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Entropy, Volume 17, Issue 2 (February 2015), Pages 483-913

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Editorial

Jump to: Research, Review

Open AccessEditorial Entropy Best Paper Award 2015
Entropy 2015, 17(2), 882-884; doi:10.3390/e17020882
Received: 3 February 2014 / Accepted: 15 February 2015 / Published: 16 February 2015
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Abstract
We are pleased to announce the “Entropy Best Paper Award” for 2015. Nominations were selected by the Editor-in-Chief and designated Editorial Board Members from all the papers published in 2011. Reviews and research papers were evaluated separately. We gladly announce that the
[...] Read more.
We are pleased to announce the “Entropy Best Paper Award” for 2015. Nominations were selected by the Editor-in-Chief and designated Editorial Board Members from all the papers published in 2011. Reviews and research papers were evaluated separately. We gladly announce that the following three papers have won the Entropy Best Paper Award in 2015:[...] Full article
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Research

Jump to: Editorial, Review

Open AccessArticle Analyses of Heart Rate, Respiration and Cardiorespiratory Coupling in Patients with Schizophrenia
Entropy 2015, 17(2), 483-501; doi:10.3390/e17020483
Received: 28 October 2014 / Accepted: 20 January 2015 / Published: 23 January 2015
Cited by 7 | PDF Full-text (1059 KB) | HTML Full-text | XML Full-text
Abstract
Schizophrenia is a severe mental disorder associated with a significantly increased cardiovascular mortality rate. However, the underlying mechanisms leading to this cardiovascular disease (CVD) are not fully known. Therefore, the objective of this study was to characterize the cardiorespiratory influence by investigating heart
[...] Read more.
Schizophrenia is a severe mental disorder associated with a significantly increased cardiovascular mortality rate. However, the underlying mechanisms leading to this cardiovascular disease (CVD) are not fully known. Therefore, the objective of this study was to characterize the cardiorespiratory influence by investigating heart rate, respiration and the causal strength and direction of cardiorespiratory coupling (CRC), based mainly on entropy measures. We investigated 23 non-medicated patients with schizophrenia (SZ), comparing them to 23 age- and gender-matched healthy controls (CO). A significantly reduced complexity was found for the heart rate and a significantly increased complexity in respiration and CRC in SZ patients when compared to corresponding measurements from CO (p < 0.001). CRC analyses revealed a clear coupling, with a driver-responder relationship from respiration to heart rate in SZ patients. Moreover, a slight driver-responder relationship from heart rate to respiration could be recognized. These findings lead to the assumption that SZ should be considered to be a high-risk group for CVD. We hypothesize that the varying cardiorespiratory regulation contributes to the increased risk for cardiac mortality. Therefore, regular monitoring of the cardiorespiratory status of SZ is suggested to identify autonomic regulation impairment at an early stage—to develop timely and effective treatment and intervention strategies. Full article
(This article belongs to the Special Issue Entropy and Cardiac Physics)
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Open AccessArticle Reshaping the Science of Reliability with the Entropy Function
Entropy 2015, 17(2), 502-508; doi:10.3390/e17020502
Received: 1 December 2014 / Revised: 17 December 2014 / Accepted: 15 January 2015 / Published: 26 January 2015
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Abstract
The present paper revolves around two argument points. As first, we have observed a certain parallel between the reliability of systems and the progressive disorder of thermodynamical systems; and we import the notion of reversibility/irreversibility into the reliability domain. As second, we note
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The present paper revolves around two argument points. As first, we have observed a certain parallel between the reliability of systems and the progressive disorder of thermodynamical systems; and we import the notion of reversibility/irreversibility into the reliability domain. As second, we note that the reliability theory is a very active area of research which although has not yet become a mature discipline. This is due to the majority of researchers who adopt the inductive logic instead of the deductive logic typical of mature scientific sectors. The deductive approach was inaugurated by Gnedenko in the reliability domain. We mean to continue Gnedenko’s work and we use the Boltzmann-like entropy to pursue this objective. This paper condenses the papers published in the past decade which illustrate the calculus of the Boltzmann-like entropy. It is demonstrated how the every result complies with the deductive logic and are consistent with Gnedenko’s achievements. Full article
