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Search Results (1,394)

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Keywords = symmetric networks

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20 pages, 1644 KiB  
Article
A Symmetric Multi-Scale Convolutional Transformer Network for Plant Disease Image Classification
by Chuncheng Xu and Tianjin Yang
Symmetry 2025, 17(8), 1232; https://doi.org/10.3390/sym17081232 - 4 Aug 2025
Abstract
Plant disease classification is critical for effective crop management. Recent advances in deep learning, especially Vision Transformers (ViTs), have shown promise due to their strong global feature modeling capabilities. However, ViTs often overlook local features and suffer from feature extraction degradation during patch [...] Read more.
Plant disease classification is critical for effective crop management. Recent advances in deep learning, especially Vision Transformers (ViTs), have shown promise due to their strong global feature modeling capabilities. However, ViTs often overlook local features and suffer from feature extraction degradation during patch merging as channels increase. To address these issues, we propose PLTransformer, a hybrid model designed to symmetrically capture both global and local features. We design a symmetric multi-scale convolutional module that combines two different-scale receptive fields to simultaneously extract global and local features so that the model can better perceive multi-scale disease morphologies. Additionally, we propose an overlap-attentive channel downsampler that utilizes inter-channel attention mechanisms during spatial downsampling, effectively preserving local structural information and mitigating semantic loss caused by feature compression. On the PlantVillage dataset, PLTransformer achieves 99.95% accuracy, outperforming DeiT (96.33%), Twins (98.92%), and DilateFormer (98.84%). These results demonstrate its superiority in handling multi-scale disease features. Full article
(This article belongs to the Section Computer)
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22 pages, 3301 KiB  
Article
Parameter Identification of Distribution Zone Transformers Under Three-Phase Asymmetric Conditions
by Panrun Jin, Wenqin Song and Yankui Zhang
Eng 2025, 6(8), 181; https://doi.org/10.3390/eng6080181 - 2 Aug 2025
Viewed by 143
Abstract
As a core device in low-voltage distribution networks, the distribution zone transformer (DZT) is influenced by short circuits, overloads, and unbalanced loads, which cause thermal aging, mechanical stress, and eventually deformation of the winding, resulting in parameter deviations from nameplate values and impairing [...] Read more.
As a core device in low-voltage distribution networks, the distribution zone transformer (DZT) is influenced by short circuits, overloads, and unbalanced loads, which cause thermal aging, mechanical stress, and eventually deformation of the winding, resulting in parameter deviations from nameplate values and impairing system operation. However, existing identification methods typically require synchronized high- and low-voltage data and are limited to symmetric three-phase conditions, which limits their application in practical distribution systems. To address these challenges, this paper proposes a parameter identification method for DZTs under three-phase unbalanced conditions. Firstly, based on the transformer’s T-equivalent circuit considering the load, the power flow equations are derived without involving the synchronization issue of high-voltage and low-voltage side data, and the sum of the impedances on both sides is treated as an independent parameter. Then, a novel power flow equation under three-phase unbalanced conditions is established, and an adaptive recursive least squares (ARLS) solution method is constructed using the measurement data sequence provided by the smart meter of the intelligent transformer terminal unit (TTU) to achieve online identification of the transformer winding parameters. The effectiveness and robustness of the method are verified through practical case studies. Full article
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16 pages, 4587 KiB  
Article
FAMNet: A Lightweight Stereo Matching Network for Real-Time Depth Estimation in Autonomous Driving
by Jingyuan Zhang, Qiang Tong, Na Yan and Xiulei Liu
Symmetry 2025, 17(8), 1214; https://doi.org/10.3390/sym17081214 - 1 Aug 2025
Viewed by 212
Abstract
Accurate and efficient stereo matching is fundamental to real-time depth estimation from symmetric stereo cameras in autonomous driving systems. However, existing high-accuracy stereo matching networks typically rely on computationally expensive 3D convolutions, which limit their practicality in real-world environments. In contrast, real-time methods [...] Read more.
