Entropy

26 pages, 1191 KiB

Open AccessArticle

Extended Multicriteria Group Decision Making with a Novel Aggregation Operator for Emergency Material Supplier Selection

by Ling Liu, Qiuyi Zhu, Dan Yang and Sen Liu

Entropy 2023, 25(4), 702; https://doi.org/10.3390/e25040702 - 21 Apr 2023

Viewed by 1320

Abstract

How to ensure the normal production of industries in an uncertain emergency environment has aroused a lot of concern in society. Selecting the best emergency material suppliers using the multicriteria group decision making (MCGDM) method will ensure the normal production of industries in [...] Read more.

How to ensure the normal production of industries in an uncertain emergency environment has aroused a lot of concern in society. Selecting the best emergency material suppliers using the multicriteria group decision making (MCGDM) method will ensure the normal production of industries in this environment. However, there are few studies in emergency environments that consider the impact of the decision order of decision makers (DMs) on the decision results. Therefore, in order to fill the research gap, we propose an extended MCGDM method, whose main steps include the following: Firstly, the DMs give their assessment of all alternatives. Secondly, we take the AHP method and entropy weight method to weight the criteria and the DMs. Thirdly, we take the intuitionistic fuzzy hybrid priority weight average (IFHPWA) operator we proposed to aggregate evaluation information and take the TOPSIS method to rank all the alternatives. Finally, the proposed method is applied in a case to prove its practicability and effectiveness. The proposed method considers the influence of the decision order of the DMs on the decision results, which improves the accuracy and efficiency of decision-making results. Full article

(This article belongs to the Special Issue Entropy Methods for Multicriteria Decision Making)

► Show Figures

Figure 1

15 pages, 19902 KiB

Open AccessArticle

Acoustic Emissions in Rock Deformation and Failure: New Insights from Q-Statistical Analysis

by Sergio C. Vinciguerra, Annalisa Greco, Alessandro Pluchino, Andrea Rapisarda and Constantino Tsallis

Entropy 2023, 25(4), 701; https://doi.org/10.3390/e25040701 - 21 Apr 2023

Cited by 1 | Viewed by 1190

Abstract

We propose a new statistical analysis of the Acoustic Emissions (AE) produced in a series of triaxial deformation experiments leading to fractures and failure of two different rocks, namely, Darley Dale Sandstone (DDS) and AG Granite (AG). By means of q-statistical formalism, we [...] Read more.

We propose a new statistical analysis of the Acoustic Emissions (AE) produced in a series of triaxial deformation experiments leading to fractures and failure of two different rocks, namely, Darley Dale Sandstone (DDS) and AG Granite (AG). By means of q-statistical formalism, we are able to characterize the pre-failure processes in both types of rocks. In particular, we study AE inter-event time and AE inter-event distance distributions. Both of them can be reproduced with q-exponential curves, showing universal features that are observed here for the first time and could be important in order to understand more in detail the dynamics of rock fractures. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

► Show Figures

Figure 1

17 pages, 1011 KiB

Open AccessArticle

Continuous Adaptive Finite-Time Sliding Mode Control for Fractional-Order Buck Converter Based on Riemann-Liouville Definition

by Zhongze Cai and Qingshuang Zeng

Entropy 2023, 25(4), 700; https://doi.org/10.3390/e25040700 - 21 Apr 2023

Viewed by 1017

Abstract

This study proposes a continuous adaptive finite-time fractional-order sliding mode control method for fractional-order Buck converters. In order to establish a more accurate model, a fractional-order model based on the Riemann-Liouville (R-L) definition of the Buck converter is developed, which takes into account [...] Read more.

This study proposes a continuous adaptive finite-time fractional-order sliding mode control method for fractional-order Buck converters. In order to establish a more accurate model, a fractional-order model based on the Riemann-Liouville (R-L) definition of the Buck converter is developed, which takes into account the non-integer order characteristics of electronic components. The R-L definition is found to be more effective in describing the Buck converter than the Caputo definition. To deal with parameter uncertainties and external disturbances, the proposed approach combines these factors as lumped matched disturbances and mismatched disturbances. Unlike previous literature that assumes a known upper bound of disturbances, adaptive algorithms are developed to estimate and compensate for unknown bounded disturbances in this paper. A continuous finite-time sliding mode controller is then developed using a backstepping method to achieve a chattering-free response and ensure a finite-time convergence. The convergence time for the sliding mode reaching phase and sliding mode phase is estimated, and the fractional-order Lyapunov theory is utilized to prove the finite-time stability of the system. Finally, simulation results demonstrate the robustness and effectiveness of the proposed controller. Full article

(This article belongs to the Section Complexity)

► Show Figures

Figure 1

9 pages, 287 KiB

Open AccessArticle

The Modes of the Poisson Distribution of Order 3 and 4

by Yeil Kwon and Andreas N. Philippou

Entropy 2023, 25(4), 699; https://doi.org/10.3390/e25040699 - 21 Apr 2023

Cited by 7 | Viewed by 1169

Abstract

In this article, new properties of the Poisson distribution of order k with parameter

λ

are found. Based on them, the modes of the Poisson distributions of order

k = 3

and 4 are derived for

λ

in

(0, 1)

[...] Read more.

In this article, new properties of the Poisson distribution of order k with parameter

λ

are found. Based on them, the modes of the Poisson distributions of order

k = 3

and 4 are derived for

λ

in

(0, 1)

. They are 0, 3, 5, and 0, 4, 7, 8, respectively, for

λ

in specified subintervals of (0, 1). In addition, using Mathematica, computational results for the modes of the Poisson distributions of order

k = 2, 3

, and 4 are presented for

λ

in specified subintervals of

(0, 2)

. Full article

25 pages, 424 KiB

Open AccessArticle

Ruin Analysis on a New Risk Model with Stochastic Premiums and Dependence Based on Time Series for Count Random Variables

by Lihong Guan and Xiaohong Wang

Entropy 2023, 25(4), 698; https://doi.org/10.3390/e25040698 - 21 Apr 2023

Viewed by 1426

Abstract

In this paper, we propose a new discrete-time risk model of an insurance portfolio with stochastic premiums, in which the temporal dependence among the premium numbers of consecutive periods is fitted by the first-order integer-valued autoregressive (INAR(1)) process and the temporal dependence among [...] Read more.