Open AccessArticle EWnFM: An Environment States Oriented Web Service Non-Functional Property Model
Entropy 2015, 17(2), 509-527; doi:10.3390/e17020509
Received: 7 October 2014 / Accepted: 26 January 2015 / Published: 28 January 2015
Cited by 1 | PDF Full-text (1217 KB) | HTML Full-text | XML Full-text
Abstract
A proper model of Web service non-functional properties is the key foundation to the evaluation of non-functional properties of Adaptive Service Based Software (ASBS) systems. As the environment in which a Web service is deployed may keep changing, environmental factors would affect the
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A proper model of Web service non-functional properties is the key foundation to the evaluation of non-functional properties of Adaptive Service Based Software (ASBS) systems. As the environment in which a Web service is deployed may keep changing, environmental factors would affect the non-functional properties of a Web service a lot. However, available non-functional property models usually ignore the impact of environmental factors, leading to insufficient modeling power of non-functional properties, limited effect of system wide non-functional property evaluation based on these models, and the inability to support environment states oriented specifications of ASBS. This paper propose an environment states oriented Web service non-functional property model. By considering the differences of a non-functional property under different environment states, environment states of a Web service is analyzed using a Dirichlet process based method. With such a foundation, an environment states oriented Web service non-functional property model is introduced, together with the parameter estimation methods based on historical monitor data. Experiment results have shown that compared to the evaluated methods, our model could generate data that are much close to real monitored data. Full article
Open AccessArticle A New Telegrapher’s-Poisson System in Semiconductor Theory: A Singular Perturbation Approach
Entropy 2015, 17(2), 528-538; doi:10.3390/e17020528
Received: 3 December 2014 / Revised: 20 January 2015 / Accepted: 21 January 2015 / Published: 29 January 2015
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Abstract
In the theory of energy and momentum relaxation in semiconductor devices, the introduction of two temperatures and two mean velocities for electron and phonons is required. A new model, based on an asymptotic procedure for solving the kinetic equations of electrons and phonons
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In the theory of energy and momentum relaxation in semiconductor devices, the introduction of two temperatures and two mean velocities for electron and phonons is required. A new model, based on an asymptotic procedure for solving the kinetic equations of electrons and phonons is proposed, which naturally gives the displaced Maxwellian at the leading order. After that, balance equations for the electron number, energy densities and momentum densities are constructed, which constitute now a system of five equations for the chemical potential of electrons, the temperatures and the drift velocities. Moreover, Poisson’s equation is coupled, in order to calculate the self-consistent electric field. In Bloch’s approximation, we derive a telegrapher’s-Poisson system for the electron number density and the electric potential, which could allow simple semiconductor calculations, but still including wave propagation effects. Full article
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
Open AccessArticle Effects of Direct Fuel Injection Strategies on Cycle-by-Cycle Variability in a Gasoline Homogeneous Charge Compression Ignition Engine: Sample Entropy Analysis
Entropy 2015, 17(2), 539-559; doi:10.3390/e17020539
Received: 4 December 2014 / Revised: 29 December 2014 / Accepted: 23 January 2015 / Published: 29 January 2015
Cited by 2 | PDF Full-text (2588 KB) | HTML Full-text | XML Full-text
Abstract
In this study we summarize and analyze experimental observations of cyclic variability in homogeneous charge compression ignition (HCCI) combustion in a single-cylinder gasoline engine. The engine was configured with negative valve overlap (NVO) to trap residual gases from prior cycles and thus enable
