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Entropy, Volume 17, Issue 10 (October 2015) – 39 articles , Pages 6534-7297

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Open AccessArticle
Quantifying Emergent Behavior of Autonomous Robots
Entropy 2015, 17(10), 7266-7297; https://doi.org/10.3390/e17107266 - 23 Oct 2015
Cited by 3 | Viewed by 3231
Abstract
Quantifying behaviors of robots which were generated autonomously from task-independent objective functions is an important prerequisite for objective comparisons of algorithms and movements of animals. The temporal sequence of such a behavior can be considered as a time series and hence complexity measures [...] Read more.
Quantifying behaviors of robots which were generated autonomously from task-independent objective functions is an important prerequisite for objective comparisons of algorithms and movements of animals. The temporal sequence of such a behavior can be considered as a time series and hence complexity measures developed for time series are natural candidates for its quantification. The predictive information and the excess entropy are such complexity measures. They measure the amount of information the past contains about the future and thus quantify the nonrandom structure in the temporal sequence. However, when using these measures for systems with continuous states one has to deal with the fact that their values will depend on the resolution with which the systems states are observed. For deterministic systems both measures will diverge with increasing resolution. We therefore propose a new decomposition of the excess entropy in resolution dependent and resolution independent parts and discuss how they depend on the dimensionality of the dynamics, correlations and the noise level. For the practical estimation we propose to use estimates based on the correlation integral instead of the direct estimation of the mutual information based on next neighbor statistics because the latter allows less control of the scale dependencies. Using our algorithm we are able to show how autonomous learning generates behavior of increasing complexity with increasing learning duration. Full article
(This article belongs to the Special Issue Information Theoretic Incentives for Cognitive Systems)
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Open AccessArticle
Exergy Losses in the Szewalski Binary Vapor Cycle
Entropy 2015, 17(10), 7242-7265; https://doi.org/10.3390/e17107242 - 23 Oct 2015
Cited by 14 | Viewed by 2612
Abstract
In this publication, we present an energy and exergy analysis of the Szewalski binary vapor cycle based on a model of a supercritical steam power plant. We used energy analysis to conduct a preliminary optimization of the cycle. Exergy loss analysis was employed [...] Read more.
In this publication, we present an energy and exergy analysis of the Szewalski binary vapor cycle based on a model of a supercritical steam power plant. We used energy analysis to conduct a preliminary optimization of the cycle. Exergy loss analysis was employed to perform a comparison of heat-transfer processes, which are essential for hierarchical cycles. The Szewalski binary vapor cycle consists of a steam cycle bottomed with an organic Rankine cycle installation. This coupling has a negative influence on the thermal efficiency of the cycle. However, the primary aim of this modification is to reduce the size of the power unit by decreasing the low-pressure steam turbine cylinder and the steam condenser. The reduction of the “cold end” of the turbine is desirable from economic and technical standpoints. We present the Szewalski binary vapor cycle in addition to a mathematical model of the chosen power plant’s thermodynamic cycle. We elaborate on the procedure of the Szewalski cycle design and its optimization in order to attain an optimal size reduction of the power unit and limit exergy loss. Full article
(This article belongs to the Special Issue Selected Papers from 13th Joint European Thermodynamics Conference)
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Open AccessArticle
Information Dynamics in the Interaction between a Prey and a Predator Fish
Entropy 2015, 17(10), 7230-7241; https://doi.org/10.3390/e17107230 - 23 Oct 2015
Cited by 21 | Viewed by 3080
Abstract
Accessing information efficiently is vital for animals to make the optimal decisions, and it is particularly important when they are facing predators. Yet until now, very few quantitative conclusions have been drawn about the information dynamics in the interaction between animals due to [...] Read more.
Accessing information efficiently is vital for animals to make the optimal decisions, and it is particularly important when they are facing predators. Yet until now, very few quantitative conclusions have been drawn about the information dynamics in the interaction between animals due to the lack of appropriate theoretic measures. Here, we employ transfer entropy (TE), a new information-theoretic and model-free measure, to explore the information dynamics in the interaction between a predator and a prey fish. We conduct experiments in which a predator and a prey fish are confined in separate parts of an arena, but can communicate with each other visually and tactilely. TE is calculated on the pair’s coarse-grained state of the trajectories. We find that the prey’s TE is generally significantly bigger than the predator’s during trials, which indicates that the dominant information is transmitted from predator to prey. We then demonstrate that the direction of information flow is irrelevant to the parameters used in the coarse-grained procedures. We further calculate the prey’s TE at different distances between it and the predator. The resulted figure shows that there is a high plateau in the mid-range of the distance and that drops quickly at both the near and the far ends. This result reflects that there is a sensitive space zone where the prey is highly vigilant of the predator’s position. Full article
(This article belongs to the Section Complexity)
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Open AccessArticle
Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics
Entropy 2015, 17(10), 7213-7229; https://doi.org/10.3390/e17107213 - 22 Oct 2015
Cited by 11 | Viewed by 2058
Abstract
We explore the information geometric structures among the thermodynamic potentials in the κ-thermostatistics, which is a generalized thermostatistics based on the κ-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the κ-escort expectations and [...] Read more.