In this paper, we propose a new discrete-time risk model of an insurance portfolio with stochastic premiums, in which the temporal dependence among the premium numbers of consecutive periods is fitted by the first-order integer-valued autoregressive (INAR(1)) process and the temporal dependence among the claim numbers of consecutive periods is described by the integer-valued moving average (INMA(1)) process. To measure the risk of the model quantitatively, we study the explicit expression for a function whose solution is defined as the Lundberg adjustment coefficient and give the Lundberg approximation formula for the infinite-time ruin probability. In the case of heavy-tailed claim sizes, we establish the asymptotic formula for the finite-time ruin probability via the large deviations of the aggregate claims. Two numerical examples are provided in order to illustrate our theoretical findings. Full article

(This article belongs to the Special Issue Discrete-Valued Time Series)

► Show Figures

Figure 1

26 pages, 1249 KiB

Open AccessArticle

KHGCN: Knowledge-Enhanced Recommendation with Hierarchical Graph Capsule Network

by Fukun Chen, Guisheng Yin, Yuxin Dong, Gesu Li and Weiqi Zhang

Entropy 2023, 25(4), 697; https://doi.org/10.3390/e25040697 - 20 Apr 2023

Cited by 4 | Viewed by 2673

Abstract

Knowledge graphs as external information has become one of the mainstream directions of current recommendation systems. Various knowledge-graph-representation methods have been proposed to promote the development of knowledge graphs in related fields. Knowledge-graph-embedding methods can learn entity information and complex relationships between the [...] Read more.

Knowledge graphs as external information has become one of the mainstream directions of current recommendation systems. Various knowledge-graph-representation methods have been proposed to promote the development of knowledge graphs in related fields. Knowledge-graph-embedding methods can learn entity information and complex relationships between the entities in knowledge graphs. Furthermore, recently proposed graph neural networks can learn higher-order representations of entities and relationships in knowledge graphs. Therefore, the complete presentation in the knowledge graph enriches the item information and alleviates the cold start of the recommendation process and too-sparse data. However, the knowledge graph’s entire entity and relation representation in personalized recommendation tasks will introduce unnecessary noise information for different users. To learn the entity-relationship presentation in the knowledge graph while effectively removing noise information, we innovatively propose a model named

k n o w l e d g e

—

e n h a n c e d

h i e r a r c h i c a l

g r a p h

c a p s u l e

n e t w o r k

(KHGCN), which can extract node embeddings in graphs while learning the hierarchical structure of graphs. Our model eliminates noisy entities and relationship representations in the knowledge graph by the entity disentangling for the recommendation and introduces the attentive mechanism to strengthen the knowledge-graph aggregation. Our model learns the presentation of entity relationships by an original graph capsule network. The capsule neural networks represent the structured information between the entities more completely. We validate the proposed model on real-world datasets, and the validation results demonstrate the model’s effectiveness. Full article

(This article belongs to the Topic Machine and Deep Learning)

► Show Figures

Figure 1

19 pages, 6627 KiB

Open AccessArticle

Research on Performance Degradation Estimation of Key Components of High-Speed Train Bogie Based on Multi-Task Learning

by Junxiao Ren, Weidong Jin, Yunpu Wu, Zhang Sun and Liang Li

Entropy 2023, 25(4), 696; https://doi.org/10.3390/e25040696 - 20 Apr 2023

Cited by 2 | Viewed by 1157

Abstract

The safe and comfortable operation of high-speed trains has attracted extensive attention. With the operation of the train, the performance of high-speed train bogie components inevitably degrades and eventually leads to failures. At present, it is a common method to achieve performance degradation [...] Read more.

The safe and comfortable operation of high-speed trains has attracted extensive attention. With the operation of the train, the performance of high-speed train bogie components inevitably degrades and eventually leads to failures. At present, it is a common method to achieve performance degradation estimation of bogie components by processing high-speed train vibration signals and analyzing the information contained in the signals. In the face of complex signals, the usage of information theory, such as information entropy, to achieve performance degradation estimations is not satisfactory, and recent studies have more often used deep learning methods instead of traditional methods, such as information theory or signal processing, to obtain higher estimation accuracy. However, current research is more focused on the estimation for a certain component of the bogie and does not consider the bogie as a whole system to accomplish the performance degradation estimation task for several key components at the same time. In this paper, based on soft parameter sharing multi-task deep learning, a multi-task and multi-scale convolutional neural network is proposed to realize performance degradation state estimations of key components of a high-speed train bogie. Firstly, the structure takes into account the multi-scale characteristics of high-speed train vibration signals and uses a multi-scale convolution structure to better extract the key features of the signal. Secondly, considering that the vibration signal of high-speed trains contains the information of all components, the soft parameter sharing method is adopted to realize feature sharing in the depth structure and improve the utilization of information. The effectiveness and superiority of the structure proposed by the experiment is a feasible scheme for improving the performance degradation estimation of a high-speed train bogie. Full article

(This article belongs to the Special Issue Fault Diagnosis and Fault-Tolerant Control for Complex Systems)

► Show Figures

Figure 1

11 pages, 2201 KiB

Open AccessArticle

Human Information Processing of the Speed of Various Movements Estimated Based on Trajectory Change

by Hiroki Murakami and Norimasa Yamada

Entropy 2023, 25(4), 695; https://doi.org/10.3390/e25040695 - 20 Apr 2023

Cited by 1 | Viewed by 1062

Abstract

Fitts’ approach, which examines the information processing of the human motor system, has the problem that the movement speed is controlled by the difficulty index of the task, which the participant uniquely sets, but it is an arbitrary speed. This study rigorously aims [...] Read more.

