Journal Description
Entropy
Entropy
is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI. The International Society for the Study of Information (IS4SI) and Spanish Society of Biomedical Engineering (SEIB) are affiliated with Entropy and their members receive a discount on the article processing charge.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), MathSciNet, Inspec, PubMed, PMC, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Physics, Multidisciplinary) / CiteScore - Q1 (Mathematical Physics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 20.8 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Entropy.
- Companion journals for Entropy include: Foundations, Thermo and MAKE.
Impact Factor:
2.7 (2022);
5-Year Impact Factor:
2.6 (2022)
Latest Articles
Entropy-Based Methods for Motor Fault Detection: A Review
Entropy 2024, 26(4), 299; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040299 (registering DOI) - 28 Mar 2024
Abstract
In the signal analysis context, the entropy concept can characterize signal properties for detecting anomalies or non-representative behaviors in fiscal systems. In motor fault detection theory, entropy can measure disorder or uncertainty, aiding in detecting and classifying faults or abnormal operation conditions. This
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In the signal analysis context, the entropy concept can characterize signal properties for detecting anomalies or non-representative behaviors in fiscal systems. In motor fault detection theory, entropy can measure disorder or uncertainty, aiding in detecting and classifying faults or abnormal operation conditions. This is especially relevant in industrial processes, where early motor fault detection can prevent progressive damage, operational interruptions, or potentially dangerous situations. The study of motor fault detection based on entropy theory holds significant academic relevance too, effectively bridging theoretical frameworks with industrial exigencies. As industrial sectors progress, applying entropy-based methodologies becomes indispensable for ensuring machinery integrity based on control and monitoring systems. This academic endeavor enhances the understanding of signal processing methodologies and accelerates progress in artificial intelligence and other modern knowledge areas. A wide variety of entropy-based methods have been employed for motor fault detection. This process involves assessing the complexity of measured signals from electrical motors, such as vibrations or stator currents, to form feature vectors. These vectors are then fed into artificial-intelligence-based classifiers to distinguish between healthy and faulty motor signals. This paper discusses some recent references to entropy methods and a summary of the most relevant results reported for fault detection over the last 10 years.
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(This article belongs to the Special Issue The Application of Information Theory in Fault Detection and Diagnosis)
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Chaos in Opinion-Driven Disease Dynamics
by
Thomas Götz, Tyll Krüger, Karol Niedzielewski, Radomir Pestow, Moritz Schäfer and Jan Schneider
Entropy 2024, 26(4), 298; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040298 (registering DOI) - 28 Mar 2024
Abstract
During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article explores one among the many possibilities of coupled opinion–epidemic systems.
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During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article explores one among the many possibilities of coupled opinion–epidemic systems. The findings reveal either intricate periodic patterns or chaotic dynamics, leading to substantial fluctuations in opinion distribution and, consequently, significant variations in the total number of infections over time. Interestingly, the model exhibits a protective pattern.
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(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)
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Revisiting the Surface Brightness Profile of the Stellar Disk with the Statistical Mechanics of the Self-Gravitating System with the Central Body
by
Dong-Biao Kang
Entropy 2024, 26(4), 297; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040297 (registering DOI) - 28 Mar 2024
Abstract
We have explored the exponential surface brightness profile (SBP) of stellar disks, a topic extensively discussed by many authors yet seldom integrated with the study of correlations between black holes, bulges, and entire disks. Building upon our prior work in the statistical mechanics
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We have explored the exponential surface brightness profile (SBP) of stellar disks, a topic extensively discussed by many authors yet seldom integrated with the study of correlations between black holes, bulges, and entire disks. Building upon our prior work in the statistical mechanics of disk-shaped systems and aligning with methodologies from other research, we analyze the influence of the central body. This analysis reveals analytical relationships among black holes, bulges, and the entire stellar disk. Additionally, we incorporate a specific angular momentum distribution (SAMD) that aligns more closely with observational data, showing that for the self-gravitating disk, with the same surface density, a reduction in its spin results in only a slight decrease in its radius, whereas with the same SAMD, an increment in its spin significantly limits its extent. A key feature of our model is its prediction that the surface density profile of an isolated disk will invariably exhibit downbending at a sufficient distance, a hypothesis that future observations can test. Our refined equations provide a notably improved fit for SBPs, particularly in the central regions of stellar disks. While our findings underscore the significance of statistical mechanics in comprehending spiral galaxy structures, they also highlight areas in our approach that warrant further discussion and exploration.
