Entropy
http://www.mdpi.com/journal/entropy
Latest open access articles published in Entropy at http://www.mdpi.com/journal/entropy<![CDATA[Entropy, Vol. 17, Pages 7827-7847: Theoretical Search for RNA Folding Nuclei]]>
http://www.mdpi.com/1099-4300/17/11/7827
The functions of RNA molecules are defined by their spatial structure, whose folding is regulated by numerous factors making RNA very similar to proteins. Prediction of RNA folding nuclei gives the possibility to take a fresh look at the problems of the multiple folding pathways of RNA molecules and RNA stability. The algorithm previously developed for prediction of protein folding nuclei has been successfully applied to ~150 various RNA structures: hairpins, tRNAs, structures with pseudoknots, and the large structured P4-P6 domain of the Tetrahymena group I intron RNA. The calculated Φ-values for tRNA structures agree with the experimental data obtained earlier. According to the experiment the nucleotides of the D and T hairpin loops are the last to be involved in the tRNA tertiary structure. Such agreement allowed us to do a prediction for an example of large structured RNA, the P4-P6 RNA domain. One of the advantages of our method is that it allows us to make predictions about the folding nucleus for nontrivial RNA motifs: pseudoknots and tRNA.Entropy2015-11-231711Article10.3390/e17117827782778471099-43002015-11-23doi: 10.3390/e17117827Leonid PereyaslavetsOxana Galzitskaya<![CDATA[Entropy, Vol. 17, Pages 7811-7826: Thermodynamics Analysis of Variable Viscosity Hydromagnetic Couette Flow in a Rotating System with Hall Effects]]>
http://www.mdpi.com/1099-4300/17/11/7811
In this paper, we employed both first and second laws of thermodynamics to analyze the flow and thermal decomposition in a variable viscosity Couette flow of a conducting fluid in a rotating system under the combined influence of magnetic field and Hall current. The non-linear governing differential equations are obtained and solved numerically using shooting method coupled with fourth order Runge–Kutta–Fehlberg integration technique. Numerical results obtained for velocities and temperature profiles are utilized to determine the entropy generation rate, skin fictions, Nusselt number and the Bejan number. By plotting the graphs of various values of thermophysical parameters, the features of the flow characteristics are analyzed in detail. It is found that fluid rotation increases the dominant effect of heat transfer irreversibility at the upper moving plate region while the entropy production is more at the lower fixed plate region.Entropy2015-11-201711Article10.3390/e17117811781178261099-43002015-11-20doi: 10.3390/e17117811Oluwole MakindeAdetayo EegunjobiM. Tshehla<![CDATA[Entropy, Vol. 17, Pages 7798-7810: Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis]]>
http://www.mdpi.com/1099-4300/17/11/7798
We study the correlation properties of word lengths in large texts from 30 ebooks in the English language from the Gutenberg Project (www.gutenberg.org) using the natural visibility graph method (NVG). NVG converts a time series into a graph and then analyzes its graph properties. First, the original sequence of words is transformed into a sequence of values containing the length of each word, and then, it is integrated. Next, we apply the NVG to the integrated word-length series and construct the network. We show that the degree distribution of that network follows a power law, P ( k ) ∼ k - γ , with two regimes, which are characterized by the exponents γ s ≈ 1 . 7 (at short degree scales) and γ l ≈ 1 . 3 (at large degree scales). This suggests that word lengths are much more strongly correlated at large distances between words than at short distances between words. That finding is also supported by the detrended fluctuation analysis (DFA) and recurrence time distribution. These results provide new information about the universal characteristics of the structure of written texts beyond that given by word frequencies.Entropy2015-11-201711Article10.3390/e17117798779878101099-43002015-11-20doi: 10.3390/e17117798Lev Guzmán-VargasBibiana Obregón-QuintanaDaniel Aguilar-VelázquezRicardo Hernández-PérezLarry Liebovitch<![CDATA[Entropy, Vol. 17, Pages 7786-7797: The Second Law Today: Using Maximum-Minimum Entropy Generation]]>
http://www.mdpi.com/1099-4300/17/11/7786
There are a great number of thermodynamic schools, independent of each other, and without a powerful general approach, but with a split on non-equilibrium thermodynamics. In 1912, in relation to the stationary non-equilibrium states, Ehrenfest introduced the fundamental question on the existence of a functional that achieves its extreme value for stable states, as entropy does for the stationary states in equilibrium thermodynamics. Today, the new branch frontiers of science and engineering, from power engineering to environmental sciences, from chaos to complex systems, from life sciences to nanosciences, etc. require a unified approach in order to optimize results and obtain a powerful approach to non-equilibrium thermodynamics and open systems. In this paper, a generalization of the Gouy–Stodola approach is suggested as a possible answer to the Ehrenfest question.Entropy2015-11-201711Article10.3390/e17117786778677971099-43002015-11-20doi: 10.3390/e17117786Umberto LuciaGiuseppe Grazzini<![CDATA[Entropy, Vol. 17, Pages 7768-7785: A Refined Multiscale Self-Entropy Approach for the Assessment of Cardiac Control Complexity: Application to Long QT Syndrome Type 1 Patients]]>
http://www.mdpi.com/1099-4300/17/11/7768
The study proposes the contemporaneous assessment of conditional entropy (CE) and self-entropy (sE), being the two terms of the Shannon entropy (ShE) decomposition, as a function of the time scale via refined multiscale CE (RMSCE) and sE (RMSsE) with the aim at gaining insight into cardiac control in long QT syndrome type 1 (LQT1) patients featuring the KCNQ1-A341V mutation. CE was estimated via the corrected CE (CCE) and sE as the difference between the ShE and CCE. RMSCE and RMSsE were computed over the beat-to-beat series of heart period (HP) and QT interval derived from 24-hour Holter electrocardiographic recordings during daytime (DAY) and nighttime (NIGHT). LQT1 patients were subdivided into asymptomatic and symptomatic mutation carriers (AMCs and SMCs) according to the severity of symptoms and contrasted with non-mutation carriers (NMCs). We found that RMSCE and RMSsE carry non-redundant information, separate experimental conditions (i.e., DAY and NIGHT) within a given group and distinguish groups (i.e., NMC, AMC and SMC) assigned the experimental condition. Findings stress the importance of the joint evaluation of RMSCE and RMSsE over HP and QT variabilities to typify the state of the autonomic function and contribute to clarify differences between AMCs and SMCs.Entropy2015-11-191711Article10.3390/e17117768776877851099-43002015-11-19doi: 10.3390/e17117768Vlasta BariGiulia GirardengoAndrea MarchiBeatrice De MariaPaul BrinkLia CrottiPeter SchwartzAlberto Porta<![CDATA[Entropy, Vol. 17, Pages 7752-7767: Disentangling the Quantum World]]>
http://www.mdpi.com/1099-4300/17/11/7752
Correlations related to quantum entanglement have convinced many physicists that there must be some at-a-distance connection between separated events, at the quantum level. In the late 1940s, however, O. Costa de Beauregard proposed that such correlations can be explained without action at a distance, so long as the influence takes a zigzag path, via the intersecting past lightcones of the events in question. Costa de Beauregard’s proposal is related to what has come to be called the retrocausal loophole in Bell’s Theorem, but—like that loophole—it receives little attention, and remains poorly understood. Here we propose a new way to explain and motivate the idea. We exploit some simple symmetries to show how Costa de Beauregard’s zigzag needs to work, to explain the correlations at the core of Bell’s Theorem. As a bonus, the explanation shows how entanglement might be a much simpler matter than the orthodox view assumes—not a puzzling feature of quantum reality itself, but an entirely unpuzzling feature of our knowledge of reality, once zigzags are in play.Entropy2015-11-161711Article10.3390/e17117752775277671099-43002015-11-16doi: 10.3390/e17117752Huw PriceKen Wharton<![CDATA[Entropy, Vol. 17, Pages 7736-7751: Payoffs and Coherence of a Quantum Two-Player Game in a Thermal Environment]]>
http://www.mdpi.com/1099-4300/17/11/7736
A two-player quantum game is considered in the presence of a thermal decoherence modeled in terms of a rigorous Davies approach. It is shown how the energy dissipation and pure decoherence affect the payoffs of the players of the (quantum version) of prisoner dilemma. The impact of the thermal environment on a coherence of game, as a quantum system, is also presented.Entropy2015-11-131711Article10.3390/e17117736773677511099-43002015-11-13doi: 10.3390/e17117736Jerzy DajkaMarcin ŁobejkoJan Sładkowski<![CDATA[Entropy, Vol. 17, Pages 7713-7735: From Lattice Boltzmann Method to Lattice Boltzmann Flux Solver]]>
http://www.mdpi.com/1099-4300/17/11/7713
Based on the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS), which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann solvers, was proposed recently. Specifically, LBFS applies the finite volume method to solve the macroscopic governing equations which provide solutions for macroscopic flow variables at cell centers. In the meantime, numerical fluxes at each cell interface are evaluated by local reconstruction of LBM solution. In other words, in LBFS, LBM is only locally applied at the cell interface for one streaming step. This is quite different from the conventional LBM, which is globally applied in the whole flow domain. This paper shows three different versions of LBFS respectively for isothermal, thermal and compressible flows and their relationships with the standard LBM. In particular, the performance of isothermal LBFS in terms of accuracy, efficiency and stability is investigated by comparing it with the standard LBM. The thermal LBFS is simplified by using the D2Q4 lattice velocity model and its performance is examined by its application to simulate natural convection with high Rayleigh numbers. It is demonstrated that the compressible LBFS can be effectively used to simulate both inviscid and viscous flows by incorporating non-equilibrium effects into the process for inviscid flux reconstruction. Several numerical examples, including lid-driven cavity flow, natural convection in a square cavity at Rayleigh numbers of 107 and 108 and transonic flow around a staggered-biplane configuration, are tested on structured or unstructured grids to examine the performance of three LBFS versions. Good agreements have been achieved with the published data, which validates the capability of LBFS in simulating a variety of flow problems.Entropy2015-11-131711Article10.3390/e17117713771377351099-43002015-11-13doi: 10.3390/e17117713Yan WangLiming YangChang Shu<![CDATA[Entropy, Vol. 17, Pages 7698-7712: A Novel Method for PD Feature Extraction of Power Cable with Renyi Entropy]]>
http://www.mdpi.com/1099-4300/17/11/7698
Partial discharge (PD) detection can effectively achieve the status maintenance of XLPE (Cross Linked Polyethylene) cable, so it is the direction of the development of equipment maintenance in power systems. At present, a main method of PD detection is the broadband electromagnetic coupling with a high-frequency current transformer (HFCT). Due to the strong electromagnetic interference (EMI) generated among the mass amount of cables in a tunnel and the impedance mismatching of HFCT and the data acquisition equipment, the features of the pulse current generated by PD are often submerged in the background noise. The conventional method for the stationary signal analysis cannot analyze the PD signal, which is transient and non-stationary. Although the algorithm of Shannon wavelet singular entropy (SWSE) can be used to analyze the PD signal at some level, its precision and anti-interference capability of PD feature extraction are still insufficient. For the above problem, a novel method named Renyi wavelet packet singular entropy (RWPSE) is proposed and applied to the PD feature extraction on power cables. Taking a three-level system as an example, we analyze the statistical properties of Renyi entropy and the intrinsic correlation with Shannon entropy under different values of α . At the same time, discrete wavelet packet transform (DWPT) is taken instead of discrete wavelet transform (DWT), and Renyi entropy is combined to construct the RWPSE algorithm. Taking the grounding current signal from the shielding layer of XLPE cable as the research object, which includes the current pulse feature of PD, the effectiveness of the novel method is tested. The theoretical analysis and experimental results show that compared to SWSE, RWPSE can not only improve the feature extraction accuracy for PD, but also can suppress EMI effectively.Entropy2015-11-131711Article10.3390/e17117698769877121099-43002015-11-13doi: 10.3390/e17117698Jikai ChenYanhui DouZhenhao WangGuoqing Li<![CDATA[Entropy, Vol. 17, Pages 7680-7697: Using Expectation Maximization and Resource Overlap Techniques to Classify Species According to Their Niche Similarities in Mutualistic Networks]]>
http://www.mdpi.com/1099-4300/17/11/7680
Mutualistic networks in nature are widespread and play a key role in generating the diversity of life on Earth. They constitute an interdisciplinary field where physicists, biologists and computer scientists work together. Plant-pollinator mutualisms in particular form complex networks of interdependence between often hundreds of species. Understanding the architecture of these networks is of paramount importance for assessing the robustness of the corresponding communities to global change and management strategies. Advances in this problem are currently limited mainly due to the lack of methodological tools to deal with the intrinsic complexity of mutualisms, as well as the scarcity and incompleteness of available empirical data. One way to uncover the structure underlying complex networks is to employ information theoretical statistical inference methods, such as the expectation maximization (EM) algorithm. In particular, such an approach can be used to cluster the nodes of a network based on the similarity of their node neighborhoods. Here, we show how to connect network theory with the classical ecological niche theory for mutualistic plant-pollinator webs by using the EM algorithm. We apply EM to classify the nodes of an extensive collection of mutualistic plant-pollinator networks according to their connection similarity. We find that EM recovers largely the same clustering of the species as an alternative recently proposed method based on resource overlap, where one considers each party as a consuming resource for the other party (plants providing food to animals, while animals assist the reproduction of plants). Furthermore, using the EM algorithm, we can obtain a sequence of successfully-refined classifications that enables us to identify the fine-structure of the ecological network and understand better the niche distribution both for plants and animals. This is an example of how information theoretical methods help to systematize and unify work in ecology.Entropy2015-11-121711Article10.3390/e17117680768076971099-43002015-11-12doi: 10.3390/e17117680Hugo FortMuhittin Mungan<![CDATA[Entropy, Vol. 17, Pages 7658-7679: Neighborhood Approximations for Non-Linear Voter Models]]>
http://www.mdpi.com/1099-4300/17/11/7658
Non-linear voter models assume that the opinion of an agent depends on the opinions of its neighbors in a non-linear manner. This allows for voting rules different from majority voting. While the linear voter model is known to reach consensus, non-linear voter models can result in the coexistence of opposite opinions. Our aim is to derive approximations to correctly predict the time dependent dynamics, or at least the asymptotic outcome, of such local interactions. Emphasis is on a probabilistic approach to decompose the opinion distribution in a second-order neighborhood into lower-order probability distributions. This is compared with an analytic pair approximation for the expected value of the global fraction of opinions and a mean-field approximation. Our reference case is averaged stochastic simulations of a one-dimensional cellular automaton. We find that the probabilistic second-order approach captures the dynamics of the reference case very well for different non-linearities, i.e., for both majority and minority voting rules, which only partly holds for the first-order pair approximation and not at all for the mean-field approximation. We further discuss the interesting phenomenon of a correlated coexistence, characterized by the formation of large domains of opinions that dominate for some time, but slowly change.Entropy2015-11-101711Article10.3390/e17117658765876791099-43002015-11-10doi: 10.3390/e17117658Frank SchweitzerLaxmidhar Behera<![CDATA[Entropy, Vol. 17, Pages 7645-7657: Quantum Game Beats Classical Odds—Thermodynamics Implications]]>
http://www.mdpi.com/1099-4300/17/11/7645
A quantum game is described making use of coins embodied as entangled Fermions in a potential energy well. It is shown that the odds are affected by the Pauli Exclusion Principle. They depend on the elevation in the energy well where the coins are selected, ranging from being a certainty of winning at the bottom of the well to being near classical at the top. These odds differ markedly from those in a classical game in which they are independent of elevation. The thermodynamics counterpart of the quantum game is discussed. It is shown that the temperature of a Maxwellian gas column in a potential energy gradient is independent of elevation. However, the temperature of a Fermion gas is shown to drop with elevation. The game and the gas column utilize the same components. When Fermions are used, a shifting of odds is produced in the game and a shifting of kinetic energy is produced in the thermodynamic experiment, leading to a spontaneous temperature gradient.Entropy2015-11-091711Article10.3390/e17117645764576571099-43002015-11-09doi: 10.3390/e17117645George Levy<![CDATA[Entropy, Vol. 17, Pages 7628-7644: A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization]]>
http://www.mdpi.com/1099-4300/17/11/7628
The aim of this paper is to introduce and investigate a novel complex Lorenz system with a flux-controlled memristor, and to realize its synchronization. The system has an infinite number of stable and unstable equilibrium points, and can generate abundant dynamical behaviors with different parameters and initial conditions, such as limit cycle, torus, chaos, transient phenomena, etc., which are explored by means of time-domain waveforms, phase portraits, bifurcation diagrams, and Lyapunov exponents. Furthermore, an active controller is designed to achieve modified projective synchronization (MPS) of this system based on Lyapunov stability theory. The corresponding numerical simulations agree well with the theoretical analysis, and demonstrate that the response system is asymptotically synchronized with the drive system within a short time.Entropy2015-11-051711Article10.3390/e17117628762876441099-43002015-11-05doi: 10.3390/e17117628Shibing WangXingyuan WangYufei Zhou<![CDATA[Entropy, Vol. 17, Pages 7608-7627: Multi-Scale Entropy Analysis of Body Sway for Investigating Balance Ability During Exergame Play Under Different Parameter Settings]]>
http://www.mdpi.com/1099-4300/17/11/7608
The goal of this study was to investigate the parameters affecting exergame performance using multi-scale entropy analysis, with the aim of informing the design of exergames for personalized balance training. Test subjects’ center of pressure (COP) displacement data were recorded during exergame play to examine their balance ability at varying difficulty levels of a balance-based exergame; the results of a multi-scale entropy-based analysis were then compared to traditional COP indicators. For games involving static posture frames, variation in posture frame travel time was found to significantly affect the complexity of both the anterior-posterior (MSE-AP) and medio-lateral (MSE-ML) components of balancing movements. However, in games involving dynamic posture frames, only MSE-AP was found to be sensitive to the variation of parameters, namely foot-lifting speed. Findings were comparable to the COP data published by Sun et al., indicating that the use of complexity data is a feasible means of distinguishing between different parameter sets and of understanding how human design considerations must be taken into account in exergame development. Not only can this method be used as another assessment index in the future, it can also be used in the optimization of parameters within the virtual environments of exergames.Entropy2015-11-041711Article10.3390/e17117608760876271099-43002015-11-04doi: 10.3390/e17117608Chia-Hsuan LeeTien-Lung Sun<![CDATA[Entropy, Vol. 17, Pages 7596-7607: Single to Two Cluster State Transition of Primary Motor Cortex 4-posterior (MI-4p) Activities in Humans]]>
http://www.mdpi.com/1099-4300/17/11/7596
The human primary motor cortex has dual representation of the digits, namely, area 4 anterior (MI-4a) and area 4 posterior (MI-4p). We have previously demonstrated that activation of these two functional subunits can be identified independently by functional magnetic resonance imaging (fMRI) using independent component-cross correlation-sequential epoch (ICS) analysis. Subsequent studies in patients with hemiparesis due to subcortical lesions and monoparesis due to peripheral nerve injury demonstrated that MI-4p represents the initiation area of activation, whereas MI-4a is the secondarily activated motor cortex requiring a “long-loop” feedback input from secondary motor systems, likely the cerebellum. A dynamic model of hand motion based on the limit cycle oscillator predicts that the specific pattern of entrainment of neural firing may occur by applying appropriate periodic stimuli. Under normal conditions, such entrainment introduces a single phase-cluster. Under pathological conditions where entrainment stimuli have insufficient strength, the phase cluster splits into two clusters. Observable physiological phenomena of this shift from single cluster to two clusters are: doubling of firing rate of output neurons; or decay in group firing density of the system due to dampening of odd harmonics components. While the former is not testable in humans, the latter can be tested by appropriately designed fMRI experiments, the quantitative index of which is believed to reflect group behavior of neurons functionally localized, e.g., firing density in the dynamic theory. Accordingly, we performed dynamic analysis of MI-4p activation in normal volunteers and paretic patients. The results clearly indicated that MI-4p exhibits a transition from a single to a two phase-cluster state which coincided with loss of MI-4a activation. The study demonstrated that motor dysfunction (hemiparesis) in patients with a subcortical infarct is not simply due to afferent fiber disruption. Maintaining proper afferent signals from MI-4p requires proper functionality of MI-4a and, hence, appropriate feedback signals from the secondary motor system.Entropy2015-11-031711Article10.3390/e17117596759676071099-43002015-11-03doi: 10.3390/e17117596Kazunori NakadaKiyotaka SuzukiTsutomu Nakada<![CDATA[Entropy, Vol. 17, Pages 7584-7595: Choice Overload and Height Ranking of Menus in Partially-Ordered Sets]]>
http://www.mdpi.com/1099-4300/17/11/7584
When agents face incomplete information and their knowledge about the objects of choice is vague and imprecise, they tend to consider fewer choices and to process a smaller portion of the available information regarding their choices. This phenomenon is well-known as choice overload and is strictly related to the existence of a considerable amount of option-pairs that are not easily comparable. Thus, we use a finite partially-ordered set (poset) to model the subset of easily-comparable pairs within a set of options/items. The height ranking, a new ranking rule for menus, namely subposets of a finite poset, is then introduced and characterized. The height ranking rule ranks subsets of options in terms of the size of the longest chain that they include and is therefore meant to assess menus of available options in terms of the maximum number of distinct and easily-comparable alternative options that they offer.Entropy2015-10-301711Article10.3390/e17117584758475951099-43002015-10-30doi: 10.3390/e17117584Marcello BasiliStefano Vannucci<![CDATA[Entropy, Vol. 17, Pages 7567-7583: Minimum Dissipation Principle in Nonlinear Transport]]>
http://www.mdpi.com/1099-4300/17/11/7567
We extend Onsager’s minimum dissipation principle to stationary states that are only subject to local equilibrium constraints, even when the transport coefficients depend on the thermodynamic forces. Crucial to this generalization is a decomposition of the thermodynamic forces into those that are held fixed by the boundary conditions and the subspace that is orthogonal with respect to the metric defined by the transport coefficients. We are then able to apply Onsager and Machlup’s proof to the second set of forces. As an example, we consider two-dimensional nonlinear diffusion coupled to two reservoirs at different temperatures. Our extension differs from that of Bertini et al. in that we assume microscopic irreversibility, and we allow a nonlinear dependence of the fluxes on the forces.Entropy2015-10-301711Article10.3390/e17117567756775831099-43002015-10-30doi: 10.3390/e17117567Giorgio SonninoJarah EvslinAlberto Sonnino<![CDATA[Entropy, Vol. 17, Pages 7530-7566: Entropy Generation of Desalination Powered by Variable Temperature Waste Heat]]>
http://www.mdpi.com/1099-4300/17/11/7530
Powering desalination by waste heat is often proposed to mitigate energy consumption and environmental impact; however, thorough technology comparisons are lacking in the literature. This work numerically models the efficiency of six representative desalination technologies powered by waste heat at 50, 70, 90, and 120 °C, where applicable. Entropy generation and Second Law efficiency analysis are applied for the systems and their components. The technologies considered are thermal desalination by multistage flash (MSF), multiple effect distillation (MED), multistage vacuum membrane distillation (MSVMD), humidification-dehumidification (HDH), and organic Rankine cycles (ORCs) paired with mechanical technologies of reverse osmosis (RO) and mechanical vapor compression (MVC). The most efficient technology was RO, followed by MED. Performances among MSF, MSVMD, and MVC were similar but the relative performance varied with waste heat temperature or system size. Entropy generation in thermal technologies increases at lower waste heat temperatures largely in the feed or brine portions of the various heat exchangers used. This occurs largely because lower temperatures reduce recovery, increasing the relative flow rates of feed and brine. However, HDH (without extractions) had the reverse trend, only being competitive at lower temperatures. For the mechanical technologies, the energy efficiency only varies with temperature because of the significant losses from the ORC.Entropy2015-10-301711Article10.3390/e17117530753075661099-43002015-10-30doi: 10.3390/e17117530David WarsingerKaran MistryKishor NayarHyung ChungJohn Lienhard V<![CDATA[Entropy, Vol. 17, Pages 7522-7529: A Truncation Scheme for the BBGKY2 Equation]]>
http://www.mdpi.com/1099-4300/17/11/7522
In recent years, the maximum entropy principle has been applied to a wide range of different fields, often successfully. While these works are usually focussed on cross-disciplinary applications, the point of this letter is instead to reconsider a fundamental point of kinetic theory. Namely, we shall re-examine the Stosszahlansatz leading to the irreversible Boltzmann equation at the light of the MaxEnt principle. We assert that this way of thinking allows to move one step further than the factorization hypothesis and provides a coherent—though implicit—closure scheme for the two-particle distribution function. Such higher-order dependences are believed to open the way to a deeper understanding of fluctuating phenomena.Entropy2015-10-301711Article10.3390/e17117522752275291099-43002015-10-30doi: 10.3390/e17117522Gregor ChliamovitchOrestis MalaspinasBastien Chopard<![CDATA[Entropy, Vol. 17, Pages 7510-7521: Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method]]>
http://www.mdpi.com/1099-4300/17/11/7510
In this paper, a proposed computational method referred to as Projected Differential Transformation Method (PDTM) resulting from the modification of the classical Differential Transformation Method (DTM) is applied, for the first time, to the Black–Scholes Equation for European Option Valuation. The results obtained converge faster to their associated exact solution form; these easily computed results represent the analytical values of the associated European call options, and the same algorithm can be followed for European put options. It is shown that PDTM is more efficient, reliable and better than the classical DTM and other semi-analytical methods since less computational work is involved. Hence, it is strongly recommended for both linear and nonlinear stochastic differential equations (SDEs) encountered in financial mathematics.Entropy2015-10-301711Article10.3390/e17117510751075211099-43002015-10-30doi: 10.3390/e17117510Sunday EdekiOlabisi UgbeborEnahoro Owoloko<![CDATA[Entropy, Vol. 17, Pages 7493-7509: Characterization of Complex Fractionated Atrial Electrograms by Sample Entropy: An International Multi-Center Study]]>
http://www.mdpi.com/1099-4300/17/11/7493
Atrial fibrillation (AF) is the most commonly clinically-encountered arrhythmia. Catheter ablation of AF is mainly based on trigger elimination and modification of the AF substrate. Substrate mapping ablation of complex fractionated atrial electrograms (CFAEs) has emerged to be a promising technique. To improve substrate mapping based on CFAE analysis, automatic detection algorithms need to be developed in order to simplify and accelerate the ablation procedures. According to the latest studies, the level of fractionation has been shown to be promisingly well estimated from CFAE measured during radio frequency (RF) ablation of AF. The nature of CFAE is generally nonlinear and nonstationary, so the use of complexity measures is considered to be the appropriate technique for the analysis of AF records. This work proposes the use of sample entropy (SampEn), not only as a way to discern between non-fractionated and fractionated atrial electrograms (A-EGM), Entropy 2015, 17 7494 but also as a tool for characterizing the degree of A-EGM regularity, which is linked to changes in the AF substrate and to heart tissue damage. The use of SampEn combined with a blind parameter estimation optimization process enables the classification between CFAE and non-CFAE with statistical significance (p &lt; 0:001), 0.89 area under the ROC, 86% specificity and 77% sensitivity over a mixed database of A-EGM combined from two independent CFAE signal databases, recorded during RF ablation of AF in two EU countries (542 signals in total). On the basis of the results obtained in this study, it can be suggested that the use of SampEn is suitable for real-time support during navigation of RF ablation of AF, as only 1.5 seconds of signal segments need to be analyzed.Entropy2015-10-281711Article10.3390/e17117493749375091099-43002015-10-28doi: 10.3390/e17117493Eva Cirugeda–RoldánDaniel NovakVaclav KremenDavid Cuesta–FrauMatthias KellerArmin LuikMartina Srutova<![CDATA[Entropy, Vol. 17, Pages 7468-7492: Information Theoretic Measures to Infer Feedback Dynamics in Coupled Logistic Networks]]>
http://www.mdpi.com/1099-4300/17/11/7468
A process network is a collection of interacting time series nodes, in which interactions can range from weak dependencies to complete synchronization. Between these extremes, nodes may respond to each other or external forcing at certain time scales and strengths. Identification of such dependencies from time series can reveal the complex behavior of the system as a whole. Since observed time series datasets are often limited in length, robust measures are needed to quantify strengths and time scales of interactions and their unique contributions to the whole system behavior. We generate coupled chaotic logistic networks with a range of connectivity structures, time scales, noise, and forcing mechanisms, and compute variance and lagged mutual information measures to evaluate how detected time dependencies reveal system behavior. When a target node is detected to receive information from multiple sources, we compute conditional mutual information and total shared information between each source node pair to identify unique or redundant sources. While variance measures capture synchronization trends, combinations of information measures provide further distinctions regarding drivers, redundancies, and time dependencies within the network. We find that imposed network connectivity often leads to induced feedback that is identified as redundant links, and cannot be distinguished from imposed causal linkages. We find that random or external driving nodes are more likely to provide unique information than mutually dependent nodes in a highly connected network. In process networks constructed from observed data, the methods presented can be used to infer connectivity, dominant interactions, and systemic behavioral shift.Entropy2015-10-281711Article10.3390/e17117468746874921099-43002015-10-28doi: 10.3390/e17117468Allison GoodwellPraveen Kumar<![CDATA[Entropy, Vol. 17, Pages 7453-7467: Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation]]>
http://www.mdpi.com/1099-4300/17/11/7453
Consider a statistically-repeatable, shift-invariant system obeying an unknown probability law p(x) ≡ q2(x): Amplitude q(x) defines a source effect that is to be found. We show that q(x) may be found by considering the flow of Fisher information J → I from source effect to observer that occurs during macroscopic observation of the system. Such an observation is irreversible and, hence, incurs a general loss I - J of the information. By requiring stability of the law q(x), as well, it is found to obey a principle I − J = min. of “extreme physical information” (EPI). Information I is the same functional of q(x) for any shift-invariant system, and J is a functional defining a physical source effect that must be known at least approximately. The minimum of EPI implies that I ≈ J or received information tends to well-approximate reality. Past applications of EPI to predicting laws of statistical physics, chemistry, biology, economics and social organization are briefly described.Entropy2015-10-281711Review10.3390/e17117453745374671099-43002015-10-28doi: 10.3390/e17117453B. Frieden<![CDATA[Entropy, Vol. 17, Pages 7420-7452: Distribution Function of the Atoms of Spacetime and the Nature of Gravity]]>
http://www.mdpi.com/1099-4300/17/11/7420
The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the metric cannot be varied in any extremum principle to obtain the field equations; and (2) the stress-tensor of matter should appear in the variational principle through the combination Tabnanb where na is an auxiliary null vector field, which could be varied to get the field equations. This procedure uniquely selects the Lanczos–Lovelock models of gravity in D-dimensions and Einstein’s theory in D = 4. Identifying na with the normals to the null surfaces in the spacetime in the macroscopic limit leads to a thermodynamic interpretation for gravity. Several geometrical variables and the equation describing the spacetime evolution acquire a thermodynamic interpretation. Extending these ideas one level deeper, we can obtain this variational principle from a distribution function for the “atoms of spacetime”, which counts the number of microscopic degrees of freedom of the geometry. This is based on the curious fact that the renormalized spacetime endows each event with zero volume, but finite area!Entropy2015-10-281711Review10.3390/e17117420742074521099-43002015-10-28doi: 10.3390/e17117420Thanu Padmanabhan<![CDATA[Entropy, Vol. 17, Pages 7406-7419: Extension of the Improved Bounce-Back Scheme for Electrokinetic Flow in the Lattice Boltzmann Method]]>
http://www.mdpi.com/1099-4300/17/11/7406
In this paper, an improved bounce-back boundary treatment for fluid systems in the lattice Boltzmann method [Yin, X.; Zhang J. J. Comput. Phys. 2012, 231, 4295–4303] is extended to handle the electrokinetic flows with complex boundary shapes and conditions. Several numerical simulations are performed to validate the electric boundary treatment. Simulations are presented to demonstrate the accuracy and capability of this method in dealing with complex surface potential situations, and simulated results are compared with analytical predictions with excellent agreement. This method could be useful for electrokinetic simulations with complex boundaries, and can also be readily extended to other phenomena and processes.Entropy2015-10-281711Article10.3390/e17117406740674191099-43002015-10-28doi: 10.3390/e17117406Qing ChenHongping ZhouXuesong JiangLinyun XuQing LiYu Ru<![CDATA[Entropy, Vol. 17, Pages 7387-7405: Performance of a Composite Thermoelectric Generator with Different Arrangements of SiGe, BiTe and PbTe under Different Configurations]]>
http://www.mdpi.com/1099-4300/17/11/7387
In this study, we analyze the role of the thermoelectric (TE) properties, namely Seebeck coefficient α, thermal conductivity κ and electrical resistivity ρ, of three different materials in a composite thermoelectric generator (CTEG) under different configurations. The CTEG is composed of three thermoelectric modules (TEMs): (1) two TEMs thermally and electrically connected in series (SC); (2) two branches of TEMs thermally and electrically connected in parallel (PSC); and (3) three TEMs thermally and electrically connected in parallel (TEP). In general, each of the TEMs have different thermoelectric parameters, namely a Seebeck coefficient α, a thermal conductance K and an electrical resistance R. Following the framework proposed recently, we show the effect of: (1) the configuration; and (2) the arrangements of TE materials on the corresponding equivalent figure of merit Zeq and consequently on the maximum power Pmax and efficiency η of the CTEG. Firstly, we consider that the whole system is formed of the same thermoelectric material (α1,K1,R1 = α2,K2,R2 = α3,K3,R3) and, secondly, that the whole system is constituted by only two different thermoelectric materials Entropy 2015, 17 7388 (αi,Ki,Ri ≠ αj ,Kj ,Rj 6= αl,Kl,Rl, where i, j, l can be 1, 2 or 3). In this work, we propose arrangements of TEMs, which clearly have the advantage of a higher thermoelectric figure of merit value compared to a conventional thermoelectric module. A corollary about the Zeq-max for CTEG is obtained as a result of these considerations. We suggest an optimum configuration.Entropy2015-10-281711Article10.3390/e17117387738774051099-43002015-10-28doi: 10.3390/e17117387Alexander Vargas-AlmeidaMiguel Olivares-RoblesFederico Lavielle<![CDATA[Entropy, Vol. 17, Pages 7374-7386: The Measurement Problem from the Perspective of an Information-Theoretic Interpretation of Quantum Mechanics]]>
http://www.mdpi.com/1099-4300/17/11/7374
The aim of this paper is to consider the consequences of an information-theoretic interpretation of quantum mechanics for the measurement problem. The motivating idea of the interpretation is that the relation between quantum mechanics and the structure of information is analogous to the relation between special relativity and the structure of space-time. Insofar as quantum mechanics deals with a class of probabilistic correlations that includes correlations structurally different from classical correlations, the theory is about the structure of information: the possibilities for representing, manipulating, and communicating information in a genuinely indeterministic quantum world in which measurement outcomes are intrinsically random are different than we thought. Part of the measurement problem is deflated as a pseudo-problem on this view, and the theory has the resources to deal with the remaining part, given certain idealizations in the treatment of macrosystems.Entropy2015-10-281711Article10.3390/e17117374737473861099-43002015-10-28doi: 10.3390/e17117374Jeffrey Bub<![CDATA[Entropy, Vol. 17, Pages 7349-7373: Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory]]>
http://www.mdpi.com/1099-4300/17/11/7349
In this article, we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and a new family of generalized entropic measures.Entropy2015-10-281711Article10.3390/e17117349734973731099-43002015-10-28doi: 10.3390/e17117349Federico HolikGustavo BosykGuido Bellomo<![CDATA[Entropy, Vol. 17, Pages 7331-7348: Comparison Based on Exergetic Analyses of Two Hot Air Engines: A Gamma Type Stirling Engine and an Open Joule Cycle Ericsson Engine]]>
http://www.mdpi.com/1099-4300/17/11/7331
In this paper, a comparison of exergetic models between two hot air engines (a Gamma type Stirling prototype having a maximum output mechanical power of 500 W and an Ericsson hot air engine with a maximum power of 300 W) is made. Referring to previous energetic analyses, exergetic models are set up in order to quantify the exergy destruction and efficiencies in each type of engine. The repartition of the exergy fluxes in each part of the two engines are determined and represented in Sankey diagrams, using dimensionless exergy fluxes. The results show a similar proportion in both engines of destroyed exergy compared to the exergy flux from the hot source. The compression cylinders generate the highest exergy destruction, whereas the expansion cylinders generate the lowest one. The regenerator of the Stirling engine increases the exergy resource at the inlet of the expansion cylinder, which might be also set up in the Ericsson engine, using a preheater between the exhaust air and the compressed air transferred to the hot heat exchanger.Entropy2015-10-281711Article10.3390/e17117331733173481099-43002015-10-28doi: 10.3390/e17117331Houda HachemMarie CreyxRamla GheithEric DelacourtCéline MorinFethi AlouiSassi Nasrallah<![CDATA[Entropy, Vol. 17, Pages 7310-7330: Measurement, Interpretation and Information]]>
http://www.mdpi.com/1099-4300/17/11/7310
During many years since the birth of quantum mechanics, instrumentalistinterpretations prevailed: the meaning of the theory was expressed in terms of measurementsresults. However, in the last decades, several attempts to interpret it from a realist viewpointhave been proposed. Among them, modal interpretations supply a realist non-collapseaccount, according to which the system always has definite properties and the quantum staterepresents possibilities, not actualities. But the traditional modal interpretations faced someconceptual problems when addressing imperfect measurements. The modal-Hamiltonianinterpretation, on the contrary, proved to be able to supply an adequate account of themeasurement problem, both in its ideal and its non-ideal versions. Moreover, in the non-idealcase, it gives a precise criterion to distinguish between reliable and non-reliable measurements.Nevertheless, that criterion depends on the particular state of the measured system, and thismight be considered as a shortcoming of the proposal. In fact, one could ask for a criterionof reliability that does not depend on the features of what is measured but only on theproperties of the measurement device. The aim of this article is precisely to supply such acriterion: we will adopt an informational perspective for this purpose.Entropy2015-10-281711Article10.3390/e17117310731073301099-43002015-10-28doi: 10.3390/e17117310Olimpia LombardiSebastian FortinCristian López<![CDATA[Entropy, Vol. 17, Pages 7298-7309: Projective Exponential Synchronization for a Class of Complex PDDE Networks with Multiple Time Delays]]>
http://www.mdpi.com/1099-4300/17/11/7298
This paper addresses the problem of projective exponential synchronization for a class of complex spatiotemporal networks with multiple time delays satisfying the homogeneous Neumann boundary conditions, where the network is modeled by coupled partial differential-difference equations (PDDEs). A distributed proportional-spatial derivative (P-sD) controller is designed by employing Lyapunov’s direct method and Kronecker product. The controller ensures the projective exponential synchronization of the PDDE network. The main result of this paper is presented in terms of standard linear matrix inequality (LMI). A numerical example is provided to show the effectiveness of the proposed design method.Entropy2015-10-281711Article10.3390/e17117298729873091099-43002015-10-28doi: 10.3390/e17117298Chengdong YangJianlong QiuTongxing LiAncai ZhangXiangyong Chen<![CDATA[Entropy, Vol. 17, Pages 7266-7297: Quantifying Emergent Behavior of Autonomous Robots]]>
http://www.mdpi.com/1099-4300/17/10/7266
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.Entropy2015-10-231710Article10.3390/e17107266726672971099-43002015-10-23doi: 10.3390/e17107266Georg MartiusEckehard Olbrich<![CDATA[Entropy, Vol. 17, Pages 7242-7265: Exergy Losses in the Szewalski Binary Vapor Cycle]]>
http://www.mdpi.com/1099-4300/17/10/7242
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.Entropy2015-10-231710Article10.3390/e17107242724272651099-43002015-10-23doi: 10.3390/e17107242Tomasz KowalczykPaweł ZiółkowskiJanusz Badur<![CDATA[Entropy, Vol. 17, Pages 7230-7241: Information Dynamics in the Interaction between a Prey and a Predator Fish]]>
http://www.mdpi.com/1099-4300/17/10/7230
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.Entropy2015-10-231710Article10.3390/e17107230723072411099-43002015-10-23doi: 10.3390/e17107230Feng HuLi-Juan NieShi-Jian Fu<![CDATA[Entropy, Vol. 17, Pages 7213-7229: Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics]]>
http://www.mdpi.com/1099-4300/17/10/7213
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.Entropy2015-10-221710Article10.3390/e17107213721372291099-43002015-10-22doi: 10.3390/e17107213Tatsuaki WadaHiroshi MatsuzoeAntonio Scarfone<![CDATA[Entropy, Vol. 17, Pages 7201-7212: Mesoscopic Thermodynamics for the Dynamics of Small-Scale Systems]]>
http://www.mdpi.com/1099-4300/17/10/7201
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.Entropy2015-10-221710Article10.3390/e17107201720172121099-43002015-10-22doi: 10.3390/e17107201J. Rubi<![CDATA[Entropy, Vol. 17, Pages 7185-7200: Adaptive Synchronization for a Class of Uncertain Fractional-Order Neural Networks]]>
http://www.mdpi.com/1099-4300/17/10/7185
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.Entropy2015-10-221710Article10.3390/e17107185718572001099-43002015-10-22doi: 10.3390/e17107185Heng LiuShenggang LiHongxing WangYuhong HuoJunhai Luo<![CDATA[Entropy, Vol. 17, Pages 7167-7184: Wavelet Entropy Based Analysis and Forecasting of Crude Oil Price Dynamics]]>
http://www.mdpi.com/1099-4300/17/10/7167
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.Entropy2015-10-221710Article10.3390/e17107167716771841099-43002015-10-22doi: 10.3390/e17107167Yingchao ZouLean YuKaijian He<![CDATA[Entropy, Vol. 17, Pages 7149-7166: Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion]]>
http://www.mdpi.com/1099-4300/17/10/7149
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.Entropy2015-10-221710Article10.3390/e17107149714971661099-43002015-10-22doi: 10.3390/e17107149Zongze WuSiyuan PengBadong ChenHaiquan Zhao<![CDATA[Entropy, Vol. 17, Pages 7133-7148: Dynamics and Thermodynamics of Nanoclusters]]>
http://www.mdpi.com/1099-4300/17/10/7133
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.Entropy2015-10-221710Article10.3390/e17107133713371481099-43002015-10-22doi: 10.3390/e17107133Karo MichaelianIvan Santamaría-Holek<![CDATA[Entropy, Vol. 17, Pages 7118-7132: A Novel Method for Increasing the Entropy of a Sequence of Independent, Discrete Random Variables]]>
http://www.mdpi.com/1099-4300/17/10/7118
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.Entropy2015-10-221710Article10.3390/e17107118711871321099-43002015-10-22doi: 10.3390/e17107118Mieczyslaw Jessa<![CDATA[Entropy, Vol. 17, Pages 7101-7117: Multi-Level Wavelet Shannon Entropy-Based Method for Single-Sensor Fault Location]]>
http://www.mdpi.com/1099-4300/17/10/7101
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.Entropy2015-10-201710Article10.3390/e17107101710171171099-43002015-10-20doi: 10.3390/e17107101Qiaoning YangJianlin Wang<![CDATA[Entropy, Vol. 17, Pages 7087-7100: D’Alembert’s Direct and Inertial Forces Acting on Populations: The Price Equation and the Fundamental Theorem of Natural Selection]]>
http://www.mdpi.com/1099-4300/17/10/7087
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.Entropy2015-10-201710Article10.3390/e17107087708771001099-43002015-10-20doi: 10.3390/e17107087Steven Frank<![CDATA[Entropy, Vol. 17, Pages 7076-7086: A Vibration Analysis Based on Wavelet Entropy Method of a Scroll Compressor]]>
http://www.mdpi.com/1099-4300/17/10/7076
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.Entropy2015-10-191710Article10.3390/e17107076707670861099-43002015-10-19doi: 10.3390/e17107076Tao LiuZaixin Wu<![CDATA[Entropy, Vol. 17, Pages 7052-7075: Extended Thermodynamics for Dense Gases up to Whatever Order and with Only Some Symmetries]]>
http://www.mdpi.com/1099-4300/17/10/7052
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.Entropy2015-10-161710Article10.3390/e17107052705270751099-43002015-10-16doi: 10.3390/e17107052Maria CarrisiRita TchameMarcel ObounouSebastiano Pennisi<![CDATA[Entropy, Vol. 17, Pages 7021-7051: Method for Measuring the Information Content of Terrain from Digital Elevation Models]]>
http://www.mdpi.com/1099-4300/17/10/7021
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.Entropy2015-10-161710Article10.3390/e17107021702170511099-43002015-10-16doi: 10.3390/e17107021Lujin HuZongyi HeJiping LiuChunhua Zheng<![CDATA[Entropy, Vol. 17, Pages 6995-7020: A Thermodynamic Entropy Approach to Reliability Assessment with Applications to Corrosion Fatigue]]>
http://www.mdpi.com/1099-4300/17/10/6995
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.Entropy2015-10-161710Article10.3390/e17106995699570201099-43002015-10-16doi: 10.3390/e17106995Anahita ImanianMohammad Modarres<![CDATA[Entropy, Vol. 17, Pages 6969-6994: Towards Information Lasers]]>
http://www.mdpi.com/1099-4300/17/10/6969
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.Entropy2015-10-161710Concept Paper10.3390/e17106969696969941099-43002015-10-16doi: 10.3390/e17106969Andrei Khrennikov<![CDATA[Entropy, Vol. 17, Pages 6954-6968: A Novel Image Encryption Algorithm Based on DNA Encoding and Spatiotemporal Chaos]]>
http://www.mdpi.com/1099-4300/17/10/6954
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.Entropy2015-10-161710Article10.3390/e17106954695469681099-43002015-10-16doi: 10.3390/e17106954Chunyan SongYulong Qiao<![CDATA[Entropy, Vol. 17, Pages 6937-6953: Exponential Synchronization of Two Complex Dynamical Networks of Random Disturbance with Both Mixed Coupled and Time-Varying Delay by Pinning Control]]>
http://www.mdpi.com/1099-4300/17/10/6937
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.Entropy2015-10-161710Article10.3390/e17106937693769531099-43002015-10-16doi: 10.3390/e17106937Xuefei Wu<![CDATA[Entropy, Vol. 17, Pages 6925-6936: Modified Legendre Wavelets Technique for Fractional Oscillation Equations]]>
http://www.mdpi.com/1099-4300/17/10/6925
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.Entropy2015-10-161710Article10.3390/e17106925692569361099-43002015-10-16doi: 10.3390/e17106925Syed Mohyud-DinMuhammad IqbalSaleh Hassan<![CDATA[Entropy, Vol. 17, Pages 6893-6924: Thermal BEC Black Holes]]>
http://www.mdpi.com/1099-4300/17/10/6893
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 &gt; 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 &gt; 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 &gt; 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.Entropy2015-10-151710Review10.3390/e17106893689369241099-43002015-10-15doi: 10.3390/e17106893Roberto CasadioAndrea GiugnoOctavian MicuAlessio Orlandi<![CDATA[Entropy, Vol. 17, Pages 6872-6892: Topological Characterization of Complex Systems: Using Persistent Entropy]]>
http://www.mdpi.com/1099-4300/17/10/6872
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.Entropy2015-10-151710Article10.3390/e17106872687268921099-43002015-10-15doi: 10.3390/e17106872Emanuela MerelliMatteo RuccoPeter SlootLuca Tesei<![CDATA[Entropy, Vol. 17, Pages 6854-6871: Analysis of Neural Oscillations on Drosophila’s Subesophageal Ganglion Based on Approximate Entropy]]>
http://www.mdpi.com/1099-4300/17/10/6854
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.Entropy2015-10-101710Article10.3390/e17106854685468711099-43002015-10-10doi: 10.3390/e17106854Tian MeiJingda QiaoYi ZhouHuaiyu GuZiyi ChenXianghua TianKuiying Gu<![CDATA[Entropy, Vol. 17, Pages 6834-6853: Dynamical Change of Signal Complexity in the Brain During Inhibitory Control Processes]]>
http://www.mdpi.com/1099-4300/17/10/6834
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.Entropy2015-10-091710Article10.3390/e17106834683468531099-43002015-10-09doi: 10.3390/e17106834Shih-Lin HuangPhilip TsengWei-Kuang Liang<![CDATA[Entropy, Vol. 17, Pages 6801-6833: On the Calculation of System Entropy in Nonlinear Stochastic Biological Networks]]>
http://www.mdpi.com/1099-4300/17/10/6801
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.Entropy2015-10-081710Article10.3390/e17106801680168331099-43002015-10-08doi: 10.3390/e17106801Bor-Sen ChenShang-Wen WongCheng-Wei Li<![CDATA[Entropy, Vol. 17, Pages 6783-6800: New Patterns in Steady-State Chemical Kinetics: Intersections, Coincidences, Map of Events (Two-Step Mechanism)]]>
http://www.mdpi.com/1099-4300/17/10/6783
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.Entropy2015-10-071710Article10.3390/e17106783678368001099-43002015-10-07doi: 10.3390/e17106783Daniel Branco PintoGregory YablonskyGuy MarinDenis Constales<![CDATA[Entropy, Vol. 17, Pages 6765-6782: A Tale of Two Entangled Instabilities—The Dual Role of δ-O in HgBa2Can-1CunO2(n+1)+δ]]>
http://www.mdpi.com/1099-4300/17/10/6765
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(x2−y2)(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.Entropy2015-10-051710Article10.3390/e17106765676567821099-43002015-10-05doi: 10.3390/e17106765Itai Panas<![CDATA[Entropy, Vol. 17, Pages 6753-6764: Local Fractional Homotopy Perturbation Method for Solving Non-Homogeneous Heat Conduction Equations in Fractal Domains]]>
http://www.mdpi.com/1099-4300/17/10/6753
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.Entropy2015-10-051710Article10.3390/e17106753675367641099-43002015-10-05doi: 10.3390/e17106753Yu ZhangCarlo CattaniXiao-Jun Yang<![CDATA[Entropy, Vol. 17, Pages 6743-6752: Quantum Secure Direct Communication Based on Dense Coding and Detecting Eavesdropping with Four-Particle Genuine Entangled State]]>
http://www.mdpi.com/1099-4300/17/10/6743
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.Entropy2015-09-301710Article10.3390/e17106743674367521099-43002015-09-30doi: 10.3390/e17106743Jian LiZeshi PanFengqi SunYanhua ChenZheng WangZuozhi Shi<![CDATA[Entropy, Vol. 17, Pages 6712-6742: Thermodynamic Analysis of Closed Steady or Cyclic Systems]]>
http://www.mdpi.com/1099-4300/17/10/6712
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.Entropy2015-09-291710Article10.3390/e17106712671267421099-43002015-09-29doi: 10.3390/e17106712Jim McGovern<![CDATA[Entropy, Vol. 17, Pages 6698-6711: Two-Dimensional Lattice Boltzmann for Reactive Rayleigh–Bénard and Bénard–Poiseuille Regimes]]>
http://www.mdpi.com/1099-4300/17/10/6698
We perform a computer simulation of the reaction-diffusion and convection that takes place in Rayleigh–Bénard and Bénard–Poiseuille regimes. The lattice Boltzmann equation (LBE) is used along with the Boussinesq approximation to solve the non-linear coupled differential equations that govern the systems’ thermo-hydrodynamics. Another LBE, is introduced to calculate the evolution concentration of the chemical species involved in the chemical reactions. The simulations are conducted at low Reynolds numbers and in terms of steady state between the first and second thermo-hydrodynamics instability. The results presented here (with no chemical reactions) are in good agreement with those reported in the scientific literature which gives us high expectations about the reliability of the chemical kinetics simulation. Some examples are provided.Entropy2015-09-291710Article10.3390/e17106698669867111099-43002015-09-29doi: 10.3390/e17106698Suemi Rodríguez-RomoOscar Ibañez-Orozco<![CDATA[Entropy, Vol. 17, Pages 6683-6697: Feature Extraction Method of Rolling Bearing Fault Signal Based on EEMD and Cloud Model Characteristic Entropy]]>
http://www.mdpi.com/1099-4300/17/10/6683
The randomness and fuzziness that exist in rolling bearings when faults occur result in uncertainty in acquisition signals and reduce the accuracy of signal feature extraction. To solve this problem, this study proposes a new method in which cloud model characteristic entropy (CMCE) is set as the signal characteristic eigenvalue. This approach can overcome the disadvantages of traditional entropy complexity in parameter selection when solving uncertainty problems. First, the acoustic emission signals under normal and damage rolling bearing states collected from the experiments are decomposed via ensemble empirical mode decomposition. The mutual information method is then used to select the sensitive intrinsic mode functions that can reflect signal characteristics to reconstruct the signal and eliminate noise interference. Subsequently, CMCE is set as the eigenvalue of the reconstructed signal. Finally, through the comparison of experiments between sample entropy, root mean square and CMCE, the results show that CMCE can better represent the characteristic information of the fault signal.Entropy2015-09-251710Article10.3390/e17106683668366971099-43002015-09-25doi: 10.3390/e17106683Long HanChengwei LiHongchen Liu<![CDATA[Entropy, Vol. 17, Pages 6663-6682: Identification of Green, Oolong and Black Teas in China via Wavelet Packet Entropy and Fuzzy Support Vector Machine]]>
http://www.mdpi.com/1099-4300/17/10/6663
To develop an automatic tea-category identification system with a high recall rate, we proposed a computer-vision and machine-learning based system, which did not require expensive signal acquiring devices and time-consuming procedures. We captured 300 tea images using a 3-CCD digital camera, and then extracted 64 color histogram features and 16 wavelet packet entropy (WPE) features to obtain color information and texture information, respectively. Principal component analysis was used to reduce features, which were fed into a fuzzy support vector machine (FSVM). Winner-take-all (WTA) was introduced to help the classifier deal with this 3-class problem. The 10 × 10-fold stratified cross-validation results show that the proposed FSVM + WTA method yields an overall recall rate of 97.77%, higher than 5 existing methods. In addition, the number of reduced features is only five, less than or equal to existing methods. The proposed method is effective for tea identification.Entropy2015-09-251710Article10.3390/e17106663666366821099-43002015-09-25doi: 10.3390/e17106663Shuihua WangXiaojun YangYudong ZhangPreetha PhillipsJianfei YangTi-Fei Yuan<![CDATA[Entropy, Vol. 17, Pages 6643-6662: Modified Gravity Models Admitting Second Order Equations of Motion]]>
http://www.mdpi.com/1099-4300/17/10/6643
The aim of this paper is to find higher order geometrical corrections to the Einstein–Hilbert action that can lead only to second order equations of motion. The metric formalism is used, and static spherically-symmetric and Friedmann–Lemaître space-times are considered, in four dimensions. The Fulling, King, Wybourne and Cummings (FKWC) basis is introduced in order to consider all of the possible invariant scalars, and both polynomial and non-polynomial gravities are investigated.Entropy2015-09-251710Article10.3390/e17106643664366621099-43002015-09-25doi: 10.3390/e17106643Aimeric ColléauxSergio Zerbini<![CDATA[Entropy, Vol. 17, Pages 6617-6642: Shannon Entropy-Based Wavelet Transform Method for Autonomous Coherent Structure Identification in Fluid Flow Field Data]]>
http://www.mdpi.com/1099-4300/17/10/6617
The coherent secondary flow structures (i.e., swirling motions) in a curved artery model possess a variety of spatio-temporal morphologies and can be encoded over an infinitely-wide range of wavelet scales. Wavelet analysis was applied to the following vorticity fields: (i) a numerically-generated system of Oseen-type vortices for which the theoretical solution is known, used for bench marking and evaluation of the technique; and (ii) experimental two-dimensional, particle image velocimetry data. The mother wavelet, a two-dimensional Ricker wavelet, can be dilated to infinitely large or infinitesimally small scales. We approached the problem of coherent structure detection by means of continuous wavelet transform (CWT) and decomposition (or Shannon) entropy. The main conclusion of this study is that the encoding of coherent secondary flow structures can be achieved by an optimal number of binary digits (or bits) corresponding to an optimal wavelet scale. The optimal wavelet-scale search was driven by a decomposition entropy-based algorithmic approach and led to a threshold-free coherent structure detection method. The method presented in this paper was successfully utilized in the detection of secondary flow structures in three clinically-relevant blood flow scenarios involving the curved artery model under a carotid artery-inspired, pulsatile inflow condition. These scenarios were: (i) a clean curved artery; (ii) stent-implanted curved artery; and (iii) an idealized Type IV stent fracture within the curved artery.Entropy2015-09-251710Article10.3390/e17106617661766421099-43002015-09-25doi: 10.3390/e17106617Kartik BulusuMichael Plesniak<![CDATA[Entropy, Vol. 17, Pages 6598-6616: Ultrasound Detection of Scatterer Concentration by Weighted Entropy]]>
http://www.mdpi.com/1099-4300/17/10/6598
Ultrasound backscattering signals depend on the microstructures of tissues. Some studies have applied Shannon entropy to analyze the uncertainty of raw radiofrequency (RF) data. However, we found that the sensitivity of entropy in detecting various scatterer concentrations is limited; thus, we propose a weighted entropy as a new information entropy-based approach to enhance the performance of scatterer characterization. A standard simulation model of ultrasound backscattering was used to generate backscattered RF signals with different number densities of scatterers. The RF signals were used to estimate the weighted entropy according to the proposed algorithmic scheme. The weighted entropy increased from 0.08 to 0.23 (representing a dynamic range of 0.15) when the number density of scatterers increased from 2 to 32 scatterers/mm2. In the same range of scatterer concentration, the conventional entropy increased from 0.16 to 0.19 (a dynamic range of 0.03). The results indicated that the weighted entropy enables achieving a more sensitive detection of the variation of scatterer concentrations by ultrasound.Entropy2015-09-251710Article10.3390/e17106598659866161099-43002015-09-25doi: 10.3390/e17106598Po-Hsiang Tsui<![CDATA[Entropy, Vol. 17, Pages 6576-6597: Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models]]>
http://www.mdpi.com/1099-4300/17/10/6576
In this work, we propose a Bayesian methodology to make inferences for the memory parameter and other characteristics under non-standard assumptions for a class of stochastic processes. This class generalizes the Gamma-modulated process, with trajectories that exhibit long memory behavior, as well as decreasing variability as time increases. Different values of the memory parameter influence the speed of this decrease, making this heteroscedastic model very flexible. Its properties are used to implement an approximate Bayesian computation and MCMC scheme to obtain posterior estimates. We test and validate our method through simulations and real data from the big earthquake that occurred in 2010 in Chile.Entropy2015-09-251710Article10.3390/e17106576657665971099-43002015-09-25doi: 10.3390/e17106576Plinio AndradeLaura RifoSoledad TorresFrancisco Torres-Avilés<![CDATA[Entropy, Vol. 17, Pages 6560-6575: Expected Utility and Entropy-Based Decision-Making Model for Large Consumers in the Smart Grid]]>
http://www.mdpi.com/1099-4300/17/10/6560
In the smart grid, large consumers can procure electricity energy from various power sources to meet their load demands. To maximize its profit, each large consumer needs to decide their energy procurement strategy under risks such as price fluctuations from the spot market and power quality issues. In this paper, an electric energy procurement decision-making model is studied for large consumers who can obtain their electric energy from the spot market, generation companies under bilateral contracts, the options market and self-production facilities in the smart grid. Considering the effect of unqualified electric energy, the profit model of large consumers is formulated. In order to measure the risks from the price fluctuations and power quality, the expected utility and entropy is employed. Consequently, the expected utility and entropy decision-making model is presented, which helps large consumers to minimize their expected profit of electricity procurement while properly limiting the volatility of this cost. Finally, a case study verifies the feasibility and effectiveness of the proposed model.Entropy2015-09-251710Article10.3390/e17106560656065751099-43002015-09-25doi: 10.3390/e17106560Bingtuan GaoCheng WuYingjun WuYi Tang<![CDATA[Entropy, Vol. 17, Pages 6534-6559: A Bayesian Decision-Theoretic Approach to Logically-Consistent Hypothesis Testing]]>
http://www.mdpi.com/1099-4300/17/10/6534
This work addresses an important issue regarding the performance of simultaneous test procedures: the construction of multiple tests that at the same time are optimal from a statistical perspective and that also yield logically-consistent results that are easy to communicate to practitioners of statistical methods. For instance, if hypothesis A implies hypothesis B, is it possible to create optimal testing procedures that reject A whenever they reject B? Unfortunately, several standard testing procedures fail in having such logical consistency. Although this has been deeply investigated under a frequentist perspective, the literature lacks analyses under a Bayesian paradigm. In this work, we contribute to the discussion by investigating three rational relationships under a Bayesian decision-theoretic standpoint: coherence, invertibility and union consonance. We characterize and illustrate through simple examples optimal Bayes tests that fulfill each of these requisites separately. We also explore how far one can go by putting these requirements together. We show that although fairly intuitive tests satisfy both coherence and invertibility, no Bayesian testing scheme meets the desiderata as a whole, strengthening the understanding that logical consistency cannot be combined with statistical optimality in general. Finally, we associate Bayesian hypothesis testing with Bayes point estimation procedures. We prove the performance of logically-consistent hypothesis testing by means of a Bayes point estimator to be optimal only under very restrictive conditions.Entropy2015-09-241710Article10.3390/e17106534653465591099-43002015-09-24doi: 10.3390/e17106534Gustavo da SilvaLuis EstevesVictor FossaluzaRafael IzbickiSergio Wechsler<![CDATA[Entropy, Vol. 17, Pages 6519-6533: Approximate Analytical Solutions of Time Fractional Whitham–Broer–Kaup Equations by a Residual Power Series Method]]>
http://www.mdpi.com/1099-4300/17/9/6519
In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method. The efficiency and accuracy of the present method is demonstrated by two aspects. One is analyzing the approximate solutions graphically. The other is comparing the results with those of the Adomian decomposition method (ADM), the variational iteration method (VIM) and the optimal homotopy asymptotic method (OHAM). Illustrative examples reveal that the present technique outperforms the aforementioned methods and can be used as an alternative for solving fractional equations.Entropy2015-09-23179Article10.3390/e17096519651965331099-43002015-09-23doi: 10.3390/e17096519Linjun WangXumei Chen<![CDATA[Entropy, Vol. 17, Pages 6503-6518: Thermodynamic Metrics and Black Hole Physics]]>
http://www.mdpi.com/1099-4300/17/9/6503
We give a brief survey of thermodynamic metrics, in particular the Hessian of the entropy function, and how they apply to black hole thermodynamics. We then provide a detailed discussion of the Gibbs surface of Kerr black holes. In particular, we analyze its global properties and extend it to take the entropy of the inner horizon into account. A brief discussion of Kerr–Newman black holes is included.Entropy2015-09-22179Article10.3390/e17096503650365181099-43002015-09-22doi: 10.3390/e17096503Jan ÅmanIngemar BengtssonNarit Pidokrajt<![CDATA[Entropy, Vol. 17, Pages 6481-6502: A Bayesian Predictive Discriminant Analysis with Screened Data]]>
http://www.mdpi.com/1099-4300/17/9/6481
In the application of discriminant analysis, a situation sometimes arises where individual measurements are screened by a multidimensional screening scheme. For this situation, a discriminant analysis with screened populations is considered from a Bayesian viewpoint, and an optimal predictive rule for the analysis is proposed. In order to establish a flexible method to incorporate the prior information of the screening mechanism, we propose a hierarchical screened scale mixture of normal (HSSMN) model, which makes provision for flexible modeling of the screened observations. An Markov chain Monte Carlo (MCMC) method using the Gibbs sampler and the Metropolis–Hastings algorithm within the Gibbs sampler is used to perform a Bayesian inference on the HSSMN models and to approximate the optimal predictive rule. A simulation study is given to demonstrate the performance of the proposed predictive discrimination procedure.Entropy2015-09-21179Article10.3390/e17096481648165021099-43002015-09-21doi: 10.3390/e17096481Hea-Jung Kim<![CDATA[Entropy, Vol. 17, Pages 6462-6480: Subspace Coding for Networks with Different Level Messages]]>
http://www.mdpi.com/1099-4300/17/9/6462
We study the asymptotically-achievable rate region of subspace codes for wireless network coding, where receivers have different link capacities due to the access ways or the faults of the intermediate links in the network. Firstly, an outer bound of the achievable rate region in a two-receiver network is derived from a combinatorial method. Subsequently, the achievability of the outer bound is proven by code construction, which is based on superposition coding. We show that the outer bound can be achieved asymptotically by using the code presented by Koetter and Kschischang, and the outer bound can be exactly attained in some points by using a q-analog Steiner structure. Finally, the asymptotically-achievable rate region is extended to the general case when the network has m receivers with different levels.Entropy2015-09-21179Article10.3390/e17096462646264801099-43002015-09-21doi: 10.3390/e17096462Feng CaiNing CaiWangmei Guo<![CDATA[Entropy, Vol. 17, Pages 6447-6461: Rolling Bearing Fault Diagnosis Based on Wavelet Packet Decomposition and Multi-Scale Permutation Entropy]]>
http://www.mdpi.com/1099-4300/17/9/6447
This paper presents a rolling bearing fault diagnosis approach by integrating wavelet packet decomposition (WPD) with multi-scale permutation entropy (MPE). The approach uses MPE values of the sub-frequency band signals to identify faults appearing in rolling bearings. Specifically, vibration signals measured from a rolling bearing test system with different defect conditions are decomposed into a set of sub-frequency band signals by means of the WPD method. Then, each sub-frequency band signal is divided into a series of subsequences, and MPEs of all subsequences in corresponding sub-frequency band signal are calculated. After that, the average MPE value of all subsequences about each sub-frequency band is calculated, and is considered as the fault feature of the corresponding sub-frequency band. Subsequently, MPE values of all sub-frequency bands are considered as input feature vectors, and the hidden Markov model (HMM) is used to identify the fault pattern of the rolling bearing. Experimental study on a data set from the Case Western Reserve University bearing data center has shown that the presented approach can accurately identify faults in rolling bearings.Entropy2015-09-21179Article10.3390/e17096447644764611099-43002015-09-21doi: 10.3390/e17096447Li-Ye ZhaoLei WangRu-Qiang Yan<![CDATA[Entropy, Vol. 17, Pages 6433-6446: Dynamical Systems Induced on Networks Constructed from Time Series]]>
http://www.mdpi.com/1099-4300/17/9/6433
Several methods exist to construct complex networks from time series. In general, these methods claim to construct complex networks that preserve certain properties of the underlying dynamical system, and hence, they mark new ways of accessing quantitative indicators based on that dynamics. In this paper, we test this assertion by developing an algorithm to realize dynamical systems from these complex networks in such a way that trajectories of these dynamical systems produce time series that preserve certain statistical properties of the original time series (and hence, also the underlying true dynamical system). Trajectories from these networks are constructed from only the information in the network and are shown to be statistically equivalent to the original time series. In the context of this algorithm, we are able to demonstrate that the so-called adaptive k-nearest neighbour algorithm for generating networks out-performs methods based on ε-ball recurrence plots. For such networks, and with a suitable choice of parameter values, which we provide, the time series generated by this method function as a new kind of nonlinear surrogate generation algorithm. With this approach, we are able to test whether the simulation dynamics built from a complex network capture the underlying structure of the original system; whether the complex network is an adequate model of the dynamics.Entropy2015-09-18179Article10.3390/e17096433643364461099-43002015-09-18doi: 10.3390/e17096433Lvlin HouMichael SmallSongyang Lao<![CDATA[Entropy, Vol. 17, Pages 6412-6432: Energy and Exergy Analyses of a Combined Power Cycle Using the Organic Rankine Cycle and the Cold Energy of Liquefied Natural Gas]]>
http://www.mdpi.com/1099-4300/17/9/6412
In this work, energy and exergy analyses are carried out for a combined cycle consisting of an organic Rankine cycle (ORC) and a liquefied natural gas (LNG) Rankine cycle for the recovery of low-grade heat sources and LNG cold energy. The effects of the turbine inlet pressure and the working fluid on the system performance are theoretically investigated. A modified temperature-enthalpy diagram is proposed, which can be useful to see the characteristics of the combined cycle, as well as the temperature distributions in the heat exchangers. Results show that the thermal efficiency increases with an increasing turbine inlet pressure and critical temperature of the working fluid. However, the exergy efficiency has a peak value with respect to the turbine inlet pressure, and the maximum exergy efficiency and the corresponding optimum turbine inlet pressure are significantly influenced by the selection of the working fluid. The exergy destruction at the condenser is generally the greatest among the exergy destruction components of the system.Entropy2015-09-18179Article10.3390/e17096412641264321099-43002015-09-18doi: 10.3390/e17096412Ho LeeKyoung Kim<![CDATA[Entropy, Vol. 17, Pages 6397-6411: Wavelet Entropy as a Measure of Ventricular Beat Suppression from the Electrocardiogram in Atrial Fibrillation]]>
http://www.mdpi.com/1099-4300/17/9/6397
A novel method of quantifying the effectiveness of the suppression of ventricular activity from electrocardiograms (ECGs) in atrial fibrillation is proposed. The temporal distribution of the energy of wavelet coefficients is quantified by wavelet entropy at each ventricular beat. More effective ventricular activity suppression yields increased entropies at scales dominated by the ventricular and atrial components of the ECG. Two studies are undertaken to demonstrate the efficacy of the method: first, using synthesised ECGs with controlled levels of residual ventricular activity, and second, using patient recordings with ventricular activity suppressed by an average beat template subtraction algorithm. In both cases wavelet entropy is shown to be a good measure of the effectiveness of ventricular beat suppression.Entropy2015-09-17179Article10.3390/e17096397639764111099-43002015-09-17doi: 10.3390/e17096397Philip Langley<![CDATA[Entropy, Vol. 17, Pages 6379-6396: A New Process Monitoring Method Based on Waveform Signal by Using Recurrence Plot]]>
http://www.mdpi.com/1099-4300/17/9/6379
Process monitoring is an important research problem in numerous areas. This paper proposes a novel process monitoring scheme by integrating the recurrence plot (RP) method and the control chart technique. Recently, the RP method has emerged as an effective tool to analyze waveform signals. However, unlike the existing RP methods that employ recurrence quantiﬁcation analysis (RQA) to quantify the recurrence plot by a few summary statistics; we propose new concepts of template recurrence plots and continuous-scale recurrence plots to characterize the waveform signals. A new feature extraction method is developed based on continuous-scale recurrence plot. Then, a monitoring statistic based on the top- approach is constructed from the continuous-scale recurrence plot. Finally, a bootstrap control chart is built to detect the signal changes based on the constructed monitoring statistics. The comprehensive simulation studies show that the proposed monitoring scheme outperforms other RQA-based control charts. In addition, a real case study of progressive stamping processes is implemented to further evaluate the performance of the proposed scheme for process monitoring.Entropy2015-09-16179Article10.3390/e17096379637963961099-43002015-09-16doi: 10.3390/e17096379Cheng ZhouWeidong Zhang<![CDATA[Entropy, Vol. 17, Pages 6329-6378: Entropies from Coarse-graining: Convex Polytopes vs. Ellipsoids]]>
http://www.mdpi.com/1099-4300/17/9/6329
We examine the Boltzmann/Gibbs/Shannon SBGS and the non-additive Havrda-Charvát/Daróczy/Cressie-Read/Tsallis Sq and the Kaniadakis κ-entropy Sκ from the viewpoint of coarse-graining, symplectic capacities and convexity. We argue that the functional form of such entropies can be ascribed to a discordance in phase-space coarse-graining between two generally different approaches: the Euclidean/Riemannian metric one that reflects independence and picks cubes as the fundamental cells in coarse-graining and the symplectic/canonical one that picks spheres/ellipsoids for this role. Our discussion is motivated by and confined to the behaviour of Hamiltonian systems of many degrees of freedom. We see that Dvoretzky’s theorem provides asymptotic estimates for the minimal dimension beyond which these two approaches are close to each other. We state and speculate about the role that dualities may play in this viewpoint.Entropy2015-09-15179Article10.3390/e17096329632963781099-43002015-09-15doi: 10.3390/e17096329Nikos Kalogeropoulos<![CDATA[Entropy, Vol. 17, Pages 6318-6328: Viscosity-Induced Crossing of the Phantom Barrier]]>
http://www.mdpi.com/1099-4300/17/9/6318
We show explicitly, by using astrophysical data plus reasonable assumptions for the bulk viscosity in the cosmic fluid, how the magnitude of this viscosity may be high enough to drive the fluid from its position in the quintessence region at present time t = 0 across the barrier w = −1 into the phantom region in the late universe. The phantom barrier is accordingly not a sharp mathematical divide, but rather a fuzzy concept. We also calculate the limiting forms of various thermodynamical quantities, including the rate of entropy production, for a dark energy fluid near the future Big Rip singularity.Entropy2015-09-14179Article10.3390/e17096318631863281099-43002015-09-14doi: 10.3390/e17096318Iver Brevik<![CDATA[Entropy, Vol. 17, Pages 6304-6317: Metrics and Energy Landscapes in Irreversible Thermodynamics]]>
http://www.mdpi.com/1099-4300/17/9/6304
We describe how several metrics are possible in thermodynamic state space but that only one, Weinhold’s, has achieved widespread use. Lengths calculated based on this metric have been used to bound dissipation in finite-time (irreversible) processes be they continuous or discrete, and described in the energy picture or the entropy picture. Examples are provided from thermodynamics of heat conversion processes as well as chemical reactions. Even losses in economics can be bounded using a thermodynamic type metric. An essential foundation for the metric is a complete equation of state including all extensive variables of the system; examples are given. Finally, the second law of thermodynamics imposes convexity on any equation of state, be it analytical or empirical.Entropy2015-09-10179Article10.3390/e17096304630463171099-43002015-09-10doi: 10.3390/e17096304Bjarne Andresen<![CDATA[Entropy, Vol. 17, Pages 6289-6303: Modeling of a Mass-Spring-Damper System by Fractional Derivatives with and without a Singular Kernel]]>
http://www.mdpi.com/1099-4300/17/9/6289
In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo–Fabrizio derivatives are presented. The physical units of the system are preserved by introducing an auxiliary parameter σ. The input of the resulting equations is a constant and periodic source; for the Caputo case, we obtain the analytical solution, and the resulting equations are given in terms of the Mittag–Leffler function; for the Caputo–Fabrizio approach, the numerical solutions are obtained by the numerical Laplace transform algorithm. Our results show that the mechanical components exhibit viscoelastic behaviors producing temporal fractality at different scales and demonstrate the existence of Entropy 2015, 17 6290 material heterogeneities in the mechanical components. The Markovian nature of the model is recovered when the order of the fractional derivatives is equal to one.Entropy2015-09-10179Article10.3390/e17096289628963031099-43002015-09-10doi: 10.3390/e17096289José Gómez-AguilarHuitzilin Yépez-MartínezCelia Calderón-RamónInes Cruz-OrduñaRicardo Escobar-JiménezVictor Olivares-Peregrino<![CDATA[Entropy, Vol. 17, Pages 6270-6288: Determination of Sample Entropy and Fuzzy Measure Entropy Parameters for Distinguishing Congestive Heart Failure from Normal Sinus Rhythm Subjects]]>
http://www.mdpi.com/1099-4300/17/9/6270
Entropy provides a valuable tool for quantifying the regularity of physiological time series and provides important insights for understanding the underlying mechanisms of the cardiovascular system. Before any entropy calculation, certain common parameters need to be initialized: embedding dimension m, tolerance threshold r and time series length N. However, no specific guideline exists on how to determine the appropriate parameter values for distinguishing congestive heart failure (CHF) from normal sinus rhythm (NSR) subjects in clinical application. In the present study, a thorough analysis on the selection of appropriate values of m, r and N for sample entropy (SampEn) and recently proposed fuzzy measure entropy (FuzzyMEn) is presented for distinguishing two group subjects. 44 long-term NRS and 29 long-term CHF RR interval recordings from http://www.physionet.org were used as the non-pathological and pathological data respectively. Extreme (&gt;2 s) and abnormal heartbeat RR intervals were firstly removed from each RR recording and then the recording was segmented with a non-overlapping segment length N of 300 and 1000, respectively. SampEn and FuzzyMEn were performed for each RR segment under different parameter combinations: m of 1, 2, 3 and 4, and r of 0.10, 0.15, 0.20 and 0.25 respectively. The statistical significance between NSR and CHF groups under each combination of m, r and N was observed. The results demonstrated that the selection of m, r and N plays a critical role in determining the SampEn and FuzzyMEn outputs. Compared with SampEn, FuzzyMEn shows a better regularity when selecting the parameters m and r. In addition, FuzzyMEn shows a better relative consistency for distinguishing the two groups, that is, the results of FuzzyMEn in the NSR group were consistently lower than those in the CHF group while SampEn were not. The selections of m of 2 and 3 and r of 0.10 and 0.15 for SampEn and the selections of m of 1 and 2 whenever r (herein, rL = rG = r) are for FuzzyMEn (in addition to setting nL = 3 and nG = 2) were recommended to yield the fine classification results for the NSR and CHF groups.Entropy2015-09-10179Article10.3390/e17096270627062881099-43002015-09-10doi: 10.3390/e17096270Lina ZhaoShoushui WeiChengqiu ZhangYatao ZhangXinge JiangFeng LiuChengyu Liu<![CDATA[Entropy, Vol. 17, Pages 6258-6269: A Hydrodynamical Model for Carriers and Phonons With Generation-Recombination, Including Auger Effect]]>
http://www.mdpi.com/1099-4300/17/9/6258
The asymptotic procedure proposed allows to derive closed hydrodynamical equations from the kinetic equations of carriers and phonons (treated as a partecipating species) in a photon background. The direct generation-recombination processes are accounted for. The fluid-dynamical equations constructed for the chemical potentials of carriers, temperature, and drift velocity, are related to the extended thermodynamical (ET) ones for the chemical potentials of carriers, temperature, and drift velocity. In the drift-diffusion approximation the constitutive laws are derived and the Onsager relation recovered.Entropy2015-09-09179Article10.3390/e17096258625862691099-43002015-09-09doi: 10.3390/e17096258Alberto Rossani<![CDATA[Entropy, Vol. 17, Pages 6239-6257: Using Generalized Entropies and OC-SVM with Mahalanobis Kernel for Detection and Classification of Anomalies in Network Traffic]]>
http://www.mdpi.com/1099-4300/17/9/6239
Network anomaly detection and classification is an important open issue in network security. Several approaches and systems based on different mathematical tools have been studied and developed, among them, the Anomaly-Network Intrusion Detection System (A-NIDS), which monitors network traffic and compares it against an established baseline of a “normal” traffic profile. Then, it is necessary to characterize the “normal” Internet traffic. This paper presents an approach for anomaly detection and classification based on Shannon, Rényi and Tsallis entropies of selected features, and the construction of regions from entropy data employing the Mahalanobis distance (MD), and One Class Support Vector Machine (OC-SVM) with different kernels (Radial Basis Function (RBF) and Mahalanobis Kernel (MK)) for “normal” and abnormal traffic. Regular and non-regular regions built from “normal” traffic profiles allow anomaly detection, while the classification is performed under the assumption that regions corresponding to the attack classes have been previously characterized. Although this approach allows the use of as many features as required, only four well-known significant features were selected in our case. In order to evaluate our approach, two different data sets were used: one set of real traffic obtained from an Academic Local Area Network (LAN), and the other a subset of the 1998 MIT-DARPA set. For these data sets, a True positive rate up to 99.35%, a True negative rate up to 99.83% and a False negative rate at about 0.16% were yielded. Experimental results show that certain q-values of the generalized entropies and the use of OC-SVM with RBF kernel improve the detection rate in the detection stage, while the novel inclusion of MK kernel in OC-SVM and k-temporal nearest neighbors improve accuracy in classification. In addition, the results show that using the Box-Cox transformation, the Mahalanobis distance yielded high detection rates with an efficient computation time, while OC-SVM achieved detection rates slightly higher, but is more computationally expensive.Entropy2015-09-08179Article10.3390/e17096239623962571099-43002015-09-08doi: 10.3390/e17096239Jayro Santiago-PazDeni Torres-RomanAngel Figueroa-YpiñaJesus Argaez-Xool<![CDATA[Entropy, Vol. 17, Pages 6238: Correction on Davidson, R.M.; Lauritzen, A.; Seneff, S. Biological Water Dynamics and Entropy: A Biophysical Origin of Cancer and Other Diseases. Entropy 2013, 15, 3822-3876]]>
http://www.mdpi.com/1099-4300/17/9/6238
The authors wish to make the following correction to their paper [1]. The correct reference 190 in the reference list should be: [...]Entropy2015-09-08179Correction10.3390/e17096238623862381099-43002015-09-08doi: 10.3390/e17096238Robert DavidsonAnn LauritzenStephanie Seneff<![CDATA[Entropy, Vol. 17, Pages 6229-6237: On the Exact Solution of Wave Equations on Cantor Sets]]>
http://www.mdpi.com/1099-4300/17/9/6229
The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of applications in many scientific fields. Christianto and Rahul gave the derivation of Proca equations on Cantor sets. Hao et al. investigated the Helmholtz and diffusion equations in Cantorian and Cantor-Type Cylindrical Coordinates. Carpinteri and Sapora studied diffusion problems in fractal media in Cantor sets. Zhang et al. studied local fractional wave equations under fixed entropy. In this paper, we are concerned with the exact solutions of wave equations by the help of local fractional Laplace variation iteration method (LFLVIM). We develop an iterative scheme for the exact solutions of local fractional wave equations (LFWEs). The efficiency of the scheme is examined by two illustrative examples.Entropy2015-09-08179Article10.3390/e17096229622962371099-43002015-09-08doi: 10.3390/e17096229Dumitru BaleanuHasib KhanHossien JafariRahmat Khan<![CDATA[Entropy, Vol. 17, Pages 6213-6228: Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions]]>
http://www.mdpi.com/1099-4300/17/9/6213
In this paper we investigate statistical manifolds with almost quaternionic structures. We define the concept of quaternionic Kähler-like statistical manifold and derive the main properties of quaternionic Kähler-like statistical submersions, extending in a new setting some previous results obtained by K. Takano concerning statistical manifolds endowed with almost complex and almost contact structures. Finally, we give a nontrivial example and propose some open problems in the field for further research.Entropy2015-09-07179Article10.3390/e17096213621362281099-43002015-09-07doi: 10.3390/e17096213Alina-Daniela VîlcuGabriel-Eduard Vîlcu<![CDATA[Entropy, Vol. 17, Pages 6200-6212: Thixotropic Phenomena in Water: Quantitative Indicators of Casimir-Magnetic Transformations from Vacuum Oscillations (Virtual Particles)]]>
http://www.mdpi.com/1099-4300/17/9/6200
The ~1.5 × 10−20 J which is considered a universal quantity and is associated with the movement of protons in water also relates to the ratio of the magnetic moment of a proton divided by its unit charge, multiplied by viscosity and applied over the O-H distance. There is quantitative evidence that thixotropy, the “spontaneous” increased viscosity in water when undisturbed, originates from the transformation of virtual particles or vacuum oscillations to real states through conversion of Casimir-magnetic energies that involve the frequency of the neutral hydrogen line and the upper bound threshold value for intergalactic magnetic fields. The results indicate that ½ of a single electron orbit is real (particle) and the other ½ is virtual (wave). The matter equivalent per s for virtual-to-real states for electrons in 1 mL of water with a neutral pH is consistent with the numbers of protons (H+) and the measured range of molecules in the coherent domains for both width and duration of growth and is similar to widths of intergalactic dust grains from which planets and stars may condense. The de Broglie momentum for the lower boundary of the width of coherent domains multiplied by the fine structure velocity of an electron is concurrent with the quantum when one proton is being removed from another and when the upper boundary of the rest mass of a photon is transformed by the product of velocities for putative “entanglement” and light. Theoretical and experimental results indicate that components of thixotropy, such as specific domains of intercalated water molecules, could display excess correlations over very large distances. Because the energies of the universal quantity and water converge it may be a special conduit for discrete transformations from virtual to real states.Entropy2015-09-07179Concept Paper10.3390/e17096200620062121099-43002015-09-07doi: 10.3390/e17096200Michael Persinger<![CDATA[Entropy, Vol. 17, Pages 6179-6199: Wavelet Entropy Automatically Detects Episodes of Atrial Fibrillation from Single-Lead Electrocardiograms]]>
http://www.mdpi.com/1099-4300/17/9/6179
This work introduces for the first time the application of wavelet entropy (WE) to detect episodes of the most common cardiac arrhythmia, atrial fibrillation (AF), automatically from the electrocardiogram (ECG). Given that AF is often asymptomatic and usually presents very brief initial episodes, its early automatic detection is clinically relevant to improve AF treatment and prevent risks for the patients. After discarding noisy TQ intervals from the ECG, the WE has been computed over the median TQ segment obtained from the 10 previous noise-free beats under study. In this way, the P-waves or the fibrillatory waves present in the recording were highlighted or attenuated, respectively, thus enabling the patient’s rhythm identification (sinus rhythm or AF). Results provided a discriminant ability of about 95%, which is comparable to previous works. However, in contrast to most of them, which are mainly based on quantifying RR series variability, the proposed algorithm is able to deal with patients under rate-control therapy or with a reduced heart rate variability during AF. Additionally, it also presents interesting properties, such as the lowest delay in detecting AF or sinus rhythm, the ability to detect episodes as brief as five beats in length or its integration facilities under real-time beat-by-beat ECG monitoring systems. Consequently, this tool may help clinicians in the automatic detection of a wide variety of AF episodes, thus gaining further knowledge about the mechanisms initiating this arrhythmia.Entropy2015-09-07179Article10.3390/e17096179617961991099-43002015-09-07doi: 10.3390/e17096179Juan RódenasManuel GarcíaRaúl AlcarazJosé Rieta<![CDATA[Entropy, Vol. 17, Pages 6169-6178: Short-Lived Lattice Quasiparticles for Strongly Interacting Fluids]]>
http://www.mdpi.com/1099-4300/17/9/6169
It is shown that lattice kinetic theory based on short-lived quasiparticles proves very effective in simulating the complex dynamics of strongly interacting fluids (SIF). In particular, it is pointed out that the shear viscosity of lattice fluids is the sum of two contributions, one due to the usual interactions between particles (collision viscosity) and the other due to the interaction with the discrete lattice (propagation viscosity). Since the latter is negative, the sum may turn out to be orders of magnitude smaller than each of the two contributions separately, thus providing a mechanism to access SIF regimes at ordinary values of the collisional viscosity. This concept, as applied to quantum superfluids in one-dimensional optical lattices, is shown to reproduce shear viscosities consistent with the AdS-CFT holographic bound on the viscosity/entropy ratio. This shows that lattice kinetic theory continues to hold for strongly coupled hydrodynamic regimes where continuum kinetic theory may no longer be applicable.Entropy2015-09-03179Article10.3390/e17096169616961781099-43002015-09-03doi: 10.3390/e17096169Miller JimenezSauro Succi<![CDATA[Entropy, Vol. 17, Pages 6150-6168: Conformal Gauge Transformations in Thermodynamics]]>
http://www.mdpi.com/1099-4300/17/9/6150
In this work, we show that the thermodynamic phase space is naturally endowed with a non-integrable connection, defined by all of those processes that annihilate the Gibbs one-form, i.e., reversible processes. We argue that such a connection is invariant under re-scalings of the connection one-form, whilst, as a consequence of the non-integrability of the connection, its curvature is not and, therefore, neither is the associated pseudo-Riemannian geometry. We claim that this is not surprising, since these two objects are associated with irreversible processes. Moreover, we provide the explicit form in which all of the elements of the geometric structure of the thermodynamic phase space change under a re-scaling of the connection one-form. We call this transformation of the geometric structure a conformal gauge transformation. As an example, we revisit the change of the thermodynamic representation and consider the resulting change between the two metrics on the thermodynamic phase space, which induce Weinhold’s energy metric and Ruppeiner’s entropy metric. As a by-product, we obtain a proof of the well-known conformal relation between Weinhold’s and Ruppeiner’s metrics along the equilibrium directions. Finally, we find interesting properties of the almost para-contact structure and of its eigenvectors, which may be of physical interest.Entropy2015-09-02179Article10.3390/e17096150615061681099-43002015-09-02doi: 10.3390/e17096150Alessandro BravettiCesar Lopez-MonsalvoFrancisco Nettel<![CDATA[Entropy, Vol. 17, Pages 6129-6149: Nonlinear Predictive Control of a Hydropower System Model]]>
http://www.mdpi.com/1099-4300/17/9/6129
A six-dimensional nonlinear hydropower system controlled by a nonlinear predictive control method is presented in this paper. In terms of the nonlinear predictive control method; the performance index with terminal penalty function is selected. A simple method to find an appropriate terminal penalty function is introduced and its effectiveness is proved. The input-to-state-stability of the controlled system is proved by using the Lyapunov function. Subsequently a six-dimensional model of the hydropower system is presented in the paper. Different with other hydropower system models; the above model includes the hydro-turbine system; the penstock system; the generator system; and the hydraulic servo system accurately describing the operational process of a hydropower plant. Furthermore, the numerical experiments show that the six-dimensional nonlinear hydropower system controlled by the method is stable. In addition, the numerical experiment also illustrates that the nonlinear predictive control method enjoys great advantages over a traditional control method in nonlinear systems. Finally, a strategy to combine the nonlinear predictive control method with other methods is proposed to further facilitate the application of the nonlinear predictive control method into practice.Entropy2015-09-01179Article10.3390/e17096129612961491099-43002015-09-01doi: 10.3390/e17096129Runfan ZhangDiyi ChenXiaoyi Ma<![CDATA[Entropy, Vol. 17, Pages 6110-6128: Entropic Dynamics]]>
http://www.mdpi.com/1099-4300/17/9/6110
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints appropriate to the problem at hand. In this paper we review three examples of entropic dynamics. First we tackle the simpler case of a standard diffusion process which allows us to address the central issue of the nature of time. Then we show that imposing the additional constraint that the dynamics be non-dissipative leads to Hamiltonian dynamics. Finally, considerations from information geometry naturally lead to the type of Hamiltonian that describes quantum theory.Entropy2015-09-01179Review10.3390/e17096110611061281099-43002015-09-01doi: 10.3390/e17096110Ariel Caticha<![CDATA[Entropy, Vol. 17, Pages 6093-6109: Optimal Base Wavelet Selection for ECG Noise Reduction Using a Comprehensive Entropy Criterion]]>
http://www.mdpi.com/1099-4300/17/9/6093
The selection of an appropriate wavelet is an essential issue that should be addressed in the wavelet-based filtering of electrocardiogram (ECG) signals. Since entropy can measure the features of uncertainty associated with the ECG signal, a novel comprehensive entropy criterion Ecom based on multiple criteria related to entropy and energy is proposed in this paper to search for an optimal base wavelet for a specific ECG signal. Taking account of the decomposition capability of wavelets and the similarity in information between the decomposed coefficients and the analyzed signal, the proposed Ecom criterion integrates eight criteria, i.e., energy, entropy, energy-to-entropy ratio, joint entropy, conditional entropy, mutual information, relative entropy, as well as comparison information entropy for optimal wavelet selection. The experimental validation is conducted on the basis of ECG signals of sixteen subjects selected from the MIT-BIH Arrhythmia Database. The Ecom is compared with each of these eight criteria through four filtering performance indexes, i.e., output signal to noise ratio (SNRo), root mean square error (RMSE), percent root mean-square difference (PRD) and correlation coefficients. The filtering results of ninety-six ECG signals contaminated by noise have verified that Ecom has outperformed the other eight criteria in the selection of best base wavelets for ECG signal filtering. The wavelet identified by the Ecom has achieved the best filtering performance than the other comparative criteria. A hypothesis test also validates that SNRo, RMSE, PRD and correlation coefficients of Ecom are significantly different from those of the shape-matched approach (α = 0.05 , two-sided t- test).Entropy2015-09-01179Article10.3390/e17096093609361091099-43002015-09-01doi: 10.3390/e17096093Hong HeYonghong TanYuexia Wang<![CDATA[Entropy, Vol. 17, Pages 6072-6092: Distributing Secret Keys with Quantum Continuous Variables: Principle, Security and Implementations]]>
http://www.mdpi.com/1099-4300/17/9/6072
The ability to distribute secret keys between two parties with information-theoretic security, that is regardless of the capacities of a malevolent eavesdropper, is one of the most celebrated results in the field of quantum information processing and communication. Indeed, quantum key distribution illustrates the power of encoding information on the quantum properties of light and has far-reaching implications in high-security applications. Today, quantum key distribution systems operate in real-world conditions and are commercially available. As with most quantum information protocols, quantum key distribution was first designed for qubits, the individual quanta of information. However, the use of quantum continuous variables for this task presents important advantages with respect to qubit-based protocols, in particular from a practical point of view, since it allows for simple implementations that require only standard telecommunication technology. In this review article, we describe the principle of continuous-variable quantum key distribution, focusing in particular on protocols based on coherent states. We discuss the security of these protocols and report on the state-of-the-art in experimental implementations, including the issue of side-channel attacks. We conclude with promising perspectives in this research field.Entropy2015-08-31179Review10.3390/e17096072607260921099-43002015-08-31doi: 10.3390/e17096072Eleni DiamantiAnthony Leverrier<![CDATA[Entropy, Vol. 17, Pages 6056-6071: Self-Similar Solutions of Rényi’s Entropy and the Concavity of Its Entropy Power]]>
http://www.mdpi.com/1099-4300/17/9/6056
We study the class of self-similar probability density functions with finite mean and variance, which maximize Rényi’s entropy. The investigation is restricted in the Schwartz space S(Rd) and in the space of l-differentiable compactly supported functions Clc (Rd). Interestingly, the solutions of this optimization problem do not coincide with the solutions of the usual porous medium equation with a Dirac point source, as occurs in the optimization of Shannon’s entropy. We also study the concavity of the entropy power in Rd with respect to time using two different methods. The first one takes advantage of the solutions determined earlier, while the second one is based on a setting that could be used for Riemannian manifolds.Entropy2015-08-31179Article10.3390/e17096056605660711099-43002015-08-31doi: 10.3390/e17096056Agapitos Hatzinikitas<![CDATA[Entropy, Vol. 17, Pages 6044-6055: The Effect of a Long-Range Correlated-Hopping Interaction on Bariev Spin Chains]]>
http://www.mdpi.com/1099-4300/17/9/6044
We introduce a long-range particle and spin interaction into the standard Bariev model and show that this interaction is equivalent to a phase shift in the kinetic term of the Hamiltonian. When the particles circle around the chain and across the boundary, the accumulated phase shift acts as a twist boundary condition with respect to the normal periodic boundary condition. This boundary phase term depends on the total number of particles in the system and also the number of particles in different spin states, which relates to the spin fluctuations in the system. The model is solved exactly via a unitary transformation by the coordinate Bethe ansatz. We calculate the Bethe equations and work out the energy spectrum with varying number of particles and spins.Entropy2015-08-28179Article10.3390/e17096044604460551099-43002015-08-28doi: 10.3390/e17096044Tao YangFa-Kai WenKun HaoLi-Ke CaoRui-Hong Yue<![CDATA[Entropy, Vol. 17, Pages 6025-6043: New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells Equation]]>
http://www.mdpi.com/1099-4300/17/9/6025
In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM) and generalized Kudryashov method (GKM) are applied to find several exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation. Primarily, we seek some exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using ETEM. Then, we research dark soliton solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using GKM. Lastly, according to the values of some parameters, we draw two and three dimensional graphics of imaginary and real values of certain solutions found by utilizing both methods.Entropy2015-08-27179Article10.3390/e17096025602560431099-43002015-08-27doi: 10.3390/e17096025Seyma DemirayHasan Bulut