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Symmetry
Volume 17
Issue 6
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Symmetry, Volume 17, Issue 6 (June 2025) – 173 articles

Cover Story (view full-size image): This paper studies moduli spaces of principal bundles over Riemann surfaces equipped with antiholomorphic involutive symmetries, revealing that fixed-point sets correspond to bundles over real curves with notable structural properties. The main theorem establishes a derived equivalence that extends Langlands duality to settings with involutions, connecting coherent sheaves on the fixed-point sets of dual moduli spaces. From this framework, some applications to Chern–Simons theory are derived, interpreting fixed points as (B,B,B)-branes. The results provide new insights into the quantum field theory origins of the Langlands program while opening lines of research for studying real forms in higher-dimensional analogues. View this paper
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16 pages, 1553 KiB  
Article
A Voltage Parameter Adaptive Detection Method for Power Systems Under Grid Voltage Distortion Conditions
by Wenzhe Hao, Zhiyong Dai, Guangqi Li, Shuaishuai Lv, Qitao Sun, Nana Lu and Jinke Ma
Symmetry 2025, 17(6), 975; https://doi.org/10.3390/sym17060975 - 19 Jun 2025
Viewed by 287
Abstract
Accurate voltage information is important for ensuring the safe operation of power systems and their performance evaluation. However, as distributed energy sources become more prevalent, the levels of harmonics and DC components in the power grid are increasing notably, resulting in voltage waveform [...] Read more.
Accurate voltage information is important for ensuring the safe operation of power systems and their performance evaluation. However, as distributed energy sources become more prevalent, the levels of harmonics and DC components in the power grid are increasing notably, resulting in voltage waveform distortion and a breakdown of waveform symmetry. As a result, traditional voltage parameter detection methods are unable to obtain the voltage information accurately. To address this issue, this paper proposed a novel approach that leverages adaptive estimation to accurately detect voltage parameters under grid voltage distortion conditions. More importantly, the proposed method has the ability to extract the harmonics and the DC component without steady-state error and exhibits a fast dynamic response. With this approach, the amplitude of the grid voltage can be derived in 4.2 ms when the grid voltage is undistorted. In the presence of low-order harmonics, the amplitude of the grid voltage can be accurately derived in 10.7 ms. Finally, simulation results and experimental results are respectively used for model validation and functionality validation. Full article
(This article belongs to the Special Issue Symmetry in Energy Systems and Electrical Power)
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47 pages, 700 KiB  
Review
Probes for String-Inspired Foam, Lorentz, and CPT Violations in Astrophysics
by Chengyi Li and Bo-Qiang Ma
Symmetry 2025, 17(6), 974; https://doi.org/10.3390/sym17060974 - 19 Jun 2025
Viewed by 973
Abstract
Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and any proposal of its violation and breakdown of CPT symmetry that might characterize some approaches to quantum gravity should be treated with care. In this review, [...] Read more.
Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and any proposal of its violation and breakdown of CPT symmetry that might characterize some approaches to quantum gravity should be treated with care. In this review, we examine, among other scenarios, such instances in supercritical (Liouville) string theory, particularly in some brane models for “quantum foam”. Using the phenomenological formalism introduced here, we analyze the observational hints of Lorentz violation in time-of-flight lags of cosmic photons and neutrinos which fit excellently stringy space–time foam scenarios. We further demonstrate how stringent constraints from other astrophysical data, including the recent first detections of multi-TeV events in γ-ray burst 221009A and PeV cosmic photons by the Large High Altitude Air Shower Observatory (LHAASO), are satisfied in this context. Such models thus provide a unified framework for all currently observed phenomenologies of space–time symmetry breaking at Planckian scales. Full article
(This article belongs to the Special Issue Lorentz Invariance Violation and Space–Time Symmetry Breaking)
25 pages, 3201 KiB  
Article
Semi-Supervised Learning with Entropy Filtering for Intrusion Detection in Asymmetrical IoT Systems
by Badraddin Alturki and Abdulaziz A. Alsulami
Symmetry 2025, 17(6), 973; https://doi.org/10.3390/sym17060973 - 19 Jun 2025
Viewed by 953
Abstract
The growth of Internet of Things (IoT) systems has brought serious security concerns, especially in asymmetrical environments where device capabilities and communication flows vary widely. Many machine-learning-based intrusion detection systems struggle to address noise, uncertainty, and class imbalance. For that reason, intensive data [...] Read more.
The growth of Internet of Things (IoT) systems has brought serious security concerns, especially in asymmetrical environments where device capabilities and communication flows vary widely. Many machine-learning-based intrusion detection systems struggle to address noise, uncertainty, and class imbalance. For that reason, intensive data preprocessing procedures were required. These challenges are in real-world data. In this work, we introduce a semi-supervised learning approach that uses entropy-based uncertainty filtering to improve intrusion detection in IoT environments. By dynamically identifying uncertain predictions from tree-based classifiers, we retain only high-confidence results during training. Later, confident samples from the uncertain set are used to retrain the model through a self-training loop. We evaluate this method using three diverse and benchmark datasets named RT-IoT2022, CICIoT2023, and CICIoMT2024, which include up to 34 different attack types. The experimental results reveal that XGBoost and Random Forest outperformed other tree-based models while maintaining their robustness when predicting attacks in the IoT environment. In addition, our proposed model was compared with other models proposed by researchers in the field, and the findings confirmed that our model presented promising results. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Cyber Security, IoTs and Privacy)
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23 pages, 373 KiB  
Article
Few-Grid-Point Simulations of Big Bang Singularity in Quantum Cosmology
by Miloslav Znojil
Symmetry 2025, 17(6), 972; https://doi.org/10.3390/sym17060972 - 19 Jun 2025
Viewed by 323
Abstract
In the context of the current lack of compatibility of the classical and quantum approaches to gravity, exactly solvable elementary pseudo-Hermitian quantum models are analyzed, supporting the acceptability of a point-like form of the Big Bang. The purpose is served by a hypothetical [...] Read more.
In the context of the current lack of compatibility of the classical and quantum approaches to gravity, exactly solvable elementary pseudo-Hermitian quantum models are analyzed, supporting the acceptability of a point-like form of the Big Bang. The purpose is served by a hypothetical (non-covariant) identification of the “time of the Big Bang” with Kato’s exceptional-point parameter t=0. The consequences (including the ambiguity of the patterns of unfolding the singularity after the Big Bang) are studied in detail. In particular, singular values of the observables are shown to be useful in the analysis. Full article
(This article belongs to the Section Physics)
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15 pages, 408 KiB  
Article
Pseudoscalar Meson Parton Distributions Within Gauge-Invariant Nonlocal Chiral Quark Model
by Parada T. P. Hutauruk
Symmetry 2025, 17(6), 971; https://doi.org/10.3390/sym17060971 - 19 Jun 2025
Viewed by 233
Abstract
In this paper, I investigate the gluon distributions for the kaon and pion, as well as the improvement of the valence-quark distributions, in the framework of the gauge-invariant nonlocal chiral quark model (NLχQM), where the momentum dependence is taken into account. [...] Read more.