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(This article belongs to the Special Issue Statistical Mechanics of Self-Gravitating Systems)
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pRR30, pRR3.25% and Asymmetrical Entropy Descriptors in Atrial Fibrillation Detection
by
Bartosz Biczuk, Szymon Buś, Sebastian Żurek, Jarosław Piskorski and Przemysław Guzik
Entropy 2024, 26(4), 296; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040296 (registering DOI) - 28 Mar 2024
Abstract
Background: Early detection of atrial fibrillation (AF) is essential to prevent stroke and other cardiac and embolic complications. We compared the diagnostic properties for AF detection of the percentage of successive RR interval differences greater than or equal to 30 ms or 3.25%
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Background: Early detection of atrial fibrillation (AF) is essential to prevent stroke and other cardiac and embolic complications. We compared the diagnostic properties for AF detection of the percentage of successive RR interval differences greater than or equal to 30 ms or 3.25% of the previous RR interval (pRR30 and pRR3.25%, respectively), and asymmetric entropy descriptors of RR intervals. Previously, both pRR30 and pRR3.25% outperformed many other heart rate variability (HRV) parameters in distinguishing AF from sinus rhythm (SR) in 60 s electrocardiograms (ECGs). Methods: The 60 s segments with RR intervals were extracted from the publicly available Physionet Long-Term Atrial Fibrillation Database (84 recording, 24 h Holter ECG). There were 31,753 60 s segments of AF and 32,073 60 s segments of SR. The diagnostic properties of all parameters were analysed with receiver operator curve analysis, a confusion matrix and logistic regression. The best model with pRR30, pRR3.25% and total entropic features (H) had the largest area under the curve (AUC)—0.98 compared to 0.959 for pRR30—and 0.972 for pRR3.25%. However, the differences in AUC between pRR30 and pRR3.25% alone and the combined model were negligible from a practical point of view. Moreover, combining pRR30 and pRR3.25% with H significantly increased the number of false-negative cases by more than threefold. Conclusions: Asymmetric entropy has some potential in differentiating AF from SR in the 60 s RR interval time series, but the addition of these parameters does not seem to make a relevant difference compared to pRR30 and especially pRR3.25%.
Full article
(This article belongs to the Special Issue Entropy Analysis of Heart Rate and Arterial Blood Pressure Variability and Their Applications)
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Study on the Tip Leakage Loss Mechanism of a Compressor Cascade Using the Enhanced Delay Detached Eddy Simulation Method
by
Shiyan Lin, Ruiyu Li and Limin Gao
Entropy 2024, 26(4), 295; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040295 (registering DOI) - 28 Mar 2024
Abstract
The leakage flow has a significant impact on the aerodynamic losses and efficiency of the compressor. This paper investigates the loss mechanism in the tip region based on a high-load cantilevered stator cascade. Firstly, a high-fidelity flow field structure was obtained based on
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The leakage flow has a significant impact on the aerodynamic losses and efficiency of the compressor. This paper investigates the loss mechanism in the tip region based on a high-load cantilevered stator cascade. Firstly, a high-fidelity flow field structure was obtained based on the Enhanced Delay Detached Eddy Simulation (EDDES) method. Subsequently, the Liutex method was employed to study the vortex structures in the tip region. The results indicate the presence of a tip leakage vortex (TLV), passage vortex (PV), and induced vortex (IV) in the tip region. At , the induced vortex interacts with the PV and low-energy fluid, forming a “three-shape” mixed vortex. Finally, a qualitative and quantitative analysis of the loss sources in the tip flow field was conducted based on the entropy generation rate, and the impact of the incidence on the losses was explored. The loss sources in the tip flow field included endwall loss, blade profile loss, wake loss, and secondary flow loss. At , the loss primarily originated from the endwall and blade profile, accounting for and , respectively. As the incidence increased, the absolute value of losses increased, and the proportion of loss caused by secondary flow significantly increased. At , the proportion of secondary flow loss reached 47%, indicating the most significant impact.
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(This article belongs to the Special Issue Hybrid LES/RANS Simulations in Fundamental, Environmental, and Industrial Applications)
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Non-Markovian Diffusion and Adsorption–Desorption Dynamics: Analytical and Numerical Results
by
Derik W. Gryczak, Ervin K. Lenzi, Michely P. Rosseto, Luiz R. Evangelista and Rafael S. Zola
Entropy 2024, 26(4), 294; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040294 - 27 Mar 2024
Abstract
The interplay of diffusion with phenomena like stochastic adsorption–desorption, absorption, and reaction–diffusion is essential for life and manifests in diverse natural contexts. Many factors must be considered, including geometry, dimensionality, and the interplay of diffusion across bulk and surfaces. To address this complexity,
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The interplay of diffusion with phenomena like stochastic adsorption–desorption, absorption, and reaction–diffusion is essential for life and manifests in diverse natural contexts. Many factors must be considered, including geometry, dimensionality, and the interplay of diffusion across bulk and surfaces. To address this complexity, we investigate the diffusion process in heterogeneous media, focusing on non-Markovian diffusion. This process is limited by a surface interaction with the bulk, described by a specific boundary condition relevant to systems such as living cells and biomaterials. The surface can adsorb and desorb particles, and the adsorbed particles may undergo lateral diffusion before returning to the bulk. Different behaviors of the system are identified through analytical and numerical approaches.
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(This article belongs to the Special Issue Random Walks and Stochastic Processes in Complex Systems: From Physics to Socio-Economic Phenomena)
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Interpretation of Second Law of Thermodynamics in Extended Procedures for the Exploitation of the Entropy Inequality: Korteweg Fluids and Strain-Gradient Elasticity as Examples
by
Vito Antonio Cimmelli
Entropy 2024, 26(4), 293; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040293 - 27 Mar 2024
Abstract
In continuum physics the dissipation principle, first proposed by Coleman and Noll in 1963, regards second law of thermodynamics as a unilateral differential constraint on the constitutive equations. In 1996, Muschik and Ehrentraut provided a rigorous proof of such an approach under the
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In continuum physics the dissipation principle, first proposed by Coleman and Noll in 1963, regards second law of thermodynamics as a unilateral differential constraint on the constitutive equations. In 1996, Muschik and Ehrentraut provided a rigorous proof of such an approach under the assumption that, at an arbitrary instant, , in an arbitrary point, , of a continuous system, the entropy production is zero if, and only if, is in thermodynamic equilibrium. In 2022, Cimmelli and Rogolino incorporated such an assumption in a more general formulation of the second law of thermodynamics. In this paper, we prove that the same conclusions hold if both the fundamental balance laws and their gradients are substituted into the entropy inequality. Such a methodology is applied to analyze the strain-gradient elasticity.
Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
Open AccessArticle
Finite-Time H∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition Probabilities
by
Xinye Guo, Yan Li and Xikui Liu
Entropy 2024, 26(4), 292; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040292 - 27 Mar 2024
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This paper concentrates on the finite-time control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) state feedback controller and an SFT observer-based
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This paper concentrates on the finite-time control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) state feedback controller and an SFT observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov–Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes.
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Lagrangian Partition Functions Subject to a Fixed Spatial Volume Constraint in the Lovelock Theory
by
Mengqi Lu and Robert B. Mann
Entropy 2024, 26(4), 291; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040291 - 27 Mar 2024
Abstract
We evaluate here the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of a fixed proper volume in the context of Lovelock gravity, generalizing the results for Einstein gravity. It is found that
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We evaluate here the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of a fixed proper volume in the context of Lovelock gravity, generalizing the results for Einstein gravity. It is found that there are sphere saddle metrics for a partition function at a fixed spatial volume in Lovelock theory. Those stationary points take exactly the same forms as in Einstein gravity. The logarithm of Z corresponding to a zero effective cosmological constant indicates that the Bekenstein–Hawking entropy of the boundary area and that corresponding to a positive effective cosmological constant points to the Wald entropy of the boundary area. We also show the existence of zeroth-order phase transitions between different vacua, a phenomenon distinct from Einstein gravity.
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(This article belongs to the Special Issue The Black Hole Information Problem)
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A Unifying Generator Loss Function for Generative Adversarial Networks
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Justin Veiner, Fady Alajaji and Bahman Gharesifard
Entropy 2024, 26(4), 290; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040290 - 27 Mar 2024
Abstract
A unifying -parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN) that uses a canonical (or classical) discriminator loss function such as the one in the original GAN (VanillaGAN) system. The generator loss function is based on a
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A unifying -parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN) that uses a canonical (or classical) discriminator loss function such as the one in the original GAN (VanillaGAN) system. The generator loss function is based on a symmetric class probability estimation type function, , and the resulting GAN system is termed -GAN. Under an optimal discriminator, it is shown that the generator’s optimization problem consists of minimizing a Jensen- -divergence, a natural generalization of the Jensen-Shannon divergence, where is a convex function expressed in terms of the loss function . It is also demonstrated that this -GAN problem recovers as special cases a number of GAN problems in the literature, including VanillaGAN, least squares GAN (LSGAN), least kth-order GAN (LkGAN), and the recently introduced -GAN with . Finally, experimental results are provided for three datasets—MNIST, CIFAR-10, and Stacked MNIST—to illustrate the performance of various examples of the -GAN system.
Full article
(This article belongs to the Special Issue Information-Theoretic Methods in Deep Learning: Theory and Applications)
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Non-Projective Two-Weight Codes
by
Sascha Kurz
Entropy 2024, 26(4), 289; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040289 - 27 Mar 2024
Abstract
It has been known since the 1970’s that the difference of the non-zero weights of a projective -linear two-weight code has to be a power of the characteristic of the underlying field. Here, we study non-projective two-weight codes and, e.g., show
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It has been known since the 1970’s that the difference of the non-zero weights of a projective -linear two-weight code has to be a power of the characteristic of the underlying field. Here, we study non-projective two-weight codes and, e.g., show the same result under mild extra conditions. For small dimensions we give exhaustive enumerations of the feasible parameters in the binary case.
Full article
(This article belongs to the Special Issue Discrete Math in Coding Theory)
Open AccessHypothesis
Irruption and Absorption: A ‘Black-Box’ Framework for How Mind and Matter Make a Difference to Each Other
by
Tom Froese
Entropy 2024, 26(4), 288; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040288 - 27 Mar 2024
Abstract
Cognitive science is confronted by several fundamental anomalies deriving from the mind–body problem. Most prominent is the problem of mental causation and the hard problem of consciousness, which can be generalized into the hard problem of agential efficacy and the hard problem of
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Cognitive science is confronted by several fundamental anomalies deriving from the mind–body problem. Most prominent is the problem of mental causation and the hard problem of consciousness, which can be generalized into the hard problem of agential efficacy and the hard problem of mental content. Here, it is proposed to accept these explanatory gaps at face value and to take them as positive indications of a complex relation: mind and matter are one, but they are not the same. They are related in an efficacious yet non-reducible, non-observable, and even non-intelligible manner. Natural science is well equipped to handle the effects of non-observables, and so the mind is treated as equivalent to a hidden ‘black box’ coupled to the body. Two concepts are introduced given that there are two directions of coupling influence: (1) irruption denotes the unobservable mind hiddenly making a difference to observable matter, and (2) absorption denotes observable matter hiddenly making a difference to the unobservable mind. The concepts of irruption and absorption are methodologically compatible with existing information-theoretic approaches to neuroscience, such as measuring cognitive activity and subjective qualia in terms of entropy and compression, respectively. By offering novel responses to otherwise intractable theoretical problems from first principles, and by doing so in a way that is closely connected with empirical advances, irruption theory is poised to set the agenda for the future of the mind sciences.
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(This article belongs to the Section Multidisciplinary Applications)
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Markov Blankets and Mirror Symmetries—Free Energy Minimization and Mesocortical Anatomy
by
James Wright and Paul Bourke
Entropy 2024, 26(4), 287; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040287 - 27 Mar 2024
Abstract
A theoretical account of development in mesocortical anatomy is derived from the free energy principle, operating in a neural field with both Hebbian and anti-Hebbian neural plasticity. An elementary structural unit is proposed, in which synaptic connections at mesoscale are arranged in paired
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A theoretical account of development in mesocortical anatomy is derived from the free energy principle, operating in a neural field with both Hebbian and anti-Hebbian neural plasticity. An elementary structural unit is proposed, in which synaptic connections at mesoscale are arranged in paired patterns with mirror symmetry. Exchanges of synaptic flux in each pattern form coupled spatial eigenmodes, and the line of mirror reflection between the paired patterns operates as a Markov blanket, so that prediction errors in exchanges between the pairs are minimized. The theoretical analysis is then compared to the outcomes from a biological model of neocortical development, in which neuron precursors are selected by apoptosis for cell body and synaptic connections maximizing synchrony and also minimizing axonal length. It is shown that this model results in patterns of connection with the anticipated mirror symmetries, at micro-, meso- and inter-arial scales, among lateral connections, and in cortical depth. This explains the spatial organization and functional significance of neuron response preferences, and is compatible with the structural form of both columnar and noncolumnar cortex. Multi-way interactions of mirrored representations can provide a preliminary anatomically realistic model of cortical information processing.
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(This article belongs to the Special Issue From Functional Imaging to Free Energy—Dedicated to Professor Karl Friston on the Occasion of His 65th Birthday)
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Open AccessReview
The
by
Paolo Gibilisco
Entropy 2024, 26(4), 286; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040286 - 26 Mar 2024
Abstract
Due to the classifying theorems by Petz and Kubo–Ando, we know that there are bijective correspondences between Quantum Fisher Information(s), operator means, and the class of symmetric, normalized operator monotone functions on the positive half line; this last class is usually denoted as
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Due to the classifying theorems by Petz and Kubo–Ando, we know that there are bijective correspondences between Quantum Fisher Information(s), operator means, and the class of symmetric, normalized operator monotone functions on the positive half line; this last class is usually denoted as . This class of operator monotone function has a significant structure, which is worthy of study; indeed, any step in understanding , besides being interesting per se, immediately translates into a property of the classes of operator means and therefore of Quantum Fisher Information(s). In recent years, the correspondence has been introduced, which associates a non-regular element of to any regular element of the same set. In terms of operator means, this amounts to associating a mean with multiplicative character to a mean that has an additive character. In this paper, we survey a number of different settings where this technique has proven useful in Quantum Information Geometry. In Sections 1–4, all the needed background is provided. In Sections 5–14, we describe the main applications of the correspondence.
Full article
(This article belongs to the Special Issue On the Role of Geometric and Entropic Arguments in Physics: From Classical Thermodynamics to Quantum Mechanics)
Open AccessArticle
Why Does Cross-Sectional Analyst Coverage Incorporate Market-Wide Information?
by
Yunfei Hou and Changsheng Hu
Entropy 2024, 26(4), 285; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040285 - 26 Mar 2024
Abstract
This paper shows that the empirical distribution of cross-sectional analyst coverage in China’s stock markets follows an exponential law in a given month from 2011 to 2020. The findings hold in both the emerging (Shanghai) and the developed market (Hong Kong). Moreover, the
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This paper shows that the empirical distribution of cross-sectional analyst coverage in China’s stock markets follows an exponential law in a given month from 2011 to 2020. The findings hold in both the emerging (Shanghai) and the developed market (Hong Kong). Moreover, the unique distribution parameter (i.e., mean) is directly related to the amount of market-wide information. Average analyst coverage exhibits a significant negative predictive power for stock-market uncertainty, highlighting the role of security analysts in diminishing the total uncertainty. The exponential law can be derived from the maximum entropy principle (MEP). When analysts, who are constrained by average ability in generating information (i.e., the first-order moment), strive to maximize the amount of market-wide information, this objective yields the exponential distribution. Contrary to the conventional wisdom that security analysts specialize in the generation of firm-specific information, empirical findings suggest that analysts primarily produce market-wide information for 25 countries. Nevertheless, it remains unclear why cross-sectional analyst coverage reflects market-wide information, this paper provides an entropy-based explanation.
Full article
(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management II)
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Open AccessArticle
PIS-Net: Efficient Medical Image Segmentation Network with Multivariate Downsampling for Point-of-Care
by
Changrui Zhang and Jia Wang
Entropy 2024, 26(4), 284; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040284 - 26 Mar 2024
Abstract
Recently, with more portable diagnostic devices being moved to people anywhere, point-of-care (PoC) imaging has become more convenient and more popular than the traditional “bed imaging”. Instant image segmentation, as an important technology of computer vision, is receiving more and more attention in
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Recently, with more portable diagnostic devices being moved to people anywhere, point-of-care (PoC) imaging has become more convenient and more popular than the traditional “bed imaging”. Instant image segmentation, as an important technology of computer vision, is receiving more and more attention in PoC diagnosis. However, the image distortion caused by image preprocessing and the low resolution of medical images extracted by PoC devices are urgent problems that need to be solved. Moreover, more efficient feature representation is necessary in the design of instant image segmentation. In this paper, a new feature representation considering the relationships among local features with minimal parameters and a lower computational complexity is proposed. Since a feature window sliding along a diagonal can capture more pluralistic features, a Diagonal-Axial Multi-Layer Perceptron is designed to obtain the global correlation among local features for a more comprehensive feature representation. Additionally, a new multi-scale feature fusion is proposed to integrate nonlinear features with linear ones to obtain a more precise feature representation. Richer features are figured out. In order to improve the generalization of the models, a dynamic residual spatial pyramid pooling based on various receptive fields is constructed according to different sizes of images, which alleviates the influence of image distortion. The experimental results show that the proposed strategy has better performance on instant image segmentation. Notably, it yields an average improvement of 1.31% in Dice than existing strategies on the BUSI, ISIC2018 and MoNuSeg datasets.
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(This article belongs to the Topic New Developments and Applications in Bioinformatics and Computational Biology)
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Entropic Bounds on the Average Length of Codes with a Space
by
Roberto Bruno and Ugo Vaccaro
Entropy 2024, 26(4), 283; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040283 - 26 Mar 2024
Abstract
We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that their average length differs
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We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that their average length differs from the minimum possible by at most one. We obtain our results by uncovering a relation between our class of codes and the class of one-to-one codes. Additionally, we derive upper and lower bounds to the average length of optimal prefix-free codes with a space in terms of the source entropy.
Full article
(This article belongs to the Special Issue Extremal and Additive Combinatorial Aspects in Information Theory)
Open AccessArticle
Dark Matter and Mirror World
by
Rabindra N. Mohapatra
Entropy 2024, 26(4), 282; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040282 - 26 Mar 2024
Abstract
Overwhelming astronomical evidence for dark matter and absence of any laboratory evidence for it despite many dedicated searches have fueled speculation that dark matter may reside in a parallel universe interacting with the familiar universe only via gravitational interactions as well as possibly
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Overwhelming astronomical evidence for dark matter and absence of any laboratory evidence for it despite many dedicated searches have fueled speculation that dark matter may reside in a parallel universe interacting with the familiar universe only via gravitational interactions as well as possibly via some ultra-weak forces. In this scenario, we postulate that the visible universe co-exists with a mirror world consisting of an identical duplicate of forces and matter of our world, obeying a mirror symmetry. This picture, motivated by particle physics considerations, not only provides a natural candidate for dark matter but also has the potential to explain the matter dark matter coincidence problem, i.e., why the dark matter content of the universe is only a few times the visible matter content. One requirement for mirror models is that the mirror world must be colder than our world to maintain the success of big bang nucleosynthesis. After a review of the basic features of the model, we present several new results: first is that the consistency between the coldness of the mirror world and the explanation of the matter dark matter coincidence implies an upper bound on the inflation reheat temperature of the universe to be around GeV. We also argue that the coldness implies the mirror world consists mainly of mirror Helium and very little mirror hydrogen, which is the exact opposite of what we see in the visible world.
Full article
(This article belongs to the Special Issue Particle Theory and Theoretical Cosmology—Dedicated to Professor Paul Howard Frampton on the Occasion of His 80th Birthday)
Open AccessArticle
Models of Protocells Undergoing Asymmetrical Division
by
Marco Villani, Elena Alboresi and Roberto Serra
Entropy 2024, 26(4), 281; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040281 - 26 Mar 2024
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The conditions that allow for the sustained growth of a protocell population are investigated in the case of asymmetrical division. The results are compared to those of previous studies concerning models of symmetrical division, where synchronization (between duplication of the genetic material and
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The conditions that allow for the sustained growth of a protocell population are investigated in the case of asymmetrical division. The results are compared to those of previous studies concerning models of symmetrical division, where synchronization (between duplication of the genetic material and fission of the lipid container) was found under a variety of different assumptions about the kinetic equations and about the place where molecular replication takes place. Such synchronization allows a sustained proliferation of the protocell population. In the asymmetrical case, there can be no true synchronization, since the time to duplication may depend upon the initial size, but we introduce a notion of homogeneous growth that actually allows for the sustained reproduction of a population of protocells. We first analyze Surface Reaction Models, defined in the text, and we show that in many cases they undergo homogeneous growth under the same kinetic laws that lead to synchronization in the symmetrical case. This is the case also for Internal Reaction Models (IRMs), which, however, require a deeper understanding of what homogeneous growth actually means, as discussed below.
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Open AccessArticle
Towards Two Bloch Sphere Representation of Pure Two-Qubit States and Unitaries
by
Stanislav Filatov and Marcis Auzinsh
Entropy 2024, 26(4), 280; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040280 - 25 Mar 2024
Abstract
We extend Bloch sphere formalism to pure two-qubit systems. Combining insights from Geometric Algebra and the analysis of entanglement in different conjugate bases we identify two Bloch sphere geometry that is suitable for representing maximally entangled states. It turns out that the relative
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We extend Bloch sphere formalism to pure two-qubit systems. Combining insights from Geometric Algebra and the analysis of entanglement in different conjugate bases we identify two Bloch sphere geometry that is suitable for representing maximally entangled states. It turns out that the relative direction of the coordinate axes of the two Bloch spheres may be used to describe the states. Moreover, the coordinate axes of one Bloch sphere should be rignt-handed and those of the other one should be left-handed. We describe and depict separable and maximally entangled states as well as entangling and non-entangling rotations. We also offer a graphical representation of the workings of a CNOT gate for different inputs. Finally, we provide a way to also represent partially entangled states and describe entanglement measures related to the surface area of the sphere enclosing the state representation.
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(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
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