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In this study we summarize and analyze experimental observations of cyclic variability in homogeneous charge compression ignition (HCCI) combustion in a single-cylinder gasoline engine. The engine was configured with negative valve overlap (NVO) to trap residual gases from prior cycles and thus enable auto-ignition in successive cycles. Correlations were developed between different fuel injection strategies and cycle average combustion and work output profiles. Hypothesized physical mechanisms based on these correlations were then compared with trends in cycle-by-cycle predictability as revealed by sample entropy. The results of these comparisons help to clarify how fuel injection strategy can interact with prior cycle effects to affect combustion stability and so contribute to design control methods for HCCI engines. Full article
Open AccessArticle Symbolic Entropy of the Amplitude rather than the Instantaneous Frequency of EEG Varies in Dementia
Entropy 2015, 17(2), 560-579; doi:10.3390/e17020560
Received: 17 October 2014 / Accepted: 26 January 2015 / Published: 29 January 2015
Cited by 2 | PDF Full-text (908 KB) | HTML Full-text | XML Full-text
Abstract
The dynamics of human electroencephalography (EEG) have been proved to be related to cognitive activities. This study separately assessed the two EEG components, amplitude and rhythm, aiming to capture their individual contributions to cognitive functions. We extracted the local peaks of EEGs under
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The dynamics of human electroencephalography (EEG) have been proved to be related to cognitive activities. This study separately assessed the two EEG components, amplitude and rhythm, aiming to capture their individual contributions to cognitive functions. We extracted the local peaks of EEGs under rest or photic stimulation and calculated the symbolic dynamics of their voltages (amplitude) and interpeak intervals (instantaneous frequency), individually. The sample consisted of 89 geriatric outpatients in three patient groups: 38 fresh cases of vascular dementia (VD), 22 fresh cases of Alzheimer’s disease (AD) and 29 controls. Both sample entropy and number of forbidden words revealed significantly less regular symbolic dynamics in the whole EEG tracings of the VD than the AD and control groups. We found consistent results between groups with the symbolic dynamics in the local-peak voltage sequence rather than the interpeak interval sequence. Photic stimulation amplified the differences between groups. These results suggest that the EEG dynamics which relates to either cognitive functions or the underlying pathologies of dementia are embedded within the dynamics of the amount of but not the interval between each synchronized firing of adjacent cerebral neurons. Full article
(This article belongs to the Special Issue Entropy in Human Brain Networks)
Open AccessArticle Study on Droplet Size and Velocity Distributions of a Pressure Swirl Atomizer Based on the Maximum Entropy Formalism
Entropy 2015, 17(2), 580-593; doi:10.3390/e17020580
Received: 5 November 2014 / Revised: 9 January 2015 / Accepted: 12 January 2015 / Published: 30 January 2015
Cited by 2 | PDF Full-text (945 KB) | HTML Full-text | XML Full-text
Abstract
A predictive model for droplet size and velocity distributions of a pressure swirl atomizer has been proposed based on the maximum entropy formalism (MEF). The constraint conditions of the MEF model include the conservation laws of mass, momentum, and energy. The effects of
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A predictive model for droplet size and velocity distributions of a pressure swirl atomizer has been proposed based on the maximum entropy formalism (MEF). The constraint conditions of the MEF model include the conservation laws of mass, momentum, and energy. The effects of liquid swirling strength, Weber number, gas-to-liquid axial velocity ratio and gas-to-liquid density ratio on the droplet size and velocity distributions of a pressure swirl atomizer are investigated. Results show that model based on maximum entropy formalism works well to predict droplet size and velocity distributions under different spray conditions. Liquid swirling strength, Weber number, gas-to-liquid axial velocity ratio and gas-to-liquid density ratio have different effects on droplet size and velocity distributions of a pressure swirl atomizer. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle A Foundational Approach to Generalising the Maximum Entropy Inference Process to the Multi-Agent Context
Entropy 2015, 17(2), 594-645; doi:10.3390/e17020594
Received: 1 December 2014 / Revised: 10 December 2014 / Accepted: 13 January 2015 / Published: 2 February 2015
Cited by 9 | PDF Full-text (496 KB) | HTML Full-text | XML Full-text
Abstract
The present paper seeks to establish a logical foundation for studying axiomatically multi-agent probabilistic reasoning over a discrete space of outcomes. We study the notion of a social inference process which generalises the concept of an inference process for a single agent which
[...] Read more.
The present paper seeks to establish a logical foundation for studying axiomatically multi-agent probabilistic reasoning over a discrete space of outcomes. We study the notion of a social inference process which generalises the concept of an inference process for a single agent which was used by Paris and Vencovská to characterise axiomatically the method of maximum entropy inference. Axioms for a social inference process are introduced and discussed, and a particular social inference process called the Social Entropy Process, or SEP, is defined which satisfies these axioms. SEP is justified heuristically by an information theoretic argument, and incorporates both the maximum entropy inference process for a single agent and the multi–agent normalised geometric mean pooling operator. Full article
(This article belongs to the Special Issue Maximum Entropy Applied to Inductive Logic and Reasoning)
Open AccessArticle Thermal and Structural Analysis of Mn49.3Ni43.7Sn7.0 Heusler Alloy Ribbons
Entropy 2015, 17(2), 646-657; doi:10.3390/e17020646
Received: 14 November 2014 / Revised: 26 January 2015 / Accepted: 28 January 2015 / Published: 2 February 2015
Cited by 3 | PDF Full-text (1188 KB) | HTML Full-text | XML Full-text
Abstract
The martensitic transformation and the solidification structures of Mn49.3Ni43.7Sn7.0 alloy ribbons prepared by melt-spinning were investigated by means of scanning electron microscopy, X-ray diffraction and differential scanning calorimetry. In those experiments special attention was given to melt spinning
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The martensitic transformation and the solidification structures of Mn49.3Ni43.7Sn7.0 alloy ribbons prepared by melt-spinning were investigated by means of scanning electron microscopy, X-ray diffraction and differential scanning calorimetry. In those experiments special attention was given to melt spinning processing parameters such as the linear surface speed of the copper wheel rotating, the injection overpressure and the distance between wheel and injection quartz tube. Transformation entropy was found higher when increasing linear surface speed or the distance from injection point to wheel. The resulting samples showed chemical compositions close to the nominal ones and, at room temperature, crystallized in a monoclinic single-phase martensite with 14M modulation (without a significant variation in the cell parameters). Strong dependence of ribbon thickness on processing parameters was found. The average grain size varied between 1.6 and 6.6 μm, while the start temperature of the martensitic temperature varied from 394 to 430 K. Full article
(This article belongs to the Section Thermodynamics)
Open AccessArticle Entropy Production of Main-Sequence Stars
Entropy 2015, 17(2), 658-668; doi:10.3390/e17020658
Received: 19 November 2014 / Revised: 20 January 2015 / Accepted: 27 January 2015 / Published: 2 February 2015
Cited by 3 | PDF Full-text (1857 KB) | HTML Full-text | XML Full-text
Abstract
The entropy production (inside the volume bounded by a photosphere) of main-sequence stars is calculated based on B–V photometry data. The entropy-production distribution function and the dependences of entropy production on temperature and luminosity are obtained for these stars for the first time.
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The entropy production (inside the volume bounded by a photosphere) of main-sequence stars is calculated based on B–V photometry data. The entropy-production distribution function and the dependences of entropy production on temperature and luminosity are obtained for these stars for the first time. A very small range of variation of specific (per volume) entropy production discovered for main-sequence stars (only 0.5 to 1.8 solar magnitudes) is an interesting result that can be crucial for understanding thermodynamic processes of stars. Full article
Open AccessArticle Application of Entropy Measures on Intrinsic Mode Functions for the Automated Identification of Focal Electroencephalogram Signals
Entropy 2015, 17(2), 669-691; doi:10.3390/e17020669
Received: 8 December 2014 / Revised: 13 January 2015 / Accepted: 23 January 2015 / Published: 3 February 2015
Cited by 64 | PDF Full-text (1213 KB) | HTML Full-text | XML Full-text
Abstract
The brain is a complex structure made up of interconnected neurons, and its electrical activities can be evaluated using electroencephalogram (EEG) signals. The characteristics of the brain area affected by partial epilepsy can be studied using focal and non-focal EEG signals. In this
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The brain is a complex structure made up of interconnected neurons, and its electrical activities can be evaluated using electroencephalogram (EEG) signals. The characteristics of the brain area affected by partial epilepsy can be studied using focal and non-focal EEG signals. In this work, a method for the classification of focal and non-focal EEG signals is presented using entropy measures. These entropy measures can be useful in assessing the nonlinear interrelation and complexity of focal and non-focal EEG signals. These EEG signals are first decomposed using the empirical mode decomposition (EMD) method to extract intrinsic mode functions (IMFs). The entropy features, namely, average Shannon entropy (ShEnAvg), average Renyi’s entropy (RenEnAvg ), average approximate entropy (ApEnAvg), average sample entropy (SpEnAvg) and average phase entropies (S1Avg and S2Avg), are computed from different IMFs of focal and non-focal EEG signals. These entropies are used as the input feature set for the least squares support vector machine (LS-SVM) classifier to classify into focal and non-focal EEG signals. Experimental results show that our proposed method is able to differentiate the focal and non-focal EEG signals with an average classification accuracy of 87% correct. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Parameters Estimation of Uncertain Fractional-Order Chaotic Systems via a Modified Artificial Bee Colony Algorithm
Entropy 2015, 17(2), 692-709; doi:10.3390/e17020692
Received: 25 December 2014 / Revised: 23 January 2015 / Accepted: 27 January 2015 / Published: 4 February 2015
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Abstract
Parameter estimation for fractional-order chaotic systems has been an interesting and important issue in theory and various fields of application. In this paper, fractional orders, as well as systematic parameters of fractional-order chaotic systems are considered by treating fractional orders as additional parameters.
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Parameter estimation for fractional-order chaotic systems has been an interesting and important issue in theory and various fields of application. In this paper, fractional orders, as well as systematic parameters of fractional-order chaotic systems are considered by treating fractional orders as additional parameters. The parameter estimation is transformed into a multidimensional optimization problem, and an effective modified artificial bee colony algorithm is proposed to solve this problem. Numerical simulations are conducted on two typical fractional-order chaotic systems to show the effectiveness of the proposed scheme. Full article
(This article belongs to the Special Issue Recent Advances in Chaos Theory and Complex Networks)
Open AccessArticle Thermodynamic Analysis about Nucleation and Growth of Cubic Boron Nitride Crystals in the hBN-Li3N System under High Pressure and High Temperature
Entropy 2015, 17(2), 755-762; doi:10.3390/e17020755
Received: 21 November 2014 / Accepted: 3 February 2015 / Published: 9 February 2015
Cited by 1 | PDF Full-text (1469 KB) | HTML Full-text | XML Full-text
Abstract
The nucleation of cubic boron nitride (cBN) single crystals synthesized with lithium nitride (Li3N) as a catalyst under high pressure and high temperature (HPHT) was analyzed. Many nanometer-sized cubic boron nitride nuclei formed in the near surface layer, as detected by
[...] Read more.
The nucleation of cubic boron nitride (cBN) single crystals synthesized with lithium nitride (Li3N) as a catalyst under high pressure and high temperature (HPHT) was analyzed. Many nanometer-sized cubic boron nitride nuclei formed in the near surface layer, as detected by high resolution transmission electron microscopy. Based on the experiment results, the transformation kinetics is described by a nucleation and growth process in the thermodynamic stability region of cBN. A theoretical description is developed based on the heterogeneous nucleation and layer growth mechanism, and the relevant parameters are estimated and discussed. The critical crystal radius, r*, increases with the temperature under constant pressure; the change with temperature more pronounced at lower pressure (such as 4.5 GPa). The crystal growth velocity increased with the temperature, and it is parabolic with temperature under certain pressure. These results are consistent with experimental data. Full article
Open AccessArticle Fokker-Planck Equation and Thermodynamic System Analysis
Entropy 2015, 17(2), 763-771; doi:10.3390/e17020763
Received: 23 November 2014 / Revised: 12 January 2015 / Accepted: 5 February 2015 / Published: 9 February 2015
Cited by 2 | PDF Full-text (687 KB) | HTML Full-text | XML Full-text
Abstract
The non-linear Fokker-Planck equation or Kolmogorov forward equation is currently successfully applied for deep analysis of irreversibility and it gives an excellent approximation near the free energy minimum, just as Boltzmann’s definition of entropy follows from finding the maximum entropy state. A connection
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The non-linear Fokker-Planck equation or Kolmogorov forward equation is currently successfully applied for deep analysis of irreversibility and it gives an excellent approximation near the free energy minimum, just as Boltzmann’s definition of entropy follows from finding the maximum entropy state. A connection to Fokker-Planck dynamics and the free energy functional is presented and discussed—this approach has been particularly successful to deal with metastability. We focus our attention on investigating and discussing the fundamental role of dissipation analysis in metastable systems. The major novelty of our approach is that the obtained results enable us to reveal an appealing, and previously unexplored relationship between Fokker-Planck equation and the associated free energy functional. Namely, we point out that the dynamics may be regarded as a gradient flux, or a steepest descent, for the free energy. Full article
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
Open AccessArticle Quantropy
Entropy 2015, 17(2), 772-789; doi:10.3390/e17020772
Received: 17 December 2014 / Accepted: 30 January 2015 / Published: 9 February 2015
Cited by 3 | PDF Full-text (225 KB) | HTML Full-text | XML Full-text
Abstract
There is a well-known analogy between statistical and quantum mechanics. In statistical mechanics, Boltzmann realized that the probability for a system in thermal equilibrium to occupy a given state is proportional to \(\exp(-E/kT)\), where \(E\) is the energy of that state. In quantum
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There is a well-known analogy between statistical and quantum mechanics. In statistical mechanics, Boltzmann realized that the probability for a system in thermal equilibrium to occupy a given state is proportional to \(\exp(-E/kT)\), where \(E\) is the energy of that state. In quantum mechanics, Feynman realized that the amplitude for a system to undergo a given history is proportional to \(\exp(-S/i\hbar)\), where \(S\) is the action of that history. In statistical mechanics, we can recover Boltzmann's formula by maximizing entropy subject to a constraint on the expected energy. This raises the question: what is the quantum mechanical analogue of entropy? We give a formula for this quantity, which we call ``quantropy''. We recover Feynman's formula from assuming that histories have complex amplitudes, that these amplitudes sum to one and that the amplitudes give a stationary point of quantropy subject to a constraint on the expected action. Alternatively, we can assume the amplitudes sum to one and that they give a stationary point of a quantity that we call ``free action'', which is analogous to free energy in statistical mechanics. We compute the quantropy, expected action and free action for a free particle and draw some conclusions from the results. Full article
(This article belongs to the Section Quantum Information)
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Open AccessArticle Distributed Extreme Learning Machine for Nonlinear Learning over Network
Entropy 2015, 17(2), 818-840; doi:10.3390/e17020818
Received: 26 December 2014 / Revised: 20 January 2015 / Accepted: 6 February 2015 / Published: 12 February 2015
Cited by 2 | PDF Full-text (419 KB) | HTML Full-text | XML Full-text
Abstract
Distributed data collection and analysis over a network are ubiquitous, especially over a wireless sensor network (WSN). To our knowledge, the data model used in most of the distributed algorithms is linear. However, in real applications, the linearity of systems is not always
[...] Read more.
Distributed data collection and analysis over a network are ubiquitous, especially over a wireless sensor network (WSN). To our knowledge, the data model used in most of the distributed algorithms is linear. However, in real applications, the linearity of systems is not always guaranteed. In nonlinear cases, the single hidden layer feedforward neural network (SLFN) with radial basis function (RBF) hidden neurons has the ability to approximate any continuous functions and, thus, may be used as the nonlinear learning system. However, confined by the communication cost, using the distributed version of the conventional algorithms to train the neural network directly is usually prohibited. Fortunately, based on the theorems provided in the extreme learning machine (ELM) literature, we only need to compute the output weights of the SLFN. Computing the output weights itself is a linear learning problem, although the input-output mapping of the overall SLFN is still nonlinear. Using the distributed algorithmto cooperatively compute the output weights of the SLFN, we obtain a distributed extreme learning machine (dELM) for nonlinear learning in this paper. This dELM is applied to the regression problem and classification problem to demonstrate its effectiveness and advantages. Full article
(This article belongs to the Special Issue Recent Advances in Chaos Theory and Complex Networks)
Open AccessArticle Probabilistic Three-Party Sharing of Operation on a Remote Qubit
Entropy 2015, 17(2), 841-851; doi:10.3390/e17020841
Received: 29 October 2014 / Revised: 24 December 2014 / Accepted: 27 January 2015 / Published: 12 February 2015
Cited by 5 | PDF Full-text (196 KB) | HTML Full-text | XML Full-text
Abstract
A probabilistic tripartite single-qubit operation sharing scheme is put forward by utilizing a two-qubit and a three-qubit non-maximally entangled state as quantum channels. Some specific comparisons between our scheme and another probabilistic scheme are made. It is found that, if the product of
[...] Read more.
