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Entropy, Volume 20, Issue 10 (October 2018)

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Open AccessArticle The Middle-Income Trap and the Coping Strategies From Network-Based Perspectives
Entropy 2018, 20(10), 803; https://doi.org/10.3390/e20100803 (registering DOI)
Received: 30 July 2018 / Revised: 15 October 2018 / Accepted: 15 October 2018 / Published: 18 October 2018
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Abstract
When a developing country reaches a relatively average income level, it often stops growing further and its income does not improve. This is known as the middle-income trap. How to overcome this trap is a longstanding problem for developing countries, and has been
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When a developing country reaches a relatively average income level, it often stops growing further and its income does not improve. This is known as the middle-income trap. How to overcome this trap is a longstanding problem for developing countries, and has been studied in various research fields. In this work, we use the Fitness-Complexity method (FCM) to analyze the common characteristics of the countries that successfully get through the middle-income trap, and show the origin of the middle-income trap based on the international trade network. In the analysis, a novel method is proposed to characterize the interdependency between products. The results show that some middle-complexity products depend much on each other, which indicates that developing countries should focus on them simultaneously, implying high difficulty to escape the middle-income trap. To tackle the middle-income trap, developing countries should learn experiences from developed countries that share similar development history. we then design an effective method to evaluate the similarity between countries and recommend developed countries to a certain developing country. The effectiveness of our method is validated in the international trade network. Full article
(This article belongs to the Special Issue Economic Fitness and Complexity)
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Open AccessArticle Macroscopic Entropy of Non-Equilibrium Systems and Postulates of Extended Thermodynamics: Application to Transport Phenomena and Chemical Reactions in Nanoparticles
Entropy 2018, 20(10), 802; https://doi.org/10.3390/e20100802 (registering DOI)
Received: 18 September 2018 / Revised: 11 October 2018 / Accepted: 16 October 2018 / Published: 18 October 2018
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Abstract
In this work, we consider extended irreversible thermodynamics in assuming that the entropy density is a function of both common thermodynamic variables and their higher-order time derivatives. An expression for entropy production, and the linear phenomenological equations describing diffusion and chemical reactions, are
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In this work, we consider extended irreversible thermodynamics in assuming that the entropy density is a function of both common thermodynamic variables and their higher-order time derivatives. An expression for entropy production, and the linear phenomenological equations describing diffusion and chemical reactions, are found in the context of this approach. Solutions of the sets of linear equations with respect to fluxes and their higher-order time derivatives allows the coefficients of diffusion and reaction rate constants to be established as functions of size of the nanosystems in which these reactions occur. The Maxwell-Cattaneo and Jeffreys constitutive equations, as well as the higher-order constitutive equations, which describe the processes in reaction-diffusion systems, are obtained. Full article
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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Open AccessArticle Encryption Algorithm of Multiple-Image Using Mixed Image Elements and Two Dimensional Chaotic Economic Map
Entropy 2018, 20(10), 801; https://doi.org/10.3390/e20100801 (registering DOI)
Received: 15 September 2018 / Revised: 15 October 2018 / Accepted: 16 October 2018 / Published: 18 October 2018
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Abstract
To enhance the encryption proficiency and encourage the protected transmission of multiple images, the current work introduces an encryption algorithm for multiple images using the combination of mixed image elements (MIES) and a two-dimensional economic map. Firstly, the original images are grouped into
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To enhance the encryption proficiency and encourage the protected transmission of multiple images, the current work introduces an encryption algorithm for multiple images using the combination of mixed image elements (MIES) and a two-dimensional economic map. Firstly, the original images are grouped into one big image that is split into many pure image elements (PIES); secondly, the logistic map is used to shuffle the PIES; thirdly, it is confused with the sequence produced by the two-dimensional economic map to get MIES; finally, the MIES are gathered into a big encrypted image that is split into many images of the same size as the original images. The proposed algorithm includes a huge number key size space, and this makes the algorithm secure against hackers. Even more, the encryption results obtained by the proposed algorithm outperform existing algorithms in the literature. A comparison between the proposed algorithm and similar algorithms is made. The analysis of the experimental results and the proposed algorithm shows that the proposed algorithm is efficient and secure. Full article
(This article belongs to the Special Issue Entropy in Image Analysis)
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Open AccessArticle Heat Transfer and Flow Structures of Laminar Confined Slot Impingement Jet with Power-Law Non-Newtonian Fluid
Entropy 2018, 20(10), 800; https://doi.org/10.3390/e20100800 (registering DOI)
Received: 23 August 2018 / Revised: 22 September 2018 / Accepted: 28 September 2018 / Published: 18 October 2018
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Abstract
Heat transfer performances and flow structures of laminar impinging slot jets with power-law non-Newtonian fluids and corresponding typical industrial fluids (Carboxyl Methyl Cellulose (CMC) solutions and Xanthangum (XG) solutions) have been studied in this work. Investigations are performed for Reynolds number Re less
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Heat transfer performances and flow structures of laminar impinging slot jets with power-law non-Newtonian fluids and corresponding typical industrial fluids (Carboxyl Methyl Cellulose (CMC) solutions and Xanthangum (XG) solutions) have been studied in this work. Investigations are performed for Reynolds number Re less than 200, power-law index n ranging from 0.5 to 1.5 and consistency index K varying from 0.001 to 0.5 to explore heat transfer and flow structure of shear-thinning fluid and shear-thickening fluid. Results indicate that with the increase of n, K for a given Re, wall Nusselt number increases mainly attributing to the increase of inlet velocity U. For a given inlet velocity, wall Nusselt number decreases with the increase of n and K, which mainly attributes to the increase of apparent viscosity and the reduction of momentum diffusion. For the same Re, U and Pr, wall Nusselt number decreases with the increase of n. Among the study of industrial power-law shear-thinning fluid, CMC solution with 100 ppm shows the best heat transfer performance at a given velocity. Moreover, new correlation of Nusselt number about industrial fluid is proposed. In general, for the heat transfer of laminar confined impinging jet, it is best to use the working fluid with low viscosity. Full article
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Open AccessArticle Long-Term Independence of Solar Wind Polytropic Index on Plasma Flow Speed
Entropy 2018, 20(10), 799; https://doi.org/10.3390/e20100799
Received: 1 October 2018 / Revised: 12 October 2018 / Accepted: 16 October 2018 / Published: 17 October 2018
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Abstract
The paper derives the polytropic indices over the last two solar cycles (years 1995–2017) for the solar wind proton plasma near Earth (~1 AU). We use ~92-s datasets of proton plasma moments (speed, density, and temperature), measured from the Solar Wind Experiment instrument
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The paper derives the polytropic indices over the last two solar cycles (years 1995–2017) for the solar wind proton plasma near Earth (~1 AU). We use ~92-s datasets of proton plasma moments (speed, density, and temperature), measured from the Solar Wind Experiment instrument onboard Wind spacecraft, to estimate the moving averages of the polytropic index, as well as their weighted means and standard errors as a function of the solar wind speed and the year of measurements. The derived long-term behavior of the polytropic index agrees with the results of other previous methods. In particular, we find that the polytropic index remains quasi-constant with respect to the plasma flow speed, in agreement with earlier analyses of solar wind plasma. It is shown that most of the fluctuations of the polytropic index appear in the fast solar wind. The polytropic index remains quasi-constant, despite the frequent entropic variations. Therefore, on an annual basis, the polytropic index of the solar wind proton plasma near ~1 AU can be considered independent of the plasma flow speed. The estimated all-year weighted mean and its standard error is γ = 1.86 ± 0.09. Full article
(This article belongs to the Section Statistical Mechanics)
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Open AccessArticle Algorithmic Entropy and Landauer’s Principle Link Microscopic System Behaviour to the Thermodynamic Entropy
Entropy 2018, 20(10), 798; https://doi.org/10.3390/e20100798
Received: 12 September 2018 / Revised: 14 October 2018 / Accepted: 14 October 2018 / Published: 17 October 2018
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Abstract
Algorithmic information theory in conjunction with Landauer’s principle can quantify the cost of maintaining a reversible real-world computational system distant from equilibrium. As computational bits are conserved in an isolated reversible system, bit flows can be used to track the way a highly
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Algorithmic information theory in conjunction with Landauer’s principle can quantify the cost of maintaining a reversible real-world computational system distant from equilibrium. As computational bits are conserved in an isolated reversible system, bit flows can be used to track the way a highly improbable configuration trends toward a highly probable equilibrium configuration. In an isolated reversible system, all microstates within a thermodynamic macrostate have the same algorithmic entropy. However, from a thermodynamic perspective, when these bits primarily specify stored energy states, corresponding to a fluctuation from the most probable set of states, they represent “potential entropy”. However, these bits become “realised entropy” when, under the second law of thermodynamics, they become bits specifying the momentum degrees of freedom. The distance of a fluctuation from equilibrium is identified as the number of computational bits that move from stored energy states to momentum states to define a highly probable or typical equilibrium state. When reversibility applies, from Landauer’s principle, it costs k B l n 2 T Joules to move a bit within the system from stored energy states to the momentum states. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Some Consequences of the Thermodynamic Cost of System Identification
Entropy 2018, 20(10), 797; https://doi.org/10.3390/e20100797
Received: 17 August 2018 / Revised: 23 September 2018 / Accepted: 15 October 2018 / Published: 17 October 2018
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Abstract
The concept of a “system” is foundational to physics, but the question of how observers identify systems is seldom addressed. Classical thermodynamics restricts observers to finite, finite-resolution observations with which to identify the systems on which “pointer state” measurements are to be made.
