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Entropy, Volume 15, Issue 5 (May 2013), Pages 1486-1962

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Open AccessArticle Discretization Based on Entropy and Multiple Scanning
Entropy 2013, 15(5), 1486-1502; doi:10.3390/e15051486
Received: 28 February 2013 / Revised: 16 April 2013 / Accepted: 18 April 2013 / Published: 25 April 2013
Cited by 14 | PDF Full-text (221 KB) | HTML Full-text | XML Full-text
Abstract
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
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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). Full article
(This article belongs to the Special Issue Big Data)
Open AccessArticle Time Reversibility, Correlation Decay and the Steady State Fluctuation Relation for Dissipation
Entropy 2013, 15(5), 1503-1515; doi:10.3390/e15051503
Received: 4 March 2013 / Revised: 17 April 2013 / Accepted: 19 April 2013 / Published: 25 April 2013
Cited by 8 | PDF Full-text (320 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Maximum Entropy Production)
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Open AccessArticle Phase-Space Position-Momentum Correlation and Potentials
Entropy 2013, 15(5), 1516-1527; doi:10.3390/e15051516
Received: 14 March 2013 / Revised: 13 April 2013 / Accepted: 16 April 2013 / Published: 25 April 2013
Cited by 2 | PDF Full-text (1113 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
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Open AccessArticle Characterization and Synthesis of Silver Nanostructures in Rare Earth Activated GeO2-PbO Glass Matrix Using Matrix Adjustment Thermal Reduction Method
Entropy 2013, 15(5), 1528-1539; doi:10.3390/e15051528
Received: 5 February 2013 / Revised: 24 April 2013 / Accepted: 25 April 2013 / Published: 25 April 2013
Cited by 2 | PDF Full-text (1665 KB) | HTML Full-text | XML Full-text
Abstract
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, Yb2O
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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. Full article
Open AccessArticle A Direct Numerical Simulation-Based Analysis of Entropy Generation in Turbulent Premixed Flames
Entropy 2013, 15(5), 1540-1566; doi:10.3390/e15051540
Received: 8 January 2013 / Revised: 12 April 2013 / Accepted: 23 April 2013 / Published: 29 April 2013
Cited by 12 | PDF Full-text (1139 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
Open AccessArticle Kernel Spectral Clustering for Big Data Networks
Entropy 2013, 15(5), 1567-1586; doi:10.3390/e15051567
Received: 1 March 2013 / Revised: 25 April 2013 / Accepted: 29 April 2013 / Published: 3 May 2013
Cited by 29 | PDF Full-text (2683 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Big Data)
Open AccessArticle Function Identification in Neuron Populations via Information Bottleneck
Entropy 2013, 15(5), 1587-1608; doi:10.3390/e15051587
Received: 26 February 2013 / Revised: 27 March 2013 / Accepted: 22 April 2013 / Published: 6 May 2013
Cited by 1 | PDF Full-text (825 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue The Information Bottleneck Method)
Open AccessArticle A Novel Nonparametric Distance Estimator for Densities with Error Bounds
Entropy 2013, 15(5), 1609-1623; doi:10.3390/e15051609
Received: 19 December 2012 / Revised: 25 April 2013 / Accepted: 28 April 2013 / Published: 6 May 2013
Cited by 1 | PDF Full-text (620 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Estimating Information-Theoretic Quantities from Data)
Open AccessArticle Genetic Algorithm-Based Identification of Fractional-Order Systems
Entropy 2013, 15(5), 1624-1642; doi:10.3390/e15051624
Received: 14 March 2013 / Revised: 23 April 2013 / Accepted: 25 April 2013 / Published: 6 May 2013
Cited by 17 | PDF Full-text (353 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Dynamical Systems) Print Edition available
Open AccessArticle Statistical Properties of the Foreign Exchange Network at Different Time Scales: Evidence from Detrended Cross-Correlation Coefficient and Minimum Spanning Tree
Entropy 2013, 15(5), 1643-1662; doi:10.3390/e15051643
Received: 15 April 2013 / Revised: 24 April 2013 / Accepted: 26 April 2013 / Published: 6 May 2013
Cited by 24 | PDF Full-text (211 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the collection Advances in Applied Statistical Mechanics)
Open AccessArticle Application of Maximum Entropy Method to Semiconductor Engineering
Entropy 2013, 15(5), 1663-1689; doi:10.3390/e15051663
Received: 15 March 2013 / Revised: 25 April 2013 / Accepted: 1 May 2013 / Published: 7 May 2013
Cited by 3 | PDF Full-text (1315 KB) | HTML Full-text | XML Full-text
Abstract
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.