In this paper, I investigate the gluon distributions for the kaon and pion, as well as the improvement of the valence-quark distributions, in the framework of the gauge-invariant nonlocal chiral quark model (NLχQM), where the momentum dependence is taken into account. I then compute the gluon distributions for the kaon and pion that are dynamically generated from the splitting functions in the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) QCD evolution. In a comparison with the recent lattice QCD and JAM global analysis results, it is found that the results for the pion gluon distributions at Q= 2 GeV, which is set based on the lattice QCD, have a good agreement with the recent lattice QCD data; this is followed up with the up valence-quark distribution of the pion results at Q= 5.2 GeV in comparison with the reanalysis experimental data. The prediction for the kaon gluon distributions at Q=2 GeV is consistent with the recent lattice QCD calculation. Full article
(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)
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26 pages, 5631 KiB  
Article
Decentralized Federated Learning with Node Incentive and Role Switching Mechanism for Network Traffic Prediction in NFV Environment
by Ying Hu, Ben Liu, Jianyong Li and Linlin Jia
Symmetry 2025, 17(6), 970; https://doi.org/10.3390/sym17060970 - 18 Jun 2025
Viewed by 268
Abstract
In network function virtualization (NFV) environments, dynamic network traffic prediction with unique symmetric and asymmetric traffic patterns is critical for efficient resource orchestration and service chain optimization. Traditional centralized prediction models face risks of cross-provider data privacy leakage when network service providers collaborate [...] Read more.
In network function virtualization (NFV) environments, dynamic network traffic prediction with unique symmetric and asymmetric traffic patterns is critical for efficient resource orchestration and service chain optimization. Traditional centralized prediction models face risks of cross-provider data privacy leakage when network service providers collaborate with resource providers to deliver services. To address this issue, we propose a decentralized federated learning method for network traffic prediction, which ensures that historical network traffic data remain stored locally without requiring cross-provider sharing. To further mitigate interference from malicious provider behaviors on network traffic prediction, we design a node incentive mechanism that dynamically adjusts node roles (e.g., “Aggregator”, “Worker Node”, “Residual Node”, and “Evaluator”). When a node exhibits malicious behavior, its contribution score is reduced; otherwise, it is rewarded. Simulation experiments conducted on an NFV platform using public network traffic datasets demonstrate that the proposed method maintains prediction accuracy even in scenarios with a high proportion of malicious nodes, alleviates their adverse effects, and ensures prediction stability. Full article
(This article belongs to the Special Issue Symmetry in Solving NP-Hard Problems)
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20 pages, 3628 KiB  
Article
Homomorphic Encryption-Based Federated Active Learning on GCNs
by Xiaohu He, Zhihao Song, Dandan Zhang, Hongwei Ju and Qingfang Meng
Symmetry 2025, 17(6), 969; https://doi.org/10.3390/sym17060969 - 18 Jun 2025
Viewed by 310
Abstract
With the dramatic growth in dataset size, active learning has become one of the effective methods to deal with large-scale unlabeled data. However, most of the existing active learning methods are inefficient due poor target models and lack the ability to utilize the [...] Read more.
With the dramatic growth in dataset size, active learning has become one of the effective methods to deal with large-scale unlabeled data. However, most of the existing active learning methods are inefficient due poor target models and lack the ability to utilize the feature similarity between labeled and unlabeled data. Furthermore, data leakage is a serious threat to data privacy. In this paper, considering the features of the data itself, an augmented graph convolutional network is proposed which acts as a sampler for data selection in active learning, avoiding the involvement of the initial poor target model. Then, by applying the proposed GCN as a substitute for the initial poor target model, this paper proposes an active learning model based on augmented GCNs, which is able to select more representative data, enabling the active learning model to achieve better classification performance with limited labeled data. Finally, this paper proposes a homomorphic encryption-based federated active learning model to improve the data utilization and enhance the security of private data. Experiments were conducted on three datasets, Cora, CiteSeer and PubMed, and achieved accuracy rates of 94.47%, 92.86% and 91.51%, respectively, while providing provable security guarantees. Furthermore, the highest malicious user detection accuracy was 88.07%, and the global model test accuracy reached 88.42%, 84.22% and 81.46%, under a model poisoning attack. Full article
(This article belongs to the Special Issue Applications Based on Symmetry in Applied Cryptography)
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33 pages, 3435 KiB  
Article
Investigation of General Sombor Index for Optimal Values in Bicyclic Graphs, Trees, and Unicyclic Graphs Using Well-Known Transformations
by Miraj Khan, Muhammad Yasin Khan, Gohar Ali and Ioan-Lucian Popa
Symmetry 2025, 17(6), 968; https://doi.org/10.3390/sym17060968 - 18 Jun 2025
Viewed by 677
Abstract
The field related to indices was developed by researchers for various purposes. Optimization is one of the purposes used by researchers in different situations. In this article, a generalized Sombor index is considered. This work is related to the idea of optimization in [...] Read more.
The field related to indices was developed by researchers for various purposes. Optimization is one of the purposes used by researchers in different situations. In this article, a generalized Sombor index is considered. This work is related to the idea of optimization in the families of bicyclic graphs, trees, and unicyclic graphs. We investigated optimal values in the stated families by means of well-known transformations. The transformations include the following: Transformation A, Transformation B, Transformation C, and Transformation D. Transformation A and Transformation B increase the value of the generalized Sombor index, while Transformation C and Transformation D are used for minimal values. Full article
(This article belongs to the Special Issue Symmetry and Graph Theory, 2nd Edition)
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12 pages, 11398 KiB  
Article
Tuning the Ellipticity of High-Order Harmonics from Helium in Orthogonal Two-Color Laser Fields
by Shushan Zhou, Hao Wang, Yue Qiao, Nan Xu, Fuming Guo, Yujun Yang and Muhong Hu
Symmetry 2025, 17(6), 967; https://doi.org/10.3390/sym17060967 - 18 Jun 2025
Viewed by 320
Abstract
High-order harmonic generation in atomic systems driven by laser fields with tailored symmetries provides a powerful approach for producing structured ultrafast light sources. In this work, we theoretically investigate the ellipticity control of high-order harmonics emitted from helium atoms exposed to orthogonally polarized [...] Read more.
High-order harmonic generation in atomic systems driven by laser fields with tailored symmetries provides a powerful approach for producing structured ultrafast light sources. In this work, we theoretically investigate the ellipticity control of high-order harmonics emitted from helium atoms exposed to orthogonally polarized two-color laser pulses with a 1:3 frequency ratio. The polarization properties of the harmonics are governed by the interplay between the spatial symmetry of the driving field and the atomic potential. By numerically solving the time-dependent Schrödinger equation, we show that fine-tuning the relative phase and amplitude ratio between the fundamental and third-harmonic components enables selective symmetry breaking, resulting in the emission of elliptically and circularly polarized harmonics. Remarkably, we achieve near-perfect circular polarization (ellipticity ≈ 0.995) for the 5th harmonic, as well as highly circularly polarized 17th (0.945), 21st (0.96), and 23rd (0.935) harmonics, demonstrating a level of polarization control and efficiency that exceeds previous schemes. Our results highlight the advantage of using a 1:3 frequency ratio orthogonally polarized two-color laser field over the conventional 1:2 configuration, offering a promising route toward tunable attosecond light sources with tailored polarization characteristics. Full article
(This article belongs to the Section Physics)
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24 pages, 5085 KiB  
Article
Stellar-YOLO: A Graphite Ore Grade Detection Method Based on Improved YOLO11
by Zeyang Qiu, Xueyu Huang, Sifan Li and Jionghui Wang
Symmetry 2025, 17(6), 966; https://doi.org/10.3390/sym17060966 - 18 Jun 2025
Viewed by 880
Abstract
Mineral recognition technology is crucial for improving mining efficiency and advancing smart mining development. To enable the efficient deployment of graphite ore grade detection on edge computing devices, we propose Stellar-YOLO, a YOLO11-based detection framework with asymmetrical architecture optimizations tailored for real-world conditions. [...] Read more.
Mineral recognition technology is crucial for improving mining efficiency and advancing smart mining development. To enable the efficient deployment of graphite ore grade detection on edge computing devices, we propose Stellar-YOLO, a YOLO11-based detection framework with asymmetrical architecture optimizations tailored for real-world conditions. The backbone is replaced by the lightweight StarNet to enhance computational efficiency, while the C3k2-CAS module, integrating convolution and additive attention, is embedded in the neck to improve feature expressiveness. The head incorporates the SEAM module, forming the Detect-SEAM, to boost the recognition of complex mineral details. Moreover, to robustly adapt to real mining environments, we apply simulated data augmentation techniques involving motion blur, dust noise, and low brightness conditions. Stellar-YOLO achieves 93.6% mAP based on a custom-built graphite ore dataset, outperforming the baseline by 4.5% and reducing the FLOPs, parameters, and model size by 27%, 26%, and 23%, respectively. This work explores how asymmetrical architectural innovations and robustness-oriented evaluation contribute to a lightweight and effective approach for computer vision-based mineral quality assessment, demonstrating strong potential for practical applications in real-world industrial environments. Full article
(This article belongs to the Special Issue Asymmetric and Symmetric in Deep Computer Vision and Generative Modeling)
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32 pages, 1160 KiB  
Article
Optimizing Fractional Routing with Algebraic Transformations, AI, and Quantum Computing for Next-Generation Networks
by Vanitha Muthu. P and Karthiyayini. R
Symmetry 2025, 17(6), 965; https://doi.org/10.3390/sym17060965 - 17 Jun 2025
Viewed by 349
Abstract
In fractional routing, the flows are distributed through different paths; this allows the maximum efficiency to be achieved by using several partial capacities to balance flow. However, the mathematical formalism for dynamic and scalable implementation is yet to be developed. This paper proposes [...] Read more.
In fractional routing, the flows are distributed through different paths; this allows the maximum efficiency to be achieved by using several partial capacities to balance flow. However, the mathematical formalism for dynamic and scalable implementation is yet to be developed. This paper proposes the aforementioned hybrid framework of edge-linear transformations, AIs, and QCs for fractional routing optimizations. The system encodes flows by means of vector linear transformations over finite fields, supports real-time reconfiguration via deep reinforcement learning, and employs quantum algorithms such as QAOA and HHL for efficient minimization of path costs. The Python 3-based implementations of the model were utilized to test DAGs of a small- and medium-scale, showing a 30% increase in computational efficiency and a 25% drop in runtime compared to classical implementations. The evidence states that the practical-scalability results can be used for the real-time applications of emerging IoT and 6G networks. Full article
(This article belongs to the Section Computer)
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22 pages, 3277 KiB  
Article
Power Oscillation Emergency Support Strategy for Wind Power Clusters Based on Doubly Fed Variable-Speed Pumped Storage Power Support
by Weidong Chen and Jianyuan Xu
Symmetry 2025, 17(6), 964; https://doi.org/10.3390/sym17060964 - 17 Jun 2025
Viewed by 292
Abstract
Single-phase short-circuit faults are severe asymmetrical fault modes in high renewable energy power systems. They can easily cause large-scale renewable energy to enter the low-voltage ride-through (LVRT) state. When such symmetrical or asymmetrical faults occur in the transmission channels of high-proportion wind power [...] Read more.
Single-phase short-circuit faults are severe asymmetrical fault modes in high renewable energy power systems. They can easily cause large-scale renewable energy to enter the low-voltage ride-through (LVRT) state. When such symmetrical or asymmetrical faults occur in the transmission channels of high-proportion wind power clusters, they may trigger the tripping of thermal power units and a transient voltage drop in most wind turbines in the high-proportion wind power area. This causes an instantaneous active power deficiency and poses a low-frequency oscillation risk. To address the deficiencies of wind turbine units in fault ride-through (FRT) and active frequency regulation capabilities, a power emergency support scheme for wind power clusters based on doubly fed variable-speed pumped storage dynamic excitation is proposed. A dual-channel energy control model for variable-speed pumped storage units is established via AC excitation control. This model provides inertia support and FRT energy simultaneously through AC excitation control of variable-speed pumped storage units. Considering the transient stability of the power network in the wind power cluster transmission system, this scheme prioritizes offering dynamic reactive power to support voltage recovery and suppresses power oscillations caused by power deficiency during LVRT. The electromagnetic torque completed the power regulation within 0.4 s. Finally, the effectiveness of the proposed strategy is verified through modeling and analysis based on the actual power network of a certain region in Northeast China. Full article
(This article belongs to the Special Issue Advances in Intelligent Power Electronics with Symmetry/Asymmetry)
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15 pages, 332 KiB  
Article
Sliding Mode Control for Stochastic SIR Models with Telegraph and Lévy Noise: Theory and Applications
by Lu Liu, Yi Zhang, Yufeng Tian, Dapeng Wei and Zhanjun Huang
Symmetry 2025, 17(6), 963; https://doi.org/10.3390/sym17060963 - 17 Jun 2025
Cited by 1 | Viewed by 221
Abstract
This paper establishes a new stochastic SIR epidemic model that incorporates telegraph noise and Lévy noise to simulate the complex environmental disturbances affecting disease transmission. Given the susceptibility of epidemic spread to environmental noise and its intricate dynamics, an adaptive sliding mode controller [...] Read more.
This paper establishes a new stochastic SIR epidemic model that incorporates telegraph noise and Lévy noise to simulate the complex environmental disturbances affecting disease transmission. Given the susceptibility of epidemic spread to environmental noise and its intricate dynamics, an adaptive sliding mode controller based on an integral sliding surface and an adaptive control law is proposed. This controller is capable of stabilizing the constructed model and effectively suppressing the spread of the disease. The main contributions of this paper include the following: establishing a comprehensive and realistic stochastic SIR model that accounts for the complex impacts of telegraph noise (symbolizing periodic environmental changes) and Lévy noise (representing sudden environmental shocks) on the dynamics of disease transmission; employing T-S fuzzy modeling, which considers the design of fuzzy rules and the symmetry of membership functions, to ensure linearization of the model; constructing an integral sliding surface and designing an adaptive sliding mode controller for the fuzzy-processed model. Finally, the effectiveness of the proposed control method is validated through numerical simulations. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Neural Networks)
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33 pages, 10136 KiB  
Article
Carbon Price Forecasting Using a Hybrid Deep Learning Model: TKMixer-BiGRU-SA
by Yuhong Li, Nan Yang, Guihong Bi, Shiyu Chen, Zhao Luo and Xin Shen
Symmetry 2025, 17(6), 962; https://doi.org/10.3390/sym17060962 - 17 Jun 2025
Viewed by 435
Abstract
As a core strategy for carbon emission reduction, carbon trading plays a critical role in policy guidance and market stability. Accurate forecasting of carbon prices is essential, yet remains challenging due to the nonlinear, non-stationary, noisy, and uncertain nature of carbon price time [...] Read more.
As a core strategy for carbon emission reduction, carbon trading plays a critical role in policy guidance and market stability. Accurate forecasting of carbon prices is essential, yet remains challenging due to the nonlinear, non-stationary, noisy, and uncertain nature of carbon price time series. To address this, this paper proposes a novel hybrid deep learning framework that integrates dual-mode decomposition and a TKMixer-BiGRU-SA model for carbon price prediction. First, external variables with high correlation to carbon prices are identified through correlation analysis and incorporated as inputs. Then, the carbon price series is decomposed using Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) to extract multi-scale features embedded in the original data. The core prediction model, TKMixer-BiGRU-SA Net, comprises three integrated branches: the first processes the raw carbon price and highly relevant external time series, and the second and third process multi-scale components obtained from VMD and EWT, respectively. The proposed model embeds Kolmogorov–Arnold Networks (KANs) into the Time-Series Mixer (TSMixer) module, replacing the conventional time-mapping layer to form the TKMixer module. Each branch alternately applies the TKMixer along the temporal and feature-channel dimensions to capture dependencies across time steps and variables. Hierarchical nonlinear transformations enhance higher-order feature interactions and improve nonlinear modeling capability. Additionally, the BiGRU component captures bidirectional long-term dependencies, while the Self-Attention (SA) mechanism adaptively weights critical features for integrated prediction. This architecture is designed to uncover global fluctuation patterns in carbon prices, multi-scale component behaviors, and external factor correlations, thereby enabling autonomous learning and the prediction of complex non-stationary and nonlinear price dynamics. Empirical evaluations using data from the EU Emission Allowance (EUA) and Hubei Emission Allowance (HBEA) demonstrate the model’s high accuracy in both single-step and multi-step forecasting tasks. For example, the eMAPE of EUA predictions for 1–4 step forecasts are 0.2081%, 0.5660%, 0.8293%, and 1.1063%, respectively—outperforming benchmark models and confirming the proposed method’s effectiveness and robustness. This study provides a novel approach to carbon price forecasting with practical implications for market regulation and decision-making. Full article
(This article belongs to the Section Computer)
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21 pages, 4050 KiB  
Article
SAFE-GTA: Semantic Augmentation-Based Multimodal Fake News Detection via Global-Token Attention
by Like Zhang, Chaowei Zhang, Zewei Zhang and Yuchao Huang
Symmetry 2025, 17(6), 961; https://doi.org/10.3390/sym17060961 - 17 Jun 2025
Viewed by 405
Abstract
Large pre-trained models (PLMs) have provided tremendous opportunities and potentialities for multimodal fake news detection. However, existing multimodal fake news detection methods never manipulate the token-wise hierarchical semantics of news yielded from PLMs and extremely rely on contrastive learning but ignore the symmetry [...] Read more.
Large pre-trained models (PLMs) have provided tremendous opportunities and potentialities for multimodal fake news detection. However, existing multimodal fake news detection methods never manipulate the token-wise hierarchical semantics of news yielded from PLMs and extremely rely on contrastive learning but ignore the symmetry between text and image in terms of the abstract level. This paper proposes a novel multimodal fake news detection method that helps to balance the understanding between text and image via (1) designing a global-token across-attention mechanism to capture the correlations between global text and tokenwise image representations (or tokenwise text and global image representations) obtained from BERT and ViT; (2) proposing a QK-sharing strategy within cross-attention to enforce model symmetry that reduces information redundancy and accelerates fusion without sacrificing representational power; (3) deploying a semantic augmentation module that systematically extracts token-wise multilayered text semantics from stacked BERT blocks via CNN and Bi-LSTM layers, thereby rebalancing abstract-level disparities by symmetrically enriching shallow and deep textual signals. We also prove the effectiveness of our approach by comparing it with four state-of-the-art baselines. All the comparisons were conducted using three widely adopted multimodal fake news datasets. The results show that our approach outperforms the benchmarks by 0.8% in accuracy and 2.2% in F1-score on average across the three datasets, which demonstrates a symmetric, token-centric fusion of fine-grained semantic fusion, thereby driving more robust fake news detection. Full article
(This article belongs to the Special Issue Symmetries and Symmetry-Breaking in Data Security)
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22 pages, 6159 KiB  
Article
Symmetrical Traditional Patterns and User Perception: A Study on Innovation in Home Textile Design
by Mengqi Qin, Jianfang Wang, Xueying Ding and Haihong Zhang
Symmetry 2025, 17(6), 960; https://doi.org/10.3390/sym17060960 - 17 Jun 2025
Viewed by 346
Abstract
With the increasing diversification of modern home textile design (HTD), the integration of traditional cultural elements has become an important trend. This study investigates the impact of symmetry in traditional patterns on the optimization of home textile product design and examines its role [...] Read more.
With the increasing diversification of modern home textile design (HTD), the integration of traditional cultural elements has become an important trend. This study investigates the impact of symmetry in traditional patterns on the optimization of home textile product design and examines its role in consumer acceptance. First, the affinity diagram method was employed to collect core affective vocabularies. Based on a selection of home textile products incorporating traditional patterns available in the market, a questionnaire was developed to solicit consumers’ evaluations of these affective descriptors. Principal component analysis (PCA) was conducted to extract key perceptual dimensions, with particular emphasis on the influence of pattern symmetry on consumer perception. Subsequently, the Fuzzy Analytic Hierarchy Process (FAHP) was applied to determine the relative weights of the affective terms. Incorporating expert input, five representative traditional patterns from the Homespun Fabric of Jiangnan (HFoJ) were selected and reinterpreted with a focus on symmetrical design. Through the Quality Function Deployment (QFD) method, the effective vocabularies were mapped to the redesigned patterns, leading to the identification of the scheme that most effectively embodied the symmetrical principle for integration into HTD. Finally, the Grey Relation Analysis (GRA) was used to conduct a comprehensive evaluation of multiple design alternatives. The optimal design was selected and subsequently validated through consumer feedback to assess its market feasibility. This study contributes a symmetric approach to the application of symmetry in traditional pattern design, offering both traditional insights and practical guidance for the modernization and innovative transformation of cultural elements in HTD. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Computer-Aided Industrial Design)
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29 pages, 577 KiB  
Article
Symmetric Adjustable Tail-Risk Measure for Distributionally Robust Optimization in Portfolio Allocation
by Haonan Wang, Yunxiao Zhao, Yixin Guo, Changhe Liu and Xinlin Zhang
Symmetry 2025, 17(6), 959; https://doi.org/10.3390/sym17060959 - 17 Jun 2025
Viewed by 356
Abstract
In this study, we begin by extending the mathematical formulation of the expectile risk measure through a key modification: replacing the expectation in its defining equation with expected shortfall. This substitution leads to a revised risk measure that more precisely captures downside risk. [...] Read more.
In this study, we begin by extending the mathematical formulation of the expectile risk measure through a key modification: replacing the expectation in its defining equation with expected shortfall. This substitution leads to a revised risk measure that more precisely captures downside risk. To handle the uncertainty of the underlying distribution, we then adopt a distributionally robust optimization framework. Notably, this robust optimization problem can be reformulated as a linear programming problem, and by employing suitable approximation techniques, we derive an analytical solution. In numerical experiments, our portfolio problem exhibits superior performance when compared to several traditional and distributionally robust optimized portfolio problems. Full article
(This article belongs to the Special Issue Symmetry in Optimal Control and Applications)
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21 pages, 7053 KiB  
Article
Research on Coordinated Control of Multi-PMSM for Shaftless Overprinting System
by Yuntao Xu, Cheng Liu, Zihao Huang, Shiyuan Sun and Zewei Cui
Symmetry 2025, 17(6), 958; https://doi.org/10.3390/sym17060958 - 16 Jun 2025
Viewed by 281
Abstract
In response to the limitations of suboptimal control accuracy, compromised synchronization capability, and reduced stability inherent in PID control for conventional shaftless multi-permanent magnet synchronous motor drive systems, this article establishes a three-motor synchronous control system model for a shaftless printing system. On [...] Read more.
In response to the limitations of suboptimal control accuracy, compromised synchronization capability, and reduced stability inherent in PID control for conventional shaftless multi-permanent magnet synchronous motor drive systems, this article establishes a three-motor synchronous control system model for a shaftless printing system. On this basis, the speed loop adopts a sliding mode controller (NSMC) based on a new approach law, and the current loop adopts an improved super spiral structure. At the same time, the compensator of the deviation coupling control structure (NDCS) is optimized by weighted arithmetic mean. Finally, comparative simulation experiments were conducted on the system model using various algorithms. The results show that the deviation coupling control structure based on improved sliding mode control has better anti-interference ability, control accuracy, and synchronization in the synchronous control strategy of a multi-permanent magnet motor drive in a shaftless printing system, which is conducive to the safe and stable operation of shaftless printing systems under multiple working conditions. Full article
(This article belongs to the Special Issue New Developments of Algorithms Optimization with Symmetry/Asymmetry)
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18 pages, 1968 KiB  
Article
Novel Methods for Multi-Switch Generalized Projective Anti-Synchronization of Fractional Chaotic System Under Caputo–Fabrizio Derivative via Lyapunov Stability Theorem and Adaptive Control
by Yu Zhao, Tianzeng Li, Yu Wang and Rong Kang
Symmetry 2025, 17(6), 957; https://doi.org/10.3390/sym17060957 - 16 Jun 2025
Viewed by 233
Abstract
The issue of multi-switch generalized projective anti-synchronization of fractional-order chaotic systems is investigated in this work. The model is constructed using Caputo–Fabrizio derivatives, which have been rarely addressed in previous research. In order to expand the symmetric and asymmetric synchronization modes of chaotic [...] Read more.
The issue of multi-switch generalized projective anti-synchronization of fractional-order chaotic systems is investigated in this work. The model is constructed using Caputo–Fabrizio derivatives, which have been rarely addressed in previous research. In order to expand the symmetric and asymmetric synchronization modes of chaotic systems, we consider modeling chaotic systems under such fractional calculus definitions. Firstly, a new fractional-order differential inequality is proven, which facilitates the rapid confirmation of a suitable Lyapunov function. Secondly, an effective multi-switching controller is designed to confirm the convergence of the error system within a short moment to achieve synchronization asymptotically. Simultaneously, a multi-switching parameter adaptive principle is developed to appraise the uncertain parameters in the system. Finally, two simulation examples are presented to affirm the correctness and superiority of the introduced approach. It can be said that the symmetric properties of Caputo–Fabrizio fractional derivative are making outstanding contributions to the research on chaos synchronization. Full article
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13 pages, 456 KiB  
Article
Relationship Between Offensive Performance and Symmetry of Muscle Function, and Injury Factors in Elite Volleyball Players
by Chaofan Chen, Panpan Shi, Munku Song, Yonghwan Kim and Jiyoung Lee
Symmetry 2025, 17(6), 956; https://doi.org/10.3390/sym17060956 - 16 Jun 2025
Viewed by 359
Abstract
In volleyball, successful offensive performance is influenced not only by physical muscle function but also by injury status. The purpose of this study was to analyze the relationship between muscle function—including strength, balance, and symmetry—and injury history in relation to offensive performance (OP) [...] Read more.
In volleyball, successful offensive performance is influenced not only by physical muscle function but also by injury status. The purpose of this study was to analyze the relationship between muscle function—including strength, balance, and symmetry—and injury history in relation to offensive performance (OP) and ultimately sought to find factors required to improve OP. The final analysis included 60 players in attacking positions (36 in the symmetry group and 24 in the asymmetry group). Muscle strength was assessed using isokinetic testing for shoulder and knee extension. Balance was evaluated using the Upper Quarter Y-Balance Test (UQ-YBT) and the Lower Quarter Y-Balance Test (LQ-YBT). The asymmetry index (AI, ≥10%) was calculated by comparing the dominant and non-dominant sides. The results showed that the asymmetry group had a higher injury rate and lower offensive performance (OP) than the symmetry group (p < 0.05). In multiple regression analysis, no significant predictors were found on the non-dominant side, whereas significant variables were identified only on the dominant side. The key variables influencing OP were shoulder and knee extension strength, UQ-YBT scores, and the AI of knee extension. A 13.8% improvement in shoulder extension strength on the dominant side increased the likelihood of enhanced offensive performance (OP) by 2.54 times. A 10.5% improvement in the asymmetry index (AI) of knee extension was associated with a 1.52-fold increase in OP (p < 0.05). Shoulder and knee flexion did not significantly affect OP in any of the tests (p > 0.05). In conclusion, offensive performance in volleyball is associated with the greater shoulder and knee extension strength of the dominant side, as well as positive changes in UQ-YBT scores and the AI of knee extension. Full article
(This article belongs to the Section Life Sciences)
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28 pages, 4712 KiB  
Article
Distributed Maximum Correntropy Linear Filter Based on Rational Quadratic Kernel Against Non-Gaussian Noise
by Xuehua Zhao, Dejun Mu and Jiahui Yang
Symmetry 2025, 17(6), 955; https://doi.org/10.3390/sym17060955 - 16 Jun 2025
Viewed by 364
Abstract
This paper investigates the distributed state estimation problem for the linear system against non-Gaussian noise, where every sensor commutates information only within its adjacent sensors without the need for a fusion center. Correntropy is a similarity metric based on a kernel function that [...] Read more.
This paper investigates the distributed state estimation problem for the linear system against non-Gaussian noise, where every sensor commutates information only within its adjacent sensors without the need for a fusion center. Correntropy is a similarity metric based on a kernel function that has symmetry. Symmetry means that for any two data points, the output value of the kernel function does not depend on the order of the data points. By adopting a correntropy cost function based on the rational quadratic kernel function approximation to restrain non-Gaussian heavy-tailed noise, a centralized maximum correntropy Kalman filter is first derived for the linear sens+or network system at first. Then the corresponding centralized maximum correntropy information filter is attained by employing the information matrices, which is a foundation for further designing distributed information algorithms under multi-sensor networks. Thirdly, the distributed rational quadratic maximum correntropy information filter and distributed adaptive rational quadratic maximum correntropy information filter are designed by exploiting the weighted census average to solve the non-Gaussian heavy-tailed noise interference in sensor networks. Finally, the performance of the proposed algorithms is illustrated through numerical simulations on the sensor network system. Full article
(This article belongs to the Section Computer)
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21 pages, 1317 KiB  
Article
Research on Hidden Backdoor Prompt Attack Method
by Huanhuan Gu, Qianmu Li, Yufei Wang, Yu Jiang, Aniruddha Bhattacharjya, Haichao Yu and Qian Zhao
Symmetry 2025, 17(6), 954; https://doi.org/10.3390/sym17060954 - 16 Jun 2025
Viewed by 499
Abstract
Existing studies on backdoor attacks in large language models (LLMs) have contributed significantly to the literature by exploring trigger-based strategies—such as rare tokens or syntactic anomalies—that, however, limit both their stealth and generalizability, rendering them susceptible to detection. In this study, we propose [...] Read more.
Existing studies on backdoor attacks in large language models (LLMs) have contributed significantly to the literature by exploring trigger-based strategies—such as rare tokens or syntactic anomalies—that, however, limit both their stealth and generalizability, rendering them susceptible to detection. In this study, we propose HDPAttack, a novel hidden backdoor prompt attack method which is designed to overcome these limitations by leveraging the semantic and structural properties of prompts as triggers rather than relying on explicit markers. Not symmetric to traditional approaches, HDPAttack injects carefully crafted fake demonstrations into the training data, semantically re-expressing prompts to generate examples that exhibit high consistency in input semantics and corresponding labels. This method guides models to learn latent trigger patterns embedded in their deep representations, thereby enabling backdoor activation through natural language prompts without altering user inputs or introducing conspicuous anomalies. Experimental results across datasets (SST-2, SMS, AGNews, Amazon) reveal that HDPAttack achieved an average attack success rate of 99.87%, outperforming baseline methods by 2–20% while incurring a classification accuracy loss of ≤1%. These findings set a new benchmark for undetectable backdoor attacks and underscore the urgent need for advancements in prompt-based defense strategies. Full article
(This article belongs to the Section Mathematics)
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17 pages, 10816 KiB  
Article
On the Symmetry and Domination Integrity of Some Bidegreed Graphs
by Balaraman Ganesan and Sundareswaran Raman
Symmetry 2025, 17(6), 953; https://doi.org/10.3390/sym17060953 - 16 Jun 2025
Viewed by 263
Abstract
Graphs are one of the dynamic tools used to solve network-related problems and real-time application models. The stability of the network plays a crucial role in ensuring uninterrupted data flow. A network becomes vulnerable when a node or a link becomes non-functional. To [...] Read more.
Graphs are one of the dynamic tools used to solve network-related problems and real-time application models. The stability of the network plays a crucial role in ensuring uninterrupted data flow. A network becomes vulnerable when a node or a link becomes non-functional. To maintain a stable network connection, it is essential for the nodes to be able to interact with each other. The vulnerability of a network can be defined as the level of resistance it exhibits following the failure of communication links. Graphs serve as vital tools for depicting molecular structures, where atoms are shown as vertices and bonds as edges. The domination number quantifies the least number of atoms (vertices) required to dominate the entire molecular framework. Domination integrity reflects the impact of removing specific atoms on the overall molecular structure. This concept is valuable for forecasting fragmentation and decomposition pathways. In contrast to the domination number, domination integrity evaluates the extent to which the molecule remains intact following the removal of reactive or controlling atoms. It aids in assessing stability, particularly in the contexts of drug design, polymer analysis, or catalytic systems. This work focuses on the vulnerability parameter, specifically examining the domination integrity of a specific group of bidegreed hexagonal chemical network systems such as pyrene PY(p), prolate rectangle Rp,q, honeycomb HC(p), and hexabenzocoronene HBC(p). This work also extends to the calculation of the domination integrity value for Cyclic Silicate CCp and Chain Silicate CSp chemical structure networks. Full article
(This article belongs to the Section Mathematics)
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18 pages, 4601 KiB  
Article
An Intrusion Detection Method Based on Symmetric Federated Deep Learning in Complex Networks
by Lei Wang, Xuanrui Ren and Chunyi Wu
Symmetry 2025, 17(6), 952; https://doi.org/10.3390/sym17060952 - 15 Jun 2025
Viewed by 372
Abstract
The rapid development of the current 5G/6G network has added tremendous pressure to traditional security detection in the scenario of dealing with large-scale network attacks, resulting in high time complexity and low efficiency of attack identification. According to the deep network and its [...] Read more.