We explore the information geometric structures among the thermodynamic potentials in the κ-thermostatistics, which is a generalized thermostatistics based on the κ-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the κ-escort expectations and the other with the standard expectations. The associated κ-generalized metrics are derived and related to the κ-generalized fluctuation-response relations among the thermodynamic potentials in the κ-thermostatistics. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)
Open AccessArticle
Mesoscopic Thermodynamics for the Dynamics of Small-Scale Systems
Entropy 2015, 17(10), 7201-7212; https://doi.org/10.3390/e17107201 - 22 Oct 2015
Cited by 1 | Viewed by 2137
Abstract
We analyze the mesoscopic dynamics of small-scale systems from the perspective of mesoscopic non-equilibrium thermodynamics. The theory obtains the Fokker–Planck equation as a diffusion equation for the probability density of the mesoscopic variables and the nonlinear relationships between activation rates and affinities proper [...] Read more.
We analyze the mesoscopic dynamics of small-scale systems from the perspective of mesoscopic non-equilibrium thermodynamics. The theory obtains the Fokker–Planck equation as a diffusion equation for the probability density of the mesoscopic variables and the nonlinear relationships between activation rates and affinities proper of activated processes. The situations that can be studied with this formalism include, among others, barrier crossing dynamics and non-linear transport in a great variety of systems. We, in particular, consider the cases of single-molecule stretching and activated processes in small systems. Full article
(This article belongs to the Special Issue Nanothermodynamics)
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Open AccessArticle
Adaptive Synchronization for a Class of Uncertain Fractional-Order Neural Networks
Entropy 2015, 17(10), 7185-7200; https://doi.org/10.3390/e17107185 - 22 Oct 2015
Cited by 38 | Viewed by 2233
Abstract
In this paper, synchronization for a class of uncertain fractional-order neural networks subject to external disturbances and disturbed system parameters is studied. Based on the fractional-order extension of the Lyapunov stability criterion, an adaptive synchronization controller is designed, and fractional-order adaptation law is [...] Read more.
In this paper, synchronization for a class of uncertain fractional-order neural networks subject to external disturbances and disturbed system parameters is studied. Based on the fractional-order extension of the Lyapunov stability criterion, an adaptive synchronization controller is designed, and fractional-order adaptation law is proposed to update the controller parameter online. The proposed controller can guarantee that the synchronization errors between two uncertain fractional-order neural networks converge to zero asymptotically. By using some proposed lemmas, the quadratic Lyapunov functions are employed in the stability analysis. Finally, numerical simulations are presented to confirm the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics)
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Open AccessArticle
Wavelet Entropy Based Analysis and Forecasting of Crude Oil Price Dynamics
Entropy 2015, 17(10), 7167-7184; https://doi.org/10.3390/e17107167 - 22 Oct 2015
Cited by 8 | Viewed by 2357
Abstract
For the modeling of complex and nonlinear crude oil price dynamics and movement, wavelet analysis can decompose the time series and produce multiple economically meaningful decomposition structures based on different assumptions of wavelet families and decomposition scale. However, the determination of the optimal [...] Read more.
For the modeling of complex and nonlinear crude oil price dynamics and movement, wavelet analysis can decompose the time series and produce multiple economically meaningful decomposition structures based on different assumptions of wavelet families and decomposition scale. However, the determination of the optimal model specification will critically affect the forecasting accuracy. In this paper, we propose a new wavelet entropy based approach to identify the optimal model specification and construct the effective wavelet entropy based forecasting models. The wavelet entropy algorithm is introduced to determine the optimal wavelet families and decomposition scale, that will produce the improved forecasting performance. Empirical studies conducted in the crude oil markets show that the proposed algorithm outperforms the benchmark model, in terms of conventional performance evaluation criteria for the model forecasting accuracy. Full article
(This article belongs to the Special Issue Wavelet Entropy: Computation and Applications)
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Open AccessArticle
Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion
Entropy 2015, 17(10), 7149-7166; https://doi.org/10.3390/e17107149 - 22 Oct 2015
Cited by 50 | Viewed by 2279
Abstract
The maximum correntropy criterion (MCC) has recently been successfully applied to adaptive filtering. Adaptive algorithms under MCC show strong robustness against large outliers. In this work, we apply the MCC criterion to develop a robust Hammerstein adaptive filter. Compared with the traditional Hammerstein [...] Read more.
The maximum correntropy criterion (MCC) has recently been successfully applied to adaptive filtering. Adaptive algorithms under MCC show strong robustness against large outliers. In this work, we apply the MCC criterion to develop a robust Hammerstein adaptive filter. Compared with the traditional Hammerstein adaptive filters, which are usually derived based on the well-known mean square error (MSE) criterion, the proposed algorithm can achieve better convergence performance especially in the presence of impulsive non-Gaussian (e.g., α-stable) noises. Additionally, some theoretical results concerning the convergence behavior are also obtained. Simulation examples are presented to confirm the superior performance of the new algorithm. Full article
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Open AccessArticle
Dynamics and Thermodynamics of Nanoclusters
Entropy 2015, 17(10), 7133-7148; https://doi.org/10.3390/e17107133 - 22 Oct 2015
Cited by 3 | Viewed by 1861
Abstract
The dynamic and thermodynamic properties of nanoclusters are studied in two different environments: the canonical and microcanonical ensembles. A comparison is made to thermodynamic properties of the bulk. It is shown that consistent and reproducible results on nanoclusters can only be obtained in [...] Read more.