Fitts’ approach, which examines the information processing of the human motor system, has the problem that the movement speed is controlled by the difficulty index of the task, which the participant uniquely sets, but it is an arbitrary speed. This study rigorously aims to examine the relationship between movement speed and information processing using Woodworth’s method to control movement speed. Furthermore, we examined movement information processing using an approach that calculates probability-based information entropy and mutual information quantity between points from trajectory analysis. Overall, 17 experimental conditions were applied, 16 being externally controlled and one being self-paced with maximum speed. Considering that information processing occurs when irregularities decrease, the point at which information processing occurs switches at a movement frequency of approximately 3.0–3.25 Hz. Previous findings have suggested that motor control switches with increasing movement speed; thus, our approach helps explore human information processing in detail. Note that the characteristics of information processing in movement speed changes that were identified in this study were derived from one participant, but they are important characteristics of human motor control. Full article

► Show Figures

Figure 1

19 pages, 584 KiB

Open AccessArticle

Programming Quantum Neural Networks on NISQ Systems: An Overview of Technologies and Methodologies

by Stefano Markidis

Entropy 2023, 25(4), 694; https://doi.org/10.3390/e25040694 - 20 Apr 2023

Cited by 2 | Viewed by 3104

Abstract

Noisy Intermediate-Scale Quantum (NISQ) systems and associated programming interfaces make it possible to explore and investigate the design and development of quantum computing techniques for Machine Learning (ML) applications. Among the most recent quantum ML approaches, Quantum Neural Networks (QNN) emerged as an [...] Read more.

Noisy Intermediate-Scale Quantum (NISQ) systems and associated programming interfaces make it possible to explore and investigate the design and development of quantum computing techniques for Machine Learning (ML) applications. Among the most recent quantum ML approaches, Quantum Neural Networks (QNN) emerged as an important tool for data analysis. With the QNN advent, higher-level programming interfaces for QNN have been developed. In this paper, we survey the current state-of-the-art high-level programming approaches for QNN development. We discuss target architectures, critical QNN algorithmic components, such as the hybrid workflow of Quantum Annealers and Parametrized Quantum Circuits, QNN architectures, optimizers, gradient calculations, and applications. Finally, we overview the existing programming QNN frameworks, their software architecture, and associated quantum simulators. Full article

(This article belongs to the Special Issue Quantum Machine Learning 2022)

► Show Figures

Figure 1

14 pages, 1381 KiB

Open AccessArticle

An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method

by Jia-Fen Chen, Xian-Ming Gu, Liang Li and Ping Zhou

Entropy 2023, 25(4), 693; https://doi.org/10.3390/e25040693 - 19 Apr 2023

Viewed by 976

Abstract

An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the [...] Read more.

An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the computational domain. The discretized linear system of the HDG method on each subdomain is solved by a sparse direct solver. The solution of the interface linear system in the domain decomposition framework is accelerated by a Krylov subspace method. We study the spectral radius of the iteration matrix of the Schwarz method for the LORM problems, and thus propose an optimized parameter for the transmission condition, which is different from that for the classical electromagnetic problems. The numerical results show that the proposed method is effective. Full article

(This article belongs to the Special Issue Machine Learning and Modern Numerical Methods in Partial Differential Equations)

► Show Figures

Figure 1

16 pages, 335 KiB

Open AccessArticle

Non-Stationary Non-Hermitian “Wrong-Sign” Quantum Oscillators and Their Meaningful Physical Interpretation

by Miloslav Znojil

Entropy 2023, 25(4), 692; https://doi.org/10.3390/e25040692 - 19 Apr 2023

Cited by 3 | Viewed by 978

Abstract

In the framework of quantum mechanics using quasi-Hermitian operators the standard unitary evolution of a non-stationary but still closed quantum system is only properly described in the non-Hermitian interaction picture (NIP). In this formulation of the theory both the states and the observables [...] Read more.

In the framework of quantum mechanics using quasi-Hermitian operators the standard unitary evolution of a non-stationary but still closed quantum system is only properly described in the non-Hermitian interaction picture (NIP). In this formulation of the theory both the states and the observables vary with time. A few aspects of implementation of this picture are illustrated via the “wrong-sign” quartic oscillators. It is shown that in contrast to the widespread belief, both of the related Schrödinger-equation generators

G (t)

and the Heisenberg-equation generators

Σ (t)

are just auxiliary concepts. Their spectra are phenomenologically irrelevant and, in general, complex. It is argued that only the sum

H (t) = G (t) + Σ (t)

of the latter operators retains the standard physical meaning of the instantaneous energy of the unitary quantum system in question. Full article

(This article belongs to the Special Issue Quantum Dynamics with Non-hermitian Hamiltonians II)

► Show Figures

Figure 1

13 pages, 1627 KiB

Open AccessArticle

A Note on Cherry-Picking in Meta-Analyses

by Daisuke Yoneoka and Bastian Rieck

Entropy 2023, 25(4), 691; https://doi.org/10.3390/e25040691 - 19 Apr 2023

Cited by 1 | Viewed by 1232

Abstract

We study selection bias in meta-analyses by assuming the presence of researchers (meta-analysts) who intentionally or unintentionally cherry-pick a subset of studies by defining arbitrary inclusion and/or exclusion criteria that will lead to their desired results. When the number of studies is sufficiently [...] Read more.

We study selection bias in meta-analyses by assuming the presence of researchers (meta-analysts) who intentionally or unintentionally cherry-pick a subset of studies by defining arbitrary inclusion and/or exclusion criteria that will lead to their desired results. When the number of studies is sufficiently large, we theoretically show that a meta-analysts might falsely obtain (non)significant overall treatment effects, regardless of the actual effectiveness of a treatment. We analyze all theoretical findings based on extensive simulation experiments and practical clinical examples. Numerical evaluations demonstrate that the standard method for meta-analyses has the potential to be cherry-picked. Full article

(This article belongs to the Special Issue Biostatistics, Bioinformatics, and Data Analysis)

► Show Figures

Figure 1

12 pages, 2900 KiB

Open AccessArticle

Application of Multiscale Sample Entropy in Assessing Effects of Exercise Training on Skin Blood Flow Oscillations in People with Spinal Cord Injury

by Fuyuan Liao, Hengyang Zhao, Cheng-Feng Lin, Panpan Chen, Philbert Chen, Kingsley Onyemere and Yih-Kuen Jan

Entropy 2023, 25(4), 690; https://doi.org/10.3390/e25040690 - 19 Apr 2023

Viewed by 1147

Abstract

Spinal cord injury (SCI) causes a disruption of autonomic nervous regulation to the cardiovascular system, leading to various cardiovascular and microvascular diseases. Exercise training is an effective intervention for reducing risk for microvascular diseases in healthy people. However, the effectiveness of exercise training [...] Read more.

Spinal cord injury (SCI) causes a disruption of autonomic nervous regulation to the cardiovascular system, leading to various cardiovascular and microvascular diseases. Exercise training is an effective intervention for reducing risk for microvascular diseases in healthy people. However, the effectiveness of exercise training on improving microvascular function in people with SCI is largely unknown. The purpose of this study was to compare blood flow oscillations in people with spinal cord injury and different physical activity levels to determine if such a lifestyle might influence skin blood flow. A total of 37 participants were recruited for this study, including 12 athletes with SCI (ASCI), 9 participants with SCI and a sedentary lifestyle (SSCI), and 16 healthy able-bodied controls (AB). Sacral skin blood flow (SBF) in response to local heating at 42 °C for 50 min was measured using laser Doppler flowmetry. The degree of the regularity of blood flow oscillations (BFOs) was quantified using a multiscale entropy approach. The results showed that BFO was significantly more irregular in ASCI and AB compared to SSCI during the maximal vasodilation period. Our results also demonstrate that the difference in the regularity of BFOs between original SBF signal and phase-randomized surrogate time series was larger in ASCI and AB compared to SSCI. Our findings indicate that SCI causes a loss of complexity of BFOs and exercise training may improve complexity in people with SCI. This study demonstrates that multiscale entropy is a sensitive method for detecting differences between different categories of people with SCI and might be able to detect effects of exercise training related to skin blood flow. Full article

(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications III)

► Show Figures

Figure 1

14 pages, 10278 KiB

Open AccessArticle

Spatio-Temporal Analysis of Marine Water Quality Data Based on Cross-Recurrence Plot (CRP) and Cross-Recurrence Quantitative Analysis (CRQA)

by Zhigang Li, Ting Sun, Yu Wang, Yujie Liu and Xiaochuan Sun

Entropy 2023, 25(4), 689; https://doi.org/10.3390/e25040689 - 19 Apr 2023

Cited by 1 | Viewed by 1047

Abstract

In recent years, with the frequency of marine disasters, water quality has become an important environmental problem for researchers, and much effort has been put into the prediction of marine water quality. The temporal and spatial correlation of marine water quality parameters directly [...] Read more.

In recent years, with the frequency of marine disasters, water quality has become an important environmental problem for researchers, and much effort has been put into the prediction of marine water quality. The temporal and spatial correlation of marine water quality parameters directly determines whether the marine time-series data prediction task can be completed efficiently. However, existing research has only focused on the correlation analysis of marine data in a certain area and has ignored the temporal and spatial characteristics of marine data in complex and changeable marine environments. Therefore, we constructed a spatio-temporal dynamic analysis model of marine water quality based on a cross-recurrence plot (CRP) and cross-recurrence quantitative analysis (CRQA). The time-series data of marine water quality were first mapped to high-dimensional space through phase space reconstruction, and then the dynamic relationship among various factors affecting water quality was visually displayed through CRP. Finally, their correlation was quantitatively explained by CRQA. The experimental results showed that our scheme demonstrated well the dynamic correlation of various factors affecting water quality in different locations, providing important data support for the spatio-temporal prediction of marine water quality. Full article

(This article belongs to the Special Issue Spatial–Temporal Data Analysis and Its Applications)

► Show Figures

Figure 1

27 pages, 4072 KiB

Open AccessArticle

Network Synchronization of MACM Circuits and Its Application to Secure Communications

by Rodrigo Méndez-Ramírez, Adrian Arellano-Delgado and Miguel Ángel Murillo-Escobar

Entropy 2023, 25(4), 688; https://doi.org/10.3390/e25040688 - 19 Apr 2023

Cited by 2 | Viewed by 1355

Abstract

In recent years, chaotic synchronization has received a lot of interest in applications in different fields, including in the design of private and secure communication systems. The purpose of this paper was to achieve the synchronization of the Méndez–Arellano–Cruz–Martínez (MACM) 3D chaotic system [...] Read more.

In recent years, chaotic synchronization has received a lot of interest in applications in different fields, including in the design of private and secure communication systems. The purpose of this paper was to achieve the synchronization of the Méndez–Arellano–Cruz–Martínez (MACM) 3D chaotic system coupled in star topology. The MACM electronic circuit is used as chaotic nodes in the communication channels to achieve synchronization in the proposed star network; the corresponding electrical hardware in the slave stages receives the coupling signal from the master node. In addition, a novel application to the digital image encryption process is proposed using the coupled-star-network; and the switching parameter technique is finally used to transmit an image as an encrypted message from the master node to the slave coupled nodes. Finally, the cryptosystem is submitted to statistical tests in order to show the effectiveness in multi-user secure image applications. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

► Show Figures

Figure 1

13 pages, 381 KiB

Open AccessArticle

Restricted Phase Space Thermodynamics of Einstein-Power-Yang–Mills AdS Black Hole

by Yun-Zhi Du, Huai-Fan Li, Yang Zhang, Xiang-Nan Zhou and Jun-Xin Zhao

Entropy 2023, 25(4), 687; https://doi.org/10.3390/e25040687 - 19 Apr 2023

Cited by 5 | Viewed by 971

Abstract

We consider the thermodynamics of the Einstein-power-Yang–Mills AdS black holes in the context of the gauge-gravity duality. Under this framework, Newton’s gravitational constant and the cosmological constant are varied in the system. We rewrite the thermodynamic first law in a more extended form [...] Read more.