A probabilistic tripartite single-qubit operation sharing scheme is put forward by utilizing a two-qubit and a three-qubit non-maximally entangled state as quantum channels. Some specific comparisons between our scheme and another probabilistic scheme are made. It is found that, if the product of the two minimal coefficients characterizing channel entanglements is greater than 3/16, our scheme is more superior than the other one. Nonetheless, the price is that more classical and quantum resources are consumed, and the operation difficulty is rather increased. Moreover, some important features of the scheme, such as its security, probability and sharer symmetry, are revealed through concrete discussions. Additionally, the experimental feasibility of our scheme is analyzed and subsequently confirmed according to the current experimental techniques. Full article
(This article belongs to the Special Issue Quantum Computation and Information: Multi-Particle Aspects)
Open AccessArticle Relational Probabilistic Conditionals and Their Instantiations under Maximum Entropy Semantics for First-Order Knowledge Bases
Entropy 2015, 17(2), 852-865; doi:10.3390/e17020852
Received: 26 December 2014 / Revised: 29 January 2015 / Accepted: 9 February 2015 / Published: 13 February 2015
Cited by 4 | PDF Full-text (304 KB) | HTML Full-text | XML Full-text
Abstract
For conditional probabilistic knowledge bases with conditionals based on propositional logic, the principle of maximum entropy (ME) is well-established, determining a unique model inductively completing the explicitly given knowledge. On the other hand, there is no general agreement on how to extend the
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For conditional probabilistic knowledge bases with conditionals based on propositional logic, the principle of maximum entropy (ME) is well-established, determining a unique model inductively completing the explicitly given knowledge. On the other hand, there is no general agreement on how to extend the ME principle to relational conditionals containing free variables. In this paper, we focus on two approaches to ME semantics that have been developed for first-order knowledge bases: aggregating semantics and a grounding semantics. Since they use different variants of conditionals, we define the logic PCI, which covers both approaches as special cases and provides a framework where the effects of both approaches can be studied in detail. While the ME models under PCI-grounding and PCI-aggregating semantics are different in general, we point out that parametric uniformity of a knowledge base ensures that both semantics coincide. Using some concrete knowledge bases, we illustrate the differences and common features of both approaches, looking in particular at the ground instances of the given conditionals. Full article
(This article belongs to the Special Issue Maximum Entropy Applied to Inductive Logic and Reasoning)
Open AccessArticle Optimal Design of Magnetohydrodynamic Mixed Convection Flow in a Vertical Channel with Slip Boundary Conditions and Thermal Radiation Effects by Using an Entropy Generation Minimization Method
Entropy 2015, 17(2), 866-881; doi:10.3390/e17020866
Received: 18 November 2014 / Revised: 29 December 2014 / Accepted: 5 February 2015 / Published: 13 February 2015
Cited by 14 | PDF Full-text (799 KB) | HTML Full-text | XML Full-text
Abstract
Investigation of the effect of thermal radiation on a fully developed magnetohydrodynamic (MHD) convective flow of a Newtonian, incompressible and electrically conducting fluid in a vertical microchannel bounded by two infinite vertical parallel plates with constant temperature walls through a lateral magnetic field
[...] Read more.
Investigation of the effect of thermal radiation on a fully developed magnetohydrodynamic (MHD) convective flow of a Newtonian, incompressible and electrically conducting fluid in a vertical microchannel bounded by two infinite vertical parallel plates with constant temperature walls through a lateral magnetic field of uniform strength is presented. The Rosseland model for the conduction radiation heat transfer in an absorbing medium and two plates with slip-flow and no-slip conditions are assumed. In addition, the induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The non-dimensional governing equations are solved numerically using Runge–Kutta–Fehlberg method with a shooting technique. The channel is optimized based on the Second Law of Thermodynamics by changing various parameters such as the thermal radiation parameter, the temperature parameter, Hartmann number, Grashof to Reynolds ratio, velocity slip length, and temperature jump. Full article
(This article belongs to the Section Thermodynamics)
Open AccessArticle On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem
Entropy 2015, 17(2), 885-902; doi:10.3390/e17020885
Received: 24 November 2014 / Revised: 15 January 2015 / Accepted: 15 January 2015 / Published: 16 February 2015
Cited by 24 | PDF Full-text (251 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of
[...] Read more.
