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Three-Dimensional Sound Source Localization with Microphone Array Combining Spatial Entropy Quantification and Machine Learning Correction. 结合空间熵量化和机器学习校正的传声器阵列三维声源定位。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-09 DOI: 10.3390/e27090942
Guangneng Li, Feiyu Zhao, Wei Tian, Tong Yang
{"title":"Three-Dimensional Sound Source Localization with Microphone Array Combining Spatial Entropy Quantification and Machine Learning Correction.","authors":"Guangneng Li, Feiyu Zhao, Wei Tian, Tong Yang","doi":"10.3390/e27090942","DOIUrl":"10.3390/e27090942","url":null,"abstract":"<p><p>In recent years, with the popularization of intelligent scene monitoring, sound source localization (SSL) has become a major means for indoor monitoring and target positioning. However, existing sound source localization solutions are difficult to extend to multi-source and three-dimensional scenarios. To address this, this paper proposes a three-dimensional sound source localization technology based on eight microphones. Specifically, the method employs a rectangular eight-microphone array and captures Direction-of-Arrival (DOA) information via the direct path relative transfer function (DP-RTF). It introduces spatial entropy to quantify the uncertainty caused by the exponentially growing DOA combinations as the number of sound sources increases, while further reducing the spatial entropy of sound source localization through geometric intersection. This solves the problem that traditional sound source localization methods cannot be applied to multi-source and three-dimensional scenarios. On the other hand, machine learning is used to eliminate coordinate deviations caused by DOA estimation errors of the direct path relative transfer function (DP-RTF) and deviations in microphone geometric parameters. Both simulation experiments and real-scene experiments show that the positioning error of the proposed method in three-dimensional scenarios is about 10.0 cm.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468556/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174284","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
Federated Learning over MU-MIMO Vehicular Networks. 基于MU-MIMO车载网络的联邦学习。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-09 DOI: 10.3390/e27090941
Maria Raftopoulou, José Mairton B da Silva, Remco Litjens, H Vincent Poor, Piet Van Mieghem
{"title":"Federated Learning over MU-MIMO Vehicular Networks.","authors":"Maria Raftopoulou, José Mairton B da Silva, Remco Litjens, H Vincent Poor, Piet Van Mieghem","doi":"10.3390/e27090941","DOIUrl":"10.3390/e27090941","url":null,"abstract":"<p><p>Many algorithms related to vehicular applications, such as enhanced perception of the environment, benefit from frequent updates and the use of data from multiple vehicles. Federated learning is a promising method to improve the accuracy of algorithms in the context of vehicular networks. However, limited communication bandwidth, varying wireless channel quality, and potential latency requirements may impact the number of vehicles selected for training per communication round and their assigned radio resources. In this work, we characterize the vehicles participating in federated learning based on their importance to the learning process and their use of wireless resources. We then address the joint vehicle selection and resource allocation problem, considering multi-cell networks with multi-user multiple-input multiple-output (MU-MIMO)-capable base stations and vehicles. We propose a \"vehicle-beam-iterative\" algorithm to approximate the solution to the resulting optimization problem. We then evaluate its performance through extensive simulations, using realistic road and mobility models, for the task of object classification of European traffic signs. Our results indicate that MU-MIMO improves the convergence time of the global model. Moreover, the application-specific accuracy targets are reached faster in scenarios where the vehicles have the same training data set sizes than in scenarios where the data set sizes differ.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468685/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174467","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
Determining the Upper-Bound on the Code Distance of Quantum Stabilizer Codes Through the Monte Carlo Method Based on Fully Decoupled Belief Propagation. 基于完全解耦信念传播的蒙特卡罗方法确定量子稳定器码距上界。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-09 DOI: 10.3390/e27090940
Zhipeng Liang, Zicheng Wang, Zhengzhong Yi, Fusheng Yang, Xuan Wang
{"title":"Determining the Upper-Bound on the Code Distance of Quantum Stabilizer Codes Through the Monte Carlo Method Based on Fully Decoupled Belief Propagation.","authors":"Zhipeng Liang, Zicheng Wang, Zhengzhong Yi, Fusheng Yang, Xuan Wang","doi":"10.3390/e27090940","DOIUrl":"10.3390/e27090940","url":null,"abstract":"<p><p>The code distance is a critical parameter of quantum stabilizer codes (QSCs), and determining it-whether exactly or approximately-is known to be an NP-complete problem. However, its upper bound can be determined efficiently by some methods such as the Monte Carlo method. Leveraging the Monte Carlo method, we propose an algorithm to compute the upper bound on the code distance of a given QSC using fully decoupled belief propagation combined with ordered statistics decoding (FDBP-OSD). Our algorithm demonstrates high precision: for various QSCs with known distances, the computed upper bounds match the actual values. Additionally, we explore upper bounds for the minimum weight of logical <i>X</i> operators in the Z-type Tanner-graph-recursive-expansion (Z-TGRE) code and the Chamon code-an XYZ product code constructed from three repetition codes. The results on Z-TGRE codes align with theoretical analysis, while the results on Chamon codes suggest that XYZ product codes may achieve a code distance of O(N2/3), which supports the conjecture of Leverrier et al.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468434/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174178","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
Multivariate Time Series Anomaly Detection Based on Inverted Transformer with Multivariate Memory Gate. 基于多元存储门的逆变变压器多元时间序列异常检测。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-08 DOI: 10.3390/e27090939
Yuan Ma, Weiwei Liu, Changming Xu, Luyi Bai, Ende Zhang, Junwei Wang
{"title":"Multivariate Time Series Anomaly Detection Based on Inverted Transformer with Multivariate Memory Gate.","authors":"Yuan Ma, Weiwei Liu, Changming Xu, Luyi Bai, Ende Zhang, Junwei Wang","doi":"10.3390/e27090939","DOIUrl":"10.3390/e27090939","url":null,"abstract":"<p><p>In the industrial IoT, it is vital to detect anomalies in multivariate time series, yet it faces numerous challenges, including highly imbalanced datasets, complex and high-dimensional data, and large disparities across variables. Despite the recent surge in proposals for deep learning-based methods, these approaches typically treat the multivariate data at each point in time as a unique token, weakening the personalized features and dependency relationships between variables. As a result, their performance tends to degrade under highly imbalanced conditions, and reconstruction-based models are prone to overfitting abnormal patterns, leading to excessive reconstruction of anomalous inputs. In this paper, we propose ITMMG, an inverted Transformer with a multivariate memory gate. ITMMG employs an inverted token embedding strategy and multivariate memory to capture deep dependencies among variables and the normal patterns of individual variables. The experimental results obtained demonstrate that the proposed method exhibits superior performance in terms of detection accuracy and robustness compared with existing baseline methods across a range of standard time series anomaly detection datasets. This significantly reduces the probability of misclassifying anomalous samples during reconstruction.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12469927/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174150","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
GNSS Interference Identification Driven by Eye Pattern Features: ICOA-CNN-ResNet-BiLSTM Optimized Deep Learning Architecture. 眼动特征驱动的GNSS干扰识别:ICOA-CNN-ResNet-BiLSTM优化深度学习架构。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-07 DOI: 10.3390/e27090938
Chuanyu Wu, Yuanfa Ji, Xiyan Sun
{"title":"GNSS Interference Identification Driven by Eye Pattern Features: ICOA-CNN-ResNet-BiLSTM Optimized Deep Learning Architecture.","authors":"Chuanyu Wu, Yuanfa Ji, Xiyan Sun","doi":"10.3390/e27090938","DOIUrl":"10.3390/e27090938","url":null,"abstract":"<p><p>In this study, the key challenges faced by global navigation satellite systems (GNSSs) in the field of security are addressed, and an eye diagram-based deep learning framework for intelligent classification of interference types is proposed. GNSS signals are first transformed into two-dimensional eye diagrams, enabling a novel visual representation wherein interference types are distinguished through entropy-centric feature analysis. Specifically, the quantification of information entropy within these diagrams serves as a theoretical foundation for extracting salient discriminative features, reflecting the structural complexity and uncertainty of the underlying signal distortions. We designed a hybrid architecture that integrates spatial feature extraction, gradient stability enhancement, and time dynamics modeling capabilities and combines the advantages of a convolutional neural network, residual network, and bidirectional long short-term memory network. To further improve model performance, we propose an improved coati optimization algorithm (ICOA), which combines chaotic mapping, an elite perturbation mechanism, and an adaptive weighting strategy for hyperparameter optimization. Compared with mainstream optimization methods, this algorithm improves the convergence accuracy by more than 30%. Experimental results on jamming datasets (continuous wave interference, chirp interference, pulse interference, frequency-modulated interference, amplitude-modulated interference, and spoofing interference) demonstrate that our method achieved performance in terms of accuracy, precision, recall, F1 score, and specificity, with values of 98.02%, 97.09%, 97.24%, 97.14%, and 99.65%, respectively, which represent improvements of 1.98%, 2.80%, 6.10%, 4.59%, and 0.33% over the next-best model. This study provides an efficient, entropy-aware, intelligent, and practically feasible solution for GNSS interference identification.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468706/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174456","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
3V-GM: A Tri-Layer "Point-Line-Plane" Critical Node Identification Algorithm for New Power Systems. 新型电力系统的三层“点-线-面”关键节点识别算法。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-07 DOI: 10.3390/e27090937
Yuzhuo Dai, Min Zhao, Gengchen Zhang, Tianze Zhao
{"title":"3V-GM: A Tri-Layer \"Point-Line-Plane\" Critical Node Identification Algorithm for New Power Systems.","authors":"Yuzhuo Dai, Min Zhao, Gengchen Zhang, Tianze Zhao","doi":"10.3390/e27090937","DOIUrl":"10.3390/e27090937","url":null,"abstract":"<p><p>With the increasing penetration of renewable energy, the stochastic and intermittent nature of its generation increases operational uncertainty and vulnerability, posing significant challenges for grid stability. However, traditional algorithms typically identify critical nodes by focusing solely on the network topology or power flow, or by combining the two, which leads to the inaccurate and incomplete identification of essential nodes. To address this, we propose the Three-Dimensional Value-Based Gravity Model (3V-GM), which integrates structural and electrical-physical attributes across three layers. In the plane layer, we combine each node's global topological position with its real-time supply-demand voltage state. In the line layer, we introduce an electrical coupling distance to quantify the strength of electromagnetic interactions between nodes. In the point layer, we apply eigenvector centrality to detect latent hub nodes whose influence is not immediately apparent. The performance of our proposed method was evaluated by examining the change in the load loss rate as nodes were sequentially removed. To assess the effectiveness of the 3V-GM approach, simulations were conducted on the IEEE 39 system, as well as six other benchmark networks. The simulations were performed using Python scripts, with operational parameters such as bus voltages, active and reactive power flows, and branch impedances obtained from standard test cases provided by MATPOWER v7.1. The results consistently show that removing the same number of nodes identified by 3V-GM leads to a greater load loss compared to the six baseline methods. This demonstrates the superior accuracy and stability of our approach. Additionally, an ablation experiment, which decomposed and recombined the three layers, further highlights the unique contribution of each component to the overall performance.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468754/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145173581","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
Infodemic Source Detection with Information Flow: Foundations and Scalable Computation. 信息流的信息源检测:基础和可扩展计算。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-06 DOI: 10.3390/e27090936
Zimeng Wang, Chao Zhao, Qiaoqiao Zhou, Chee Wei Tan, Chung Chan
{"title":"Infodemic Source Detection with Information Flow: Foundations and Scalable Computation.","authors":"Zimeng Wang, Chao Zhao, Qiaoqiao Zhou, Chee Wei Tan, Chung Chan","doi":"10.3390/e27090936","DOIUrl":"10.3390/e27090936","url":null,"abstract":"<p><p>We consider the problem of identifying the source of a rumor in a network, given only a snapshot observation of infected nodes after the rumor has spread. Classical approaches, such as the maximum likelihood (ML) and joint maximum likelihood (JML) estimators based on the conventional Susceptible-Infectious (SI) model, exhibit degeneracy, failing to uniquely identify the source even in simple network structures. To address these limitations, we propose a generalized estimator that incorporates independent random observation times. To capture the structure of information flow beyond graphs, our formulations consider rate constraints on the rumor and the multicast capacities for cyclic polylinking networks. Furthermore, we develop forward elimination and backward search algorithms for rate-constrained source detection and validate their effectiveness and scalability through comprehensive simulations. Our study establishes a rigorous and scalable foundation on the infodemic source detection.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12469017/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174441","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
Application of the Three-Group Model to the 2024 US Elections. 三群模型在2024年美国大选中的应用。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-06 DOI: 10.3390/e27090935
Miron Kaufman, Sanda Kaufman, Hung T Diep
{"title":"Application of the Three-Group Model to the 2024 US Elections.","authors":"Miron Kaufman, Sanda Kaufman, Hung T Diep","doi":"10.3390/e27090935","DOIUrl":"10.3390/e27090935","url":null,"abstract":"<p><p>Political polarization in Western democracies has accelerated in the last decade, with negative social consequences. Research across disciplines on antecedents, manifestations and societal impacts is hindered by social systems' complexity: their constant flux impedes tracing causes of observed trends and prediction of consequences, hampering their mitigation. Social physics models exploit a characteristic of complex systems: what seems chaotic at one observation level may exhibit patterns at a higher level. Therefore, dynamic modeling of complex systems allows anticipation of possible events. We use this approach to anticipate 2024 US election results. We consider the highly polarized Democrats and Republicans, and Independents fluctuating between them. We generate average group-stance scenarios in time and explore how polarization and depolarization might have affected 2024 voting outcomes. We find that reducing polarization might advantage the larger voting group. We also explore ways to reduce polarization, and their potential effects on election results. The results inform regarding the perils of polarization trends, and on possibilities of changing course.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468203/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174106","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
Optimized Generalized LDPC Convolutional Codes. 优化广义LDPC卷积码。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-04 DOI: 10.3390/e27090930
Li Deng, Kai Tao, Zhiping Shi, You Zhang, Yinlong Shi, Jian Wang, Tian Liu, Yongben Wang
{"title":"Optimized Generalized LDPC Convolutional Codes.","authors":"Li Deng, Kai Tao, Zhiping Shi, You Zhang, Yinlong Shi, Jian Wang, Tian Liu, Yongben Wang","doi":"10.3390/e27090930","DOIUrl":"10.3390/e27090930","url":null,"abstract":"<p><p>In this paper, some optimized encoding and decoding schemes are proposed for the generalized LDPC convolutional codes (GLDPC-CCs). In terms of the encoding scheme, a flexible doping method is proposed, which replaces multiple single parity check (SPC) nodes with one generalized check (GC) node. Different types of BCH codes can be selected as the GC node by adjusting the number of SPC nodes to be replaced. Moreover, by fine-tuning the truncated bits and the extended parity check bits, or by reasonably adjusting the GC node distribution, the performance of GLDPC-CCs can be further improved. In terms of the decoding scheme, a hybrid layered normalized min-sum (HLNMS) decoding algorithm is proposed, where the layered normalized min-sum (LNMS) decoding is used for SPC nodes, and the Chase-Pyndiah decoding is adopted for GC nodes. Based on analysis of the decoding convergence of GC node and SPC node, an adaptive weight factor is designed for GC nodes that changes as the decoding iterations, aiming to further improve the decoding performance. In addition, an early stop decoding strategy is also proposed based on the minimum amplitude threshold of mutual information in order to reduce the decoding complexity. The simulation results have verified the superiority of the proposed scheme for GLDPC-CCs over the prior art, which has great application potential in optical communication systems.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12469000/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174245","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
Sherlock Holmes Doesn't Play Dice: The Mathematics of Uncertain Reasoning When Something May Happen, That You Are Not Even Able to Figure Out. 夏洛克·福尔摩斯不掷骰子:不确定推理的数学当事情可能发生时,你甚至无法弄清楚。
IF 2 3区 物理与天体物理
Entropy Pub Date : 2025-09-04 DOI: 10.3390/e27090931
Guido Fioretti
{"title":"Sherlock Holmes Doesn't Play Dice: The Mathematics of Uncertain Reasoning When Something May Happen, That You Are Not Even Able to Figure Out.","authors":"Guido Fioretti","doi":"10.3390/e27090931","DOIUrl":"10.3390/e27090931","url":null,"abstract":"<p><p>While Evidence Theory (also known as Dempster-Shafer Theory, or Belief Functions Theory) is being increasingly used in data fusion, its potentialities in the Social and Life Sciences are often obscured by lack of awareness of its distinctive features. In particular, with this paper I stress that an extended version of Evidence Theory can express the uncertainty deriving from the fear that events may materialize, that one is not even able to figure out. By contrast, Probability Theory must limit itself to the possibilities that a decision-maker is currently envisaging. I compare this extended version of Evidence Theory to cutting-edge extensions of Probability Theory, such as imprecise and sub-additive probabilities, as well as unconventional versions of Information Theory that are employed in data fusion and transmission of cultural information. A possible application to creative usage of Large Language Models is outlined, and further extensions to multi-agent interactions are outlined.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12468343/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145174274","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
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