Accurate and efficient stereo matching is fundamental to real-time depth estimation from symmetric stereo cameras in autonomous driving systems. However, existing high-accuracy stereo matching networks typically rely on computationally expensive 3D convolutions, which limit their practicality in real-world environments. In contrast, real-time methods often sacrifice accuracy or generalization capability. To address these challenges, we propose FAMNet (Fusion Attention Multi-Scale Network), a lightweight and generalizable stereo matching framework tailored for real-time depth estimation in autonomous driving applications. FAMNet consists of two novel modules: Fusion Attention-based Cost Volume (FACV) and Multi-scale Attention Aggregation (MAA). FACV constructs a compact yet expressive cost volume by integrating multi-scale correlation, attention-guided feature fusion, and channel reweighting, thereby reducing reliance on heavy 3D convolutions. MAA further enhances disparity estimation by fusing multi-scale contextual cues through pyramid-based aggregation and dual-path attention mechanisms. Extensive experiments on the KITTI 2012 and KITTI 2015 benchmarks demonstrate that FAMNet achieves a favorable trade-off between accuracy, efficiency, and generalization. On KITTI 2015, with the incorporation of FACV and MAA, the prediction accuracy of the baseline model is improved by 37% and 38%, respectively, and a total improvement of 42% is achieved by our final model. These results highlight FAMNet’s potential for practical deployment in resource-constrained autonomous driving systems requiring real-time and reliable depth perception. Full article
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19 pages, 2649 KiB  
Article
Short-Circuit Current Calculation of Single-Phase to Ground Fault in Petal-Shaped Distribution Network
by Yilong Kang, Huanruo Qi, Rui Liu, Xiangyang Yan, Chen Chen, Fei Guo, Fang Guo and Xiaoxiao Dong
Processes 2025, 13(8), 2393; https://doi.org/10.3390/pr13082393 - 28 Jul 2025
Viewed by 236
Abstract
Petal-shaped distribution networks are receiving increasing attention due to their enhanced reliability. However, the integration of distributed generators (DGs) significantly alters the fault characteristics during single-phase to ground faults. Traditional short-circuit calculation methods become inadequate due to the unmodeled effects of negative sequence [...] Read more.
Petal-shaped distribution networks are receiving increasing attention due to their enhanced reliability. However, the integration of distributed generators (DGs) significantly alters the fault characteristics during single-phase to ground faults. Traditional short-circuit calculation methods become inadequate due to the unmodeled effects of negative sequence current control in DGs. To address this challenge, this study establishes, for the first time, a mathematical model for single-phase to ground faults in a petal-shaped network with DG integration under both positive and negative sequence control. It explicitly derives the DGs’ output current under three control goals: maintaining constant active power, maintaining constant reactive power, and injecting a symmetric three-phase current. Utilizing the symmetrical component method, a composite sequence network incorporating the DGs’ negative sequence current output is developed. Based on the node–voltage relationships, an analytical short-circuit current calculation method suitable for multiple control goals is proposed. Validation via MATLAB R2022a simulations demonstrates high-fidelity accuracy: in Case 1 with different fault locations, the maximum relative error is 0.31%, while in Case 2, it is 2.04%. These results quantify the critical impact of the negative sequence current—reaching up to 14.78% of the DG output during severe voltage sags—providing theoretical support for the protection design of a petal-shaped distribution network with high DG integration. Full article
(This article belongs to the Section Energy Systems)
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19 pages, 13424 KiB  
Article
A Comprehensive Analysis of Security Challenges in ZigBee 3.0 Networks
by Akbar Ghobakhlou, Duaa Zuhair Al-Hamid, Sara Zandi and James Cato
Sensors 2025, 25(15), 4606; https://doi.org/10.3390/s25154606 - 25 Jul 2025
Viewed by 272
Abstract
ZigBee, a wireless technology standard for the Internet of Things (IoT) devices based on IEEE 802.15.4, faces significant security challenges that threaten the confidentiality, integrity, and availability of its networks. Despite using 128-bit Advanced Encryption Standard (AES) with symmetric keys for node authentication [...] Read more.
