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Entropy, Volume 18, Issue 9 (September 2016)

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Open AccessArticle The Differential Entropy of the Joint Distribution of Eigenvalues of Random Density Matrices
Entropy 2016, 18(9), 342; https://doi.org/10.3390/e18090342
Received: 5 August 2016 / Revised: 11 September 2016 / Accepted: 19 September 2016 / Published: 21 September 2016
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Abstract
We derive exactly the differential entropy of the joint distribution of eigenvalues of Wishart matrices. Based on this result, we calculate the differential entropy of the joint distribution of eigenvalues of random mixed quantum states, which is induced by taking the partial trace
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We derive exactly the differential entropy of the joint distribution of eigenvalues of Wishart matrices. Based on this result, we calculate the differential entropy of the joint distribution of eigenvalues of random mixed quantum states, which is induced by taking the partial trace over the environment of Haar-distributed bipartite pure states. Then, we investigate the differential entropy of the joint distribution of diagonal entries of random mixed quantum states. Finally, we investigate the relative entropy between these two kinds of distributions. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Effects of Fatty Infiltration of the Liver on the Shannon Entropy of Ultrasound Backscattered Signals
Entropy 2016, 18(9), 341; https://doi.org/10.3390/e18090341
Received: 20 June 2016 / Revised: 7 September 2016 / Accepted: 19 September 2016 / Published: 21 September 2016
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Abstract
This study explored the effects of fatty infiltration on the signal uncertainty of ultrasound backscattered echoes from the liver. Standard ultrasound examinations were performed on 107 volunteers. For each participant, raw ultrasound image data of the right lobe of liver were acquired using
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This study explored the effects of fatty infiltration on the signal uncertainty of ultrasound backscattered echoes from the liver. Standard ultrasound examinations were performed on 107 volunteers. For each participant, raw ultrasound image data of the right lobe of liver were acquired using a clinical scanner equipped with a 3.5-MHz convex transducer. An algorithmic scheme was proposed for ultrasound B-mode and entropy imaging. Fatty liver stage was evaluated using a sonographic scoring system. Entropy values constructed using the ultrasound radiofrequency (RF) and uncompressed envelope signals (denoted by HR and HE, respectively) as a function of fatty liver stage were analyzed using the Pearson correlation coefficient. Data were expressed as the median and interquartile range (IQR). Receiver operating characteristic (ROC) curve analysis with 95% confidence intervals (CIs) was performed to obtain the area under the ROC curve (AUC). The brightness of the entropy image typically increased as the fatty stage varied from mild to severe. The median value of HR monotonically increased from 4.69 (IQR: 4.60–4.79) to 4.90 (IQR: 4.87–4.92) as the severity of fatty liver increased (r = 0.63, p < 0.0001). Concurrently, the median value of HE increased from 4.80 (IQR: 4.69–4.89) to 5.05 (IQR: 5.02–5.07) (r = 0.69, p < 0.0001). In particular, the AUCs obtained using HE (95% CI) were 0.93 (0.87–0.99), 0.88 (0.82–0.94), and 0.76 (0.65–0.87) for fatty stages ≥mild, ≥moderate, and ≥severe, respectively. The sensitivity, specificity, and accuracy were 93.33%, 83.11%, and 86.00%, respectively (≥mild). Fatty infiltration increases the uncertainty of backscattered signals from livers. Ultrasound entropy imaging has potential for the routine examination of fatty liver disease. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessEditorial Quantum Computation and Information: Multi-Particle Aspects
Entropy 2016, 18(9), 339; https://doi.org/10.3390/e18090339
Received: 14 September 2016 / Accepted: 14 September 2016 / Published: 20 September 2016
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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 Quantum Computation and Information: Multi-Particle Aspects)
Open AccessArticle The Constant Information Radar
Entropy 2016, 18(9), 338; https://doi.org/10.3390/e18090338
Received: 12 August 2016 / Revised: 9 September 2016 / Accepted: 14 September 2016 / Published: 19 September 2016
Cited by 5 | PDF Full-text (510 KB) | HTML Full-text | XML Full-text
Abstract
The constant information radar, or CIR, is a tracking radar that modulates target revisit time by maintaining a fixed mutual information measure. For highly dynamic targets that deviate significantly from the path predicted by the tracking motion model, the CIR adjusts by illuminating
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The constant information radar, or CIR, is a tracking radar that modulates target revisit time by maintaining a fixed mutual information measure. For highly dynamic targets that deviate significantly from the path predicted by the tracking motion model, the CIR adjusts by illuminating the target more frequently than it would for well-modeled targets. If SNR is low, the radar delays revisit to the target until the state entropy overcomes noise uncertainty. As a result, we show that the information measure is highly dependent on target entropy and target measurement covariance. A constant information measure maintains a fixed spectral efficiency to support the RF convergence of radar and communications. The result is a radar implementing a novel target scheduling algorithm based on information instead of heuristic or ad hoc methods. The CIR mathematically ensures that spectral use is justified. Full article
(This article belongs to the Special Issue Radar and Information Theory)
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Open AccessArticle Entropy Minimizing Curves with Application to Flight Path Design and Clustering
Entropy 2016, 18(9), 337; https://doi.org/10.3390/e18090337
Received: 26 July 2016 / Revised: 8 September 2016 / Accepted: 8 September 2016 / Published: 15 September 2016
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Abstract
Air traffic management (ATM) aims at providing companies with a safe and ideally optimal aircraft trajectory planning. Air traffic controllers act on flight paths in such a way that no pair of aircraft come closer than the regulatory separation norms. With the increase
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Air traffic management (ATM) aims at providing companies with a safe and ideally optimal aircraft trajectory planning. Air traffic controllers act on flight paths in such a way that no pair of aircraft come closer than the regulatory separation norms. With the increase of traffic, it is expected that the system will reach its limits in the near future: a paradigm change in ATM is planned with the introduction of trajectory-based operations. In this context, sets of well-separated flight paths are computed in advance, tremendously reducing the number of unsafe situations that must be dealt with by controllers. Unfortunately, automated tools used to generate such planning generally issue trajectories not complying with operational practices or even flight dynamics. In this paper, a means of producing realistic air routes from the output of an automated trajectory design tool is investigated. For that purpose, the entropy of a system of curves is first defined, and a mean of iteratively minimizing it is presented. The resulting curves form a route network that is suitable for use in a semi-automated ATM system with human in the loop. The tool introduced in this work is quite versatile and may be applied also to unsupervised classification of curves: an example is given for French traffic. Full article
(This article belongs to the Special Issue Differential Geometrical Theory of Statistics) Printed Edition available
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Open AccessArticle Combined Forecasting of Streamflow Based on Cross Entropy
Entropy 2016, 18(9), 336; https://doi.org/10.3390/e18090336
Received: 23 June 2016 / Revised: 6 September 2016 / Accepted: 6 September 2016 / Published: 15 September 2016
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Abstract
In this study, we developed a model of combined streamflow forecasting based on cross entropy to solve the problems of streamflow complexity and random hydrological processes. First, we analyzed the streamflow data obtained from Wudaogou station on the Huifa River, which is the
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In this study, we developed a model of combined streamflow forecasting based on cross entropy to solve the problems of streamflow complexity and random hydrological processes. First, we analyzed the streamflow data obtained from Wudaogou station on the Huifa River, which is the second tributary of the Songhua River, and found that the streamflow was characterized by fluctuations and periodicity, and it was closely related to rainfall. The proposed method involves selecting similar years based on the gray correlation degree. The forecasting results obtained by the time series model (autoregressive integrated moving average), improved grey forecasting model, and artificial neural network model (a radial basis function) were used as a single forecasting model, and from the viewpoint of the probability density, the method for determining weights was improved by using the cross entropy model. The numerical results showed that compared with the single forecasting model, the combined forecasting model improved the stability of the forecasting model, and the prediction accuracy was better than that of conventional combined forecasting models. Full article
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Open AccessArticle Enhanced Energy Distribution for Quantum Information Heat Engines
Entropy 2016, 18(9), 335; https://doi.org/10.3390/e18090335
Received: 5 August 2016 / Revised: 6 September 2016 / Accepted: 12 September 2016 / Published: 14 September 2016
Cited by 1 | PDF Full-text (903 KB) | HTML Full-text | XML Full-text
Abstract
A new scenario for energy distribution, security and shareability is presented that assumes the availability of quantum information heat engines and a thermal bath. It is based on the convertibility between entropy and work in the presence of a thermal reservoir. Our approach
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A new scenario for energy distribution, security and shareability is presented that assumes the availability of quantum information heat engines and a thermal bath. It is based on the convertibility between entropy and work in the presence of a thermal reservoir. Our approach to the informational content of physical systems that are distributed between users is complementary to the conventional perspective of quantum communication. The latter places the value on the unpredictable content of the transmitted quantum states, while our interest focuses on their certainty. Some well-known results in quantum communication are reused in this context. Particularly, we describe a way to securely distribute quantum states to be used for unlocking energy from thermal sources. We also consider some multi-partite entangled and classically correlated states for a collaborative multi-user sharing of work extraction possibilities. In addition, the relation between the communication and work extraction capabilities is analyzed and written as an equation. Full article
(This article belongs to the Special Issue Quantum Information 2016)
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Open AccessArticle Study on the Inherent Complex Features and Chaos Control of IS–LM Fractional-Order Systems
Entropy 2016, 18(9), 332; https://doi.org/10.3390/e18090332
Received: 24 June 2016 / Revised: 24 August 2016 / Accepted: 5 September 2016 / Published: 14 September 2016
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Abstract
Based on the traditional IS–LM economic theory, which shows the relationship between interest rates and output in the goods and services market and the money market in macroeconomic. We established a four-dimensional IS–LM model involving four variables. With the Caputo fractional calculus theory,
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Based on the traditional IS–LM economic theory, which shows the relationship between interest rates and output in the goods and services market and the money market in macroeconomic. We established a four-dimensional IS–LM model involving four variables. With the Caputo fractional calculus theory, we improved it into a fractional order nonlinear model, analyzed the complexity and stability of the fractional order system. The existences conditions of attractors under different order conditions are compared, and obtain the orders when the system reaches a stable state. Have the detail analysis on the dynamic phenomena, such as the strange attractor, sensitivity to initial values through phase diagram and the power spectral. The order changes in two ways: orders changes synchronously or single order changes. The results show regardless of which the order situation is, the economic system will enter into multiple states, such as strong divergence, strange attractor and the convergence, finally, system will enter into the stable state under a certain order; parameter changes have similar effects on the economic system. Therefore, selecting an appropriate order is significant for an economic system, which guarantees a steady development. Furthermore, this paper construct the chaos control to IS–LM fractional-order macroeconomic model by means of linear feedback control method, by calculating and adjusting the feedback coefficient, we make the system return to the convergence state. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
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Open AccessArticle Sparse Trajectory Prediction Based on Multiple Entropy Measures
Entropy 2016, 18(9), 327; https://doi.org/10.3390/e18090327
Received: 9 June 2016 / Revised: 29 August 2016 / Accepted: 30 August 2016 / Published: 14 September 2016
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Abstract
Trajectory prediction is an important problem that has a large number of applications. A common approach to trajectory prediction is based on historical trajectories. However, existing techniques suffer from the “data sparsity problem”. The available historical trajectories are far from enough to cover
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Trajectory prediction is an important problem that has a large number of applications. A common approach to trajectory prediction is based on historical trajectories. However, existing techniques suffer from the “data sparsity problem”. The available historical trajectories are far from enough to cover all possible query trajectories. We propose the sparsity trajectory prediction algorithm based on multiple entropy measures (STP-ME) to address the data sparsity problem. Firstly, the moving region is iteratively divided into a two-dimensional plane grid graph, and each trajectory is represented as a grid sequence with temporal information. Secondly, trajectory entropy is used to evaluate trajectory’s regularity, the L-Z entropy estimator is implemented to calculate trajectory entropy, and a new trajectory space is generated through trajectory synthesis. We define location entropy and time entropy to measure the popularity of locations and timeslots respectively. Finally, a second-order Markov model that contains a temporal dimension is adopted to perform sparse trajectory prediction. The experiments show that when trip completed percentage increases towards 90%, the coverage of the baseline algorithm decreases to almost 25%, while the STP-ME algorithm successfully copes with it as expected with only an unnoticeable drop in coverage, and can constantly answer almost 100% of query trajectories. It is found that the STP-ME algorithm improves the prediction accuracy generally by as much as 8%, 3%, and 4%, compared to the baseline algorithm, the second-order Markov model (2-MM), and sub-trajectory synthesis (SubSyn) algorithm, respectively. At the same time, the prediction time of STP-ME algorithm is negligible (10 μ s ), greatly outperforming the baseline algorithm (100 ms ). Full article
(This article belongs to the Special Issue Information Theoretic Learning)
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Open AccessArticle Fuzzy Adaptive Repetitive Control for Periodic Disturbance with Its Application to High Performance Permanent Magnet Synchronous Motor Speed Servo Systems
Entropy 2016, 18(9), 261; https://doi.org/10.3390/e18090261
Received: 12 May 2016 / Revised: 8 July 2016 / Accepted: 8 July 2016 / Published: 14 September 2016
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Abstract
For reducing the steady state speed ripple, especially in high performance speed servo system applications, the steady state precision is more and more important for real servo systems. This paper investigates the steady state speed ripple periodic disturbance problem for a permanent magnet
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For reducing the steady state speed ripple, especially in high performance speed servo system applications, the steady state precision is more and more important for real servo systems. This paper investigates the steady state speed ripple periodic disturbance problem for a permanent magnet synchronous motor (PMSM) servo system; a fuzzy adaptive repetitive controller is designed in the speed loop based on repetitive control and fuzzy information theory for reducing periodic disturbance. Firstly, the various sources of the PMSM speed ripple problem are described and analyzed. Then, the mathematical model of PMSM is given. Subsequently, a fuzzy adaptive repetitive controller based on repetitive control and fuzzy logic control is designed for the PMSM speed servo system. In addition, the system stability analysis is also deduced. Finally, the simulation and experiment implementation are respectively based on the MATLAB/Simulink and TMS320F2808 of Texas instrument company, DSP (digital signal processor) hardware platform. Comparing to the proportional integral (PI) controller, simulation and experimental results show that the proposed fuzzy adaptive repetitive controller has better periodic disturbance rejection ability and higher steady state precision. Full article
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Open AccessEditorial Special Issue on Entropy-Based Applied Cryptography and Enhanced Security for Ubiquitous Computing
Entropy 2016, 18(9), 334; https://doi.org/10.3390/e18090334
Received: 7 September 2016 / Accepted: 7 September 2016 / Published: 13 September 2016
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Abstract
Entropy is a basic and important concept in information theory. It is also often used as a measure of the unpredictability of a cryptographic key in cryptography research areas. Ubiquitous computing (Ubi-comp) has emerged rapidly as an exciting new paradigm. In this special
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Entropy is a basic and important concept in information theory. It is also often used as a measure of the unpredictability of a cryptographic key in cryptography research areas. Ubiquitous computing (Ubi-comp) has emerged rapidly as an exciting new paradigm. In this special issue, we mainly selected and discussed papers related with ore theories based on the graph theory to solve computational problems on cryptography and security, practical technologies; applications and services for Ubi-comp including secure encryption techniques, identity and authentication; credential cloning attacks and countermeasures; switching generator with resistance against the algebraic and side channel attacks; entropy-based network anomaly detection; applied cryptography using chaos function, information hiding and watermark, secret sharing, message authentication, detection and modeling of cyber attacks with Petri Nets, and quantum flows for secret key distribution, etc. Full article
Open AccessArticle Design of Light-Weight High-Entropy Alloys
Entropy 2016, 18(9), 333; https://doi.org/10.3390/e18090333
Received: 2 July 2016 / Revised: 21 August 2016 / Accepted: 5 September 2016 / Published: 13 September 2016
Cited by 23 | PDF Full-text (4197 KB) | HTML Full-text | XML Full-text
Abstract
High-entropy alloys (HEAs) are a new class of solid-solution alloys that have attracted worldwide attention for their outstanding properties. Owing to the demand from transportation and defense industries, light-weight HEAs have also garnered widespread interest from scientists for use as potential structural materials.
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High-entropy alloys (HEAs) are a new class of solid-solution alloys that have attracted worldwide attention for their outstanding properties. Owing to the demand from transportation and defense industries, light-weight HEAs have also garnered widespread interest from scientists for use as potential structural materials. Great efforts have been made to study the phase-formation rules of HEAs to accelerate and refine the discovery process. In this paper, many proposed solid-solution phase-formation rules are assessed, based on a series of known and newly-designed light-weight HEAs. The results indicate that these empirical rules work for most compositions but also fail for several alloys. Light-weight HEAs often involve the additions of Al and/or Ti in great amounts, resulting in large negative enthalpies for forming solid-solution phases and/or intermetallic compounds. Accordingly, these empirical rules need to be modified with the new experimental data. In contrast, CALPHAD (acronym of the calculation of phase diagrams) method is demonstrated to be an effective approach to predict the phase formation in HEAs as a function of composition and temperature. Future perspectives on the design of light-weight HEAs are discussed in light of CALPHAD modeling and physical metallurgy principles. Full article
(This article belongs to the Special Issue High-Entropy Alloys and High-Entropy-Related Materials)
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Open AccessArticle Network Entropies of the Chinese Financial Market
Entropy 2016, 18(9), 331; https://doi.org/10.3390/e18090331
Received: 23 July 2016 / Revised: 22 August 2016 / Accepted: 3 September 2016 / Published: 8 September 2016
Cited by 1 | PDF Full-text (1082 KB) | HTML Full-text | XML Full-text
Abstract
Based on the data from the Chinese financial market, this paper focuses on analyzing three types of network entropies of the financial market, namely, Shannon, Renyi and Tsallis entropies. The findings suggest that Shannon entropy can reflect the volatility of the financial market,
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Based on the data from the Chinese financial market, this paper focuses on analyzing three types of network entropies of the financial market, namely, Shannon, Renyi and Tsallis entropies. The findings suggest that Shannon entropy can reflect the volatility of the financial market, that Renyi and Tsallis entropies also have this function when their parameter has a positive value, and that Renyi and Tsallis entropies can reflect the extreme case of the financial market when their parameter has a negative value. Full article
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Open AccessArticle Short Term Electrical Load Forecasting Using Mutual Information Based Feature Selection with Generalized Minimum-Redundancy and Maximum-Relevance Criteria
Entropy 2016, 18(9), 330; https://doi.org/10.3390/e18090330
Received: 21 July 2016 / Revised: 5 September 2016 / Accepted: 5 September 2016 / Published: 8 September 2016
Cited by 2 | PDF Full-text (2218 KB) | HTML Full-text | XML Full-text
Abstract
A feature selection method based on the generalized minimum redundancy and maximum relevance (G-mRMR) is proposed to improve the accuracy of short-term load forecasting (STLF). First, mutual information is calculated to analyze the relations between the original features and the load sequence, as
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A feature selection method based on the generalized minimum redundancy and maximum relevance (G-mRMR) is proposed to improve the accuracy of short-term load forecasting (STLF). First, mutual information is calculated to analyze the relations between the original features and the load sequence, as well as the redundancy among the original features. Second, a weighting factor selected by statistical experiments is used to balance the relevance and redundancy of features when using the G-mRMR. Third, each feature is ranked in a descending order according to its relevance and redundancy as computed by G-mRMR. A sequential forward selection method is utilized for choosing the optimal subset. Finally, a STLF predictor is constructed based on random forest with the obtained optimal subset. The effectiveness and improvement of the proposed method was tested with actual load data. Full article
(This article belongs to the Section Information Theory)
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Open AccessArticle Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation
Entropy 2016, 18(9), 329; https://doi.org/10.3390/e18090329
Received: 8 July 2016 / Revised: 30 August 2016 / Accepted: 31 August 2016 / Published: 8 September 2016
Cited by 3 | PDF Full-text (2008 KB) | HTML Full-text | XML Full-text
Abstract
The approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives graphical presentations
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The approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives graphical presentations of the effect of the reaction terms on the solution profile for various anomalous exponents of particular cases, to predict damping of the field variable. Numerical computations of the convergence control parameter, used to evaluate the convergence of approximate series solution through minimizing error, are also presented graphically for these cases. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
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