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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. Full article
Open AccessArticle An Estimate of Mutual Information that Permits Closed-Form Optimisation
Entropy 2013, 15(5), 1690-1704; doi:10.3390/e15051690
Received: 1 February 2013 / Revised: 18 April 2013 / Accepted: 28 April 2013 / Published: 8 May 2013
Cited by 2 | PDF Full-text (740 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Estimating Information-Theoretic Quantities from Data)
Open AccessArticle Information-Dispersion-Entropy-Based Blind Recognition of Binary BCH Codes in Soft Decision Situations
Entropy 2013, 15(5), 1705-1725; doi:10.3390/e15051705
Received: 18 March 2013 / Revised: 24 April 2013 / Accepted: 1 May 2013 / Published: 8 May 2013
Cited by 7 | PDF Full-text (301 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
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Open AccessArticle Equiangular Vectors Approach to Mutually Unbiased Bases
Entropy 2013, 15(5), 1726-1737; doi:10.3390/e15051726
Received: 26 April 2013 / Accepted: 6 May 2013 / Published: 8 May 2013
Cited by 3 | PDF Full-text (239 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Quantum Information 2012)
Open AccessArticle Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data
Entropy 2013, 15(5), 1738-1755; doi:10.3390/e15051738
Received: 16 February 2013 / Revised: 24 April 2013 / Accepted: 2 May 2013 / Published: 10 May 2013
Cited by 4 | PDF Full-text (1877 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Estimating Information-Theoretic Quantities from Data)
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Open AccessArticle The Data-Constrained Generalized Maximum Entropy Estimator of the GLM: Asymptotic Theory and Inference
Entropy 2013, 15(5), 1756-1775; doi:10.3390/e15051756
Received: 7 April 2013 / Revised: 23 April 2013 / Accepted: 7 May 2013 / Published: 14 May 2013
Cited by 4 | PDF Full-text (297 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
Open AccessArticle A Unification between Dynamical System Theory and Thermodynamics Involving an Energy, Mass, and Entropy State Space Formalism
Entropy 2013, 15(5), 1821-1846; doi:10.3390/e15051821
Received: 29 March 2013 / Revised: 10 May 2013 / Accepted: 10 May 2013 / Published: 16 May 2013
Cited by 3 | PDF Full-text (177 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Dynamical Systems) Print Edition available
Open AccessArticle Entanglement Structure in Expanding Universes
Entropy 2013, 15(5), 1847-1874; doi:10.3390/e15051847
Received: 15 April 2013 / Revised: 7 May 2013 / Accepted: 13 May 2013 / Published: 16 May 2013
Cited by 7 | PDF Full-text (1471 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Quantum Information 2012)
Open AccessArticle Genuine Tripartite Entanglement and Nonlocality in Bose-Einstein Condensates by Collective Atomic Recoil
Entropy 2013, 15(5), 1875-1886; doi:10.3390/e15051875
Received: 22 April 2013 / Revised: 10 May 2013 / Accepted: 16 May 2013 / Published: 17 May 2013
Cited by 3 | PDF Full-text (2075 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Quantum Information 2012)
Open AccessArticle Quantifying Morphological Computation
Entropy 2013, 15(5), 1887-1915; doi:10.3390/e15051887
Received: 10 March 2013 / Revised: 23 April 2013 / Accepted: 9 May 2013 / Published: 21 May 2013
Cited by 6 | PDF Full-text (2234 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
The field of embodied intelligence emphasises the importance of the morphology and environment with respect to the behaviour of a cognitive system. The contribution of the morphology to the behaviour, commonly known as morphological computation, is well-recognised in this community. We believe that
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The field of embodied intelligence emphasises the importance of the morphology and environment with respect to the behaviour of a cognitive system. The contribution of the morphology to the behaviour, commonly known as morphological computation, is well-recognised in this community. We believe that the field would benefit from a formalisation of this concept as we would like to ask how much the morphology and the environment contribute to an embodied agent’s behaviour, or how an embodied agent can maximise the exploitation of its morphology within its environment. In this work we derive two concepts of measuring morphological computation, and we discuss their relation to the Information Bottleneck Method. The first concepts asks how much the world contributes to the overall behaviour and the second concept asks how much the agent’s action contributes to a behaviour. Various measures are derived from the concepts and validated in two experiments that highlight their strengths and weaknesses. Full article
