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Volume 23
Issue 3
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Entropy, Volume 23, Issue 3 (March 2021) – 120 articles

Cover Story (view full-size image): State changes of systems due to interventions of "intelligent beings'' that can lead to a decrease in entropy are widely discussed in the literature. We propose here to take them as examples of "conditional actions'' and to describe them mathematically as "instruments'' following the quantum theory of measurement. As a detailed case study, we calculate the imperfect erasure of a qubit, which can also be considered as a conditional action and is realized by coupling a spin to another small spin system in its ground state. This analysis casts a critical light on the widely accepted Landauer–Bennett principle. From our point of view, erasing memory content appears as an additional conditional action, but it is neither necessary nor sufficient to solve Maxwell's demon paradox. View this paper
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26 pages, 3947 KiB  
Article
Non Stationary Multi-Armed Bandit: Empirical Evaluation of a New Concept Drift-Aware Algorithm
by Emanuele Cavenaghi, Gabriele Sottocornola, Fabio Stella and Markus Zanker
Entropy 2021, 23(3), 380; https://doi.org/10.3390/e23030380 - 23 Mar 2021
Cited by 10 | Viewed by 3979
Abstract
The Multi-Armed Bandit (MAB) problem has been extensively studied in order to address real-world challenges related to sequential decision making. In this setting, an agent selects the best action to be performed at time-step t, based on the past rewards received by [...] Read more.
The Multi-Armed Bandit (MAB) problem has been extensively studied in order to address real-world challenges related to sequential decision making. In this setting, an agent selects the best action to be performed at time-step t, based on the past rewards received by the environment. This formulation implicitly assumes that the expected payoff for each action is kept stationary by the environment through time. Nevertheless, in many real-world applications this assumption does not hold and the agent has to face a non-stationary environment, that is, with a changing reward distribution. Thus, we present a new MAB algorithm, named f-Discounted-Sliding-Window Thompson Sampling (f-dsw TS), for non-stationary environments, that is, when the data streaming is affected by concept drift. The f-dsw TS algorithm is based on Thompson Sampling (TS) and exploits a discount factor on the reward history and an arm-related sliding window to contrast concept drift in non-stationary environments. We investigate how to combine these two sources of information, namely the discount factor and the sliding window, by means of an aggregation function f(.). In particular, we proposed a pessimistic (f=min), an optimistic (f=max), as well as an averaged (f=mean) version of the f-dsw TS algorithm. A rich set of numerical experiments is performed to evaluate the f-dsw TS algorithm compared to both stationary and non-stationary state-of-the-art TS baselines. We exploited synthetic environments (both randomly-generated and controlled) to test the MAB algorithms under different types of drift, that is, sudden/abrupt, incremental, gradual and increasing/decreasing drift. Furthermore, we adapt four real-world active learning tasks to our framework—a prediction task on crimes in the city of Baltimore, a classification task on insects species, a recommendation task on local web-news, and a time-series analysis on microbial organisms in the tropical air ecosystem. The f-dsw TS approach emerges as the best performing MAB algorithm. At least one of the versions of f-dsw TS performs better than the baselines in synthetic environments, proving the robustness of f-dsw TS under different concept drift types. Moreover, the pessimistic version (f=min) results as the most effective in all real-world tasks. Full article
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26 pages, 383 KiB  
Article
Potential Well in Poincaré Recurrence
by Miguel Abadi, Vitor Amorim and Sandro Gallo
Entropy 2021, 23(3), 379; https://doi.org/10.3390/e23030379 - 23 Mar 2021
Cited by 1 | Viewed by 1726
Abstract
From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence [...] Read more.
From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence time distributions in mixing stochastic processes and dynamical systems. Besides providing a review of the different scaling factors used in the literature in recurrence times, the present work contributes two new results: (1) For ϕ-mixing and ψ-mixing processes, we give a new exponential approximation for hitting and return times using the potential well as the scaling parameter. The error terms are explicit and sharp. (2) We analyse the uniform positivity of the potential well. Our results apply to processes on countable alphabets and do not assume a complete grammar. Full article
(This article belongs to the Special Issue Extreme Value Theory)
11 pages, 1362 KiB  
Article
Design of Optimal Rainfall Monitoring Network Using Radar and Road Networks
by Taeyong Kwon, Seongsim Yoon and Sanghoo Yoon
Entropy 2021, 23(3), 378; https://doi.org/10.3390/e23030378 - 23 Mar 2021
Viewed by 1641
Abstract
Uncertainty in the rainfall network can lead to mistakes in dam operation. Sudden increases in dam water levels due to rainfall uncertainty are a high disaster risk. In order to prevent these losses, it is necessary to configure an appropriate rainfall network that [...] Read more.
