Entropy

14 pages, 3451 KiB

Open AccessArticle

Effect of Solution Treatment on the Shape Memory Functions of (TiZrHf)₅₀Ni₂₅Co₁₀Cu₁₅ High Entropy Shape Memory Alloy

by Hao-Chen Lee, Yue-Jin Chen and Chih-Hsuan Chen

Entropy 2019, 21(10), 1027; https://doi.org/10.3390/e21101027 - 22 Oct 2019

Cited by 24 | Viewed by 5062

This study investigated the effects of solution treatment at 1000 °C on the transformation behaviors, microstructure, and shape memory functions of a novel (TiZrHf)₅₀Ni₂₅Co₁₀Cu₁₅ high entropy shape memory alloy (HESMA). The solution treatment caused partial dissolution [...] Read more.

This study investigated the effects of solution treatment at 1000 °C on the transformation behaviors, microstructure, and shape memory functions of a novel (TiZrHf)₅₀Ni₂₅Co₁₀Cu₁₅ high entropy shape memory alloy (HESMA). The solution treatment caused partial dissolution of non-oxygen-stabilized Ti₂Ni-like phase. This phenomenon resulted in the increment of (Ti, Zr, Hf) content in the matrix and thus increment of the M_s and A_f temperatures. At the same time, the solution treatment induced a high entropy effect and thus increased the degree of lattice distortion, which led to increment of the friction force during martensitic transformation, resulting in a broad transformation temperature range. The dissolution of the Ti₂Ni-like phase also improved the functional performance of the HESMA by reducing its brittleness and increasing its strength. The experimental results presented in this study demonstrate that solution treatment is an effective and essential way to improve the functional performance of the HESMA. Full article

(This article belongs to the Special Issue High-Entropy Materials)

► Show Figures

Graphical abstract

24 pages, 28547 KiB

Open AccessArticle

A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit

by Licai Liu, Chuanhong Du, Lixiu Liang and Xiefu Zhang

Entropy 2019, 21(10), 1026; https://doi.org/10.3390/e21101026 - 22 Oct 2019

Cited by 23 | Viewed by 3300

Abstract

As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system [...] Read more.

As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system with high complexity and hidden attractors is proposed. Analyzing the nonlinear characteristics of the system, we can find that the system has new chaotic attractors and many novel quasi-periodic limit cycles; the unique attractor structure of the Poincaré map also reflects the complexity and novelty of the hidden attractor for the system; the system has a very high complexity when measured through spectral entropy. In addition, under different initial conditions, the system exhibits the coexistence of chaotic attractors with different topologies, quasi-periodic limit cycles, and chaotic attractors. At the same time, an interesting transient chaos phenomenon, one kind of novel quasi-periodic, and weak chaotic hidden attractors are found. Finally, we realize the memristor model circuit and the proposed chaotic system use off-the-shelf electronic components. The experimental results of the circuit are consistent with the numerical simulation, which shows that the system is physically achievable and provides a new option for the application of memristive chaotic systems. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors II)

► Show Figures

Figure 1

15 pages, 4060 KiB

Open AccessArticle

Research on Bearing Fault Diagnosis Method Based on Filter Features of MOMLMEDA and LSTM

by Yong Li, Gang Cheng, Xihui Chen and Yusong Pang

Entropy 2019, 21(10), 1025; https://doi.org/10.3390/e21101025 - 22 Oct 2019

Cited by 8 | Viewed by 3111

Abstract

As the supporting unit of rotating machinery, bearing can ensure efficient operation of the equipment. Therefore, it is very important to monitor the status of bearings accurately. A bearing fault diagnosis mothed based on Multipoint Optimal Minimum Local Mean Entropy Deconvolution Adjusted (MOMLMEDA) [...] Read more.

As the supporting unit of rotating machinery, bearing can ensure efficient operation of the equipment. Therefore, it is very important to monitor the status of bearings accurately. A bearing fault diagnosis mothed based on Multipoint Optimal Minimum Local Mean Entropy Deconvolution Adjusted (MOMLMEDA) and Long Short-Term Memory (LSTM) is proposed. MOMLMEDA is an improved algorithm based on Multipoint Optimal Minimum Entropy Deconvolution Adjusted (MOMEDA). By setting the local kurtosis mean as a new selection criterion, it can effectively avoid the interference of false kurtosis caused by noise and improve the accuracy of optimal kurtosis position. The optimal filter designed by optimal kurtosis position has periodic and amplitude characteristics, which are used as the fault feature in this paper. However, this feature has temporal characteristics and cannot be used as input of general neural network directly. LSTM is selected as the classification network in this paper. It can effectively avoid the influence of the temporal problem existing in feature vectors. Accurate diagnosis of bearing faults is realized by training classification neural network with samples. The overall recognition rate is up to 93.50%. Full article

(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)

► Show Figures

Figure 1

13 pages, 1502 KiB

Open AccessArticle

Multiscale Entropy of Cardiac and Postural Control Reflects a Flexible Adaptation to a Cognitive Task

by Estelle Blons, Laurent M. Arsac, Pierre Gilfriche and Veronique Deschodt-Arsac

Entropy 2019, 21(10), 1024; https://doi.org/10.3390/e21101024 - 21 Oct 2019

Cited by 15 | Viewed by 3260

Abstract

In humans, physiological systems involved in maintaining stable conditions for health and well-being are complex, encompassing multiple interactions within and between system components. This complexity is mirrored in the temporal structure of the variability of output signals. Entropy has been recognized as a [...] Read more.

In humans, physiological systems involved in maintaining stable conditions for health and well-being are complex, encompassing multiple interactions within and between system components. This complexity is mirrored in the temporal structure of the variability of output signals. Entropy has been recognized as a good marker of systems complexity, notably when calculated from heart rate and postural dynamics. A degraded entropy is generally associated with frailty, aging, impairments or diseases. In contrast, high entropy has been associated with the elevated capacity to adjust to an ever-changing environment, but the link is unknown between entropy and the capacity to cope with cognitive tasks in a healthy young to middle-aged population. Here, we addressed classic markers (time and frequency domains) and refined composite multiscale entropy (MSE) markers (after pre-processing) of heart rate and postural sway time series in 34 participants during quiet versus cognitive task conditions. Recordings lasted 10 min for heart rate and 51.2 s for upright standing, providing time series lengths of 500–600 and 2048 samples, respectively. The main finding was that entropy increased during cognitive tasks. This highlights the possible links between our entropy measures and the systems complexity that probably facilitates a control remodeling and a flexible adaptability in our healthy participants. We conclude that entropy is a reliable marker of neurophysiological complexity and adaptability in autonomic and somatic systems. Full article

(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis)

► Show Figures

Figure 1

27 pages, 495 KiB

Open AccessArticle

Teaching Ordinal Patterns to a Computer: Efficient Encoding Algorithms Based on the Lehmer Code

by Sebastian Berger, Andrii Kravtsiv, Gerhard Schneider and Denis Jordan

Entropy 2019, 21(10), 1023; https://doi.org/10.3390/e21101023 - 21 Oct 2019

Cited by 13 | Viewed by 3044

Abstract

Ordinal patterns are the common basis of various techniques used in the study of dynamical systems and nonlinear time series analysis. The present article focusses on the computational problem of turning time series into sequences of ordinal patterns. In a first step, a [...] Read more.

Ordinal patterns are the common basis of various techniques used in the study of dynamical systems and nonlinear time series analysis. The present article focusses on the computational problem of turning time series into sequences of ordinal patterns. In a first step, a numerical encoding scheme for ordinal patterns is proposed. Utilising the classical Lehmer code, it enumerates ordinal patterns by consecutive non-negative integers, starting from zero. This compact representation considerably simplifies working with ordinal patterns in the digital domain. Subsequently, three algorithms for the efficient extraction of ordinal patterns from time series are discussed, including previously published approaches that can be adapted to the Lehmer code. The respective strengths and weaknesses of those algorithms are discussed, and further substantiated by benchmark results. One of the algorithms stands out in terms of scalability: its run-time increases linearly with both the pattern order and the sequence length, while its memory footprint is practically negligible. These properties enable the study of high-dimensional pattern spaces at low computational cost. In summary, the tools described herein may improve the efficiency of virtually any ordinal pattern-based analysis method, among them quantitative measures like permutation entropy and symbolic transfer entropy, but also techniques like forbidden pattern identification. Moreover, the concepts presented may allow for putting ideas into practice that up to now had been hindered by computational burden. To enable smooth evaluation, a function library written in the C programming language, as well as language bindings and native implementations for various numerical computation environments are provided in the supplements. Full article

(This article belongs to the Section Signal and Data Analysis)

► Show Figures

Graphical abstract

80 pages, 1639 KiB

Open AccessFeature PaperArticle

On Data-Processing and Majorization Inequalities for f-Divergences with Applications

by Igal Sason

Entropy 2019, 21(10), 1022; https://doi.org/10.3390/e21101022 - 21 Oct 2019

Cited by 16 | Viewed by 4130

Abstract

This paper is focused on the derivation of data-processing and majorization inequalities for f-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first introduced without proofs, followed by exemplifications of the theorems [...] Read more.

This paper is focused on the derivation of data-processing and majorization inequalities for f-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first introduced without proofs, followed by exemplifications of the theorems with further related analytical results, interpretations, and information-theoretic applications. One application refers to the performance analysis of list decoding with either fixed or variable list sizes; some earlier bounds on the list decoding error probability are reproduced in a unified way, and new bounds are obtained and exemplified numerically. Another application is related to a study of the quality of approximating a probability mass function, induced by the leaves of a Tunstall tree, by an equiprobable distribution. The compression rates of finite-length Tunstall codes are further analyzed for asserting their closeness to the Shannon entropy of a memoryless and stationary discrete source. Almost all the analysis is relegated to the appendices, which form the major part of this manuscript. Full article

(This article belongs to the Special Issue Information Measures with Applications)

► Show Figures

Figure 1

21 pages, 967 KiB

Open AccessArticle

Fast, Asymptotically Efficient, Recursive Estimation in a Riemannian Manifold

by Jialun Zhou and Salem Said

Entropy 2019, 21(10), 1021; https://doi.org/10.3390/e21101021 - 21 Oct 2019

Cited by 6 | Viewed by 2355

Abstract

Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a statistical parameter which belongs to a Riemannian manifold. Roughly, this task amounts to [...] Read more.

Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a statistical parameter which belongs to a Riemannian manifold. Roughly, this task amounts to stochastic minimisation of a statistical divergence function. The following problem is considered: how to obtain fast, asymptotically efficient, recursive estimates, using a Riemannian stochastic optimisation algorithm with decreasing step sizes. In solving this problem, several original results are introduced. First, without any convexity assumptions on the divergence function, we proved that, with an adequate choice of step sizes, the algorithm computes recursive estimates which achieve a fast non-asymptotic rate of convergence. Second, the asymptotic normality of these recursive estimates is proved by employing a novel linearisation technique. Third, it is proved that, when the Fisher information metric is used to guide the algorithm, these recursive estimates achieve an optimal asymptotic rate of convergence, in the sense that they become asymptotically efficient. These results, while relatively familiar in the Euclidean context, are here formulated and proved for the first time in the Riemannian context. In addition, they are illustrated with a numerical application to the recursive estimation of elliptically contoured distributions. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

► Show Figures

Figure 1

20 pages, 893 KiB

Open AccessFeature PaperArticle

Quasi-Entropies and Non-Markovianity

by Fabio Benatti and Luigi Brancati

Entropy 2019, 21(10), 1020; https://doi.org/10.3390/e21101020 - 21 Oct 2019

Cited by 2 | Viewed by 3097

Abstract

We address an informational puzzle that appears with a non-Markovian open qubit dynamics: namely the fact that, while, according to the existing witnesses of information flows, a single qubit affected by that dissipative dynamics does not show information returning to it from its [...] Read more.

We address an informational puzzle that appears with a non-Markovian open qubit dynamics: namely the fact that, while, according to the existing witnesses of information flows, a single qubit affected by that dissipative dynamics does not show information returning to it from its environment, instead two qubits do show such information when evolving independently under the same dynamics. We solve the puzzle by adding the so-called quasi-entropies to the possible witnesses of information flows. Full article

(This article belongs to the Special Issue Quantum Entropies and Complexity)

► Show Figures

Figure 1

14 pages, 2908 KiB

Open AccessArticle

State Clustering of the Hot Strip Rolling Process via Kernel Entropy Component Analysis and Weighted Cosine Distance

by Chaojun Wang and Fei He

Entropy 2019, 21(10), 1019; https://doi.org/10.3390/e21101019 - 21 Oct 2019

Cited by 2 | Viewed by 2283

Abstract

In the hot strip rolling process, many process parameters are related to the quality of the final products. Sometimes, the process parameters corresponding to different steel grades are close to, or even overlap, each other. In reality, locating overlap regions and detecting products [...] Read more.

In the hot strip rolling process, many process parameters are related to the quality of the final products. Sometimes, the process parameters corresponding to different steel grades are close to, or even overlap, each other. In reality, locating overlap regions and detecting products with abnormal quality are crucial, yet challenging. To address this challenge, in this work, a novel method named kernel entropy component analysis (KECA)-weighted cosine distance is introduced for fault detection and overlap region locating. First, KECA is used to cluster the training samples of multiple steel grades, and the samples with incorrect classes are seen as the boundary of the sample distribution. Next, the concepts of recursive-based regional center and weighted cosine distance are introduced. For each steel grade, the regional center and the weight coefficients are determined. Finally, the weighted cosine distance between the testing sample and the regional center is chosen as the index to judge abnormal batches. The samples in the overlap region of multiple steel grades need to be focused on in the real production process, which is conducive to quality grade and combined production. The weighted cosine distances between the testing sample and different regional centers are used to locate the overlap region. A dataset from a hot steel rolling process is used to evaluate the performance of the proposed methods. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

► Show Figures

Figure 1

18 pages, 1549 KiB

Open AccessArticle

Complexity Synchronization of Energy Volatility Monotonous Persistence Duration Dynamics

by Linlu Jia, Jinchuan Ke and Jun Wang

Entropy 2019, 21(10), 1018; https://doi.org/10.3390/e21101018 - 20 Oct 2019

Viewed by 2106

Abstract

A new concept named volatility monotonous persistence duration (VMPD) dynamics is introduced into the research of energy markets, in an attempt to describe nonlinear fluctuation behaviors from a new perspective. The VMPD sequence unites the maximum fluctuation difference and the continuous variation length, [...] Read more.

A new concept named volatility monotonous persistence duration (VMPD) dynamics is introduced into the research of energy markets, in an attempt to describe nonlinear fluctuation behaviors from a new perspective. The VMPD sequence unites the maximum fluctuation difference and the continuous variation length, which is regarded as a novel indicator to evaluate risks and optimize portfolios. Further, two main aspects of statistical and nonlinear empirical research on the energy VMPD sequence are observed: probability distribution and autocorrelation behavior. Moreover, a new nonlinear method named the cross complexity-invariant distance (CID) FuzzyEn (CCF) which is composed of cross-fuzzy entropy and complexity-invariant distance is firstly proposed to study the complexity synchronization properties of returns and VMPD series for seven representative energy items. We also apply the ensemble empirical mode decomposition (EEMD) to resolve returns and VMPD sequence into the intrinsic mode functions, and the degree that they follow the synchronization features of the initial sequence is investigated. Full article

(This article belongs to the Section Multidisciplinary Applications)

► Show Figures

Figure 1

28 pages, 853 KiB

Open AccessArticle

Coalescence of Kerr Black Holes—Binary Systems from GW150914 to GW170814

by Bogeun Gwak

Entropy 2019, 21(10), 1017; https://doi.org/10.3390/e21101017 - 20 Oct 2019

Cited by 3 | Viewed by 2430

Abstract

We investigate the energy of the gravitational wave from a binary black hole merger by the coalescence of two Kerr black holes with an orbital angular momentum. The coalescence is constructed to be consistent with particle absorption in the limit in which the [...] Read more.

We investigate the energy of the gravitational wave from a binary black hole merger by the coalescence of two Kerr black holes with an orbital angular momentum. The coalescence is constructed to be consistent with particle absorption in the limit in which the primary black hole is sufficiently large compared with the secondary black hole. In this limit, we analytically obtain an effective gravitational spin–orbit interaction dependent on the alignments of the angular momenta. Then, binary systems with various parameters including equal masses are numerically analyzed. According to the numerical analysis, the energy of the gravitational wave still depends on the effective interactions, as expected from the analytical form. In particular, we ensure that the final black hole obtains a large portion of its spin angular momentum from the orbital angular momentum of the initial binary black hole. To estimate the angular momentum released by the gravitational wave in the actual binary black hole, we apply our results to observations at the Laser Interferometer Gravitational-Wave Observatory: GW150914, GW151226, GW170104, GW170608 and GW170814. Full article

(This article belongs to the Section Astrophysics, Cosmology, and Black Holes)

► Show Figures

Figure 1

14 pages, 994 KiB

Open AccessArticle

Optimized Dimensionality Reduction Methods for Interval-Valued Variables and Their Application to Facial Recognition

by Jorge Arce Garro and Oldemar Rodríguez Rojas

Entropy 2019, 21(10), 1016; https://doi.org/10.3390/e21101016 - 19 Oct 2019

Cited by 2 | Viewed by 2793

Abstract

The center method, which was first proposed in Rev. Stat. Appl. 1997 by Cazes et al. and Stat. Anal. Data Mining 2011 by Douzal-Chouakria et al., extends the well-known Principal Component Analysis (PCA) method to particular types of symbolic objects that are characterized [...] Read more.

The center method, which was first proposed in Rev. Stat. Appl. 1997 by Cazes et al. and Stat. Anal. Data Mining 2011 by Douzal-Chouakria et al., extends the well-known Principal Component Analysis (PCA) method to particular types of symbolic objects that are characterized by multivalued interval-type variables. In contrast to classical data, symbolic data have internal variation. The authors who originally proposed the center method used the center of a hyper-rectangle in

R^{m}

as a base point to carry out PCA, followed by the projection of all vertices of the hyper-rectangles as supplementary elements. Since these publications, the center point of the hyper-rectangle has typically been assumed to be the best point for the initial PCA. However, in this paper, we show that this is not always the case, if the aim is to maximize the variance of projections or minimize the squared distance between the vertices and their respective projections. Instead, we propose the use of an optimization algorithm that maximizes the variance of the projections (or that minimizes the distances between the squares of the vertices and their respective projections) and finds the optimal point for the initial PCA. The vertices of the hyper-rectangles are, then, projected as supplementary variables to this optimal point, which we call the “Best Point” for projection. For this purpose, we propose four new algorithms and two new theorems. The proposed methods and algorithms are illustrated using a data set comprised of measurements of facial characteristics from a study on facial recognition patterns for use in surveillance. The performance of our approach is compared with that of another procedure in the literature, and the results show that our symbolic analyses provide more accurate information. Our approach can be regarded as an optimization method, as it maximizes the explained variance or minimizes the squared distance between projections and the original points. In addition, the symbolic analyses generate more informative conclusions, compared with the classical analysis in which classical surrogates replace intervals. All the methods proposed in this paper can be executed in the RSDA package developed in R. Full article

(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications II)

► Show Figures

Figure 1

13 pages, 261 KiB

Open AccessArticle

An Entropy-Based Machine Learning Algorithm for Combining Macroeconomic Forecasts

by Carles Bretó, Priscila Espinosa, Penélope Hernández and Jose M. Pavía

Entropy 2019, 21(10), 1015; https://doi.org/10.3390/e21101015 - 19 Oct 2019

Cited by 6 | Viewed by 3236

Abstract

This paper applies a Machine Learning approach with the aim of providing a single aggregated prediction from a set of individual predictions. Departing from the well-known maximum-entropy inference methodology, a new factor capturing the distance between the true and the estimated aggregated predictions [...] Read more.

This paper applies a Machine Learning approach with the aim of providing a single aggregated prediction from a set of individual predictions. Departing from the well-known maximum-entropy inference methodology, a new factor capturing the distance between the true and the estimated aggregated predictions presents a new problem. Algorithms such as ridge, lasso or elastic net help in finding a new methodology to tackle this issue. We carry out a simulation study to evaluate the performance of such a procedure and apply it in order to forecast and measure predictive ability using a dataset of predictions on Spanish gross domestic product. Full article

(This article belongs to the Special Issue Entropy Application for Forecasting)

11 pages, 2071 KiB

Open AccessArticle

Predicting Premature Video Skipping and Viewer Interest from EEG Recordings

by Arno Libert and Marc M. Van Hulle

Entropy 2019, 21(10), 1014; https://doi.org/10.3390/e21101014 - 19 Oct 2019

Cited by 12 | Viewed by 3626

Abstract

Brain–computer interfacing has enjoyed growing attention, not only due to the stunning demonstrations with severely disabled patients, but also the advent of economically viable solutions in areas such as neuromarketing, mental state monitoring, and future human–machine interaction. An interesting case, at least for [...] Read more.

Brain–computer interfacing has enjoyed growing attention, not only due to the stunning demonstrations with severely disabled patients, but also the advent of economically viable solutions in areas such as neuromarketing, mental state monitoring, and future human–machine interaction. An interesting case, at least for neuromarketers, is to monitor the customer’s mental state in response to watching a commercial. In this paper, as a novelty, we propose a method to predict from electroencephalography (EEG) recordings whether individuals decide to skip watching a video trailer. Based on multiscale sample entropy and signal power, indices were computed that gauge the viewer’s engagement and emotional affect. We then trained a support vector machine (SVM), a k-nearest neighbor (kNN), and a random forest (RF) classifier to predict whether the viewer declares interest in watching the video and whether he/she decides to skip it prematurely. Our model achieved an average single-subject classification accuracy of 75.803% for skipping and 73.3% for viewer interest for the SVM, 82.223% for skipping and 78.333% for viewer interest for the kNN, and 80.003% for skipping and 75.555% for interest for the RF. We conclude that EEG can provide indications of viewer interest and skipping behavior and provide directions for future research. Full article

(This article belongs to the Special Issue Information Theory and Complexity Science Approaches to Health Conditions and Cognitive Decline)

► Show Figures

Figure 1

19 pages, 1167 KiB

Open AccessArticle

Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

by David Cuesta-Frau, Antonio Molina-Picó, Borja Vargas and Paula González

Entropy 2019, 21(10), 1013; https://doi.org/10.3390/e21101013 - 18 Oct 2019

Cited by 11 | Viewed by 2574

Abstract

Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly [...] Read more.

Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear

{I R}^{n}

mapping into

I R

, where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures. Full article

(This article belongs to the Special Issue Theoretical Developments and Applications of Entropy and Ordinal Patterns)

► Show Figures

Figure 1

19 pages, 14074 KiB

Open AccessArticle

Communication Enhancement through Quantum Coherent Control of N Channels in an Indefinite Causal-Order Scenario

by Lorenzo M. Procopio, Francisco Delgado, Marco Enríquez, Nadia Belabas and Juan Ariel Levenson

Entropy 2019, 21(10), 1012; https://doi.org/10.3390/e21101012 - 18 Oct 2019

Cited by 48 | Viewed by 4240

Abstract

In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control [...] Read more.

In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number N of channels with arbitrary individual capacity i.e., information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of N channels in an indefinite causal order scenario yielding the output of such transmission. Then, we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for

N = 2

,

N = 3

as a function of all involved parameters. We find in the case

N = 3

that the transmission of information for three channels is twice that of transmission of the two-channel case when a full superposition of all possible causal orders is used. Full article

(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)

► Show Figures

Figure 1

12 pages, 1321 KiB

Open AccessArticle

Performance Improvement of Underwater Continuous-Variable Quantum Key Distribution via Photon Subtraction

by Qingquan Peng, Guojun Chen, Xuan Li, Qin Liao and Ying Guo

Entropy 2019, 21(10), 1011; https://doi.org/10.3390/e21101011 - 17 Oct 2019

Cited by 12 | Viewed by 2790

Abstract

Considering the ocean water’s optical attenuation is significantly larger than that of Fiber Channel, we propose an approach to enhance the security of underwater continuous-variable quantum key distribution (CVQKD). In particular, the photon subtraction operation is performed at the emitter to enhance quantum [...] Read more.

Considering the ocean water’s optical attenuation is significantly larger than that of Fiber Channel, we propose an approach to enhance the security of underwater continuous-variable quantum key distribution (CVQKD). In particular, the photon subtraction operation is performed at the emitter to enhance quantum entanglement, thereby improving the underwater transmission performance of the CVQKD. Simulation results show that the photon subtraction operation can effectively improve the performance of CVQKD in terms of underwater transmission distance. We also compare the performance of the proposed protocol in different water qualities, which shows the advantage of our protocol against water deterioration. Therefore, we provide a suitable scheme for establishing secure communication between submarine and submarine vehicles. Full article

(This article belongs to the Collection Quantum Information)

► Show Figures

Figure 1

10 pages, 294 KiB

Open AccessArticle

Residual Predictive Information Flow in the Tight Coupling Limit: Analytic Insights from a Minimalistic Model

by Benjamin Wahl, Ulrike Feudel, Jaroslav Hlinka, Matthias Wächter, Joachim Peinke and Jan A. Freund

Entropy 2019, 21(10), 1010; https://doi.org/10.3390/e21101010 - 17 Oct 2019

Cited by 1 | Viewed by 3447

Abstract

In a coupled system, predictive information flows from the causing to the caused variable. The amount of transferred predictive information can be quantified through the use of transfer entropy or, for Gaussian variables, equivalently via Granger causality. It is natural to expect and [...] Read more.

In a coupled system, predictive information flows from the causing to the caused variable. The amount of transferred predictive information can be quantified through the use of transfer entropy or, for Gaussian variables, equivalently via Granger causality. It is natural to expect and has been repeatedly observed that a tight coupling does not permit to reconstruct a causal connection between causing and caused variables. Here, we show that for a model of interacting social groups, carried from the master equation to the Fokker–Planck level, a residual predictive information flow can remain for a pair of uni-directionally coupled variables even in the limit of infinite coupling strength. We trace this phenomenon back to the question of how the synchronizing force and the noise strength scale with the coupling strength. A simplified model description allows us to derive analytic expressions that fully elucidate the interplay between deterministic and stochastic model parts. Full article

(This article belongs to the Special Issue Information Transfer, Entropy Production, Irreversibility and Time Series Analysis)

► Show Figures

Figure 1

20 pages, 1632 KiB

Open AccessArticle

A Comparison of the Maximum Entropy Principle Across Biological Spatial Scales

by Rodrigo Cofré, Rubén Herzog, Derek Corcoran and Fernando E. Rosas

Entropy 2019, 21(10), 1009; https://doi.org/10.3390/e21101009 - 16 Oct 2019

Cited by 13 | Viewed by 4020

Abstract

Despite their differences, biological systems at different spatial scales tend to exhibit common organizational patterns. Unfortunately, these commonalities are often hard to grasp due to the highly specialized nature of modern science and the parcelled terminology employed by various scientific sub-disciplines. To explore [...] Read more.

Despite their differences, biological systems at different spatial scales tend to exhibit common organizational patterns. Unfortunately, these commonalities are often hard to grasp due to the highly specialized nature of modern science and the parcelled terminology employed by various scientific sub-disciplines. To explore these common organizational features, this paper provides a comparative study of diverse applications of the maximum entropy principle, which has found many uses at different biological spatial scales ranging from amino acids up to societies. By presenting these studies under a common approach and language, this paper aims to establish a unified view over these seemingly highly heterogeneous scenarios. Full article

(This article belongs to the Special Issue Information Theory Applications in Biology)

► Show Figures

Figure 1

13 pages, 2018 KiB

Open AccessArticle

Multiscale Horizontal Visibility Graph Analysis of Higher-Order Moments for Estimating Statistical Dependency

by Keqiang Dong, Haowei Che and Zhi Zou

Entropy 2019, 21(10), 1008; https://doi.org/10.3390/e21101008 - 16 Oct 2019

Cited by 5 | Viewed by 3969

Abstract

The horizontal visibility graph is not only a powerful tool for the analysis of complex systems, but also a promising way to analyze time series. In this paper, we present an approach to measure the nonlinear interactions between a non-stationary time series based [...] Read more.

The horizontal visibility graph is not only a powerful tool for the analysis of complex systems, but also a promising way to analyze time series. In this paper, we present an approach to measure the nonlinear interactions between a non-stationary time series based on the horizontal visibility graph. We describe how a horizontal visibility graph may be calculated based on second-order and third-order statistical moments. We compare the new methods with the first-order measure, and then give examples including stock markets and aero-engine performance parameters. These analyses suggest that measures derived from the horizontal visibility graph may be of particular relevance to the growing interest in quantifying the information exchange between time series. Full article

(This article belongs to the Special Issue Entropy, Nonlinear Dynamics and Complexity)

► Show Figures

Figure 1

14 pages, 6223 KiB

Open AccessArticle

Conjugate Heat Transfer Investigation on Swirl-Film Cooling at the Leading Edge of a Gas Turbine Vane

by Haifen Du, Ziyue Mei, Jiayao Zou, Wei Jiang and Danmei Xie

Entropy 2019, 21(10), 1007; https://doi.org/10.3390/e21101007 - 15 Oct 2019

Cited by 12 | Viewed by 3716

Abstract

Numerical calculation of conjugate heat transfer was carried out to study the effect of combined film and swirl cooling at the leading edge of a gas turbine vane with a cooling chamber inside. Two cooling chambers (C₁ and C₂ cases) were [...] Read more.

Numerical calculation of conjugate heat transfer was carried out to study the effect of combined film and swirl cooling at the leading edge of a gas turbine vane with a cooling chamber inside. Two cooling chambers (C₁ and C₂ cases) were specially designed to generate swirl in the chamber, which could enhance overall cooling effectiveness at the leading edge. A simple cooling chamber (C₀ case) was designed as a baseline. The effects of different cooling chambers were studied. Compared with the C₀ case, the cooling chamber in the C₁ case consists of a front cavity and a back cavity and two cavities are connected by a passage on the pressure side to improve the overall cooling effectiveness of the vane. The area-averaged overall cooling effectiveness of the leading edge (

\bar{\bar{ϕ}}

) was improved by approximately 57%. Based on the C₁ case, the passage along the vane was divided into nine segments in the C₂ case to enhance the cooling effectiveness at the leading edge, and

\bar{\bar{ϕ}}

was enhanced by 75% compared with that in the C₀ case. Additionally, the cooling efficiency on the pressure side was improved significantly by using swirl-cooling chambers. Pressure loss in the C₂ and C₁ cases was larger than that in the C₀ case. Full article

(This article belongs to the Special Issue Thermal Physic Processes, Phase Transitions and Chemical Reactions in High-Temperature Gas, Vapour and Liquid Systems)

► Show Figures

Figure 1

41 pages, 434 KiB

Open AccessArticle

The Generalized Stochastic Smoluchowski Equation

by Pierre-Henri Chavanis

Entropy 2019, 21(10), 1006; https://doi.org/10.3390/e21101006 - 15 Oct 2019

Cited by 26 | Viewed by 3751

Abstract

We study the dynamics of a system of overdamped Brownian particles governed by the generalized stochastic Smoluchowski equation associated with a generalized form of entropy and involving a long-range potential of interaction [P.H. Chavanis, Entropy 17, 3205 (2015)]. We first neglect fluctuations [...] Read more.

We study the dynamics of a system of overdamped Brownian particles governed by the generalized stochastic Smoluchowski equation associated with a generalized form of entropy and involving a long-range potential of interaction [P.H. Chavanis, Entropy 17, 3205 (2015)]. We first neglect fluctuations and provide a macroscopic description of the system based on the deterministic mean field Smoluchowski equation. We then take fluctuations into account and provide a mesoscopic description of the system based on the stochastic mean field Smoluchowski equation. We establish the main properties of this equation and derive the Kramers escape rate formula, giving the lifetime of a metastable state, from the theory of instantons. We relate the properties of the generalized stochastic Smoluchowski equation to a principle of maximum dissipation of free energy. We also discuss the connection with the dynamical density functional theory of simple liquids. Full article

(This article belongs to the Special Issue Entropy Production and Its Applications: From Cosmology to Biology)

33 pages, 3933 KiB

Open AccessArticle

Thermodynamics of a Phase-Driven Proximity Josephson Junction

by Francesco Vischi, Matteo Carrega, Alessandro Braggio, Pauli Virtanen and Francesco Giazotto

Entropy 2019, 21(10), 1005; https://doi.org/10.3390/e21101005 - 15 Oct 2019

Cited by 5 | Viewed by 4152

Abstract

We study the thermodynamic properties of a superconductor/normal metal/superconductor Josephson junction in the short limit. Owing to the proximity effect, such a junction constitutes a thermodynamic system where phase difference, supercurrent, temperature and entropy are thermodynamical variables connected by equations of state. These [...] Read more.

We study the thermodynamic properties of a superconductor/normal metal/superconductor Josephson junction in the short limit. Owing to the proximity effect, such a junction constitutes a thermodynamic system where phase difference, supercurrent, temperature and entropy are thermodynamical variables connected by equations of state. These allow conceiving quasi-static processes that we characterize in terms of heat and work exchanged. Finally, we combine such processes to construct a Josephson-based Otto and Stirling cycles. We study the related performance in both engine and refrigerator operating mode. Full article

(This article belongs to the Special Issue Quantum Thermodynamics II)

► Show Figures

Figure 1

15 pages, 1616 KiB

Open AccessArticle

A Novel S-Box Design Algorithm Based on a New Compound Chaotic System

by Qing Lu, Congxu Zhu and Guojun Wang

Entropy 2019, 21(10), 1004; https://doi.org/10.3390/e21101004 - 14 Oct 2019

Cited by 65 | Viewed by 4261

Abstract

Substitution-boxes (S-Boxes) are important non-linear components in block cryptosystem, which play an important role in the security of cryptosystems. Constructing S-Boxes with a strong cryptographic feature is an important step in designing block cipher systems. In this paper, a novel algorithm for constructing [...] Read more.

Substitution-boxes (S-Boxes) are important non-linear components in block cryptosystem, which play an important role in the security of cryptosystems. Constructing S-Boxes with a strong cryptographic feature is an important step in designing block cipher systems. In this paper, a novel algorithm for constructing S-Boxes based on a new compound chaotic system is presented. Firstly, the new chaotic system, tent–logistic system, is proposed, which has better chaotic performance and wider chaotic range than the tent and logistic system, and can not only increase the randomness of the chaotic sequences but also expand the key space of cryptosystems. Secondly, a novel linear mapping is employed to construct the initial S-Box. Then, the permutation operation on the initial S-Box is performed by using chaotic sequence generated with the tent–logistic system, which improves the cryptographic features of the S-Box. The idea behind the proposed work is to make supplementary safe S-box. Detail tests for cryptographic strength of the proposed S-Box are performed by using different standard benchmarks. The test results and performance analysis show that our proposed S-Box has very smaller values of linear probability (LP) and differential probability (DP) and a satisfactory average value of nonlinearity compared with other S-Boxes, showing its excellent application potential in block cipher system. Full article

(This article belongs to the Section Multidisciplinary Applications)

► Show Figures

Figure 1

16 pages, 856 KiB

Open AccessArticle

Enhanced Negative Nonlocal Conductance in an Interacting Quantum Dot Connected to Two Ferromagnetic Leads and One Superconducting Lead

by Cong Lee, Bing Dong and Xiao-Lin Lei

Entropy 2019, 21(10), 1003; https://doi.org/10.3390/e21101003 - 14 Oct 2019

Cited by 1 | Viewed by 2405

Abstract

In this paper, we investigate the electronic transport properties of a quantum dot (QD) connected to two ferromagnetic leads and one superconducting lead in the Kondo regime by means of the finite-U slave boson mean field approach and the nonequilibrium Green function [...] Read more.

In this paper, we investigate the electronic transport properties of a quantum dot (QD) connected to two ferromagnetic leads and one superconducting lead in the Kondo regime by means of the finite-U slave boson mean field approach and the nonequilibrium Green function technique. In this three-terminal hybrid nanodevice, we focus our attention on the joint effects of the Kondo correlation, superconducting proximity pairing, and spin polarization of leads. It is found that the superconducting proximity effect will suppress the linear local conductance (LLC) stemming from the weakened Kondo peak, and when its coupling

Γ_{s}

is bigger than the tunnel-coupling

Γ

of two normal leads, the linear cross conductance (LCC) becomes negative in the Kondo region. Regarding the antiparallel configuration, increasing spin polarization further suppresses LLC but enhances LCC, i.e., causing larger negative values of LCC, since it is beneficial for the emergence of cross Andreev reflection. On the contrary, for the parallel configuration, with increasing spin polarization, the LLC decreases and greatly widens with the appearance of shoulders, and eventually splits into four peaks, while the LCC decreases relatively rapidly to the normal conductance. Full article

(This article belongs to the Special Issue Quantum Transport in Mesoscopic Systems)

► Show Figures

Figure 1

19 pages, 2137 KiB

Open AccessArticle

Fitness Gain of Individually Sensed Information by Cells

by Tetsuya J. Kobayashi and Yuki Sughiyama

Entropy 2019, 21(10), 1002; https://doi.org/10.3390/e21101002 - 13 Oct 2019

Cited by 4 | Viewed by 2522

Abstract

Mutual information and its causal variant, directed information, have been widely used to quantitatively characterize the performance of biological sensing and information transduction. However, once coupled with selection in response to decision-making, the sensing signal could have more or less evolutionary value than [...] Read more.

Mutual information and its causal variant, directed information, have been widely used to quantitatively characterize the performance of biological sensing and information transduction. However, once coupled with selection in response to decision-making, the sensing signal could have more or less evolutionary value than its mutual or directed information. In this work, we show that an individually sensed signal always has a better fitness value, on average, than its mutual or directed information. The fitness gain, which satisfies fluctuation relations (FRs), is attributed to the selection of organisms in a population that obtain a better sensing signal by chance. A new quantity, similar to the coarse-grained entropy production in information thermodynamics, is introduced to quantify the total fitness gain from individual sensing, which also satisfies FRs. Using this quantity, the optimizing fitness gain of individual sensing is shown to be related to fidelity allocations for individual environmental histories. Our results are supplemented by numerical verifications of FRs, and a discussion on how this problem is linked to information encoding and decoding. Full article

(This article belongs to the Special Issue Information Flow and Entropy Production in Biomolecular Networks)

► Show Figures

Figure 1

22 pages, 9953 KiB

Open AccessArticle

Permutation Entropy-Based Analysis of Temperature Complexity Spatial-Temporal Variation and Its Driving Factors in China

by Ting Zhang, Changxiu Cheng and Peichao Gao

Entropy 2019, 21(10), 1001; https://doi.org/10.3390/e21101001 - 13 Oct 2019

Cited by 6 | Viewed by 3684

Abstract

Air temperature fluctuation complexity (TFC) describes the uncertainty of temperature changes. The analysis of its spatial and temporal variation is of great significance to evaluate prediction uncertainty of the regional temperature trends and the climate change. In this study, annual-TFC from 1979–2017 and [...] Read more.

Air temperature fluctuation complexity (TFC) describes the uncertainty of temperature changes. The analysis of its spatial and temporal variation is of great significance to evaluate prediction uncertainty of the regional temperature trends and the climate change. In this study, annual-TFC from 1979–2017 and seasonal-TFC from 1983–2017 in China were calculated by permutation entropy (PE). Their temporal trend is described by the Mann-Kendall method. Driving factors of their spatial variations are explored through GeoDetector. The results show that: (1). TFC shows a downward trend generally, with obvious time variation. (2). The spatial variation of TFC is mainly manifested in the differences among the five sub-regions in China. There is low uncertainty in the short-term temperature trends in the northwest and southeast. The northeastern and southwestern regions show high uncertainties. TFC in the central region is moderate. (3). The vegetation is the main factor of spatial variation, followed by the climate and altitude, and the latitude and terrain display the lowest impact. The interactions of vegetation-altitude, vegetation-climate and altitude-latitude can interpret more than 50% of the spatial variations. These results provide insights into causes and mechanisms of the complexity of the climate system. They can help to determine the influencing process of various factors. Full article

(This article belongs to the Special Issue Spatial Information Theory)

► Show Figures

Figure 1

21 pages, 3915 KiB

Open AccessArticle

Recognition of Voltage Sag Sources Based on Phase Space Reconstruction and Improved VGG Transfer Learning

by Yuting Pu, Honggeng Yang, Xiaoyang Ma and Xiangxun Sun

Entropy 2019, 21(10), 999; https://doi.org/10.3390/e21100999 - 12 Oct 2019

Cited by 3 | Viewed by 2933

Abstract

The recognition of the voltage sag sources is the basis for formulating a voltage sag governance plan and clarifying the responsibility for the accident. Aiming at the recognition problem of voltage sag sources, a recognition method of voltage sag sources based on phase [...] Read more.

The recognition of the voltage sag sources is the basis for formulating a voltage sag governance plan and clarifying the responsibility for the accident. Aiming at the recognition problem of voltage sag sources, a recognition method of voltage sag sources based on phase space reconstruction and improved Visual Geometry Group (VGG) transfer learning is proposed from the perspective of image classification. Firstly, phase space reconstruction technology is used to transform voltage sag signals, generate reconstruction images of voltage sag, and analyze the intuitive characteristics of different sag sources from reconstruction images. Secondly, combined with the attention mechanism, the standard VGG 16 model is improved to extract the features completely and prevent over-fitting. Finally, VGG transfer learning model uses the idea of transfer learning for training, which improves the efficiency of model training and the recognition accuracy of sag sources. The purpose of the training model is to minimize the cross entropy loss function. The simulation analysis verifies the effectiveness and superiority of the proposed method. Full article

► Show Figures

Figure 1

19 pages, 1294 KiB

Open AccessArticle

Physical-Layer Security Analysis over M-Distributed Fading Channels

by Sheng-Hong Lin, Rong-Rong Lu, Xian-Tao Fu, An-Ling Tong and Jin-Yuan Wang

Entropy 2019, 21(10), 998; https://doi.org/10.3390/e21100998 - 12 Oct 2019

Cited by 5 | Viewed by 2519

Abstract

In this paper, the physical layer security over the M-distributed fading channel is investigated. Initially, an exact expression of secrecy outage probability (SOP) is derived, which has an integral term. To get a closed-form expression, a lower bound of SOP is obtained. After [...] Read more.

In this paper, the physical layer security over the M-distributed fading channel is investigated. Initially, an exact expression of secrecy outage probability (SOP) is derived, which has an integral term. To get a closed-form expression, a lower bound of SOP is obtained. After that, the exact expression for the probability of strictly positive secrecy capacity (SPSC) is derived, which is in closed-form. Finally, an exact expression of ergodic secrecy capacity (ESC) is derived, which has two integral terms. To reduce its computational complexity, a closed-from expression for the lower bound of ESC is obtained. As special cases of M-distributed fading channels, the secure performance of the K, exponential, and Gamma-Gamma fading channels are also derived, respectively. Numerical results show that all theoretical results match well with Monte-Carlo simulation results. Specifically, when the average signal-to-noise ratio of main channel is larger than 40 dB, the relative errors for the lower bound of SOP, the probability of SPSC, and the lower bound of ESC are less than 1.936%, 6.753%, and 1.845%, respectively. This indicates that the derived theoretical expressions can be directly used to evaluate system performance without time-consuming simulations. Moreover, the derived results regarding parameters that influence the secrecy performance will enable system designers to quickly determine the optimal available parameter choices when facing different security risks. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

► Show Figures

Graphical abstract

17 pages, 5433 KiB

Open AccessArticle

On the Calculation of the Effective Polytropic Index in Space Plasmas

by Georgios Nicolaou, George Livadiotis and Robert T. Wicks

Entropy 2019, 21(10), 997; https://doi.org/10.3390/e21100997 - 12 Oct 2019

Cited by 11 | Viewed by 4001

Abstract

The polytropic index of space plasmas is typically determined from the relationship between the measured plasma density and temperature. In this study, we quantify the errors in the determination of the polytropic index, due to uncertainty in the analyzed measurements. We model the [...] Read more.

The polytropic index of space plasmas is typically determined from the relationship between the measured plasma density and temperature. In this study, we quantify the errors in the determination of the polytropic index, due to uncertainty in the analyzed measurements. We model the plasma density and temperature measurements for a certain polytropic index, and then, we apply the standard analysis to derive the polytropic index. We explore the accuracy of the derived polytropic index for a range of uncertainties in the modeled density and temperature and repeat for various polytropic indices. Our analysis shows that the uncertainties in the plasma density introduce a systematic error in the determination of the polytropic index which can lead to artificial isothermal relations, while the uncertainties in the plasma temperature increase the statistical error of the calculated polytropic index value. We analyze Wind spacecraft observations of the solar wind protons and we derive the polytropic index in selected intervals over 2002. The derived polytropic index is affected by the plasma measurement uncertainties, in a similar way as predicted by our model. Finally, we suggest a new data-analysis approach, based on a physical constraint, that reduces the amount of erroneous derivations. Full article

(This article belongs to the Special Issue Theoretical Aspects of Kappa Distributions)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Entropy, Volume 21, Issue 10 (October 2019) – 111 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI