Entropy

11 pages, 11378 KiB

Open AccessArticle

Multiscale Information Propagation in Emergent Functional Networks

by Arsham Ghavasieh and Manlio De Domenico

Entropy 2021, 23(10), 1369; https://doi.org/10.3390/e23101369 - 19 Oct 2021

Cited by 3 | Viewed by 2178

Complex biological systems consist of large numbers of interconnected units, characterized by emergent properties such as collective computation. In spite of all the progress in the last decade, we still lack a deep understanding of how these properties arise from the coupling between [...] Read more.

Complex biological systems consist of large numbers of interconnected units, characterized by emergent properties such as collective computation. In spite of all the progress in the last decade, we still lack a deep understanding of how these properties arise from the coupling between the structure and dynamics. Here, we introduce the multiscale emergent functional state, which can be represented as a network where links encode the flow exchange between the nodes, calculated using diffusion processes on top of the network. We analyze the emergent functional state to study the distribution of the flow among components of 92 fungal networks, identifying their functional modules at different scales and, more importantly, demonstrating the importance of functional modules for the information content of networks, quantified in terms of network spectral entropy. Our results suggest that the topological complexity of fungal networks guarantees the existence of functional modules at different scales keeping the information entropy, and functional diversity, high. Full article

(This article belongs to the Special Issue Foundations of Biological Computation)

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12 pages, 15573 KiB

Open AccessTechnical Note

Scikit-Dimension: A Python Package for Intrinsic Dimension Estimation

by Jonathan Bac, Evgeny M. Mirkes, Alexander N. Gorban, Ivan Tyukin and Andrei Zinovyev

Entropy 2021, 23(10), 1368; https://doi.org/10.3390/e23101368 - 19 Oct 2021

Cited by 34 | Viewed by 4747

Abstract

Dealing with uncertainty in applications of machine learning to real-life data critically depends on the knowledge of intrinsic dimensionality (ID). A number of methods have been suggested for the purpose of estimating ID, but no standard package to easily apply them one by [...] Read more.

Dealing with uncertainty in applications of machine learning to real-life data critically depends on the knowledge of intrinsic dimensionality (ID). A number of methods have been suggested for the purpose of estimating ID, but no standard package to easily apply them one by one or all at once has been implemented in Python. This technical note introduces scikit-dimension, an open-source Python package for intrinsic dimension estimation. The scikit-dimension package provides a uniform implementation of most of the known ID estimators based on the scikit-learn application programming interface to evaluate the global and local intrinsic dimension, as well as generators of synthetic toy and benchmark datasets widespread in the literature. The package is developed with tools assessing the code quality, coverage, unit testing and continuous integration. We briefly describe the package and demonstrate its use in a large-scale (more than 500 datasets) benchmarking of methods for ID estimation for real-life and synthetic data. Full article

(This article belongs to the Special Issue Uncertainty in Large Neural Systems: Validation, Explanation and Correction of Multidimensional Intelligence in a Multidimensional World)

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3 pages, 175 KiB

Open AccessEditorial

The Statistical Foundations of Entropy

by Petr Jizba and Jan Korbel

Entropy 2021, 23(10), 1367; https://doi.org/10.3390/e23101367 - 19 Oct 2021

Viewed by 2234

Abstract

During the last few decades, the notion of entropy has become omnipresent in many scientific disciplines, ranging from traditional applications in statistical physics and chemistry, information theory, and statistical estimation to more recent applications in biology, astrophysics, geology, financial markets, or social networks [...] Read more.

During the last few decades, the notion of entropy has become omnipresent in many scientific disciplines, ranging from traditional applications in statistical physics and chemistry, information theory, and statistical estimation to more recent applications in biology, astrophysics, geology, financial markets, or social networks [...] Full article

(This article belongs to the Special Issue The Statistical Foundations of Entropy)

9 pages, 1817 KiB

Open AccessArticle

Anharmonic Effects on the Thermodynamic Properties of Quartz from First Principles Calculations

by Mara Murri and Mauro Prencipe

Entropy 2021, 23(10), 1366; https://doi.org/10.3390/e23101366 - 19 Oct 2021

Cited by 1 | Viewed by 1634

Abstract

The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been [...] Read more.

The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been studied since decades. Alpha quartz is stable up to 2.5 GPa at room temperature where it converts to coesite, and at ambient pressure up to 847 K where it transforms to the beta phase. In particular, the displacive phase transition at 847 K at ambient pressure is driven by intrinsic anharmonicity effects (soft-mode phase transition) and its precise mechanism is difficult to be investigated experimentally. Therefore, we studied these anharmonic effects by means of ab initio calculations in the framework of the statistical thermodynamics approach. We determined the principal thermodynamic quantities accounting for the intrinsic anharmonicity and compared them against experimental data. Our results up to 700 K show a very good agreement with experiments. The same procedures and algorithms illustrated here can also be applied to determine the thermodynamic properties of other crystalline phases possibly affected by intrinsic anharmonic effects, that could partially invalidate the standard quasi-harmonic approach. Full article

(This article belongs to the Special Issue Statistical Thermodynamics: From First Principles Computations to Macroscopic Properties of Matter)

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17 pages, 4631 KiB

Open AccessArticle

Gene Network Analysis of Alzheimer’s Disease Based on Network and Statistical Methods

by Chen Zhou, Haiyan Guo and Shujuan Cao

Entropy 2021, 23(10), 1365; https://doi.org/10.3390/e23101365 - 19 Oct 2021

Cited by 2 | Viewed by 1886

Abstract

Gene network associated with Alzheimer’s disease (AD) is constructed from multiple data sources by considering gene co-expression and other factors. The AD gene network is divided into modules by Cluster one, Markov Clustering (MCL), Community Clustering (Glay) and Molecular Complex Detection (MCODE). Then [...] Read more.