Uncertainty in the rainfall network can lead to mistakes in dam operation. Sudden increases in dam water levels due to rainfall uncertainty are a high disaster risk. In order to prevent these losses, it is necessary to configure an appropriate rainfall network that can effectively reflect the characteristics of the watershed. In this study, conditional entropy was used to calculate the uncertainty of the watershed using rainfall and radar data observed from 2018 to 2019 in the Goesan Dam and Hwacheon Dam watersheds. The results identified radar data suitable for the characteristics of the watershed and proposed a site for an additional rainfall gauge. It is also necessary to select the location of the additional rainfall gauged by limiting the points where smooth movement and installation, for example crossing national borders, are difficult. The proposed site emphasized accessibility and usability by leveraging road information and selecting a radar grid near the road. As a practice result, the uncertainty of precipitation in the Goesan and Hwacheon Dam watersheds could be decreased by 70.0% and 67.9%, respectively, when four and three additional gauge sites were installed without any restriction. When these were installed near to the road, with five and four additional gauge sites, the uncertainty in the Goesan Dam and Hwacheon Dam watersheds were reduced by up to 71.1%. Therefore, due to the high degree of uncertainty, it is necessary to measure precipitation. The operation of the rainfall gauge can provide a smooth site and configure an appropriate monitoring network. Full article
(This article belongs to the Special Issue Application of Information-Theoretic Concepts in Bio-, Environmental and Engineering Science Research)
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14 pages, 326 KiB  
Article
On the Classical Capacity of General Quantum Gaussian Measurement
by Alexander Holevo
Entropy 2021, 23(3), 377; https://doi.org/10.3390/e23030377 - 21 Mar 2021
Cited by 6 | Viewed by 2349
Abstract
In this paper, we consider the classical capacity problem for Gaussian measurement channels. We establish Gaussianity of the average state of the optimal ensemble in the general case and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. Then, we [...] Read more.
In this paper, we consider the classical capacity problem for Gaussian measurement channels. We establish Gaussianity of the average state of the optimal ensemble in the general case and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. Then, we consider the case of one mode in detail, including the dual problem of accessible information of a Gaussian ensemble. Our findings are relevant to practical situations in quantum communications where the receiver is Gaussian (say, a general-dyne detection) and concatenation of the Gaussian channel and the receiver can be considered as one Gaussian measurement channel. Our efforts in this and preceding papers are then aimed at establishing full Gaussianity of the optimal ensemble (usually taken as an assumption) in such schemes. Full article
(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher)
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18 pages, 1247 KiB  
Article
A Generative Adversarial Network for Infrared and Visible Image Fusion Based on Semantic Segmentation
by Jilei Hou, Dazhi Zhang, Wei Wu, Jiayi Ma and Huabing Zhou
Entropy 2021, 23(3), 376; https://doi.org/10.3390/e23030376 - 21 Mar 2021
Cited by 40 | Viewed by 4354
Abstract
This paper proposes a new generative adversarial network for infrared and visible image fusion based on semantic segmentation (SSGAN), which can consider not only the low-level features of infrared and visible images, but also the high-level semantic information. Source images can be divided [...] Read more.
This paper proposes a new generative adversarial network for infrared and visible image fusion based on semantic segmentation (SSGAN), which can consider not only the low-level features of infrared and visible images, but also the high-level semantic information. Source images can be divided into foregrounds and backgrounds by semantic masks. The generator with a dual-encoder-single-decoder framework is used to extract the feature of foregrounds and backgrounds by different encoder paths. Moreover, the discriminator’s input image is designed based on semantic segmentation, which is obtained by combining the foregrounds of the infrared images with the backgrounds of the visible images. Consequently, the prominence of thermal targets in the infrared images and texture details in the visible images can be preserved in the fused images simultaneously. Qualitative and quantitative experiments on publicly available datasets demonstrate that the proposed approach can significantly outperform the state-of-the-art methods. Full article
(This article belongs to the Special Issue Advances in Image Fusion)
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13 pages, 798 KiB  
Article
The Impact of Visual Input and Support Area Manipulation on Postural Control in Subjects after Osteoporotic Vertebral Fracture
by Michalina Błażkiewicz, Justyna Kędziorek and Anna Hadamus
Entropy 2021, 23(3), 375; https://doi.org/10.3390/e23030375 - 20 Mar 2021
Cited by 6 | Viewed by 2234
Abstract
Osteoporosis is a prevalent health concern among older adults and is associated with an increased risk of falls that may result in fracture, injury, or even death. Identifying the risk factors for falls and assessing the complexity of postural control within this population [...] Read more.
Osteoporosis is a prevalent health concern among older adults and is associated with an increased risk of falls that may result in fracture, injury, or even death. Identifying the risk factors for falls and assessing the complexity of postural control within this population is essential for developing effective regimes for fall prevention. The aim of this study was to assess postural control in individuals recovering from osteoporotic vertebral fractures while performing various stability tasks. Seventeen individuals with type II osteoporosis and 17 healthy subjects participated in this study. The study involved maintaining balance while standing barefoot on both feet for 20 s on an Advanced Mechanical Technology Inc. (AMTI) plate, with eyes open, eyes closed, and eyes closed in conjunction with a dual-task. Another three trials lasting 10 s each were undertaken during a single-leg stance under the same conditions. Fall risk was assessed using the Biodex Balance platform. Nonlinear measures were used to assess center of pressure (CoP) dynamics in all trials. Reducing the support area or elimination of the visual control led to increased sample entropy and fractal dimension. Results of the nonlinear measurements indicate that individuals recovering from osteoporotic vertebral fractures are characterized by decreased irregularity, mainly in the medio-lateral direction and reduced complexity. Full article
(This article belongs to the Special Issue Information Theory in Biomedical Data Mining)
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14 pages, 3405 KiB  
Communication
Industry 4.0 Quantum Strategic Organizational Design Configurations. The Case of 3 Qubits: One Reports to Two
by Javier Villalba-Diez, Juan Carlos Losada, Rosa María Benito and Ana González-Marcos
Entropy 2021, 23(3), 374; https://doi.org/10.3390/e23030374 - 20 Mar 2021
Cited by 5 | Viewed by 2081
Abstract
In this work we explore how the relationship between one subordinate reporting to two leaders influences the alignment of the latter with the company’s strategic objectives in an Industry 4.0 environment. We do this through the implementation of quantum circuits that represent decision [...] Read more.
In this work we explore how the relationship between one subordinate reporting to two leaders influences the alignment of the latter with the company’s strategic objectives in an Industry 4.0 environment. We do this through the implementation of quantum circuits that represent decision networks. This is done for two cases: One in which the leaders do not communicate with each other, and one in which they do. Through the quantum simulation of strategic organizational design configurations (QSOD) through 500 quantum circuit simulations, we conclude that in the first case both leaders are not simultaneously in alignment, and in the second case that both reporting nodes need to have an alignment probability higher than 90% to support the leader node. Full article
(This article belongs to the Special Issue Quantum Approach to Game Theory and Social Science)
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24 pages, 3104 KiB  
Article
Vector Arithmetic in the Triangular Grid
by Khaled Abuhmaidan, Monther Aldwairi and Benedek Nagy
Entropy 2021, 23(3), 373; https://doi.org/10.3390/e23030373 - 20 Mar 2021
Cited by 2 | Viewed by 2366
Abstract
Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: [...] Read more.
Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid. Full article
(This article belongs to the Special Issue Exploring the NP-Complexity of Nature: Critical Phenomena, Chaos, Fractals, Graphs, Boson Sampling, Quantum Computing and More)
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16 pages, 483 KiB  
Article
Monitoring the Zero-Inflated Time Series Model of Counts with Random Coefficient
by Cong Li, Shuai Cui and Dehui Wang
Entropy 2021, 23(3), 372; https://doi.org/10.3390/e23030372 - 20 Mar 2021
Cited by 3 | Viewed by 2499
Abstract
In this research, we consider monitoring mean and correlation changes from zero-inflated autocorrelated count data based on the integer-valued time series model with random survival rate. A cumulative sum control chart is constructed due to its efficiency, the corresponding calculation methods of average [...] Read more.
In this research, we consider monitoring mean and correlation changes from zero-inflated autocorrelated count data based on the integer-valued time series model with random survival rate. A cumulative sum control chart is constructed due to its efficiency, the corresponding calculation methods of average run length and the standard deviation of the run length are given. Practical guidelines concerning the chart design are investigated. Extensive computations based on designs of experiments are conducted to illustrate the validity of the proposed method. Comparisons with the conventional control charting procedure are also provided. The analysis of the monthly number of drug crimes in the city of Pittsburgh is displayed to illustrate our current method of process monitoring. Full article
(This article belongs to the Special Issue Time Series Modelling)
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15 pages, 3549 KiB  
Article
Demonstration of Three True Random Number Generator Circuits Using Memristor Created Entropy and Commercial Off-the-Shelf Components
by Scott Stoller and Kristy A. Campbell
Entropy 2021, 23(3), 371; https://doi.org/10.3390/e23030371 - 20 Mar 2021
Cited by 9 | Viewed by 2903
Abstract
In this work, we build and test three memristor-based true random number generator (TRNG) circuits: two previously presented in the literature and one which is our own design. The functionality of each circuit is assessed using the National Institute of Standards and Technology [...] Read more.
In this work, we build and test three memristor-based true random number generator (TRNG) circuits: two previously presented in the literature and one which is our own design. The functionality of each circuit is assessed using the National Institute of Standards and Technology (NIST) Statistical Test Suite (STS). The TRNG circuits were built using commercially available off-the-shelf parts, including the memristor. The results of this work confirm the usefulness of memristors for successful implementation of TRNG circuits, as well as the ease with which a TRNG can be built using simple circuit designs and off-the-shelf breadboard circuit components. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II)
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27 pages, 409 KiB  
Article
The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity
by Massimo Tessarotto and Claudio Cremaschini
Entropy 2021, 23(3), 370; https://doi.org/10.3390/e23030370 - 20 Mar 2021
Cited by 3 | Viewed by 1665
Abstract
An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum [...] Read more.
An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics. Full article
(This article belongs to the Special Issue Quantum Regularization of Singular Black Hole Solutions)
11 pages, 1340 KiB  
Article
Spectral Ranking of Causal Influence in Complex Systems
by Errol Zalmijn, Tom Heskes and Tom Claassen
Entropy 2021, 23(3), 369; https://doi.org/10.3390/e23030369 - 20 Mar 2021
Cited by 1 | Viewed by 3727
Abstract
Similar to natural complex systems, such as the Earth’s climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors measure relevant process variables at appropriate [...] Read more.
Similar to natural complex systems, such as the Earth’s climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors measure relevant process variables at appropriate sampling rates, to provide time series as primary sources for system diagnostics. However, high-dimensionality, non-linearity and non-stationarity of the data are major challenges to efficiently, yet accurately, diagnose rare or new system issues by merely using model-based approaches. To reliably narrow down the causal search space, we validate a ranking algorithm that applies transfer entropy for bivariate interaction analysis of a system’s multivariate time series to obtain a weighted directed graph, and graph eigenvector centrality to identify the system’s most important sources of original information or causal influence. The results suggest that this approach robustly identifies the true drivers or causes of a complex system’s deviant behavior, even when its reconstructed information transfer network includes redundant edges. Full article
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18 pages, 3275 KiB  
Article
Stirling Refrigerating Machine Modeling Using Schmidt and Finite Physical Dimensions Thermodynamic Models: A Comparison with Experiments
by Cătălina Dobre, Lavinia Grosu, Alexandru Dobrovicescu, Georgiana Chişiu and Mihaela Constantin
Entropy 2021, 23(3), 368; https://doi.org/10.3390/e23030368 - 19 Mar 2021
Cited by 6 | Viewed by 2824
Abstract
The purpose of the study is to show that two simple models that take into account only the irreversibility due to temperature difference in the heat exchangers and imperfect regeneration are able to indicate refrigerating machine behavior. In the present paper, the finite [...] Read more.
The purpose of the study is to show that two simple models that take into account only the irreversibility due to temperature difference in the heat exchangers and imperfect regeneration are able to indicate refrigerating machine behavior. In the present paper, the finite physical dimensions thermodynamics (FPDT) method and 0-D modeling using the Schmidt model with imperfect regeneration were applied in the study of a β type Stirling refrigeration machine.The 0-D modeling is improved by including the irreversibility caused by imperfect regeneration and the finite temperature difference between the gas and the heat exchangers wall. A flowchart of the Stirling refrigerator exergy balance is presented to show the internal and external irreversibilities. It is found that the irreversibility at the regenerator level is more important than that at the heat exchangers level. The energies exchanged by the working gas are expressed according to the practical parameters, necessary for the engineer during the entire project. The results of the two thermodynamic models are presented in comparison with the experimental results, which leads to validation of the proposed FPDT model for the functional and constructive parameters of the studied refrigerating machine. Full article
(This article belongs to the Special Issue Carnot Cycle and Heat Engine Fundamentals and Applications II)
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25 pages, 412 KiB  
Article
Robust Estimation for Bivariate Poisson INGARCH Models
by Byungsoo Kim, Sangyeol Lee and Dongwon Kim
Entropy 2021, 23(3), 367; https://doi.org/10.3390/e23030367 - 19 Mar 2021
Cited by 7 | Viewed by 2277
Abstract
In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we consider a robust estimation method for bivariate Poisson INGARCH models while using the [...] Read more.
In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we consider a robust estimation method for bivariate Poisson INGARCH models while using the minimum density power divergence estimator. We demonstrate the proposed estimator is consistent and asymptotically normal under certain regularity conditions. Monte Carlo simulations are conducted to evaluate the performance of the estimator in the presence of outliers. Finally, a real data analysis using monthly count series of crimes in New South Wales and an artificial data example are provided as an illustration. Full article
(This article belongs to the Special Issue Time Series Modelling)
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16 pages, 318 KiB  
Article
Classical and Quantum H-Theorem Revisited: Variational Entropy and Relaxation Processes
by Carlos Medel-Portugal, Juan Manuel Solano-Altamirano and José Luis E. Carrillo-Estrada
Entropy 2021, 23(3), 366; https://doi.org/10.3390/e23030366 - 19 Mar 2021
Cited by 2 | Viewed by 2350
Abstract
We propose a novel framework to describe the time-evolution of dilute classical and quantum gases, initially out of equilibrium and with spatial inhomogeneities, towards equilibrium. Briefly, we divide the system into small cells and consider the local equilibrium hypothesis. We subsequently define a [...] Read more.
We propose a novel framework to describe the time-evolution of dilute classical and quantum gases, initially out of equilibrium and with spatial inhomogeneities, towards equilibrium. Briefly, we divide the system into small cells and consider the local equilibrium hypothesis. We subsequently define a global functional that is the sum of cell H-functionals. Each cell functional recovers the corresponding Maxwell–Boltzmann, Fermi–Dirac, or Bose–Einstein distribution function, depending on the classical or quantum nature of the gas. The time-evolution of the system is described by the relationship dH/dt≤0, and the equality condition occurs if the system is in the equilibrium state. Via the variational method, proof of the previous relationship, which might be an extension of the H-theorem for inhomogeneous systems, is presented for both classical and quantum gases. Furthermore, the H-functionals are in agreement with the correspondence principle. We discuss how the H-functionals can be identified with the system’s entropy and analyze the relaxation processes of out-of-equilibrium systems. Full article
(This article belongs to the Special Issue The Statistical Foundations of Entropy)
22 pages, 561 KiB  
Article
TSARM-UDP: An Efficient Time Series Association Rules Mining Algorithm Based on Up-to-Date Patterns
by Qiang Zhao, Qing Li, Deshui Yu and Yinghua Han
Entropy 2021, 23(3), 365; https://doi.org/10.3390/e23030365 - 19 Mar 2021
Cited by 4 | Viewed by 2221
Abstract
In many industrial domains, there is a significant interest in obtaining temporal relationships among multiple variables in time-series data, given that such relationships play an auxiliary role in decision making. However, when transactions occur frequently only for a period of time, it is [...] Read more.
In many industrial domains, there is a significant interest in obtaining temporal relationships among multiple variables in time-series data, given that such relationships play an auxiliary role in decision making. However, when transactions occur frequently only for a period of time, it is difficult for a traditional time-series association rules mining algorithm (TSARM) to identify this kind of relationship. In this paper, we propose a new TSARM framework and a novel algorithm named TSARM-UDP. A TSARM mining framework is used to mine time-series association rules (TSARs) and an up-to-date pattern (UDP) is applied to discover rare patterns that only appear in a period of time. Based on the up-to-date pattern mining, the proposed TSAR-UDP method could extract temporal relationship rules with better generality. The rules can be widely used in the process industry, the stock market, etc. Experiments are then performed on the public stock data and real blast furnace data to verify the effectiveness of the proposed algorithm. We compare our algorithm with three state-of-the-art algorithms, and the experimental results show that our algorithm can provide greater efficiency and interpretability in TSARs and that it has good prospects. Full article
(This article belongs to the Section Signal and Data Analysis)
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32 pages, 459 KiB  
Review
Telegraphic Transport Processes and Their Fractional Generalization: A Review and Some Extensions
by Jaume Masoliver
Entropy 2021, 23(3), 364; https://doi.org/10.3390/e23030364 - 18 Mar 2021
Cited by 14 | Viewed by 1852
Abstract
We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of [...] Read more.
We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations. Full article
(This article belongs to the Special Issue Fractional Calculus and the Future of Science)
10 pages, 777 KiB  
Article
Discrete Versions of Jensen–Fisher, Fisher and Bayes–Fisher Information Measures of Finite Mixture Distributions
by Omid Kharazmi and Narayanaswamy Balakrishnan
Entropy 2021, 23(3), 363; https://doi.org/10.3390/e23030363 - 18 Mar 2021
Viewed by 1834
Abstract
In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing parameter vector of a finite mixture probability mass function [...] Read more.
In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback–Leibler, Jeffreys and Jensen–Shannon divergences. Full article
(This article belongs to the Special Issue Measures of Information)
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29 pages, 1389 KiB  
Article
Mechanism Integrated Information
by Leonardo S. Barbosa, William Marshall, Larissa Albantakis and Giulio Tononi
Entropy 2021, 23(3), 362; https://doi.org/10.3390/e23030362 - 18 Mar 2021
Cited by 22 | Viewed by 5328
Abstract
The Integrated Information Theory (IIT) of consciousness starts from essential phenomenological properties, which are then translated into postulates that any physical system must satisfy in order to specify the physical substrate of consciousness. We recently introduced an information measure (Barbosa et al., 2020) [...] Read more.
The Integrated Information Theory (IIT) of consciousness starts from essential phenomenological properties, which are then translated into postulates that any physical system must satisfy in order to specify the physical substrate of consciousness. We recently introduced an information measure (Barbosa et al., 2020) that captures three postulates of IIT—existence, intrinsicality and information—and is unique. Here we show that the new measure also satisfies the remaining postulates of IIT—integration and exclusion—and create the framework that identifies maximally irreducible mechanisms. These mechanisms can then form maximally irreducible systems, which in turn will specify the physical substrate of conscious experience. Full article
(This article belongs to the Special Issue Integrated Information Theory and Consciousness)
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23 pages, 23313 KiB  
Article
Hyper-Chaotic Color Image Encryption Based on Transformed Zigzag Diffusion and RNA Operation
by Duzhong Zhang, Lexing Chen and Taiyong Li
Entropy 2021, 23(3), 361; https://doi.org/10.3390/e23030361 - 17 Mar 2021
Cited by 34 | Viewed by 2637
Abstract
With increasing utilization of digital multimedia and the Internet, protection on this digital information from cracks has become a hot topic in the communication field. As a path for protecting digital visual information, image encryption plays a crucial role in modern society. In [...] Read more.
With increasing utilization of digital multimedia and the Internet, protection on this digital information from cracks has become a hot topic in the communication field. As a path for protecting digital visual information, image encryption plays a crucial role in modern society. In this paper, a novel six-dimensional (6D) hyper-chaotic encryption scheme with three-dimensional (3D) transformed Zigzag diffusion and RNA operation (HCZRNA) is proposed for color images. For this HCZRNA scheme, four phases are included. First, three pseudo-random matrices are generated from the 6D hyper-chaotic system. Second, plaintext color image would be permuted by using the first pseudo-random matrix to convert to an initial cipher image. Third, the initial cipher image is placed on cube for 3D transformed Zigzag diffusion using the second pseudo-random matrix. Finally, the diffused image is converted to RNA codons array and updated through RNA codons tables, which are generated by codons and the third pseudo-random matrix. After four phases, a cipher image is obtained, and the experimental results show that HCZRNA has high resistance against well-known attacks and it is superior to other schemes. Full article
(This article belongs to the Special Issue Entropy in Image Analysis III)
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11 pages, 2020 KiB  
Article
Experimental and Theoretical Analysis of Metal Complex Diffusion through Cell Monolayer
by Katarzyna Gałczyńska, Jarosław Rachuna, Karol Ciepluch, Magdalena Kowalska, Sławomir Wąsik, Tadeusz Kosztołowicz, Katarzyna D. Lewandowska, Jacek Semaniak, Krystyna Kurdziel and Michał Arabski
Entropy 2021, 23(3), 360; https://doi.org/10.3390/e23030360 - 17 Mar 2021
Cited by 2 | Viewed by 1775
Abstract
The study of drugs diffusion through different biological membranes constitutes an essential step in the development of new pharmaceuticals. In this study, the method based on the monolayer cell culture of CHO-K1 cells has been developed in order to emulate the epithelial cells [...] Read more.
The study of drugs diffusion through different biological membranes constitutes an essential step in the development of new pharmaceuticals. In this study, the method based on the monolayer cell culture of CHO-K1 cells has been developed in order to emulate the epithelial cells barrier in permeability studies by laser interferometry. Laser interferometry was employed for the experimental analysis of nickel(II) and cobalt(II) complexes with 1-allylimidazole or their chlorides’ diffusion through eukaryotic cell monolayers. The amount (mol) of nickel(II) and cobalt(II) chlorides transported through the monolayer was greater than that of metals complexed with 1-allylimidazole by 4.34-fold and 1.45-fold, respectively, after 60 min. Thus, laser interferometry can be used for the quantitative analysis of the transport of compounds through eukaryotic cell monolayers, and the resulting parameters can be used to formulate a mathematical description of this process. Full article
(This article belongs to the Special Issue Thermodynamic Modelling in Membrane)
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11 pages, 1608 KiB  
Article
Are Gait and Balance Problems in Neurological Patients Interdependent? Enhanced Analysis Using Gait Indices, Cyclograms, Balance Parameters and Entropy
by Malgorzata Syczewska, Ewa Szczerbik, Malgorzata Kalinowska, Anna Swiecicka and Grazyna Graff
Entropy 2021, 23(3), 359; https://doi.org/10.3390/e23030359 - 17 Mar 2021
Cited by 3 | Viewed by 1726
Abstract
Background: Balance and locomotion are two main complex functions, which require intact and efficient neuromuscular and sensory systems, and their proper integration. In many studies the assumption of their dependence is present, and some rehabilitation approaches are based on it. Other papers undermine [...] Read more.
Background: Balance and locomotion are two main complex functions, which require intact and efficient neuromuscular and sensory systems, and their proper integration. In many studies the assumption of their dependence is present, and some rehabilitation approaches are based on it. Other papers undermine this assumption. Therefore the aim of this study was to examine the possible dependence between gait and balance in patients with neurological or sensory integration problems, which affected their balance. Methods: 75 patients (52 with neurological diseases, 23 with sensory integration problems) participated in the study. They underwent balance assessment on Kistler force plate in two conditions, six tests on a Balance Biodex System and instrumented gait analysis with VICON. The gait and balances parameters and indices, together with entropy and cyclograms were used for the analysis. Spearman correlation, multiple regression, cluster analysis, and discriminant analysis were used as analytical tools. Results: The analysis divided patients into 2 groups with 100% correctly classified cases. Some balance and gait measures are better in the first group, but some others in the second. Conclusions: This finding confirms the hypothesis that there is no direct link between gait and balance deficits. Full article
(This article belongs to the Special Issue Information Theory in Biomedical Data Mining)
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17 pages, 495 KiB  
Article
Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities
by Gamal G. L. Nashed and Kazuharu Bamba
Entropy 2021, 23(3), 358; https://doi.org/10.3390/e23030358 - 17 Mar 2021
Cited by 4 | Viewed by 2035
Abstract
We explore the quadratic form of the f(R)=R+bR2 gravitational theory to derive rotating N-dimensions black hole solutions with ai,i≥1 rotation parameters. Here, R is the Ricci scalar and [...] Read more.
We explore the quadratic form of the f(R)=R+bR2 gravitational theory to derive rotating N-dimensions black hole solutions with ai,i≥1 rotation parameters. Here, R is the Ricci scalar and b is the dimensional parameter. We assumed that the N-dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter b, whereas, in the case of N>4, it depends on parameter b, owing to the contribution of the correction R2 term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter b to be b<116Λ to obtain a positive entropy. Full article
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology III)
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14 pages, 325 KiB  
Article
Critical Comparison of MaxCal and Other Stochastic Modeling Approaches in Analysis of Gene Networks
by Taylor Firman, Jonathan Huihui, Austin R. Clark and Kingshuk Ghosh
Entropy 2021, 23(3), 357; https://doi.org/10.3390/e23030357 - 17 Mar 2021
Cited by 1 | Viewed by 2206
Abstract
Learning the underlying details of a gene network with feedback is critical in designing new synthetic circuits. Yet, quantitative characterization of these circuits remains limited. This is due to the fact that experiments can only measure partial information from which the details of [...] Read more.
Learning the underlying details of a gene network with feedback is critical in designing new synthetic circuits. Yet, quantitative characterization of these circuits remains limited. This is due to the fact that experiments can only measure partial information from which the details of the circuit must be inferred. One potentially useful avenue is to harness hidden information from single-cell stochastic gene expression time trajectories measured for long periods of time—recorded at frequent intervals—over multiple cells. This raises the feasibility vs. accuracy dilemma while deciding between different models of mining these stochastic trajectories. We demonstrate that inference based on the Maximum Caliber (MaxCal) principle is the method of choice by critically evaluating its computational efficiency and accuracy against two other typical modeling approaches: (i) a detailed model (DM) with explicit consideration of multiple molecules including protein-promoter interaction, and (ii) a coarse-grain model (CGM) using Hill type functions to model feedback. MaxCal provides a reasonably accurate model while being significantly more computationally efficient than DM and CGM. Furthermore, MaxCal requires minimal assumptions since it is a top-down approach and allows systematic model improvement by including constraints of higher order, in contrast to traditional bottom-up approaches that require more parameters or ad hoc assumptions. Thus, based on efficiency, accuracy, and ability to build minimal models, we propose MaxCal as a superior alternative to traditional approaches (DM, CGM) when inferring underlying details of gene circuits with feedback from limited data. Full article
(This article belongs to the Special Issue Information Theory and Biology: Seeking General Principles)
14 pages, 315 KiB  
Article
Results on Varextropy Measure of Random Variables
by Nastaran Marzban Vaselabadi, Saeid Tahmasebi, Mohammad Reza Kazemi and Francesco Buono
Entropy 2021, 23(3), 356; https://doi.org/10.3390/e23030356 - 17 Mar 2021
Cited by 8 | Viewed by 1927
Abstract
In 2015, Lad, Sanfilippo and Agrò proposed an alternative measure of uncertainty dual to the entropy known as extropy. This paper provides some results on a dispersion measure of extropy of random variables which is called varextropy and studies several properties of this [...] Read more.
In 2015, Lad, Sanfilippo and Agrò proposed an alternative measure of uncertainty dual to the entropy known as extropy. This paper provides some results on a dispersion measure of extropy of random variables which is called varextropy and studies several properties of this concept. Especially, the varextropy measure of residual and past lifetimes, order statistics, record values and proportional hazard rate models are discussed. Moreover, the conditional varextropy is considered and some properties of this measure are studied. Finally, a new stochastic comparison method, named varextropy ordering, is introduced and some of its properties are presented. Full article
(This article belongs to the Special Issue Measures of Information)
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18 pages, 310 KiB  
Article
Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory
by Andrei Khrennikov and Noboru Watanabe
Entropy 2021, 23(3), 355; https://doi.org/10.3390/e23030355 - 16 Mar 2021
Cited by 6 | Viewed by 1839
Abstract
This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the [...] Read more.
This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence. Full article
(This article belongs to the Special Issue Quantum Models of Cognition and Decision-Making)
16 pages, 5950 KiB  
Review
Beating Standard Quantum Limit with Weak Measurement
by Geng Chen, Peng Yin, Wen-Hao Zhang, Gong-Chu Li, Chuan-Feng Li and Guang-Can Guo
Entropy 2021, 23(3), 354; https://doi.org/10.3390/e23030354 - 16 Mar 2021
Cited by 11 | Viewed by 2984
Abstract
Weak measurements have been under intensive investigation in both experiment and theory. Numerous experiments have indicated that the amplified meter shift is produced by the post-selection, yielding an improved precision compared to conventional methods. However, this amplification effect comes at the cost of [...] Read more.
Weak measurements have been under intensive investigation in both experiment and theory. Numerous experiments have indicated that the amplified meter shift is produced by the post-selection, yielding an improved precision compared to conventional methods. However, this amplification effect comes at the cost of a reduced rate of acquiring data, which leads to an increasing uncertainty to determine the level of meter shift. From this point of view, a number of theoretical works have suggested that weak measurements cannot improve the precision, or even damage the metrology information due to the post-selection. In this review, we give a comprehensive analysis of the weak measurements to justify their positive effect on prompting measurement precision. As a further step, we introduce two modified weak measurement protocols to boost the precision beyond the standard quantum limit. Compared to previous works beating the standard quantum limit, these protocols are free of using entangled or squeezed states. The achieved precision outperforms that of the conventional method by two orders of magnitude and attains a practical Heisenberg scaling up to n=106 photons. Full article
(This article belongs to the Special Issue Lectures on Recent Experimental Achievements in Quantum-Enhanced Technologies)
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13 pages, 497 KiB  
Article
Simulating Finite-Time Isothermal Processes with Superconducting Quantum Circuits
by Jin-Fu Chen, Ying Li and Hui Dong
Entropy 2021, 23(3), 353; https://doi.org/10.3390/e23030353 - 16 Mar 2021
Cited by 8 | Viewed by 2101
Abstract
Finite-time isothermal processes are ubiquitous in quantum-heat-engine cycles, yet complicated due to the coexistence of the changing Hamiltonian and the interaction with the thermal bath. Such complexity prevents classical thermodynamic measurements of a performed work. In this paper, the isothermal process is decomposed [...] Read more.
Finite-time isothermal processes are ubiquitous in quantum-heat-engine cycles, yet complicated due to the coexistence of the changing Hamiltonian and the interaction with the thermal bath. Such complexity prevents classical thermodynamic measurements of a performed work. In this paper, the isothermal process is decomposed into piecewise adiabatic and isochoric processes to measure the performed work as the internal energy change in adiabatic processes. The piecewise control scheme allows the direct simulation of the whole process on a universal quantum computer, which provides a new experimental platform to study quantum thermodynamics. We implement the simulation on ibmqx2 to show the 1/τ scaling of the extra work in finite-time isothermal processes. Full article
(This article belongs to the Special Issue Carnot Cycle and Heat Engine Fundamentals and Applications II)
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19 pages, 4805 KiB  
Article
Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market
by Janusz Miśkiewicz
Entropy 2021, 23(3), 352; https://doi.org/10.3390/e23030352 - 15 Mar 2021
Cited by 6 | Viewed by 2325
Abstract
Within the paper, the problem of globalisation during financial crises is analysed. The research is based on the Forex exchange rates. In the analysis, the power law classification scheme (PLCS) is used. The study shows that during crises cross-correlations increase resulting in significant [...] Read more.
Within the paper, the problem of globalisation during financial crises is analysed. The research is based on the Forex exchange rates. In the analysis, the power law classification scheme (PLCS) is used. The study shows that during crises cross-correlations increase resulting in significant growth of cliques, and also the ranks of nodes on the converging time series network are growing. This suggests that the crises expose the globalisation processes, which can be verified by the proposed analysis. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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14 pages, 716 KiB  
Article
Interstage Pressures of a Multistage Compressor with Intercooling
by Helen Lugo-Méndez, Teresa Lopez-Arenas, Alejandro Torres-Aldaco, Edgar Vicente Torres-González, Mauricio Sales-Cruz and Raúl Lugo-Leyte
Entropy 2021, 23(3), 351; https://doi.org/10.3390/e23030351 - 15 Mar 2021
Cited by 6 | Viewed by 2415
Abstract
This paper considers the criterion of minimum compression work to derive an expression for the interstage pressure of a multistage compressor with intercooling that includes the gas properties, pressure drops in the intercoolers, different suction gas temperatures, and isentropic efficiencies in each compression [...] Read more.
This paper considers the criterion of minimum compression work to derive an expression for the interstage pressure of a multistage compressor with intercooling that includes the gas properties, pressure drops in the intercoolers, different suction gas temperatures, and isentropic efficiencies in each compression stage. The analytical expression for the interstage pressures is applied to estimate the number of compression stages and to evaluate its applicability in order to estimate interstage pressures in the operation of multistage compressors, which can be especially useful when their measurements are not available. Full article
(This article belongs to the Section Thermodynamics)
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