Entropy
http://www.mdpi.com/journal/entropy
Latest open access articles published in Entropy at http://www.mdpi.com/journal/entropy<![CDATA[Entropy, Vol. 18, Pages 56: Fractal Representation of Exergy]]>
http://www.mdpi.com/1099-4300/18/2/56
We developed a geometrical model to represent the thermodynamic concepts of exergy and anergy. The model leads to multi-scale energy lines (correlons) that we characterised by fractal dimension and entropy analyses. A specific attention will be paid to overlapping points, rising interesting remarks about trans-scale dynamics of heat flows.Entropy2016-02-06182Article10.3390/e18020056561099-43002016-02-06doi: 10.3390/e18020056Yvain CanivetDiogo Queiros-CondéLavinia Grosu<![CDATA[Entropy, Vol. 18, Pages 54: Definition and Counting of Configurational Microstates in Steady-State Two-Phase Flows in Pore Networks]]>
http://www.mdpi.com/1099-4300/18/2/54
Steady-state two-phase flow in porous media is a process whereby a wetting phase displaces a non-wetting phase within a pore network. It is an off-equilibrium stationary process—in the sense that it is maintained in dynamic equilibrium at the expense of energy supplied to the system. The efficiency of the process depends on its spontaneity, measurable by the rate of global entropy production. The latter has been proposed to comprise two components: the rate of mechanical energy dissipation at constant temperature (a thermal entropy component, Q/T, in the continuum mechanics scale) and the configurational entropy (a Boltzmann–Gibbs entropy component, klnW), due to the existence of a canonical ensemble of flow configurations, physically admissible to the externally imposed macrostate conditions. Here, we propose an analytical model to account the number of microstates, lnW, in two-phase flows in pore networks. Combinatorial analysis is implemented to evaluate the number of identified microstates per physically admissible internal flow arrangement, compatible with the imposed steady-state flow conditions. Then, Stirling’s approximation is applied to downscale the large factorial numbers. Finally, the number of microstates is estimated by contriving an appropriate mixing scheme over the canonical ensemble of the physically admissible flow configurations. Indicative computations are furnished.Entropy2016-02-06182Article10.3390/e18020054541099-43002016-02-06doi: 10.3390/e18020054Marios ValavanidesTryfon Daras<![CDATA[Entropy, Vol. 18, Pages 57: Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra]]>
http://www.mdpi.com/1099-4300/18/2/57
In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. The posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.Entropy2016-02-06182Article10.3390/e18020057571099-43002016-02-06doi: 10.3390/e18020057Kiel HockKeith Earle<![CDATA[Entropy, Vol. 18, Pages 55: Stability Analysis and Synchronization for a Class of Fractional-Order Neural Networks]]>
http://www.mdpi.com/1099-4300/18/2/55
Stability of a class of fractional-order neural networks (FONNs) is analyzed in this paper. First, two sufficient conditions for convergence of the solution for such systems are obtained by utilizing Gronwall–Bellman lemma and Laplace transform technique. Then, according to the fractional-order Lyapunov second method and linear feedback control, the synchronization problem between two fractional-order chaotic neural networks is investigated. Finally, several numerical examples are presented to justify the feasibility of the proposed methods.Entropy2016-02-06182Article10.3390/e18020055551099-43002016-02-06doi: 10.3390/e18020055Guanjun LiHeng Liu<![CDATA[Entropy, Vol. 18, Pages 53: Bounding Extremal Degrees of Edge-Independent Random Graphs Using Relative Entropy]]>
http://www.mdpi.com/1099-4300/18/2/53
Edge-independent random graphs are a model of random graphs in which each potential edge appears independently with an individual probability. Based on the relative entropy method, we determine the upper and lower bounds for the extremal vertex degrees using the edge probability matrix and its largest eigenvalue. Moreover, an application to random graphs with given expected degree sequences is presented.Entropy2016-02-05182Article10.3390/e18020053531099-43002016-02-05doi: 10.3390/e18020053Yilun Shang<![CDATA[Entropy, Vol. 18, Pages 52: Sensitivity Analysis of Entropy Generation in Nanofluid Flow inside a Channel by Response Surface Methodology]]>
http://www.mdpi.com/1099-4300/18/2/52
Nanofluids can afford excellent thermal performance and have a major role in energy conservation aspect. In this paper, a sensitivity analysis has been performed by using response surface methodology to calculate the effects of nanoparticles on the entropy generation. For this purpose, the laminar forced convection of Al2O3-water nanofluid flow inside a channel is considered. The total entropy generation rates consist of the entropy generation rates due to heat transfer and friction loss are calculated by using velocity and temperature gradients. The continuity, momentum and energy equations have been solved numerically using a finite volume method. The sensitivity of the entropy generation rate to different parameters such as the solid volume fraction, the particle diameter, and the Reynolds number is studied in detail. Series of simulations were performed for a range of solid volume fraction 0 ≤ ϕ ≤ 0.05 , particle diameter 30 nm ≤ d p ≤ 90 nm , and the Reynolds number 200 ≤ Re ≤ 800. The results showed that the total entropy generation is more sensitive to the Reynolds number rather than the nanoparticles diameter or solid volume fraction. Also, the magnitude of total entropy generation, which increases with increase in the Reynolds number, is much higher for the pure fluid rather than the nanofluid.Entropy2016-02-05182Article10.3390/e18020052521099-43002016-02-05doi: 10.3390/e18020052Bijan DarbariSaman RashidiJavad Abolfazli Esfahani<![CDATA[Entropy, Vol. 18, Pages 50: Entropy Generation and Natural Convection of CuO-Water Nanofluid in C-Shaped Cavity under Magnetic Field]]>
http://www.mdpi.com/1099-4300/18/2/50
This paper investigates the entropy generation and natural convection inside a C-shaped cavity filled with CuO-water nanofluid and subjected to a uniform magnetic field. The Brownian motion effect is considered in predicting the nanofluid properties. The governing equations are solved using the finite volume method with the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The studied parameters are the Rayleigh number (1000 ≤ Ra ≤ 15,000), Hartman number (0 ≤ Ha ≤ 45), nanofluid volume fraction (0 ≤ φ ≤ 0.06), and the cavity aspect ratio (0.1 ≤ AR ≤ 0.7). The results have shown that the nanoparticles volume fraction enhances the natural convection but undesirably increases the entropy generation rate. It is also found that the applied magnetic field can suppress both the natural convection and the entropy generation rate, where for Ra = 1000 and φ = 0.04, the percentage reductions in total entropy generation decreases from 96.27% to 48.17% for Ha = 45 compared to zero magnetic field when the aspect ratio is increased from 0.1 to 0.7. The results of performance criterion have shown that the nanoparticles addition can be useful if a compromised magnetic field value represented by a Hartman number of 30 is applied.Entropy2016-02-05182Article10.3390/e18020050501099-43002016-02-05doi: 10.3390/e18020050Ali ChamkhaMuneer IsmaelAbbas KasaeipoorTaher Armaghani<![CDATA[Entropy, Vol. 18, Pages 51: Classification Active Learning Based on Mutual Information]]>
http://www.mdpi.com/1099-4300/18/2/51
Selecting a subset of samples to label from a large pool of unlabeled data points, such that a sufficiently accurate classifier is obtained using a reasonably small training set is a challenging, yet critical problem. Challenging, since solving this problem includes cumbersome combinatorial computations, and critical, due to the fact that labeling is an expensive and time-consuming task, hence we always aim to minimize the number of required labels. While information theoretical objectives, such as mutual information (MI) between the labels, have been successfully used in sequential querying, it is not straightforward to generalize these objectives to batch mode. This is because evaluation and optimization of functions which are trivial in individual querying settings become intractable for many objectives when we are to select multiple queries. In this paper, we develop a framework, where we propose efficient ways of evaluating and maximizing the MI between labels as an objective for batch mode active learning. Our proposed framework efficiently reduces the computational complexity from an order proportional to the batch size, when no approximation is applied, to the linear cost. The performance of this framework is evaluated using data sets from several fields showing that the proposed framework leads to efficient active learning for most of the data sets.Entropy2016-02-05182Article10.3390/e18020051511099-43002016-02-05doi: 10.3390/e18020051Jamshid SouratiMurat AkcakayaJennifer DyTodd LeenDeniz Erdogmus<![CDATA[Entropy, Vol. 18, Pages 49: Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator]]>
http://www.mdpi.com/1099-4300/18/2/49
In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs). Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE) by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.Entropy2016-02-05182Article10.3390/e18020049491099-43002016-02-05doi: 10.3390/e18020049Resat YilmazerMustafa IncFairouz TchierDumitru Baleanu<![CDATA[Entropy, Vol. 18, Pages 48: Thermodynamics of Quantum Feedback Cooling]]>
http://www.mdpi.com/1099-4300/18/2/48
The ability to initialize quantum registers in pure states lies at the core of many applications of quantum technologies, from sensing to quantum information processing and computation. In this paper, we tackle the problem of increasing the polarization bias of an ensemble of two-level register spins by means of joint coherent manipulations, involving a second ensemble of ancillary spins and energy dissipation into an external heat bath. We formulate this spin refrigeration protocol, akin to algorithmic cooling, in the general language of quantum feedback control, and identify the relevant thermodynamic variables involved. Our analysis is two-fold: on the one hand, we assess the optimality of the protocol by means of suitable figures of merit, accounting for both its work cost and effectiveness; on the other hand, we characterise the nature of correlations built up between the register and the ancilla. In particular, we observe that neither the amount of classical correlations nor the quantum entanglement seem to be key ingredients fuelling our spin refrigeration protocol. We report instead that a more general indicator of quantumness beyond entanglement, the so-called quantum discord, is closely related to the cooling performance.Entropy2016-02-04182Article10.3390/e18020048481099-43002016-02-04doi: 10.3390/e18020048Pietro Liuzzo-ScorpoLuis CorreaRebecca SchmidtGerardo Adesso<![CDATA[Entropy, Vol. 18, Pages 47: Entropy Generation through Deterministic Spiral Structures in Corner Flows with Sidewall Surface Mass Injection]]>
http://www.mdpi.com/1099-4300/18/2/47
Results are presented for an innovative computational procedure that predicts time-dependent instabilities and deterministic ordered structures in three-dimensional steady-state laminar boundary-layer flows. The flow configuration considered is a corner flow with sidewall surface mass injection into a horizontal boundary-layer flow. The equations for the velocity fluctuations are cast into a spectral Lorenz-type format and incorporated into the overall computational procedure for the three-dimensional flow. The non-linear time-dependent solutions of the spectral equations predict deterministic spectral ordered structures within spiral structures. Spectral analysis of these fluctuating solutions yields the resulting entropy generation rates resulting from the dissipation of the ordered structures. The results for the entropy generation rates indicate the prediction of a strong burst of ordered structures within the range of injection velocities studied. This new computational method is applicable to only selected thermal design processes.Entropy2016-02-02182Article10.3390/e18020047471099-43002016-02-02doi: 10.3390/e18020047LaVar Isaacson<![CDATA[Entropy, Vol. 18, Pages 46: Relative Entropy in Biological Systems]]>
http://www.mdpi.com/1099-4300/18/2/46
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe the dynamics of a population or probability distribution. Under suitable assumptions, the distribution will approach an equilibrium with the passage of time. Relative entropy—that is, the Kullback–Leibler divergence, or various generalizations of this—provides a quantitative measure of how far from equilibrium the system is. We explain various theorems that give conditions under which relative entropy is nonincreasing. In biochemical applications these results can be seen as versions of the Second Law of Thermodynamics, stating that free energy can never increase with the passage of time. In ecological applications, they make precise the notion that a population gains information from its environment as it approaches equilibrium.Entropy2016-02-02182Review10.3390/e18020046461099-43002016-02-02doi: 10.3390/e18020046John BaezBlake Pollard<![CDATA[Entropy, Vol. 18, Pages 1: New Derivatives on the Fractal Subset of Real-Line]]>
http://www.mdpi.com/1099-4300/18/2/1
In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect.Entropy2016-01-29182Article10.3390/e1802000111099-43002016-01-29doi: 10.3390/e18020001Alireza Khalili GolmankhanehDumitru Baleanu<![CDATA[Entropy, Vol. 18, Pages 45: Entropy-Weighted Instance Matching Between Different Sourcing Points of Interest]]>
http://www.mdpi.com/1099-4300/18/2/45
The crucial problem for integrating geospatial data is finding the corresponding objects (the counterpart) from different sources. Most current studies focus on object matching with individual attributes such as spatial, name, or other attributes, which avoids the difficulty of integrating those attributes, but at the cost of an ineffective matching. In this study, we propose an approach for matching instances by integrating heterogeneous attributes with the allocation of suitable attribute weights via information entropy. First, a normalized similarity formula is developed, which can simplify the calculation of spatial attribute similarity. Second, sound-based and word segmentation-based methods are adopted to eliminate the semantic ambiguity when there is a lack of a normative coding standard in geospatial data to express the name attribute. Third, category mapping is established to address the heterogeneity among different classifications. Finally, to address the non-linear characteristic of attribute similarity, the weights of the attributes are calculated by the entropy of the attributes. Experiments demonstrate that the Entropy-Weighted Approach (EWA) has good performance both in terms of precision and recall for instance matching from different data sets.Entropy2016-01-28182Article10.3390/e18020045451099-43002016-01-28doi: 10.3390/e18020045Lin LiXiaoyu XingHui XiaXiaoying Huang<![CDATA[Entropy, Vol. 18, Pages 44: Feature Selection of Power Quality Disturbance Signals with an Entropy-Importance-Based Random Forest]]>
http://www.mdpi.com/1099-4300/18/2/44
Power quality signal feature selection is an effective method to improve the accuracy and efficiency of power quality (PQ) disturbance classification. In this paper, an entropy-importance (EnI)-based random forest (RF) model for PQ feature selection and disturbance classification is proposed. Firstly, 35 kinds of signal features extracted from S-transform (ST) with random noise are used as the original input feature vector of RF classifier to recognize 15 kinds of PQ signals with six kinds of complex disturbance. During the RF training process, the classification ability of different features is quantified by EnI. Secondly, without considering the features with zero EnI, the optimal perturbation feature subset is obtained by applying the sequential forward search (SFS) method which considers the classification accuracy and feature dimension. Then, the reconstructed RF classifier is applied to identify disturbances. According to the simulation results, the classification accuracy is higher than that of other classifiers, and the feature selection effect of the new approach is better than SFS and sequential backward search (SBS) without EnI. With the same feature subset, the new method can maintain a classification accuracy above 99.7% under the condition of 30 dB or above, and the accuracy under 20 dB is 96.8%.Entropy2016-01-28182Article10.3390/e18020044441099-43002016-01-28doi: 10.3390/e18020044Nantian HuangGuobo LuGuowei CaiDianguo XuJiafeng XuFuqing LiLiying Zhang<![CDATA[Entropy, Vol. 18, Pages 43: Natural Convection and Entropy Generation in Nanofluid Filled Entrapped Trapezoidal Cavities under the Influence of Magnetic Field]]>
http://www.mdpi.com/1099-4300/18/2/43
In this article, entropy generation due to natural convection in entrapped trapezoidal cavities filled with nanofluid under the influence of magnetic field was numerically investigated. The upper (lower) enclosure is filled with CuO-water (Al2O3-water) nanofluid. The top and bottom horizontal walls of the trapezoidal enclosures are maintained at constant hot temperature while other inclined walls of the enclosures are at constant cold temperature. Different combinations of Hartmann numbers are imposed on the upper and lower trapezoidal cavities. Numerical simulations are conducted for different values of Rayleigh numbers, Hartmann number and solid volume fraction of the nanofluid by using the finite element method. In the upper and lower trapezoidal cavities magnetic fields with different combinations of Hartmann numbers are imposed. It is observed that the averaged heat transfer reduction with magnetic field is more pronounced at the highest value of the Rayleigh number. When there is no magnetic field in the lower cavity, the averaged Nusselt number enhances as the value of the Hartmann number of the upper cavity increases. The heat transfer enhancement rates with nanofluids which are in the range of 10% and 12% are not affected by the presence of the magnetic field. Second law analysis of the system for various values of Hartmann number and nanoparticle volume fractions of upper and lower trapezoidal domains is performed.Entropy2016-01-28182Article10.3390/e18020043431099-43002016-01-28doi: 10.3390/e18020043Fatih SelimefendigilHakan ÖztopNidal Abu-Hamdeh<![CDATA[Entropy, Vol. 18, Pages 42: Non-Extensive Entropic Distance Based on Diffusion: Restrictions on Parameters in Entropy Formulae]]>
http://www.mdpi.com/1099-4300/18/2/42
Based on a diffusion-like master equation we propose a formula using the Bregman divergence for measuring entropic distance in terms of different non-extensive entropy expressions. We obtain the non-extensivity parameter range for a universal approach to the stationary distribution by simple diffusive dynamics for the Tsallis and the Kaniadakis entropies, for the Hanel–Thurner generalization, and finally for a recently suggested log-log type entropy formula which belongs to diverging variance in the inverse temperature superstatistics.Entropy2016-01-27182Article10.3390/e18020042421099-43002016-01-27doi: 10.3390/e18020042Tamás BiróZsolt Schram<![CDATA[Entropy, Vol. 18, Pages 38: Understanding Interdependency Through Complex Information Sharing]]>
http://www.mdpi.com/1099-4300/18/2/38
The interactions between three or more random variables are often nontrivial, poorly understood and, yet, are paramount for future advances in fields such as network information theory, neuroscience and genetics. In this work, we analyze these interactions as different modes of information sharing. Towards this end, and in contrast to most of the literature that focuses on analyzing the mutual information, we introduce an axiomatic framework for decomposing the joint entropy that characterizes the various ways in which random variables can share information. Our framework distinguishes between interdependencies where the information is shared redundantly and synergistic interdependencies where the sharing structure exists in the whole, but not between the parts. The key contribution of our approach is to focus on symmetric properties of this sharing, which do not depend on a specific point of view for differentiating roles between its components. We show that our axioms determine unique formulas for all of the terms of the proposed decomposition for systems of three variables in several cases of interest. Moreover, we show how these results can be applied to several network information theory problems, providing a more intuitive understanding of their fundamental limits.Entropy2016-01-26182Article10.3390/e18020038381099-43002016-01-26doi: 10.3390/e18020038Fernando RosasVasilis NtranosChristopher EllisonSofie PollinMarian Verhelst<![CDATA[Entropy, Vol. 18, Pages 41: Local Band Spectral Entropy Based on Wavelet Packet Applied to Surface EMG Signals Analysis]]>
http://www.mdpi.com/1099-4300/18/2/41
An efficient analytical method for electromyogram (EMG) signals is of great significance to research the inherent mechanism of a motor-control system. In this paper, we proposed an improved approach named wavelet-packet-based local band spectral entropy (WP-LBSE) by introducing the concept of frequency band local-energy (ELF) into the wavelet packet entropy, in order to characterize the time-varying complexity of the EMG signals in the local frequency band. The EMG data were recorded from the biceps brachii (BB) muscle and triceps brachii (TB) muscle at 40°, 100° and 180° of elbow flexion by 10 healthy participants. Significant differences existed among any pair of the three patterns (p &lt; 0.05). The WP-LBSE values of the EMG signals in BB muscle and TB muscle demonstrated a decreased tendency from 40° to 180° of elbow flexion, while the distributions of spectral energy were decreased to a stable state as time periods progressed under the same pattern. The result of this present work is helpful to describe the time-varying complexity characteristics of the EMG signals under different joint angles, and is meaningful to research the dynamic variation of the activated motor units and muscle fibers in the motor-control system.Entropy2016-01-26182Article10.3390/e18020041411099-43002016-01-26doi: 10.3390/e18020041Xiaoling ChenPing XieHuan LiuYan SongYihao Du<![CDATA[Entropy, Vol. 18, Pages 39: Structure of Optimal State Discrimination in Generalized Probabilistic Theories]]>
http://www.mdpi.com/1099-4300/18/2/39
We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from convex optimization. The method exploits the convex geometry of states but not other detailed conditions or relations of states and effects. We also show that properties in optimal quantum state discrimination are shared in GPTs in general: (i) no measurement sometimes gives optimal discrimination, and (ii) optimal measurement is not unique.Entropy2016-01-26182Article10.3390/e18020039391099-43002016-01-26doi: 10.3390/e18020039Joonwoo BaeDai-Gyoung KimLeong-Chuan Kwek<![CDATA[Entropy, Vol. 18, Pages 40: Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative]]>
http://www.mdpi.com/1099-4300/18/2/40
Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a mathematical equation for prediction. In this work, a model of the well-known river blindness disease is created via the Caputo and beta derivatives. A partial study of stability analysis was presented. The extended system describing the spread of this disease was solved via two analytical techniques: the Laplace perturbation and the homotopy decomposition methods. Summaries of the iteration methods used were provided to derive special solutions to the extended systems. Employing some theoretical parameters, we present some numerical simulations.Entropy2016-01-26182Article10.3390/e18020040401099-43002016-01-26doi: 10.3390/e18020040Abdon AtanganaRubayyi Alqahtani<![CDATA[Entropy, Vol. 18, Pages 37: Acknowledgement to Reviewers of Entropy in 2015]]>
http://www.mdpi.com/1099-4300/18/1/37
The editors of Entropy would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...]Entropy2016-01-21181Editorial10.3390/e18010037371099-43002016-01-21doi: 10.3390/e18010037 Entropy Editorial Office<![CDATA[Entropy, Vol. 18, Pages 35: Average Contrastive Divergence for Training Restricted Boltzmann Machines]]>
http://www.mdpi.com/1099-4300/18/1/35
This paper studies contrastive divergence (CD) learning algorithm and proposes a new algorithm for training restricted Boltzmann machines (RBMs). We derive that CD is a biased estimator of the log-likelihood gradient method and make an analysis of the bias. Meanwhile, we propose a new learning algorithm called average contrastive divergence (ACD) for training RBMs. It is an improved CD algorithm, and it is different from the traditional CD algorithm. Finally, we obtain some experimental results. The results show that the new algorithm is a better approximation of the log-likelihood gradient method and outperforms the traditional CD algorithm.Entropy2016-01-21181Article10.3390/e18010035351099-43002016-01-21doi: 10.3390/e18010035Xuesi MaXiaojie Wang<![CDATA[Entropy, Vol. 18, Pages 36: The Entropy of Laughter: Discriminative Power of Laughter’s Entropy in the Diagnosis of Depression]]>
http://www.mdpi.com/1099-4300/18/1/36
Laughter is increasingly present in biomedical literature, both in analytical neurological aspects and in applied therapeutic fields. The present paper, bridging between the analytical and the applied, explores the potential of a relevant variable of laughter’s acoustic signature—entropy—in the detection of a widespread mental disorder, depression, as well as in gauging the severity of its diagnostic. In laughter, the Shannon–Wiener entropy of the distribution of sound frequencies, which is one of the key features distinguishing its acoustic signal from the utterances of spoken language, has not been a specific focus of research yet, although the studies of human language and of animal communication have pointed out that entropy is a very important factor regarding the vocal/acoustic expression of emotions. As the experimental survey of laughter in depression herein undertaken shows, it was possible to discriminate between patients and controls with an 82.1% accuracy just by using laughter’s entropy and by applying the decision tree procedure. These experimental results, discussed in the light of the current research on laughter, point to the relevance of entropy in the spontaneous bona fide extroversion of mental states toward other individuals, as the signal of laughter seems to imply. This is in line with recent theoretical approaches that rely on the optimization of a neuro-informational free energy (and associated entropy) as the main “stuff” of brain processing.Entropy2016-01-21181Article10.3390/e18010036361099-43002016-01-21doi: 10.3390/e18010036Jorge NavarroRaquel del MoralPedro Cuesta-AlvaroRafael Lahoz-BeltraPedro Marijuán<![CDATA[Entropy, Vol. 18, Pages 33: Measure of Uncertainty in Process Models Using Stochastic Petri Nets and Shannon Entropy]]>
http://www.mdpi.com/1099-4300/18/1/33
When modelling and analysing business processes, the main emphasis is usually put on model validity and accuracy, i.e., the model meets the formal specification and also models the relevant system. In recent years, a series of metrics has begun to develop, which allows the quantification of the specific properties of process models. These characteristics are, for instance, complexity, comprehensibility, cohesion, and uncertainty. This work is focused on defining a method that allows us to measure the uncertainty of a process model, which was modelled by using stochastic Petri nets (SPN). The principle of this method consists of mapping of all reachable marking of SPN into the continuous-time Markov chain and then calculating its stationary probabilities. The uncertainty is then measured as the entropy of the Markov chain (it is possible to calculate the uncertainty of the specific subset of places as well as of whole net). Alternatively, the uncertainty index is quantified as a percentage of the calculated entropy against maximum entropy (the resulting value is normalized to the interval &lt;0,1&gt;). The calculated entropy can also be used as a measure of the model complexity.Entropy2016-01-19181Article10.3390/e18010033331099-43002016-01-19doi: 10.3390/e18010033Martin IblJan Čapek<![CDATA[Entropy, Vol. 18, Pages 34: Schroedinger vs. Navier–Stokes]]>
http://www.mdpi.com/1099-4300/18/1/34
Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck’s constant, while the volume density of entropy is proportional to Boltzmann’s constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier–Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation).Entropy2016-01-19181Article10.3390/e18010034341099-43002016-01-19doi: 10.3390/e18010034P. Fernández de CórdobaJ. IsidroJ. Vázquez Molina<![CDATA[Entropy, Vol. 18, Pages 31: Perturbation of Fractional Multi-Agent Systems in Cloud Entropy Computing]]>
http://www.mdpi.com/1099-4300/18/1/31
A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy management systems involve functions, methods, procedural approaches, and algorithms. In this study, we introduce a new perturbed algorithm based on the fractional Poisson process. The discrete dynamics are suggested by using fractional entropy and fractional type Tsallis entropy. Moreover, we study the algorithm stability.Entropy2016-01-19181Article10.3390/e18010031311099-43002016-01-19doi: 10.3390/e18010031Rabha IbrahimHamid JalabAbdullah Gani<![CDATA[Entropy, Vol. 18, Pages 32: Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent]]>
http://www.mdpi.com/1099-4300/18/1/32
The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs), are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on the time sequence, the high-dimensional traffic is projected onto the low dimension reconstructed phase space, and a reduced dynamic system is obtained from the dynamic system viewpoint. Then, a numerical method for computing the largest Lyapunov exponent of the low-dimensional dynamic system is presented. Further, the longest predictable time, which is related to chaotic behaviors in the system, is studied using the largest Lyapunov exponent, and the Wolf method is used to predict the evolution of the traffic in a local area network by both Dot and Interval predictions, and a reliable result is obtained by the presented method. As the conclusion, the results show that the largest Lyapunov exponent can be used to describe the sensitivity of the trajectory in the reconstructed phase space to the initial values. Moreover, Dot Prediction can effectively predict the flow burst. The numerical simulation also shows that the presented method is feasible and efficient for predicting the complex dynamic behaviors in LAN traffic, especially for congestion and attack in networks, which are the main two complex phenomena behaving as chaos in networks.Entropy2016-01-19181Article10.3390/e18010032321099-43002016-01-19doi: 10.3390/e18010032Yan LiuJiazhong Zhang<![CDATA[Entropy, Vol. 18, Pages 29: Distributed Consensus of Nonlinear Multi-Agent Systems on State-Controlled Switching Topologies]]>
http://www.mdpi.com/1099-4300/18/1/29
This paper considers the consensus problem of nonlinear multi-agent systems under switching directed topologies. Specifically, the dynamics of each agent incorporates an intrinsic nonlinear term and the interaction topology may not contain a spanning tree at any time. By designing a state-controlled switching law, we show that the multi-agent system with the neighbor-based protocol can achieve consensus if the switching topologies jointly contain a spanning tree. Moreover, an easily manageable algebraic criterion is deduced to unravel the underlying mechanisms in reaching consensus. Finally, a numerical example is exploited to illustrate the effectiveness of the developed theoretical results.Entropy2016-01-18181Article10.3390/e18010029291099-43002016-01-18doi: 10.3390/e18010029Kairui ChenJunwei WangYun Zhang<![CDATA[Entropy, Vol. 18, Pages 19: Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems]]>
http://www.mdpi.com/1099-4300/18/1/19
In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems.Entropy2016-01-18181Article10.3390/e18010019191099-43002016-01-18doi: 10.3390/e18010019Dagmar MarkechováBeloslav Riečan<![CDATA[Entropy, Vol. 18, Pages 30: Using Multidimensional ADTPE and SVM for Optical Modulation Real-Time Recognition]]>
http://www.mdpi.com/1099-4300/18/1/30
Based on the feature extraction of multidimensional asynchronous delay-tap plot entropy (ADTPE) and multiclass classification of support vector machine (SVM), we propose a method for recognition of multiple optical modulation formats and various data rates. We firstly present the algorithm of multidimensional ADTPE, which is extracted from asynchronous delay sampling pairs of modulated optical signal. Then, a multiclass SVM is utilized for fast and accurate classification of several widely-used optical modulation formats. In addition, a simple real-time recognition scheme is designed to reduce the computation time. Compared to the existing method based on asynchronous delay-tap plot (ADTP), the theoretical analysis and simulation results show that our recognition method can effectively enhance the tolerance of transmission impairments, obtaining relatively high accuracy. Finally, it is further demonstrated that the proposed method can be integrated in an optical transport network (OTN) with flexible expansion. Through simply adding the corresponding sub-SVM module in the digital signal processer (DSP), arbitrary new modulation formats can be recognized with high recognition accuracy in a short response time.Entropy2016-01-16181Article10.3390/e18010030301099-43002016-01-16doi: 10.3390/e18010030Junyu WeiZhiping HuangShaojing SuZhen Zuo<![CDATA[Entropy, Vol. 18, Pages 28: Entropy Generation Results of Convenience But without Purposeful Analysis and Due Comprehension—Guidelines for Authors]]>
http://www.mdpi.com/1099-4300/18/1/28
There is a growing trend in recently-submitted manuscripts and publications to present calculated results of entropy generation, also known as entropy production, as field quantities in a system or device control volume, based on prior calculation of velocity and temperature fields, frequently using CFD numerical methods. [...]Entropy2016-01-15181Editorial10.3390/e18010028281099-43002016-01-15doi: 10.3390/e18010028Milivoje Kostic<![CDATA[Entropy, Vol. 18, Pages 27: Interacting Brownian Swarms: Some Analytical Results]]>
http://www.mdpi.com/1099-4300/18/1/27
We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact). Depending on the values of the control parameters, one of the following patterns emerges after collision: (i) Both swarms remain essentially flocked, or (ii) the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings.Entropy2016-01-14181Article10.3390/e18010027271099-43002016-01-14doi: 10.3390/e18010027Guillaume SartorettiMax-Olivier Hongler<![CDATA[Entropy, Vol. 18, Pages 26: Information and the Quantum World]]>
http://www.mdpi.com/1099-4300/18/1/26
The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material world has important consequences for the amounts of information that can be stored in physical systems and for the possibilities of information transfer. In many cases, overlap between quantum states (non-orthogonality of states) blurs distinctions and impedes efficient information transfer. However, the other typical quantum feature, entanglement, makes new and seemingly mysterious ways of transporting information possible. In this article, we suggest an interpretational scheme of quantum mechanics in terms of perspectival physical properties that may provide an intelligible account of these novel quantum possibilities, while staying close to the mathematical formalism of quantum mechanics.Entropy2016-01-13181Article10.3390/e18010026261099-43002016-01-13doi: 10.3390/e18010026Dennis Dieks<![CDATA[Entropy, Vol. 18, Pages 25: Hot Spots and Persistence of Nitrate in Aquifers Across Scales]]>
http://www.mdpi.com/1099-4300/18/1/25
Nitrate-N (NO3 -- N) is one of the most pervasive contaminants in groundwater. Nitrate in groundwater exhibits long-term behavior due to complex interactions at multiple scales among various geophysical factors, such as sources of nitrate-N, characteristics of the vadose zone and aquifer attributes. To minimize contamination of nitrate-N in groundwater, it is important to estimate hot spots (&gt;10 mg/L of NO3 -- N), trends and persistence of nitrate-N in groundwater. To analyze the trends and persistence of nitrate-N in groundwater at multiple spatio-temporal scales, we developed and used an entropy-based method along with the Hurst exponent in two different hydrogeologic settings: the Trinity and Ogallala Aquifers in Texas at fine (2 km × 2 km), intermediate (10 km × 10 km) and coarse (100 km × 100 km) scales. Results show that nitrate-N exhibits long-term persistence at the intermediate and coarse scales. In the Trinity Aquifer, overall mean nitrate-N has declined with a slight increase in normalized marginal entropy (NME) over each decade from 1940 to 2008; however, the number of hot spots has increased over time. In the Ogallala Aquifer, overall mean nitrate-N has increased with slight moderation in NME since 1940; however, the number of hot spots has significantly decreased for the same period at all scales.Entropy2016-01-13181Article10.3390/e18010025251099-43002016-01-13doi: 10.3390/e18010025Dipankar DwivediBinayak Mohanty<![CDATA[Entropy, Vol. 18, Pages 24: Entropy Analysis of Solar Two-Step Thermochemical Cycles for Water and Carbon Dioxide Splitting]]>
http://www.mdpi.com/1099-4300/18/1/24
The present study provides a thermodynamic analysis of solar thermochemical cycles for splitting of H2O or CO2. Such cycles, powered by concentrated solar energy, have the potential to produce fuels in a sustainable way. We extend a previous study on the thermodynamics of water splitting by also taking into account CO2 splitting and the influence of the solar absorption efficiency. Based on this purely thermodynamic approach, efficiency trends are discussed. The comprehensive and vivid representation in T-S diagrams provides researchers in this field with the required theoretical background to improve process development. Furthermore, results about the required entropy change in the used redox materials can be used as a guideline for material developers. The results show that CO2 splitting is advantageous at higher temperature levels, while water splitting is more feasible at lower temperature levels, as it benefits from a great entropy change during the splitting step.Entropy2016-01-11181Technical Note10.3390/e18010024241099-43002016-01-11doi: 10.3390/e18010024Matthias LangeMartin RoebChristian SattlerRobert Pitz-Paal<![CDATA[Entropy, Vol. 18, Pages 23: Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series]]>
http://www.mdpi.com/1099-4300/18/1/23
According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD) is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger–Procaccia (G-P) method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO). The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA) and BP neural network (BPNN) model) in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice.Entropy2016-01-08181Article10.3390/e18010023231099-43002016-01-08doi: 10.3390/e18010023Qing LiSteven LiangJianguo YangBeizhi Li<![CDATA[Entropy, Vol. 18, Pages 22: Increment Entropy as a Measure of Complexity for Time Series]]>
http://www.mdpi.com/1099-4300/18/1/22
Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce an increment entropy to measure the complexity of time series in which each increment is mapped onto a word of two letters, one corresponding to the sign and the other corresponding to the magnitude. Increment entropy (IncrEn) is defined as the Shannon entropy of the words. Simulations on synthetic data and tests on epileptic electroencephalogram (EEG) signals demonstrate its ability of detecting abrupt changes, regardless of the energetic (e.g., spikes or bursts) or structural changes. The computation of IncrEn does not make any assumption on time series, and it can be applicable to arbitrary real-world data.Entropy2016-01-08181Article10.3390/e18010022221099-43002016-01-08doi: 10.3390/e18010022Xiaofeng LiuAimin JiangNing XuJianru Xue<![CDATA[Entropy, Vol. 18, Pages 21: Entropy Assessment on Direct Contact Condensation of Subsonic Steam Jets in a Water Tank through Numerical Investigation]]>
http://www.mdpi.com/1099-4300/18/1/21
The present article analyzes the dissipation characteristics of the direct contact condensation (DCC) phenomenon that occurs when steam is injected into a water tank at a subsonic speed using a new modeling approach for the entropy generation over the calculation domain. The developed entropy assessment model is based on the local equilibrium hypothesis of non-equilibrium thermodynamics. The fluid flow and heat transfer processes are investigated numerically. To describe the condensation and evaporation process at the vapor-liquid interface, a phase change model originated from the kinetic theory of gas is implemented with the mixture model for multiphase flow in the computational fluid dynamics (CFD) code ANSYS-FLUENT. The CFD predictions agree well with the published works, which indicates the phase change model combined with the mixture model is a promising way to simulate the DCC phenomenon. In addition, three clear stages as initial stage, developing stage and oscillatory stage are discriminated from both the thermal-hydraulic results and the entropy generation information. During different stages, different proportion of the entropy generation rate owing to heat transfer, viscous direct dissipation, turbulent dissipation and inner phase change in total entropy generation rate is estimated, which is favorable to deeper understanding the irreversibility of DCC phenomenon, designing and optimizing the equipment involved in the process.Entropy2016-01-07181Article10.3390/e18010021211099-43002016-01-07doi: 10.3390/e18010021Yu JiHao-Chun ZhangJian-Fei TongXu-Wei WangHan WangYi-Ning Zhang<![CDATA[Entropy, Vol. 18, Pages 20: Trusted Noise in Continuous-Variable Quantum Key Distribution: A Threat and a Defense]]>
http://www.mdpi.com/1099-4300/18/1/20
We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and noisy channels. The influence of such a noise on the security of Gaussian quantum cryptography can be crucial, even despite the fact that a noise is trusted, due to a strongly nonlinear behavior of the quantum entropies involved in the security analysis. We recapitulate the known effect of the preparation noise in both direct and reverse-reconciliation protocols, as well as the detection noise in the reverse-reconciliation scenario. As a new result, we show the negative role of the trusted detection noise in the direct-reconciliation scheme. We also describe the role of the trusted preparation or detection noise added at the reference side of the protocols in improving the robustness of the protocols to the channel noise, confirming the positive effect for the coherent-state reverse-reconciliation protocol. Finally, we address the combined effect of trusted noise added both in the source and the detector.Entropy2016-01-05181Article10.3390/e18010020201099-43002016-01-05doi: 10.3390/e18010020Vladyslav UsenkoRadim Filip<![CDATA[Entropy, Vol. 18, Pages 17: Three-Dimensional Lattice Boltzmann Simulation of Liquid Water Transport in Porous Layer of PEMFC]]>
http://www.mdpi.com/1099-4300/18/1/17
A three-dimensional two-phase lattice Boltzmann model (LBM) is implemented and validated for qualitative study of the fundamental phenomena of liquid water transport in the porous layer of a proton exchange membrane fuel cell (PEMFC). In the present study, the three-dimensional microstructures of a porous layer are numerically reconstructed by a random generation method. The LBM simulations focus on the effects of the porous layer porosity and boundary liquid saturation on liquid water transport in porous materials. Numerical results confirm that liquid water transport is strongly affected by the microstructures in a porous layer, and the transport process prefers the large pores as its main pathway. The preferential transport phenomenon is more profound with a decreased porous layer porosity and/or boundary liquid saturation. In the transport process, the breakup of a liquid water stream can occur under certain conditions, leading to the formation of liquid droplets inside the porous layer. This phenomenon is related to the connecting bridge or neck resistance dictated by the surface tension, and happens more frequently with a smaller porous layer porosity. Results indicate that an optimized design of porous layer porosity and the combination of various pore sizes may improve both the liquid water removal and gaseous reactant transport in the porous layer of a PEMFC.Entropy2015-12-31181Article10.3390/e18010017171099-43002015-12-31doi: 10.3390/e18010017Bo HanMeng NiHua Meng<![CDATA[Entropy, Vol. 18, Pages 18: Constitutive Explanations as a Methodological Framework for Integrating Thermodynamics and Economics]]>
http://www.mdpi.com/1099-4300/18/1/18
The common approach to integrating thermodynamics and economics is subsuming thermodynamic aspects among the set of constraints under which economic activity takes place. The causal link between energy and growth is investigated via aggregate econometric analysis. This paper discusses methodological issues of aggregate analysis and proposes an alternative framework based on recent developments in philosophy of science, in particular of the life sciences. “Constitutive explanations” eschew the covering law approach to scientific explanation and concentrate on the identification of multi-level architectures of causal mechanisms that generate phenomena. This methodology has been productively employed to organize cross-disciplinary research, and I suggest that it can also provide a framework for integrating thermodynamics and economics, since this also requires the combination of several scientific disciplines. I present the example of the “rebound effect” as a kind of constitutive explanation and put it in the context of urbanization as a complex mechanism that is the defining feature of economic growth in physical terms.Entropy2015-12-31181Article10.3390/e18010018181099-43002015-12-31doi: 10.3390/e18010018Carsten Herrmann-Pillath<![CDATA[Entropy, Vol. 18, Pages 9: Analysis of Entropy Generation in Natural Convection of Nanofluid inside a Square Cavity Having Hot Solid Block: Tiwari and Das’ Model]]>
http://www.mdpi.com/1099-4300/18/1/9
A computational work has been performed in this study to investigate the effects of solid isothermal partition insertion in a nanofluid filled cavity that is cooled via corner isothermal cooler. Mathematical model formulated in dimensionless primitive variables has been solved by finite volume method. The study is performed for different geometrical ratio of solid inserted block and corner isothermal cooler, Rayleigh number and solid volume fraction parameter of nanoparticles. It is observed that an insertion of nanoparticles leads to enhancement of heat transfer and attenuation of convective flow inside the cavity.Entropy2015-12-31181Article10.3390/e1801000991099-43002015-12-31doi: 10.3390/e18010009Mikhail SheremetHakan OztopIoan PopNidal Abu-Hamdeh<![CDATA[Entropy, Vol. 18, Pages 5: Towards the Development of a Universal Expression for the Configurational Entropy of Mixing]]>
http://www.mdpi.com/1099-4300/18/1/5
This work discusses the development of analytical expressions for the configurational entropy of different states of matter using a method based on the identification of the energy-independent complexes (clustering of atoms) in the system and the calculation of their corresponding probabilities. The example of short-range order (SRO) in Nb-H interstitial solid solution is used to illustrate the choice of the atomic complexes and their structural changes with H concentration, providing an alternative methodology to describe critical properties. The calculated critical composition of the miscibility gap is xc = 0.307, in remarkable agreement with the experimental value of xc ~ 0.31. The same methodology is applied to deduce the equation of state (EOS) of a hard sphere system. The EOS is suitable to describe the percolation thresholds and fulfills both the low and random close packing limits. The model, based on the partition of the space into Voronoi cells, can be applied to any off-lattice system, thus introducing the possibility of computing the configurational entropy of gases, liquids and glasses with the same level of accuracy.Entropy2015-12-31181Article10.3390/e1801000551099-43002015-12-31doi: 10.3390/e18010005Jorge Garcés<![CDATA[Entropy, Vol. 18, Pages 16: Stochastic Reorder Point-Lot Size (r,Q) Inventory Model under Maximum Entropy Principle]]>
http://www.mdpi.com/1099-4300/18/1/16
This paper takes into account the continuous-review reorder point-lot size (r,Q) inventory model under stochastic demand, with the backorders-lost sales mixture. Moreover, to reflect the practical circumstance in which full information about the demand distribution lacks, we assume that only an estimate of the mean and of the variance is available. Contrarily to the typical approach in which the lead-time demand is supposed Gaussian or is obtained according to the so-called minimax procedure, we take a different perspective. That is, we adopt the maximum entropy principle to model the lead-time demand distribution. In particular, we consider the density that maximizes the entropy over all distributions with given mean and variance. With the aim of minimizing the expected total cost per time unit, we then propose an exact algorithm and a heuristic procedure. The heuristic method exploits an approximated expression of the total cost function achieved by means of an ad hoc first-order Taylor polynomial. We finally carry out numerical experiments with a twofold objective. On the one hand we examine the efficiency of the approximated solution procedure. On the other hand we investigate the performance of the maximum entropy principle in approximating the true lead-time demand distribution.Entropy2015-12-30181Article10.3390/e18010016161099-43002015-12-30doi: 10.3390/e18010016Davide Castellano<![CDATA[Entropy, Vol. 18, Pages 15: Thermal Characteristics of a Primary Surface Heat Exchanger with Corrugated Channels]]>
http://www.mdpi.com/1099-4300/18/1/15
This paper presents the heat transfer and pressure drop characteristics of a primary surface heat exchanger (PSHE) with corrugated surfaces. The PSHE was experimentally investigated for a Reynolds number range of 156–921 under various flow conditions on the hot and cold sides. The inlet temperature of the hot side was maintained at 40 °C, while that of the cold side was maintained at 20 °C. A counterflow was used as it has a higher temperature proximity in comparison with a parallel flow. The heat transfer rate and pressure drop were measured for various Reynolds numbers on both the hot and cold sides of the PSHE, with the heat transfer coefficients for both sides computed using a modified Wilson plot method. Based on the results of the experiment, both Nusselt number and friction factor correlations were suggested for a PSHE with corrugated surfaces.Entropy2015-12-30181Article10.3390/e18010015151099-43002015-12-30doi: 10.3390/e18010015Jang-Won SeoChanyong ChoSangrae LeeYoung-Don Choi<![CDATA[Entropy, Vol. 18, Pages 14: Cloud Entropy Management System Involving a Fractional Power]]>
http://www.mdpi.com/1099-4300/18/1/14
Cloud computing (CC) capacities deliver high quality, connected with demand services and service-oriented construction. Nevertheless, a cloud service (CS) is normally derived from numerous stages of facilities and concert features, which determine the value of the cloud service. Therefore, it is problematic for the users to estimate these cloud services and select them to appropriate their requirements. In this study, a new algorithm is carried out for a multi-agent system (MAS) based on fractional power. The study depends on a fractional difference equation of type two point boundary value problem (BVP) based on the fractional entropy. We discuss the existence of solutions for the system as well as the stability, utilizing the Hadamard well-posed problem. Experimental results show that the proposed method demonstrates stability and performance.Entropy2015-12-29181Article10.3390/e18010014141099-43002015-12-29doi: 10.3390/e18010014Rabha IbrahimHamid JalabAbdullah Gani<![CDATA[Entropy, Vol. 18, Pages 10: Effect of Magnetic Field on Entropy Generation in a Microchannel Heat Sink with Offset Fan Shaped]]>
http://www.mdpi.com/1099-4300/18/1/10
In this study, convection flow in microchannel heat sink with offset fan-shaped reentrant cavities in sidewall filled with Fe3O4-water is numerically investigated. The effects of changing some parameters such as Reynolds number and magnetic field are considered. The nanofluid flow is laminar, steady and incompressible, while the thermo-physical properties of nanoparticles were assumed constant. A finite volume method and two phase mixture models were used to simulate the flow. The obtained results show that the frictional entropy generation increases as Reynolds number increases, while a reverse trend is observed for thermal entropy generation. By applying a non-uniform magnetic field, the entropy generation due to heat transfer decreases at first and then increases. When using the uniform magnetic field, the frictional entropy generation and thermal entropy generation is negligible. For all studied cases, the total entropy generation decreases using non-uniform magnetic fields. The results indicate that by increasing the magnetic field power, the total entropy generation decreases.Entropy2015-12-29181Article10.3390/e18010010101099-43002015-12-29doi: 10.3390/e18010010Mohammad NasiriMohammad RashidiGiulio Lorenzini<![CDATA[Entropy, Vol. 18, Pages 8: Wavelet Energy and Wavelet Coherence as EEG Biomarkers for the Diagnosis of Parkinson’s Disease-Related Dementia and Alzheimer’s Disease]]>
http://www.mdpi.com/1099-4300/18/1/8
Parkinson’s disease (PD) and Alzheimer’s disease (AD) can coexist in severely affected; elderly patients. Since they have different pathological causes and lesions and consequently require different treatments; it is critical to distinguish PD-related dementia (PD-D) from AD. Conventional electroencephalograph (EEG) analysis has produced poor results. This study investigated the possibility of using relative wavelet energy (RWE) and wavelet coherence (WC) analysis to distinguish between PD-D patients; AD patients and healthy elderly subjects. In EEG signals; we found that low-frequency wavelet energy increased and high-frequency wavelet energy decreased in PD-D patients and AD patients relative to healthy subjects. This result suggests that cognitive decline in both diseases is potentially related to slow EEG activity; which is consistent with previous studies. More importantly; WC values were lower in AD patients and higher in PD-D patients compared with healthy subjects. In particular; AD patients exhibited decreased WC primarily in the γ band and in links related to frontal regions; while PD-D patients exhibited increased WC primarily in the α and β bands and in temporo-parietal links. Linear discriminant analysis (LDA) of RWE produced a maximum accuracy of 79.18% for diagnosing PD-D and 81.25% for diagnosing AD. The discriminant accuracy was 73.40% with 78.78% sensitivity and 69.47% specificity. In distinguishing between the two diseases; the maximum performance of LDA using WC was 80.19%. We suggest that using a wavelet approach to evaluate EEG results may facilitate discrimination between PD-D and AD. In particular; RWE is useful for differentiating individuals with and without dementia and WC is useful for differentiating between PD-D and AD.Entropy2015-12-29181Article10.3390/e1801000881099-43002015-12-29doi: 10.3390/e18010008Dong-Hwa JeongYoung-Do KimIn-Uk SongYong-An ChungJaeseung Jeong<![CDATA[Entropy, Vol. 18, Pages 13: Improvement of the k-nn Entropy Estimator with Applications in Systems Biology]]>
http://www.mdpi.com/1099-4300/18/1/13
In this paper, we investigate efficient estimation of differential entropy for multivariate random variables. We propose bias correction for the nearest neighbor estimator, which yields more accurate results in higher dimensions. In order to demonstrate the accuracy of the improvement, we calculated the corrected estimator for several families of random variables. For multivariate distributions, we considered the case of independent marginals and the dependence structure between the marginal distributions described by Gaussian copula. The presented solution may be particularly useful for high dimensional data, like those analyzed in the systems biology field. To illustrate such an application, we exploit differential entropy to define the robustness of biochemical kinetic models.Entropy2015-12-29181Article10.3390/e18010013131099-43002015-12-29doi: 10.3390/e18010013Agata CharzyńskaAnna Gambin<![CDATA[Entropy, Vol. 18, Pages 12: Wide Range Multiscale Entropy Changes through Development]]>
http://www.mdpi.com/1099-4300/18/1/12
How variability in the brain’s neurophysiologic signals evolves during development is important for a global, system-level understanding of brain maturation and its disturbance in neurodevelopmental disorders. In the current study, we use multiscale entropy (MSE), a measure that has been related to signal complexity, to investigate how this variability evolves during development across a broad range of temporal scales. We computed MSE, standard deviation (STD) and standard spectral analyses on resting EEG from 188 healthy individuals aged 8–22 years old. We found age-related increases in entropy at lower scales (&lt;~20 ms) and decreases in entropy at higher scales (~60–80 ms). Decreases in the overall signal STD were anticorrelated with entropy, especially in the lower scales, where regression analyses showed substantial covariation of observed changes. Our findings document for the first time the scale dependency of developmental changes from childhood to early adulthood, challenging a parsimonious MSE-based account of brain maturation along a unidimensional, complexity measure. At the level of analysis permitted by electroencephalography (EEG), MSE could capture critical spatiotemporal variations in the role of noise in the brain. However, interpretations critically rely on defining how signal STD affects MSE properties.Entropy2015-12-29181Article10.3390/e18010012121099-43002015-12-29doi: 10.3390/e18010012Nicola PolizzottoTetsuya TakahashiChristopher WalkerRaymond Cho<![CDATA[Entropy, Vol. 18, Pages 11: Improving Fraudster Detection in Online Auctions by Using Neighbor-Driven Attributes]]>
http://www.mdpi.com/1099-4300/18/1/11
Online auction websites use a simple reputation system to help their users to evaluate the trustworthiness of sellers and buyers. However, to improve their reputation in the reputation system, fraudulent users can easily deceive the reputation system by creating fake transactions. This inflated-reputation fraud poses a major problem for online auction websites because it can lead legitimate users into scams. Numerous approaches have been proposed in the literature to address this problem, most of which involve using social network analysis (SNA) to derive critical features (e.g., k-core, center weight, and neighbor diversity) for distinguishing fraudsters from legitimate users. This paper discusses the limitations of these SNA features and proposes a class of SNA features referred to as neighbor-driven attributes (NDAs). The NDAs of users are calculated from the features of their neighbors. Because fraudsters require collusive neighbors to provide them with positive ratings in the reputation system, using NDAs can be helpful for detecting fraudsters. Although the idea of NDAs is not entirely new, experimental results on a real-world dataset showed that using NDAs improves classification accuracy compared with state-of-the-art methods that use the k-core, center weight, and neighbor diversity.Entropy2015-12-26181Article10.3390/e18010011111099-43002015-12-26doi: 10.3390/e18010011Jun-Lin LinLaksamee Khomnotai<![CDATA[Entropy, Vol. 18, Pages 7: Mechanical Fault Diagnosis of High Voltage Circuit Breakers Based on Wavelet Time-Frequency Entropy and One-Class Support Vector Machine]]>
http://www.mdpi.com/1099-4300/18/1/7
Mechanical faults of high voltage circuit breakers (HVCBs) are one of the most important factors that affect the reliability of power system operation. Because of the limitation of a lack of samples of each fault type; some fault conditions can be recognized as a normal condition. The fault diagnosis results of HVCBs seriously affect the operation reliability of the entire power system. In order to improve the fault diagnosis accuracy of HVCBs; a method for mechanical fault diagnosis of HVCBs based on wavelet time-frequency entropy (WTFE) and one-class support vector machine (OCSVM) is proposed. In this method; the S-transform (ST) is proposed to analyze the energy time-frequency distribution of HVCBs’ vibration signals. Then; WTFE is selected as the feature vector that reflects the information characteristics of vibration signals in the time and frequency domains. OCSVM is used for judging whether a mechanical fault of HVCBs has occurred or not. In order to improve the fault detection accuracy; a particle swarm optimization (PSO) algorithm is employed to optimize the parameters of OCSVM; including the window width of the kernel function and error limit. If the mechanical fault is confirmed; a support vector machine (SVM)-based classifier will be used to recognize the fault type. The experiments carried on a real SF6 HVCB demonstrated the improved effectiveness of the new approach.Entropy2015-12-26181Article10.3390/e1801000771099-43002015-12-26doi: 10.3390/e18010007Nantian HuangHuaijin ChenShuxin ZhangGuowei CaiWeiguo LiDianguo XuLihua Fang<![CDATA[Entropy, Vol. 18, Pages 6: Information-Theoretic Neuro-Correlates Boost Evolution of Cognitive Systems]]>
http://www.mdpi.com/1099-4300/18/1/6
Genetic Algorithms (GA) are a powerful set of tools for search and optimization that mimic the process of natural selection, and have been used successfully in a wide variety of problems, including evolving neural networks to solve cognitive tasks. Despite their success, GAs sometimes fail to locate the highest peaks of the fitness landscape, in particular if the landscape is rugged and contains multiple peaks. Reaching distant and higher peaks is difficult because valleys need to be crossed, in a process that (at least temporarily) runs against the fitness maximization objective. Here we propose and test a number of information-theoretic (as well as network-based) measures that can be used in conjunction with a fitness maximization objective (so-called “neuro-correlates”) to evolve neural controllers for two widely different tasks: a behavioral task that requires information integration, and a cognitive task that requires memory and logic. We find that judiciously chosen neuro-correlates can significantly aid GAs to find the highest peaks.Entropy2015-12-25181Article10.3390/e1801000661099-43002015-12-25doi: 10.3390/e18010006Jory SchossauChristoph AdamiArend Hintze<![CDATA[Entropy, Vol. 18, Pages 4: Comprehensive Study on Lexicon-based Ensemble Classification Sentiment Analysis]]>
http://www.mdpi.com/1099-4300/18/1/4
We propose a novel method for counting sentiment orientation that outperforms supervised learning approaches in time and memory complexity and is not statistically significantly different from them in accuracy. Our method consists of a novel approach to generating unigram, bigram and trigram lexicons. The proposed method, called frequentiment, is based on calculating the frequency of features (words) in the document and averaging their impact on the sentiment score as opposed to documents that do not contain these features. Afterwards, we use ensemble classification to improve the overall accuracy of the method. What is important is that the frequentiment-based lexicons with sentiment threshold selection outperform other popular lexicons and some supervised learners, while being 3–5 times faster than the supervised approach. We compare 37 methods (lexicons, ensembles with lexicon’s predictions as input and supervised learners) applied to 10 Amazon review data sets and provide the first statistical comparison of the sentiment annotation methods that include ensemble approaches. It is one of the most comprehensive comparisons of domain sentiment analysis in the literature.Entropy2015-12-25181Article10.3390/e1801000441099-43002015-12-25doi: 10.3390/e18010004Łukasz AugustyniakPiotr SzymańskiTomasz KajdanowiczWłodzimierz Tuligłowicz<![CDATA[Entropy, Vol. 18, Pages 3: Multiscale Entropy Analysis on Human Operating Behavior]]>
http://www.mdpi.com/1099-4300/18/1/3
By exploiting the statistical analysis method, human dynamics provides new insights to the research of human behavior. In this paper, we analyze the characteristics of the computer operating behavior through a modified multiscale entropy algorithm with both the interval time series and the number series of individuals’ operating behavior been investigated. We also discuss the activity of individuals’ behavior from the three groups denoted as the retiree group, the student group and the worker group based on the nature of their jobs. We find that the operating behavior of the retiree group exhibits more complex dynamics than the other two groups and further present a reasonable explanation for this phenomenon. Our findings offer new insights for the further understanding of individual behavior at different time scales.Entropy2015-12-22181Article10.3390/e1801000331099-43002015-12-22doi: 10.3390/e18010003Junshan PanHanping HuXiang LiuYong Hu<![CDATA[Entropy, Vol. 18, Pages 2: A Lattice Gas Automata Model for the Coupled Heat Transfer and Chemical Reaction of Gas Flow Around and Through a Porous Circular Cylinder]]>
http://www.mdpi.com/1099-4300/18/1/2
Coupled heat transfer and chemical reaction of fluid flow in complex boundaries are explored by introducing two additional properties, i.e. particle type and energy state into the Lattice gas automata (LGA) Frisch–Hasslacher–Pomeau (FHP-II) model. A mix-redistribute of energy and type of particles is also applied on top of collision rules to ensure randomness while maintaining the conservation of mass, momentum and energy. Simulations of heat transfer and heterogeneous reaction of gas flow passing a circular porous cylinder in a channel are presented. The effects of porosity of cylinder, gas inlet velocity, and reaction probability on the reaction process are further analyzed with respect to the characteristics of solid morphology, product concentration, and temperature profile. Numerical results indicate that the reaction rate increases with increasing reaction probability as well as gas inlet velocity. Cylinders with a higher value of porosity and more homogeneous structure also react with gas particles faster. These results agree well with the basic theories of gas–solid reactions, indicating the present model provides a method for describing gas–solid reactions in complex boundaries at mesoscopic level.Entropy2015-12-22181Article10.3390/e1801000221099-43002015-12-22doi: 10.3390/e18010002Hongsheng ChenZhong ZhengZhiwei ChenXiaotao Bi<![CDATA[Entropy, Vol. 17, Pages 8341-8345: Gravitational Entropy and the Second Law of Thermodynamics]]>
http://www.mdpi.com/1099-4300/17/12/7883
The spontaneous violation of Lorentz and diffeomorphism invariance in a phase near the big bang lowers the entropy, allowing for an arrow of time and the second law of thermodynamics. The spontaneous symmetry breaking leads to O(3,1) → O(3) × R , where O(3) is the rotational symmetry of the Friedmann–Lemaître–Robertson–Walker spacetime. The Weyl curvature tensor Cμνρσ vanishes in the FLRW spacetime satisfying the Penrose zero Weyl curvature conjecture. The requirement of a measure of gravitational entropy is discussed. The vacuum expectation value 〈0|ψμ|0〉 ≠ 0 for a vector field ψμ acts as an order parameter and at the critical temperature Tc a phase transition occurs breaking the Lorentz symmetry spontaneously. During the ordered O(3) symmetry phase the entropy is vanishingly small and for T &lt; Tc as the universe expands the anti-restored O(3,1) Lorentz symmetry leads to a disordered phase and a large increase in entropy creating the arrow of time.Entropy2015-12-211712Article10.3390/e1712788383411099-43002015-12-21doi: 10.3390/e17127883John Moffat<![CDATA[Entropy, Vol. 17, Pages 8325-8340: Entropy Production and Equilibrium Conditions of General-Covariant Spin Systems]]>
http://www.mdpi.com/1099-4300/17/12/7884
In generalizing the special-relativistic one-component version of Eckart’s continuum thermodynamics to general-relativistic space-times with Riemannian or post-Riemannian geometry as presented by Schouten (Schouten, J.A. Ricci-Calculus, 1954) and Blagojevic (Blagojevic, M. Gauge Theories of Gravitation, 2013) we consider the entropy production and other thermodynamical quantities, such as the entropy flux and the Gibbs fundamental equation. We discuss equilibrium conditions in gravitational theories, which are based on such geometries. In particular, thermodynamic implications of the non-symmetry of the energy-momentum tensor and the related spin balance equations are investigated, also for the special case of general relativity.Entropy2015-12-211712Article10.3390/e1712788483251099-43002015-12-21doi: 10.3390/e17127884Wolfgang MuschikHorst-Heino von Borzeszkowski<![CDATA[Entropy, Vol. 17, Pages 8312-8324: A New Tight Upper Bound on the Entropy of Sums]]>
http://www.mdpi.com/1099-4300/17/12/7881
We consider the independent sum of a given random variable with a Gaussian variable and an infinitely divisible one. We find a novel tight upper bound on the entropy of the sum which still holds when the variable possibly has an infinite second moment. The proven bound has several implications on both information theoretic problems and infinitely divisible noise channels’ transmission rates.Entropy2015-12-191712Article10.3390/e1712788183121099-43002015-12-19doi: 10.3390/e17127881Jihad FahsIbrahim Abou-Faycal<![CDATA[Entropy, Vol. 17, Pages 8299-8311: Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System]]>
http://www.mdpi.com/1099-4300/17/12/7882
The fractional-order hyperchaotic Lorenz system is solved as a discrete map by applying the Adomian decomposition method (ADM). Lyapunov Characteristic Exponents (LCEs) of this system are calculated according to this deduced discrete map. Complexity of this system versus parameters are analyzed by LCEs, bifurcation diagrams, phase portraits, complexity algorithms. Results show that this system has rich dynamical behaviors. Chaos and hyperchaos can be generated by decreasing fractional order q in this system. It also shows that the system is more complex when q takes smaller values. SE and C 0 complexity algorithms provide a parameter choice criteria for practice applications of fractional-order chaotic systems. The fractional-order system is implemented by digital signal processor (DSP), and a pseudo-random bit generator is designed based on the implemented system, which passes the NIST test successfully.Entropy2015-12-181712Article10.3390/e1712788282991099-43002015-12-18doi: 10.3390/e17127882Shaobo HeKehui SunHuihai Wang<![CDATA[Entropy, Vol. 17, Pages 8297-8298: Comments by Author regarding: Levy, G.S. Thermoelectric Effects under Adiabatic Conditions. Entropy 2013, 15, 4700–4715]]>
http://www.mdpi.com/1099-4300/17/12/7879
This comment by the author discusses paragraph 3.3. Adiabatic Phenomena—An Analogy of the published article [1]. The paragraph draws an incorrect analogy between Maxwellian gases such as found in the atmosphere, and non-Maxwellian gases embodied, for example, by electrical carriers in thermoelectric materials. As reported by the author in more recent articles, Maxwellian gases do not produce spontaneous temperature gradients in the presence of a force field. However, non-Maxwellian gases, such as Fermions or Bosons, can produce such gradients.Entropy2015-12-171712Comment10.3390/e1712787982971099-43002015-12-17doi: 10.3390/e17127879George Levy<![CDATA[Entropy, Vol. 17, Pages 8278-8296: Pathological Brain Detection by a Novel Image Feature—Fractional Fourier Entropy]]>
http://www.mdpi.com/1099-4300/17/12/7877
Aim: To detect pathological brain conditions early is a core procedure for patients so as to have enough time for treatment. Traditional manual detection is either cumbersome, or expensive, or time-consuming. We aim to offer a system that can automatically identify pathological brain images in this paper. Method: We propose a novel image feature, viz., Fractional Fourier Entropy (FRFE), which is based on the combination of Fractional Fourier Transform (FRFT) and Shannon entropy. Afterwards, the Welch’s t-test (WTT) and Mahalanobis distance (MD) were harnessed to select distinguishing features. Finally, we introduced an advanced classifier: twin support vector machine (TSVM). Results: A 10 × K-fold stratified cross validation test showed that this proposed “FRFE + WTT + TSVM” yielded an accuracy of 100.00%, 100.00%, and 99.57% on datasets that contained 66, 160, and 255 brain images, respectively. Conclusions: The proposed “FRFE + WTT + TSVM” method is superior to 20 state-of-the-art methods.Entropy2015-12-171712Article10.3390/e1712787782781099-43002015-12-17doi: 10.3390/e17127877Shuihua WangYudong ZhangXiaojun YangPing SunZhengchao DongAijun LiuTi-Fei Yuan<![CDATA[Entropy, Vol. 17, Pages 8267-8277: On the Complex and Hyperbolic Structures for the (2 + 1)-Dimensional Boussinesq Water Equation]]>
http://www.mdpi.com/1099-4300/17/12/7878
In this study, we have applied the modified exp(−Ω(ξ))-expansion function method to the (2 + 1)-dimensional Boussinesq water equation. We have obtained some new analytical solutions such as exponential function, complex function and hyperbolic function solutions. It has been observed that all analytical solutions have been verified to the (2 + 1)-dimensional Boussinesq water equation by using Wolfram Mathematica 9. We have constructed the two- and three-dimensional surfaces for all analytical solutions obtained in this paper using the same computer program.Entropy2015-12-171712Article10.3390/e1712787882671099-43002015-12-17doi: 10.3390/e17127878Figen ÖzpinarHaci BaskonusHasan Bulut<![CDATA[Entropy, Vol. 17, Pages 8240-8266: Hydrodynamic Force Evaluation by Momentum Exchange Method in Lattice Boltzmann Simulations]]>
http://www.mdpi.com/1099-4300/17/12/7876
As a native scheme to evaluate hydrodynamic force in the lattice Boltzmann method, the momentum exchange method has some excellent features, such as simplicity, accuracy, high efficiency and easy parallelization. Especially, it is independent of boundary geometry, preventing from solving the Navier–Stokes equations on complex boundary geometries in the boundary-integral methods. We review the origination and main developments of the momentum exchange method in lattice Boltzmann simulations. Then several practical techniques to fill newborn fluid nodes are discussed for the simulations of fluid-structure interactions. Finally, some representative applications show the wide applicability of the momentum exchange method, such as movements of rigid particles, interactions of deformation particles, particle suspensions in turbulent flow and multiphase flow, etc.Entropy2015-12-171712Review10.3390/e1712787682401099-43002015-12-17doi: 10.3390/e17127876Binghai WenChaoying ZhangHaiping Fang<![CDATA[Entropy, Vol. 17, Pages 8228-8239: Numerical Study of Entropy Generation Within Thermoacoustic Heat Exchangers with Plane Fins]]>
http://www.mdpi.com/1099-4300/17/12/7875
In this paper a simplified two-dimensional computational model for studying the entropy generation characteristics of thermoacoustic heat exchangers with plane fins is presented. The model integrates the equations of the standard linear thermoacoustic theory into an energy balance-based numerical calculus scheme. Relevant computation results are the spatial distribution of the time-averaged temperature, heat fluxes and entropy generation rates within a channel of a parallel-plate stack and adjoining heat exchangers. For a thermoacoustic device working in the refrigeration mode, this study evidences as a target refrigeration output level can be achieved selecting simultaneously the heat exchangers fin length and fin interspacing for minimum entropy generation and that the resulting configuration is a point of maximum coefficient of performance. The proposed methodology, when extended to other configurations, could be used as a viable design tool for heat exchangers in thermoacoustic applications.Entropy2015-12-161712Article10.3390/e1712787582281099-43002015-12-16doi: 10.3390/e17127875Antonio Piccolo<![CDATA[Entropy, Vol. 17, Pages 8217-8227: Some New Properties for Degree-Based Graph Entropies]]>
http://www.mdpi.com/1099-4300/17/12/7871
The graph entropies inspired by Shannon’s entropy concept become the information-theoretic quantities for measuring the structural information of graphs and complex networks. In this paper, we continue studying some new properties of the graph entropies based on information functionals involving vertex degrees. We prove the monotonicity of the graph entropies with respect to the power exponent. Considering only the maximum and minimum degrees of the ( n , m ) -graph, we obtain some upper and lower bounds for the degree-based graph entropy. These bounds have different performances to restrict the degree-based graph entropy in different kinds of graphs. Moreover the degree-based graph entropy can be estimated by these bounds.Entropy2015-12-161712Article10.3390/e1712787182171099-43002015-12-16doi: 10.3390/e17127871Guoxiang LuBingqing LiLijia Wang<![CDATA[Entropy, Vol. 17, Pages 8207-8216: Permutation Entropy for Random Binary Sequences]]>
http://www.mdpi.com/1099-4300/17/12/7872
In this paper, we generalize the permutation entropy (PE) measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences.Entropy2015-12-151712Article10.3390/e1712787282071099-43002015-12-15doi: 10.3390/e17127872Lingfeng LiuSuoxia MiaoMengfan ChengXiaojing Gao<![CDATA[Entropy, Vol. 17, Pages 8187-8206: Preliminary Numerical Investigations of Entropy Generation in Electric Machines Based on a Canonical Configuration]]>
http://www.mdpi.com/1099-4300/17/12/7874
The present paper analyzes numerically the entropy generation induced by forced convection in a canonical configuration. The configuration itself includes two well known fluid dynamic problems: (1) an external flow (flow around a cylinder, Kármán flow); and (2) an internal flow (flow between two concentric rotating cylinders, Couette flow). In many daily engineering issues (e.g., cooling of electric machines), a combination of these problems occurs and has to be investigated. Using the canonical configuration, the fields of entropy generation are analyzed in this work for a constant wall heat flux but varying two key parameters (Reynolds numbers Re∞ and Re0). The entropy generation due to conduction shows an absolute minimum around Re0 = 10,000. The same minima can be found by a detailed analysis of the temperature profile. Thus, entropy generation seems to be a suitable indicator for optimizing heat exchange processes and delivers a large amount of information concerning fluid and heat transport.Entropy2015-12-151712Article10.3390/e1712787481871099-43002015-12-15doi: 10.3390/e17127874Toni EgerThomas BolDominique ThéveninRüdiger SchrothGábor Janiga<![CDATA[Entropy, Vol. 17, Pages 8174-8186: Entropy and Quantum Gravity]]>
http://www.mdpi.com/1099-4300/17/12/7873
We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS)/conformal field theory (CFT) correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.Entropy2015-12-151712Review10.3390/e1712787381741099-43002015-12-15doi: 10.3390/e17127873Bernard Kay<![CDATA[Entropy, Vol. 17, Pages 8152-8173: Design and Thermodynamic Analysis of a Steam Ejector Refrigeration/Heat Pump System for Naval Surface Ship Applications]]>
http://www.mdpi.com/1099-4300/17/12/7869
Naval surface ships should use thermally driven heating and cooling technologies to continue the Navy’s leadership role in protecting the marine environment. Steam ejector refrigeration (SER) or steam ejector heat pump (SEHP) systems are thermally driven heating and cooling technologies and seem to be a promising technology to reduce emissions for heating and cooling on board naval surface ships. In this study, design and thermodynamic analysis of a seawater cooled SER and SEHP as an HVAC system for a naval surface ship application are presented and compared with those of a current typical naval ship system case, an H2O-LiBr absorption heat pump and a vapour-compression heat pump. The off-design study estimated the coefficient of performances (COPs) were 0.29–0.11 for the cooling mode and 1.29–1.11 for the heating mode, depending on the pressure of the exhaust gas boiler at off-design conditions. In the system operating at the exhaust gas boiler pressure of 0.2 MPa, the optimum area ratio obtained was 23.30.Entropy2015-12-111712Article10.3390/e1712786981521099-43002015-12-11doi: 10.3390/e17127869Cüneyt EzgiIbrahim Girgin<![CDATA[Entropy, Vol. 17, Pages 8130-8151: Measures of Morphological Complexity of Gray Matter on Magnetic Resonance Imaging for Control Age Grouping]]>
http://www.mdpi.com/1099-4300/17/12/7868
Current brain-age prediction methods using magnetic resonance imaging (MRI) attempt to estimate the physiological brain age via some kind of machine learning of chronological brain age data to perform the classification task. Such a predictive approach imposes greater risk of either over-estimate or under-estimate, mainly due to limited training data. A new conceptual framework for more reliable MRI-based brain-age prediction is by systematic brain-age grouping via the implementation of the phylogenetic tree reconstruction and measures of information complexity. Experimental results carried out on a public MRI database suggest the feasibility of the proposed concept.Entropy2015-12-091712Article10.3390/e1712786881301099-43002015-12-09doi: 10.3390/e17127868Tuan PhamTaishi AbeRyuichi OkaYung-Fu Chen<![CDATA[Entropy, Vol. 17, Pages 8111-8129: A Novel Approach to Canonical Divergences within Information Geometry]]>
http://www.mdpi.com/1099-4300/17/12/7866
A divergence function on a manifold M defines a Riemannian metric g and dually coupled affine connections ∇ and ∇ * on M. When M is dually flat, that is flat with respect to ∇ and ∇ * , a canonical divergence is known, which is uniquely determined from ( M , g , ∇ , ∇ * ) . We propose a natural definition of a canonical divergence for a general, not necessarily flat, M by using the geodesic integration of the inverse exponential map. The new definition of a canonical divergence reduces to the known canonical divergence in the case of dual flatness. Finally, we show that the integrability of the inverse exponential map implies the geodesic projection property.Entropy2015-12-091712Article10.3390/e1712786681111099-43002015-12-09doi: 10.3390/e17127866Nihat AyShun-ichi Amari<![CDATA[Entropy, Vol. 17, Pages 8099-8110: Entropy-Assisted Computing of Low-Dissipative Systems]]>
http://www.mdpi.com/1099-4300/17/12/7867
Entropy feedback is reviewed and highlighted as the guiding principle to reach extremely low dissipation. This principle is illustrated through turbulent flow simulations using the entropic lattice Boltzmann scheme.Entropy2015-12-081712Article10.3390/e1712786780991099-43002015-12-08doi: 10.3390/e17127867Ilya KarlinFabian BöschShyam ChikatamarlaSauro Succi<![CDATA[Entropy, Vol. 17, Pages 8089-8098: Multiscale Entropy Analysis of Surface Electromyographic Signals from the Urethral Sphincter as a Prognostic Indicator for Surgical Candidates with Primary Bladder Neck Obstruction]]>
http://www.mdpi.com/1099-4300/17/12/7863
To explore information hidden in the electromyographic (EMG) signals of the urethral sphincter that may be of prognostic significance for patients with primary bladder neck obstruction (PBNO), 41 patients with voiding difficulty were divided into four groups: 1) patients with primary bladder neck obstruction (PBNO) with successful (Group 1, n = 14) and 2) unsuccessful (Group 2, n = 8) surgical outcomes, 3) patients with detrusor overactivity (Group 3, n = 7), and 4) patients with detrusor-external sphincter dyssynergia (Group 4, n = 12). All patients underwent baseline urodynamic studies (preoperative for Group 1 and Group 2) for comparison. The results demonstrated that, despite no significant difference in urodynamic parameters between Group 1 and Group 2, the large-scale multiscale entropy (MSE) of preoperative EMG (i.e., MSELS(EMG)) of Group 1 was significantly higher than that of Group 2 without notable difference between Group 1 and Group 3 (i.e., patients with normal sphincter function). Moreover, the MSELS(EMG) and small-scale MSE of preoperative EMG (i.e., MSESS(EMG)) of Group 2 were notably higher than those of Group 4 (i.e., patients with abnormal sphincter function), while both MSELS(EMG) and MSESS(EMG) of Group 3 were notably higher than those of Group 2. In conclusion, using MSE analysis for assessing preoperative urethral sphincter EMG signals successfully distinguished between PBNO patients with subsequent successful surgery from those with surgical failure possibly due to subtle functional impairment of the urethral sphincter that cannot be detected by routine urodynamic studies. The results, therefore, highlight the potential clinical significance of this analytical tool in guiding urologists regarding their choice of medical versus surgical treatment for this patient population.Entropy2015-12-081712Article10.3390/e1712786380891099-43002015-12-08doi: 10.3390/e17127863Hsien-Tsai WuYuan-Hong JiangAn-Bang LiuChun-Wei LiuYu-Nian OuHann-Chorng KuoCheuk-Kwan Sun<![CDATA[Entropy, Vol. 17, Pages 8073-8088: Evolution Characteristics of Complex Fund Network and Fund Strategy Identification]]>
http://www.mdpi.com/1099-4300/17/12/7861
Earlier investment practices show that there lies a discrepancy between the actual fund strategy and stated fund strategy. Using a minimum spanning tree (MST) and planar maximally-filtered graph (PMFG), we build a network of open-ended funds in China’s market and investigate the evolution characteristics of the networks over multiple time periods and timescales. The evolution characteristics, especially the locations of clustering central nodes, show that the actual strategy of the open-ended funds in China’s market significantly differs from the original stated strategy. When the investment horizon and timescale extend, the funds approach an identical actual strategy. This work introduces a novel network-based quantitative method to help investors identify the actual strategy of open-ended funds.Entropy2015-12-081712Article10.3390/e1712786180731099-43002015-12-08doi: 10.3390/e17127861Honglin YangPenglan FangHong WanYucan LiuHui Lei<![CDATA[Entropy, Vol. 17, Pages 8056-8072: Reentrant Phase Transitions and van der Waals Behaviour for Hairy Black Holes]]>
http://www.mdpi.com/1099-4300/17/12/7862
We study the extended phase space thermodynamics for hairy AdS black hole solutions to Einstein-Maxwell-Λ theory conformally coupled to a scalar field in five dimensions. We find these solutions to exhibit van der Waals behaviour in both the charged/uncharged cases, and reentrant phase transitions in the charged case. This is the first example of reentrant phase transitions in a five dimensional gravitational system which does not include purely gravitational higher curvature corrections.Entropy2015-12-081712Article10.3390/e1712786280561099-43002015-12-08doi: 10.3390/e17127862Robie HennigarRobert Mann<![CDATA[Entropy, Vol. 17, Pages 8031-8055: An Information-Based Approach to Precision Analysis of Indoor WLAN Localization Using Location Fingerprint]]>
http://www.mdpi.com/1099-4300/17/12/7859
In this paper, we proposed a novel information-based approach to precision analysis of indoor wireless local area network (WLAN) localization using location fingerprint. First of all, by using the Fisher information matrix (FIM), we derive the fundamental limit of WLAN fingerprint-based localization precision considering different signal distributions in characterizing the variation of received signal strengths (RSSs) in the target environment. After that, we explore the relationship between the localization precision and access point (AP) placement, which can provide valuable suggestions for the design of the highly-precise localization system. Second, we adopt the heuristic simulated annealing (SA) algorithm to optimize the AP locations for the sake of approaching the fundamental limit of localization precision. Finally, the extensive simulations and experiments are conducted in both regular line-of-sight (LOS) and irregular non-line-of-sight (NLOS) environments to demonstrate that the proposed approach can not only effectively improve the WLAN fingerprint-based localization precision, but also reduce the time overhead.Entropy2015-12-051712Article10.3390/e1712785980311099-43002015-12-05doi: 10.3390/e17127859Mu ZhouFeng QiuZengshan TianHaibo WuQiao ZhangWei He<![CDATA[Entropy, Vol. 17, Pages 8019-8030: Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes]]>
http://www.mdpi.com/1099-4300/17/12/7860
A recent work reported a local stability analysis of a thermo-economical model of an irreversible heat engine working under maximum power conditions. That work showed that after small perturbations to the working temperatures, the system decreases exponentially to the steady state characterized by two different relaxation times. This work extends the local stability analysis considering other performance regimes: the Maximum Efficient Power (MEP) and the Ecological Function (EF) regimes. The relaxation time was shown under different performance regimes as functions of the temperature ratio τ = T2/T1, with T1 &gt; T2, the fractional fuel cost f and a lumped parameter R related to the internal irreversibilities degree. Under Maximum Efficient Power conditions the relaxation times are less than the relaxation times under both Maximum Ecological function and Maximum Power. At Maximum Power Efficient conditions, the model gives better stability conditions than for the other two regimes.Entropy2015-12-041712Article10.3390/e1712786080191099-43002015-12-04doi: 10.3390/e17127860Marco Barranco-JiménezNorma Sánchez-SalasIsrael Reyes-Ramírez<![CDATA[Entropy, Vol. 17, Pages 8007-8018: Energy Flows in Low-Entropy Complex Systems]]>
http://www.mdpi.com/1099-4300/17/12/7857
Nature’s many complex systems—physical, biological, and cultural—are islands of low-entropy order within increasingly disordered seas of surrounding, high-entropy chaos. Energy is a principal facilitator of the rising complexity of all such systems in the expanding Universe, including galaxies, stars, planets, life, society, and machines. A large amount of empirical evidence—relating neither entropy nor information, rather energy—suggests that an underlying simplicity guides the emergence and growth of complexity among many known, highly varied systems in the 14-billion-year-old Universe, from big bang to humankind. Energy flows are as centrally important to life and society as they are to stars and galaxies. In particular, the quantity energy rate density—the rate of energy flow per unit mass—can be used to explicate in a consistent, uniform, and unifying way a huge collection of diverse complex systems observed throughout Nature. Operationally, those systems able to utilize optimal amounts of energy tend to survive and those that cannot are non-randomly eliminated.Entropy2015-12-041712Review10.3390/e1712785780071099-43002015-12-04doi: 10.3390/e17127857Eric Chaisson<![CDATA[Entropy, Vol. 17, Pages 7996-8006: An Optimal Segmentation Method Using Jensen–Shannon Divergence via a Multi-Size Sliding Window Technique]]>
http://www.mdpi.com/1099-4300/17/12/7858
In this paper we develop a new procedure for entropic image edge detection. The presented method computes the Jensen–Shannon divergence of the normalized grayscale histogram of a set of multi-sized double sliding windows over the entire image. The procedure presents a good performance in images with textures, contrast variations and noise. We illustrate our procedure in the edge detection of medical images.Entropy2015-12-041712Article10.3390/e1712785879961099-43002015-12-04doi: 10.3390/e17127858Qutaibeh KatatbehJosé Martínez-ArozaJuan Gómez-LoperaDavid Blanco-Navarro<![CDATA[Entropy, Vol. 17, Pages 7979-7995: Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals]]>
http://www.mdpi.com/1099-4300/17/12/7856
Long-memory processes, in particular fractional Gaussian noise processes, have been applied as models for many phenomena occurring in nature. Non-stationarities, such as trends, mean level-shifts, etc., impact the accuracy of long-memory parameter estimators, giving rise to biases and misinterpretations of the phenomena. In this article, a novel methodology for the detection and location of mean level-shifts in stationary long-memory fractional Gaussian noise (fGn) signals is proposed. It is based on a joint application of the wavelet-Tsallis q-entropy as a preprocessing technique and a peak detection methodology. Extensive simulation experiments in synthesized fGn signals with mean level-shifts confirm that the proposed methodology not only detects, but also locates level-shifts with high accuracy. A comparative study against standard techniques of level-shift detection and location shows that the technique based on wavelet-Tsallis q-entropy outperforms the one based on trees and the Bai and Perron procedure, as well.Entropy2015-12-041712Article10.3390/e1712785679791099-43002015-12-04doi: 10.3390/e17127856Julio Ramírez-PachecoLuis Rizo-DomínguezJoaquin Cortez-González<![CDATA[Entropy, Vol. 17, Pages 7967-7978: Self-Organization during Friction of Slide Bearing Antifriction Materials]]>
http://www.mdpi.com/1099-4300/17/12/7855
This article discusses the peculiarities of self-organization behavior and formation of dissipative structures during friction of antifriction alloys for slide bearings against a steel counterbody. It shows that during self-organization, the moment of friction in a tribosystem may be decreasing with the load growth and in the bifurcations of the coefficient of friction with respect to load. Self-organization and the formation of dissipative structures lead to an increase in the seizure load.Entropy2015-12-041712Article10.3390/e1712785579671099-43002015-12-04doi: 10.3390/e17127855Iosif GershmanAlexander MironovEugeniy GershmanGerman Fox-RabinovichStephen Veldhuis<![CDATA[Entropy, Vol. 17, Pages 7948-7966: A Robust Image Tampering Detection Method Based on Maximum Entropy Criteria]]>
http://www.mdpi.com/1099-4300/17/12/7854
This paper proposes a novel image watermarking method based on local energy and maximum entropy aiming to improve the robustness. First, the image feature distribution is extracted by employing the local energy model and then it is transformed as a digital watermark by employing a Discrete Cosine Transform (DCT). An offset image is thus obtained according to the difference between the extracted digital watermarking and the feature distribution of the watermarked image. The entropy of the pixel value distribution is computed first. The Lorenz curve is used to measure the polarization degree of the pixel value distribution. In the pixel location distribution flow, the maximum entropy criteria is applied in segmenting the offset image into potentially tampered regions and unchanged regions. All-connected graph and 2-D Gaussian probability are utilized to obtain the probability distribution of the pixel location. Finally, the factitious tampering probability value of a pending detected image is computed through combining the weighting factors of pixel value and pixel location distribution. Experimental results show that the proposed method is more robust against the commonly used image processing operations, such as Gaussian noise, impulse noise, etc. Simultaneously, the proposed method achieves high sensitivity against factitious tampering.Entropy2015-12-011712Article10.3390/e1712785479481099-43002015-12-01doi: 10.3390/e17127854Bo ZhaoGuihe QinPingping Liu<![CDATA[Entropy, Vol. 17, Pages 7926-7947: Multiscale Entropy Analysis of Center-of-Pressure Dynamics in Human Postural Control: Methodological Considerations]]>
http://www.mdpi.com/1099-4300/17/12/7849
Multiscale entropy (MSE) is a widely used metric for characterizing the nonlinear dynamics of physiological processes. Significant variability, however, exists in the methodological approaches to MSE which may ultimately impact results and their interpretations. Using publications focused on balance-related center of pressure (COP) dynamics, we highlight sources of methodological heterogeneity that can impact study findings. Seventeen studies were systematically identified that employed MSE for characterizing COP displacement dynamics. We identified five key methodological procedures that varied significantly between studies: (1) data length; (2) frequencies of the COP dynamics analyzed; (3) sampling rate; (4) point matching tolerance and sequence length; and (5) filtering of displacement changes from drifts, fidgets, and shifts. We discuss strengths and limitations of the various approaches employed and supply flowcharts to assist in the decision making process regarding each of these procedures. Our guidelines are intended to more broadly inform the design and analysis of future studies employing MSE for continuous time series, such as COP.Entropy2015-11-301712Review10.3390/e1712784979261099-43002015-11-30doi: 10.3390/e17127849Brian GowChung-Kang PengPeter WayneAndrew Ahn<![CDATA[Entropy, Vol. 17, Pages 7888-7899: Identify the Rotating Stall in Centrifugal Compressors by Fractal Dimension in Reconstructed Phase Space]]>
http://www.mdpi.com/1099-4300/17/12/7848
Based on phase space reconstruction and fractal dynamics in nonlinear dynamics, a method is proposed to extract and analyze the dynamics of the rotating stall in the impeller of centrifugal compressor, and some numerical examples are given to verify the results as well. First, the rotating stall of an existing low speed centrifugal compressor (LSCC) is numerically simulated, and the time series of pressure in the rotating stall is obtained at various locations near the impeller outlet. Then, the phase space reconstruction is applied to these pressure time series, and a low-dimensional dynamical system, which the dynamics properties are included in, is reconstructed. In phase space reconstruction, C–C method is used to obtain the key parameters, such as time delay and the embedding dimension of the reconstructed phase space. Further, the fractal characteristics of the rotating stall are analyzed in detail, and the fractal dimensions are given for some examples to measure the complexity of the flow in the post-rotating stall. The results show that the fractal structures could reveal the intrinsic dynamics of the rotating stall flow and could be considered as a characteristic to identify the rotating stall.Entropy2015-11-301712Article10.3390/e1712784878881099-43002015-11-30doi: 10.3390/e17127848Le WangJiazhong ZhangWenfan Zhang<![CDATA[Entropy, Vol. 17, Pages 7900-7925: Feeding Back the Output or Sharing the State: Which Is Better for the State-Dependent Wiretap Channel?]]>
http://www.mdpi.com/1099-4300/17/12/7852
In this paper, the general wiretap channel with channel state information (CSI) at the transmitter and noiseless feedback is investigated, where the feedback is from the legitimate receiver to the transmitter, and the CSI is available at the transmitter in a causal or noncausal manner. The capacity-equivocation regions are determined for this model in both causal and noncausal cases, and the results are further explained via Gaussian and binary examples. For the Gaussian model, we find that in some particular cases, the noiseless feedback performs better than Chia and El Gamal’s CSI sharing scheme, i.e., the secrecy capacity of this feedback scheme is larger than that of the CSI sharing scheme. For the degraded binary model, we find that the noiseless feedback performs no better than Chia and El Gamal’s CSI sharing scheme. However, if the cross-over probability of the wiretap channel is large enough, we show that the two schemes perform the same.Entropy2015-11-301712Article10.3390/e1712785279001099-43002015-11-30doi: 10.3390/e17127852Bin DaiZheng MaLinman Yu<![CDATA[Entropy, Vol. 17, Pages 7875-7887: Distributed Vector Quantization Based on Kullback-Leibler Divergence]]>
http://www.mdpi.com/1099-4300/17/12/7851
The goal of vector quantization is to use a few reproduction vectors to represent original vectors/data while maintaining the necessary fidelity of the data. Distributed signal processing has received much attention in recent years, since in many applications data are dispersedly collected/stored in distributed nodes over networks, but centralizing all these data to one processing center is sometimes impractical. In this paper, we develop a distributed vector quantization (VQ) algorithm based on Kullback-Leibler (K-L) divergence. We start from the centralized case and propose to minimize the K-L divergence between the distribution of global original data and the distribution of global reproduction vectors, and then obtain an online iterative solution to this optimization problem based on the Robbins-Monro stochastic approximation. Afterwards, we extend the solution to apply to distributed cases by introducing diffusion cooperation among nodes. Numerical simulations show that the performances of the distributed K-L–based VQ algorithm are very close to the corresponding centralized algorithm. Besides, both the centralized and distributed K-L–based VQ show more robustness to outliers than the (centralized) Linde-Buzo-Gray (LBG) algorithm and the (centralized) self-organization map (SOM) algorithm.Entropy2015-11-301712Article10.3390/e1712785178751099-43002015-11-30doi: 10.3390/e17127851Pengcheng ShenChunguang LiYiliang Luo<![CDATA[Entropy, Vol. 17, Pages 7859-7874: The Bogdanov–Takens Normal Form: A Minimal Model for Single Neuron Dynamics]]>
http://www.mdpi.com/1099-4300/17/12/7850
Conductance-based (CB) models are a class of high dimensional dynamical systems derived from biophysical principles to describe in detail the electrical dynamics of single neurons. Despite the high dimensionality of these models, the dynamics observed for realistic parameter values is generically planar and can be minimally described by two equations. In this work, we derive the conditions to have a Bogdanov–Takens (BT) bifurcation in CB models, and we argue that it is plausible that these conditions are verified for experimentally-sensible values of the parameters. We show numerically that the cubic BT normal form, a two-variable dynamical system, exhibits all of the diversity of bifurcations generically observed in single neuron models. We show that the Morris–Lecar model is approximately equivalent to the cubic Bogdanov–Takens normal form for realistic values of parameters. Furthermore, we explicitly calculate the quadratic coefficient of the BT normal form for a generic CB model, obtaining that by constraining the theoretical I-V curve’s curvature to match experimental observations, the normal form appears to be naturally cubic. We propose the cubic BT normal form as a robust minimal model for single neuron dynamics that can be derived from biophysically-realistic CB models.Entropy2015-11-301712Article10.3390/e1712785078591099-43002015-11-30doi: 10.3390/e17127850Ulises PereiraPierre CoulletEnrique Tirapegui<![CDATA[Entropy, Vol. 17, Pages 7848-7858: The Fisher Thermodynamics of Quasi-Probabilities]]>
http://www.mdpi.com/1099-4300/17/12/7853
With reference to Lee’s treatment of quasi-probabilities, it is seen that the three phase space quasi-probabilities, known as the P-, Husimi and Wigner ones, plus other intermediate ones, generate a common, single Fisher thermodynamics, along the lines developed by Frieden et al. We explore some facets of such thermodynamics and encounter complementarity between two different kinds of Fisher information.Entropy2015-11-271712Article10.3390/e1712785378481099-43002015-11-27doi: 10.3390/e17127853Flavia PenniniAngelo Plastino<![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