ZigBee, a wireless technology standard for the Internet of Things (IoT) devices based on IEEE 802.15.4, faces significant security challenges that threaten the confidentiality, integrity, and availability of its networks. Despite using 128-bit Advanced Encryption Standard (AES) with symmetric keys for node authentication and data confidentiality, ZigBee’s design constraints, such as low cost and low power, have allowed security issues to persist. While ZigBee 3.0 introduces enhanced security features such as install codes and trust centre link key updates, there remains a lack of empirical research evaluating their effectiveness in real-world deployments. This research addresses the gap by conducting a comprehensive, hardware-based analysis of ZigBee 3.0 networks using XBee 3 radio modules and ZigBee-compatible devices. We investigate the following three core security issues: (a) the security of symmetric keys, focusing on vulnerabilities that could allow attackers to obtain these keys; (b) the impact of compromised symmetric keys on network confidentiality; and (c) susceptibility to Denial-of-Service (DoS) attacks due to insufficient protection mechanisms. Our experiments simulate realistic attack scenarios under both Centralised and Distributed Security Models to assess the protocol’s resilience. The findings reveal that while ZigBee 3.0 improves upon earlier versions, certain vulnerabilities remain exploitable. We also propose practical security controls and best practices to mitigate these attacks and enhance network security. This work contributes novel insights into the operational security of ZigBee 3.0, offering guidance for secure IoT deployments and advancing the understanding of protocol-level defences in constrained environments. Full article
(This article belongs to the Section Communications)
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23 pages, 11560 KiB  
Article
An N-Shaped Beam Symmetrical Vibration Energy Harvester for Structural Health Monitoring of Aviation Pipelines
by Xutao Lu, Yingwei Qin, Zihao Jiang and Jing Li
Micromachines 2025, 16(8), 858; https://doi.org/10.3390/mi16080858 - 25 Jul 2025
Viewed by 247
Abstract
Wireless sensor networks provide a solution for structural health monitoring of aviation pipelines. In the installation environment of aviation pipelines, widespread vibrations can be utilized to extract energy through vibration energy harvesting technology to achieve self-powering of sensors. This study analyzed the vibration [...] Read more.
Wireless sensor networks provide a solution for structural health monitoring of aviation pipelines. In the installation environment of aviation pipelines, widespread vibrations can be utilized to extract energy through vibration energy harvesting technology to achieve self-powering of sensors. This study analyzed the vibration characteristics of aviation pipeline structures. The vibration characteristics and influencing factors of typical aviation pipeline structures were obtained through simulations and experiments. An N-shaped symmetric vibration energy harvester was designed considering the limited space in aviation pipeline structures. To improve the efficiency of electrical energy extraction from the vibration energy harvester, expand its operating frequency band, and achieve efficient vibration energy harvesting, this study first analyzed its natural frequency characteristics through theoretical analysis. Finite element simulation software was then used to analyze the effects of the external excitation acceleration direction, mass and combination of counterweights, piezoelectric sheet length, and piezoelectric material placement on the output power of the energy harvester. The structural parameters of the vibration energy harvester were optimized, and the optimal working conditions were determined. The experimental results indicate that the N-shaped symmetric vibration energy harvester designed and optimized in this study improves the efficiency of vibration energy harvesting and can be arranged in the limited space of aviation pipeline structures. It achieves efficient energy harvesting under multi-modal conditions, different excitation directions, and a wide operating frequency band, thus meeting the practical application requirement and engineering feasibility of aircraft design. Full article
(This article belongs to the Special Issue Micro-Energy Harvesting Technologies and Self-Powered Sensing Systems)
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18 pages, 396 KiB  
Article
A Novel Bondage Parameter for Network Analysis
by Hande Tuncel Golpek
Symmetry 2025, 17(8), 1170; https://doi.org/10.3390/sym17081170 - 22 Jul 2025
Viewed by 242
Abstract
In this study, we explore the paired disjunctive domination number—a recently introduced parameter by Henning et al.—within the broader framework of graph and network sensitivity and vulnerability analysis. Building on this concept, we introduce and investigate the paired disjunctive bondage number (PDBN), which [...] Read more.
In this study, we explore the paired disjunctive domination number—a recently introduced parameter by Henning et al.—within the broader framework of graph and network sensitivity and vulnerability analysis. Building on this concept, we introduce and investigate the paired disjunctive bondage number (PDBN), which measures the minimum number of edge deletions required to increase the paired disjunctive domination number of a graph or its corresponding network model. We begin by computing this new bondage number for several well-known network classes. The focus then shifts to specific families of trees, where we first determine their paired disjunctive domination numbers in detail. Using these values, we calculate the corresponding bondage numbers for various structurally symmetric, hierarchical, and compound tree structures, including double star, comet, double comet, Ept, and binomial trees, all of which model different types of infrastructural networks. Finally, we present an algorithm for computing PDBN, accompanied by a complexity analysis, and illustrate the practical relevance of the parameter through a case study applying it to a real-life network problem. Our results offer foundational insights into the behavior of this new domination parameter and its bondage variant, contributing to the growing literature on graph vulnerability and suggesting potential applications in the design of resilient and failure-aware networks. Full article
(This article belongs to the Special Issue Symmetry in Security and Theoretical Computer Science)
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25 pages, 1047 KiB  
Article
Integrated Blockchain and Federated Learning for Robust Security in Internet of Vehicles Networks
by Zhikai He, Rui Xu, Binyu Wang, Qisong Meng, Qiang Tang, Li Shen, Zhen Tian and Jianyu Duan
Symmetry 2025, 17(7), 1168; https://doi.org/10.3390/sym17071168 - 21 Jul 2025
Viewed by 340
Abstract
The Internet of Vehicles (IoV) operates in an environment characterized by asymmetric security threats, where centralized vulnerabilities create a critical imbalance that can be disproportionately exploited by attackers. This study addresses this imbalance by proposing a symmetrical security framework that integrates Blockchain and [...] Read more.
The Internet of Vehicles (IoV) operates in an environment characterized by asymmetric security threats, where centralized vulnerabilities create a critical imbalance that can be disproportionately exploited by attackers. This study addresses this imbalance by proposing a symmetrical security framework that integrates Blockchain and Federated Learning (FL) to restore equilibrium in the Vehicle–Road–Cloud ecosystem. The evolution toward sixth-generation (6G) technologies amplifies both the potential of vehicle-to-everything (V2X) communications and its inherent security risks. The proposed framework achieves a delicate balance between robust security and operational efficiency. By leveraging blockchain’s symmetrical and decentralized distribution of trust, the framework ensures data and model integrity. Concurrently, the privacy-preserving approach of FL balances the need for collaborative intelligence with the imperative of safeguarding sensitive vehicle data. A novel Cloud Proxy Re-Encryption Offloading (CPRE-IoV) algorithm is introduced to facilitate efficient model updates. The architecture employs a partitioned blockchain and a smart contract-driven FL pipeline to symmetrically neutralize threats from malicious nodes. Finally, extensive simulations validate the framework’s effectiveness in establishing a resilient and symmetrically secure foundation for next-generation IoV networks. Full article
(This article belongs to the Section Computer)
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22 pages, 13310 KiB  
Article
Dual-Domain Joint Learning Reconstruction Method (JLRM) Combined with Physical Process for Spectral Computed Tomography (SCT)
by Genwei Ma, Ping Yang and Xing Zhao
Symmetry 2025, 17(7), 1165; https://doi.org/10.3390/sym17071165 - 21 Jul 2025
Viewed by 157
Abstract
Spectral computed tomography (SCT) enables material decomposition, artifact reduction, and contrast enhancement, leveraging symmetry principles across its technical framework to enhance material differentiation and image quality. However, its nonlinear data acquisition process involving noise and scatter leads to a highly ill-posed inverse problem. [...] Read more.
