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Entropy, Volume 17, Issue 5 (May 2015), Pages 2556-3517

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Open AccessArticle Information Decomposition and Synergy
Entropy 2015, 17(5), 3501-3517; https://doi.org/10.3390/e17053501
Received: 26 March 2015 / Revised: 12 May 2015 / Accepted: 19 May 2015 / Published: 22 May 2015
Cited by 21 | PDF Full-text (259 KB) | HTML Full-text | XML Full-text
Abstract
Recently, a series of papers addressed the problem of decomposing the information of two random variables into shared information, unique information and synergistic information. Several measures were proposed, although still no consensus has been reached. Here, we compare these proposals with an older
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Recently, a series of papers addressed the problem of decomposing the information of two random variables into shared information, unique information and synergistic information. Several measures were proposed, although still no consensus has been reached. Here, we compare these proposals with an older approach to define synergistic information based on the projections on exponential families containing only up to k-th order interactions. We show that these measures are not compatible with a decomposition into unique, shared and synergistic information if one requires that all terms are always non-negative (local positivity). We illustrate the difference between the two measures for multivariate Gaussians. Full article
(This article belongs to the Special Issue Information Processing in Complex Systems)
Open AccessArticle Operational Reliability Assessment of Compressor Gearboxes with Normalized Lifting Wavelet Entropy from Condition Monitoring Information
Entropy 2015, 17(5), 3479-3500; https://doi.org/10.3390/e17053479
Received: 12 April 2015 / Accepted: 14 May 2015 / Published: 20 May 2015
PDF Full-text (1431 KB) | HTML Full-text | XML Full-text
Abstract
Classical reliability assessment methods have predominantly focused on probability and statistical theories, which are insufficient in assessing the operational reliability of individual mechanical equipment with time-varying characteristics. A new approach to assess machinery operational reliability with normalized lifting wavelet entropy from condition monitoring
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Classical reliability assessment methods have predominantly focused on probability and statistical theories, which are insufficient in assessing the operational reliability of individual mechanical equipment with time-varying characteristics. A new approach to assess machinery operational reliability with normalized lifting wavelet entropy from condition monitoring information is proposed, which is different from classical reliability assessment methods depending on probability and statistics analysis. The machinery vibration signals with time-varying operational characteristics are firstly decomposed and reconstructed by means of a lifting wavelet package transform. The relative energy of every reconstructed signal is computed as an energy percentage of the reconstructed signal in the whole signal energy. Moreover, a normalized lifting wavelet entropy is defined by the relative energy to reveal the machinery operational uncertainty. Finally, operational reliability degree is defined by the quantitative value obtained by the normalized lifting wavelet entropy belonging to the range of [0, 1]. The proposed method is applied in the operational reliability assessment of the gearbox in an oxy-generator compressor to validate the effectiveness. Full article
(This article belongs to the Special Issue Wavelet Entropy: Computation and Applications)
Open AccessArticle Nonparametric Denoising Methods Based on Contourlet Transform with Sharp Frequency Localization: Application to Low Exposure Time Electron Microscopy Images
Entropy 2015, 17(5), 3461-3478; https://doi.org/10.3390/e17053461
Received: 24 February 2015 / Accepted: 29 April 2015 / Published: 20 May 2015
Cited by 4 | PDF Full-text (4085 KB) | HTML Full-text | XML Full-text
Abstract
Image denoising is a very important step in cryo-transmission electron microscopy (cryo-TEM) and the energy filtering TEM images before the 3D tomography reconstruction, as it addresses the problem of high noise in these images, that leads to a loss of the contained information.
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Image denoising is a very important step in cryo-transmission electron microscopy (cryo-TEM) and the energy filtering TEM images before the 3D tomography reconstruction, as it addresses the problem of high noise in these images, that leads to a loss of the contained information. High noise levels contribute in particular to difficulties in the alignment required for 3D tomography reconstruction. This paper investigates the denoising of TEM images that are acquired with a very low exposure time, with the primary objectives of enhancing the quality of these low-exposure time TEM images and improving the alignment process. We propose denoising structures to combine multiple noisy copies of the TEM images. The structures are based on Bayesian estimation in the transform domains instead of the spatial domain to build a novel feature preserving image denoising structures; namely: wavelet domain, the contourlet transform domain and the contourlet transform with sharp frequency localization. Numerical image denoising experiments demonstrate the performance of the Bayesian approach in the contourlet transform domain in terms of improving the signal to noise ratio (SNR) and recovering fine details that may be hidden in the data. The SNR and the visual quality of the denoised images are considerably enhanced using these denoising structures that combine multiple noisy copies. The proposed methods also enable a reduction in the exposure time. Full article
Open AccessEditorial Maximum Entropy Applied to Inductive Logic and Reasoning
Entropy 2015, 17(5), 3458-3460; https://doi.org/10.3390/e17053458
Received: 8 May 2015 / Accepted: 13 May 2015 / Published: 18 May 2015
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Abstract
This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers. Full article
(This article belongs to the Special Issue Maximum Entropy Applied to Inductive Logic and Reasoning)
Open AccessArticle Heat Transfer and Pressure Drop Characteristics in Straight Microchannel of Printed Circuit Heat Exchangers
Entropy 2015, 17(5), 3438-3457; https://doi.org/10.3390/e17053438
Received: 11 January 2015 / Revised: 11 May 2015 / Accepted: 13 May 2015 / Published: 18 May 2015
Cited by 10 | PDF Full-text (4133 KB) | HTML Full-text | XML Full-text
Abstract
Performance tests were carried out for a microchannel printed circuit heat exchanger (PCHE), which was fabricated with micro photo-etching and diffusion bonding technologies. The microchannel PCHE was tested for Reynolds numbers in the range of 100‒850 varying the hot-side inlet temperature between 40
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Performance tests were carried out for a microchannel printed circuit heat exchanger (PCHE), which was fabricated with micro photo-etching and diffusion bonding technologies. The microchannel PCHE was tested for Reynolds numbers in the range of 100‒850 varying the hot-side inlet temperature between 40 °C–50 °C while keeping the cold-side temperature fixed at 20 °C. It was found that the average heat transfer rate and heat transfer performance of the countercurrrent configuration were 6.8% and 10%‒15% higher, respectively, than those of the parallel flow. The average heat transfer rate, heat transfer performance and pressure drop increased with increasing Reynolds number in all experiments. Increasing inlet temperature did not affect the heat transfer performance while it slightly decreased the pressure drop in the experimental range considered. Empirical correlations have been developed for the heat transfer coefficient and pressure drop factor as functions of the Reynolds number. Full article
Open AccessArticle Minimum Error Entropy Algorithms with Sparsity Penalty Constraints
Entropy 2015, 17(5), 3419-3437; https://doi.org/10.3390/e17053419
Received: 30 January 2015 / Revised: 28 April 2015 / Accepted: 5 May 2015 / Published: 18 May 2015
Cited by 7 | PDF Full-text (915 KB) | HTML Full-text | XML Full-text
Abstract
Recently, sparse adaptive learning algorithms have been developed to exploit system sparsity as well as to mitigate various noise disturbances in many applications. In particular, in sparse channel estimation, the parameter vector with sparsity characteristic can be well estimated from noisy measurements through
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Recently, sparse adaptive learning algorithms have been developed to exploit system sparsity as well as to mitigate various noise disturbances in many applications. In particular, in sparse channel estimation, the parameter vector with sparsity characteristic can be well estimated from noisy measurements through a sparse adaptive filter. In previous studies, most works use the mean square error (MSE) based cost to develop sparse filters, which is rational under the assumption of Gaussian distributions. However, Gaussian assumption does not always hold in real-world environments. To address this issue, we incorporate in this work an l1-norm or a reweighted l1-norm into the minimum error entropy (MEE) criterion to develop new sparse adaptive filters, which may perform much better than the MSE based methods, especially in heavy-tailed non-Gaussian situations, since the error entropy can capture higher-order statistics of the errors. In addition, a new approximator of l0-norm, based on the correntropy induced metric (CIM), is also used as a sparsity penalty term (SPT). We analyze the mean square convergence of the proposed new sparse adaptive filters. An energy conservation relation is derived and a sufficient condition is obtained, which ensures the mean square convergence. Simulation results confirm the superior performance of the new algorithms. Full article
Open AccessArticle Entropy Approximation in Lossy Source Coding Problem
Entropy 2015, 17(5), 3400-3418; https://doi.org/10.3390/e17053400
Received: 26 March 2015 / Revised: 11 May 2015 / Accepted: 12 May 2015 / Published: 18 May 2015
Cited by 4 | PDF Full-text (359 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we investigate a lossy source coding problem, where an upper limit on the permitted distortion is defined for every dataset element. It can be seen as an alternative approach to rate distortion theory where a bound on the allowed average
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In this paper, we investigate a lossy source coding problem, where an upper limit on the permitted distortion is defined for every dataset element. It can be seen as an alternative approach to rate distortion theory where a bound on the allowed average error is specified. In order to find the entropy, which gives a statistical length of source code compatible with a fixed distortion bound, a corresponding optimization problem has to be solved. First, we show how to simplify this general optimization by reducing the number of coding partitions, which are irrelevant for the entropy calculation. In our main result, we present a fast and feasible for implementation greedy algorithm, which allows one to approximate the entropy within an additive error term of log2 e. The proof is based on the minimum entropy set cover problem, for which a similar bound was obtained. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Non-Abelian Topological Approach to Non-Locality of a Hypergraph State
Entropy 2015, 17(5), 3376-3399; https://doi.org/10.3390/e17053376
Received: 16 February 2015 / Revised: 16 April 2015 / Accepted: 8 May 2015 / Published: 15 May 2015
Cited by 3 | PDF Full-text (3729 KB) | HTML Full-text | XML Full-text
Abstract
We present a theoretical study of new families of stochastic complex information modules encoded in the hypergraph states which are defined by the fractional entropic descriptor. The essential connection between the Lyapunov exponents and d-regular hypergraph fractal set is elucidated. To further
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We present a theoretical study of new families of stochastic complex information modules encoded in the hypergraph states which are defined by the fractional entropic descriptor. The essential connection between the Lyapunov exponents and d-regular hypergraph fractal set is elucidated. To further resolve the divergence in the complexity of classical and quantum representation of a hypergraph, we have investigated the notion of non-amenability and its relation to combinatorics of dynamical self-organization for the case of fractal system of free group on finite generators. The exact relation between notion of hypergraph non-locality and quantum encoding through system sets of specified non-Abelian fractal geometric structures is presented. Obtained results give important impetus towards designing of approximation algorithms for chip imprinted circuits in scalable quantum information systems. Full article
(This article belongs to the Special Issue Quantum Computation and Information: Multi-Particle Aspects)
Open AccessArticle Nonlinear Stochastic Control and Information Theoretic Dualities: Connections, Interdependencies and Thermodynamic Interpretations
Entropy 2015, 17(5), 3352-3375; https://doi.org/10.3390/e17053352
Received: 2 February 2015 / Revised: 21 April 2015 / Accepted: 29 April 2015 / Published: 15 May 2015
Cited by 5 | PDF Full-text (748 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we present connections between recent developments on the linearly-solvable stochastic optimal control framework with early work in control theory based on the fundamental dualities between free energy and relative entropy. We extend these connections to nonlinear stochastic systems with non-affine
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In this paper, we present connections between recent developments on the linearly-solvable stochastic optimal control framework with early work in control theory based on the fundamental dualities between free energy and relative entropy. We extend these connections to nonlinear stochastic systems with non-affine controls by using the generalized version of the Feynman–Kac lemma. We present alternative formulations of the linearly-solvable stochastic optimal control framework and discuss information theoretic and thermodynamic interpretations. On the algorithmic side, we present iterative stochastic optimal control algorithms and applications to nonlinear stochastic systems. We conclude with an overview of the frameworks presented and discuss limitations, differences and future directions. Full article