The rapid development of the current 5G/6G network has added tremendous pressure to traditional security detection in the scenario of dealing with large-scale network attacks, resulting in high time complexity and low efficiency of attack identification. According to the deep network and its symmetry principle, this paper proposes a complex network intrusion detection and recognition method based on symmetric federation optimization, named IDS, which aims to reduce the time complexity and improve the accuracy and efficiency of attack identification. By using a symmetric network UNet-based deep feature learning to reconstruct data and construct the input matrix, we optimize the federated deep learning algorithm with a symmetric auto-encoder to make it more suitable for a complex network environment. The experimental results demonstrate that the technology based on the symmetric network proposed in this paper possesses significant advantages in terms of intrusion detection accuracy and effectiveness, which can effectively identify network intrusion and improve the accuracy of current complex network intrusion detection. The proposed symmetric intrusion detection method not only solves the bottleneck of traditional detection methods and improves the training efficiency of the model, but it also provides a new idea and solution for network security research. Full article
(This article belongs to the Special Issue Symmetry in Deep Learning Networks and Its Applications in the Real World)
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26 pages, 1854 KiB  
Article
Quantitative State Evaluation Method for Relay Protection Equipment Based on Improved Conformer Optimized by Two-Stage APO
by Yanhong Li, Min Zhang, Shaofan Zhang and Yifan Zhou
Symmetry 2025, 17(6), 951; https://doi.org/10.3390/sym17060951 - 15 Jun 2025
Viewed by 344
Abstract
State evaluation of relay protection equipment constitutes a crucial component in ensuring the stable, secure, and symmetric operation of power systems. Current methodologies predominantly encompass fuzzy-rule-based control systems and data-driven machine learning approaches. The former relies on manual experience for designing fuzzy rules [...] Read more.
State evaluation of relay protection equipment constitutes a crucial component in ensuring the stable, secure, and symmetric operation of power systems. Current methodologies predominantly encompass fuzzy-rule-based control systems and data-driven machine learning approaches. The former relies on manual experience for designing fuzzy rules and membership functions and exhibits limitations in high-dimensional data integration and analysis. The latter predominantly formulates state evaluation as a classification task, which demonstrates its ineffectiveness in identifying equipment at boundary states and faces challenges in model parameter selection. To address these limitations, this paper proposes a quantitative state evaluation method for relay protection equipment based on a two-stage artificial protozoa optimizer (two-stage APO) optimized improved Conformer (two-stage APO-IConf) model. First, we modify the Conformer architecture by replacing pre-layer normalization (Pre-LN) in residual networks with post-batch normalization (post-BN) and introducing dynamic weighting coefficients to adaptively regulate the connection strengths between the first and second feed-forward network layers, thereby enhancing the capability of the model to fit relay protection state evaluation data. Subsequently, an improved APO algorithm with two-stage optimization is developed, integrating good point set initialization and elitism preservation strategies to achieve dynamic equilibrium between global exploration and local exploitation in the Conformer hyperparameter space. Experimental validation using operational data from a substation demonstrates that the proposed model achieves a RMSE of 0.5064 and a MAE of 0.2893, representing error reductions of 33.6% and 35.0% compared to the baseline Conformer, and 9.1% and 15.2% error reductions over the improved Conformer, respectively. This methodology can provide a quantitative state evaluation and guidance for developing maintenance strategies for substations. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry Studies in Modern Power Systems)
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21 pages, 23794 KiB  
Article
Towards Faithful Local Explanations: Leveraging SVM to Interpret Black-Box Machine Learning Models
by Jiaxiang Xu, Zhanhao Zhang, Junfei Wang, Biao Ouyang, Benkuan Zhou, Jianxiong Zhao, Hanfang Ge and Bo Xu
Symmetry 2025, 17(6), 950; https://doi.org/10.3390/sym17060950 - 15 Jun 2025
Viewed by 382
Abstract
Although machine learning (ML) models are widely used in many fields, their prediction processes are often hard to understand. This lack of transparency makes it harder for people to trust them, especially in high-stakes fields like healthcare and finance. Human-interpretable explanations for model [...] Read more.
Although machine learning (ML) models are widely used in many fields, their prediction processes are often hard to understand. This lack of transparency makes it harder for people to trust them, especially in high-stakes fields like healthcare and finance. Human-interpretable explanations for model predictions are crucial in these contexts. While existing local interpretation methods have been proposed, many suffer from low local fidelity, instability, and limited effectiveness when applied to highly nonlinear models. This paper presents SVM-X, a model-agnostic local explanation approach designed to address these challenges. By leveraging the inherent symmetry of the SVM hyperplane, SVM-X precisely captures the local decision boundaries of complex nonlinear models, providing more accurate and stable explanations. Experimental evaluations on the UCI Adult dataset, the Bank Marketing dataset, and the Amazon Product Review dataset demonstrate that SVM-X consistently outperforms state-of-the-art methods like LIME and LEMNA. Notably, SVM-X achieves up to a 27.2% improvement in accuracy. Our work introduces a reliable and interpretable framework for understanding machine learning predictions, offering a promising new direction for future research. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry Studies in Data Mining & Machine Learning of Large Language Models)
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12 pages, 958 KiB  
Article
Two-Step Two-Photon Absorption Dynamics in π-π Conjugated Carbazole-Phthalocyanine/Graphene Quantum Dot Hybrids Under Picosecond Pulse Excitation
by Quan Miao, Erping Sun and Yan Xu
Symmetry 2025, 17(6), 949; https://doi.org/10.3390/sym17060949 - 14 Jun 2025
Viewed by 330
Abstract
In carbazole-substituted phthalocyanine complexes 2,3,9,10,16,17,23,24-octakis-(3,6-dibromo-9Hcarbazol) phthalocyaninato zinc(II) (Pc 2) and 2,3,9,10,16,17,23,24-Octakis-(9H-carbazol-9-yl) phthalocyaninato zinc(II) (Pc 4) and their conjugated complexes to graphene quantum dots (GQDs), we studied the nonlinear absorption and propagating of picosecond pulse trains. Each pulse train contains 25 subpulses with width [...] Read more.
In carbazole-substituted phthalocyanine complexes 2,3,9,10,16,17,23,24-octakis-(3,6-dibromo-9Hcarbazol) phthalocyaninato zinc(II) (Pc 2) and 2,3,9,10,16,17,23,24-Octakis-(9H-carbazol-9-yl) phthalocyaninato zinc(II) (Pc 4) and their conjugated complexes to graphene quantum dots (GQDs), we studied the nonlinear absorption and propagating of picosecond pulse trains. Each pulse train contains 25 subpulses with width 100 ps seperated by space 13 ns. During the interaction with pulse trains, the structures of Pcs can be simplified to the five-state energy model. In our calculations, the coupled rate equations and two-dimensional paraxial field were solved using the Crank–Nicholson numerical method. The effects of substituted carbazoles and conjugated GQDs were investigated. Pcs and their conjugated complexes with GQDs exhibit optical limiting (OL) properties, and GQDs could decrease the OL of Pcs. One-photon absorption cross section σS0S1 or σT1T2 is the critical factor to determine the limiting value of energy transmittance in weak- or strong-intensity regions, respectively. The two-step two-photon absorption (TPA) tunnel (S0→S1)×(T1→T2) is the main absorption mechanism; therefore, the effective population transfer time τST from S0 to T1 is another critical factor that is determined by one-photon absorption cross section σS0S1 and intersystem crossing time τisc. Through further exploration it is found that a high incident intensity will lead to an asymmetric shape of output intensity due to different absorption mechanisms in the front and latter subpulses of the pulse train. Full article
(This article belongs to the Section Engineering and Materials)
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20 pages, 1320 KiB  
Article
Sequential Fusion Least Squares Method for State Estimation of Multi-Sensor Linear Systems Under Noise Cross-Correlation
by Xu Liang and Chenglin Wen
Symmetry 2025, 17(6), 948; https://doi.org/10.3390/sym17060948 - 14 Jun 2025
Viewed by 249
Abstract
This paper investigates a multi-sensor system for the state estimation of a maneuvering target, wherein the process noise of the target dynamics and the measurement noise of the sensor network are mutually correlated, and the measurement noises across different sensors are also cross-correlated. [...] Read more.
This paper investigates a multi-sensor system for the state estimation of a maneuvering target, wherein the process noise of the target dynamics and the measurement noise of the sensor network are mutually correlated, and the measurement noises across different sensors are also cross-correlated. Under such conditions, we propose a globally optimal sequential least squares fusion estimation algorithm within the framework of linear minimum mean square error (LMMSE) estimation. This method is specifically designed to preserve structural symmetry and to accommodate the time-ordered arrival of sensor observations transmitted over a network. Rigorous theoretical analysis establishes the performance equivalence between the proposed sequential fusion estimator and the centralized Kalman filter. Numerical simulations further demonstrate the algorithm’s superior estimation accuracy and stability under symmetry constraints, particularly when the noise statistics exhibit spatial or temporal symmetry. Full article
(This article belongs to the Section Engineering and Materials)
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20 pages, 3898 KiB  
Article
Symmetry-Aware CVAE-ACGAN-Based Feature Generation Model and Its Application in Fault Diagnosis
by Long Ma, Yingjie Liu, Yue Zhang and Ming Chu
Symmetry 2025, 17(6), 947; https://doi.org/10.3390/sym17060947 - 14 Jun 2025
Viewed by 316
Abstract
Traditional fault feature generation models often face issues of uncontrollability, singularity, and slow convergence, limiting diagnostic accuracy. To address these challenges, this paper proposes a symmetry-aware approach that combines a conditional variational autoencoder (CVAE) and an auxiliary classifier generative adversarial network (ACGAN) for [...] Read more.
Traditional fault feature generation models often face issues of uncontrollability, singularity, and slow convergence, limiting diagnostic accuracy. To address these challenges, this paper proposes a symmetry-aware approach that combines a conditional variational autoencoder (CVAE) and an auxiliary classifier generative adversarial network (ACGAN) for fault feature generation, leveraging symmetry characteristics inherent in fault data distributions and adversarial learning. Specifically, symmetrical Gaussian distributions in the CVAE enable robust extraction of latent fault features conditioned on fault classes, which are then input to the symmetrical adversarial framework of the ACGAN to guide the generator and discriminator toward a symmetrical Nash equilibrium. The original and generated features are jointly utilized in a convolutional neural network (CNN) for fault classification. Experimental results on the CWRU dataset show that the proposed CVAE-ACGAN achieves an average accuracy of 99.21%, precision of 97.81%, and recall of 98.24%, surpassing the baseline CNN. Similar improvements are achieved on the PADERBORN dataset. Furthermore, the model achieves significantly lower root mean square error (RMSE) and mean absolute error (MAE) than competing methods, confirming high consistency between the generated and real features and supporting its superior generalization and reliability. Visualization via confusion matrices and t-SNE further demonstrates clear boundaries between fault categories. These results affirm the value of incorporating symmetry principles into feature generation for mechanical fault diagnosis. Full article
(This article belongs to the Section Engineering and Materials)
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22 pages, 8629 KiB  
Article
3D UAV Route Optimization in Complex Environments Using an Enhanced Artificial Lemming Algorithm
by Yuxuan Xie, Zhe Sun, Kai Yuan and Zhixin Sun
Symmetry 2025, 17(6), 946; https://doi.org/10.3390/sym17060946 - 13 Jun 2025
Cited by 1 | Viewed by 296
Abstract
The use of UAVs for logistics delivery has become a hot topic in current research, and how to plan a reasonable delivery route is the key to the problem. Therefore, this paper proposes a multi-environment logistics delivery route planning model that is based [...] Read more.
The use of UAVs for logistics delivery has become a hot topic in current research, and how to plan a reasonable delivery route is the key to the problem. Therefore, this paper proposes a multi-environment logistics delivery route planning model that is based on UAVs, is characterized by a 3D environment model, and aims at the shortest delivery route with minimum flight undulation. In order to find the optimal route in various environments, a multi-strategy improved artificial lemming algorithm, which integrates the Cubic chaotic map initialization, double adaptive t-distribution perturbation, and population dynamic optimization, is proposed. The symmetric nature of the t-distribution ensures that the lemmings conduct extensive searches in both directions within the solution space, thus improving the convergence speed and preventing them from falling into local optimal solutions. Through data experiments and simulation analysis, the improved algorithm can be successfully applied to the 3D route planning model, and the route quality is superior. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
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