Gene network associated with Alzheimer’s disease (AD) is constructed from multiple data sources by considering gene co-expression and other factors. The AD gene network is divided into modules by Cluster one, Markov Clustering (MCL), Community Clustering (Glay) and Molecular Complex Detection (MCODE). Then these division methods are evaluated by network structure entropy, and optimal division method, MCODE. Through functional enrichment analysis, the functional module is identified. Furthermore, we use network topology properties to predict essential genes. In addition, the logical regression algorithm under Bayesian framework is used to predict essential genes of AD. Based on network pharmacology, four kinds of AD’s herb-active compounds-active compound targets network and AD common core network are visualized, then the better herbs and herb compounds of AD are selected through enrichment analysis. Full article

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18 pages, 1829 KiB

Open AccessArticle

Anti-Quantum Lattice-Based Ring Signature Scheme and Applications in VANETs

by Chunhong Jiao and Xinyin Xiang

Entropy 2021, 23(10), 1364; https://doi.org/10.3390/e23101364 - 19 Oct 2021

Cited by 6 | Viewed by 1671

Abstract

Message authentication is crucial because it encourages participants to accept countermeasures and further transmit messages to legitimate users in a network while maintaining the legitimacy of the identity of network members. An unauthorized user cannot transmit false messages to a given network. Although [...] Read more.

Message authentication is crucial because it encourages participants to accept countermeasures and further transmit messages to legitimate users in a network while maintaining the legitimacy of the identity of network members. An unauthorized user cannot transmit false messages to a given network. Although traditional public key cryptography is suitable for message authentication, it is also easy to manage and generate keys, and, with the expansion of an entire network, the system needs a lot of computing power, which creates additional risks to network security. A more effective method, such as ring signature, can realize this function and guarantee more security. In this paper, we propose an anti-quantum ring signature scheme based on lattice, functionality analysis, and performance evaluation to demonstrate that this scheme supports unconditional anonymity and unforgeability. After efficiency analysis, our scheme proved more effective than the existing ring signature schemes in processing signature generation and verification. The proposed scheme was applied to VANETs that support strong security and unconditional anonymity to vehicles. Full article

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18 pages, 1513 KiB

Open AccessArticle

Study of Kinetic Freeze-Out Parameters as a Function of Rapidity in pp Collisions at CERN SPS Energies

by Muhammad Waqas, Huai-Min Chen, Guang-Xiong Peng, Abd Al Karim Haj Ismail, Muhammad Ajaz, Zafar Wazir, Ramoona Shehzadi, Sabiha Jamal and Atef AbdelKader

Entropy 2021, 23(10), 1363; https://doi.org/10.3390/e23101363 - 19 Oct 2021

Cited by 15 | Viewed by 1596

Abstract

We used the blast wave model with the Boltzmann–Gibbs statistics and analyzed the experimental data measured by the NA61/SHINE Collaboration in inelastic (INEL) proton–proton collisions at different rapidity slices at different center-of-mass energies. The particles used in this study were

π^{+}

, [...] Read more.

We used the blast wave model with the Boltzmann–Gibbs statistics and analyzed the experimental data measured by the NA61/SHINE Collaboration in inelastic (INEL) proton–proton collisions at different rapidity slices at different center-of-mass energies. The particles used in this study were

π^{+}

,

π^{-}

,

K^{+}

,

K^{-}

, and

\bar{p}

. We extracted the kinetic freeze-out temperature, transverse flow velocity, and kinetic freeze-out volume from the transverse momentum spectra of the particles. We observed that the kinetic freeze-out temperature is rapidity and energy dependent, while the transverse flow velocity does not depend on them. Furthermore, we observed that the kinetic freeze-out volume is energy dependent, but it remains constant with changing the rapidity. We also observed that all three parameters are mass dependent. In addition, with the increase of mass, the kinetic freeze-out temperature increases, and the transverse flow velocity, as well as kinetic freeze-out volume decrease. Full article

(This article belongs to the Special Issue Zimányi School: Hydrodynamics and Thermodynamics in High Energy Particle and Nuclear Physics)

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28 pages, 12843 KiB

Open AccessArticle

Multi-Focus Image Fusion Method Based on Multi-Scale Decomposition of Information Complementary

by Hui Wan, Xianlun Tang, Zhiqin Zhu and Weisheng Li

Entropy 2021, 23(10), 1362; https://doi.org/10.3390/e23101362 - 19 Oct 2021

Cited by 2 | Viewed by 1989

Abstract

Multi-focus image fusion is an important method used to combine the focused parts from source multi-focus images into a single full-focus image. Currently, to address the problem of multi-focus image fusion, the key is on how to accurately detect the focus regions, especially [...] Read more.

Multi-focus image fusion is an important method used to combine the focused parts from source multi-focus images into a single full-focus image. Currently, to address the problem of multi-focus image fusion, the key is on how to accurately detect the focus regions, especially when the source images captured by cameras produce anisotropic blur and unregistration. This paper proposes a new multi-focus image fusion method based on the multi-scale decomposition of complementary information. Firstly, this method uses two groups of large-scale and small-scale decomposition schemes that are structurally complementary, to perform two-scale double-layer singular value decomposition of the image separately and obtain low-frequency and high-frequency components. Then, the low-frequency components are fused by a rule that integrates image local energy with edge energy. The high-frequency components are fused by the parameter-adaptive pulse-coupled neural network model (PA-PCNN), and according to the feature information contained in each decomposition layer of the high-frequency components, different detailed features are selected as the external stimulus input of the PA-PCNN. Finally, according to the two-scale decomposition of the source image that is structure complementary, and the fusion of high and low frequency components, two initial decision maps with complementary information are obtained. By refining the initial decision graph, the final fusion decision map is obtained to complete the image fusion. In addition, the proposed method is compared with 10 state-of-the-art approaches to verify its effectiveness. The experimental results show that the proposed method can more accurately distinguish the focused and non-focused areas in the case of image pre-registration and unregistration, and the subjective and objective evaluation indicators are slightly better than those of the existing methods. Full article

(This article belongs to the Special Issue Advances in Image Fusion)

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3 pages, 155 KiB

Open AccessEditorial

Information Theory and Symbolic Analysis: Theory and Applications

by Mariano Matilla-García and Manuel Ruiz Marín

Entropy 2021, 23(10), 1361; https://doi.org/10.3390/e23101361 - 19 Oct 2021

Cited by 1 | Viewed by 1232

Abstract

Symbolic analysis has been developed and used successfully in very diverse fields [...] Full article

(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)

16 pages, 2611 KiB

Open AccessArticle

Information Bottleneck Theory Based Exploration of Cascade Learning

by Xin Du, Katayoun Farrahi and Mahesan Niranjan

Entropy 2021, 23(10), 1360; https://doi.org/10.3390/e23101360 - 18 Oct 2021

Cited by 1 | Viewed by 2527

Abstract

In solving challenging pattern recognition problems, deep neural networks have shown excellent performance by forming powerful mappings between inputs and targets, learning representations (features) and making subsequent predictions. A recent tool to help understand how representations are formed is based on observing the [...] Read more.

In solving challenging pattern recognition problems, deep neural networks have shown excellent performance by forming powerful mappings between inputs and targets, learning representations (features) and making subsequent predictions. A recent tool to help understand how representations are formed is based on observing the dynamics of learning on an information plane using mutual information, linking the input to the representation (

I (X; T)

) and the representation to the target (

I (T; Y)

). In this paper, we use an information theoretical approach to understand how Cascade Learning (CL), a method to train deep neural networks layer-by-layer, learns representations, as CL has shown comparable results while saving computation and memory costs. We observe that performance is not linked to information–compression, which differs from observation on End-to-End (E2E) learning. Additionally, CL can inherit information about targets, and gradually specialise extracted features layer-by-layer. We evaluate this effect by proposing an information transition ratio,

I (T; Y) / I (X; T)

, and show that it can serve as a useful heuristic in setting the depth of a neural network that achieves satisfactory accuracy of classification. Full article

(This article belongs to the Special Issue Information-Theoretic Data Mining)

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40 pages, 1510 KiB

Open AccessArticle

Beware the Black-Box: On the Robustness of Recent Defenses to Adversarial Examples

by Kaleel Mahmood, Deniz Gurevin, Marten van Dijk and Phuoung Ha Nguyen

Entropy 2021, 23(10), 1359; https://doi.org/10.3390/e23101359 - 18 Oct 2021

Cited by 5 | Viewed by 2431

Abstract

Many defenses have recently been proposed at venues like NIPS, ICML, ICLR and CVPR. These defenses are mainly focused on mitigating white-box attacks. They do not properly examine black-box attacks. In this paper, we expand upon the analyses of these defenses to include [...] Read more.

Many defenses have recently been proposed at venues like NIPS, ICML, ICLR and CVPR. These defenses are mainly focused on mitigating white-box attacks. They do not properly examine black-box attacks. In this paper, we expand upon the analyses of these defenses to include adaptive black-box adversaries. Our evaluation is done on nine defenses including Barrage of Random Transforms, ComDefend, Ensemble Diversity, Feature Distillation, The Odds are Odd, Error Correcting Codes, Distribution Classifier Defense, K-Winner Take All and Buffer Zones. Our investigation is done using two black-box adversarial models and six widely studied adversarial attacks for CIFAR-10 and Fashion-MNIST datasets. Our analyses show most recent defenses (7 out of 9) provide only marginal improvements in security (<25%), as compared to undefended networks. For every defense, we also show the relationship between the amount of data the adversary has at their disposal, and the effectiveness of adaptive black-box attacks. Overall, our results paint a clear picture: defenses need both thorough white-box and black-box analyses to be considered secure. We provide this large scale study and analyses to motivate the field to move towards the development of more robust black-box defenses. Full article