Open AccessFeature PaperArticle An Information-Theoretic Perspective on Coarse-Graining, Including the Transition from Micro to Macro
Entropy 2015, 17(5), 3332-3351; https://doi.org/10.3390/e17053332
Received: 13 March 2015 / Accepted: 11 May 2015 / Published: 14 May 2015
Cited by 2 | PDF Full-text (8499 KB) | HTML Full-text | XML Full-text
Abstract
An information-theoretic perspective on coarse-graining is presented. It starts with an information characterization of configurations at the micro-level using a local information quantity that has a spatial average equal to a microscopic entropy. With a reversible micro dynamics, this entropy is conserved. In
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An information-theoretic perspective on coarse-graining is presented. It starts with an information characterization of configurations at the micro-level using a local information quantity that has a spatial average equal to a microscopic entropy. With a reversible micro dynamics, this entropy is conserved. In the micro-macro transition, it is shown how this local information quantity is transformed into a macroscopic entropy, as the local states are aggregated into macroscopic concentration variables. The information loss in this transition is identified, and the connection to the irreversibility of the macro dynamics and the second law of thermodynamics is discussed. This is then connected to a process of further coarse-graining towards higher characteristic length scales in the context of chemical reaction-diffusion dynamics capable of pattern formation. On these higher levels of coarse-graining, information flows across length scales and across space are defined. These flows obey a continuity equation for information, and they are connected to the thermodynamic constraints of the system, via an outflow of information from macroscopic to microscopic levels in the form of entropy production, as well as an inflow of information, from an external free energy source, if a spatial chemical pattern is to be maintained. Full article
(This article belongs to the Special Issue Information Processing in Complex Systems)
Open AccessArticle A Mean-Variance Hybrid-Entropy Model for Portfolio Selection with Fuzzy Returns
Entropy 2015, 17(5), 3319-3331; https://doi.org/10.3390/e17053319
Received: 4 February 2015 / Accepted: 20 April 2015 / Published: 14 May 2015
Cited by 4 | PDF Full-text (791 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we define the portfolio return as fuzzy average yield and risk as hybrid-entropy and variance to deal with the portfolio selection problem with both random uncertainty and fuzzy uncertainty, and propose a mean-variance hybrid-entropy model (MVHEM). A multi-objective genetic algorithm
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In this paper, we define the portfolio return as fuzzy average yield and risk as hybrid-entropy and variance to deal with the portfolio selection problem with both random uncertainty and fuzzy uncertainty, and propose a mean-variance hybrid-entropy model (MVHEM). A multi-objective genetic algorithm named Non-dominated Sorting Genetic Algorithm II (NSGA-II) is introduced to solve the model. We make empirical comparisons by using the data from the Shanghai and Shenzhen stock exchanges in China. The results show that the MVHEM generally performs better than the traditional portfolio selection models. Full article
Open AccessArticle The Homological Nature of Entropy
Entropy 2015, 17(5), 3253-3318; https://doi.org/10.3390/e17053253
Received: 31 January 2015 / Revised: 3 May 2015 / Accepted: 5 May 2015 / Published: 13 May 2015
Cited by 4 | PDF Full-text (510 KB) | HTML Full-text | XML Full-text
Abstract
We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: (1) classical probabilities and random variables; (2) quantum probabilities and observable operators; (3) dynamic
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We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: (1) classical probabilities and random variables; (2) quantum probabilities and observable operators; (3) dynamic probabilities and observation trees. This gives rise to a new kind of topology for information processes, that accounts for the main information functions: entropy, mutual-informations at all orders, and Kullback–Leibler divergence and generalizes them in several ways. The article is divided into two parts, that can be read independently. In the first part, the introduction, we provide an overview of the results, some open questions, future results and lines of research, and discuss briefly the application to complex data. In the second part we give the complete definitions and proofs of the theorems A, C and E in the introduction, which show why entropy is the first homological invariant of a structure of information in four contexts: static classical or quantum probability, dynamics of classical or quantum strategies of observation of a finite system. Full article
