IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-28 DOI: 10.3390/e27090913

José M Amigó, Roberto Dale

{"title":"Permutation-Based Distances for Groups and Group-Valued Time Series.","authors":"José M Amigó, Roberto Dale","doi":"10.3390/e27090913","DOIUrl":"10.3390/e27090913","url":null,"abstract":"Permutations on a set, endowed with function composition, build a group called a symmetric group. In addition to their algebraic structure, symmetric groups have two metrics that are of particular interest to us here: the Cayley distance and the Kendall tau distance. In fact, the aim of this paper is to introduce the concept of distance in a general finite group based on them. The main tool that we use to this end is Cayley's theorem, which states that any finite group is isomorphic to a subgroup of a certain symmetric group. We also discuss the advantages and disadvantage of these permutation-based distances compared to the conventional generator-based distances in finite groups. The reason why we are interested in distances on groups is that finite groups appear in symbolic representations of time series, most notably in the so-called ordinal representations, whose symbols are precisely permutations, usually called ordinal patterns in that context. The natural extension from groups to group-valued time series is also discussed, as well as how such metric tools can be applied in time series analysis. Both theory and applications are illustrated with examples and numerical simulations.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468715/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Numerical Integration of Stochastic Differential Equations: The Heun Algorithm Revisited and the Itô-Stratonovich Calculus. 随机微分方程的数值积分：重新审视的Heun算法和Itô-Stratonovich微积分。

IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-28 DOI: 10.3390/e27090910

Riccardo Mannella

引用次数: 0

Entropy Reduction Across Odor Fields. 跨气味场的熵减少。

IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-28 DOI: 10.3390/e27090909

Hugo Magalhães, Lino Marques

{"title":"Entropy Reduction Across Odor Fields.","authors":"Hugo Magalhães, Lino Marques","doi":"10.3390/e27090909","DOIUrl":"10.3390/e27090909","url":null,"abstract":"Cognitive Odor Source Localization (OSL) strategies are reliable search strategies for turbulent environments, where chemical cues are sparse and intermittent. These methods estimate a probabilistic belief over the source location using Bayesian inference and guide the searching movement by evaluating expected entropy reduction at candidate new positions. By maximizing expected information gain, agents make informed decisions rather than simply reacting to sensor readings. However, computing entropy reductions is computationally expensive, making real-time implementation challenging for resource-constrained platforms. Interestingly, search trajectories produced by cognitive algorithms often resemble those of small insects, suggesting that informative movement patterns might be replicated using simpler, bio-inspired searching strategies. This work investigates that possibility by analysing spatial distribution of entropy reductions across the entire search area. Rather than focusing on searching algorithms and local decisions, the analysis maps information gain over the full environment, identifying consistent high-gain regions that may serve as navigational cues. Results show that these regions often emerge near the source and along plume borders and that expected entropy reduction is strongly influenced by prior belief shape and sensor observations. This global perspective enables identification of spatial patterns and high-gain regions that remain hidden when analysis is restricted to local neighborhoods. These insights enable synthesis of hybrid search strategies that preserve cognitive effectiveness while significantly reducing computational cost.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468182/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Enhanced Key Node Identification in Complex Networks Based on Fractal Dimension and Entropy-Driven Spring Model. 基于分形维数和熵驱动弹簧模型的复杂网络关键节点增强识别。

IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-28 DOI: 10.3390/e27090911

Zhaoliang Zhou, Xiaoli Huang, Zhaoyan Li, Wenbo Jiang

{"title":"Enhanced Key Node Identification in Complex Networks Based on Fractal Dimension and Entropy-Driven Spring Model.","authors":"Zhaoliang Zhou, Xiaoli Huang, Zhaoyan Li, Wenbo Jiang","doi":"10.3390/e27090911","DOIUrl":"10.3390/e27090911","url":null,"abstract":"How to identify the key nodes in a complex network is a major challenge. In this paper, we propose a Second-Order Neighborhood Entropy Fuzzy Local Dimension Spring Model (SNEFLD-SM). SNEFLD-SM model combines a variety of centrality methods based on spring model, such as second-order neighborhood centrality, betweenness centrality, and fractal dimension, to evaluate the importance of nodes. Fractal technology can effectively boost the framework's proficiency in understanding network self-similarity and hierarchical structure in multi-scale complex networks. It overcomes the limitation of the traditional centrality method which only focuses on local or global information. The method introduces information entropy and node influence range; information entropy can effectively capture the local and global features of the network. The node influence rangecan increase the node importance distinction and reduce the calculation cost. Meanwhile, an attenuation factor is introduced to suppress the \"rich-club\" phenomenon. Tests on six networks show that SNEFLD-SM has higher accuracy in critical node detection than traditional methods. Furthermore, the application of information entropy further strengthens the model's capability to recognize key nodes.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12469013/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Performance Analysis of Non-Orthogonal Multiple Access-Enhanced Autonomous Aerial Vehicle-Assisted Internet of Vehicles over Rician Fading Channels. 非正交多址增强自主飞行器辅助车联网在衰落信道下的性能分析。

IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-27 DOI: 10.3390/e27090907

Zheming Zhang, Yixin He, Yifan Lei, Zehui Cai, Fanghui Huang, Xingchen Zhao, Dawei Wang, Lujuan Li

{"title":"Performance Analysis of Non-Orthogonal Multiple Access-Enhanced Autonomous Aerial Vehicle-Assisted Internet of Vehicles over Rician Fading Channels.","authors":"Zheming Zhang, Yixin He, Yifan Lei, Zehui Cai, Fanghui Huang, Xingchen Zhao, Dawei Wang, Lujuan Li","doi":"10.3390/e27090907","DOIUrl":"10.3390/e27090907","url":null,"abstract":"The increasing number of intelligent connected vehicles (ICVs) is leading to a growing scarcity of spectrum resources for the Internet of Vehicles (IoV), which has created an urgent need for the use of full-duplex non-orthogonal multiple access (FD-NOMA) techniques in vehicle-to-everything (V2X) communications. Meanwhile, for the flexibility of autonomous aerial vehicles (AAVs), V2X communications assisted by AAVs are regarded as a potential solution to achieve reliable communication between ICVs. However, if the integration of FD-NOMA and AAVs can satisfy the requirements of V2X communications, then quickly and accurately analyzing the total achievable rate becomes a challenge. Motivated by the above, an accurate analytical expression for the total achievable rate over Rician fading channels is proposed to evaluate the transmission performance of NOMA-enhanced AAV-assisted IoV with imperfect channel state information (CSI). Then, we derive an approximate expression with the truncated error, based on which the closed-form expression for the approximate error is theoretically provided. Finally, the simulation results demonstrate the accuracy of the obtained approximate results, where the maximum approximate error does not exceed 0.5%. Moreover, the use of the FD-NOMA technique in AAV-assisted IoV can significantly improve the total achievable rate compared to existing work. Furthermore, the influence of key network parameters (e.g., the speed and Rician factor) on achievable rate is thoroughly discussed.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468140/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Experimental and Numerical Study of Coupled Metronomes on a Floating Platform. 浮动平台上耦合节拍器的实验与数值研究。

IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-27 DOI: 10.3390/e27090908

Xiaolongzi Wu, Caiyi Zheng, Zhao Lei, Yu Qian, Zengru Di, Xiaohua Cui

{"title":"Experimental and Numerical Study of Coupled Metronomes on a Floating Platform.","authors":"Xiaolongzi Wu, Caiyi Zheng, Zhao Lei, Yu Qian, Zengru Di, Xiaohua Cui","doi":"10.3390/e27090908","DOIUrl":"10.3390/e27090908","url":null,"abstract":"We investigated synchronization behavior using an experimental setup consisting of two metronomes placed on a platform floating over water. By setting the metronomes to oscillate perpendicular to the line between them, we observed three distinct modes of movement: in-phase synchronization, anti-phase synchronization, and synchronization with a fixed phase difference. While this last mode resembles phase-locking, it is important to distinguish that phase-locking typically refers to an oscillator's response to external pacing, whereas the fixed phase difference observed in our study emerges from the mutual interaction between two metronomes. The frequencies of oscillations, and the placement of the metronomes are also changed to check the reliability of the new phenomenon. Even if we changed the material of the platform to a heavier one or turned around one of the metronomes, synchronization with a fixed time delay still was still observed. Drawing on previous research, we developed mathematical equations to model the coupled metronomes and performed numerical simulations that successfully reproduced all three observed phenomena. The simulation results showed excellent agreement with our experimental observations. These findings contribute to our understanding of coupled oscillators and may have potential applications in various fields.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12469052/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

HQRNN-FD: A Hybrid Quantum Recurrent Neural Network for Fraud Detection. HQRNN-FD：用于欺诈检测的混合量子递归神经网络。

IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-27 DOI: 10.3390/e27090906

Yao-Chong Li, Yi-Fan Zhang, Rui-Qing Xu, Ri-Gui Zhou, Yi-Lin Dong

{"title":"HQRNN-FD: A Hybrid Quantum Recurrent Neural Network for Fraud Detection.","authors":"Yao-Chong Li, Yi-Fan Zhang, Rui-Qing Xu, Ri-Gui Zhou, Yi-Lin Dong","doi":"10.3390/e27090906","DOIUrl":"10.3390/e27090906","url":null,"abstract":"Detecting financial fraud is a critical aspect of modern intelligent financial systems. Despite the advances brought by deep learning in predictive accuracy, challenges persist-particularly in capturing complex, high-dimensional nonlinear features. This study introduces a novel hybrid quantum recurrent neural network for fraud detection (HQRNN-FD). The model utilizes variational quantum circuits (VQCs) incorporating angle encoding, data reuploading, and hierarchical entanglement to project transaction features into quantum state spaces, thereby facilitating quantum-enhanced feature extraction. For sequential analysis, the model integrates a recurrent neural network (RNN) with a self-attention mechanism to effectively capture temporal dependencies and uncover latent fraudulent patterns. To mitigate class imbalance, the synthetic minority over-sampling technique (SMOTE) is employed during preprocessing, enhancing both class representation and model generalizability. Experimental evaluations reveal that HQRNN-FD attains an accuracy of 0.972 on publicly available fraud detection datasets, outperforming conventional models by 2.4%. In addition, the framework exhibits robustness against quantum noise and improved predictive performance with increasing qubit numbers, validating its efficacy and scalability for imbalanced financial classification tasks.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468836/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On a Model of Rumors Spreading Through Social Media. 关于谣言通过社交媒体传播的模型。

IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-26 DOI: 10.3390/e27090903

Laurance Fakih, Andrei Halanay, Florin Avram

引用次数: 0

Arrow of Time in Quantum Mechanics and Set Theory. 量子力学和集合论中的时间之箭。

IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-26 DOI: 10.3390/e27090904

Jerzy Król

引用次数: 0

Fault Diagnosis of a Bogie Gearbox Based on Pied Kingfisher Optimizer-Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, Improved Multi-Scale Weighted Permutation Entropy, and Starfish Optimization Algorithm-Least-Squares Support Vector Machine. 基于Pied Kingfisher优化器-改进的自适应噪声完全集成经验模态分解、改进的多尺度加权排列熵和海星优化算法-最小二乘支持向量机的转向架齿轮箱故障诊断。

IF 2 3区物理与天体物理

Entropy Pub Date : 2025-08-26 DOI: 10.3390/e27090905

Guangjian Zhang, Shilun Ma, Xulong Wang

{"title":"Fault Diagnosis of a Bogie Gearbox Based on Pied Kingfisher Optimizer-Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, Improved Multi-Scale Weighted Permutation Entropy, and Starfish Optimization Algorithm-Least-Squares Support Vector Machine.","authors":"Guangjian Zhang, Shilun Ma, Xulong Wang","doi":"10.3390/e27090905","DOIUrl":"10.3390/e27090905","url":null,"abstract":"Current methods of detecting bogie gearbox faults mainly depend on manual judgment, which leads to inaccurate fault identification. In this study, a fault diagnosis model is proposed based on a pied kingfisher optimizer-improved complete ensemble empirical mode decomposition with adaptive noise (PKO-ICEEMDAN), improved multi-scale weighted permutation entropy (IMWPE), and a starfish optimization algorithm optimizing a least-squares support vector machine (SFOA-LSSVM). Firstly, the acceleration signals of a bogie gearbox under six different working conditions were extracted through experiments. Secondly, the acceleration signals were decomposed by ICEEMDAN optimized by PKO to obtain the intrinsic mode function (IMF). Thirdly, IMFs with rich fault information were selected to reconstruct the signals according to the double screening criteria of both the correlation coefficient and variance contribution rate, and the IMWPE of the reconstructed signals was extracted. Finally, IMWPE as a feature vector was input into LSSVM optimized by the SFOA for fault diagnosis and compared with various models. The results show that the average accuracy of the training data of the proposed model was 99.13%, and the standard deviation was 0.09, while the average accuracy of the testing data was 99.44%, and the standard deviation was 0.12. Thus, the effectiveness of the proposed fault diagnosis model for the bogie gearbox was verified.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468919/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Entropy最新文献