We consider the thermodynamics of the Einstein-power-Yang–Mills AdS black holes in the context of the gauge-gravity duality. Under this framework, Newton’s gravitational constant and the cosmological constant are varied in the system. We rewrite the thermodynamic first law in a more extended form containing both the pressure and the central charge of the dual conformal field theory, i.e., the restricted phase transition formula. A novel phenomena arises: the dual quantity of pressure is the effective volume, not the geometric one. That leads to a new behavior of the Van de Waals-like phase transition for this system with the fixed central charge: the supercritical phase transition. From the Ehrenfest’s scheme perspective, we check out the second-order phase transition of the EPYM AdS black hole. Furthermore the effect of the non-linear Yang–Mills parameter on these thermodynamic properties is also investigated. Full article

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

► Show Figures

Figure 1

13 pages, 405 KiB

Open AccessArticle

Weighted BATS Codes with LDPC Precoding

by Wenyue Zhang and Min Zhu

Entropy 2023, 25(4), 686; https://doi.org/10.3390/e25040686 - 19 Apr 2023

Cited by 1 | Viewed by 863

Abstract

Batched Sparse (BATS) codes are a type of network coding scheme that use a combination of random linear network coding (RLNC) and fountain coding to enhance the reliability and efficiency of data transmission. In order to achieve unequal error protection for different data, [...] Read more.

Batched Sparse (BATS) codes are a type of network coding scheme that use a combination of random linear network coding (RLNC) and fountain coding to enhance the reliability and efficiency of data transmission. In order to achieve unequal error protection for different data, researchers have proposed unequal error protection BATS (UEP-BATS) codes. However, current UEP-BATS codes suffer from high error floors in their decoding performance, which restricts their practical applications. To address this issue, we propose a novel UEP-BATS code scheme that employs a precoding stage prior to the weighted BATS code. The proposed precoding stage utilizes a partially regular low-density parity-check (PR-LDPC) code, which helps to mitigate the high error floors in the weighted BATS code We derive the asymptotic performance of the proposed scheme based on density evolution (DE). Additionally, we propose a searching algorithm to optimize precoding degree distribution within the complexity range of the precoding stage. Simulation results show that compared to the conventional weighted BATS codes, our proposed scheme offers superior UEP performance and lower error floor, which verifies the effectiveness of our scheme. Full article

(This article belongs to the Special Issue Selected Feature Papers from China Information Theory Conference (CIT) & the Annual Conference on Information Theory of the Chinese Institute of Electronics (CIEIT))

► Show Figures

Figure 1

11 pages, 647 KiB

Open AccessFeature PaperArticle

Outlier-Robust Surrogate Modeling of Ion–Solid Interaction Simulations

by Roland Preuss and Udo von Toussaint

Entropy 2023, 25(4), 685; https://doi.org/10.3390/e25040685 - 19 Apr 2023

Viewed by 700

Abstract

Data for complex plasma–wall interactions require long-running and expensive computer simulations. Furthermore, the number of input parameters is large, which results in low coverage of the (physical) parameter space. Unpredictable occasions of outliers create a need to conduct the exploration of this multi-dimensional [...] Read more.

Data for complex plasma–wall interactions require long-running and expensive computer simulations. Furthermore, the number of input parameters is large, which results in low coverage of the (physical) parameter space. Unpredictable occasions of outliers create a need to conduct the exploration of this multi-dimensional space using robust analysis tools. We restate the Gaussian process (GP) method as a Bayesian adaptive exploration method for establishing surrogate surfaces in the variables of interest. On this basis, we expand the analysis by the Student-t process (TP) method in order to improve the robustness of the result with respect to outliers. The most obvious difference between both methods shows up in the marginal likelihood for the hyperparameters of the covariance function, where the TP method features a broader marginal probability distribution in the presence of outliers. Eventually, we provide first investigations, with a mixture likelihood of two Gaussians within a Gaussian process ansatz for describing either outlier or non-outlier behavior. The parameters of the two Gaussians are set such that the mixture likelihood resembles the shape of a Student-t likelihood. Full article

(This article belongs to the Special Issue MaxEnt 2022—the 41st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering)

► Show Figures

Figure 1

21 pages, 1573 KiB

Open AccessArticle

A 3D Approach Using a Control Algorithm to Minimize the Effects on the Healthy Tissue in the Hyperthermia for Cancer Treatment

by Gustavo Resende Fatigate, Marcelo Lobosco and Ruy Freitas Reis

Entropy 2023, 25(4), 684; https://doi.org/10.3390/e25040684 - 19 Apr 2023

Cited by 1 | Viewed by 1471

Abstract

According to the World Health Organization, cancer is a worldwide health problem. Its high mortality rate motivates scientists to study new treatments. One of these new treatments is hyperthermia using magnetic nanoparticles. This treatment consists in submitting the target region with a low-frequency [...] Read more.

According to the World Health Organization, cancer is a worldwide health problem. Its high mortality rate motivates scientists to study new treatments. One of these new treatments is hyperthermia using magnetic nanoparticles. This treatment consists in submitting the target region with a low-frequency magnetic field to increase its temperature over 43 °C, as the threshold for tissue damage and leading the cells to necrosis. This paper uses an in silico three-dimensional Pennes’ model described by a set of partial differential equations (PDEs) to estimate the percentage of tissue damage due to hyperthermia. Differential evolution, an optimization method, suggests the best locations to inject the nanoparticles to maximize tumor cell death and minimize damage to healthy tissue. Three different scenarios were performed to evaluate the suggestions obtained by the optimization method. The results indicate the positive impact of the proposed technique: a reduction in the percentage of healthy tissue damage and the complete damage of the tumors were observed. In the best scenario, the optimization method was responsible for decreasing the healthy tissue damage by