Open AccessArticle Generalized Stochastic Fokker-Planck Equations
Entropy 2015, 17(5), 3205-3252; https://doi.org/10.3390/e17053205
Received: 2 March 2015 / Revised: 23 April 2015 / Accepted: 27 April 2015 / Published: 13 May 2015
Cited by 4 | PDF Full-text (382 KB) | HTML Full-text | XML Full-text
Abstract
We consider a system of Brownian particles with long-range interactions. We go beyond the mean field approximation and take fluctuations into account. We introduce a new class of stochastic Fokker-Planck equations associated with a generalized thermodynamical formalism. Generalized thermodynamics arises in the case
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We consider a system of Brownian particles with long-range interactions. We go beyond the mean field approximation and take fluctuations into account. We introduce a new class of stochastic Fokker-Planck equations associated with a generalized thermodynamical formalism. Generalized thermodynamics arises in the case of complex systems experiencing small-scale constraints. In the limit of short-range interactions, we obtain a generalized class of stochastic Cahn-Hilliard equations. Our formalism has application for several systems of physical interest including self-gravitating Brownian particles, colloid particles at a fluid interface, superconductors of type II, nucleation, the chemotaxis of bacterial populations, and two-dimensional turbulence. We also introduce a new type of generalized entropy taking into account anomalous diffusion and exclusion or inclusion constraints. Full article
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
Open AccessArticle Quantum Data Locking for Secure Communication against an Eavesdropper with Time-Limited Storage
Entropy 2015, 17(5), 3194-3204; https://doi.org/10.3390/e17053194
Received: 6 April 2015 / Revised: 6 May 2015 / Accepted: 7 May 2015 / Published: 13 May 2015
Cited by 2 | PDF Full-text (94 KB) | HTML Full-text | XML Full-text
Abstract
Quantum cryptography allows for unconditionally secure communication against an eavesdropper endowed with unlimited computational power and perfect technologies, who is only constrained by the laws of physics. We review recent results showing that, under the assumption that the eavesdropper can store quantum information
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Quantum cryptography allows for unconditionally secure communication against an eavesdropper endowed with unlimited computational power and perfect technologies, who is only constrained by the laws of physics. We review recent results showing that, under the assumption that the eavesdropper can store quantum information only for a limited time, it is possible to enhance the performance of quantum key distribution in both a quantitative and qualitative fashion. We consider quantum data locking as a cryptographic primitive and discuss secure communication and key distribution protocols. For the case of a lossy optical channel, this yields the theoretical possibility of generating secret key at a constant rate of 1 bit per mode at arbitrarily long communication distances. Full article
(This article belongs to the Special Issue Quantum Cryptography)
Open AccessArticle Exact Solutions of Non-Linear Lattice Equations by an Improved Exp-Function Method
Entropy 2015, 17(5), 3182-3193; https://doi.org/10.3390/e17053182
Received: 9 April 2015 / Revised: 29 April 2015 / Accepted: 30 April 2015 / Published: 13 May 2015
Cited by 4 | PDF Full-text (233 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, the exp-function method is improved to construct exact solutions of non-linear lattice equations by modifying its exponential function ansätz. The improved method has two advantages. One is that it can solve non-linear lattice equations with variable coefficients, and the other
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In this paper, the exp-function method is improved to construct exact solutions of non-linear lattice equations by modifying its exponential function ansätz. The improved method has two advantages. One is that it can solve non-linear lattice equations with variable coefficients, and the other is that it is not necessary to balance the highest order derivative with the highest order nonlinear term in the procedure of determining the exponential function ansätz. To show the advantages of this improved method, a variable-coefficient mKdV lattice equation is considered. As a result, new exact solutions, which include kink-type solutions and bell-kink-type solutions, are obtained. Full article
(This article belongs to the Special Issue Non-Linear Lattice) Printed Edition available
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