(This article belongs to the Special Issue The Information Bottleneck Method)
Open AccessArticle The Demon in a Vacuum Tube
Entropy 2013, 15(5), 1916-1928; doi:10.3390/e15051916
Received: 23 April 2013 / Revised: 7 May 2013 / Accepted: 17 May 2013 / Published: 21 May 2013
Cited by 1 | PDF Full-text (730 KB) | HTML Full-text | XML Full-text
Abstract
In the present paper, several issues concerning the second law of thermodynamics, Maxwell’s demon and Landauer’s principle are dealt with. I argue that if the demon and the system on which it operates without dissipation of external energy are made of atoms and
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In the present paper, several issues concerning the second law of thermodynamics, Maxwell’s demon and Landauer’s principle are dealt with. I argue that if the demon and the system on which it operates without dissipation of external energy are made of atoms and molecules (gas, liquid or solid) in thermal equilibrium (whose behaviour is described by a canonical distribution), then the unavoidable reason why the demon cannot successfully operate resides in the ubiquity of thermal fluctuations and friction. Landauer’s principle appears to be unnecessary. I also suggest that if the behaviour of the demon and the system on which it acts is not always describable by a canonical distribution, as would happen for instance with the ballistic motion of electrons at early stages of thermionic emission, then a successful working demon cannot be ruled out a priori. A critical review of two recent experiments on thermionic emission Maxwell’s demons is also given. Full article
(This article belongs to the Special Issue Maxwell’s Demon 2013)

Review

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Open AccessReview Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications
Entropy 2013, 15(5), 1776-1820; doi:10.3390/e15051776
Received: 14 March 2013 / Revised: 3 May 2013 / Accepted: 8 May 2013 / Published: 16 May 2013
Cited by 52 | PDF Full-text (623 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Quantum Information 2012)
Open AccessReview Deepening the Conception of Functional Information in the Description of Zoonotic Infectious Diseases
Entropy 2013, 15(5), 1929-1962; doi:10.3390/e15051929
Received: 22 February 2013 / Revised: 2 May 2013 / Accepted: 10 May 2013 / Published: 22 May 2013
Cited by 3 | PDF Full-text (255 KB) | HTML Full-text | XML Full-text
Abstract
Infectious agents, their hosts, and relevant abiotic components are directly involved in the complex dynamic process of maintaining infectious diseases in Nature. The current tendency to focus on host-pathogen interactions at the molecular and organismal levels does not advance our knowledge about infectious
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Infectious agents, their hosts, and relevant abiotic components are directly involved in the complex dynamic process of maintaining infectious diseases in Nature. The current tendency to focus on host-pathogen interactions at the molecular and organismal levels does not advance our knowledge about infectious diseases, as much as it potentially could, by ignoring the ecological context pivotal for understanding the biology of the diseases. A new model of investigation requires a dynamic shift of perspectives in the “simplicity-complexity” dimension: from virulence factors to multi-sided descriptions of the pathogens; from particular microbes to wide microbial communities; from clinical manifestations to a variety of infectious patterns; from findings of infectious agents to defining a natural focus of the infection as a self-regulated system; from single factors affecting host-parasite relations to the complex ecological context. Various aspects of interactions between hosts, vectors, pathogens, and environmental niches should be integrated at multiple spatiotemporal scales and at different levels of biological organization (molecular, genomic, organismal, population, and ecosystem). Full article
(This article belongs to the Special Issue Biosemiotic Entropy: Disorder, Disease, and Mortality)

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