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The concept of a “system” is foundational to physics, but the question of how observers identify systems is seldom addressed. Classical thermodynamics restricts observers to finite, finite-resolution observations with which to identify the systems on which “pointer state” measurements are to be made. It is shown that system identification is at best approximate, even in a finite world, and that violations of the Leggett–Garg and Bell/CHSH (Clauser-Horne-Shimony-Holt) inequalities emerge naturally as requirements for successful system identification. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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Open AccessCorrection Correction: Naudts, J. Quantum Statistical Manifolds. Entropy 2018, 20, 472
Entropy 2018, 20(10), 796; https://doi.org/10.3390/e20100796
Received: 6 September 2018 / Accepted: 12 October 2018 / Published: 17 October 2018
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Abstract
Section 4 of “Naudts J. Quantum Statistical Manifolds. Entropy 2018, 20, 472” contains errors. They have limited consequences for the remainder of the paper. A new version of this Section is found here. Some smaller shortcomings of the paper are taken care
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Section 4 of “Naudts J. Quantum Statistical Manifolds. Entropy 2018, 20, 472” contains errors. They have limited consequences for the remainder of the paper. A new version of this Section is found here. Some smaller shortcomings of the paper are taken care of as well. In particular, the proof of Theorem 3 was not complete, and is therefore amended. Also, a few missing references are added. Full article
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
Open AccessArticle The Interaction Analysis between the Sympathetic and Parasympathetic Systems in CHF by Using Transfer Entropy Method
Entropy 2018, 20(10), 795; https://doi.org/10.3390/e20100795
Received: 9 September 2018 / Revised: 5 October 2018 / Accepted: 9 October 2018 / Published: 16 October 2018
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Abstract
Congestive heart failure (CHF) is a cardiovascular disease associated with autonomic dysfunction, where sympathovagal imbalance was reported in many studies using heart rate variability (HRV). To learn more about the dynamic interaction in the autonomic nervous system (ANS), we explored the directed interaction
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Congestive heart failure (CHF) is a cardiovascular disease associated with autonomic dysfunction, where sympathovagal imbalance was reported in many studies using heart rate variability (HRV). To learn more about the dynamic interaction in the autonomic nervous system (ANS), we explored the directed interaction between the sympathetic nervous system (SNS) and the parasympathetic nervous system (PNS) with the help of transfer entropy (TE). This article included 24-h RR interval signals of 54 healthy subjects (31 males and 23 females, 61.38 ± 11.63 years old) and 44 CHF subjects (8 males and 2 females, 19 subjects’ gender were unknown, 55.51 ± 11.44 years old, 4 in class I, 8 in class II and 32 in class III~IV, according to the New York Heart Association Function Classification), obtained from the PhysioNet database and then segmented into 5-min non-overlapping epochs using cubic spline interpolation. For each segment in the normal group and CHF group, frequency-domain features included low-frequency (LF) power, high-frequency (HF) power and LF/HF ratio were extracted as classical estimators of autonomic activity. In the nonlinear domain, TE between LF and HF were calculated to quantify the information exchanging between SNS and PNS. Compared with the normal group, an extreme decrease in LF/HF ratio (p = 0.000) and extreme increases in both TE(LF→HF) (p = 0.000) and TE(HF→LF) (p = 0.000) in the CHF group were observed. Moreover, both in normal and CHF groups, TE(LF→HF) was a lot greater than TE(HF→LF) (p = 0.000), revealing that TE was able to distinguish the difference in the amount of directed information transfer among ANS. Extracted features were further applied in discriminating CHF using IBM SPSS Statistics discriminant analysis. The combination of the LF/HF ratio, TE(LF→HF) and TE(HF→LF) reached the highest screening accuracy (83.7%). Our results suggested that TE could serve as a complement to traditional index LF/HF in CHF screening. Full article
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Open AccessEditorial Evaluation of Systems’ Irregularity and Complexity: Sample Entropy, Its Derivatives, and Their Applications across Scales and Disciplines
Entropy 2018, 20(10), 794; https://doi.org/10.3390/e20100794
Received: 8 October 2018 / Accepted: 9 October 2018 / Published: 16 October 2018
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Open AccessArticle An Information-Theoretic Approach to Self-Organisation: Emergence of Complex Interdependencies in Coupled Dynamical Systems
Entropy 2018, 20(10), 793; https://doi.org/10.3390/e20100793
Received: 16 August 2018 / Revised: 3 October 2018 / Accepted: 3 October 2018 / Published: 16 October 2018
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Abstract
Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or
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Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or attractors, we see self-organisation as a consequence of the interdependencies that those attractors induce. Building on this intuition, in this work we develop a theoretical framework for understanding and quantifying self-organisation based on coupled dynamical systems and multivariate information theory. We propose a metric of global structural strength that identifies when self-organisation appears, and a multi-layered decomposition that explains the emergent structure in terms of redundant and synergistic interdependencies. We illustrate our framework on elementary cellular automata, showing how it can detect and characterise the emergence of complex structures. Full article
(This article belongs to the Section Complexity)
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Open AccessArticle Identifying Systemically Important Companies by Using the Credit Network of an Entire Nation
Entropy 2018, 20(10), 792; https://doi.org/10.3390/e20100792
Received: 27 July 2018 / Revised: 8 October 2018 / Accepted: 8 October 2018 / Published: 16 October 2018
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Abstract
The notions of systemic importance and systemic risk of financial institutions are closely related to the topology of financial liability networks. In this work, we reconstruct and analyze the financial liability network of an entire economy using data of 50,159 firms and banks.
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The notions of systemic importance and systemic risk of financial institutions are closely related to the topology of financial liability networks. In this work, we reconstruct and analyze the financial liability network of an entire economy using data of 50,159 firms and banks. Our analysis contains 80.2% of the total liabilities of firms towards banks and all interbank liabilities in the Austrian banking system. The combination of firm-bank networks and interbank networks allows us to extend the concept of systemic risk to the real economy. In particular, the systemic importance of individual companies can be assessed, and for the first time, the financial ties between the financial and the real economy become explicitly visible. We find that firms contribute to systemic risk in similar ways as banks do. We identify a set of mid-sized companies that carry substantial systemic risk. Their default would affect up to 40% of the Austrian financial market. We find that all firms together create more systemic risk than the entire financial sector. In 2008, the total systemic risk of the Austrian interbank network amounted to only 29% of the total systemic risk of the entire financial network consisting of firms and banks. The work demonstrates that the notions of systemically important financial institutions (SIFIs) can be directly extended to firms. Full article
(This article belongs to the Special Issue Economic Fitness and Complexity)
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Open AccessEditorial How to Teach Heat Transfer More Systematically by Involving Entropy
Entropy 2018, 20(10), 791; https://doi.org/10.3390/e20100791
Received: 11 September 2018 / Accepted: 8 October 2018 / Published: 15 October 2018
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Abstract
In order to teach heat transfer systematically and with a clear physical background, it is recommended that entropy should not be ignored as a fundamental quantity. Heat transfer processes are characterized by introducing the so-called “entropic potential” of the transferred energy, and an
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In order to teach heat transfer systematically and with a clear physical background, it is recommended that entropy should not be ignored as a fundamental quantity. Heat transfer processes are characterized by introducing the so-called “entropic potential” of the transferred energy, and an assessment number is based on this new quantity. Full article
(This article belongs to the Special Issue Entropy Generation and Heat Transfer)
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Open AccessArticle Maximum Entropy Probability Density Principle in Probabilistic Investigations of Dynamic Systems
Entropy 2018, 20(10), 790; https://doi.org/10.3390/e20100790
Received: 21 September 2018 / Revised: 11 October 2018 / Accepted: 11 October 2018 / Published: 15 October 2018
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Abstract
In this study, we consider a method for investigating the stochastic response of a nonlinear dynamical system affected by a random seismic process. We present the solution of the probability density of a single/multiple-degree of freedom (SDOF/MDOF) system with several statically stable equilibrium
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In this study, we consider a method for investigating the stochastic response of a nonlinear dynamical system affected by a random seismic process. We present the solution of the probability density of a single/multiple-degree of freedom (SDOF/MDOF) system with several statically stable equilibrium states and with possible jumps of the snap-through type. The system is a Hamiltonian system with weak damping excited by a system of non-stationary Gaussian white noise. The solution based on the Gibbs principle of the maximum entropy of probability could potentially be implemented in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker–Planck equation (FPE) for the system considered or from the system of ordinary differential equations for the stochastic moments of the response derived from the relevant FPE. In terms of the application type, this strategy is most suitable for SDOF/MDOF systems containing polynomial type nonlinearities. Thus, the solution links up with the customary formulation of the finite elements discretization for strongly nonlinear continuous systems. Full article
Open AccessArticle Alternation of Defects and Phase Turbulence Induces Extreme Events in an Extended Microcavity Laser
Entropy 2018, 20(10), 789; https://doi.org/10.3390/e20100789
Received: 10 August 2018 / Revised: 8 October 2018 / Accepted: 9 October 2018 / Published: 15 October 2018
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Abstract
Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable
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Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable absorber media. This system is known to give rise experimentally and theoretically to extreme events characterized by rare and high amplitude optical pulses following the onset of spatiotemporal chaos. Based on a theoretical model, we reveal a dynamical behavior characterized by the chaotic alternation of phase and amplitude turbulence. The highest amplitude pulses, i.e., the extreme events, are observed in the phase turbulence zones. This chaotic alternation behavior between different turbulent regimes is at contrast to what is usually observed in a generic amplitude equation model such as the Ginzburg–Landau model. Hence, these regimes provide some insight into the poorly known properties of the complex spatiotemporal dynamics exhibited by secondary instabilities of an Andronov–Hopf bifurcation. Full article
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Open AccessArticle A Fast Feature Selection Algorithm by Accelerating Computation of Fuzzy Rough Set-Based Information Entropy
Entropy 2018, 20(10), 788; https://doi.org/10.3390/e20100788
Received: 30 August 2018 / Revised: 21 September 2018 / Accepted: 9 October 2018 / Published: 13 October 2018
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Abstract
The information entropy developed by Shannon is an effective measure of uncertainty in data, and the rough set theory is a useful tool of computer applications to deal with vagueness and uncertainty data circumstances. At present, the information entropy has been extensively applied
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The information entropy developed by Shannon is an effective measure of uncertainty in data, and the rough set theory is a useful tool of computer applications to deal with vagueness and uncertainty data circumstances. At present, the information entropy has been extensively applied in the rough set theory, and different information entropy models have also been proposed in rough sets. In this paper, based on the existing feature selection method by using a fuzzy rough set-based information entropy, a corresponding fast algorithm is provided to achieve efficient implementation, in which the fuzzy rough set-based information entropy taking as the evaluation measure for selecting features is computed by an improved mechanism with lower complexity. The essence of the acceleration algorithm is to use iterative reduced instances to compute the lambda-conditional entropy. Numerical experiments are further conducted to show the performance of the proposed fast algorithm, and the results demonstrate that the algorithm acquires the same feature subset to its original counterpart, but with significantly less time. Full article
(This article belongs to the Section Information Theory)
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Open AccessArticle Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane
Entropy 2018, 20(10), 787; https://doi.org/10.3390/e20100787
Received: 1 September 2018 / Revised: 8 October 2018 / Accepted: 8 October 2018 / Published: 13 October 2018
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Abstract
Any quantization maps linearly function on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with the symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary
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Any quantization maps linearly function on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with the symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all resources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. We first review this quantization scheme before revisiting the cases where symmetry covariance is described by the Weyl-Heisenberg group and the affine group respectively, and we emphasize the fundamental role played by Fourier transform in both cases. As an original outcome of our generalisations of the Wigner-Weyl transform, we show that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations. Full article
Open AccessArticle A QUBO Formulation of the Stereo Matching Problem for D-Wave Quantum Annealers
Entropy 2018, 20(10), 786; https://doi.org/10.3390/e20100786
Received: 6 August 2018 / Revised: 8 October 2018 / Accepted: 8 October 2018 / Published: 12 October 2018
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Abstract
In this paper, we propose a methodology to solve the stereo matching problem through quantum annealing optimization. Our proposal takes advantage of the existing Min-Cut/Max-Flow network formulation of computer vision problems. Based on this network formulation, we construct a quadratic pseudo-Boolean function and
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In this paper, we propose a methodology to solve the stereo matching problem through quantum annealing optimization. Our proposal takes advantage of the existing Min-Cut/Max-Flow network formulation of computer vision problems. Based on this network formulation, we construct a quadratic pseudo-Boolean function and then optimize it through the use of the D-Wave quantum annealing technology. Experimental validation using two kinds of stereo pair of images, random dot stereograms and gray-scale, shows that our methodology is effective. Full article
(This article belongs to the Section Quantum Information)
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Open AccessArticle Colombian Export Capabilities: Building the Firms-Products Network
Entropy 2018, 20(10), 785; https://doi.org/10.3390/e20100785
Received: 31 July 2018 / Revised: 1 October 2018 / Accepted: 2 October 2018 / Published: 12 October 2018
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Abstract
In this paper, we analyse the bipartite Colombian firms-products network, throughout a period of five years, from 2010 to 2014. Our analysis depicts a strongly modular system, with several groups of firms specializing in the export of specific categories of products. These clusters
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In this paper, we analyse the bipartite Colombian firms-products network, throughout a period of five years, from 2010 to 2014. Our analysis depicts a strongly modular system, with several groups of firms specializing in the export of specific categories of products. These clusters have been detected by running the bipartite variant of the traditional modularity maximization, revealing a bi-modular structure. Interestingly, this finding is refined by applying a recently proposed algorithm for projecting bipartite networks on the layer of interest and, then, running the Louvain algorithm on the resulting monopartite representations. Important structural differences emerge upon comparing the Colombian firms-products network with the World Trade Web, in particular, the bipartite representation of the latter is not characterized by a similar block-structure, as the modularity maximization fails in revealing (bipartite) nodes clusters. This points out that economic systems behave differently at different scales: while countries tend to diversify their production—potentially exporting a large number of different products—firms specialize in exporting (substantially very limited) baskets of basically homogeneous products. Full article
(This article belongs to the Special Issue Economic Fitness and Complexity)
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Open AccessArticle Entropy Inequalities for Lattices
Entropy 2018, 20(10), 784; https://doi.org/10.3390/e20100784
Received: 1 September 2018 / Revised: 26 September 2018 / Accepted: 10 October 2018 / Published: 12 October 2018
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Abstract
We study entropy inequalities for variables that are related by functional dependencies. Although the powerset on four variables is the smallest Boolean lattice with non-Shannon inequalities, there exist lattices with many more variables where the Shannon inequalities are sufficient. We search for conditions
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We study entropy inequalities for variables that are related by functional dependencies. Although the powerset on four variables is the smallest Boolean lattice with non-Shannon inequalities, there exist lattices with many more variables where the Shannon inequalities are sufficient. We search for conditions that exclude the existence of non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group. In order to formulate and prove the results, one has to bridge lattice theory, group theory, the theory of functional dependences and the theory of conditional independence. It is demonstrated that the Shannon inequalities are sufficient for planar modular lattices. The proof applies a gluing technique that uses that if the Shannon inequalities are sufficient for the pieces, then they are also sufficient for the whole lattice. It is conjectured that the Shannon inequalities are sufficient if and only if the lattice does not contain a special lattice as a sub-semilattice. Full article
(This article belongs to the Special Issue Entropy and Information Inequalities)
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Open AccessArticle A New and Stable Estimation Method of Country Economic Fitness and Product Complexity
Entropy 2018, 20(10), 783; https://doi.org/10.3390/e20100783
Received: 26 July 2018 / Revised: 3 October 2018 / Accepted: 4 October 2018 / Published: 12 October 2018
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Abstract
We present a new metric estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a
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We present a new metric estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a suitable rescaling of the relevant quantities, the non homogeneous terms are eventually set to zero so that this new metric is parameter free. This new map almost reproduces the results of the original homogeneous metrics already defined in literature and allows for an approximate analytic solution in case of actual binarized matrices based on the Revealed Comparative Advantage (RCA) indicator. This solution is connected with a new quantity describing the neighborhood of nodes in bipartite graphs, representing in this work the relations between countries and exported products. Moreover, we define the new indicator of country net-efficiency quantifying how a country efficiently invests in capabilities able to generate innovative complex high quality products. Eventually, we demonstrate analytically the local convergence of the algorithm involved. Full article
(This article belongs to the Special Issue Economic Fitness and Complexity)
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Open AccessArticle From Nash Equilibria to Chain Recurrent Sets: An Algorithmic Solution Concept for Game Theory
Entropy 2018, 20(10), 782; https://doi.org/10.3390/e20100782
Received: 14 August 2018 / Revised: 19 September 2018 / Accepted: 25 September 2018 / Published: 12 October 2018
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Abstract
In 1950, Nash proposed a natural equilibrium solution concept for games hence called Nash equilibrium, and proved that all finite games have at least one. The proof is through a simple yet ingenious application of Brouwer’s (or, in another version Kakutani’s) fixed point
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In 1950, Nash proposed a natural equilibrium solution concept for games hence called Nash equilibrium, and proved that all finite games have at least one. The proof is through a simple yet ingenious application of Brouwer’s (or, in another version Kakutani’s) fixed point theorem, the most sophisticated result in his era’s topology—in fact, recent algorithmic work has established that Nash equilibria are computationally equivalent to fixed points. In this paper, we propose a new class of universal non-equilibrium solution concepts arising from an important theorem in the topology of dynamical systems that was unavailable to Nash. This approach starts with both a game and a learning dynamics, defined over mixed strategies. The Nash equilibria are fixpoints of the dynamics, but the system behavior is captured by an object far more general than the Nash equilibrium that is known in dynamical systems theory as chain recurrent set. Informally, once we focus on this solution concept—this notion of “the outcome of the game”—every game behaves like a potential game with the dynamics converging to these states. In other words, unlike Nash equilibria, this solution concept is algorithmic in the sense that it has a constructive proof of existence. We characterize this solution for simple benchmark games under replicator dynamics, arguably the best known evolutionary dynamics in game theory. For (weighted) potential games, the new concept coincides with the fixpoints/equilibria of the dynamics. However, in (variants of) zero-sum games with fully mixed (i.e., interior) Nash equilibria, it covers the whole state space, as the dynamics satisfy specific information theoretic constants of motion. We discuss numerous novel computational, as well as structural, combinatorial questions raised by this chain recurrence conception of games. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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Open AccessArticle Quantum-Inspired Evolutionary Approach for the Quadratic Assignment Problem
Entropy 2018, 20(10), 781; https://doi.org/10.3390/e20100781
Received: 12 August 2018 / Revised: 4 October 2018 / Accepted: 5 October 2018 / Published: 12 October 2018
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Abstract
The paper focuses on the opportunity of the application of the quantum-inspired evolutionary algorithm for determining minimal costs of the assignment in the quadratic assignment problem. The idea behind the paper is to present how the algorithm has to be adapted to this
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The paper focuses on the opportunity of the application of the quantum-inspired evolutionary algorithm for determining minimal costs of the assignment in the quadratic assignment problem. The idea behind the paper is to present how the algorithm has to be adapted to this problem, including crossover and mutation operators and introducing quantum principles in particular procedures. The results have shown that the performance of our approach in terms of converging to the best solutions is satisfactory. Moreover, we have presented the results of the selected parameters of the approach on the quality of the obtained solutions. Full article
(This article belongs to the Special Issue Quantum Walks and Related Issues)
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Open AccessArticle Bouncing Oil Droplets, de Broglie’s Quantum Thermostat, and Convergence to Equilibrium
Entropy 2018, 20(10), 780; https://doi.org/10.3390/e20100780
Received: 24 August 2018 / Revised: 1 October 2018 / Accepted: 3 October 2018 / Published: 11 October 2018
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Abstract
Recently, the properties of bouncing oil droplets, also known as “walkers,” have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behavior. They indeed constitute a macroscopic realization of wave-particle duality, in the sense that
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Recently, the properties of bouncing oil droplets, also known as “walkers,” have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behavior. They indeed constitute a macroscopic realization of wave-particle duality, in the sense that their trajectories are guided by a self-generated surrounding wave. The aim of this paper is to try to describe walker phenomenology in terms of de Broglie–Bohm dynamics and of a stochastic version thereof. In particular, we first study how a stochastic modification of the de Broglie pilot-wave theory, à la Nelson, affects the process of relaxation to quantum equilibrium, and we prove an H-theorem for the relaxation to quantum equilibrium under Nelson-type dynamics. We then compare the onset of equilibrium in the stochastic and the de Broglie–Bohm approaches and we propose some simple experiments by which one can test the applicability of our theory to the context of bouncing oil droplets. Finally, we compare our theory to actual observations of walker behavior in a 2D harmonic potential well. Full article
(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)
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Open AccessArticle From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time
Entropy 2018, 20(10), 779; https://doi.org/10.3390/e20100779
Received: 15 August 2018 / Revised: 8 October 2018 / Accepted: 10 October 2018 / Published: 11 October 2018
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Abstract
For historic reasons, industrial knowledge of reproducibility and restrictions imposed by regulations, open-loop feeding control approaches dominate in industrial fed-batch cultivation processes. In this study, a generic gray box biomass modeling procedure uses relative entropy as a key to approach the posterior similarly
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For historic reasons, industrial knowledge of reproducibility and restrictions imposed by regulations, open-loop feeding control approaches dominate in industrial fed-batch cultivation processes. In this study, a generic gray box biomass modeling procedure uses relative entropy as a key to approach the posterior similarly to how prior distribution approaches the posterior distribution by the multivariate path of Lagrange multipliers, for which a description of a nuisance time is introduced. The ultimate purpose of this study was to develop a numerical semi-global convex optimization procedure that is dedicated to the calculation of feeding rate time profiles during the fed-batch cultivation processes. The proposed numerical semi-global convex optimization of relative entropy is neither restricted to the gray box model nor to the bioengineering application. From the bioengineering application perspective, the proposed bioprocess design technique has benefits for both the regular feed-forward control and the advanced adaptive control systems, in which the model for biomass growth prediction is compulsory. After identification of the gray box model parameters, the options and alternatives in controllable industrial biotechnological processes are described. The main aim of this work is to achieve high reproducibility, controllability, and desired process performance. Glucose concentration measurements, which were used for the development of the model, become unnecessary for the development of the desired microbial cultivation process. Full article
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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Open AccessArticle Unconventional Deformation Behaviours of Nanoscaled High-Entropy Alloys
Entropy 2018, 20(10), 778; https://doi.org/10.3390/e20100778
Received: 7 September 2018 / Revised: 20 September 2018 / Accepted: 28 September 2018 / Published: 11 October 2018
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Abstract
The bulk high-entropy alloys (HEAs) exhibit similar deformation behaviours as traditional metals. These bulk behaviours are likely an averaging of the behaviours exhibited at the nanoscale. Herein, in situ atomic-scale observation of deformation behaviours in nanoscaled CoCrCuFeNi face-centred cubic (FCC) HEA was performed.
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The bulk high-entropy alloys (HEAs) exhibit similar deformation behaviours as traditional metals. These bulk behaviours are likely an averaging of the behaviours exhibited at the nanoscale. Herein, in situ atomic-scale observation of deformation behaviours in nanoscaled CoCrCuFeNi face-centred cubic (FCC) HEA was performed. The deformation behaviours of this nanoscaled FCC HEA (i.e., nanodisturbances and phase transformations) were distinct from those of nanoscaled traditional FCC metals and corresponding bulk HEA. First-principles calculations revealed an obvious fluctuation of the stacking fault energy and stability difference at the atomic scale in the HEA. The stability difference was highlighted only in the nanoscaled HEA and induced unconventional deformation behaviours. Our work suggests that the nanoscaled HEA may provide more chances to discover the long-expected essential distinction between the HEAs and traditional metals. Full article
(This article belongs to the Special Issue New Advances in High-Entropy Alloys)
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Open AccessArticle Link Prediction in Bipartite Nested Networks
Entropy 2018, 20(10), 777; https://doi.org/10.3390/e20100777
Received: 31 July 2018 / Revised: 8 October 2018 / Accepted: 8 October 2018 / Published: 10 October 2018
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Abstract
Real networks typically studied in various research fields—ecology and economic complexity, for example—often exhibit a nested topology, which means that the neighborhoods of high-degree nodes tend to include the neighborhoods of low-degree nodes. Focusing on nested networks, we study the problem of link
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Real networks typically studied in various research fields—ecology and economic complexity, for example—often exhibit a nested topology, which means that the neighborhoods of high-degree nodes tend to include the neighborhoods of low-degree nodes. Focusing on nested networks, we study the problem of link prediction in complex networks, which aims at identifying likely candidates for missing links. We find that a new method that takes network nestedness into account outperforms well-established link-prediction methods not only when the input networks are sufficiently nested, but also for networks where the nested structure is imperfect. Our study paves the way to search for optimal methods for link prediction in nested networks, which might be beneficial for World Trade and ecological network analysis. Full article
(This article belongs to the Special Issue Economic Fitness and Complexity)
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Open AccessArticle Green Technology Fitness
Entropy 2018, 20(10), 776; https://doi.org/10.3390/e20100776
Received: 31 July 2018 / Revised: 27 September 2018 / Accepted: 8 October 2018 / Published: 10 October 2018
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Abstract
The present study provides an analysis of empirical regularities in the development of green technology. We use patent data to examine inventions that can be traced to the environment-related catalogue (ENV-Tech) covering technologies in environmental management, water-related adaptation and climate change
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The present study provides an analysis of empirical regularities in the development of green technology. We use patent data to examine inventions that can be traced to the environment-related catalogue (ENV-Tech) covering technologies in environmental management, water-related adaptation and climate change mitigation. Furthermore, we employ the Economic Fitness-Complexity (EFC) approach to assess their development and geographical distribution across countries between 1970 and 2010. This allows us to identify three typologies of countries: leaders, laggards and catch-up. While, as expected, there is a direct relationship between GDP per capita and invention capacity, we also document the remarkable growth of East Asia countries that started from the periphery and rapidly established themselves as key actors. This geographical pattern coincides with higher integration across domains so that, while the relative development of individual areas may have peaked, there is now demand for greater interoperability across green technologies. Full article
(This article belongs to the Special Issue Economic Fitness and Complexity)
Open AccessArticle Statistical Mechanics of On-Line Learning Under Concept Drift
Entropy 2018, 20(10), 775; https://doi.org/10.3390/e20100775
Received: 4 September 2018 / Revised: 3 October 2018 / Accepted: 8 October 2018 / Published: 10 October 2018
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Abstract
We introduce a modeling framework for the investigation of on-line machine learning processes in non-stationary environments. We exemplify the approach in terms of two specific model situations: In the first, we consider the learning of a classification scheme from clustered data by means
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We introduce a modeling framework for the investigation of on-line machine learning processes in non-stationary environments. We exemplify the approach in terms of two specific model situations: In the first, we consider the learning of a classification scheme from clustered data by means of prototype-based Learning Vector Quantization (LVQ). In the second, we study the training of layered neural networks with sigmoidal activations for the purpose of regression. In both cases, the target, i.e., the classification or regression scheme, is considered to change continuously while the system is trained from a stream of labeled data. We extend and apply methods borrowed from statistical physics which have been used frequently for the exact description of training dynamics in stationary environments. Extensions of the approach allow for the computation of typical learning curves in the presence of concept drift in a variety of model situations. First results are presented and discussed for stochastic drift processes in classification and regression problems. They indicate that LVQ is capable of tracking a classification scheme under drift to a non-trivial extent. Furthermore, we show that concept drift can cause the persistence of sub-optimal plateau states in gradient based training of layered neural networks for regression. Full article
(This article belongs to the Special Issue Statistical Mechanics of Neural Networks)
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Open AccessArticle Information Transfer Among the Components in Multi-Dimensional Complex Dynamical Systems
Entropy 2018, 20(10), 774; https://doi.org/10.3390/e20100774
Received: 13 September 2018 / Revised: 2 October 2018 / Accepted: 7 October 2018 / Published: 9 October 2018
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Abstract
In this paper, a rigorous formalism of information transfer within a multi-dimensional deterministic dynamic system is established for both continuous flows and discrete mappings. The underlying mechanism is derived from entropy change and transfer during the evolutions of multiple components. While this work
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In this paper, a rigorous formalism of information transfer within a multi-dimensional deterministic dynamic system is established for both continuous flows and discrete mappings. The underlying mechanism is derived from entropy change and transfer during the evolutions of multiple components. While this work is mainly focused on three-dimensional systems, the analysis of information transfer among state variables can be generalized to high-dimensional systems. Explicit formulas are given and verified in the classical Lorenz and Chua’s systems. The uncertainty of information transfer is quantified for all variables, with which a dynamic sensitivity analysis could be performed statistically as an additional benefit. The generalized formalisms can be applied to study dynamical behaviors as well as asymptotic dynamics of the system. The simulation results can help to reveal some underlying information for understanding the system better, which can be used for prediction and control in many diverse fields. Full article
(This article belongs to the Special Issue Entropy in Dynamic Systems)
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