59 %

when the nanoparticles injection sites were located in the non-intuitive points indicated by the optimization method. The numerical solution of the PDEs is computationally expensive. This work also describes the implemented parallel strategy based on CUDA to reduce the computational costs involved in the PDEs resolution. Compared to the sequential version executed on the CPU, the proposed parallel implementation was able to speed the execution time up to

84.4

times. Full article

(This article belongs to the Special Issue Special Issue Dedicated to the 15th International Special Track on Biomedical and Bioinformatics Challenges for Computer Science)

► Show Figures

Figure 1

3 pages, 195 KiB

Open AccessEditorial

Information and Divergence Measures

by Alex Karagrigoriou and Andreas Makrides

Entropy 2023, 25(4), 683; https://doi.org/10.3390/e25040683 - 19 Apr 2023

Viewed by 807

Abstract

The present Special Issue of Entropy, entitled Information and Divergence Measures, covers various aspects and applications in the general area of Information and Divergence Measures [...] Full article

(This article belongs to the Special Issue Information and Divergence Measures)

17 pages, 12355 KiB

Open AccessArticle

Zero-Watermarking for Vector Maps Combining Spatial and Frequency Domain Based on Constrained Delaunay Triangulation Network and Discrete Fourier Transform

by Xu Xi, Yang Hua, Yi Chen and Qiande Zhu

Entropy 2023, 25(4), 682; https://doi.org/10.3390/e25040682 - 19 Apr 2023

Cited by 3 | Viewed by 1098

Abstract

With its lossless properties, zero-watermarking has attracted a lot of attention in the field of copyright protection for vector maps. However, the common zero-watermarking algorithm puts too much emphasis on mining for global features, making it vulnerable to cropping attacks, and the robustness [...] Read more.

With its lossless properties, zero-watermarking has attracted a lot of attention in the field of copyright protection for vector maps. However, the common zero-watermarking algorithm puts too much emphasis on mining for global features, making it vulnerable to cropping attacks, and the robustness is not comprehensive enough. This study provides a vector map zero-watermarking scheme that utilizes spatial statistical information and frequency domain transformation methods in an effort to solve the aforementioned issue. In order to make the scheme more resistant to cropping and compression, it is constructed on the basis of feature point extraction and point constraint blocking of the original vector map. Within each sub-block, feature points are used to build constraint Delaunay triangulation networks (CDTN), and the angular values within the triangle networks are then extracted as spatial statistics. The angle value sequence is further transformed by discrete Fourier transform (DFT), and the binarized phase sequence is used as the final feature information to build a zero watermark by executing an exclusive disjunction operation with the encrypted copyright watermark image, both of which contribute to the scheme’s robustness and security. The results of the attack experiments show that the proposed vector map zero-watermarking can restore identifiable copyright images under common geometric attacks, cropping attacks, and coordinate system transformations, demonstrating a high level of robustness. The theoretical basis for the robustness of this watermarking scheme is the stability of CDTN and the geometric invariance of DFT coefficients, and both theory and experiment validate the method’s validity. Full article

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

► Show Figures

Figure 1

13 pages, 4528 KiB

Open AccessArticle

Semi-Supervised Semantic Segmentation of Remote Sensing Images Based on Dual Cross-Entropy Consistency

by Mengtian Cui, Kai Li, Yulan Li, Dany Kamuhanda and Claudio J. Tessone

Entropy 2023, 25(4), 681; https://doi.org/10.3390/e25040681 - 19 Apr 2023

Cited by 3 | Viewed by 1461

Abstract

Semantic segmentation is a growing topic in high-resolution remote sensing image processing. The information in remote sensing images is complex, and the effectiveness of most remote sensing image semantic segmentation methods depends on the number of labels; however, labeling images requires significant time [...] Read more.

Semantic segmentation is a growing topic in high-resolution remote sensing image processing. The information in remote sensing images is complex, and the effectiveness of most remote sensing image semantic segmentation methods depends on the number of labels; however, labeling images requires significant time and labor costs. To solve these problems, we propose a semi-supervised semantic segmentation method based on dual cross-entropy consistency and a teacher–student structure. First, we add a channel attention mechanism to the encoding network of the teacher model to reduce the predictive entropy of the pseudo label. Secondly, the two student networks share a common coding network to ensure consistent input information entropy, and a sharpening function is used to reduce the information entropy of unsupervised predictions for both student networks. Finally, we complete the alternate training of the models via two entropy-consistent tasks: (1) semi-supervising student prediction results via pseudo-labels generated from the teacher model, (2) cross-supervision between student models. Experimental results on publicly available datasets indicate that the suggested model can fully understand the hidden information in unlabeled images and reduce the information entropy in prediction, as well as reduce the number of required labeled images with guaranteed accuracy. This allows the new method to outperform the related semi-supervised semantic segmentation algorithm at half the proportion of labeled images. Full article

(This article belongs to the Special Issue Complexity, Entropy and the Physics of Information)

► Show Figures

Figure 1

18 pages, 377 KiB

Open AccessArticle

Quantum Error-Correcting Codes Based on Orthogonal Arrays

by Rong Yan, Shanqi Pang, Mengqian Chen and Fuyuan Yang

Entropy 2023, 25(4), 680; https://doi.org/10.3390/e25040680 - 19 Apr 2023

Cited by 2 | Viewed by 2708

Abstract

In this paper, by using the Hamming distance, we establish a relation between quantum error-correcting codes

{((N, K, d + 1))}_{s}

and orthogonal arrays with orthogonal partitions. Therefore, this is a generalization of the relation between [...] Read more.

In this paper, by using the Hamming distance, we establish a relation between quantum error-correcting codes

{((N, K, d + 1))}_{s}

and orthogonal arrays with orthogonal partitions. Therefore, this is a generalization of the relation between quantum error-correcting codes

{((N, 1, d + 1))}_{s}

and irredundant orthogonal arrays. This relation is used for the construction of pure quantum error-correcting codes. As applications of this method, numerous infinite families of optimal quantum codes can be constructed explicitly such as

{((3, s, 2))}_{s}

for all

s_{i} \geq 3

,

{((4, s^{2}, 2))}_{s}

for all

s_{i} \geq 5

,

{((5, s, 3))}_{s}

for all

s_{i} \geq 4

,

{((6, s^{2}, 3))}_{s}

for all

s_{i} \geq 5

,

{((7, s^{3}, 3))}_{s}

for all

s_{i} \geq 7

,

{((8, s^{2}, 4))}_{s}

for all

s_{i} \geq 9

,

{((9, s^{3}, 4))}_{s}

for all

s_{i} \geq 11

,

{((9, s, 5))}_{s}

for all

s_{i} \geq 9

,

{((10, s^{2}, 5))}_{s}

for all

s_{i} \geq 11

,

{((11, s, 6))}_{s}

for all

s_{i} \geq 11

, and

{((12, s^{2}, 6))}_{s}

for all

s_{i} \geq 13

, where

s = s_{1} \dots s_{n}

and

s_{1}, \dots, s_{n}

are all prime powers. The advantages of our approach over existing methods lie in the facts that these results are not just existence results, but constructive results, the codes constructed are pure, and each basis state of these codes has far less terms. Moreover, the above method developed can be extended to construction of quantum error-correcting codes over mixed alphabets. Full article

(This article belongs to the Special Issue New Advances in Quantum Communication and Networks)

24 pages, 466 KiB

Open AccessArticle

by Mohammad Amin Zarrabian, Ni Ding and Parastoo Sadeghi

Entropy 2023, 25(4), 679; https://doi.org/10.3390/e25040679 - 18 Apr 2023

Cited by 2 | Viewed by 1077

Abstract

This paper investigates lift, the likelihood ratio between the posterior and prior belief about sensitive features in a dataset. Maximum and minimum lifts over sensitive features quantify the adversary’s knowledge gain and should be bounded to protect privacy. We demonstrate that max- and [...] Read more.

This paper investigates lift, the likelihood ratio between the posterior and prior belief about sensitive features in a dataset. Maximum and minimum lifts over sensitive features quantify the adversary’s knowledge gain and should be bounded to protect privacy. We demonstrate that max- and min-lifts have a distinct range of values and probability of appearance in the dataset, referred to as lift asymmetry. We propose asymmetric local information privacy (ALIP) as a compatible privacy notion with lift asymmetry, where different bounds can be applied to min- and max-lifts. We use ALIP in the watchdog and optimal random response (ORR) mechanisms, the main methods to achieve lift-based privacy. It is shown that ALIP enhances utility in these methods compared to existing local information privacy, which ensures the same (symmetric) bounds on both max- and min-lifts. We propose subset merging for the watchdog mechanism to improve data utility and subset random response for the ORR to reduce complexity. We then investigate the related lift-based measures, including

ℓ_{1}

-norm,

χ^{2}

-privacy criterion, and

α

-lift. We reveal that they can only restrict max-lift, resulting in significant min-lift leakage. To overcome this problem, we propose corresponding lift-inverse measures to restrict the min-lift. We apply these lift-based and lift-inverse measures in the watchdog mechanism. We show that they can be considered as relaxations of ALIP, where a higher utility can be achieved by bounding only average max- and min-lifts. Full article

(This article belongs to the Special Issue Information-Theoretic Privacy in Retrieval, Computing, and Learning)

► Show Figures

Figure 1

20 pages, 754 KiB

Open AccessArticle

Geometric Structures Induced by Deformations of the Legendre Transform

by Pablo A. Morales, Jan Korbel and Fernando E. Rosas

Entropy 2023, 25(4), 678; https://doi.org/10.3390/e25040678 - 18 Apr 2023

Cited by 1 | Viewed by 1525

Abstract

The recent link discovered between generalized Legendre transforms and non-dually flat statistical manifolds suggests a fundamental reason behind the ubiquity of Rényi’s divergence and entropy in a wide range of physical phenomena. However, these early findings still provide little intuition on the nature [...] Read more.

The recent link discovered between generalized Legendre transforms and non-dually flat statistical manifolds suggests a fundamental reason behind the ubiquity of Rényi’s divergence and entropy in a wide range of physical phenomena. However, these early findings still provide little intuition on the nature of this relationship and its implications for physical systems. Here we shed new light on the Legendre transform by revealing the consequences of its deformation via symplectic geometry and complexification. These findings reveal a novel common framework that leads to a principled and unified understanding of physical systems that are not well-described by classic information-theoretic quantities. Full article

(This article belongs to the Special Issue Information Geometry and Its Applications)

► Show Figures

Figure 1

22 pages, 3256 KiB

Open AccessArticle

Visibility Graph Analysis of Heartbeat Time Series: Comparison of Young vs. Old, Healthy vs. Diseased, Rest vs. Exercise, and Sedentary vs. Active

by Alejandro Muñoz-Diosdado, Éric E. Solís-Montufar and José A. Zamora-Justo

Entropy 2023, 25(4), 677; https://doi.org/10.3390/e25040677 - 18 Apr 2023

Viewed by 1819

Abstract

Using the visibility graph algorithm (VGA), a complex network can be associated with a time series, such that the properties of the time series can be obtained by studying those of the network. Any value of the time series becomes a node of [...] Read more.

