg Wolfgang Rauch Robert Sitzenfrei Cities and their infrastructure networks are always in motion and permanently changing in structure and function. This paper presents a methodology for automatically creating future water distribution networks (WDNs) that are stressed step-by-step by disconnection and connection of WDN parts. The associated effects of demand shifting and flow rearrangements are simulated and assessed with hydraulic performances. With the methodology, it is possible to test various planning and adaptation options of the future WDN, where the unknown (future) network is approximated via the co-located and known (future) road network, and hence different topological characteristics (branched vs. strongly looped layout) can be investigated. The reliability of the planning options is evaluated with the flow entropy, a measure based on Shannon’s informational entropy. Uncertainties regarding future water consumption and water loss management are included in a scenario analysis. To avoid insufficient water supply to customers during the transition process from an initial to a final WDN state, an adaptation concept is proposed where critical WDN components are replaced over time. Finally, the method is applied to the drastic urban transition of Kiruna, Sweden. Results show that without adaptation measures severe performance drops will occur after the WDN state 2023, mainly caused by the disconnection of WDN parts. However, with low adaptation efforts that consider 2–3% pipe replacement, sufficient pressure performances are achieved. Furthermore, by using an entropy-cost comparison, the best planning options are determined.

Description: Entropy, Vol. 20, Pages 714: Harmonic Sierpinski Gasket and Applications Entropy doi: 10.3390/e20090714 Authors: Emanuel Guariglia The aim of this paper is to investigate the generalization of the Sierpinski gasket through the harmonic metric. In particular, this work presents an antenna based on such a generalization. In fact, the harmonic Sierpinski gasket is used as a geometric configuration of small antennas. As with fractal antennas and Rényi entropy, their performance is characterized by the associated entropy that is studied and discussed here.

Description: Entropy, Vol. 20, Pages 713: The Impact of Entropy and Solution Density on Selected SAT Heuristics Entropy doi: 10.3390/e20090713 Authors: Dor Cohen Ofer Strichman We present a new characterization of propositional formulas called entropy, which approximates the freedom we have in assigning the variables. Like several other such measures (e.g., back-door and back-door-key variables), it is computationally expensive to compute. Nevertheless, for small and medium-size satisfiable formulas, it enables us to study the effect of this freedom on the impact of various SAT heuristics, following up on a recent study by C. Oh (Oh, SAT’15, LNCS 9340, 307–323). Oh’s findings were that the expected success of various heuristics depends on whether the input formula is satisfiable or not. With entropy, and also with the measure of solution density, we are able to refine these findings for the case of satisfiable formulas. Specifically, we found empirically that satisfiable formulas with small entropy “behave” similarly to unsatisfiable formulas.

Description: Entropy, Vol. 20, Pages 722: Analytic Study of Complex Fractional Tsallis’ Entropy with Applications in CNNs Entropy doi: 10.3390/e20100722 Authors: Rabha W. Ibrahim Maslina Darus In this paper, we study Tsallis’ fractional entropy (TFE) in a complex domain by applying the definition of the complex probability functions. We study the upper and lower bounds of TFE based on some special functions. Moreover, applications in complex neural networks (CNNs) are illustrated to recognize the accuracy of CNNs.

Description: Entropy, Vol. 20, Pages 719: Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes Entropy doi: 10.3390/e20090719 Authors: Jesús Gutiérrez-Gutiérrez Marta Zárraga-Rodríguez Pedro M. Crespo Xabier Insausti In this paper, we obtain an integral formula for the rate distortion function (RDF) of any Gaussian asymptotically wide sense stationary (AWSS) vector process. Applying this result, we also obtain an integral formula for the RDF of Gaussian moving average (MA) vector processes and of Gaussian autoregressive MA (ARMA) AWSS vector processes.

Description: Entropy, Vol. 20, Pages 717: Representation and Characterization of Nonstationary Processes by Dilation Operators and Induced Shape Space Manifolds Entropy doi: 10.3390/e20090717 Authors: Maël Dugast Guillaume Bouleux Eric Marcon We proposed in this work the introduction of a new vision of stochastic processes through geometry induced by dilation. The dilation matrices of a given process are obtained by a composition of rotation matrices built in with respect to partial correlation coefficients. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, only one dilation matrix is obtained and it corresponds therefore to Naimark dilation. When the process is nonstationary, a set of dilation matrices is obtained. They correspond to Kolmogorov decomposition. In this work, the nonstationary class of periodically correlated processes was of interest. The underlying periodicity of correlation coefficients is then transmitted to the set of dilation matrices. Because this set lives on the Lie group of rotation matrices, we can see them as points of a closed curve on the Lie group. Geometrical aspects can then be investigated through the shape of the obtained curves, and to give a complete insight into the space of curves, a metric and the derived geodesic equations are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices, and because the metric in the space of curve naturally extends to the space of shapes; this enables a comparison between curves’ shapes and allows then the classification of random processes’ measures.

Description: Entropy, Vol. 20, Pages 724: Making the Coupled Gaussian Process Dynamical Model Modular and Scalable with Variational Approximations Entropy doi: 10.3390/e20100724 Authors: Dmytro Velychko Benjamin Knopp Dominik Endres We describe a sparse, variational posterior approximation to the Coupled Gaussian Process Dynamical Model (CGPDM), which is a latent space coupled dynamical model in discrete time. The purpose of the approximation is threefold: first, to reduce training time of the model; second, to enable modular re-use of learned dynamics; and, third, to store these learned dynamics compactly. Our target applications here are human movement primitive (MP) models, where an MP is a reusable spatiotemporal component, or “module” of a human full-body movement. Besides re-usability of learned MPs, compactness is crucial, to allow for the storage of a large library of movements. We first derive the variational approximation, illustrate it on toy data, test its predictions against a range of other MP models and finally compare movements produced by the model against human perceptual expectations. We show that the variational CGPDM outperforms several other MP models on movement trajectory prediction. Furthermore, human observers find its movements nearly indistinguishable from replays of natural movement recordings for a very compact parameterization of the approximation.

Description: Entropy, Vol. 20, Pages 725: A Novel Algorithm Based on the Pixel-Entropy for Automatic Detection of Number of Lanes, Lane Centers, and Lane Division Lines Formation Entropy doi: 10.3390/e20100725 Authors: Fernando Hermosillo-Reynoso Deni Torres-Roman Jayro Santiago-Paz Julio Ramirez-Pacheco Lane detection for traffic surveillance in intelligent transportation systems is a challenge for vision-based systems. In this paper, a novel pixel-entropy based algorithm for the automatic detection of the number of lanes and their centers, as well as the formation of their division lines is proposed. Using as input a video from a static camera, each pixel behavior in the gray color space is modeled by a time series; then, for a time period τ , its histogram followed by its entropy are calculated. Three different types of theoretical pixel-entropy behaviors can be distinguished: (1) the pixel-entropy at the lane center shows a high value; (2) the pixel-entropy at the lane division line shows a low value; and (3) a pixel not belonging to the road has an entropy value close to zero. From the road video, several small rectangle areas are captured, each with only a few full rows of pixels. For each pixel of these areas, the entropy is calculated, then for each area or row an entropy curve is produced, which, when smoothed, has as many local maxima as lanes and one more local minima than lane division lines. For the purpose of testing, several real traffic scenarios under different weather conditions with other moving objects were used. However, these background objects, which are out of road, were filtered out. Our algorithm, compared to others based on trajectories of vehicles, shows the following advantages: (1) the lowest computational time for lane detection (only 32 s with a traffic flow of one vehicle/s per-lane); and (2) better results under high traffic flow with congestion and vehicle occlusion. Instead of detecting road markings, it forms lane-dividing lines. Here, the entropies of Shannon and Tsallis were used, but the entropy of Tsallis for a selected q of a finite set achieved the best results.

Description: Entropy, Vol. 20, Pages 723: Statistical Inference for Geometric Process with the Power Lindley Distribution Entropy doi: 10.3390/e20100723 Authors: Cenker Bicer The geometric process (GP) is a simple and direct approach to modeling of the successive inter-arrival time data set with a monotonic trend. In addition, it is a quite important alternative to the non-homogeneous Poisson process. In the present paper, the parameter estimation problem for GP is considered, when the distribution of the first occurrence time is Power Lindley with parameters α and λ . To overcome the parameter estimation problem for GP, the maximum likelihood, modified moments, modified L-moments and modified least-squares estimators are obtained for parameters a, α and λ . The mean, bias and mean squared error (MSE) values associated with these estimators are evaluated for small, moderate and large sample sizes by using Monte Carlo simulations. Furthermore, two illustrative examples using real data sets are presented in the paper.

Description: Entropy, Vol. 20, Pages 727: Entropy, or Information, Unifies Ecology and Evolution and Beyond Entropy doi: 10.3390/e20100727 Authors: William Bruce Sherwin This article discusses how entropy/information methods are well-suited to analyzing and forecasting the four processes of innovation, transmission, movement, and adaptation, which are the common basis to ecology and evolution. Macroecologists study assemblages of differing species, whereas micro-evolutionary biologists study variants of heritable information within species, such as DNA and epigenetic modifications. These two different modes of variation are both driven by the same four basic processes, but approaches to these processes sometimes differ considerably. For example, macroecology often documents patterns without modeling underlying processes, with some notable exceptions. On the other hand, evolutionary biologists have a long history of deriving and testing mathematical genetic forecasts, previously focusing on entropies such as heterozygosity. Macroecology calls this Gini–Simpson, and has borrowed the genetic predictions, but sometimes this measure has shortcomings. Therefore it is important to note that predictive equations have now been derived for molecular diversity based on Shannon entropy and mutual information. As a result, we can now forecast all major types of entropy/information, creating a general predictive approach for the four basic processes in ecology and evolution. Additionally, the use of these methods will allow seamless integration with other studies such as the physical environment, and may even extend to assisting with evolutionary algorithms.

Description: Entropy, Vol. 20, Pages 726: Microscopic Theory of Energy Dissipation and Decoherence in Solid-State Quantum Devices: Need for Nonlocal Scattering Models Entropy doi: 10.3390/e20100726 Authors: Rita Iotti Fausto Rossi Energy dissipation and decoherence in state-of-the-art quantum nanomaterials and related nanodevices are routinely described and simulated via local scattering models, namely relaxation-time and Boltzmann-like schemes. The incorporation of such local scattering approaches within the Wigner-function formalism may lead to anomalous results, such as suppression of intersubband relaxation, incorrect thermalization dynamics, and violation of probability-density positivity. The primary goal of this article is to investigate a recently proposed quantum-mechanical (nonlocal) generalization (Phys. Rev. B 2017, 96, 115420) of semiclassical (local) scattering models, extending such treatment to carrier–carrier interaction, and focusing in particular on the nonlocal character of Pauli-blocking contributions. In order to concretely show the intrinsic limitations of local scattering models, a few simulated experiments of energy dissipation and decoherence in a prototypical quantum-well semiconductor nanostructure are also presented.

Description: Entropy, Vol. 20, Pages 730: A Review of Physical Layer Security Techniques for Internet of Things: Challenges and Solutions Entropy doi: 10.3390/e20100730 Authors: Li Sun Qinghe Du With the uninterrupted revolution of communications technologies and the great-leap-forward development of emerging applications, the ubiquitous deployment of Internet of Things (IoT) is imperative to accommodate constantly growing user demands and market scales. Communication security is critically important for the operations of IoT. Among the communication security provisioning techniques, physical layer security (PLS), which can provide unbreakable, provable, and quantifiable secrecy from an information-theoretical point of view, has drawn considerable attention from both the academia and the industries. However, the unique features of IoT, such as low-cost, wide-range coverage, massive connection, and diversified services, impose great challenges for the PLS protocol design in IoT. In this article, we present a comprehensive review of the PLS techniques toward IoT applications. The basic principle of PLS is first briefly introduced, followed by the survey of the existing PLS techniques. Afterwards, the characteristics of IoT are identified, based on which the challenges faced by PLS protocol design are summarized. Then, three newly-proposed PLS solutions are highlighted, which match the features of IoT well and are expected to be applied in the near future. Finally, we conclude the paper and point out some further research directions.

Description: Entropy, Vol. 20, Pages 728: Image Thresholding Segmentation on Quantum State Space Entropy doi: 10.3390/e20100728 Authors: Xiangluo Wang Chunlei Yang Guo-Sen Xie Zhonghua Liu Aiming to implement image segmentation precisely and efficiently, we exploit new ways to encode images and achieve the optimal thresholding on quantum state space. Firstly, the state vector and density matrix are adopted for the representation of pixel intensities and their probability distribution, respectively. Then, the method based on global quantum entropy maximization (GQEM) is proposed, which has an equivalent object function to Otsu’s, but gives a more explicit physical interpretation of image thresholding in the language of quantum mechanics. To reduce the time consumption for searching for optimal thresholds, the method of quantum lossy-encoding-based entropy maximization (QLEEM) is presented, in which the eigenvalues of density matrices can give direct clues for thresholding, and then, the process of optimal searching can be avoided. Meanwhile, the QLEEM algorithm achieves two additional effects: (1) the upper bound of the thresholding level can be implicitly determined according to the eigenvalues; and (2) the proposed approaches ensure that the local information in images is retained as much as possible, and simultaneously, the inter-class separability is maximized in the segmented images. Both of them contribute to the structural characteristics of images, which the human visual system is highly adapted to extract. Experimental results show that the proposed methods are able to achieve a competitive quality of thresholding and the fastest computation speed compared with the state-of-the-art methods.

Description: Entropy, Vol. 20, Pages 729: Numerical and Non-Asymptotic Analysis of Elias’s and Peres’s Extractors with Finite Input Sequences Entropy doi: 10.3390/e20100729 Authors: Amonrat Prasitsupparote Norio Konno Junji Shikata Many cryptographic systems require random numbers, and the use of weak random numbers leads to insecure systems. In the modern world, there are several techniques for generating random numbers, of which the most fundamental and important methods are deterministic extractors proposed by von Neumann, Elias, and Peres. Elias’s extractor achieves the optimal rate (i.e., information-theoretic upper bound) h ( p ) if the block size tends to infinity, where h ( · ) is the binary entropy function and p is the probability that each bit of input sequences occurs. Peres’s extractor achieves the optimal rate h ( p ) if the length of the input and the number of iterations tend to infinity. Previous research related to both extractors has made no reference to practical aspects including running time and memory size with finite input sequences. In this paper, based on some heuristics, we derive a lower bound on the maximum redundancy of Peres’s extractor, and we show that Elias’s extractor is better than Peres’s extractor in terms of the maximum redundancy (or the rates) if we do not pay attention to the time complexity or space complexity. In addition, we perform numerical and non-asymptotic analysis of both extractors with a finite input sequence with any biased probability under the same environments. To do so, we implemented both extractors on a general PC and simple environments. Our empirical results show that Peres’s extractor is much better than Elias’s extractor for given finite input sequences under a very similar running time. As a consequence, Peres’s extractor would be more suitable to generate uniformly random sequences in practice in applications such as cryptographic systems.

Description: Entropy, Vol. 20, Pages 720: Fractional Form of a Chaotic Map without Fixed Points: Chaos, Entropy and Control Entropy doi: 10.3390/e20100720 Authors: Adel Ouannas Xiong Wang Amina-Aicha Khennaoui Samir Bendoukha Viet-Thanh Pham Fawaz E. Alsaadi In this paper, we investigate the dynamics of a fractional order chaotic map corresponding to a recently developed standard map that exhibits a chaotic behavior with no fixed point. This is the first study to explore a fractional chaotic map without a fixed point. In our investigation, we use phase plots and bifurcation diagrams to examine the dynamics of the fractional map and assess the effect of varying the fractional order. We also use the approximate entropy measure to quantify the level of chaos in the fractional map. In addition, we propose a one-dimensional stabilization controller and establish its asymptotic convergence by means of the linearization method.

Description: Entropy, Vol. 20, Pages 596: Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems Entropy doi: 10.3390/e20080596 Authors: D. Renger In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or GENERIC system in the space of fluxes. In a general setting we study how flux gradient or GENERIC systems are related to gradient systems of concentrations. This shows that many gradient or GENERIC systems arise from an underlying gradient or GENERIC system where fluxes rather than densities are being driven by (free) energies. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well.

Description: Entropy, Vol. 20, Pages 594: Bayesian Optimization Based on K-Optimality Entropy doi: 10.3390/e20080594 Authors: Liang Yan Xiaojun Duan Bowen Liu Jin Xu Bayesian optimization (BO) based on the Gaussian process (GP) surrogate model has attracted extensive attention in the field of optimization and design of experiments (DoE). It usually faces two problems: the unstable GP prediction due to the ill-conditioned Gram matrix of the kernel and the difficulty of determining the trade-off parameter between exploitation and exploration. To solve these problems, we investigate the K-optimality, aiming at minimizing the condition number. Firstly, the Sequentially Bayesian K-optimal design (SBKO) is proposed to ensure the stability of the GP prediction, where the K-optimality is given as the acquisition function. We show that the SBKO reduces the integrated posterior variance and maximizes the hyper-parameters’ information gain simultaneously. Secondly, a K-optimal enhanced Bayesian Optimization (KO-BO) approach is given for the optimization problems, where the K-optimality is used to define the trade-off balance parameters which can be output automatically. Specifically, we focus our study on the K-optimal enhanced Expected Improvement algorithm (KO-EI). Numerical examples show that the SBKO generally outperforms the Monte Carlo, Latin hypercube sampling, and sequential DoE approaches by maximizing the posterior variance with the highest precision of prediction. Furthermore, the study of the optimization problem shows that the KO-EI method beats the classical EI method due to its higher convergence rate and smaller variance.

Description: Entropy, Vol. 20, Pages 593: The Duality of Entropy/Extropy, and Completion of the Kullback Information Complex Entropy doi: 10.3390/e20080593 Authors: Frank Lad Giuseppe Sanfilippo Gianna Agrò The refinement axiom for entropy has been provocative in providing foundations of information theory, recognised as thoughtworthy in the writings of both Shannon and Jaynes. A resolution to their concerns has been provided recently by the discovery that the entropy measure of a probability distribution has a dual measure, a complementary companion designated as “extropy”. We report here the main results that identify this fact, specifying the dual equations and exhibiting some of their structure. The duality extends beyond a simple assessment of entropy, to the formulation of relative entropy and the Kullback symmetric distance between two forecasting distributions. This is defined by the sum of a pair of directed divergences. Examining the defining equation, we notice that this symmetric measure can be generated by two other explicable pairs of functions as well, neither of which is a Bregman divergence. The Kullback information complex is constituted by the symmetric measure of entropy/extropy along with one of each of these three function pairs. It is intimately related to the total logarithmic score of two distinct forecasting distributions for a quantity under consideration, this being a complete proper score. The information complex is isomorphic to the expectations that the two forecasting distributions assess for their achieved scores, each for its own score and for the score achieved by the other. Analysis of the scoring problem exposes a Pareto optimal exchange of the forecasters’ scores that both are willing to engage. Both would support its evaluation for assessing the relative quality of the information they provide regarding the observation of an unknown quantity of interest. We present our results without proofs, as these appear in source articles that are referenced. The focus here is on their content, unhindered. The mathematical syntax of probability we employ relies upon the operational subjective constructions of Bruno de Finetti.

Description: Entropy, Vol. 20, Pages 590: The Use of LPC and Wavelet Transform for Influenza Disease Modeling Entropy doi: 10.3390/e20080590 Authors: Khaled Daqrouq Mohammed Ajour In this paper, we investigated the modeling of the pathological features of the influenza disease on the human speech. The presented work is novel research based on a real database and a new combination of previously used methods, discrete wavelet transform (DWT) and linear prediction coding (LPC). Three verification system experiments, Normal/Influenza, Smokers/Influenza, and Normal/Smokers, were studied. For testing the proposed pathological system, several classification scores were calculated for the recorded database, from which we can see that the proposed method achieved very high scores, particularly for the Normal with Influenza verification system. The performance of the proposed system was also compared with other published recognition systems. The experiments of these schemes show that the proposed method is superior.

Description: Entropy, Vol. 20, Pages 595: Thermodynamic Analysis of Irreversible Desiccant Systems Entropy doi: 10.3390/e20080595 Authors: Niccolò Giannetti Seiichi Yamaguchi Andrea Rocchetti Kiyoshi Saito A new general thermodynamic mapping of desiccant systems’ performance is conducted to estimate the potentiality and determine the proper application field of the technology. This targets certain room conditions and given outdoor temperature and humidity prior to the selection of the specific desiccant material and technical details of the system configuration. This allows the choice of the operative state of the system to be independent from the limitations of the specific design and working fluid. An expression of the entropy balance suitable for describing the operability of a desiccant system at steady state is obtained by applying a control volume approach, defining sensible and latent effectiveness parameters, and assuming ideal gas behaviour of the air-vapour mixture. This formulation, together with mass and energy balances, is used to conduct a general screening of the system performance. The theoretical advantage and limitation of desiccant dehumidification air conditioning, maximum efficiency for given conditions constraints, least irreversible configuration for a given operative target, and characteristics of the system for a target efficiency can be obtained from this thermodynamic mapping. Once the thermo-physical properties and the thermodynamic equilibrium relationship of the liquid desiccant mixture or solid coating material are known, this method can be applied to a specific technical case to select the most appropriate working medium and guide the specific system design to achieve the target performance.

Description: Entropy, Vol. 20, Pages 592: Using the Data Agreement Criterion to Rank Experts’ Beliefs Entropy doi: 10.3390/e20080592 Authors: Duco Veen Diederick Stoel Naomi Schalken Kees Mulder Rens van de Schoot Experts’ beliefs embody a present state of knowledge. It is desirable to take this knowledge into account when making decisions. However, ranking experts based on the merit of their beliefs is a difficult task. In this paper, we show how experts can be ranked based on their knowledge and their level of (un)certainty. By letting experts specify their knowledge in the form of a probability distribution, we can assess how accurately they can predict new data, and how appropriate their level of (un)certainty is. The expert’s specified probability distribution can be seen as a prior in a Bayesian statistical setting. We evaluate these priors by extending an existing prior-data (dis)agreement measure, the Data Agreement Criterion, and compare this approach to using Bayes factors to assess prior specification. We compare experts with each other and the data to evaluate their appropriateness. Using this method, new research questions can be asked and answered, for instance: Which expert predicts the new data best? Is there agreement between my experts and the data? Which experts’ representation is more valid or useful? Can we reach convergence between expert judgement and data? We provided an empirical example ranking (regional) directors of a large financial institution based on their predictions of turnover.

Description: Entropy, Vol. 20, Pages 591: Fuzzy and Sample Entropies as Predictors of Patient Survival Using Short Ventricular Fibrillation Recordings during out of Hospital Cardiac Arrest Entropy doi: 10.3390/e20080591 Authors: Beatriz Chicote Unai Irusta Elisabete Aramendi Raúl Alcaraz José Joaquín Rieta Iraia Isasi Daniel Alonso María del Mar Baqueriza Karlos Ibarguren Optimal defibrillation timing guided by ventricular fibrillation (VF) waveform analysis would contribute to improved survival of out-of-hospital cardiac arrest (OHCA) patients by minimizing myocardial damage caused by futile defibrillation shocks and minimizing interruptions to cardiopulmonary resuscitation. Recently, fuzzy entropy (FuzzyEn) tailored to jointly measure VF amplitude and regularity has been shown to be an efficient defibrillation success predictor. In this study, 734 shocks from 296 OHCA patients (50 survivors) were analyzed, and the embedding dimension (m) and matching tolerance (r) for FuzzyEn and sample entropy (SampEn) were adjusted to predict defibrillation success and patient survival. Entropies were significantly larger in successful shocks and in survivors, and when compared to the available methods, FuzzyEn presented the best prediction results, marginally outperforming SampEn. The sensitivity and specificity of FuzzyEn were 83.3% and 76.7% when predicting defibrillation success, and 83.7% and 73.5% for patient survival. Sensitivities and specificities were two points above those of the best available methods, and the prediction accuracy was kept even for VF intervals as short as 2s. These results suggest that FuzzyEn and SampEn may be promising tools for optimizing the defibrillation time and predicting patient survival in OHCA patients presenting VF.

Description: Entropy, Vol. 20, Pages 589: Tsallis Entropy of Product MV-Algebra Dynamical Systems Entropy doi: 10.3390/e20080589 Authors: Dagmar Markechová Beloslav Riečan This paper is concerned with the mathematical modelling of Tsallis entropy in product MV-algebra dynamical systems. We define the Tsallis entropy of order α, where α∈(0, 1)∪(1, ∞), of a partition in a product MV-algebra and its conditional version and we examine their properties. Among other, it is shown that the Tsallis entropy of order α, where α > 1, has the property of sub-additivity. This property allows us to define, for α > 1, the Tsallis entropy of a product MV-algebra dynamical system. It is proven that the proposed entropy measure is invariant under isomorphism of product MV-algebra dynamical systems.

Description: Entropy, Vol. 20, Pages 599: Intrinsic Computation of a Monod-Wyman-Changeux Molecule Entropy doi: 10.3390/e20080599 Authors: Marzen Causal states are minimal sufficient statistics of prediction of a stochastic process, their coding cost is called statistical complexity, and the implied causal structure yields a sense ofthe process’ “intrinsic computation”. We discuss how statistical complexity changes with slight changes to the underlying model– in this case, a biologically-motivated dynamical model, that of aMonod-Wyman-Changeux molecule. Perturbations to kinetic rates cause statistical complexity to jump from finite to infinite. The same is not true for excess entropy, the mutual information between past and future, or for the molecule’s transfer function. We discuss the implications of this for the relationship between intrinsic and functional computation of biological sensory systems.