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Entropy, Volume 25, Issue 8 (August 2023) – 134 articles

Cover Story (view full-size image): Let us consider a triangular hypergraph with three vertices and three hyperedges in an n-dim space, n ≥ 3. If we tried to assign 0 and 1 to vertices, so that just one vertex within each of the three hyperedges is assigned 1, we would realise that this is not possible. The hypergraph exhibits a non-Kochen–Specker (KS) contextuality. Why “non-”? Because KS hypergraphs violate the same condition, but each of their hyperedges must contain n vertices. How can we generate non-KS hypergraphs? Via a dimensional upscaling which does not scale with dimension. The minimal number of their hyperedges is ≤ 9 in up to 16-dim spaces. View this paper
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15 pages, 343 KiB  
Article
Quality of Security Guarantees for and with Physical Unclonable Functions and Biometric Secrecy Systems
by Onur Günlü, Rafael F. Schaefer and H. Vincent Poor
Entropy 2023, 25(8), 1243; https://doi.org/10.3390/e25081243 - 21 Aug 2023
Viewed by 1013
Abstract
Unique digital circuit outputs, considered as physical unclonable function (PUF) circuit outputs, can facilitate a secure and reliable secret key agreement. To tackle noise and high correlations between the PUF circuit outputs, transform coding methods combined with scalar quantizers are typically applied to [...] Read more.
Unique digital circuit outputs, considered as physical unclonable function (PUF) circuit outputs, can facilitate a secure and reliable secret key agreement. To tackle noise and high correlations between the PUF circuit outputs, transform coding methods combined with scalar quantizers are typically applied to extract the uncorrelated bit sequences reliably. In this paper, we create realistic models for these transformed outputs by fitting truncated distributions to them. We also show that the state-of-the-art models are inadequate to guarantee a target reliability level for all PUF outputs, which also means that secrecy cannot be guaranteed. Therefore, we introduce a quality of security parameter to control the percentage of the PUF circuit outputs for which a target security level can be guaranteed. By applying the finite-length information theory results to a public ring oscillator output dataset, we illustrate that security guarantees can be provided for each bit extracted from any PUF device by eliminating only a small subset of PUF circuit outputs. Furthermore, we conversely show that it is not possible to provide reliability or security guarantees without eliminating any PUF circuit output. Our holistic methods and analyses can be applied to any PUF type, as well as any biometric secrecy system, with continuous-valued outputs to extract secret keys with low hardware complexity. Full article
(This article belongs to the Special Issue Information Security and Privacy: From IoT to IoV)
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10 pages, 299 KiB  
Article
A Maximum Entropy Resolution to the Wine/Water Paradox
by Michael C. Parker and Chris Jeynes
Entropy 2023, 25(8), 1242; https://doi.org/10.3390/e25081242 - 21 Aug 2023
Cited by 1 | Viewed by 1005
Abstract
The Principle of Indifference (‘PI’: the simplest non-informative prior in Bayesian probability) has been shown to lead to paradoxes since Bertrand (1889). Von Mises (1928) introduced the ‘Wine/Water Paradox’ as a resonant example of a ‘Bertrand paradox’, which has been presented as demonstrating [...] Read more.
The Principle of Indifference (‘PI’: the simplest non-informative prior in Bayesian probability) has been shown to lead to paradoxes since Bertrand (1889). Von Mises (1928) introduced the ‘Wine/Water Paradox’ as a resonant example of a ‘Bertrand paradox’, which has been presented as demonstrating that the PI must be rejected. We now resolve these paradoxes using a Maximum Entropy (MaxEnt) treatment of the PI that also includes information provided by Benford’s ‘Law of Anomalous Numbers’ (1938). We show that the PI should be understood to represent a family of informationally identical MaxEnt solutions, each solution being identified with its own explicitly justified boundary condition. In particular, our solution to the Wine/Water Paradox exploits Benford’s Law to construct a non-uniform distribution representing the universal constraint of scale invariance, which is a physical consequence of the Second Law of Thermodynamics. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
20 pages, 5422 KiB  
Article
Projective Synchronization of Delayed Uncertain Coupled Memristive Neural Networks and Their Application
by Zhen Han, Naipeng Chen, Xiaofeng Wei, Manman Yuan and Huijia Li
Entropy 2023, 25(8), 1241; https://doi.org/10.3390/e25081241 - 21 Aug 2023
Cited by 1 | Viewed by 920
Abstract
In this article, the authors analyzed the nonlinear effects of projective synchronization between coupled memristive neural networks (MNNs) and their applications. Since the complete signal transmission is difficult under parameter mismatch and different projective factors, the delays, which are time-varying, and uncertainties have [...] Read more.
In this article, the authors analyzed the nonlinear effects of projective synchronization between coupled memristive neural networks (MNNs) and their applications. Since the complete signal transmission is difficult under parameter mismatch and different projective factors, the delays, which are time-varying, and uncertainties have been taken to realize the projective synchronization of MNNs with multi-links under the nonlinear control method. Through the extended comparison principle and a new approach to dealing with the mismatched parameters, sufficient criteria have been determined under different types of projective factors and the framework of the Lyapunov–Krasovskii functional (LKF) for projective convergence of the coupled MNNs. Instead of the classical treatment for secure communication, the concept of error of synchronization between the drive and response systems has been applied to solve the signal encryption/decryption problem. Finally, the simulations in numerical form have been demonstrated graphically to confirm the adaptability of the theoretical results. Full article
(This article belongs to the Special Issue Signal and Information Processing in Networks)
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13 pages, 980 KiB  
Article
Spreading Dynamics of Capital Flow Transfer in Complex Financial Networks
by Wenyan Peng, Tingting Chen, Bo Zheng and Xiongfei Jiang
Entropy 2023, 25(8), 1240; https://doi.org/10.3390/e25081240 - 21 Aug 2023
Cited by 1 | Viewed by 1087
Abstract
The financial system, a complex network, operates primarily through the exchange of capital, where the role of information is critical. This study utilizes the transfer entropy method to examine the strength and direction of information flow among different capital flow time series and [...] Read more.
The financial system, a complex network, operates primarily through the exchange of capital, where the role of information is critical. This study utilizes the transfer entropy method to examine the strength and direction of information flow among different capital flow time series and investigate the community structure within the transfer networks. Moreover, the spreading dynamics of the capital flow transfer networks are observed, and the importance and traveling time of each node are explored. The results imply a dominant role for the food and drink industry within the Chinese market, with increased attention towards the computer industry starting in 2014. The community structure of the capital flow transfer networks significantly differs from those constructed from stock prices, with the main sector predominantly encompassing industry leaders favored by primary funds with robust capital flow connections. The average traveling time from sectors such as food and drink, coal, and utilities to other sectors is the shortest, and the dynamic flow between these sectors displays a significant role. These findings highlight that comprehension of information flow and community structure within the financial system can offer valuable insights into market dynamics and help to identify key sectors and companies. Full article
(This article belongs to the Special Issue Complexity, Entropy and the Physics of Information)
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16 pages, 2563 KiB  
Article
Quantifying Entropy in Response Times (RT) Distributions Using the Cumulative Residual Entropy (CRE) Function
by Daniel Fitousi
Entropy 2023, 25(8), 1239; https://doi.org/10.3390/e25081239 - 21 Aug 2023
Cited by 1 | Viewed by 985
Abstract
Response times (RT) distributions are routinely used by psychologists and neuroscientists in the assessment and modeling of human behavior and cognition. The statistical properties of RT distributions are valuable in uncovering unobservable psychological mechanisms. A potentially important statistical aspect of RT distributions is [...] Read more.
Response times (RT) distributions are routinely used by psychologists and neuroscientists in the assessment and modeling of human behavior and cognition. The statistical properties of RT distributions are valuable in uncovering unobservable psychological mechanisms. A potentially important statistical aspect of RT distributions is their entropy. However, to date, no valid measure of entropy on RT distributions has been developed, mainly because available extensions of discrete entropy measures to continuous distributions were fraught with problems and inconsistencies. The present work takes advantage of the cumulative residual entropy (CRE) function—a well-known differential entropy measure that can circumvent those problems. Applications of the CRE to RT distributions are presented along with concrete examples and simulations. In addition, a novel measure of instantaneous CRE is developed that captures the rate of entropy reduction (or information gain) from a stimulus as a function of processing time. Taken together, the new measures of entropy in RT distributions proposed here allow for stronger statistical inferences, as well as motivated theoretical interpretations of psychological constructs such as mental effort and processing efficiency. Full article
(This article belongs to the Section Entropy and Biology)
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21 pages, 1341 KiB  
Article
Comparative Study of Variations in Quantum Approximate Optimization Algorithms for the Traveling Salesman Problem
by Wenyang Qian, Robert A. M. Basili, Mary Mehrnoosh Eshaghian-Wilner, Ashfaq Khokhar, Glenn Luecke and James P. Vary
Entropy 2023, 25(8), 1238; https://doi.org/10.3390/e25081238 - 21 Aug 2023
Cited by 2 | Viewed by 1567
Abstract
The traveling salesman problem (TSP) is one of the most often-used NP-hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the [...] Read more.
The traveling salesman problem (TSP) is one of the most often-used NP-hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this paper, we tackle the TSP using the quantum approximate optimization algorithm (QAOA) approach by formulating it as an optimization problem. By adopting an improved qubit encoding strategy and a layer-wise learning optimization protocol, we present numerical results obtained from the gate-based digital quantum simulator, specifically targeting TSP instances with 3, 4, and 5 cities. We focus on the evaluations of three distinctive QAOA mixer designs, considering their performances in terms of numerical accuracy and optimization cost. Notably, we find that a well-balanced QAOA mixer design exhibits more promising potential for gate-based simulators and realistic quantum devices in the long run, an observation further supported by our noise model simulations. Furthermore, we investigate the sensitivity of the simulations to the TSP graph. Overall, our simulation results show that the digital quantum simulation of problem-inspired ansatz is a successful candidate for finding optimal TSP solutions. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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18 pages, 5071 KiB  
Article
Synergetic Theory of Information Entropy Based on Failure Approach Index for Stability Analysis of Surrounding Rock System
by Lijun Xiong, Haiping Yuan, Gaoliang Liu, Hengzhe Li, Yangyao Zou, Xiaohu Liu and Xiaoming Li
Entropy 2023, 25(8), 1237; https://doi.org/10.3390/e25081237 - 20 Aug 2023
Cited by 1 | Viewed by 1027
Abstract
It is generally acknowledged that the stability evaluation of surrounding rock denotes nonlinear complex system engineering. In order to accurately and quantitatively assess the safety states of surrounding rock and provide a scientific basis for the prevention and control of surrounding rock stability, [...] Read more.
It is generally acknowledged that the stability evaluation of surrounding rock denotes nonlinear complex system engineering. In order to accurately and quantitatively assess the safety states of surrounding rock and provide a scientific basis for the prevention and control of surrounding rock stability, the analysis method of the synergetic theory of information entropy using the failure approach index has been proposed. By means of deriving the general relationship between the total two-dimensional plastic shear strain and the total three-dimensional plastic shear strain and obtaining the numerical limit analysis step of the plastic shear strain, the threshold value of the ultimate plastic shear strain can be determined, which has provided the key criterion for the calculation of the information entropy based on the failure approach index. In addition, combining with the synergetic theory of the principle of maximum information entropy, the evolution equation of the excavation step and information entropy based on the failure approach index of the surrounding rock system in underground mining space are established, and the equations of the general solution and particular solution as well as the expression of the destabilizing excavation step are given. To account for this, the method is applied to analyze the failure states of the floor surrounding rock after the mining of the 71 coal seam in Xutuan Coal Mine and involve the disturbance effect and stability control method of the underlying 72 coal seam roof from the macroscopic and microscopic aspects. Consequently, the validity of the analysis method of synergetic theory of information entropy based on the failure approach index has been verified, which presents an updated approach for the stability evaluation of surrounding rock systems that is of satisfactory capability and value in engineering applications. Full article
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19 pages, 11607 KiB  
Article
A Wealth Distribution Agent Model Based on a Few Universal Assumptions
by Matheus Calvelli and Evaldo M. F. Curado
Entropy 2023, 25(8), 1236; https://doi.org/10.3390/e25081236 - 19 Aug 2023
Viewed by 1083
Abstract
We propose a new agent-based model for studying wealth distribution. We show that a model that links wealth to information (interaction and trade among agents) and to trade advantage is able to qualitatively reproduce real wealth distributions, as well as their evolution over [...] Read more.
We propose a new agent-based model for studying wealth distribution. We show that a model that links wealth to information (interaction and trade among agents) and to trade advantage is able to qualitatively reproduce real wealth distributions, as well as their evolution over time and equilibrium distributions. These distributions are shown in four scenarios, with two different taxation schemes where, in each scenario, only one of the taxation schemes is applied. In general, the evolving end state is one of extreme wealth concentration, which can be counteracted with an appropriate wealth-based tax. Taxation on annual income alone cannot prevent the evolution towards extreme wealth concentration. Full article
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22 pages, 2170 KiB  
Article
Variational Bayesian Algorithms for Maneuvering Target Tracking with Nonlinear Measurements in Sensor Networks
by Yumei Hu, Quan Pan, Bao Deng, Zhen Guo, Menghua Li and Lifeng Chen
Entropy 2023, 25(8), 1235; https://doi.org/10.3390/e25081235 - 18 Aug 2023
Viewed by 899
Abstract
The variational Bayesian method solves nonlinear estimation problems by iteratively computing the integral of the marginal density. Many researchers have demonstrated the fact its performance depends on the linear approximation in the computation of the variational density in the iteration and the degree [...] Read more.
The variational Bayesian method solves nonlinear estimation problems by iteratively computing the integral of the marginal density. Many researchers have demonstrated the fact its performance depends on the linear approximation in the computation of the variational density in the iteration and the degree of nonlinearity of the underlying scenario. In this paper, two methods for computing the variational density, namely, the natural gradient method and the simultaneous perturbation stochastic method, are used to implement a variational Bayesian Kalman filter for maneuvering target tracking using Doppler measurements. The latter are collected from a set of sensors subject to single-hop network constraints. We propose a distributed fusion variational Bayesian Kalman filter for a networked maneuvering target tracking scenario and both of the evidence lower bound and the posterior Cramér–Rao lower bound of the proposed methods are presented. The simulation results are compared with centralized fusion in terms of posterior Cramér–Rao lower bounds, root-mean-squared errors and the 3σ bound. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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27 pages, 536 KiB  
Article
Convergence Rates for the Constrained Sampling via Langevin Monte Carlo
by Yuanzheng Zhu
Entropy 2023, 25(8), 1234; https://doi.org/10.3390/e25081234 - 18 Aug 2023
Viewed by 1114
Abstract
Sampling from constrained distributions has posed significant challenges in terms of algorithmic design and non-asymptotic analysis, which are frequently encountered in statistical and machine-learning models. In this study, we propose three sampling algorithms based on Langevin Monte Carlo with the Metropolis–Hastings steps to [...] Read more.
Sampling from constrained distributions has posed significant challenges in terms of algorithmic design and non-asymptotic analysis, which are frequently encountered in statistical and machine-learning models. In this study, we propose three sampling algorithms based on Langevin Monte Carlo with the Metropolis–Hastings steps to handle the distribution constrained within some convex body. We present a rigorous analysis of the corresponding Markov chains and derive non-asymptotic upper bounds on the convergence rates of these algorithms in total variation distance. Our results demonstrate that the sampling algorithm, enhanced with the Metropolis–Hastings steps, offers an effective solution for tackling some constrained sampling problems. The numerical experiments are conducted to compare our methods with several competing algorithms without the Metropolis–Hastings steps, and the results further support our theoretical findings. Full article
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
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33 pages, 7932 KiB  
Article
Fault Diagnosis of Rolling Bearings in Primary Mine Fans under Sample Imbalance Conditions
by Wei Cui, Jun Ding, Guoying Meng, Zhengyan Lv, Yahui Feng, Aiming Wang and Xingwei Wan
Entropy 2023, 25(8), 1233; https://doi.org/10.3390/e25081233 - 18 Aug 2023
Cited by 1 | Viewed by 1213
Abstract
Rolling bearings are crucial parts of primary mine fans. In order to guarantee the safety of coal mine production, primary mine fans commonly work during regular operation and are immediately shut down for repair in case of failure. This causes the sample imbalance [...] Read more.
Rolling bearings are crucial parts of primary mine fans. In order to guarantee the safety of coal mine production, primary mine fans commonly work during regular operation and are immediately shut down for repair in case of failure. This causes the sample imbalance phenomenon in fault diagnosis (FD), i.e., there are many more normal state samples than faulty ones, seriously affecting the precision of FD. Therefore, the current study presents an FD approach for the rolling bearings of primary mine fans under sample imbalance conditions via symmetrized dot pattern (SDP) images, denoising diffusion probabilistic models (DDPMs), the image generation method, and a convolutional neural network (CNN). First, the 1D bearing vibration signal was transformed into an SDP image with significant characteristics, and the DDPM was employed to create a generated image with similar feature distributions to the real fault image of the minority class. Then, the generated images were supplemented into the imbalanced dataset for data augmentation to balance the minority class samples with the majority ones. Finally, a CNN was utilized as a fault diagnosis model to identify and detect the rolling bearings’ operating conditions. In order to assess the efficiency of the presented method, experiments were performed using the regular rolling bearing dataset and primary mine fan rolling bearing data under actual operating situations. The experimental results indicate that the presented method can more efficiently fit the real image samples’ feature distribution and generate image samples with higher similarity than other commonly used methods. Moreover, the diagnostic precision of the FD model can be effectively enhanced by gradually expanding and enhancing the unbalanced dataset. Full article
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21 pages, 3041 KiB  
Article
Microgravity Spherical Droplet Evaporation and Entropy Effects
by Seyedamirhossein Madani and Christopher Depcik
Entropy 2023, 25(8), 1232; https://doi.org/10.3390/e25081232 - 18 Aug 2023
Viewed by 1105
Abstract
Recent efforts to understand low-temperature combustion (LTC) in internal combustion engines highlight the need to improve chemical kinetic mechanisms involved in the negative temperature coefficient (aka cool flame) regime. Interestingly, microgravity droplet combustion experiments demonstrate this cool flame behavior, allowing a greater focus [...] Read more.
Recent efforts to understand low-temperature combustion (LTC) in internal combustion engines highlight the need to improve chemical kinetic mechanisms involved in the negative temperature coefficient (aka cool flame) regime. Interestingly, microgravity droplet combustion experiments demonstrate this cool flame behavior, allowing a greater focus on chemistry after buoyancy, and the corresponding influence of the conservation of momentum is removed. In Experimental terms, the LTC regime is often characterized by a reduction in heat transfer losses. Novel findings in this area demonstrate that lower entropy generation, in conjunction with diminished heat transfer losses, could more definitively define the LTC regime. As a result, the simulation of the entropy equation for spherical droplet combustion under microgravity could help us to investigate fundamental LTC chemical kinetic pathways. To provide a starting point for researchers who are new to this field, this effort first provides a comprehensive and detailed derivation of the conservation of entropy equation using spherical coordinates and gathers all relevant information under one cohesive framework, which is a resource not readily available in the literature. Subsequently, the well-known d2 law analytical model is determined and compared to experimental data that highlight shortcomings of the law. The potential improvements in the d2 law are then discussed, and a numerical model is presented that includes entropy. The resulting codes are available in an online repository to ensure that other researchers interested in expanding this field of work have a fundamental starting point. Full article
(This article belongs to the Special Issue Thermodynamic Evaluation and Optimization of Combustion Processes)
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17 pages, 1695 KiB  
Article
First Detection and Tunneling Time of a Quantum Walk
by Zhenbo Ni and Yujun Zheng
Entropy 2023, 25(8), 1231; https://doi.org/10.3390/e25081231 - 18 Aug 2023
Cited by 1 | Viewed by 835
Abstract
We consider the first detection problem for a one-dimensional quantum walk with repeated local measurements. Employing the stroboscopic projective measurement protocol and the renewal equation, we study the effect of tunneling on the detection time. Specifically, we study the continuous-time quantum walk on [...] Read more.
We consider the first detection problem for a one-dimensional quantum walk with repeated local measurements. Employing the stroboscopic projective measurement protocol and the renewal equation, we study the effect of tunneling on the detection time. Specifically, we study the continuous-time quantum walk on an infinite tight-binding lattice for two typical situations with physical reality. The first is the case of a quantum walk in the absence of tunneling with a Gaussian initial state. The second is the case where a barrier is added to the system. It is shown that the transition of the decay behavior of the first detection probability can be observed by modifying the initial condition, and in the presence of a tunneling barrier, the particle can be detected earlier than the impurity-free lattice. This suggests that the evolution of the walker is expedited when it tunnels through the barrier under repeated measurement. The first detection tunneling time is introduced to investigate the tunneling time of the quantum walk. In addition, we analyze the critical transitive point by deriving an asymptotic formula. Full article
(This article belongs to the Section Quantum Information)
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14 pages, 2020 KiB  
Article
Nonequilibrium Thermodynamics of the Majority Vote Model
by Felipe Hawthorne, Pedro E. Harunari, Mário J. de Oliveira and Carlos E. Fiore
Entropy 2023, 25(8), 1230; https://doi.org/10.3390/e25081230 - 18 Aug 2023
Cited by 2 | Viewed by 967
Abstract
The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. This model, as well as many other stochastic lattice models, are formulated in terms of stochastic rules with no connection [...] Read more.
The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. This model, as well as many other stochastic lattice models, are formulated in terms of stochastic rules with no connection to thermodynamics, precluding the achievement of quantities such as power and heat, as well as their behaviors at phase transition regimes. Here, we circumvent this limitation by introducing the idea of a distinct and well-defined thermal reservoir associated to each local configuration. Thermodynamic properties are derived for a generic majority vote model, irrespective of its neighborhood and lattice topology. The behavior of energy/heat fluxes at phase transitions, whether continuous or discontinuous, in regular and complex topologies, is investigated in detail. Unraveling the contribution of each local configuration explains the nature of the phase diagram and reveals how dissipation arises from the dynamics. Full article
(This article belongs to the Special Issue Non-equilibrium Phase Transitions)
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20 pages, 34080 KiB  
Article
A Hybrid Model for Cardiac Perfusion: Coupling a Discrete Coronary Arterial Tree Model with a Continuous Porous-Media Flow Model of the Myocardium
by João R. Alves, Lucas A. Berg, Evandro D. Gaio, Bernardo M. Rocha, Rafael A. B. de Queiroz and Rodrigo W. dos Santos
Entropy 2023, 25(8), 1229; https://doi.org/10.3390/e25081229 - 18 Aug 2023
Viewed by 1041
Abstract
This paper presents a novel hybrid approach for the computational modeling of cardiac perfusion, combining a discrete model of the coronary arterial tree with a continuous porous-media flow model of the myocardium. The constructive constrained optimization (CCO) algorithm captures the detailed topology and [...] Read more.
This paper presents a novel hybrid approach for the computational modeling of cardiac perfusion, combining a discrete model of the coronary arterial tree with a continuous porous-media flow model of the myocardium. The constructive constrained optimization (CCO) algorithm captures the detailed topology and geometry of the coronary arterial tree network, while Poiseuille’s law governs blood flow within this network. Contrast agent dynamics, crucial for cardiac MRI perfusion assessment, are modeled using reaction–advection–diffusion equations within the porous-media framework. The model incorporates fibrosis–contrast agent interactions and considers contrast agent recirculation to simulate myocardial infarction and Gadolinium-based late-enhancement MRI findings. Numerical experiments simulate various scenarios, including normal perfusion, endocardial ischemia resulting from stenosis, and myocardial infarction. The results demonstrate the model’s efficacy in establishing the relationship between blood flow and stenosis in the coronary arterial tree and contrast agent dynamics and perfusion in the myocardial tissue. The hybrid model enables the integration of information from two different exams: computational fractional flow reserve (cFFR) measurements of the heart coronaries obtained from CT scans and heart perfusion and anatomy derived from MRI scans. The cFFR data can be integrated with the discrete arterial tree, while cardiac perfusion MRI data can be incorporated into the continuum part of the model. This integration enhances clinical understanding and treatment strategies for managing cardiovascular disease. Full article
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16 pages, 463 KiB  
Article
Multi-User PIR with Cyclic Wraparound Multi-Access Caches
by Kanishak Vaidya and Balaji Sundar Rajan
Entropy 2023, 25(8), 1228; https://doi.org/10.3390/e25081228 - 18 Aug 2023
Viewed by 970
Abstract
We consider the problem of multi-access cache-aided multi-user Private Information Retrieval (MACAMuPIR) with cyclic wraparound cache access. In MACAMuPIR, several files are replicated across multiple servers. There are multiple users and multiple cache nodes. When the network is not congested, servers fill these [...] Read more.
We consider the problem of multi-access cache-aided multi-user Private Information Retrieval (MACAMuPIR) with cyclic wraparound cache access. In MACAMuPIR, several files are replicated across multiple servers. There are multiple users and multiple cache nodes. When the network is not congested, servers fill these cache nodes with the content of the files. During peak network traffic, each user accesses several cache nodes. Every user wants to retrieve one file from the servers but does not want the servers to know their demands. This paper proposes a private retrieval scheme for MACAMuPIR and characterizes the transmission cost for multi-access systems with cyclic wraparound cache access. We formalize privacy and correctness constraints and analyze transmission costs. The scheme outperforms the previously known dedicated cache setup, offering efficient and private retrieval. Results demonstrate the effectiveness of the multi-access approach. Our research contributes an efficient, privacy-preserving solution for multi-user PIR, advancing secure data retrieval from distributed servers. Full article
(This article belongs to the Special Issue Information Theory for Distributed Systems)
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16 pages, 1608 KiB  
Article
Quantum Knowledge in Phase Space
by Davi Geiger
Entropy 2023, 25(8), 1227; https://doi.org/10.3390/e25081227 - 17 Aug 2023
Cited by 1 | Viewed by 1123
Abstract
Quantum physics through the lens of Bayesian statistics considers probability to be a degree of belief and subjective. A Bayesian derivation of the probability density function in phase space is presented. Then, a Kullback–Liebler divergence in phase space is introduced to define interference [...] Read more.
Quantum physics through the lens of Bayesian statistics considers probability to be a degree of belief and subjective. A Bayesian derivation of the probability density function in phase space is presented. Then, a Kullback–Liebler divergence in phase space is introduced to define interference and entanglement. Comparisons between each of these two quantities and the entropy are made. A brief presentation of entanglement in phase space to the spin degree of freedom and an extension to mixed states completes the work. Full article
(This article belongs to the Special Issue Shannon Entropy: Mathematical View)
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8 pages, 272 KiB  
Tutorial
Second Law and Its Amendment: The Axiom of No-Reversible Directions Revisited
by Wolfgang Muschik
Entropy 2023, 25(8), 1226; https://doi.org/10.3390/e25081226 - 17 Aug 2023
Cited by 2 | Viewed by 756
Abstract
A toy model is used to describe the following steps to achieve the no-reversible-direction axiom in a tutorial manner: (i) choose a state space results in the balance equations on state space which are linear in the process directions, (ii) avoid a reversible [...] Read more.
A toy model is used to describe the following steps to achieve the no-reversible-direction axiom in a tutorial manner: (i) choose a state space results in the balance equations on state space which are linear in the process directions, (ii) avoid a reversible process direction that cannot be generated via a combination of non-reversible ones, (iii) process directions that are in the kernel of the balance equations and do not enter the entropy production. The Coleman–Mizel formulation of the second law and the Liu relations follow immediately. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
23 pages, 1111 KiB  
Article
Students’ Learning Behaviour in Programming Education Analysis: Insights from Entropy and Community Detection
by Tai Tan Mai, Martin Crane and Marija Bezbradica
Entropy 2023, 25(8), 1225; https://doi.org/10.3390/e25081225 - 17 Aug 2023
Cited by 2 | Viewed by 1643
Abstract
The high dropout rates in programming courses emphasise the need for monitoring and understanding student engagement, enabling early interventions. This activity can be supported by insights into students’ learning behaviours and their relationship with academic performance, derived from student learning log data in [...] Read more.
The high dropout rates in programming courses emphasise the need for monitoring and understanding student engagement, enabling early interventions. This activity can be supported by insights into students’ learning behaviours and their relationship with academic performance, derived from student learning log data in learning management systems. However, the high dimensionality of such data, along with their numerous features, pose challenges to their analysis and interpretability. In this study, we introduce entropy-based metrics as a novel manner to represent students’ learning behaviours. Employing these metrics, in conjunction with a proven community detection method, we undertake an analysis of learning behaviours across higher- and lower-performing student communities. Furthermore, we examine the impact of the COVID-19 pandemic on these behaviours. The study is grounded in the analysis of empirical data from 391 Software Engineering students over three academic years. Our findings reveal that students in higher-performing communities typically tend to have lower volatility in entropy values and reach stable learning states earlier than their lower-performing counterparts. Importantly, this study provides evidence of the use of entropy as a simple yet insightful metric for educators to monitor study progress, enhance understanding of student engagement, and enable timely interventions. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)
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16 pages, 6724 KiB  
Article
Efficient Numerical Simulation of Biochemotaxis Phenomena in Fluid Environments
by Xingying Zhou, Guoqing Bian, Yan Wang and Xufeng Xiao
Entropy 2023, 25(8), 1224; https://doi.org/10.3390/e25081224 - 17 Aug 2023
Viewed by 884
Abstract
A novel dimension splitting method is proposed for the efficient numerical simulation of a biochemotaxis model, which is a coupled system of chemotaxis–fluid equations and incompressible Navier–Stokes equations. A second-order pressure correction method is employed to decouple the velocity and pressure for the [...] Read more.
A novel dimension splitting method is proposed for the efficient numerical simulation of a biochemotaxis model, which is a coupled system of chemotaxis–fluid equations and incompressible Navier–Stokes equations. A second-order pressure correction method is employed to decouple the velocity and pressure for the Navier–Stokes equations. Then, the alternating direction implicit scheme is used to solve the velocity equation, and the operator with dimension splitting effect is used instead of the traditional elliptic operator to solve the pressure equation. For the chemotactic equation, the operator splitting method and extrapolation technique are used to solve oxygen and cell density to achieve second-order time accuracy. The proposed dimension splitting method splits the two-dimensional problem into a one-dimensional problem by splitting the spatial derivative, which reduces the computation and storage costs. Finally, through interesting experiments, we show the evolution of the cell plume shape during the descent process. The effect of changing specific parameters on the velocity and plume shape during the descent process is also studied. Full article
(This article belongs to the Topic Numerical Methods for Partial Differential Equations)
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22 pages, 4289 KiB  
Article
Application of the Fuzzy Approach for Evaluating and Selecting Relevant Objects, Features, and Their Ranges
by Wiesław Paja
Entropy 2023, 25(8), 1223; https://doi.org/10.3390/e25081223 - 17 Aug 2023
Viewed by 764
Abstract
Relevant attribute selection in machine learning is a key aspect aimed at simplifying the problem, reducing its dimensionality, and consequently accelerating computation. This paper proposes new algorithms for selecting relevant features and evaluating and selecting a subset of relevant objects in a dataset. [...] Read more.
Relevant attribute selection in machine learning is a key aspect aimed at simplifying the problem, reducing its dimensionality, and consequently accelerating computation. This paper proposes new algorithms for selecting relevant features and evaluating and selecting a subset of relevant objects in a dataset. Both algorithms are mainly based on the use of a fuzzy approach. The research presented here yielded preliminary results of a new approach to the problem of selecting relevant attributes and objects and selecting appropriate ranges of their values. Detailed results obtained on the Sonar dataset show the positive effects of this approach. Moreover, the observed results may suggest the effectiveness of the proposed method in terms of identifying a subset of truly relevant attributes from among those identified by traditional feature selection methods. Full article
(This article belongs to the Section Signal and Data Analysis)
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17 pages, 359 KiB  
Article
Joint Probabilities Approach to Quantum Games with Noise
by Alexis R. Legón and Ernesto Medina
Entropy 2023, 25(8), 1222; https://doi.org/10.3390/e25081222 - 16 Aug 2023
Viewed by 893
Abstract
A joint probability formalism for quantum games with noise is proposed, inspired by the formalism of non-factorizable probabilities that connects the joint probabilities to quantum games with noise. Using this connection, we show that the joint probabilities are non-factorizable; thus, noise does not [...] Read more.
A joint probability formalism for quantum games with noise is proposed, inspired by the formalism of non-factorizable probabilities that connects the joint probabilities to quantum games with noise. Using this connection, we show that the joint probabilities are non-factorizable; thus, noise does not generically destroy entanglement. This formalism was applied to the Prisoner’s Dilemma, the Chicken Game, and the Battle of the Sexes, where noise is coupled through a single parameter μ. We find that for all the games except for the Battle of the Sexes, the Nash inequalities are maintained up to a threshold value of the noise. Beyond the threshold value, the inequalities no longer hold for quantum and classical strategies. For the Battle of the sexes, the Nash inequalities always hold, no matter the noise strength. This is due to the symmetry and anti-symmetry of the parameters that determine the joint probabilities for that game. Finally, we propose a new correlation measure for the games with classical and quantum strategies, where we obtain that the incorporation of noise, when we have quantum strategies, does not affect entanglement, but classical strategies result in behavior that approximates quantum games with quantum strategies without the need to saturate the system with the maximum value of noise. In this manner, these correlations can be understood as entanglement for our game approach. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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57 pages, 592 KiB  
Article
Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group
by Christopher S. Jackson and Carlton M. Caves
Entropy 2023, 25(8), 1221; https://doi.org/10.3390/e25081221 - 16 Aug 2023
Cited by 2 | Viewed by 936
Abstract
The canonical commutation relation, [Q,P]=i, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the [...] Read more.
The canonical commutation relation, [Q,P]=i, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformations of Hilbert space and the canonical (also known as contact) transformations of classical phase space. Now that the theory of quantum measurement is essentially complete (this took a while), it is possible to revisit the canonical commutation relation in a way that sets the foundation of quantum theory not on unitary transformations but on positive transformations. This paper shows how the concept of simultaneous measurement leads to a fundamental differential geometric problem whose solution shows us the following. The simultaneous P and Q measurement (SPQM) defines a universal measuring instrument, which takes the shape of a seven-dimensional manifold, a universal covering group we call the instrumental Weyl-Heisenberg (IWH) group. The group IWH connects the identity to classical phase space in unexpected ways that are significant enough that the positive-operator-valued measure (POVM) offers a complete alternative to energy quantization. Five of the dimensions define processes that can be easily recognized and understood. The other two dimensions, the normalization and phase in the center of the IWH group, are less familiar. The normalization, in particular, requires special handling in order to describe and understand the SPQM instrument. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
29 pages, 2475 KiB  
Article
Consistent Model Selection Procedure for Random Coefficient INAR Models
by Kaizhi Yu and Tielai Tao
Entropy 2023, 25(8), 1220; https://doi.org/10.3390/e25081220 - 16 Aug 2023
Cited by 1 | Viewed by 859
Abstract
In the realm of time series data analysis, information criteria constructed on the basis of likelihood functions serve as crucial instruments for determining the appropriate lag order. However, the intricate structure of random coefficient integer-valued time series models, which are founded on thinning [...] Read more.
In the realm of time series data analysis, information criteria constructed on the basis of likelihood functions serve as crucial instruments for determining the appropriate lag order. However, the intricate structure of random coefficient integer-valued time series models, which are founded on thinning operators, complicates the establishment of likelihood functions. Consequently, employing information criteria such as AIC and BIC for model selection becomes problematic. This study introduces an innovative methodology that formulates a penalized criterion by utilizing the estimation equation within conditional least squares estimation, effectively addressing the aforementioned challenge. Initially, the asymptotic properties of the penalized criterion are derived, followed by a numerical simulation study and a comparative analysis. The findings from both theoretical examinations and simulation investigations reveal that this novel approach consistently selects variables under relatively relaxed conditions. Lastly, the applications of this method to infectious disease data and seismic frequency data produce satisfactory outcomes. Full article
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51 pages, 7033 KiB  
Article
Bounded Confidence and Cohesion-Moderated Pressure: A General Model for the Large-Scale Dynamics of Ordered Opinion
by Fangyikuang Ding, Yang Li and Kejian Ding
Entropy 2023, 25(8), 1219; https://doi.org/10.3390/e25081219 - 16 Aug 2023
Viewed by 1328
Abstract
Due to the development of social media, the mechanisms underlying consensus and chaos in opinion dynamics have become open questions and have been extensively researched in disciplines such as sociology, statistical physics, and nonlinear mathematics. In this regard, our paper establishes a general [...] Read more.
Due to the development of social media, the mechanisms underlying consensus and chaos in opinion dynamics have become open questions and have been extensively researched in disciplines such as sociology, statistical physics, and nonlinear mathematics. In this regard, our paper establishes a general model of opinion evolution based on micro-mechanisms such as bounded confidence, out-group pressure, and in-group cohesion. Several core conclusions are derived through theorems and simulation results in the model: (1) assimilation and high reachability in social networks lead to global consensus; (2) assimilation and low reachability result in local consensus; (3) exclusion and high reachability cause chaos; and (4) a strong “cocoon room effect” can sustain the existence of local consensus. These conclusions collectively form the “ideal synchronization theory”, which also includes findings related to convergence rates, consensus bifurcation, and other exploratory conclusions. Additionally, to address questions about consensus and chaos, we develop a series of mathematical and statistical methods, including the “energy decrease method”, the “cross-d search method”, and the statistical test method for the dynamical models, contributing to a broader understanding of stochastic dynamics. Full article
(This article belongs to the Special Issue Statistical Physics of Opinion Formation and Social Phenomena)
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21 pages, 495 KiB  
Article
Energy Conversion and Entropy Production in Biased Random Walk Processes—From Discrete Modeling to the Continuous Limit
by Henning Kirchberg and Abraham Nitzan
Entropy 2023, 25(8), 1218; https://doi.org/10.3390/e25081218 - 16 Aug 2023
Cited by 1 | Viewed by 896
Abstract
We considered discrete and continuous representations of a thermodynamic process in which a random walker (e.g., a molecular motor on a molecular track) uses periodically pumped energy (work) to pass N sites and move energetically downhill while dissipating heat. Interestingly, we found that, [...] Read more.
We considered discrete and continuous representations of a thermodynamic process in which a random walker (e.g., a molecular motor on a molecular track) uses periodically pumped energy (work) to pass N sites and move energetically downhill while dissipating heat. Interestingly, we found that, starting from a discrete model, the limit in which the motion becomes continuous in space and time (N) is not unique and depends on what physical observables are assumed to be unchanged in the process. In particular, one may (as usually done) choose to keep the speed and diffusion coefficient fixed during this limiting process, in which case, the entropy production is affected. In addition, we also studied processes in which the entropy production is kept constant as N at the cost of a modified speed or diffusion coefficient. Furthermore, we also combined this dynamics with work against an opposing force, which made it possible to study the effect of discretization of the process on the thermodynamic efficiency of transferring the power input to the power output. Interestingly, we found that the efficiency was increased in the limit of N. Finally, we investigated the same process when transitions between sites can only happen at finite time intervals and studied the impact of this time discretization on the thermodynamic variables as the continuous limit is approached. Full article
(This article belongs to the Collection Disorder and Biological Physics)
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11 pages, 823 KiB  
Article
A Joint Extraction Model for Entity Relationships Based on Span and Cascaded Dual Decoding
by Tao Liao, Haojie Sun and Shunxiang Zhang
Entropy 2023, 25(8), 1217; https://doi.org/10.3390/e25081217 - 16 Aug 2023
Cited by 1 | Viewed by 1134
Abstract
The entity–relationship joint extraction model plays a significant role in entity relationship extraction. The existing entity–relationship joint extraction model cannot effectively identify entity–relationship triples in overlapping relationships. This paper proposes a new joint entity–relationship extraction model based on the span and a cascaded [...] Read more.
The entity–relationship joint extraction model plays a significant role in entity relationship extraction. The existing entity–relationship joint extraction model cannot effectively identify entity–relationship triples in overlapping relationships. This paper proposes a new joint entity–relationship extraction model based on the span and a cascaded dual decoding. The model includes a Bidirectional Encoder Representations from Transformers (BERT) encoding layer, a relational decoding layer, and an entity decoding layer. The model first converts the text input into the BERT pretrained language model into word vectors. Then, it divides the word vectors based on the span to form a span sequence and decodes the relationship between the span sequence to obtain the relationship type in the span sequence. Finally, the entity decoding layer fuses the span sequences and the relationship type obtained by relation decoding and uses a bi-directional long short-term memory (Bi-LSTM) neural network to obtain the head entity and tail entity in the span sequence. Using the combination of span division and cascaded double decoding, the overlapping relations existing in the text can be effectively identified. Experiments show that compared with other baseline models, the F1 value of the model is effectively improved on the NYT dataset and WebNLG dataset. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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18 pages, 2746 KiB  
Article
Hybrid DAER Based Cross-Modal Retrieval Exploiting Deep Representation Learning
by Zhao Huang, Haowu Hu and Miao Su
Entropy 2023, 25(8), 1216; https://doi.org/10.3390/e25081216 - 16 Aug 2023
Viewed by 1064
Abstract
Information retrieval across multiple modes has attracted much attention from academics and practitioners. One key challenge of cross-modal retrieval is to eliminate the heterogeneous gap between different patterns. Most of the existing methods tend to jointly construct a common subspace. However, very little [...] Read more.
Information retrieval across multiple modes has attracted much attention from academics and practitioners. One key challenge of cross-modal retrieval is to eliminate the heterogeneous gap between different patterns. Most of the existing methods tend to jointly construct a common subspace. However, very little attention has been given to the study of the importance of different fine-grained regions of various modalities. This lack of consideration significantly influences the utilization of the extracted information of multiple modalities. Therefore, this study proposes a novel text-image cross-modal retrieval approach that constructs a dual attention network and an enhanced relation network (DAER). More specifically, the dual attention network tends to precisely extract fine-grained weight information from text and images, while the enhanced relation network is used to expand the differences between different categories of data in order to improve the computational accuracy of similarity. The comprehensive experimental results on three widely-used major datasets (i.e., Wikipedia, Pascal Sentence, and XMediaNet) show that our proposed approach is effective and superior to existing cross-modal retrieval methods. Full article
(This article belongs to the Special Issue Information Theory for Data Science)
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31 pages, 25254 KiB  
Article
Gaussian of Differences: A Simple and Efficient General Image Fusion Method
by Rifat Kurban
Entropy 2023, 25(8), 1215; https://doi.org/10.3390/e25081215 - 15 Aug 2023
Cited by 7 | Viewed by 1859
Abstract
The separate analysis of images obtained from a single source using different camera settings or spectral bands, whether from one or more than one sensor, is quite difficult. To solve this problem, a single image containing all of the distinctive pieces of information [...] Read more.
The separate analysis of images obtained from a single source using different camera settings or spectral bands, whether from one or more than one sensor, is quite difficult. To solve this problem, a single image containing all of the distinctive pieces of information in each source image is generally created by combining the images, a process called image fusion. In this paper, a simple and efficient, pixel-based image fusion method is proposed that relies on weighting the edge information associated with each pixel of all of the source images proportional to the distance from their neighbors by employing a Gaussian filter. The proposed method, Gaussian of differences (GD), was evaluated using multi-modal medical images, multi-sensor visible and infrared images, multi-focus images, and multi-exposure images, and was compared to existing state-of-the-art fusion methods by utilizing objective fusion quality metrics. The parameters of the GD method are further enhanced by employing the pattern search (PS) algorithm, resulting in an adaptive optimization strategy. Extensive experiments illustrated that the proposed GD fusion method ranked better on average than others in terms of objective quality metrics and CPU time consumption. Full article
(This article belongs to the Section Signal and Data Analysis)
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30 pages, 983 KiB  
Article
A Machine Learning Approach to Simulate Gene Expression and Infer Gene Regulatory Networks
by Francesco Zito, Vincenzo Cutello and Mario Pavone
Entropy 2023, 25(8), 1214; https://doi.org/10.3390/e25081214 - 15 Aug 2023
Cited by 3 | Viewed by 2519
Abstract
The ability to simulate gene expression and infer gene regulatory networks has vast potential applications in various fields, including medicine, agriculture, and environmental science. In recent years, machine learning approaches to simulate gene expression and infer gene regulatory networks have gained significant attention [...] Read more.
The ability to simulate gene expression and infer gene regulatory networks has vast potential applications in various fields, including medicine, agriculture, and environmental science. In recent years, machine learning approaches to simulate gene expression and infer gene regulatory networks have gained significant attention as a promising area of research. By simulating gene expression, we can gain insights into the complex mechanisms that control gene expression and how they are affected by various environmental factors. This knowledge can be used to develop new treatments for genetic diseases, improve crop yields, and better understand the evolution of species. In this article, we address this issue by focusing on a novel method capable of simulating the gene expression regulation of a group of genes and their mutual interactions. Our framework enables us to simulate the regulation of gene expression in response to alterations or perturbations that can affect the expression of a gene. We use both artificial and real benchmarks to empirically evaluate the effectiveness of our methodology. Furthermore, we compare our method with existing ones to understand its advantages and disadvantages. We also present future ideas for improvement to enhance the effectiveness of our method. Overall, our approach has the potential to greatly improve the field of gene expression simulation and gene regulatory network inference, possibly leading to significant advancements in genetics. Full article
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