Using the visibility graph algorithm (VGA), a complex network can be associated with a time series, such that the properties of the time series can be obtained by studying those of the network. Any value of the time series becomes a node of the network, and the number of other nodes that it is connected to can be quantified. The degree of connectivity of a node is positively correlated with its magnitude. The slope of the regression line is denoted by k-M, and, in this work, this parameter was calculated for the cardiac interbeat time series of different contrasting groups, namely: young vs. elderly; healthy subjects vs. patients with congestive heart failure (CHF); young subjects and adults at rest vs. exercising young subjects and adults; and, finally, sedentary young subjects and adults vs. active young subjects and adults. In addition, other network parameters, including the average degree and the average path length, of these time series networks were also analyzed. Significant differences were observed in the k-M parameter, average degree, and average path length for all analyzed groups. This methodology based on the analysis of the three mentioned parameters of complex networks has the advantage that such parameters are very easy to calculate, and it is useful to classify heartbeat time series of subjects with CHF vs. healthy subjects, and also for young vs. elderly subjects and sedentary vs. active subjects. Full article

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

► Show Figures

Figure 1

12 pages, 5357 KiB

Open AccessArticle

Ranking Plant Network Nodes Based on Their Centrality Measures

by Nilesh Kumar and M. Shahid Mukhtar

Entropy 2023, 25(4), 676; https://doi.org/10.3390/e25040676 - 18 Apr 2023

Cited by 5 | Viewed by 1902

Abstract

Biological networks are often large and complex, making it difficult to accurately identify the most important nodes. Node prioritization algorithms are used to identify the most influential nodes in a biological network by considering their relationships with other nodes. These algorithms can help [...] Read more.

Biological networks are often large and complex, making it difficult to accurately identify the most important nodes. Node prioritization algorithms are used to identify the most influential nodes in a biological network by considering their relationships with other nodes. These algorithms can help us understand the functioning of the network and the role of individual nodes. We developed CentralityCosDist, an algorithm that ranks nodes based on a combination of centrality measures and seed nodes. We applied this and four other algorithms to protein–protein interactions and co-expression patterns in Arabidopsis thaliana using pathogen effector targets as seed nodes. The accuracy of the algorithms was evaluated through functional enrichment analysis of the top 10 nodes identified by each algorithm. Most enriched terms were similar across algorithms, except for DIAMOnD. CentralityCosDist identified more plant–pathogen interactions and related functions and pathways compared to the other algorithms. Full article

(This article belongs to the Special Issue Foundations of Network Analysis)

► Show Figures

Figure 1

21 pages, 3482 KiB

Open AccessArticle

Improved Physics-Informed Neural Networks Combined with Small Sample Learning to Solve Two-Dimensional Stefan Problem

by Jiawei Li, Wei Wu and Xinlong Feng

Entropy 2023, 25(4), 675; https://doi.org/10.3390/e25040675 - 18 Apr 2023

Cited by 1 | Viewed by 1691

Abstract

With the remarkable development of deep learning in the field of science, deep neural networks provide a new way to solve the Stefan problem. In this paper, deep neural networks combined with small sample learning and a general deep learning framework are proposed [...] Read more.

With the remarkable development of deep learning in the field of science, deep neural networks provide a new way to solve the Stefan problem. In this paper, deep neural networks combined with small sample learning and a general deep learning framework are proposed to solve the two-dimensional Stefan problem. In the case of adding less sample data, the model can be modified and the prediction accuracy can be improved. In addition, by solving the forward and inverse problems of the two-dimensional single-phase Stefan problem, it is verified that the improved method can accurately predict the solutions of the partial differential equations of the moving boundary and the dynamic interface. Full article

(This article belongs to the Special Issue Machine Learning and Modern Numerical Methods in Partial Differential Equations)

► Show Figures

Figure 1

22 pages, 2700 KiB

Open AccessArticle

A Second-Order Network Structure Based on Gradient-Enhanced Physics-Informed Neural Networks for Solving Parabolic Partial Differential Equations

by Kuo Sun and Xinlong Feng

Entropy 2023, 25(4), 674; https://doi.org/10.3390/e25040674 - 18 Apr 2023

Cited by 3 | Viewed by 2098

Abstract

Physics-informed neural networks (PINNs) are effective for solving partial differential equations (PDEs). This method of embedding partial differential equations and their initial boundary conditions into the loss functions of neural networks has successfully solved forward and inverse PDE problems. In this study, we [...] Read more.

Physics-informed neural networks (PINNs) are effective for solving partial differential equations (PDEs). This method of embedding partial differential equations and their initial boundary conditions into the loss functions of neural networks has successfully solved forward and inverse PDE problems. In this study, we considered a parametric light wave equation, discretized it using the central difference, and, through this difference scheme, constructed a new neural network structure named the second-order neural network structure. Additionally, we used the adaptive activation function strategy and gradient-enhanced strategy to improve the performance of the neural network and used the deep mixed residual method (MIM) to reduce the high computational cost caused by the enhanced gradient. At the end of this paper, we give some numerical examples of nonlinear parabolic partial differential equations to verify the effectiveness of the method. Full article

(This article belongs to the Special Issue Machine Learning and Modern Numerical Methods in Partial Differential Equations)

► Show Figures

Figure 1

14 pages, 8131 KiB

Open AccessArticle

Hydrogen Embrittlement of CrCoNi Medium-Entropy Alloy with Millimeter-Scale Grain Size: An In Situ Hydrogen Charging Study

by Shaohua Yan, Xipei He and Zhongyin Zhu

Entropy 2023, 25(4), 673; https://doi.org/10.3390/e25040673 - 18 Apr 2023

Cited by 3 | Viewed by 1634

Abstract

In this study, we examined the effect of charging current density on the hydrogen embrittlement (HE) of MEA and the associated HE mechanisms using electron backscattered diffraction (EBSD). Results show that MEA is susceptible to HE, but is stronger than as-rolled and 3D-printed [...] Read more.

In this study, we examined the effect of charging current density on the hydrogen embrittlement (HE) of MEA and the associated HE mechanisms using electron backscattered diffraction (EBSD). Results show that MEA is susceptible to HE, but is stronger than as-rolled and 3D-printed Cantor alloy and stainless steel. The HE susceptibility of MEA decreases with increasing current density. Ductile fracture with transgranular dimples switches to intergranular brittle fracture with clear slip bands in the interior of grains. EBSD results uncovered that hydrogen facilitates localized slips and deformation twins. Hydrogen-enhanced localized plasticity and hydrogen decohesion are the possible HE mechanisms. Full article

(This article belongs to the Special Issue Recent Advances in Refractory High Entropy Alloys)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Entropy, Volume 25, Issue 4 (April 2023) – 156 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI