http://www.mdpi.com/journal/entropy Latest open access articles published in Entropy at http://www.mdpi.com/journal/entropy http://www.mdpi.com/1099-4300/15/5/1875 We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper. Entropy 2013-05-17 15 5 Article 10.3390/e15051875 1875 1886 1099-4300 2013-05-17 doi: 10.3390/e15051875 Samanta Piano Gerardo Adesso http://www.mdpi.com/1099-4300/15/5/1847 We investigate entanglement of a quantum field in de Sitter spacetime using a particle detector model. By considering the entanglement between two comoving detectors interacting with a scalar field, it is possible to detect the entanglement of the scalar field by swapping it to detectors. For the massless minimal scalar field, we find that the entanglement between the detectors cannot be detected when their physical separation exceeds the Hubble horizon scale. This behavior supports the appearance of the classical nature of quantum fluctuations generated during the inflationary era. Entropy 2013-05-16 15 5 Article 10.3390/e15051847 1847 1874 1099-4300 2013-05-16 doi: 10.3390/e15051847 Yasusada Nambu http://www.mdpi.com/1099-4300/15/5/1821 In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model involving heat flow, work energy, and chemical reactions, we develop a state-space dynamical system model that captures the key aspects of thermodynamics, including its fundamental laws. In addition, we show that our thermodynamically consistent dynamical system model is globally semistable with system states converging to a state of temperature equipartition. Furthermore, in the presence of chemical reactions, we use the law of mass-action and the notion of chemical potential to show that the dynamic system states converge to a state of temperature equipartition and zero affinity corresponding to a state of chemical equilibrium. Entropy 2013-05-16 15 5 Article 10.3390/e15051821 1821 1846 1099-4300 2013-05-16 doi: 10.3390/e15051821 Wassim Haddad http://www.mdpi.com/1099-4300/15/5/1776 Entanglement concentration is of most importance in long distance quantum communication and quantum computation. It is to distill maximally entangled states from pure partially entangled states based on the local operation and classical communication. In this review, we will mainly describe two kinds of entanglement concentration protocols. One is to concentrate the partially entangled Bell-state, and the other is to concentrate the partially entangled W state. Some protocols are feasible in current experimental conditions and suitable for the optical, electric and quantum-dot and optical microcavity systems. Entropy 2013-05-16 15 5 Review 10.3390/e15051776 1776 1820 1099-4300 2013-05-16 doi: 10.3390/e15051776 Yu-Bo Sheng Lan Zhou http://www.mdpi.com/1099-4300/15/5/1756 Maximum entropy methods of parameter estimation are appealing because they impose no additional structure on the data, other than that explicitly assumed by the analyst. In this paper we prove that the data constrained GME estimator of the general linear model is consistent and asymptotically normal. The approach we take in establishing the asymptotic properties concomitantly identifies a new computationally efficient method for calculating GME estimates. Formulae are developed to compute asymptotic variances and to perform Wald, likelihood ratio, and Lagrangian multiplier statistical tests on model parameters. Monte Carlo simulations are provided to assess the performance of the GME estimator in both large and small sample situations. Furthermore, we extend our results to maximum cross-entropy estimators and indicate a variant of the GME estimator that is unbiased. Finally, we discuss the relationship of GME estimators to Bayesian estimators, pointing out the conditions under which an unbiased GME estimator would be efficient. Entropy 2013-05-14 15 5 Article 10.3390/e15051756 1756 1775 1099-4300 2013-05-14 doi: 10.3390/e15051756 Ron Mittelhammer Nicholas Cardell Thomas Marsh http://www.mdpi.com/1099-4300/15/5/1738 Mutual information (MI) quantifies the statistical dependency between a pair of random variables, and plays a central role in the analysis of engineering and biological systems. Estimation of MI is difficult due to its dependence on an entire joint distribution, which is difficult to estimate from samples. Here we discuss several regularized estimators for MI that employ priors based on the Dirichlet distribution. First, we discuss three “quasi-Bayesian” estimators that result from linear combinations of Bayesian estimates for conditional and marginal entropies. We show that these estimators are not in fact Bayesian, and do not arise from a well-defined posterior distribution and may in fact be negative. Second, we show that a fully Bayesian MI estimator proposed by Hutter (2002), which relies on a fixed Dirichlet prior, exhibits strong prior dependence and has large bias for small datasets. Third, we formulate a novel Bayesian estimator using a mixture-of-Dirichlets prior, with mixing weights designed to produce an approximately flat prior over MI. We examine the performance of these estimators with a variety of simulated datasets and show that, surprisingly, quasi-Bayesian estimators generally outperform our Bayesian estimator. We discuss outstanding challenges for MI estimation and suggest promising avenues for future research. Entropy 2013-05-10 15 5 Article 10.3390/e15051738 1738 1755 1099-4300 2013-05-10 doi: 10.3390/e15051738 Evan Archer Il Park Jonathan Pillow http://www.mdpi.com/1099-4300/15/5/1726 Two orthonormal bases in the d-dimensional Hilbert space are said to be unbiased if the square modulus of the inner product of any vector of one basis with any vector of the other equals 1 d . The presence of a modulus in the problem of finding a set of mutually unbiased bases constitutes a source of complications from the numerical point of view. Therefore, we may ask the question: Is it possible to get rid of the modulus? After a short review of various constructions of mutually unbiased bases in Cd, we show how to transform the problem of finding d + 1 mutually unbiased bases in the d-dimensional space Cd (with a modulus for the inner product) into the one of finding d(d+1) vectors in the d2-dimensional space Cd2 (without a modulus for the inner product). The transformation from Cd to Cd2 corresponds to the passage from equiangular lines to equiangular vectors. The transformation formulas are discussed in the case where d is a prime number. Entropy 2013-05-08 15 5 Article 10.3390/e15051726 1726 1737 1099-4300 2013-05-08 doi: 10.3390/e15051726 Maurice Kibler http://www.mdpi.com/1099-4300/15/5/1705 A method of blind recognition of the coding parameters for binary Bose-Chaudhuri-Hocquenghem (BCH) codes is proposed in this paper. We consider an intelligent communication receiver which can blindly recognize the coding parameters of the received data stream. The only knowledge is that the stream is encoded using binary BCH codes, while the coding parameters are unknown. The problem can be addressed on the context of the non-cooperative communications or adaptive coding and modulations (ACM) for cognitive radio networks. The recognition processing includes two major procedures: code length estimation and generator polynomial reconstruction. A hard decision method has been proposed in a previous literature. In this paper we propose the recognition approach in soft decision situations with Binary-Phase-Shift-Key modulations and Additive-White-Gaussian-Noise (AWGN) channels. The code length is estimated by maximizing the root information dispersion entropy function. And then we search for the code roots to reconstruct the primitive and generator polynomials. By utilizing the soft output of the channel, the recognition performance is improved and the simulations show the efficiency of the proposed algorithm. Entropy 2013-05-08 15 5 Article 10.3390/e15051705 1705 1725 1099-4300 2013-05-08 doi: 10.3390/e15051705 Jing Zhou Zhiping Huang Chunwu Liu Shaojing Su Yimeng Zhang http://www.mdpi.com/1099-4300/15/5/1690 We introduce a new estimate of mutual information between a dataset and a target variable that can be maximised analytically and has broad applicability in the field of machine learning and statistical pattern recognition. This estimate has previously been employed implicitly as an approximation to quadratic mutual information. In this paper we will study the properties of these estimates of mutual information in more detail, and provide a derivation from a perspective of pairwise interactions. From this perspective, we will show a connection between our proposed estimate and Laplacian eigenmaps, which so far has not been shown to be related to mutual information. Compared with other popular measures of mutual information, which can only be maximised through an iterative process, ours can be maximised much more efficiently and reliably via closed-form eigendecomposition. Entropy 2013-05-08 15 5 Article 10.3390/e15051690 1690 1704 1099-4300 2013-05-08 doi: 10.3390/e15051690 Raymond Liu Duncan Gillies http://www.mdpi.com/1099-4300/15/5/1663 The maximum entropy method (MEM) is widely used in research fields such as linguistics, meteorology, physics, and chemistry. Recently, MEM application has become a subject of interest in the semiconductor engineering field, in which devices utilize very thin films composed of many materials. For thin film fabrication, it is essential to thoroughly understand atomic-scale structures, internal fixed charges, and bulk/interface traps, and many experimental techniques have been developed for evaluating these. However, the difficulty in interpreting the data they provide prevents the improvement of device fabrication processes. As a candidate for a very practical data analyzing technique, MEM is a promising approach to solve this problem. In this paper, we review the application of MEM to thin films used in semiconductor engineering. The method provides interesting and important information that cannot be obtained with conventional methods. This paper explains its theoretical background, important points for practical use, and application results. Entropy 2013-05-07 15 5 Article 10.3390/e15051663 1663 1689 1099-4300 2013-05-07 doi: 10.3390/e15051663 Yoshiki Yonamoto http://www.mdpi.com/1099-4300/15/5/1643 We investigate the statistical properties of the foreign exchange (FX) network at different time scales by two approaches, namely the methods of detrended cross-correlation coefficient (DCCA coefficient) and minimum spanning tree (MST). The daily FX rates of 44 major currencies in the period of 2007–2012 are chosen as the empirical data. Based on the analysis of statistical properties of cross-correlation coefficients, we find that the cross-correlation coefficients of the FX market are fat-tailed. By examining three MSTs at three special time scales (i.e., the minimum, medium, and maximum scales), we come to some conclusions: USD and EUR are confirmed as the predominant world currencies; the Middle East cluster is very stable while the Asian cluster and the Latin America cluster are not stable in the MSTs; the Commonwealth cluster is also found in the MSTs. By studying four evaluation criteria, we find that the MSTs of the FX market present diverse topological and statistical properties at different time scales. The scale-free behavior is observed in the FX network at most of time scales. We also find that most of links in the FX network survive from one time scale to the next. Entropy 2013-05-06 15 5 Article 10.3390/e15051643 1643 1662 1099-4300 2013-05-06 doi: 10.3390/e15051643 Gang-Jin Wang Chi Xie Yi-Jun Chen Shou Chen http://www.mdpi.com/1099-4300/15/5/1624 Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering problems is to achieve the parameter identification of fractional-order systems. A time-domain identification algorithm based on a genetic algorithm (GA) is proposed in this paper. The multi-variable parameter identification is converted into a parameter optimization by applying GA to the identification of fractional-order systems. To evaluate the identification accuracy and stability, the time-domain output error considering the condition variation is designed as the fitness function for parameter optimization. The identification process is established under various noise levels and excitation levels. The effects of external excitation and the noise level on the identification accuracy are analyzed in detail. The simulation results show that the proposed method could identify the parameters of both commensurate rate and non-commensurate rate fractional-order systems from the data with noise. It is also observed that excitation signal is an important factor influencing the identification accuracy of fractional-order systems. Entropy 2013-05-06 15 5 Article 10.3390/e15051624 1624 1642 1099-4300 2013-05-06 doi: 10.3390/e15051624 Shengxi Zhou Junyi Cao Yangquan Chen http://www.mdpi.com/1099-4300/15/5/1609 The use of a metric to assess distance between probability densities is an important practical problem. In this work, a particular metric induced by an α-divergence is studied. The Hellinger metric can be interpreted as a particular case within the framework of generalized Tsallis divergences and entropies. The nonparametric Parzen’s density estimator emerges as a natural candidate to estimate the underlying probability density function, since it may account for data from different groups, or experiments with distinct instrumental precisions, i.e., non-independent and identically distributed (non-i.i.d.) data. However, the information theoretic derived metric of the nonparametric Parzen’s density estimator displays infinite variance, limiting the direct use of resampling estimators. Based on measure theory, we present a change of measure to build a finite variance density allowing the use of resampling estimators. In order to counteract the poor scaling with dimension, we propose a new nonparametric two-stage robust resampling estimator of Hellinger’s metric error bounds for heterocedastic data. The approach presents very promising results allowing the use of different covariances for different clusters with impact on the distance evaluation. Entropy 2013-05-06 15 5 Article 10.3390/e15051609 1609 1623 1099-4300 2013-05-06 doi: 10.3390/e15051609 Alexandre Carvalho João Tavares Jose Principe http://www.mdpi.com/1099-4300/15/5/1587 It is plausible to hypothesize that the spiking responses of certain neurons represent functions of the spiking signals of other neurons. A natural ensuing question concerns how to use experimental data to infer what kind of a function is being computed. Model-based approaches typically require assumptions on how information is represented. By contrast, information measures are sensitive only to relative behavior: information is unchanged by applying arbitrary invertible transformations to the involved random variables. This paper develops an approach based on the information bottleneck method that attempts to find such functional relationships in a neuron population. Specifically, the information bottleneck method is used to provide appropriate compact representations which can then be parsed to infer functional relationships. In the present paper, the parsing step is specialized to the case of remapped-linear functions. The approach is validated on artificial data and then applied to recordings from the motor cortex of a macaque monkey performing an arm-reaching task. Functional relationships are identified and shown to exhibit some degree of persistence across multiple trials of the same experiment. Entropy 2013-05-06 15 5 Article 10.3390/e15051587 1587 1608 1099-4300 2013-05-06 doi: 10.3390/e15051587 S. Buddha Kelvin So Jose Carmena Michael Gastpar http://www.mdpi.com/1099-4300/15/5/1567 This paper shows the feasibility of utilizing the Kernel Spectral Clustering (KSC) method for the purpose of community detection in big data networks. KSC employs a primal-dual framework to construct a model. It results in a powerful property of effectively inferring the community affiliation for out-of-sample extensions. The original large kernel matrix cannot fitinto memory. Therefore, we select a smaller subgraph that preserves the overall community structure to construct the model. It makes use of the out-of-sample extension property for community membership of the unseen nodes. We provide a novel memory- and computationally efficient model selection procedure based on angular similarity in the eigenspace. We demonstrate the effectiveness of KSC on large scale synthetic networks and real world networks like the YouTube network, a road network of California and the Livejournal network. These networks contain millions of nodes and several million edges. Entropy 2013-05-03 15 5 Article 10.3390/e15051567 1567 1586 1099-4300 2013-05-03 doi: 10.3390/e15051567 Raghvendra Mall Rocco Langone Johan Suykens http://www.mdpi.com/1099-4300/15/5/1540 A compressible single step chemistry Direct Numerical Simulation (DNS) database of freely propagating premixed flames has been used to analyze different entropy generation mechanisms. The entropy generation due to viscous dissipation within the flames remains negligible in comparison to the other mechanisms of entropy generation. It has been found that the entropy generation increases significantly due to turbulence and the relative magnitudes of the augmentation of entropy generation and burning rates under turbulent conditions ultimately determine the value of turbulent second law efficiency in comparison to the corresponding laminar values. It has been found that the entropy generation mechanisms due to chemical reaction, thermal conduction and mass diffusion in turbulent flames strengthen with decreasing global Lewis number in comparison to the corresponding values in laminar flames. The ratio of second law efficiency under turbulent conditions to its corresponding laminar value has been found to decrease with increasing global Lewis number. An increase in heat release parameter significantly augments the entropy generation due to thermal conduction, whereas other mechanisms of entropy generation are marginally affected. However, the effects of augmented entropy generation due to thermal conduction at high values of heat release parameter are eclipsed by the increased change in availability due to chemical reaction, which leads to an increase in the second law efficiency with increasing heat release parameter for identical flow conditions. The combustion regime does not have any major influence on the augmentation of entropy generation due to chemical reaction, thermal conduction and mass diffusion in turbulent flames in comparison to corresponding laminar flames, whereas the extent of augmentation of entropy generation due to viscous dissipation in turbulent conditions in comparison to corresponding laminar flames, is more significant in the thin reaction zones regime than in the corrugated flamelets regime. However, the ratio of second law efficiency under turbulent conditions to its corresponding laminar value does not get significantly affected by the regime of combustion, as viscous dissipation plays a marginal role in the overall entropy generation in premixed flames. Entropy 2013-04-29 15 5 Article 10.3390/e15051540 1540 1566 1099-4300 2013-04-29 doi: 10.3390/e15051540 Richard Farran Nilanjan Chakraborty http://www.mdpi.com/1099-4300/15/5/1528 This paper reports matrix adjustment thermal reduction method to synthesize silver nanostructures in Er3+/Yb3+ activated GeO2-PbO glass matrix. The GeO2-PbO glass, the medium of nanoparticle formation, doped with Er2O3, Yb2O3 and AgNO3 was prepared by a melt quenching method. Annealing of the glass for different times was utilized, not only due to thermally reduce Ag+ ions to Ag nanostructures, but also to influence the glassy network. This is because, the glass structural transformation temperature is near to 435 °C and heating at more than this temperature can cause some structural changes in the glass matrix. According to TEM images, samples that tolerate 450 °C annealing temperature for one hour show the formation of basil-like silver nanostructures with a mean length of 54 nm and mean diameter of 13 nm embedded in the glass matrix, whereas with annealing at 450 °C for 5 to 20 h, silver nanoparticles of about 3–4 nm mean diameter size are formed. Annealing for 30 h causes silver nanoparticles to aggregate to form larger particles due to an Oswald ripening process. Observation of the characteristic Ag-NP SPR band at 400–500 nm in the UV-visible absorption spectra confirms the existence of silver nanoparticles. The SPR band widens to longer wavelengths in one hour annealed samples, which relates to the existence of nanostructures with different size or fractal shapes. In addition, an increment in the peak of the SPR band by increasing the duration of annealing indicates the formation of more nanoparticles. Furthermore, the existence of a peak at 470 cm–1 in the FTIR spectra of annealed samples and its absence in the samples not exposed to an annealing process suggests that the glass matrix is polymerized by Pb-O chains during the 450 °C annealing process. This is the main source of different nanostructures because of the dissimilar stabilizing media. The tighter media cap the particles to form small and dense nanoparticles but a loose environment leads to the creation of basil-like particles in the glass matrix. Entropy 2013-04-25 15 5 Article 10.3390/e15051528 1528 1539 1099-4300 2013-04-25 doi: 10.3390/e15051528 Hamid-Reza Bahari Reza Zamiri Hj. Sidek Azmi Zakaria Faisal Adikan http://www.mdpi.com/1099-4300/15/5/1516 Solutions to the radial Schr¨odinger equation of a particle in a quantum corral are used to probe how the statistical correlation between the position, and The momentum of the particle depends on the effective potential. The analysis is done via the Wigner function and its Shannon entropy. We show by comparison to the particle-in-a-box model that the attractive potential increases the magnitude of the correlation, while a repulsive potential decreases the magnitude of this correlation. Varying the magnitude of the repulsive potential yields that the correlation decreases with a stronger repulsive potential. Entropy 2013-04-25 15 5 Article 10.3390/e15051516 1516 1527 1099-4300 2013-04-25 doi: 10.3390/e15051516 Humberto Laguna Robin Sagar http://www.mdpi.com/1099-4300/15/5/1503 Steady state fluctuation relations for nonequilibrium systems are under intense investigation because of their important practical implications in nanotechnology and biology. However the precise conditions under which they hold need clarification. Using the dissipation function, which is related to the entropy production of linear irreversible thermodynamics, we show time reversibility, ergodic consistency and a recently introduced form of correlation decay, called T-mixing, are sufficient conditions for steady state fluctuation relations to hold. Our results are not restricted to a particular model and show that the steady state fluctuation relation for the dissipation function holds near or far from equilibrium subject to these conditions. The dissipation function thus plays a comparable role in nonequilibrium systems to thermodynamic potentials in equilibrium systems. Entropy 2013-04-25 15 5 Article 10.3390/e15051503 1503 1515 1099-4300 2013-04-25 doi: 10.3390/e15051503 Debra Searles Barbara Johnston Denis Evans Lamberto Rondoni http://www.mdpi.com/1099-4300/15/5/1486 In this paper we present entropy driven methodology for discretization. Recently, the original entropy based discretization was enhanced by including two options of selecting the best numerical attribute. In one option, Dominant Attribute, an attribute with the smallest conditional entropy of the concept given the attribute is selected for discretization and then the best cut point is determined. In the second option, Multiple Scanning, all attributes are scanned a number of times, and at the same time the best cut points are selected for all attributes. The results of experiments on 17 benchmark data sets, including large data sets, with 175 attributes or 25,931 cases, are presented. For comparison, the results of experiments on the same data sets using the global versions of well-known discretization methods of Equal Interval Width and Equal Frequency per Interval are also included. The entropy driven technique enhanced both of these methods by converting them into globalized methods. Results of our experiments show that the Multiple Scanning methodology is significantly better than both: Dominant Attribute and the better results of Globalized Equal Interval Width and Equal Frequency per Interval methods (using two-tailed test and 0.01 level of significance). Entropy 2013-04-25 15 5 Article 10.3390/e15051486 1486 1502 1099-4300 2013-04-25 doi: 10.3390/e15051486 Jerzy Grzymala-Busse http://www.mdpi.com/1099-4300/15/4/1464 The quantification and analysis of uncertainties is important in all cases where maps and models of uncertain properties are the basis for further decisions. Once these uncertainties are identified, the logical next step is to determine how they can be reduced. Information theory provides a framework for the analysis of spatial uncertainties when different subregions are considered as random variables. In the work presented here, joint entropy, conditional entropy, and mutual information are applied for a detailed analysis of spatial uncertainty correlations. The aim is to determine (i) which areas in a spatial analysis share information, and (ii) where, and by how much, additional information would reduce uncertainties. As an illustration, a typical geological example is evaluated: the case of a subsurface layer with uncertain depth, shape and thickness. Mutual information and multivariate conditional entropies are determined based on multiple simulated model realisations. Even for this simple case, the measures not only provide a clear picture of uncertainties and their correlations but also give detailed insights into the potential reduction of uncertainties at each position, given additional information at a different location. The methods are directly applicable to other types of spatial uncertainty evaluations, especially where multiple realisations of a model simulation are analysed. In summary, the application of information theoretic measures opens up the path to a better understanding of spatial uncertainties, and their relationship to information and prior knowledge, for cases where uncertain property distributions are spatially analysed and visualised in maps and models. Entropy 2013-04-22 15 4 Article 10.3390/e15041464 1464 1485 1099-4300 2013-04-22 doi: 10.3390/e15041464 J. Wellmann http://www.mdpi.com/1099-4300/15/4/1416 Glyphosate, the active ingredient in Roundup®, is the most popular herbicide used worldwide. The industry asserts it is minimally toxic to humans, but here we argue otherwise. Residues are found in the main foods of the Western diet, comprised primarily of sugar, corn, soy and wheat. Glyphosate's inhibition of cytochrome P450 (CYP) enzymes is an overlooked component of its toxicity to mammals. CYP enzymes play crucial roles in biology, one of which is to detoxify xenobiotics. Thus, glyphosate enhances the damaging effects of other food borne chemical residues and environmental toxins. Negative impact on the body is insidious and manifests slowly over time as inflammation damages cellular systems throughout the body. Here, we show how interference with CYP enzymes acts synergistically with disruption of the biosynthesis of aromatic amino acids by gut bacteria, as well as impairment in serum sulfate transport. Consequences are most of the diseases and conditions associated with a Western diet, which include gastrointestinal disorders, obesity, diabetes, heart disease, depression, autism, infertility, cancer and Alzheimer’s disease. We explain the documented effects of glyphosate and its ability to induce disease, and we show that glyphosate is the “textbook example” of exogenous semiotic entropy: the disruption of homeostasis by environmental toxins. Entropy 2013-04-18 15 4 Review 10.3390/e15041416 1416 1463 1099-4300 2013-04-18 doi: 10.3390/e15041416 Anthony Samsel Stephanie Seneff http://www.mdpi.com/1099-4300/15/4/1408 An analog of the Carnot engine reversibly operating within the framework of pure-state quantum mechanics is discussed. A general formula is derived for the efficiency of such an engine with an arbitrary confining potential. Its expression is given in terms of an energy spectrum and shows how the efficiency depends on a potential as the analog of a working material in thermodynamics, in general. This non-universal nature results from the fact that there exists no analog of the second law of thermodynamics in pure-state quantum mechanics where the von Neumann entropy identically vanishes. A special class of spectra, which leads to a common form of the efficiency, is identified. Entropy 2013-04-17 15 4 Article 10.3390/e15041408 1408 1415 1099-4300 2013-04-17 doi: 10.3390/e15041408 Sumiyoshi Abe http://www.mdpi.com/1099-4300/15/4/1388 An enormous dissipation of the order of 2 kJ/L takes place during the natural mixing process of fresh river water entering the salty sea. “Capacitive mixing” is a promising technique to efficiently harvest this energy in an environmentally clean and sustainable fashion. This method has its roots in the ability to store a very large amount of electric charge inside supercapacitor or battery electrodes dipped in a saline solution. Three different schemes have been studied so far, namely, Capacitive Double Layer Expansion (CDLE), Capacitive Donnan Potential (CDP) and Mixing Entropy Battery (MEB), respectively based on the variation upon salinity change of the electric double layer capacity, on the Donnan membrane potential, and on the electrochemical energy of intercalated ions. Entropy 2013-04-17 15 4 Review 10.3390/e15041388 1388 1407 1099-4300 2013-04-17 doi: 10.3390/e15041388 Raúl Rica Roberto Ziano Domenico Salerno Francesco Mantegazza Renéa van Roij Doriano Brogioli http://www.mdpi.com/1099-4300/15/4/1375 Analysis of knee joint vibration or vibroarthrographic (VAG) signals using signal processing and machine learning algorithms possesses high potential for the noninvasive detection of articular cartilage degeneration, which may reduce unnecessary exploratory surgery. Feature representation of knee joint VAG signals helps characterize the pathological condition of degenerative articular cartilages in the knee. This paper used the kernel-based probability density estimation method to model the distributions of the VAG signals recorded from healthy subjects and patients with knee joint disorders. The estimated densities of the VAG signals showed explicit distributions of the normal and abnormal signal groups, along with the corresponding contours in the bivariate feature space. The signal classifications were performed by using the Fisher’s linear discriminant analysis, support vector machine with polynomial kernels, and the maximal posterior probability decision criterion. The maximal posterior probability decision criterion was able to provide the total classification accuracy of 86.67% and the area (Az) of 0.9096 under the receiver operating characteristics curve, which were superior to the results obtained by either the Fisher’s linear discriminant analysis (accuracy: 81.33%, Az: 0.8564) or the support vector machine with polynomial kernels (accuracy: 81.33%, Az: 0.8533). Such results demonstrated the merits of the bivariate feature distribution estimation and the superiority of the maximal posterior probability decision criterion for analysis of knee joint VAG signals. Entropy 2013-04-17 15 4 Article 10.3390/e15041375 1375 1387 1099-4300 2013-04-17 doi: 10.3390/e15041375 Yunfeng Wu Suxian Cai Shanshan Yang Fang Zheng Ning Xiang http://www.mdpi.com/1099-4300/15/4/1357 This paper addresses the global outer synchronization problem between two fractional-order complex networks coupled in a drive-response configuration. In particular, for a given fractional-order complex network composed of Lur’e systems, an observer-type response network with non-fragile output feedback controllers is constructed. Both additive and multiplicative uncertainties that perturb the control gain matrices are considered. Then, using the stability theory of fractional-order systems and eigenvalue distribution of the Kronecker sum of matrices, we establish some sufficient conditions for global outer synchronization. Interestingly, the developed results are cast in the format of linear matrix inequalities (LMIs), which can be efficiently solved via the MATLAB LMI Control Toolbox. Finally, numerical simulations on fractional-order networks with nearest-neighbor and small-world topologies are given to support the theoretical analysis. Entropy 2013-04-15 15 4 Article 10.3390/e15041357 1357 1374 1099-4300 2013-04-15 doi: 10.3390/e15041357 Meichun Zhao Junwei Wang http://www.mdpi.com/1099-4300/15/4/1342 Receiver operating characteristic (ROC) curves have application in analysis of the performance of diagnostic indicators used in the assessment of disease risk in clinical and veterinary medicine and in crop protection. For a binary indicator, an ROC curve summarizes the two distributions of risk scores obtained by retrospectively categorizing subjects as cases or controls using a gold standard. An ROC curve may be symmetric about the negative diagonal of the graphical plot, or skewed towards the left-hand axis or the upper axis of the plot. ROC curves with different symmetry properties may have the same area under the curve. Here, we characterize the symmetry properties of bi-Normal and bi-gamma ROC curves in terms of the Kullback-Leibler divergences (KLDs) between the case and control distributions of risk scores. The KLDs describe the known symmetry properties of bi-Normal ROC curves, and newly characterize the symmetry properties of constant-shape and constant-scale bi-gamma ROC curves. It is also of interest to note an application of KLDs where their asymmetry—often an inconvenience—has a useful interpretation. Entropy 2013-04-10 15 4 Article 10.3390/e15041342 1342 1356 1099-4300 2013-04-10 doi: 10.3390/e15041342 Gareth Hughes Bhaskar Bhattacharya http://www.mdpi.com/1099-4300/15/4/1324 The temporal interactions between water and carbon cycling and the controlling environmental variables are investigated using wavelets and information theory. We used 3.5 years of eddy covariance station observations from an abandoned agricultural field in the central U.S. Time-series of the entropy of water and carbon fluxes exhibit pronounced annual cycles, primarily explained by the modulation of the diurnal flux amplitude by other variables, such as the net radiation. Entropies of soil moisture and precipitation show almost no annual cycle, but the data were collected during above average precipitation years, which limits the role of moisture stress on the resultant fluxes. We also investigated the information contribution to resultant fluxes from selected environmental variables as a function of time-scale using relative entropy. The relative entropy of latent heat flux and ecosystem respiration show that the radiation terms contribute the most information to these fluxes at scales up to the diurnal scale. Vapor pressure deficit and air temperature contribute to the most information for the gross primary productivity and net ecosystem exchange at the daily time-scale. The relative entropy between the fluxes and soil moisture illustrates that soil moisture contributes information at approximately weekly time-scales, while the relative entropy with precipitation contributes information predominantly at the monthly time-scale. The use of information theory metrics is a relatively new technique for assessing biosphere-atmosphere interactions, and this study illustrates the utility of the approach for assessing the dominant time-scales of these interactions. Entropy 2013-04-10 15 4 Article 10.3390/e15041324 1324 1341 1099-4300 2013-04-10 doi: 10.3390/e15041324 Nathaniel Brunsell Cassandra Wilson http://www.mdpi.com/1099-4300/15/4/1311 In this paper, the resilient minimum entropy filter problem is investigated for the stochastic systems with non-Gaussian disturbances. The goal of designing the filter is to guarantee that the entropy of the estimation error is monotonically decreasing, moreover, the error system is exponentially ultimately bounded in the mean square. Based on the entropy performance function, a filter gain updating algorithm is presented to make the entropy decrease at every sampling instant k. Then the boundedness of the gain updating law is analyzed using the kernel density estimation technique. Furthermore, a suboptimal resilient filter gain is designed in terms of LMI. Finally, a simulation example is given to show the effectiveness of the proposed results. Entropy 2013-04-10 15 4 Article 10.3390/e15041311 1311 1323 1099-4300 2013-04-10 doi: 10.3390/e15041311 Yan Wang Hong Wang Lei Guo http://www.mdpi.com/1099-4300/15/4/1289 From algorithmic information theory, which connects the information content of a data set to the shortest computer program that can produce it, it is known that there are strong analogies between compression, knowledge, inference and prediction. The more we know about a data generating process, the better we can predict and compress the data. A model that is inferred from data should ideally be a compact description of those data. In theory, this means that hydrological knowledge could be incorporated into compression algorithms to more efficiently compress hydrological data and to outperform general purpose compression algorithms. In this study, we develop such a hydrological data compressor, named HydroZIP, and test in practice whether it can outperform general purpose compression algorithms on hydrological data from 431 river basins from the Model Parameter Estimation Experiment (MOPEX) data set. HydroZIP compresses using temporal dependencies and parametric distributions. Resulting file sizes are interpreted as measures of information content, complexity and model adequacy. These results are discussed to illustrate points related to learning from data, overfitting and model complexity. Entropy 2013-04-10 15 4 Article 10.3390/e15041289 1289 1310 1099-4300 2013-04-10 doi: 10.3390/e15041289 Steven Weijs Nick van de Giesen Marc Parlange http://www.mdpi.com/1099-4300/15/4/1271 More than three decades ago, Tykodi and Hummel proposed a procedure to investigate the self-consistency thermodynamical criterion for equations of the state of gases. The main criterion used by these authors consists of requiring that an equation of state must not be inconsistent with certain thermodynamical identities from the first and second laws of thermodynamics. This paper explores the possibility of another self-consistency method based on relativistic transformations of the thermodynamical variables. It is shown that the virial coefficients have to be corrected by a relativistic factor if the equation of state is considered in a moving relativistic reference frame. Some relativistic and non-relativistic equations of state are analyzed. Entropy 2013-04-09 15 4 Article 10.3390/e15041271 1271 1288 1099-4300 2013-04-09 doi: 10.3390/e15041271 Gonzalo de Parga Adriana Vargas Benjamín López-Carrera http://www.mdpi.com/1099-4300/15/4/1247 State-of-the-art heuristic algorithms to solve the vehicle routing problem with time windows (VRPTW) usually present slow speeds during the early iterations and easily fall into local optimal solutions. Focusing on solving the above problems, this paper analyzes the particle encoding and decoding strategy of the particle swarm optimization algorithm, the construction of the vehicle route and the judgment of the local optimal solution. Based on these, a hybrid chaos-particle swarm optimization algorithm (HPSO) is proposed to solve VRPTW. The chaos algorithm is employed to re-initialize the particle swarm. An efficient insertion heuristic algorithm is also proposed to build the valid vehicle route in the particle decoding process. A particle swarm premature convergence judgment mechanism is formulated and combined with the chaos algorithm and Gaussian mutation into HPSO when the particle swarm falls into the local convergence. Extensive experiments are carried out to test the parameter settings in the insertion heuristic algorithm and to evaluate that they are corresponding to the data’s real-distribution in the concrete problem. It is also revealed that the HPSO achieves a better performance than the other state-of-the-art algorithms on solving VRPTW. Entropy 2013-04-09 15 4 Article 10.3390/e15041247 1247 1270 1099-4300 2013-04-09 doi: 10.3390/e15041247 Wenbin Hu Huanle Liang Chao Peng Bo Du Qi Hu http://www.mdpi.com/1099-4300/15/4/1232 Molecular dynamics simulations are used to study the evaporation of water droplets containing either dissolved LiCl, NaCl or KCl salt in a gaseous surrounding (nitrogen) with a constant high temperature of 600 K. The initial droplet has 298 K temperature and contains 1,120 water molecules, 0, 40, 80 or 120 salt molecules. The effects of the salt type and concentration on the evaporation rate are examined. Three stages with different evaporation rates are observed for all cases. In the initial stage of evaporation, the droplet evaporates slowly due to low droplet temperature and high evaporation latent heat for water, and pure water and aqueous solution have almost the same evaporation rates. In the second stage, evaporation rate is increased significantly, and evaporation is somewhat slower for the aqueous salt-containing droplet than the pure water droplet due to the attracted ion-water interaction and hydration effect. The Li+-water has the strongest interaction and hydration effect, so LiCl aqueous droplets evaporate the slowest, then NaCl and KCl. Higher salt concentration also enhances the ion-water interaction and hydration effect, and hence corresponds to a slower evaporation. In the last stage of evaporation, only a small amount of water molecules are left in the droplet, leading to a significant increase in ion-water interactions, so that the evaporation becomes slower compared to that in the second stage. Entropy 2013-04-08 15 4 Article 10.3390/e15041232 1232 1246 1099-4300 2013-04-08 doi: 10.3390/e15041232 Bing-Bing Wang Xiao-Dong Wang Min Chen Jin-Liang Xu http://www.mdpi.com/1099-4300/15/4/1221 The one-dimensional (1D) power law velocity distribution, commonly used for computing velocities in open channel flow, has been derived empirically. However, a multitude of problems, such as scour around bridge piers, cutoffs and diversions, pollutant dispersion, and so on, require the velocity distribution in two dimensions. This paper employs the Shannon entropy theory for deriving the power law velocity distribution in two-dimensions (2D). The development encompasses the rectangular domain, but can be extended to any arbitrary domain, including a trapezoidal domain. The derived methodology requires only a few parameters and the good agreement is confirmed by comparing the velocity values calculated using the proposed methodology with values derived from both the 1D power law model and a logarithmic velocity distribution available in the literature. Entropy 2013-04-08 15 4 Article 10.3390/e15041221 1221 1231 1099-4300 2013-04-08 doi: 10.3390/e15041221 Vijay Singh Gustavo Marini Nicola Fontana http://www.mdpi.com/1099-4300/15/4/1202 Studies of learning algorithms typically concentrate on situations where potentially ever growing training sample is available. Yet, there can be situations (e.g., detection of differentially expressed genes on unreplicated data or estimation of time delay in non-stationary gravitationally lensed photon streams) where only extremely small samples can be used in order to perform an inference. On unreplicated data, the inference has to be performed on the smallest sample possible—sample of size 1. We study whether anything useful can be learnt in such extreme situations by concentrating on a Bayesian approach that can account for possible prior information on expected counts. We perform a detailed information theoretic study of such Bayesian estimation and quantify the effect of Bayesian averaging on its first two moments. Finally, to analyze potential benefits of the Bayesian approach, we also consider Maximum Likelihood (ML) estimation as a baseline approach. We show both theoretically and empirically that the Bayesian model averaging can be potentially beneficial. Entropy 2013-04-08 15 4 Article 10.3390/e15041202 1202 1220 1099-4300 2013-04-08 doi: 10.3390/e15041202 Peter Tiňo http://www.mdpi.com/1099-4300/15/4/1186 The performance and design criteria of air powered multistage turbines are studied thermodynamically in this paper. In-house code is developed in the C++ environment and the characteristics of four-stage turbines with inter-heating are analyzed in terms of maximum thermal efficiency, maximum exergy efficiency and maximum work output over the inlet temperature range of 293 K–793 K with inlet pressure of 70 bar. It is found that the maximum thermal efficiency, maximum exergy efficiency and maximum work output are 62.6%, 91.9%, 763.2 kJ/s, respectively. However, the thermal efficiency, exergy efficiency and work output are not equivalent for the four-stage radial turbine. It is suggested that at low working temperatures both maximum exergy efficiency and maximum work output can be used as the design objective, however, only maximum work output can be used as the design objective for the four-stage radial turbine over the working temperature range in this work. Entropy 2013-03-28 15 4 Article 10.3390/e15041186 1186 1201 1099-4300 2013-03-28 doi: 10.3390/e15041186 Xuehui Zhang Haisheng Chen Xiaohui Yan Xinjing Zhang Chunqing Tan http://www.mdpi.com/1099-4300/15/4/1171 Many cities around the World have established the development objective of becoming a low-carbon city. Evaluation of such a city is important for its progress. A new evaluation framework of urban low-carbon development level is proposed in this paper, which integrates synthetic evaluation based on a bottom-up idea and analytical diagnosis based on a top-down idea. Further, set pair analysis is combined for synthetic evaluation and analytical diagnosis by comparing urban low-carbon development levels of different cities, through which the comprehensive state of urban low-carbon development level can be obtained and limiting factors identified. Based on the proposed framework and set pair analysis, low-carbon development levels of 12 Chinese cities are compared. Some suggestions are provided, based on results of overall situations of urban low-carbon development level and concrete performances of various factors and specific indicators. We conclude that both synthetic evaluation and analytical diagnosis are important for evaluation of urban low-carbon development level. The proposed framework and method can be widely applied in the evaluation of different cities over a long-term period. Entropy 2013-03-27 15 4 Article 10.3390/e15041171 1171 1185 1099-4300 2013-03-27 doi: 10.3390/e15041171 Meirong Su Ronghua Li Weiwei Lu Chen Chen Bin Chen Zhifeng Yang http://www.mdpi.com/1099-4300/15/4/1152 Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings). The first misunderstanding: entropy is a measure of disorder. This is an old and very common opinion. The second misconception is that the entropy production minimizes in the evolution of nonequilibrium systems. However, as it has recently become clear, evolution (progress) in Nature demonstrates the opposite, i.e., maximization of the entropy production. The principal questions connected with this maximization are considered herein. The two misconceptions mentioned above can lead to the apparent contradiction between the conclusions of modern thermodynamics and the basic conceptions of evolution existing in biology. In this regard, the analysis of these issues seems extremely important and timely as it contributes to the deeper understanding of the laws of development of the surrounding World and the place of humans in it. Entropy 2013-03-26 15 4 Review 10.3390/e15041152 1152 1170 1099-4300 2013-03-26 doi: 10.3390/e15041152 Leonid Martyushev http://www.mdpi.com/1099-4300/15/3/1135 Several models have been proposed to explain the dark energy that is causing universe expansion to accelerate. Here the acceleration predicted by the Holographic Dark Information Energy (HDIE) model is compared to the acceleration that would be produced by a cosmological constant. While identical to a cosmological constant at low redshifts, z < 1, the HDIE model results in smaller Hubble parameter values at higher redshifts, z > 1, reaching a maximum difference of 2.6 ± 0.5% around z ~ 1.7. The next generation of dark energy measurements, both those scheduled to be made in space (ESA’s Euclid and NASA’s WFIRST missions) and those to be made on the ground (BigBOSS, LSST and Dark Energy Survey), should be capable of determining whether such a difference exists or not. In addition a computer simulation thought experiment is used to show that the algorithmic entropy of the universe always increases because the extra states produced by the accelerating expansion compensate for the loss of entropy from star formation. Entropy 2013-03-22 15 3 Article 10.3390/e15031135 1135 1151 1099-4300 2013-03-22 doi: 10.3390/e15031135 Michael Gough http://www.mdpi.com/1099-4300/15/3/1118 In plasmas, Debye screening structures the possible correlations between particles. We identify a phase space minimum h* in non-equilibrium space plasmas that connects the energy of particles in a Debye sphere to an equivalent wave frequency. In particular, while there is no a priori reason to expect a single value of h* across plasmas, we find a very similar value of h* ≈ (7.5 ± 2.4)×10−22 J·s using four independent methods: (1) Ulysses solar wind measurements, (2) space plasmas that typically reside in stationary states out of thermal equilibrium and spanning a broad range of physical properties, (3) an entropic limit emerging from statistical mechanics, (4) waiting-time distributions of explosive events in space plasmas. Finding a quasi-constant value for the phase space minimum in a variety of different plasmas, similar to the classical Planck constant but 12 orders of magnitude larger may be revealing a new type of quantization in many plasmas and correlated systems more generally. Entropy 2013-03-22 15 3 Article 10.3390/e15031118 1118 1134 1099-4300 2013-03-22 doi: 10.3390/e15031118 George Livadiotis David McComas http://www.mdpi.com/1099-4300/15/3/1100 In this paper we propose an approach to the estimation and simulation of loss distributions based on Maximum Entropy (ME), a non-parametric technique that maximizes the Shannon entropy of the data under moment constraints. Special cases of the ME density correspond to standard distributions; therefore, this methodology is very general as it nests most classical parametric approaches. Sampling the ME distribution is essential in many contexts, such as loss models constructed via compound distributions. Given the difficulties in carrying out exact simulation,we propose an innovative algorithm, obtained by means of an extension of Adaptive Importance Sampling (AIS), for the approximate simulation of the ME distribution. Several numerical experiments confirm that the AIS-based simulation technique works well, and an application to insurance data gives further insights in the usefulness of the method for modelling, estimating and simulating loss distributions. Entropy 2013-03-22 15 3 Article 10.3390/e15031100 1100 1117 1099-4300 2013-03-22 doi: 10.3390/e15031100 Marco Bee http://www.mdpi.com/1099-4300/15/3/1085 The opening/closure of the catalytic loop 6 over the active site in apo triosephosphate isomerase (TIM) has been previously shown to be driven by the global motions of the enzyme, specifically the counter-clockwise rotation of the subunits. In this work, the effect of the substrate dihydroxyacetone phosphate (DHAP) on TIM dynamics is assessed using two apo and two DHAP-bound molecular dynamics (MD) trajectories (each 60 ns long). Multiple events of catalytic loop opening/closure take place during 60 ns runs for both apo TIM and its DHAP-complex. However, counter-clockwise rotation observed in apo TIM is suppressed and bending-type motions are linked to loop dynamics in the presence of DHAP. Bound DHAP molecules also reduce the overall mobility of the enzyme and change the pattern of orientational cross-correlations, mostly those within each subunit. The fluctuations of pseudodihedral angles of the loop 6 residues are enhanced towards the C-terminus, when DHAP is bound at the active site. Entropy 2013-03-18 15 3 Article 10.3390/e15031085 1085 1099 1099-4300 2013-03-18 doi: 10.3390/e15031085 Zeynep Kurkcuoglu Pemra Doruker http://www.mdpi.com/1099-4300/15/3/1069 Multiscale entropy (MSE) was recently developed to evaluate the complexity of time series over different time scales. Although the MSE algorithm has been successfully applied in a number of different fields, it encounters a problem in that the statistical reliability of the sample entropy (SampEn) of a coarse-grained series is reduced as a time scale factor is increased. Therefore, in this paper, the concept of a composite multiscale entropy (CMSE) is introduced to overcome this difficulty. Simulation results on both white noise and 1/f noise show that the CMSE provides higher entropy reliablity than the MSE approach for large time scale factors. On real data analysis, both the MSE and CMSE are applied to extract features from fault bearing vibration signals. Experimental results demonstrate that the proposed CMSE-based feature extractor provides higher separability than the MSE-based feature extractor. Entropy 2013-03-18 15 3 Article 10.3390/e15031069 1069 1084 1099-4300 2013-03-18 doi: 10.3390/e15031069 Shuen-De Wu Chiu-Wen Wu Shiou-Gwo Lin Chun-Chieh Wang Kung-Yen Lee http://www.mdpi.com/1099-4300/15/3/1057 Using the new global embedding approach we investigate Unruh/Hawking temperature of the 5-dimensional minimal gauged supergravity black hole with double rotating parameters in a general (1 + 1) space-time. Our results verify that views of Banerjee and Majhi, and extend this approach to a higher dimension situation. Entropy 2013-03-18 15 3 Article 10.3390/e15031057 1057 1068 1099-4300 2013-03-18 doi: 10.3390/e15031057 Hui-Hua Zhao Li-Chun Zhang Guang-Liang Li http://www.mdpi.com/1099-4300/15/3/1035 The many moments model for dense gases and macromolecular fluids is considered here, where the upper order moment is chosen in accordance to the suggestions of the non-relativistic limit of the corresponding relativistic model. The solutions of the restrictions imposed by the entropy principle and that of Galilean relativity were, until now, obtained in the literature by using Taylor expansions around equilibrium and without proving convergence. Here, an exact solution without using expansions is found. The particular case with only 14 moments has already been treated in the literature in a completely different way. Here, it is proven that this particular closure is included in the presently more general one. Entropy 2013-03-11 15 3 Article 10.3390/e15031035 1035 1056 1099-4300 2013-03-11 doi: 10.3390/e15031035 Maria Carrisi Stefania Montisci Sebastiano Pennisi http://www.mdpi.com/1099-4300/15/3/1014 A solar-aided coal-fired power plant realizes the integration of a fossil fuel (coal or gas) and clean energy (solar). In this paper, a conventional 600 MW coal-fired power plant and a 600 MW solar-aided coal-fired power plant have been taken as the study case to understand the merits of solar-aided power generation (SAPG) technology. The plants in the case study have been analyzed by using the First and Second Laws of Thermodynamics principles. The solar irradiation and load ratio have been considered in the analysis. We conclude that if the solar irradiation was 925 W/m2 and load ratio of the SAPG plant was 100%, the exergy efficiency would be 44.54% and the energy efficiency of the plant (46.35%). It was found that in the SAPG plant the largest exergy loss was from the boiler, which accounted for about 76.74% of the total loss. When the load ratio of the unit remains at 100%, and the solar irradiation varies from 500 W/m2 to 1,100 W/m2, the coal savings would be in the range of 8.6 g/kWh to 15.8 g/kWh. If the solar irradiation were kept at 925 W/m2 while the load ratio of the plant changed from 30% to 100%, the coal savings could be in the range of 11.99 g/kWh to 13.75 g/kWh. Entropy 2013-03-11 15 3 Article 10.3390/e15031014 1014 1034 1099-4300 2013-03-11 doi: 10.3390/e15031014 Rongrong Zhai Yong Zhu Yongping Yang Kaiyu Tan Eric Hu http://www.mdpi.com/1099-4300/15/3/999 In the modern world, the fine balance and delicate relationship between human society and the environment in which we exist has been affected by the phenomena of urbanisation and urban development. Today, various environmental factors give rise to horizontal dispersion, spread and growth of cities. One of the most important results of this is climatic change which is directly affected by the urban sprawl of every metropolis. The aim of this study is to identify the relationship between the various horizontally distributed components of Tehran city and changes in essential microclimate clusters, by means of the humidex index. Results showed that, when the humidex was calculated for each of the obtained clusters, it was evident that it had increased with time, in parallel with Shannon’s entropy, as a consequence of the average temperature and relative humidity of each cluster. At the same time, results have shown that both temperature and relative humidity of the study area are related with urban sprawl, urbanisation and development, as defined by Shannon’s entropy and, in consequence, with humidex. In consequence, this new concept must be considered in future research works to predict and control urban sprawl and microclimate conditions in cities. Entropy 2013-03-07 15 3 Article 10.3390/e15030999 999 1013 1099-4300 2013-03-07 doi: 10.3390/e15030999 Abdolazim Ghanghermeh Gholamreza Roshan José Orosa José Calvo-Rolle Ángel Costa http://www.mdpi.com/1099-4300/15/3/988 Velocity distribution in an open channel flow can be very useful to model many hydraulic phenomena. Among the others, several 1D models based on the concept of entropy are available in the literature, which allow estimating the velocity distribution by measuring velocities only in a few points. Nevertheless, since 1D models have often a limited practical use, a 2D entropy based model was recently developed. The model provides a reliable estimation of the velocity distribution for open channel flow with a rectangular cross section, if the maximum velocity and the average velocity are known. In this paper results from the proposed model were compared with measured velocities carried out from laboratory experiments. Calculated values were also compared with results inferred from a 2D model available in the literature, resulting in a greater ease of use and a more reliable estimate of the velocity profile. Entropy 2013-03-06 15 3 Article 10.3390/e15030988 988 998 1099-4300 2013-03-06 doi: 10.3390/e15030988 Nicola Fontana Gustavo Marini Francesco Paola http://www.mdpi.com/1099-4300/15/3/972 Boundary line models for N2O emissions from agricultural soils provide a means of estimating emissions within defined ranges. Boundary line models partition a two-dimensional region of parameter space into sub-regions by means of thresholds based on relationships between N2O emissions and explanatory variables, typically using soil data available from laboratory or field studies. Such models are intermediate in complexity between the use of IPCC emission factors and complex process-based models. Model calibration involves characterizing the extent to which observed data are correctly forecast. Writing the numerical results from graphical two-threshold boundary line models as 3×3 prediction-realization tables facilitates calculation of expected mutual information, a measure of the amount of information about the observations contained in the forecasts. Whereas mutual information characterizes the performance of a forecaster averaged over all forecast categories, specific information and relative entropy both characterize aspects of the amount of information contained in particular forecasts. We calculate and interpret these information quantities for experimental N2O emissions data. Entropy 2013-03-05 15 3 Article 10.3390/e15030972 972 987 1099-4300 2013-03-05 doi: 10.3390/e15030972 Cairistiona Topp Weijin Wang Joanna Cloy Robert Rees Gareth Hughes http://www.mdpi.com/1099-4300/15/3/960 We show that the thermodynamics of ideal gases may be derived solely from the Democritean concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent of the laws of motion, aside from the law of energy conservation. Only a single corpuscle in contact with a heat bath submitted to a z and t-invariant force is considered. Most of the end results are known but the method appears to be novel. The mathematics being elementary, the present paper should facilitate the understanding of the ideal gas law and of classical thermodynamics even though not-usually-taught concepts are being introduced. Entropy 2013-02-27 15 3 Article 10.3390/e15030960 960 971 1099-4300 2013-02-27 doi: 10.3390/e15030960 Jacques Arnaud Laurent Chusseau Fabrice Philippe http://www.mdpi.com/1099-4300/15/3/943 Generally, the controller design should be performed to narrow the shape of the probability density function of the tracking error. A small information entropy value corresponds to a narrow distribution function, which means that the uncertainty of the related random variable is small. In this paper, information entropy is introduced in the field of control performance assessment (CPA). For the unknown time delay case, the minimum information entropy (MIE) benchmark is presented, and a MIE-based performance index is defined. For the known time delay case, a tight upper bound of MIE is derived and adopted as a performance benchmark to assess the stochastic control performance. Based on these, the control performance assessment procedures are developed for both the steady and the transient processes. Simulation tests and an industrial case study of a main steam pressure system of a 1,000MW power unit are utilized to verify the effectiveness of the proposed procedures. Entropy 2013-02-27 15 3 Article 10.3390/e15030943 943 959 1099-4300 2013-02-27 doi: 10.3390/e15030943 Qing-Wei Meng Fang Fang Ji-Zhen Liu http://www.mdpi.com/1099-4300/15/3/926 Providing accurate load forecast to electric utility corporations is essential in order to reduce their operational costs and increase profits. Hence, training set selection is an important preprocessing step which has to be considered in practice in order to increase the accuracy of load forecasts. The usage of mutual information (MI) has been recently proposed in regression tasks, mostly for feature selection and for identifying the real instances from training sets that contains noise and outliers. This paper proposes a methodology for the training set selection in a least squares support vector machines (LS-SVMs) load forecasting model. A new application of the concept of MI is presented for the selection of a training set based on MI computation between initial training set instances and testing set instances. Accordingly, several LS-SVMs models have been trained, based on the proposed methodology, for hourly prediction of electric load for one day ahead. The results obtained from a real-world data set indicate that the proposed method increases the accuracy of load forecasting as well as reduces the size of the initial training set needed for model training. Entropy 2013-02-27 15 3 Article 10.3390/e15030926 926 942 1099-4300 2013-02-27 doi: 10.3390/e15030926 Miloš Božić Miloš Stojanović Zoran Stajić Nenad Floranović http://www.mdpi.com/1099-4300/15/3/789 This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties, and the problem of quantum measurement. A considerable progress has been achieved, based on four distinct new ideas. First, objective properties are associated with states rather than with values of observables. Second, all classical properties are selected properties of certain high entropy quantum states of macroscopic systems. Third, registration of a quantum system is strongly disturbed by systems of the same type in the environment. Fourth, detectors must be distinguished from ancillas and the states of registered systems are partially dissipated and lost in the detectors. The paper has two aims: a clear explanation of all new results and a coherent and contradiction-free account of the whole quantum mechanics including all necessary changes of its current textbook version. Entropy 2013-02-27 15 3 Review 10.3390/e15030789 789 925 1099-4300 2013-02-27 doi: 10.3390/e15030789 Petr Hájíček http://www.mdpi.com/1099-4300/15/3/767 A method is shown for computing transfer entropy over multiple time lags for coupled autoregressive processes using formulas for the differential entropy of multivariate Gaussian processes. Two examples are provided: (1) a first-order filtered noise process whose state is measured with additive noise, and (2) two first-order coupled processes each of which is driven by white process noise. We found that, for the first example, increasing the first-order AR coefficient while keeping the correlation coefficient between filtered and measured process fixed, transfer entropy increased since the entropy of the measured process was itself increased. For the second example, the minimum correlation coefficient occurs when the process noise variances match. It was seen that matching of these variances results in minimum information flow, expressed as the sum of transfer entropies in both directions. Without a match, the transfer entropy is larger in the direction away from the process having the larger process noise. Fixing the process noise variances, transfer entropies in both directions increase with the coupling strength. Finally, we note that the method can be generally employed to compute other information theoretic quantities as well. Entropy 2013-02-25 15 3 Article 10.3390/e15030767 767 788 1099-4300 2013-02-25 doi: 10.3390/e15030767 Daniel Hahs Shawn Pethel http://www.mdpi.com/1099-4300/15/3/753 Analysis of gait dynamics in children may help understand the development of neuromuscular control and maturation of locomotor function. This paper applied the nonparametric Parzen-window estimation method to establish the probability density function (PDF) models for the stride interval time series of 50 children (25 boys and 25 girls). Four statistical parameters, in terms of averaged stride interval (ASI), variation of stride interval (VSI), PDF skewness (SK), and PDF kurtosis (KU), were computed with the Parzen-window PDFs to study the maturation of stride interval in children. By analyzing the results of the children in three age groups (aged 3–5 years, 6–8 years, and 10–14 years), we summarize the key findings of the present study as follows. (1) The gait cycle duration, in terms of ASI, increases until 14 years of age. On the other hand, the gait variability, in terms of VSI, decreases rapidly until 8 years of age, and then continues to decrease at a slower rate. (2) The SK values of both the histograms and Parzen-window PDFs for all of the three age groups are positive, which indicates an imbalance in the stride interval distribution within an age group. However, such an imbalance would be meliorated when the children grow up. (3) The KU values of both the histograms and Parzen-window PDFs decrease with the body growth in children, which suggests that the musculoskeletal growth enables the children to modulate a gait cadence with ease. (4) The SK and KU results also demonstrate the superiority of the Parzen-window PDF estimation method to the Gaussian distribution modeling, for the study of gait maturation in children. Entropy 2013-02-25 15 3 Article 10.3390/e15030753 753 766 1099-4300 2013-02-25 doi: 10.3390/e15030753 Ning Xiang Suxian Cai Shanshan Yang Zhangting Zhong Fang Zheng Jia He Yunfeng Wu http://www.mdpi.com/1099-4300/15/3/721 The Minimum Mutual Information (MinMI) Principle provides the least committed, maximum-joint-entropy (ME) inferential law that is compatible with prescribed marginal distributions and empirical cross constraints. Here, we estimate MI bounds (the MinMI values) generated by constraining sets Tcr comprehended by mcr linear and/or nonlinear joint expectations, computed from samples of N iid outcomes. Marginals (and their entropy) are imposed by single morphisms of the original random variables. N-asymptotic formulas are given both for the distribution of cross expectation’s estimation errors, the MinMI estimation bias, its variance and distribution. A growing Tcr leads to an increasing MinMI, converging eventually to the total MI. Under N-sized samples, the MinMI increment relative to two encapsulated sets Tcr1 ⊂ Tcr2 (with numbers of constraints mcr1<mcr2 ) is the test-difference δH = Hmax 1, N - Hmax 2, N ≥ 0  between the two respective estimated MEs. Asymptotically, δH follows a Chi-Squared distribution 1/2NΧ2 (mcr2-mcr1) whose upper quantiles determine if constraints in Tcr2/Tcr1 explain significant extra MI. As an example, we have set marginals to being normally distributed (Gaussian) and have built a sequence of MI bounds, associated to successive non-linear correlations due to joint non-Gaussianity. Noting that in real-world situations available sample sizes can be rather low, the relationship between MinMI bias, probability density over-fitting and outliers is put in evidence for under-sampled data. Entropy 2013-02-25 15 3 Article 10.3390/e15030721 721 752 1099-4300 2013-02-25 doi: 10.3390/e15030721 Carlos Pires Rui Perdigão http://www.mdpi.com/1099-4300/15/2/700 Although stock option markets have grown dramatically over the past several decades, the relation between an option and its underlying asset, especially bidirectional conduction, is not particularly clear. So far, there have been many debates about this topic. We try to investigate this problem from a novel angle: an artificial stock market including a stock option is constructed in this paper. The model includes two parts, one is a stock trade module based on the Santa Fe Institute Artificial Stock Market (SFI-ASM), and the other is an option trade module. In the latter module, three types of option traders are employed. The results show that the model is effective, and experiments illustrate that option markets have a remarkable effect on stock markets. Furthermore, by appending options, the model replicates some stylized properties, such as volatility clustering and GARCH effect, which can be observed in real financial markets. Entropy 2013-02-22 15 2 Article 10.3390/e15020700 700 720 1099-4300 2013-02-22 doi: 10.3390/e15020700 Hai-Jun Yang Gui-Ping Sun http://www.mdpi.com/1099-4300/15/2/698 The journal Entropy is initiating a “Best Paper” award to recognize outstanding papers in the area of entropy and information studies published in Entropy. We are pleased to announce the first “Entropy Best Paper Award” for 2013. Nominations were selected by the Editor-in-Chief and selected Editorial Board Members from all the papers published in 2009 and evaluated by the Entropy Best Paper Award Committee. Reviews and articles were evaluated separately. A first prize is awarded to the selected review paper, and a first and second prize is awarded to the top two selected research articles. Entropy 2013-02-20 15 2 Editorial 10.3390/e15020698 698 699 1099-4300 2013-02-20 doi: 10.3390/e15020698 Kevin Knuth http://www.mdpi.com/1099-4300/15/2/678 In this paper, we study a new bus communication model, where two transmitters wish to send their corresponding private messages and a common message to a destination, while they also wish to send the common message to another receiver connected to the same wire. From an information-theoretical point of view, we first study a general case of this new model (with discrete memoryless channels). The capacity region composed of all achievable (R0,R1,R2) triples is determined for this general model, where R1 and R2 are the transmission rates of the private messages and R0 is the transmission rate of the common message. Then, the result is further explained via the Gaussian example. Finally, we give the capacity region for the new bus communication model with additive Gaussian noises and attenuation factors. This new bus communication model captures various communication scenarios, such as the bus systems in vehicles, and the bus type of communication channel in power line communication (PLC) networks. Entropy 2013-02-18 15 2 Article 10.3390/e15020678 678 697 1099-4300 2013-02-18 doi: 10.3390/e15020678 Bin Dai A. J. Vinck Yuan Luo Zhuojun Zhuang http://www.mdpi.com/1099-4300/15/2/650 This research presents a unified approach to power limits in power producing and power consuming systems, in particular those using renewable resources. As a benchmark system which generates or consumes power, a well-known standardized arrangement is considered, in which two different reservoirs are separated by an engine or a heat pump. Either of these units is located between a resource fluid (‘upper’ fluid 1) and the environmental fluid (‘lower’ fluid, 2). Power yield or power consumption is determined in terms of conductivities, reservoir temperatures and internal irreversibility coefficient, F. While bulk temperatures Ti of reservoirs’ are the only necessary state coordinates describing purely thermal units, in chemical (electrochemical) engines, heat pumps or separators it is necessary to use both temperatures and chemical potentials mk. Methods of mathematical programming and dynamic optimization are applied to determine limits on power yield or power consumption in various energy systems, such as thermal engines, heat pumps, solar dryers, electrolysers, fuel cells, etc. Methodological similarities when treating power limits in engines, separators, and heat pumps are shown. Numerical approaches to multistage systems are based on methods of dynamic programming (DP) or on Pontryagin’s maximum principle. The first method searches for properties of optimal work and is limited to systems with low dimensionality of state vector, whereas the second investigates properties of differential (canonical) equations derived from the process Hamiltonian. A relatively unknown symmetry in behaviour of power producers (engines) and power consumers is enunciated in this paper. An approximate evaluation shows that, at least ¼ of power dissipated in the natural transfer process must be added to a separator or a heat pump in order to assure a required process rate. Applications focus on drying systems which, by nature, require a large amount of thermal or solar energy. We search for minimum power consumed in one-stage and multi-stage operation of fluidized drying. This multi-stage system is supported by heat pumps. We outline the related dynamic programming procedure, and also point out a link between the present irreversible approach and the classical problem of minimum reversible work driving the system. Entropy 2013-02-11 15 2 Article 10.3390/e15020650 650 677 1099-4300 2013-02-11 doi: 10.3390/e15020650 Stanisław Sieniutycz http://www.mdpi.com/1099-4300/15/2/624 Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced. Entropy 2013-02-07 15 2 Article 10.3390/e15020624 624 649 1099-4300 2013-02-07 doi: 10.3390/e15020624 Antonio Scarfone http://www.mdpi.com/1099-4300/15/2/606 Comparisons of eddy covariance (EC) tower measurements of CO2 concentration with mid-tropospheric observations from the Atmospheric Infrared Sounder (AIRS) allow for evaluation of the rising global signal of this greenhouse gas in relation to surface carbon dynamics. Using an information theory approach combining relative entropy and wavelet multi-resolution analysis, this study has explored correlations and divergences between mid-tropospheric and surface CO2 concentrations in grasslands of northeastern Kansas. Results show that surface CO2 measurements at the Kansas Field Station (KFS) and the Konza Prairie Biological Stations 1B (KZU) and 4B (K4B) with different land-cover types correlate well with mid-tropospheric CO2 in this region at the 512-day timescale between 2007 and 2010. Relative entropy further reveals that AIRS observations are indicative of surface CO2 concentrations for all land-cover types on monthly (32-day) and longer timescales. AIRS observations are also similar to CO2 concentrations at shorter timescales at sites KFS and K4B experiencing woody encroachment, though these results require further investigation. Differences in species composition and microclimate add to the variability of surface concentrations compared with mid-tropospheric observations. Entropy 2013-02-06 15 2 Article 10.3390/e15020606 606 623 1099-4300 2013-02-06 doi: 10.3390/e15020606 Ferdouz Cochran Nathaniel Brunsell David Mechem http://www.mdpi.com/1099-4300/15/2/559 We summarize the present state of research on the darkon fluid as a model for the dark sector of the Universe. Nonrelativistic massless particles are introduced as a realization of the Galilei group in an enlarged phase space. The additional degrees of freedom allow for a nonstandard, minimal coupling to gravity respecting Einstein’s equivalence principle. Extended to a self-gravitating fluid the Poisson equation for the gravitational potential contains a dynamically generated effective gravitational mass density of either sign. The equations of motion (EOMs) contain no free parameters and are invariant w.r.t. Milne gauge transformations. Fixing the gauge eliminates the unphysical degrees of freedom. The resulting Lagrangian possesses no free particle limit. The particles it describes, darkons, exist only as fluid particles of a self-gravitating fluid. This darkon fluid realizes the zero-mass Galilean algebra extended by dilations with dynamical exponent z = 5/3 . We reduce the EOMs to Friedmann-like equations and derive conserved quantities and a unique Hamiltonian dynamics by implementing dilation symmetry. By the Casimir of the Poisson-bracket (PB)-algebra we foliate the phase space and construct a Lagrangian in reduced phase space. We solve the Friedmann-like equations with the transition redshift and the value of the Casimir as integration constants. We obtain a deceleration phase for the early Universe and an acceleration phase for the late Universe in agreement with observations. Steady state equations in the spherically symmetric case may model a galactic halo. Numerical solutions of a nonlinear differential equation for the gravitational potential lead to predictions for the dark matter (DM) part of the rotation curves (RCs) of galaxies in qualitative agreement with observational data. We also present a general covariant generalization of the model. Entropy 2013-02-05 15 2 Article 10.3390/e15020559 559 605 1099-4300 2013-02-05 doi: 10.3390/e15020559 Peter Stichel Wojtek Zakrzewski http://www.mdpi.com/1099-4300/15/2/544 In a recent review an optimal thermodynamics and associated new upper bounds have been proposed, but it was only relative to power delivered by engines. In fact, it appears that for systems and processes with more than one utility (mainly mechanical or electrical power), energy conservation (First Law) is limited for representing their efficiency. Consequently, exergy analysis combining the First and Second Law seems essential for optimization of systems or processes situated in their environment. For thermomechanical systems recent papers report on comparisons between energy and exergy analysis and corresponding optimization, but the proposed models mainly use heat transfer conductance modelling, except for internal combustion engine. Here we propose to reconsider direct and inverse configurations of Carnot machines, with two examples. The first example is concerned with “thermofrigo-pump” where the two utilities are hot and cold thermal exergies due to the difference in the temperature level compared to the ambient one. The second one is relative to a “combined heat and power” (CHP) system. In the two cases, the model is developed based on the Carnot approach, and use of the efficiency-NTU method to characterize the heat exchangers. Obtained results are original thermodynamics optima, that represent exergy upper bounds for these two cases. Extension of the proposed method to other systems and processes is examined, with added technical constraints or not. Entropy 2013-02-01 15 2 Article 10.3390/e15020544 544 558 1099-4300 2013-02-01 doi: 10.3390/e15020544 Michel Feidt http://www.mdpi.com/1099-4300/15/2/524 We propose a thermodynamic interpretation of transfer entropy near equilibrium, using a specialised Boltzmann’s principle. The approach relates conditional probabilities to the probabilities of the corresponding state transitions. This in turn characterises transfer entropy as a difference of two entropy rates: the rate for a resultant transition and another rate for a possibly irreversible transition within the system affected by an additional source. We then show that this difference, the local transfer entropy, is proportional to the external entropy production, possibly due to irreversibility. Near equilibrium, transfer entropy is also interpreted as the difference in equilibrium stabilities with respect to two scenarios: a default case and the case with an additional source. Finally, we demonstrated that such a thermodynamic treatment is not applicable to information flow, a measure of causal effect. Entropy 2013-02-01 15 2 Article 10.3390/e15020524 524 543 1099-4300 2013-02-01 doi: 10.3390/e15020524 Mikhail Prokopenko Joseph Lizier Don Price http://www.mdpi.com/1099-4300/15/2/507 A computer-aided detection (CAD) system is helpful for radiologists to detect pulmonary nodules at an early stage. In this paper, we propose a novel pulmonary nodule detection method based on hierarchical block classification. The proposed CAD system consists of three steps. In the first step, input computed tomography images are split into three-dimensional block images, and we apply entropy analysis on the block images to select informative blocks. In the second step, the selected block images are segmented and adjusted for detecting nodule candidates. In the last step, we classify the nodule candidate images into nodules and non-nodules. We extract feature vectors of the objects in the selected blocks. Lastly, the support vector machine is applied to classify the extracted feature vectors. Performance of the proposed system is evaluated on the Lung Image Database Consortium database. The proposed method has reduced the false positives in the nodule candidates significantly. It achieved 95.28% sensitivity with only 2.27 false positives per scan. Entropy 2013-01-31 15 2 Article 10.3390/e15020507 507 523 1099-4300 2013-01-31 doi: 10.3390/e15020507 Wook-Jin Choi Tae-Sun Choi http://www.mdpi.com/1099-4300/15/2/490 It is difficult to fully satisfy the energy demand of today’s society with renewables. Nevertheless, most of the energy we use is lost as non-functional waste energy, whereas a large part of the built environment’s energy demand is only for low-quality energy, so the initial demand for primary, high-quality energy can be reduced by more effective usage, such as by low-exergy means. Gaining insight into the parameters of energy demands and local renewable and residual energy potentials enables matching energy demand with a fitting potential, not only concerning quantity but taking into account location, temporality and quality as well. The method of Energy Potential Mapping (EPM) aims to visualise the energy potentials and demands by making information of quantity, quality and location of demand and supply accessible. The aspect of quality specifically applies to heat and cold. The methodology of EPM will be described and explained with case studies. The focus specifically lies on mapping heat (and cold), one of the main reasons for energy demand in the built environment. The visualisation of exergy, to be simplified as the quality of energy, becomes an extra parameter in the case of Dutch Heat Maps. These maps can help finding opportunities of practical implementations of exchanging or cascading heat or cold. This way EPM and Heat Mapping (HM) enables application of exergy principles in the built environment. EPM and HM can be seen as a local energy catalogue and can be useful in spatial planning for energy-based urban and rural plans. Entropy 2013-01-28 15 2 Article 10.3390/e15020490 490 506 1099-4300 2013-01-28 doi: 10.3390/e15020490 Siebe Broersma Michiel Fremouw Andy Dobbelsteen http://www.mdpi.com/1099-4300/15/2/474 This paper presents an abbreviated method for estimating exergy destruction in a heat exchanger, requiring only black-box data of the exchanger’s inputs and outputs, and eliminating part of the mathematical difficulties associated with the calculations. A well-known model for temperature distributions in an exchanger is adapted for this case, and is used to distinguish between the contributions of the three major causes of the total exergetic loss: heat transfer, fluid friction and energy dissipation to the surroundings. This provides insight into the relative importance of the three, allowing for identification of potential improvements to a given design. Entropy 2013-01-28 15 2 Article 10.3390/e15020474 474 489 1099-4300 2013-01-28 doi: 10.3390/e15020474 Ignacio López Paniagua Javier Rodríguez Martín Celina González Fernandez Ángel Jiménez Alvaro Rafael Nieto Carlier http://www.mdpi.com/1099-4300/15/2/445 In this paper, we investigate the model of wiretap channel with action-dependent channel state information. Given the message to be communicated, the transmitter chooses an action sequence that affects the formation of the channel states, and then generates the channel input sequence based on the state sequence and the message. The main channel and the wiretap channel are two discrete memoryless channels (DMCs), and they are connected with the legitimate receiver and the wiretapper, respectively. Moreover, the transition probability distribution of the main channel depends on the channel state. Measuring wiretapper’s uncertainty about the message by equivocation, inner and outer bounds on the capacity-equivocation region are provided both for the case where the channel inputs are allowed to depend non-causally on the state sequence and the case where they are restricted to causal dependence. Furthermore, the secrecy capacities for both cases are bounded, which provide the best transmission rate with perfect secrecy. The result is further explained via a binary example. Entropy 2013-01-28 15 2 Article 10.3390/e15020445 445 473 1099-4300 2013-01-28 doi: 10.3390/e15020445 Bin Dai A. Vinck Yuan Luo Xiaohu Tang http://www.mdpi.com/1099-4300/15/2/434 Optomechanics may be viewed as a light-mechanics interface to realize hybrid structures for (classical or quantum) information processing, switching or storage. Using the two-laser technique, in this paper, we theoretically devise a protocol for quantum light memory via a cavity optomechanical system composed of a Fabry–Perot cavity and a mechanical resonator. Due to the long-lived mechanical resonator, this quantum memory for light based on optomechanically induced transparency (OMIT) can serve as a long-term memory that can store the full quantum light contained in an optical pulse. It is shown that, with the tunable pump laser, the quantum signal light can be reaccelerated and converted back on demand. Our presented work could open the door to all-optical routers for light memory devices and have a guide to actual experiments. Entropy 2013-01-24 15 2 Article 10.3390/e15020434 434 444 1099-4300 2013-01-24 doi: 10.3390/e15020434 Jinjin Li Wen Bin Ka-Di Zhu http://www.mdpi.com/1099-4300/15/2/416 The objective of this research is to investigate the feasibility of utilizing the multi-scale analysis and support vector machine (SVM) classification scheme to diagnose the bearing faults in rotating machinery. For complicated signals, the characteristics of dynamic systems may not be apparently observed in a scale, particularly for the fault-related features of rotating machinery. In this research, the multi-scale analysis is employed to extract the possible fault-related features in different scales, such as the multi-scale entropy (MSE), multi-scale permutation entropy (MPE), multi-scale root-mean-square (MSRMS) and multi-band spectrum entropy (MBSE). Some of the features are then selected as the inputs of the support vector machine (SVM) classifier through the Fisher score (FS) as well as the Mahalanobis distance (MD) evaluations. The vibration signals of bearing test data at Case Western Reserve University (CWRU) are utilized as the illustrated examples. The analysis results demonstrate that an accurate bearing defect diagnosis can be achieved by using the extracted machine features in different scales. It can be also noted that the diagnostic results of bearing faults can be further enhanced through the feature selection procedures of FS and MD evaluations. Entropy 2013-01-24 15 2 Article 10.3390/e15020416 416 433 1099-4300 2013-01-24 doi: 10.3390/e15020416 Shuen-De Wu Chiu-Wen Wu Tian-Yau Wu Chun-Chieh Wang http://www.mdpi.com/1099-4300/15/1/407 Recent years have witnessed an increased interest towards compression-based methods and their applications to remote sensing, as these have a data-driven and parameter-free approach and can be thus succesfully employed in several applications, especially in image information mining. This paper expands the algorithmic information theory frame, on which these methods are based. On the one hand, algorithms originally defined in the pattern matching domain are reformulated, allowing a better understanding of the available compression-based tools for remote sensing applications. On the other hand, the use of existing compression algorithms is proposed to store satellite images with added semantic value. Entropy 2013-01-22 15 1 Article 10.3390/e15010407 407 415 1099-4300 2013-01-22 doi: 10.3390/e15010407 Daniele Cerra Mihai Datcu http://www.mdpi.com/1099-4300/15/1/372 This paper makes two claims: (1) autism can be characterized as a chronic low-grade encephalopathy, associated with excess exposure to nitric oxide, ammonia and glutamate in the central nervous system, which leads to hippocampal pathologies and resulting cognitive impairment, and (2), encephalitis is provoked by a systemic deficiency in sulfate, but associated seizures and fever support sulfate restoration. We argue that impaired synthesis of cholesterol sulfate in the skin and red blood cells, catalyzed by sunlight and nitric oxide synthase enzymes, creates a state of colloidal instability in the blood manifested as a low zeta potential and increased interfacial stress. Encephalitis, while life-threatening, can result in partial renewal of sulfate supply, promoting neuronal survival. Research is cited showing how taurine may not only help protect neurons from hypochlorite exposure, but also provide a source for sulfate renewal. Several environmental factors can synergistically promote the encephalopathy of autism, including the herbicide, glyphosate, aluminum, mercury, lead, nutritional deficiencies in thiamine and zinc, and yeast overgrowth due to excess dietary sugar. Given these facts, dietary and lifestyle changes, including increased sulfur ingestion, organic whole foods, increased sun exposure, and avoidance of toxins such as aluminum, mercury, and lead, may help to alleviate symptoms or, in some instances, to prevent autism altogether. Entropy 2013-01-22 15 1 Review 10.3390/e15010372 372 406 1099-4300 2013-01-22 doi: 10.3390/e15010372 Stephanie Seneff Ann Lauritzen Robert Davidson Laurie Lentz-Marino http://www.mdpi.com/1099-4300/15/1/361 Maximum entropy method has been successfully used for underdetermined systems. Network design problem, with routing and topology subproblems, is an underdetermined system and a good candidate for maximum entropy method application. Wireless ad-hoc networks with rapidly changing topology and link quality, where the speed of recalculation is of crucial importance, have been recently successfully investigated by maximum entropy method application. In this paper we prove a theorem that establishes asymptotic properties of the maximum entropy routing solution. This result, besides being theoretically interesting, can be used to direct initial approximation for iterative optimization algorithms and to speed up their convergence. Entropy 2013-01-21 15 1 Article 10.3390/e15010361 361 371 1099-4300 2013-01-21 doi: 10.3390/e15010361 Milan Tuba http://www.mdpi.com/1099-4300/15/1/327 Information flow, or information transfer as it may be referred to, is a fundamental notion in general physics which has wide applications in scientific disciplines. Recently, a rigorous formalism has been established with respect to both deterministic and stochastic systems, with flow measures explicitly obtained. These measures possess some important properties, among which is flow or transfer asymmetry. The formalism has been validated and put to application with a variety of benchmark systems, such as the baker transformation, Hénon map, truncated Burgers-Hopf system, Langevin equation, etc. In the chaotic Burgers-Hopf system, all the transfers, save for one, are essentially zero, indicating that the processes underlying a dynamical phenomenon, albeit complex, could be simple. (Truth is simple.) In the Langevin equation case, it is found that there could be no information flowing from one certain time series to another series, though the two are highly correlated. Information flow/transfer provides a potential measure of the cause–effect relation between dynamical events, a relation usually hidden behind the correlation in a traditional sense. Entropy 2013-01-18 15 1 Review 10.3390/e15010327 327 360 1099-4300 2013-01-18 doi: 10.3390/e15010327 X. Liang http://www.mdpi.com/1099-4300/15/1/311 One of the most important issues in theoretical biology is to understand how control mechanisms are deployed by organisms to maintain their homeostasis and ensure their survival. A crucial issue is how organisms deal with environmental information in a way that ensures appropriate exchanges with the environment — even in the most basic of life forms (namely, bacteria). In this paper, I present an information theoretic formulation of how Escherichia coli responds to environmental information during chemotaxis and, more generally, a cybernetic model of the relationship between information and biophysical (metabolic) dynamics. Entropy 2013-01-18 15 1 Article 10.3390/e15010311 311 326 1099-4300 2013-01-18 doi: 10.3390/e15010311 Gennaro Auletta http://www.mdpi.com/1099-4300/15/1/287 Process modeling by means of Gaussian-based algorithms often suffers from redundant information which usually increases the estimation computational complexity without significantly improving the estimation performance. In this article, a non-arbitrary measurement selection criterion for Gaussian-based algorithms is proposed. The measurement selection criterion is based on the determination of the most significant measurement from both an estimation convergence perspective and the covariance matrix associated with the measurement. The selection criterion is independent from the nature of the measured variable. This criterion is used in conjunction with three Gaussian-based algorithms: the EIF (Extended Information Filter), the EKF (Extended Kalman Filter) and the UKF (Unscented Kalman Filter). Nevertheless, the measurement selection criterion shown herein can also be applied to other Gaussian-based algorithms. Although this work is focused on environment modeling, the results shown herein can be applied to other Gaussian-based algorithm implementations. Mathematical descriptions and implementation results that validate the proposal are also included in this work. Entropy 2013-01-17 15 1 Article 10.3390/e15010287 287 310 1099-4300 2013-01-17 doi: 10.3390/e15010287 Fernando Cheein http://www.mdpi.com/1099-4300/15/1/262 The use of exergy to correlate energy-utilization efficiencies and energy research investments is described. Specifically, energy and exergy losses are compared with energy research and development expenditures, demonstrating that the latter correlates with energy losses, even though it would be more sensible to allocate energy research and development funding in line with exergy losses, as they represent the actual deviation of efficiency from the ideal. The methodology is outlined and illustrated with two case studies. The case studies consider the province of Ontario, Canada and the United States. The investigation utilizes data on the energy utilization in a country or region, including flows of energy and exergy through the main sectors of the economy. The results are expected to be of use to government and public authorities that administer research and development funding and resources and should help improve the effectiveness of such investments. Entropy 2013-01-16 15 1 Article 10.3390/e15010262 262 286 1099-4300 2013-01-16 doi: 10.3390/e15010262 Marc Rosen http://www.mdpi.com/1099-4300/15/1/234 Biosemiotic entropy involves the deterioration of biological sign systems. The genome is a coded sign system that is connected to phenotypic outputs through the interpretive functions of the tRNA/ribosome machinery. This symbolic sign system (semiosis) at the core of all biology has been termed “biosemiosis”. Layers of biosemiosis and cellular information management are analogous in varying degrees to the semiotics of computer programming, spoken, and written human languages. Biosemiotic entropy — an error or deviation from a healthy state — results from errors in copying functional information (mutations) and errors in the appropriate context or quantity of gene expression (epigenetic imbalance). The concept of biosemiotic entropy is a deeply imbedded assumption in the study of cancer biology. Cells have a homeostatic, preprogrammed, ideal or healthy state that is rooted in genomics, strictly orchestrated by epigenetic regulation, and maintained by DNA repair mechanisms. Cancer is an eminent illustration of biosemiotic entropy, in which the corrosion of genetic information via substitutions, deletions, insertions, fusions, and aberrant regulation results in malignant phenotypes. However, little attention has been given to explicitly outlining the paradigm of biosemiotic entropy in the context of cancer. Herein we distill semiotic theory (from the familiar and well understood spheres of human language and computer code) to draw analogies useful for understanding the operation of biological semiosis at the genetic level. We propose that the myriad checkpoints, error correcting mechanisms, and immunities are all systems whose primary role is to defend against the constant pressure of biosemiotic entropy, which malignancy must shut down in order to achieve advanced stages. In lieu of the narrower tumor suppressor/oncogene model, characterization of oncogenesis into the biosemiotic framework of sign, index, or object entropy may allow for more effective explanatory hypotheses for cancer diagnosis, with consequence in improving profiling and bettering therapeutic outcomes. Entropy 2013-01-16 15 1 Concept Paper 10.3390/e15010234 234 261 1099-4300 2013-01-16 doi: 10.3390/e15010234 Berkley Gryder Chase Nelson Samuel Shepard http://www.mdpi.com/1099-4300/15/1/220 This study deals with the combined effects of convective heating and suction/injection on the entropy generation rate in a steady flow of an incompressible viscous fluid through a channel with permeable walls. The model equations for momentum and energy balance are solved numerically using shooting quadrature. Both the velocity and temperature profiles are obtained and utilized to compute the entropy generation number. The effects of the key parameters on the fluid velocity, temperature, entropy generation rate and Bejan number are depicted graphically and analyzed in detail. Entropy 2013-01-11 15 1 Article 10.3390/e15010220 220 233 1099-4300 2013-01-11 doi: 10.3390/e15010220 Oluwole Makinde Adetayo Eegunjobi http://www.mdpi.com/1099-4300/15/1/198 We present a framework for the estimation of transfer entropy (TE) under the conditions typical of physiological system analysis, featuring short multivariate time series and the presence of instantaneous causality (IC). The framework is based on recognizing that TE can be interpreted as the difference between two conditional entropy (CE) terms, and builds on an efficient CE estimator that compensates for the bias occurring for high dimensional conditioning vectors and follows a sequential embedding procedure whereby the conditioning vectors are formed progressively according to a criterion for CE minimization. The issue of IC is faced accounting for zero-lag interactions according to two alternative empirical strategies: if IC is deemed as physiologically meaningful, zero-lag effects are assimilated to lagged effects to make them causally relevant; if not, zero-lag effects are incorporated in both CE terms to obtain a compensation. The resulting compensated TE (cTE) estimator is tested on simulated time series, showing that its utilization improves sensitivity (from 61% to 96%) and specificity (from 5/6 to 0/6 false positives) in the detection of information transfer respectively when instantaneous effect are causally meaningful and non-meaningful. Then, it is evaluated on examples of cardiovascular and neurological time series, supporting the feasibility of the proposed framework for the investigation of physiological mechanisms. Entropy 2013-01-11 15 1 Article 10.3390/e15010198 198 219 1099-4300 2013-01-11 doi: 10.3390/e15010198 Luca Faes Giandomenico Nollo Alberto Porta http://www.mdpi.com/1099-4300/15/1/177 We present a new interpretation of a local framework for informationdynamics, including the transfer entropy, by defining a moving frame of reference for theobserver of dynamics in lattice systems. This formulation is inspired by the idea ofinvestigating “relativistic” effects on observing the dynamics of information - in particular,we investigate a Galilean transformation of the lattice system data. In applying thisinterpretation to elementary cellular automata, we demonstrate that using a moving frameof reference certainly alters the observed spatiotemporal measurements of informationdynamics, yet still returns meaningful results in this context. We find that, as expected,an observer will report coherent spatiotemporal structures that are moving in their frame asinformation transfer, and structures that are stationary in their frame as information storage.Crucially, the extent to which the shifted frame of reference alters the results dependson whether the shift of frame retains, adds or removes relevant information regarding thesource-destination interaction. Entropy 2013-01-10 15 1 Article 10.3390/e15010177 177 197 1099-4300 2013-01-10 doi: 10.3390/e15010177 Joseph Lizier John Mahoney http://www.mdpi.com/1099-4300/15/1/162 This short review examines recent progress in understanding dark matter, dark energy, and galactic halos using theory that departs minimally from standard particle physics and cosmology. Strict conformal symmetry (local Weyl scaling covariance), postulated for all elementary massless fields, retains standard fermion and gauge boson theory but modifies Einstein–Hilbert general relativity and the Higgs scalar field model, with no new physical fields. Subgalactic phenomenology is retained. Without invoking dark matter, conformal gravity and a conformal Higgs model fit empirical data on galactic rotational velocities, galactic halos, and Hubble expansion including dark energy. Entropy 2013-01-09 15 1 Review 10.3390/e15010162 162 176 1099-4300 2013-01-09 doi: 10.3390/e15010162 Robert Nesbet http://www.mdpi.com/1099-4300/15/1/156 Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results confirm that there is a profound connection between gravity and thermodynamics. Entropy 2013-01-08 15 1 Article 10.3390/e15010156 156 161 1099-4300 2013-01-08 doi: 10.3390/e15010156 Rongjia Yang http://www.mdpi.com/1099-4300/15/1/144 This article mainly concerns theoretical research on entropy generation influences due to heat transfer and flow in nanofluid suspensions. A conventional nanofluid of alumina-water (Al2O3-H2O) was considered as the fluid model. Due to the sensitivity of entropy to duct diameter, mini- and microchannels with diameters of 3 mm and 0.05 mm were considered, and a laminar flow regime was assumed. The conductivity and viscosity of two different nanofluid models were examined with the help of theoretical and experimentally determined parameter values. It was shown that order of the magnitude analysis can be used for estimating entropy generation characteristics of nanofluids in mini- and microchannels. It was found that using highly viscous alumina-water nanofluid under laminar flow regime in microchannels was not desirable. Thus, there is a need for the development of low viscosity alumina-water (Al2O3-H2O) nanofluids for use in microchannels under laminar flow condition. On the other hand, Al2O3-H2O nanofluid was a superior coolant under laminar flow regime in minichannels. The presented results also indicate that flow friction and thermal irreversibility are, respectively, more significant at lower and higher tube diameters. Entropy 2013-01-07 15 1 Article 10.3390/e15010144 144 155 1099-4300 2013-01-07 doi: 10.3390/e15010144 Mohammadreza Hassan Rad Sadri Goodarz Ahmadi Mahidzal Dahari Salim Kazi Mohammad Safaei Emad Sadeghinezhad http://www.mdpi.com/1099-4300/15/1/113 This report reviews the conceptual and theoretical links between Granger causality and directed information theory. We begin with a short historical tour of Granger causality, concentrating on its closeness to information theory. The definitions of Granger causality based on prediction are recalled, and the importance of the observation set is discussed. We present the definitions based on conditional independence. The notion of instantaneous coupling is included in the definitions. The concept of Granger causality graphs is discussed. We present directed information theory from the perspective of studies of causal influences between stochastic processes. Causal conditioning appears to be the cornerstone for the relation between information theory and Granger causality. In the bivariate case, the fundamental measure is the directed information, which decomposes as the sum of the transfer entropies and a term quantifying instantaneous coupling. We show the decomposition of the mutual information into the sums of the transfer entropies and the instantaneous coupling measure, a relation known for the linear Gaussian case. We study the multivariate case, showing that the useful decomposition is blurred by instantaneous coupling. The links are further developed by studying how measures based on directed information theory naturally emerge from Granger causality inference frameworks as hypothesis testing. Entropy 2012-12-28 15 1 Review 10.3390/e15010113 113 143 1099-4300 2012-12-28 doi: 10.3390/e15010113 Pierre-Olivier Amblard Olivier Michel http://www.mdpi.com/1099-4300/15/1/80 Mutual information (MI) is useful for detecting statistical independence between random variables, and it has been successfully applied to solving various machine learning problems. Recently, an alternative to MI called squared-loss MI (SMI) was introduced. While ordinary MI is the Kullback–Leibler divergence from the joint distribution to the product of the marginal distributions, SMI is its Pearson divergence variant. Because both the divergences belong to the ƒ-divergence family, they share similar theoretical properties. However, a notable advantage of SMI is that it can be approximated from data in a computationally more efficient and numerically more stable way than ordinary MI. In this article, we review recent development in SMI approximation based on direct density-ratio estimation and SMI-based machine learning techniques such as independence testing, dimensionality reduction, canonical dependency analysis, independent component analysis, object matching, clustering, and causal inference. Entropy 2012-12-27 15 1 Review 10.3390/e15010080 80 112 1099-4300 2012-12-27 doi: 10.3390/e15010080 Masashi Sugiyama http://www.mdpi.com/1099-4300/15/1/53 A modified form of the Townsend equations for the fluctuating velocity wave vectors is applied to a laminar three-dimensional boundary-layer flow. These equations are cast into a Lorenz-type system of equations. The initial system of Lorenz equations yields the generation of masked output signals containing internal ordered regions. The self-synchronizing property of the Lorenz system of equations is then exploited by considering the initial Lorenz system as a transmitter system providing chaotic masked information signals to a series of identical Lorenz receiver systems. The output signal from each successive receiver system indicates the growing recovery of ordered regions in the chaotic output signal. Finally, the three-dimensional graph of the output velocity wave vector signal from the fourth receiver system and the spectral entropy rates for the output axial velocity wave vector indicate the presence of ordered regions which are characterized as axially-directed spiral vortices. Entropy 2012-12-24 15 1 Article 10.3390/e15010053 53 79 1099-4300 2012-12-24 doi: 10.3390/e15010053 LaVar Isaacson http://www.mdpi.com/1099-4300/15/1/32 In this paper, the fault detection in uncertain multivariate nonlinear non-Gaussian stochastic systems is further investigated. Entropy is introduced to characterize the stochastic behavior of the detection errors, and the entropy optimization principle is established for the fault detection problem. The principle is to maximize the entropies of the stochastic detection errors in the presence of faults and to minimize the entropies of the detection errors in the presence of disturbances. In order to calculate the entropies, the formulations of the joint probability density functions (JPDFs) of the stochastic errors are presented in terms of the known JPDFs of both the disturbances and the faults. By using the novel performance indexes and the formulations for the entropies of the detection errors, new fault detection design methods are provided for the considered multivariate nonlinear non-Gaussian plants. Finally, a simulation example is given to illustrate the efficiency of the proposed fault detection algorithm. Entropy 2012-12-21 15 1 Article 10.3390/e15010032 32 52 1099-4300 2012-12-21 doi: 10.3390/e15010032 Liping Yin Li Zhou http://www.mdpi.com/1099-4300/15/1/10 A spatial approach that incorporates three economic components and one environmental factor has been developed to evaluate the dynamic behaviours of the rural areas at a provincial level. An artificial fish swarm algorithm with variable population size (AFSAVP) is proposed for the spatial problem. A functional region affecting index θ is employed as a fitness function for the AFSAVP driven optimisation, in which a gross domestic product (GDP) based method is utilised to estimate the CO2 emission of all provinces. A simulation for the administrative provinces of China has been implemented, and the results have shown that the modelling method based on GDP data can assess the spatial dynamic behaviours and can be taken as an operational tool for the policy planners. Entropy 2012-12-20 15 1 Article 10.3390/e15010010 10 31 1099-4300 2012-12-20 doi: 10.3390/e15010010 Yi Chen Guangfeng Zhang Yiyang Li Yi Ding Bin Zheng Qiang Miao http://www.mdpi.com/1099-4300/15/1/1 Urban ecosystem health assessments can be applied extensively in urban management to evaluate the status quo of the urban ecosystem, identify the limiting factors, identify key problems, optimize the scheme and guide ecological regulation. Regarding the multi-layer roles of urban ecosystems, urban ecosystem health should be assessed at different scales with each assessment providing a specific reference to urban management from its own viewpoint. Therefore, a novel framework of multi-scale urban ecosystem health assessment is established on global, national, regional and local scales. A demonstration of the framework is shown by using a case study in Guangzhou City, China, where urban ecosystem health assessment is conducted in the order of global, national, regional, and local scales, from macro to micro, and rough to detailed analysis. The new multi-scale framework can be utilized to generate a more comprehensive understanding of urban ecosystem health, more accurate orientation of urban development, and more feasible regulation and management programs when compared with the traditional urban ecosystem health assessment focusing at the local scale. Entropy 2012-12-20 15 1 Concept Paper 10.3390/e15010001 1 9 1099-4300 2012-12-20 doi: 10.3390/e15010001 Meirong Su Zhifeng Yang Bin Chen Gengyuan Liu Yan Zhang Lixiao Zhang Linyu Xu Yanwei Zhao http://www.mdpi.com/1099-4300/14/12/2611 This work shows the power of the variational approach for studying the efficiency of thermal engines in the context of the Finite Time Thermodynamics (FTT). Using an endoreversible Curzon–Ahlborn (CA) heat engine as a model for actual thermal engines, three different criteria for thermal efficiency were analyzed: maximum power output, ecological function, and maximum power density. By means of this procedure, the performance of the CA heat engine with a nonlinear heat transfer law (the Stefan–Boltzmann law) was studied to describe the heat exchanges between the working substance and its thermal reservoirs. The specific case of the Müser engine for all the criteria was analyzed. The results confirmed some previous findings using other procedures and additionally new results for the Müser engine performance were obtained. Entropy 2012-12-17 14 12 Article 10.3390/e14122611 2611 2625 1099-4300 2012-12-17 doi: 10.3390/e14122611 Juan Chimal-Eguía Norma Sánchez-Salas Marco Barranco-Jiménez http://www.mdpi.com/1099-4300/14/12/2589 Capacity bounds for a three-node binary symmetric relay channel with orthogonal components at the destination are studied. The cut-set upper bound and the rates achievable using decode-and-forward (DF), partial DF and compress-and-forward (CF) relaying are first evaluated. Then relaying strategies with finite memory-length are considered. An efficient algorithm for optimizing the relay functions is presented. The Boolean Fourier transform is then employed to unveil the structure of the optimized mappings. Interestingly, the optimized relay functions exhibit a simple structure. Numerical results illustrate that the rates achieved using the optimized low-dimensional functions are either comparable to those achieved by CF or superior to those achieved by DF relaying. In particular, the optimized low-dimensional relaying scheme can improve on DF relaying when the quality of the source-relay link is worse than or comparable to that of other links. Entropy 2012-12-17 14 12 Article 10.3390/e14122589 2589 2610 1099-4300 2012-12-17 doi: 10.3390/e14122589 Majid Khormuji Mikael Skoglund http://www.mdpi.com/1099-4300/14/12/2578 Current formulas for calculating scour depth below of a free over fall are mostly deterministic in nature and do not adequately consider the uncertainties of various scouring parameters. A reliability-based assessment of scour, taking into account uncertainties of parameters and coefficients involved, should be performed. This paper studies the reliability of a dam foundation under the threat of scour. A model for calculating the reliability of scour and estimating the probability of failure of the dam foundation subjected to scour is presented. The Maximum Entropy Method is applied to construct the probability density function (PDF) of the performance function subject to the moment constraints. Monte Carlo simulation (MCS) is applied for uncertainty analysis. An example is considered, and there liability of its scour is computed, the influence of various random variables on the probability failure is analyzed. Entropy 2012-12-14 14 12 Article 10.3390/e14122578 2578 2588 1099-4300 2012-12-14 doi: 10.3390/e14122578 Chuanqi Li Shuai Wang Wei Wang http://www.mdpi.com/1099-4300/14/12/2550 Abstract: Past theories on total lifetime energy expenditures and entropy generation in biological systems (BS) dealt with whole systems, but the recent literature suggests that the total metabolic rate of a BS,q̇body (W) is a sum of product of specific metabolic rate q̇k,m (W/kg of organ k) of each vital life organ, k {k = brain, heart, kidney and liver, or abbreviated as BHKL, and rest of the organ mass (R)} and mass of each organ k (mk). Using this hypothesis, Kleiber’s law on metabolic rate of BS (q̇body) for animals of different sizes was validated. In this work, a similar procedure is adopted in estimating total entropy generation rate of whole human body (σ̇body, W/K) as a sum of product of specific entropy generation rate for each organ, σ̇k,m (W/{K kg of organ k·}) and the organ mass at any given age (t). Further integrating over life span for each organ (tlife), the lifetime specific entropy generated by organ k, σk,m,life (J of organ k/ {K kg organ k}) is calculated. Then lifetime entropy generation of unit body mass, σbody,M,life (J/{K kg body mass·}) is calculated as a sum of the corresponding values contributed by all vital organs to unit body mass and verified with previously published literature. The higher the σk,m,life , the higher the entropy stress level (which is a measure of energy released by unit organ mass of k as heat) and the irreversibility within the organ, resulting in faster degradation of organ and the consequent health problems for the whole BS. In order to estimate σ̇k (W/K of organ k), data on energy release rate (q̇) is needed over lifetime for each organ. While the Adequate Macronutrients Distribution Range (AMDR)/Adequate Intake (AI) publication can be used in estimating the energy intake of whole body vs. age for the human body, the energy expenditure data is not available at organ level. Hence the σk,m,life was computed using existing allometric laws developed for the metabolism of the organs, the relation between the mk of organ and body mass mB, and the body mass growth data mB(t) over the lifetime. Based on the values of σk, m, life, the organs were ranked from highest to lowest entropy generation and the heart is found to be the most entropy-stressed organ. The entropy stress levels of the other organs are then normalized to the entropy stress level (NESH) of the heart. The NESH values for organs are as follows: Heart: 1.0, Kidney: 0.92, Brain: 0.46, Liver: 0.41, Rest of BS: 0.027. If normalized to rest of body (R), NESR, heart: 37, Kidney: 34, Brain: 17, Liver: 15, Rest of BS: 1.0; so heart will fail first followed by kidney and other organs in order. Supporting data is provided. Entropy 2012-12-12 14 12 Article 10.3390/e14122550 2550 2577 1099-4300 2012-12-12 doi: 10.3390/e14122550 Kalyan Annamalai Carlos Silva http://www.mdpi.com/1099-4300/14/12/2531 We propose a quantum protocol to authenticate classical messages that can be used to replace Wegman–Carter’s classical authentication scheme in quantum key distribution (QKD) protocols. We show that the proposed scheme achieves greater conditional entropy of the seed for the intruder given her (quantum) observation than the classical case. The proposed scheme is suitable for situations where the shared symmetric key used in authentication becomes dangerously short (due to noise or eavesdropping), and there is a threat that it might be completely consumed without being replaced. Our protocol is an improvement over a classical scheme by Brassard and takes advantage of quantum channel properties. It is motivated by information-theoretical results. We stress that the proposed authentication protocol can also be used as an independent authentication protocol that is not a part of a QKD. However by adopting it, QKD becomes a fully quantum protocol. We prove that quantum resources can improve both the secrecy of the key generated by the PRG and the secrecy of the tag obtained with a hidden hash function. We conclude that the proposed quantum encoding offers more security than the classical scheme and, by applying a classical result, we show that it can be used under noisy quantum channels. Entropy 2012-12-11 14 12 Article 10.3390/e14122531 2531 2549 1099-4300 2012-12-11 doi: 10.3390/e14122531 Francisco Assis Aleksandar Stojanovic Paulo Mateus Yasser Omar http://www.mdpi.com/1099-4300/14/12/2492 Theoretical inferences, based on biophysical, biochemical, and biosemiotic considerations, are related here to the pathogenesis of cardiovascular disease, diabetes, and other degenerative conditions. We suggest that the “daytime” job of endothelial nitric oxide synthase (eNOS), when sunlight is available, is to catalyze sulfate production. There is a striking alignment between cell types that produce either cholesterol sulfate or sulfated polysaccharides and those that contain eNOS. The signaling gas, nitric oxide, a well-known product of eNOS, produces pathological effects not shared by hydrogen sulfide, a sulfur-based signaling gas. We propose that sulfate plays an essential role in HDL-A1 cholesterol trafficking and in sulfation of heparan sulfate proteoglycans (HSPGs), both critical to lysosomal recycling (or disposal) of cellular debris. HSPGs are also crucial in glucose metabolism, protecting against diabetes, and in maintaining blood colloidal suspension and capillary flow, through systems dependent on water-structuring properties of sulfate, an anionic kosmotrope. When sunlight exposure is insufficient, lipids accumulate in the atheroma in order to supply cholesterol and sulfate to the heart, using a process that depends upon inflammation. The inevitable conclusion is that dietary sulfur and adequate sunlight can help prevent heart disease, diabetes, and other disease conditions. Entropy 2012-12-07 14 12 Review 10.3390/e14122492 2492 2530 1099-4300 2012-12-07 doi: 10.3390/e14122492 Stephanie Seneff Ann Lauritzen Robert Davidson Laurie Lentz-Marino http://www.mdpi.com/1099-4300/14/12/2478 Recent studies have shown that the Gibbs density function is a good model for visual patterns and that its parameters can be learned from pattern category training data by a gradient algorithm optimizing a constrained entropy criterion. These studies represented each pattern category by a single density. However, the patterns in a category can be so complex as to require a representation spread over several densities to more accurately account for the shape of their distribution in the feature space. The purpose of the present study is to investigate a representation of visual pattern category by several Gibbs densities using a Kohonen neural structure. In this Gibbs density based Kohonen network, which we call a Gibbsian Kohonen network, each node stores the parameters of a Gibbs density. Collectively, these Gibbs densities represent the pattern category. The parameters are learned by a gradient update rule so that the corresponding Gibbs densities maximize entropy subject to reproducing observed feature statistics of the training patterns. We verified the validity of the method and the efficiency of the ensuing Gibbs density pattern representation on a handwritten character recognition application. Entropy 2012-12-04 14 12 Article 10.3390/e14122478 2478 2491 1099-4300 2012-12-04 doi: 10.3390/e14122478 Neila Mezghani Amar Mitiche Mohamed Cheriet http://www.mdpi.com/1099-4300/14/12/2456 The effect of gravity upon changes of the entropy of a gravity-dominated system is discussed. In a universe dominated by vacuum energy, gravity is repulsive, and there is accelerated expansion. Furthermore, inhomogeneities are inflated and the universe approaches a state of thermal equilibrium. The difference between the evolution of the cosmic entropy in a co-moving volume in an inflationary era with repulsive gravity and a matter-dominated era with attractive gravity is discussed. The significance of conversion of gravitational energy to thermal energy in a process with gravitational clumping, in order that the entropy of the universe shall increase, is made clear. Entropy of black holes and cosmic horizons are considered. The contribution to the gravitational entropy according to the Weyl curvature hypothesis is discussed. The entropy history of the Universe is reviewed. Entropy 2012-12-04 14 12 Article 10.3390/e14122456 2456 2477 1099-4300 2012-12-04 doi: 10.3390/e14122456 Øyvind Grøn http://www.mdpi.com/1099-4300/14/12/2439 Parametric studies of the effects of slip irreversibility in concentrating solar power (CSP)-powered bio-digester assemblies are investigated. Complexities regarding the identification of the appropriate electro-kinetic phenomena for certain electrolyte phases are reviewed. The application of exergy analysis to the design of energy conversion devices, like solar thermal collectors, for the required heat of formation in a downdraft waste food bio-digester, is discussed. Thermal management in the silicon-based substrate of the energy system is analyzed. The rectangular-shaped micro-channels are simulated with a finite-volume, staggered coupling of the pressure-velocity fields. Entropy generation transport within the energy system is determined and coupled with the solution procedure. Consequently, the effects of channel size perturbation, Reynolds number, and pressure ratios on the thermal performance and exergy destruction are presented. A comparative analysis of the axial heat conduction for thermal management in energy conversion devices is proposed. Entropy 2012-12-04 14 12 Article 10.3390/e14122439 2439 2455 1099-4300 2012-12-04 doi: 10.3390/e14122439 Emmanuel Ogedengbe Marc Rosen