(This article belongs to the Topic Artificial Intelligence and Sustainable Energy Systems)

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19 pages, 15317 KiB

Open AccessArticle

An Adaptive Deblurring Vehicle Detection Method for High-Speed Moving Drones: Resistance to Shake

by Yan Liu, Jingwen Wang, Tiantian Qiu and Wenting Qi

Entropy 2021, 23(10), 1358; https://doi.org/10.3390/e23101358 - 18 Oct 2021

Cited by 4 | Viewed by 1876

Abstract

Vehicle detection is an essential part of an intelligent traffic system, which is an important research field in drone application. Because unmanned aerial vehicles (UAVs) are rarely configured with stable camera platforms, aerial images are easily blurred. There is a challenge for detectors [...] Read more.

Vehicle detection is an essential part of an intelligent traffic system, which is an important research field in drone application. Because unmanned aerial vehicles (UAVs) are rarely configured with stable camera platforms, aerial images are easily blurred. There is a challenge for detectors to accurately locate vehicles in blurred images in the target detection process. To improve the detection performance of blurred images, an end-to-end adaptive vehicle detection algorithm (DCNet) for drones is proposed in this article. First, the clarity evaluation module is used to determine adaptively whether the input image is a blurred image using improved information entropy. An improved GAN called Drone-GAN is proposed to enhance the vehicle features of blurred images. Extensive experiments were performed, the results of which show that the proposed method can detect both blurred and clear images well in poor environments (complex illumination and occlusion). The detector proposed achieves larger gains compared with SOTA detectors. The proposed method can enhance the vehicle feature details in blurred images effectively and improve the detection accuracy of blurred aerial images, which shows good performance with regard to resistance to shake. Full article

(This article belongs to the Special Issue Adaptive Signal Processing and Machine Learning Using Entropy and Information Theory)

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21 pages, 15624 KiB

Open AccessFeature PaperArticle

The Resolved Mutual Information Function as a Structural Fingerprint of Biomolecular Sequences for Interpretable Machine Learning Classifiers

by Katrin Sophie Bohnsack, Marika Kaden, Julia Abel, Sascha Saralajew and Thomas Villmann

Entropy 2021, 23(10), 1357; https://doi.org/10.3390/e23101357 - 17 Oct 2021

Cited by 3 | Viewed by 2371

Abstract

In the present article we propose the application of variants of the mutual information function as characteristic fingerprints of biomolecular sequences for classification analysis. In particular, we consider the resolved mutual information functions based on Shannon-, Rényi-, and Tsallis-entropy. In combination with interpretable [...] Read more.

In the present article we propose the application of variants of the mutual information function as characteristic fingerprints of biomolecular sequences for classification analysis. In particular, we consider the resolved mutual information functions based on Shannon-, Rényi-, and Tsallis-entropy. In combination with interpretable machine learning classifier models based on generalized learning vector quantization, a powerful methodology for sequence classification is achieved which allows substantial knowledge extraction in addition to the high classification ability due to the model-inherent robustness. Any potential (slightly) inferior performance of the used classifier is compensated by the additional knowledge provided by interpretable models. This knowledge may assist the user in the analysis and understanding of the used data and considered task. After theoretical justification of the concepts, we demonstrate the approach for various example data sets covering different areas in biomolecular sequence analysis. Full article

(This article belongs to the Special Issue Information Theory Based Methods in Machine Learning and Bioinformatics)

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38 pages, 7648 KiB

Open AccessArticle

Entropy and Wealth

by Demetris Koutsoyiannis and G.-Fivos Sargentis

Entropy 2021, 23(10), 1356; https://doi.org/10.3390/e23101356 - 17 Oct 2021

Cited by 18 | Viewed by 7674

Abstract

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, [...] Read more.

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches to it, we show that entropy has a universal stochastic definition, which is not disorder. Hence, we contend that entropy should be used as a mathematical (stochastic) concept as rigorously as possible, free of metaphoric meanings. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept, and promotes entropy as the mother of creativity and evolution. As the social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether maximum entropy, applied to the distribution of a wealth-related variable, namely annual income, can give an objective description. Using publicly available income data, we show that income distribution is consistent with the principle of maximum entropy. The increase in entropy is associated to increases in society’s wealth, yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in the development of and increase in the entropy of income. Such findings are contrary to the theory of ecological economics and other theories that use the term entropy in a Malthusian perspective. Full article

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22 pages, 1829 KiB

Open AccessArticle

Numerical Prediction of Two-Phase Flow through a Tube Bundle Based on Reduced-Order Model and a Void Fraction Correlation

by Claire Dubot, Cyrille Allery, Vincent Melot, Claudine Béghein, Mourad Oulghelou and Clément Bonneau

Entropy 2021, 23(10), 1355; https://doi.org/10.3390/e23101355 - 16 Oct 2021

Viewed by 2088

Abstract

Predicting the void fraction of a two-phase flow outside of tubes is essential to evaluate the thermohydraulic behaviour in steam generators. Indeed, it determines two-phase mixture properties and affects two-phase mixture velocity, which enable evaluating the pressure drop of the system. The two-fluid [...] Read more.

Predicting the void fraction of a two-phase flow outside of tubes is essential to evaluate the thermohydraulic behaviour in steam generators. Indeed, it determines two-phase mixture properties and affects two-phase mixture velocity, which enable evaluating the pressure drop of the system. The two-fluid model for the numerical simulation of two-phase flows requires interaction laws between phases which are not known and/or reliable for a flow within a tube bundle. Therefore, the mixture model, for which it is easier to implement suitable correlations for tube bundles, is used. Indeed, by expressing the relative velocity as a function of slip, the void fraction model of Feenstra et al. and Hibiki et al. developed for upward cross-flow through horizontal tube bundles is introduced and compared. With the method suggested in this paper, the physical phenomena that occur in tube bundles are taken into consideration. Moreover, the tube bundle is modelled using a porous media approach where the Darcy–Forchheimer term is usually defined by correlations found in the literature. However, for some tube bundle geometries, these correlations are not available. The second goal of the paper is to quickly compute, in quasi-real-time, this term by a non-intrusive parametric reduced model based on Proper Orthogonal Decomposition. This method, named Bi-CITSGM (Bi-Calibrated Interpolation on the Tangent Subspace of the Grassmann Manifold), consists in interpolating the spatial and temporal bases by ITSGM (Interpolation on the Tangent Subspace of the Grassmann Manifold) in order to define the solution for a new parameter. The two developed methods are validated based on the experimental results obtained by Dowlati et al. for a two-phase cross-flow through a horizontal tube bundle. Full article

(This article belongs to the Special Issue Statistical Fluid Dynamics)

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21 pages, 4274 KiB

Open AccessArticle

A General Rate-Distortion Optimization Method for Block Compressed Sensing of Images

by Qunlin Chen, Derong Chen and Jiulu Gong

Entropy 2021, 23(10), 1354; https://doi.org/10.3390/e23101354 - 16 Oct 2021

Cited by 1 | Viewed by 1524

Abstract

Block compressed sensing (BCS) is a promising technology for image sampling and compression for resource-constrained applications, but it needs to balance the sampling rate and quantization bit-depth for a bit-rate constraint. In this paper, we summarize the commonly used CS quantization frameworks into [...] Read more.

Block compressed sensing (BCS) is a promising technology for image sampling and compression for resource-constrained applications, but it needs to balance the sampling rate and quantization bit-depth for a bit-rate constraint. In this paper, we summarize the commonly used CS quantization frameworks into a unified framework, and a new bit-rate model and a model of the optimal bit-depth are proposed for the unified CS framework. The proposed bit-rate model reveals the relationship between the bit-rate, sampling rate, and bit-depth based on the information entropy of generalized Gaussian distribution. The optimal bit-depth model can predict the optimal bit-depth of CS measurements at a given bit-rate. Then, we propose a general algorithm for choosing sampling rate and bit-depth based on the proposed models. Experimental results show that the proposed algorithm achieves near-optimal rate-distortion performance for the uniform quantization framework and predictive quantization framework in BCS. Full article

(This article belongs to the Special Issue Data Compression and Complexity)

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13 pages, 11972 KiB

Open AccessEditor’s ChoiceArticle

Quantum Probes for the Characterization of Nonlinear Media

by Alessandro Candeloro, Sholeh Razavian, Matteo Piccolini, Berihu Teklu, Stefano Olivares and Matteo G. A. Paris

Entropy 2021, 23(10), 1353; https://doi.org/10.3390/e23101353 - 16 Oct 2021

Cited by 13 | Viewed by 1799

Abstract

Active optical media leading to interaction Hamiltonians of the form

H = \tilde{λ} {(a + a^{†})}^{ζ}

represent a crucial resource for quantum optical technology. In this paper, we address the characterization of those nonlinear media using quantum probes, [...] Read more.

Active optical media leading to interaction Hamiltonians of the form

H = \tilde{λ} {(a + a^{†})}^{ζ}

represent a crucial resource for quantum optical technology. In this paper, we address the characterization of those nonlinear media using quantum probes, as opposed to semiclassical ones. In particular, we investigate how squeezed probes may improve individual and joint estimation of the nonlinear coupling

\tilde{λ}

and of the nonlinearity order

ζ

. Upon using tools from quantum estimation, we show that: (i) the two parameters are compatible, i.e., the may be jointly estimated without additional quantum noise; (ii) the use of squeezed probes improves precision at fixed overall energy of the probe; (iii) for low energy probes, squeezed vacuum represent the most convenient choice, whereas for increasing energy an optimal squeezing fraction may be determined; (iv) using optimized quantum probes, the scaling of the corresponding precision with energy improves, both for individual and joint estimation of the two parameters, compared to semiclassical coherent probes. We conclude that quantum probes represent a resource to enhance precision in the characterization of nonlinear media, and foresee potential applications with current technology. Full article

(This article belongs to the Special Issue Quantum Communication)

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21 pages, 370 KiB

Open AccessArticle

Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale

by Jean Mawhin, Ewa Skrzypek and Katarzyna Szymańska-Dȩbowska

Entropy 2021, 23(10), 1352; https://doi.org/10.3390/e23101352 - 16 Oct 2021

Viewed by 1416

Abstract

This paper is devoted to study the existence of solutions and their regularity in the

p (t)

–Laplacian Dirichlet problem on a bounded time scale. First, we prove a lemma of du Bois–Reymond type in time-scale settings. Then, using direct variational [...] Read more.

This paper is devoted to study the existence of solutions and their regularity in the

p (t)

–Laplacian Dirichlet problem on a bounded time scale. First, we prove a lemma of du Bois–Reymond type in time-scale settings. Then, using direct variational methods and the mountain pass methodology, we present several sufficient conditions for the existence of solutions to the Dirichlet problem. Full article

18 pages, 3206 KiB

Open AccessArticle

A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise

by Chenghao Shan, Weidong Zhou, Yefeng Yang and Hanyu Shan

Entropy 2021, 23(10), 1351; https://doi.org/10.3390/e23101351 - 16 Oct 2021

Cited by 3 | Viewed by 1703

Abstract

In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussian-Student’s t [...] Read more.

In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussian-Student’s t-mixture distribution via employing a Bernoulli random variable (BM). Secondly, by utilizing another Bernoulli random variable (BL), the form of the likelihood function consisting of two mixture distributions was converted from a weight sum to an exponential product and a new hierarchical Gaussian state-space model was therefore established. Finally, the system state vector, BM, BL, the intermediate random variables, the mixing probability, and the UTVMLP were jointly inferred by employing the variational Bayesian technique. Simulation results revealed that in the scenario of NSHTMN, the proposed filter had a better performance than current algorithms and further improved the estimation accuracy of UTVMLP. Full article

(This article belongs to the Special Issue Advances in Image Fusion)

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12 pages, 340 KiB

Open AccessArticle

Minimum Entropy Production Effect on a Quantum Scale

by Ferenc Márkus and Katalin Gambár

Entropy 2021, 23(10), 1350; https://doi.org/10.3390/e23101350 - 15 Oct 2021

Cited by 3 | Viewed by 1451

Abstract

The discovery of quantized electric conductance by the group of van Wees in 1988 was a major breakthrough in physics. A decade later, the group of Schwab has proven the existence of quantized thermal conductance. Advancing from these and many other aspects of [...] Read more.

The discovery of quantized electric conductance by the group of van Wees in 1988 was a major breakthrough in physics. A decade later, the group of Schwab has proven the existence of quantized thermal conductance. Advancing from these and many other aspects of the quantized conductances in other phenomena of nature, the concept of quantized entropy current can be established and it eases the description of a transferred quantized energy package. This might yield a universal transport behavior of the microscopic world. During the transfer of a single energy quantum, hν, between two neighboring domains, the minimum entropy increment is calculated. It is pointed out that the possible existence of the minimal entropy transfer can be formulated. Moreover, as a new result, it is proved that this minimal entropy transfer principle is equivalent to the Lagrangian description of thermodynamics. Full article

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11 pages, 692 KiB

Open AccessArticle

A Multi-Modal Fusion Method Based on Higher-Order Orthogonal Iteration Decomposition

by Fen Liu , Jianfeng Chen , Weijie Tan and Chang Cai

Entropy 2021, 23(10), 1349; https://doi.org/10.3390/e23101349 - 15 Oct 2021

Cited by 6 | Viewed by 1869

Abstract

Multi-modal fusion can achieve better predictions through the amalgamation of information from different modalities. To improve the performance of accuracy, a method based on Higher-order Orthogonal Iteration Decomposition and Projection (HOIDP) is proposed, in the fusion process, higher-order orthogonal iteration decomposition algorithm and [...] Read more.

Multi-modal fusion can achieve better predictions through the amalgamation of information from different modalities. To improve the performance of accuracy, a method based on Higher-order Orthogonal Iteration Decomposition and Projection (HOIDP) is proposed, in the fusion process, higher-order orthogonal iteration decomposition algorithm and factor matrix projection are used to remove redundant information duplicated inter-modal and produce fewer parameters with minimal information loss. The performance of the proposed method is verified by three different multi-modal datasets. The numerical results validate the accuracy of the performance of the proposed method having 0.4% to 4% improvement in sentiment analysis, 0.3% to 8% improvement in personality trait recognition, and 0.2% to 25% improvement in emotion recognition at three different multi-modal datasets compared with other 5 methods. Full article

(This article belongs to the Special Issue Advances in Image Fusion)

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24 pages, 583 KiB

Open AccessArticle

Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application

by Eugene A. Opoku, Syed Ejaz Ahmed and Farouk S. Nathoo

Entropy 2021, 23(10), 1348; https://doi.org/10.3390/e23101348 - 15 Oct 2021

Cited by 2 | Viewed by 1424

Abstract

In a host of business applications, biomedical and epidemiological studies, the problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis for linear mixed models (LMM). We consider an efficient estimation strategy for high-dimensional data application, where the dimensions [...] Read more.

In a host of business applications, biomedical and epidemiological studies, the problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis for linear mixed models (LMM). We consider an efficient estimation strategy for high-dimensional data application, where the dimensions of the parameters are larger than the number of observations. In this paper, we are interested in estimating the fixed effects parameters of the LMM when it is assumed that some prior information is available in the form of linear restrictions on the parameters. We propose the pretest and shrinkage estimation strategies using the ridge full model as the base estimator. We establish the asymptotic distributional bias and risks of the suggested estimators and investigate their relative performance with respect to the ridge full model estimator. Furthermore, we compare the numerical performance of the LASSO-type estimators with the pretest and shrinkage ridge estimators. The methodology is investigated using simulation studies and then demonstrated on an application exploring how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease. Full article

(This article belongs to the Special Issue Big Data Analytics and Information Science for Business and Biomedical Applications II)

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19 pages, 3193 KiB

Open AccessArticle

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

by Qian Wang and Marko Robnik

Entropy 2021, 23(10), 1347; https://doi.org/10.3390/e23101347 - 15 Oct 2021

Cited by 11 | Viewed by 2155

Abstract

We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical [...] Read more.

We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos. Full article

(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)

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26 pages, 2784 KiB

Open AccessArticle

A Network Theory Approach to Curriculum Design

by John O’Meara and Ashwin Vaidya

Entropy 2021, 23(10), 1346; https://doi.org/10.3390/e23101346 - 15 Oct 2021

Cited by 6 | Viewed by 3042

Abstract

In this paper we hypothesize that education, especially at the scale of curriculum, should be treated as a complex system composed of different ideas and concepts which are inherently connected. Therefore, the task of a good teacher lies in elucidating these connections and [...] Read more.

In this paper we hypothesize that education, especially at the scale of curriculum, should be treated as a complex system composed of different ideas and concepts which are inherently connected. Therefore, the task of a good teacher lies in elucidating these connections and helping students make their own connections. Such a pedagogy allows students to personalize learning and strive to be ‘creative’ and make meaning out of old ideas. The novel contribution of this work lies in the mathematical approach we undertake to verify our hypothesis. We take the example of a precalculus course curriculum to make our case. We treat textbooks as exemplars of a specific pedagogy and map several texts into networks of isolated (nodes) and interconnected concepts (edges) thereby permitting computations of metrics which have much relevance to the education theorists, teachers and all others involved in the field of education. We contend that network metrics such as average path length, clustering coefficient and degree distribution provide valuable insights to teachers and students about the kind of pedagogy which encourages good teaching and learning. Full article

(This article belongs to the Special Issue Entropy and Organization in Natural and Social Systems)

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11 pages, 1450 KiB

Open AccessArticle

The Spread of Ideas in a Network—The Garbage-Can Model

by Dorota Żuchowska-Skiba, Maria Stojkow, Malgorzata J. Krawczyk and Krzysztof Kułakowski

Entropy 2021, 23(10), 1345; https://doi.org/10.3390/e23101345 - 14 Oct 2021

Cited by 1 | Viewed by 1700

Abstract

The main goal of our work is to show how ideas change in social networks. Our analysis is based on three concepts: (i) temporal networks, (ii) the Axelrod model of culture dissemination, (iii) the garbage can model of organizational choice. The use of [...] Read more.

The main goal of our work is to show how ideas change in social networks. Our analysis is based on three concepts: (i) temporal networks, (ii) the Axelrod model of culture dissemination, (iii) the garbage can model of organizational choice. The use of the concept of temporal networks allows us to show the dynamics of ideas spreading processes in networks, thanks to the analysis of contacts between agents in networks. The Axelrod culture dissemination model allows us to use the importance of cooperative behavior for the dynamics of ideas disseminated in networks. In the third model decisions on solutions of problems are made as an outcome of sequences of pseudorandom numbers. The origin of this model is the Herbert Simon’s view on bounded rationality. In the Axelrod model, ideas are conveyed by strings of symbols. The outcome of the model should be the diversity of evolving ideas as dependent on the chain length, on the number of possible values of symbols and on the threshold value of Hamming distance which enables the combination. Full article

(This article belongs to the Special Issue Entropy and Social Physics)

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11 pages, 379 KiB

Open AccessArticle

Economic Cycles of Carnot Type

by Constantin Udriste, Vladimir Golubyatnikov and Ionel Tevy

Entropy 2021, 23(10), 1344; https://doi.org/10.3390/e23101344 - 14 Oct 2021

Cited by 2 | Viewed by 1734

Abstract

Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature [...] Read more.

Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. The first aim of this paper is to introduce and study the economic Carnot cycles concerning Roegenian economics, using our thermodynamic–economic dictionary. These cycles are described in both a

Q - P

diagram and a

E - I

diagram. An economic Carnot cycle has a maximum efficiency for a reversible economic “engine”. Three problems together with their solutions clarify the meaning of the economic Carnot cycle, in our context. Then we transform the ideal gas theory into the ideal income theory. The second aim is to analyze the economic Van der Waals equation, showing that the diffeomorphic-invariant information about the Van der Waals surface can be obtained by examining a cuspidal potential. Full article

(This article belongs to the Special Issue Geometric Structure of Thermodynamics: Theory and Applications)

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13 pages, 1036 KiB

Open AccessArticle

Dynein-Inspired Multilane Exclusion Process with Open Boundary Conditions

by Riya Nandi, Uwe C. Täuber and Priyanka

Entropy 2021, 23(10), 1343; https://doi.org/10.3390/e23101343 - 14 Oct 2021

Cited by 2 | Viewed by 1557

Abstract

Motivated by the sidewise motions of dynein motors shown in experiments, we use a variant of the exclusion process to model the multistep dynamics of dyneins on a cylinder with open ends. Due to the varied step sizes of the particles in a [...] Read more.

Motivated by the sidewise motions of dynein motors shown in experiments, we use a variant of the exclusion process to model the multistep dynamics of dyneins on a cylinder with open ends. Due to the varied step sizes of the particles in a quasi-two-dimensional topology, we observe the emergence of a novel phase diagram depending on the various load conditions. Under high-load conditions, our numerical findings yield results similar to the TASEP model with the presence of all three standard TASEP phases, namely the low-density (LD), high-density (HD), and maximal-current (MC) phases. However, for medium- to low-load conditions, for all chosen influx and outflux rates, we only observe the LD and HD phases, and the maximal-current phase disappears. Further, we also measure the dynamics for a single dynein particle which is logarithmically slower than a TASEP particle with a shorter waiting time. Our results also confirm experimental observations of the dwell time distribution: The dwell time distribution for dyneins is exponential in less crowded conditions, whereas a double exponential emerges under overcrowded conditions. Full article

(This article belongs to the Special Issue Statistical Physics of Living Systems)

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8 pages, 1844 KiB

Open AccessArticle

Intelligent Reflecting Surface Assisted Multi-User Robust Secret Key Generation for Low-Entropy Environments

by Yuwei Gao, Dengke Guo, Jun Xiong and Dongtang Ma

Entropy 2021, 23(10), 1342; https://doi.org/10.3390/e23101342 - 14 Oct 2021

Cited by 3 | Viewed by 1500

Abstract

Channel secret key generation (CSKG), assisted by the new material intelligent reflecting surface (IRS), has become a new research hotspot recently. In this paper, the key extraction method in the IRS-aided low-entropy communication scenario with adjacent multi-users is investigated. Aiming at the problem [...] Read more.

Channel secret key generation (CSKG), assisted by the new material intelligent reflecting surface (IRS), has become a new research hotspot recently. In this paper, the key extraction method in the IRS-aided low-entropy communication scenario with adjacent multi-users is investigated. Aiming at the problem of low key generation efficiency due to the high similarity of channels between users, we propose a joint user allocation and IRS reflection parameter adjustment scheme, while the reliability of information exchange during the key generation process is also considered. Specifically, the relevant key capability expressions of the IRS-aided communication system is analyzed. Then, we study how to adjust the IRS reflection matrix and allocate the corresponding users to minimize the similarity of different channels and ensure the robustness of key generation. The simulation results show that the proposed scheme can bring higher gains to the performance of key generation. Full article

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15 pages, 39821 KiB

Open AccessArticle

A Hidden Chaotic System with Multiple Attractors

by Xiefu Zhang, Zean Tian, Jian Li, Xianming Wu and Zhongwei Cui

Entropy 2021, 23(10), 1341; https://doi.org/10.3390/e23101341 - 14 Oct 2021

Cited by 6 | Viewed by 1545

Abstract

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven [...] Read more.

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability. Full article

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14 pages, 3223 KiB

Open AccessReview

Entropy: From Thermodynamics to Information Processing

by Jordão Natal, Ivonete Ávila, Victor Batista Tsukahara, Marcelo Pinheiro and Carlos Dias Maciel

Entropy 2021, 23(10), 1340; https://doi.org/10.3390/e23101340 - 14 Oct 2021

Cited by 12 | Viewed by 6017

Abstract

Entropy is a concept that emerged in the 19th century. It used to be associated with heat harnessed by a thermal machine to perform work during the Industrial Revolution. However, there was an unprecedented scientific revolution in the 20th century due to one [...] Read more.

Entropy is a concept that emerged in the 19th century. It used to be associated with heat harnessed by a thermal machine to perform work during the Industrial Revolution. However, there was an unprecedented scientific revolution in the 20th century due to one of its most essential innovations, i.e., the information theory, which also encompasses the concept of entropy. Therefore, the following question is naturally raised: “what is the difference, if any, between concepts of entropy in each field of knowledge?” There are misconceptions, as there have been multiple attempts to conciliate the entropy of thermodynamics with that of information theory. Entropy is most commonly defined as “disorder”, although it is not a good analogy since “order” is a subjective human concept, and “disorder” cannot always be obtained from entropy. Therefore, this paper presents a historical background on the evolution of the term “entropy”, and provides mathematical evidence and logical arguments regarding its interconnection in various scientific areas, with the objective of providing a theoretical review and reference material for a broad audience. Full article

(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)

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Entropy, Volume 23, Issue 10 (October 2021) – 133 articles

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