The dynamic and thermodynamic properties of nanoclusters are studied in two different environments: the canonical and microcanonical ensembles. A comparison is made to thermodynamic properties of the bulk. It is shown that consistent and reproducible results on nanoclusters can only be obtained in the canonical ensemble. Nanoclusters in the microcanonical ensemble are trapped systems, and inconsistencies will be found if thermodynamic formalism is applied. An analytical model is given for the energy dependence of the phase space volume of nanoclusters, which allows the prediction of both dynamical and thermodynamical properties. Full article
(This article belongs to the Special Issue Nanothermodynamics)
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Open AccessArticle
A Novel Method for Increasing the Entropy of a Sequence of Independent, Discrete Random Variables
Entropy 2015, 17(10), 7118-7132; https://doi.org/10.3390/e17107118 - 22 Oct 2015
Viewed by 1408
Abstract
In this paper, we propose a novel method for increasing the entropy of a sequence of independent, discrete random variables with arbitrary distributions. The method uses an auxiliary table and a novel theorem that concerns the entropy of a sequence in which the [...] Read more.
In this paper, we propose a novel method for increasing the entropy of a sequence of independent, discrete random variables with arbitrary distributions. The method uses an auxiliary table and a novel theorem that concerns the entropy of a sequence in which the elements are a bitwise exclusive-or sum of independent discrete random variables. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
Open AccessArticle
Multi-Level Wavelet Shannon Entropy-Based Method for Single-Sensor Fault Location
Entropy 2015, 17(10), 7101-7117; https://doi.org/10.3390/e17107101 - 20 Oct 2015
Cited by 19 | Viewed by 2748
Abstract
In actual application, sensors are prone to failure because of harsh environments, battery drain, and sensor aging. Sensor fault location is an important step for follow-up sensor fault detection. In this paper, two new multi-level wavelet Shannon entropies (multi-level wavelet time [...] Read more.
In actual application, sensors are prone to failure because of harsh environments, battery drain, and sensor aging. Sensor fault location is an important step for follow-up sensor fault detection. In this paper, two new multi-level wavelet Shannon entropies (multi-level wavelet time Shannon entropy and multi-level wavelet time-energy Shannon entropy) are defined. They take full advantage of sensor fault frequency distribution and energy distribution across multi-subband in wavelet domain. Based on the multi-level wavelet Shannon entropy, a method is proposed for single sensor fault location. The method firstly uses a criterion of maximum energy-to-Shannon entropy ratio to select the appropriate wavelet base for signal analysis. Then multi-level wavelet time Shannon entropy and multi-level wavelet time-energy Shannon entropy are used to locate the fault. The method is validated using practical chemical gas concentration data from a gas sensor array. Compared with wavelet time Shannon entropy and wavelet energy Shannon entropy, the experimental results demonstrate that the proposed method can achieve accurate location of a single sensor fault and has good anti-noise ability. The proposed method is feasible and effective for single-sensor fault location. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory I)
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Open AccessArticle
D’Alembert’s Direct and Inertial Forces Acting on Populations: The Price Equation and the Fundamental Theorem of Natural Selection
Entropy 2015, 17(10), 7087-7100; https://doi.org/10.3390/e17107087 - 20 Oct 2015
Cited by 6 | Viewed by 2112
Abstract
I develop a framework for interpreting the forces that act on any population described by frequencies. The conservation of total frequency, or total probability, shapes the characteristics of force. I begin with Fisher’s fundamental theorem of natural selection. That theorem partitions the total [...] Read more.
I develop a framework for interpreting the forces that act on any population described by frequencies. The conservation of total frequency, or total probability, shapes the characteristics of force. I begin with Fisher’s fundamental theorem of natural selection. That theorem partitions the total evolutionary change of a population into two components. The first component is the partial change caused by the direct force of natural selection, holding constant all aspects of the environment. The second component is the partial change caused by the changing environment. I demonstrate that Fisher’s partition of total change into the direct force of selection and the forces from the changing environmental frame of reference is identical to d’Alembert’s principle of mechanics, which separates the work done by the direct forces from the work done by the inertial forces associated with the changing frame of reference. In d’Alembert’s principle, there exist inertial forces from a change in the frame of reference that exactly balance the direct forces. I show that the conservation of total probability strongly shapes the form of the balance between the direct and inertial forces. I then use the strong results for conserved probability to obtain general results for the change in any system quantity, such as biological fitness or energy. Those general results derive from simple coordinate changes between frequencies and system quantities. Ultimately, d’Alembert’s separation of direct and inertial forces provides deep conceptual insight into the interpretation of forces and the unification of disparate fields of study. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
Open AccessArticle
A Vibration Analysis Based on Wavelet Entropy Method of a Scroll Compressor
Entropy 2015, 17(10), 7076-7086; https://doi.org/10.3390/e17107076 - 19 Oct 2015
Cited by 4 | Viewed by 3794
Abstract
Vibration-based condition monitoring and fault diagnosis is an effective approach to maintain the reliable operation of a scroll compressor. Unfortunately, the vibration signal from the scroll compressor always has characteristics of being non-linear and non-stationary, which makes vibration signal analysis and fault feature [...] Read more.
Vibration-based condition monitoring and fault diagnosis is an effective approach to maintain the reliable operation of a scroll compressor. Unfortunately, the vibration signal from the scroll compressor always has characteristics of being non-linear and non-stationary, which makes vibration signal analysis and fault feature extraction very difficult. To extract the significant fault features, a vibration analysis method based on Wavelet entropy is proposed in this paper. Two forms of the wavelet entropy, namely the wavelet space feature spectrum entropy (WSFSE) and the wavelet energy spectrum entropy (WESE), are defined to depict instantaneous characteristics of the local variation of the vibration signal. Four types of mechanical faulty vibration signal, namely unbalanced rotor, malfunctioning scroll, loosened mechanical assembly, and loosened bearing, are analyzed by using the proposed approach. The experimental results show that feature components and energy distribution of each fault signal is accurately identified and revealed, which proves that the combined application of WSFSE and WESE approach is a successful scheme for the vibration analysis of scroll compressors. Full article
(This article belongs to the Special Issue Wavelet Entropy: Computation and Applications)
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Open AccessArticle
Extended Thermodynamics for Dense Gases up to Whatever Order and with Only Some Symmetries
Entropy 2015, 17(10), 7052-7075; https://doi.org/10.3390/e17107052 - 16 Oct 2015
Cited by 6 | Viewed by 1809
Abstract
Extended Thermodynamics of dense gases is characterized by two hierarchies of field equations, which allow one to overcome some restrictions on the generality of the previous models. This idea has been introduced by Arima, Taniguchi, Ruggeri and Sugiyama. In the case of a [...] Read more.
Extended Thermodynamics of dense gases is characterized by two hierarchies of field equations, which allow one to overcome some restrictions on the generality of the previous models. This idea has been introduced by Arima, Taniguchi, Ruggeri and Sugiyama. In the case of a 14-moment model, they have found the closure of the balance equations up to second order with respect to equilibrium. Here, the closure is obtained up to whatever order and imposing only the necessary symmetry conditions. It comes out that the first non-symmetric parts of the higher order fluxes appear only at third order with respect to equilibrium, even if Arima, Taniguchi, Ruggeri and Sugiyama found a non-symmetric part proportional to an arbitrary constant also at first order with respect to equilibrium. Consequently, this constant must be zero, as Arima, Taniguchi, Ruggeri and Sugiyama assumed in the applications and on an intuitive ground. Full article
(This article belongs to the Section Thermodynamics)
Open AccessArticle
Method for Measuring the Information Content of Terrain from Digital Elevation Models
Entropy 2015, 17(10), 7021-7051; https://doi.org/10.3390/e17107021 - 16 Oct 2015
Cited by 12 | Viewed by 2626
Abstract
As digital terrain models are indispensable for visualizing and modeling geographic processes, terrain information content is useful for terrain generalization and representation. For terrain generalization, if the terrain information is considered, the generalized terrain may be of higher fidelity. In other words, the [...] Read more.
As digital terrain models are indispensable for visualizing and modeling geographic processes, terrain information content is useful for terrain generalization and representation. For terrain generalization, if the terrain information is considered, the generalized terrain may be of higher fidelity. In other words, the richer the terrain information at the terrain surface, the smaller the degree of terrain simplification. Terrain information content is also important for evaluating the quality of the rendered terrain, e.g., the rendered web terrain tile service in Google Maps (Google Inc., Mountain View, CA, USA). However, a unified definition and measures for terrain information content have not been established. Therefore, in this paper, a definition and measures for terrain information content from Digital Elevation Model (DEM, i.e., a digital model or 3D representation of a terrain’s surface) data are proposed and are based on the theory of map information content, remote sensing image information content and other geospatial information content. The information entropy was taken as the information measuring method for the terrain information content. Two experiments were carried out to verify the measurement methods of the terrain information content. One is the analysis of terrain information content in different geomorphic types, and the results showed that the more complex the geomorphic type, the richer the terrain information content. The other is the analysis of terrain information content with different resolutions, and the results showed that the finer the resolution, the richer the terrain information. Both experiments verified the reliability of the measurements of the terrain information content proposed in this paper. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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Open AccessArticle
A Thermodynamic Entropy Approach to Reliability Assessment with Applications to Corrosion Fatigue
Entropy 2015, 17(10), 6995-7020; https://doi.org/10.3390/e17106995 - 16 Oct 2015
Cited by 22 | Viewed by 2243
Abstract
This paper outlines a science-based explanation of damage and reliability of critical components and structures within the second law of thermodynamics. The approach relies on the fundamentals of irreversible thermodynamics, specifically the concept of entropy generation as an index of degradation and damage [...] Read more.
This paper outlines a science-based explanation of damage and reliability of critical components and structures within the second law of thermodynamics. The approach relies on the fundamentals of irreversible thermodynamics, specifically the concept of entropy generation as an index of degradation and damage in materials. All damage mechanisms share a common feature, namely energy dissipation. Dissipation, a fundamental measure for irreversibility in a thermodynamic treatment of non-equilibrium processes, is quantified by entropy generation. An entropic-based damage approach to reliability and integrity characterization is presented and supported by experimental validation. Using this theorem, which relates entropy generation to dissipative phenomena, the corrosion fatigue entropy generation function is derived, evaluated, and employed for structural integrity and reliability assessment of aluminum 7075-T651 specimens. Full article
(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes 2015)
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Open AccessConcept Paper
Towards Information Lasers
Entropy 2015, 17(10), 6969-6994; https://doi.org/10.3390/e17106969 - 16 Oct 2015
Cited by 12 | Viewed by 1949
Abstract
Recently, the methods of quantum theory (QT), especially quantum information and probability, started to be widely applied outside of physics: in cognitive, social and political sciences, psychology, economics, finances, decision making, molecular biology and genetics. Such models can be called quantum-like, in contrast [...] Read more.
Recently, the methods of quantum theory (QT), especially quantum information and probability, started to be widely applied outside of physics: in cognitive, social and political sciences, psychology, economics, finances, decision making, molecular biology and genetics. Such models can be called quantum-like, in contrast to real quantum physical cognitive and biological models. Quantum-like means that only the information and probability structures of QT are explored. This approach matches the information interpretation of QT well (e.g., Zeilinger and Brukner, Fuchs and Mermin, D’Ariano), as well as the informational viewpoint on physics in general (e.g., Wheeler’s “it from bit” paradigm). In this paper, we propose a quantum-like model of an information laser by precessing the assumptions on the structure of state spaces of information processors, “information atoms” (i-atoms) and information fields. The basic assumption is the discrete structure of state spaces related to quantization of an information analog of energy. To analyze a possible structure of the state space of i-atoms leading to the possibility to create information lasers, we have to develop a purely information version of quantum thermodynamics. We did this by placing the main attention on the derivation of the conditions for the equilibrium of information exchange between i-atoms and a quantized information field. Full article
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Open AccessArticle
A Novel Image Encryption Algorithm Based on DNA Encoding and Spatiotemporal Chaos
Entropy 2015, 17(10), 6954-6968; https://doi.org/10.3390/e17106954 - 16 Oct 2015
Cited by 33 | Viewed by 2637
Abstract
DNA computing based image encryption is a new, promising field. In this paper, we propose a novel image encryption scheme based on DNA encoding and spatiotemporal chaos. In particular, after the plain image is primarily diffused with the bitwise Exclusive-OR operation, the DNA [...] Read more.
DNA computing based image encryption is a new, promising field. In this paper, we propose a novel image encryption scheme based on DNA encoding and spatiotemporal chaos. In particular, after the plain image is primarily diffused with the bitwise Exclusive-OR operation, the DNA mapping rule is introduced to encode the diffused image. In order to enhance the encryption, the spatiotemporal chaotic system is used to confuse the rows and columns of the DNA encoded image. The experiments demonstrate that the proposed encryption algorithm is of high key sensitivity and large key space, and it can resist brute-force attack, entropy attack, differential attack, chosen-plaintext attack, known-plaintext attack and statistical attack. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics)
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Open AccessArticle
Exponential Synchronization of Two Complex Dynamical Networks of Random Disturbance with Both Mixed Coupled and Time-Varying Delay by Pinning Control
Entropy 2015, 17(10), 6937-6953; https://doi.org/10.3390/e17106937 - 16 Oct 2015
Cited by 3 | Viewed by 1690
Abstract
In this paper, the exponentially synchronization in the mean square is investigated for two different stochastic complex networks with hybrid coupling and time-varying delay via pinning control. By utilizing the Lyapunov stability theory, stochastic analysis theory, as well as matrix analysis, the sufficient [...] Read more.
In this paper, the exponentially synchronization in the mean square is investigated for two different stochastic complex networks with hybrid coupling and time-varying delay via pinning control. By utilizing the Lyapunov stability theory, stochastic analysis theory, as well as matrix analysis, the sufficient conditions are derived to guarantee the exponential synchronization for any initial values through a feedback scheme. The numerical simulation is provided to show the effectiveness of the theoretical results. Full article
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Open AccessArticle
Modified Legendre Wavelets Technique for Fractional Oscillation Equations
Entropy 2015, 17(10), 6925-6936; https://doi.org/10.3390/e17106925 - 16 Oct 2015
Cited by 13 | Viewed by 2146
Abstract
Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among [...] Read more.
Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinear fractional order oscillation equation into a fractional order recurrence relation and then Legendre wavelets method is applied on the converted problem. In order to check the efficiency and accuracy of the suggested modification, we have considered three problems namely: fractional order force-free Duffing–van der Pol oscillator, forced Duffing–van der Pol oscillator and higher order fractional Duffing equations. The obtained results are compared with the results obtained via other techniques. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory I)
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Open AccessReview
Thermal BEC Black Holes
Entropy 2015, 17(10), 6893-6924; https://doi.org/10.3390/e17106893 - 15 Oct 2015
Cited by 23 | Viewed by 2455
Abstract
We review some features of Bose–Einstein condensate (BEC) models of black holes obtained by means of the horizon wave function formalism. We consider the Klein–Gordon equation for a toy graviton field coupled to a static matter current in a spherically-symmetric setup. The classical [...] Read more.
We review some features of Bose–Einstein condensate (BEC) models of black holes obtained by means of the horizon wave function formalism. We consider the Klein–Gordon equation for a toy graviton field coupled to a static matter current in a spherically-symmetric setup. The classical field reproduces the Newtonian potential generated by the matter source, while the corresponding quantum state is given by a coherent superposition of scalar modes with a continuous occupation number. An attractive self-interaction is needed for bound states to form, the case in which one finds that (approximately) one mode is allowed, and the system of N bosons can be self-confined in a volume of the size of the Schwarzschild radius. The horizon wave function formalism is then used to show that the radius of such a system corresponds to a proper horizon. The uncertainty in the size of the horizon is related to the typical energy of Hawking modes: it decreases with the increasing of the black hole mass (larger number of gravitons), resulting in agreement with the semiclassical calculations and which does not hold for a single very massive particle. The spectrum of these systems has two components: a discrete ground state of energy m (the bosons forming the black hole) and a continuous spectrum with energy ω > m (representing the Hawking radiation and modeled with a Planckian distribution at the expected Hawking temperature). Assuming the main effect of the internal scatterings is the Hawking radiation, the N-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy M = Nm and Entropy 2015, 17 6894 a Planckian distribution for E > M at the same Hawking temperature. This can be used to compute the partition function and to find the usual area law for the entropy, with a logarithmic correction related to the Hawking component. The backreaction of modes with ω > m is also shown to reduce the Hawking flux. The above corrections suggest that for black holes in this quantum state, the evaporation properly stops for a vanishing mass. Full article
(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)
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Open AccessArticle
Topological Characterization of Complex Systems: Using Persistent Entropy
Entropy 2015, 17(10), 6872-6892; https://doi.org/10.3390/e17106872 - 15 Oct 2015
Cited by 23 | Viewed by 3903
Abstract
In this paper, we propose a methodology for deriving a model of a complex system by exploiting the information extracted from topological data analysis. Central to our approach is the S[B] paradigm in which a complex system is represented by [...] Read more.
In this paper, we propose a methodology for deriving a model of a complex system by exploiting the information extracted from topological data analysis. Central to our approach is the S[B] paradigm in which a complex system is represented by a two-level model. One level, the structural S one, is derived using the newly-introduced quantitative concept of persistent entropy, and it is described by a persistent entropy automaton. The other level, the behavioral B one, is characterized by a network of interacting computational agents. The presented methodology is applied to a real case study, the idiotypic network of the mammalian immune system. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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Open AccessArticle
Analysis of Neural Oscillations on Drosophila’s Subesophageal Ganglion Based on Approximate Entropy
Entropy 2015, 17(10), 6854-6871; https://doi.org/10.3390/e17106854 - 10 Oct 2015
Cited by 2 | Viewed by 2504
Abstract
The suboesophageal ganglion (SOG), which connects to both central and peripheral nerves, is the primary taste-processing center in the Drosophila’s brain. The neural oscillation in this center may be of great research value yet it is rarely reported. This work aims to [...] Read more.
The suboesophageal ganglion (SOG), which connects to both central and peripheral nerves, is the primary taste-processing center in the Drosophila’s brain. The neural oscillation in this center may be of great research value yet it is rarely reported. This work aims to determine the amount of unique information contained within oscillations of the SOG and describe the variability of these patterns. The approximate entropy (ApEn) values of the spontaneous membrane potential (sMP) of SOG neurons were calculated in this paper. The arithmetic mean (MA), standard deviation (SDA) and the coefficient of variation (CVA) of ApEn were proposed as the three statistical indicators to describe the irregularity and complexity of oscillations. The hierarchical clustering method was used to classify them. As a result, the oscillations in SOG were divided into five categories, including: (1) Continuous spike pattern; (2) Mixed oscillation pattern; (3) Spikelet pattern; (4) Busting pattern and (5) Sparse spike pattern. Steady oscillation state has a low level of irregularity, and vice versa. The dopamine stimulation can distinctly cut down the complexity of the mixed oscillation pattern. The current study provides a quantitative method and some critera on mining the information carried in neural oscillations. Full article
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Open AccessArticle
Dynamical Change of Signal Complexity in the Brain During Inhibitory Control Processes
Entropy 2015, 17(10), 6834-6853; https://doi.org/10.3390/e17106834 - 09 Oct 2015
Cited by 2 | Viewed by 2110
Abstract
The ability to inhibit impulses and withdraw certain responses are essential for human’s survival in a fast-changing environment. These processes happen fast, in a complex manner, and require our brain to make a fast adaptation to inhibit the impulsive response. The present study [...] Read more.
The ability to inhibit impulses and withdraw certain responses are essential for human’s survival in a fast-changing environment. These processes happen fast, in a complex manner, and require our brain to make a fast adaptation to inhibit the impulsive response. The present study employs multiscale entropy (MSE) to analyzing electroencephalography (EEG) signals acquired alongside a behavioral stop-signal task to theoretically quantify the complexity (indicating adaptability and efficiency) of neural systems to investigate the dynamical change of complexity in the brain during the processes of inhibitory control. We found that the complexity of EEG signals was higher for successful than unsuccessful inhibition in the stage of peri-stimulus, but not in the pre-stimulus time window. In addition, we found that the dynamical change in the brain from pre-stimulus to peri-stimulus stage for inhibitory control is a process of decreasing complexity. We demonstrated both by sensor-level and source-level MSE that the processes of losing complexity is temporally slower and spatially restricted for successful inhibition, and is temporally quicker and spatially extensive for unsuccessful inhibition. Full article
(This article belongs to the Special Issue Entropy in Human Brain Networks)
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Open AccessArticle
On the Calculation of System Entropy in Nonlinear Stochastic Biological Networks
Entropy 2015, 17(10), 6801-6833; https://doi.org/10.3390/e17106801 - 08 Oct 2015
Cited by 8 | Viewed by 2507
Abstract
Biological networks are open systems that can utilize nutrients and energy from their environment for use in their metabolic processes, and produce metabolic products. System entropy is defined as the difference between input and output signal entropy, i.e., the net signal entropy [...] Read more.
Biological networks are open systems that can utilize nutrients and energy from their environment for use in their metabolic processes, and produce metabolic products. System entropy is defined as the difference between input and output signal entropy, i.e., the net signal entropy of the biological system. System entropy is an important indicator for living or non-living biological systems, as biological systems can maintain or decrease their system entropy. In this study, system entropy is determined for the first time for stochastic biological networks, and a computation method is proposed to measure the system entropy of nonlinear stochastic biological networks that are subject to intrinsic random fluctuations and environmental disturbances. We find that intrinsic random fluctuations could increase the system entropy, and that the system entropy is inversely proportional to the robustness and stability of the biological networks. It is also determined that adding feedback loops to shift all eigenvalues to the farther left-hand plane of the complex s-domain could decrease the system entropy of a biological network. Full article
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Open AccessArticle
New Patterns in Steady-State Chemical Kinetics: Intersections, Coincidences, Map of Events (Two-Step Mechanism)
Entropy 2015, 17(10), 6783-6800; https://doi.org/10.3390/e17106783 - 07 Oct 2015
Cited by 10 | Viewed by 2289
Abstract
New patterns of steady-state chemical kinetics for continuously stirred-tank reactors (CSTR) have been found, i.e., intersections, maxima and coincidences, for two-step mechanism A↔B→C. There were found elegant analytical relationships for characteristics of these patterns (space times, values of concentrations and rates) allowing [...] Read more.
New patterns of steady-state chemical kinetics for continuously stirred-tank reactors (CSTR) have been found, i.e., intersections, maxima and coincidences, for two-step mechanism A↔B→C. There were found elegant analytical relationships for characteristics of these patterns (space times, values of concentrations and rates) allowing kinetic parameters to be easily determined. It was demonstrated that for the pair of species involved into the irreversible reaction (B and C), the space time of their corresponding concentration dependence intersection is invariant and does not depend on the initial conditions of the system. Maps of patterns are presented for visualization of their combinations and ranking in space time, and values of concentration and rates. Full article
(This article belongs to the Special Issue Selected Papers from 13th Joint European Thermodynamics Conference)
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Open AccessArticle
A Tale of Two Entangled InstabilitiesThe Dual Role of δ-O in HgBa2Can-1CunO2(n+1)+δ
Entropy 2015, 17(10), 6765-6782; https://doi.org/10.3390/e17106765 - 05 Oct 2015
Cited by 4 | Viewed by 2016
Abstract
Low-energy instabilities in the hole-doped cuprates include, besides short range antiferromagnetic fluctuations and superconductivity, also ubiquitous translational and rotational symmetry breakings. The overwhelming majority of interpretations of these possibly related properties rely on mappings onto three bands spanned by the three atomic orbitals [...] Read more.
Low-energy instabilities in the hole-doped cuprates include, besides short range antiferromagnetic fluctuations and superconductivity, also ubiquitous translational and rotational symmetry breakings. The overwhelming majority of interpretations of these possibly related properties rely on mappings onto three bands spanned by the three atomic orbitals Cu3d(x2y2)(σ), O2px(σ), and O2py(σ), these three local orbitals spanning the Zhang–Rice band (ZRB), the lower Hubbard bands (LHB) and the upper Hubbard bands (UHB), respectively. Here we demonstrate by means of supercell Density Functional Theory (DFT) (a) how oxygen intercalation affects the structures of the buffer layers, and (b) how the attenuated crystal field pulls two additional oxygen bands in the CuO2 plane to the Fermi level. The self-consistent changes in electronic structure reflected in the corresponding changes in external potential comprise formal properties of the Hohenberg–Kohn theorems. Validation of present days’ approximate exchange-correlation potentials to capture these qualitative effects by means of supercell DFT is made by comparing computed doping dependent structural shifts to corresponding experimentally observed correlations. The simplest generalization of Bardeen–Cooper–Schrieffer (BCS) theory is offered to articulate high-critical temperature superconductivity (HTS) from a normal state where crystal field causes states related to two non-hybridizing bands to coalesce at EF. Full article
(This article belongs to the Special Issue Quantum Computation and Information: Multi-Particle Aspects)
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Open AccessArticle
Local Fractional Homotopy Perturbation Method for Solving Non-Homogeneous Heat Conduction Equations in Fractal Domains
Entropy 2015, 17(10), 6753-6764; https://doi.org/10.3390/e17106753 - 05 Oct 2015
Cited by 38 | Viewed by 2513
Abstract
In this article, the local fractional Homotopy perturbation method is utilized to solve the non-homogeneous heat conduction equations. The operator is considered in the sense of the local fractional differential operator. Comparative results between non-homogeneous and homogeneous heat conduction equations are presented. The [...] Read more.
In this article, the local fractional Homotopy perturbation method is utilized to solve the non-homogeneous heat conduction equations. The operator is considered in the sense of the local fractional differential operator. Comparative results between non-homogeneous and homogeneous heat conduction equations are presented. The obtained result shows the non-differentiable behavior of heat conduction of the fractal temperature field in homogeneous media. Full article
(This article belongs to the Special Issue Dynamical Equations and Causal Structures from Observations)
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Open AccessArticle
Quantum Secure Direct Communication Based on Dense Coding and Detecting Eavesdropping with Four-Particle Genuine Entangled State
Entropy 2015, 17(10), 6743-6752; https://doi.org/10.3390/e17106743 - 30 Sep 2015
Cited by 6 | Viewed by 2242
Abstract
A novel quantum secure direct communication protocol based on four-particle genuine entangled state and quantum dense coding is proposed. In this protocol, the four-particle genuine entangled state is used to detect eavesdroppers, and quantum dense coding is used to encode the message. Finally, [...] Read more.
A novel quantum secure direct communication protocol based on four-particle genuine entangled state and quantum dense coding is proposed. In this protocol, the four-particle genuine entangled state is used to detect eavesdroppers, and quantum dense coding is used to encode the message. Finally, the security of the proposed protocol is discussed. During the security analysis, the method of entropy theory is introduced, and two detection strategies are compared quantitatively by comparing the relationship between the maximal information that the eavesdroppers (Eve) can obtain, and the probability of being detected. Through the analysis we can state that our scheme is feasible and secure. Full article
(This article belongs to the Special Issue Quantum Computation and Information: Multi-Particle Aspects)
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Open AccessArticle
Thermodynamic Analysis of Closed Steady or Cyclic Systems
Entropy 2015, 17(10), 6712-6742; https://doi.org/10.3390/e17106712 - 29 Sep 2015
Viewed by 3028
Abstract
Closed, steady or cyclic thermodynamic systems, which have temperature variations over their boundaries, can represent an extremely large range of plants, devices or natural objects, such as combined heating, cooling and power plants, computers and data centres, and planets. Energy transfer rates can [...] Read more.
Closed, steady or cyclic thermodynamic systems, which have temperature variations over their boundaries, can represent an extremely large range of plants, devices or natural objects, such as combined heating, cooling and power plants, computers and data centres, and planets. Energy transfer rates can occur across the boundary, which are characterized as heat or work. We focus on the finite time thermodynamics aspects, on energy-based performance parameters, on rational efficiency and on the environmental reference temperature. To do this, we examine the net work rate of a closed, steady or cyclic system bounded by thermal resistances linked to isothermal reservoirs in terms of the first and second laws of thermodynamics. Citing relevant references from the literature, we propose a methodology that can improve the thermodynamic analysis of an energy-transforming or an exergy-destroying plant. Through the reflections and analysis presented, we have found an explanation of the second law that clarifies the link between the Clausius integral of heat over temperature and the reference temperature of the Gouy–Stodola theorem. With this insight and approach, the specification of the environmental reference temperature in exergy analysis becomes more solid. We have explained the relationship between the Curzon Ahlborn heat engine and an irreversible Carnot heat engine. We have outlined the nature of subsystem rational efficiencies and have found Rant’s anergy to play an important role. We postulate that heat transfer through thermal resistance is the sole basis of irreversibility. Full article
(This article belongs to the Special Issue Selected Papers from 13th Joint European Thermodynamics Conference)
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