In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method. Full article
(This article belongs to the Special Issue Dynamical Equations and Causal Structures from Observations)
Open AccessCommunication Thermophysical Characteristics of the Ferrofluid in a Vertical Rectangle
Entropy 2015, 17(2), 903-913; doi:10.3390/e17020903
Received: 7 November 2014 / Revised: 10 February 2015 / Accepted: 13 February 2015 / Published: 16 February 2015
Cited by 4 | PDF Full-text (923 KB) | HTML Full-text | XML Full-text
Abstract
The article aimed to analytically investigate the thermophysical behaviors of a ferrofluid in a vertical rectangle with the variation of intensity of the magnetic field, viscosity of the ferrofluid and boundary conditions. The governing equations of the ferrofluid include the continuity, momentum and
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The article aimed to analytically investigate the thermophysical behaviors of a ferrofluid in a vertical rectangle with the variation of intensity of the magnetic field, viscosity of the ferrofluid and boundary conditions. The governing equations of the ferrofluid include the continuity, momentum and energy equations for describing the thermal-fluidic behaviors of the ferrofluid and the Maxwell equation and magnetization equation are also added to consider rotating effect of the nano-sized particles. The flow behavior and heat transfer characteristics of the ferrofluid with the intensity of the magnetic field, viscosities of the ferrofluid and boundary conditions were analyzed through isotherms, velocity profiles and both mean and local Nusselt numbers. As a result, the isotherms of the ferrofluid in the vertical rectangle increased with the increase of the magnetic volume fractions and magnetic field intensities. In addition, the mean Nusselt numbers increased with the increase of magnetite volume fractions at all magnetic field intensities because of the combined effects of both heat conduction by magnetite and the magnetic volume force. Full article
(This article belongs to the Section Thermodynamics)

Review

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Open AccessReview On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies
Entropy 2015, 17(2), 710-754; doi:10.3390/e17020710
Received: 2 December 2013 / Revised: 2 December 2013 / Accepted: 27 January 2015 / Published: 5 February 2015
Cited by 3 | PDF Full-text (580 KB) | HTML Full-text | XML Full-text
Abstract
We review the concept of nonequilibrium thermodynamic entropy and observables and internal variables as state variables, introduced recently by us, and provide a simple first principle derivation of additive statistical entropy, applicable to all nonequilibrium states by treating thermodynamics as an experimental science.
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We review the concept of nonequilibrium thermodynamic entropy and observables and internal variables as state variables, introduced recently by us, and provide a simple first principle derivation of additive statistical entropy, applicable to all nonequilibrium states by treating thermodynamics as an experimental science. We establish their numerical equivalence in several cases, which includes the most important case when the thermodynamic entropy is a state function. We discuss various interesting aspects of the two entropies and show that the number of microstates in the Boltzmann entropy includes all possible microstates of non-zero probabilities even if the system is trapped in a disjoint component of the microstate space. We show that negative thermodynamic entropy can appear from nonnegative statistical entropy. Full article
(This article belongs to the Special Issue Advances in Methods and Foundations of Non-Equilibrium Thermodynamics)
Open AccessReview Factorization and Criticality in the Anisotropic XY Chain via Correlations
Entropy 2015, 17(2), 790-817; doi:10.3390/e17020790
Received: 29 December 2014 / Accepted: 30 January 2015 / Published: 9 February 2015
Cited by 17 | PDF Full-text (754 KB) | HTML Full-text | XML Full-text
Abstract
In this review, we discuss the zero and finite temperature behavior of various bipartite quantum and total correlation measures, the skew information-based quantum coherence and the local quantum uncertainty in the thermal ground state of the one-dimensional anisotropic XY model in a transverse
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In this review, we discuss the zero and finite temperature behavior of various bipartite quantum and total correlation measures, the skew information-based quantum coherence and the local quantum uncertainty in the thermal ground state of the one-dimensional anisotropic XY model in a transverse magnetic field. We compare the ability of the considered measures to correctly detect or estimate the quantum critical point and the non-trivial factorization point possessed by the spin chain. Full article
(This article belongs to the Special Issue Entanglement Entropy)
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