Spectral computed tomography (SCT) enables material decomposition, artifact reduction, and contrast enhancement, leveraging symmetry principles across its technical framework to enhance material differentiation and image quality. However, its nonlinear data acquisition process involving noise and scatter leads to a highly ill-posed inverse problem. To address this, we propose a dual-domain iterative reconstruction network that combines joint learning reconstruction with physical process modeling, which also uses the symmetric complementary properties of the two domains for optimization. A dedicated physical module models the SCT forward process to ensure stability and accuracy, while a residual-to-residual strategy reduces the computational burden of model-based iterative reconstruction (MBIR). Our method, which won the AAPM DL-Spectral CT Challenge, achieves high-accuracy material decomposition. Extensive evaluations also demonstrate its robustness under varying noise levels, confirming the method’s generalizability. This integrated approach effectively combines the strengths of physical modeling, MBIR, and deep learning. Full article
(This article belongs to the Section Mathematics)
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21 pages, 5616 KiB  
Article
Symmetry-Guided Dual-Branch Network with Adaptive Feature Fusion and Edge-Aware Attention for Image Tampering Localization
by Zhenxiang He, Le Li and Hanbin Wang
Symmetry 2025, 17(7), 1150; https://doi.org/10.3390/sym17071150 - 18 Jul 2025
Viewed by 270
Abstract
When faced with diverse types of image tampering and image quality degradation in real-world scenarios, traditional image tampering localization methods often struggle to balance boundary accuracy and robustness. To address these issues, this paper proposes a symmetric guided dual-branch image tampering localization network—FENet [...] Read more.
When faced with diverse types of image tampering and image quality degradation in real-world scenarios, traditional image tampering localization methods often struggle to balance boundary accuracy and robustness. To address these issues, this paper proposes a symmetric guided dual-branch image tampering localization network—FENet (Fusion-Enhanced Network)—that integrates adaptive feature fusion and edge attention mechanisms. This method is based on a structurally symmetric dual-branch architecture, which extracts RGB semantic features and SRM noise residual information to comprehensively capture the fine-grained differences in tampered regions at the visual and statistical levels. To effectively fuse different features, this paper designs a self-calibrating fusion module (SCF), which introduces a content-aware dynamic weighting mechanism to adaptively adjust the importance of different feature branches, thereby enhancing the discriminative power and expressiveness of the fused features. Furthermore, considering that image tampering often involves abnormal changes in edge structures, we further propose an edge-aware coordinate attention mechanism (ECAM). By jointly modeling spatial position information and edge-guided information, the model is guided to focus more precisely on potential tampering boundaries, thereby enhancing its boundary detection and localization capabilities. Experiments on public datasets such as Columbia, CASIA, and NIST16 demonstrate that FENet achieves significantly better results than existing methods. We also analyze the model’s performance under various image quality conditions, such as JPEG compression and Gaussian blur, demonstrating its robustness in real-world scenarios. Experiments in Facebook, Weibo, and WeChat scenarios show that our method achieves average F1 scores that are 2.8%, 3%, and 5.6% higher than those of existing state-of-the-art methods, respectively. Full article
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21 pages, 733 KiB  
Article
A Secure and Privacy-Preserving Approach to Healthcare Data Collaboration
by Amna Adnan, Firdous Kausar, Muhammad Shoaib, Faiza Iqbal, Ayesha Altaf and Hafiz M. Asif
Symmetry 2025, 17(7), 1139; https://doi.org/10.3390/sym17071139 - 16 Jul 2025
Viewed by 474
Abstract
Combining a large collection of patient data and advanced technology, healthcare organizations can excel in medical research and increase the quality of patient care. At the same time, health records present serious privacy and security challenges because they are confidential and can be [...] Read more.
Combining a large collection of patient data and advanced technology, healthcare organizations can excel in medical research and increase the quality of patient care. At the same time, health records present serious privacy and security challenges because they are confidential and can be breached through networks. Even traditional methods with federated learning are used to share data, patient information might still be at risk of interference while updating the model. This paper proposes the Privacy-Preserving Federated Learning with Homomorphic Encryption (PPFLHE) framework, which strongly supports secure cooperation in healthcare and at the same time providing symmetric privacy protection among participating institutions. Everyone in the collaboration used the same EfficientNet-B0 architecture and training conditions and keeping the model symmetrical throughout the network to achieve a balanced learning process and fairness. All the institutions used CKKS encryption symmetrically for their models to keep data concealed and stop any attempts at inference. Our federated learning process uses FedAvg on the server to symmetrically aggregate encrypted model updates and decrease any delays in our server communication. We attained a classification accuracy of 83.19% and 81.27% when using the APTOS 2019 Blindness Detection dataset and MosMedData CT scan dataset, respectively. Such findings confirm that the PPFLHE framework is generalizable among the broad range of medical imaging methods. In this way, patient data are kept secure while encouraging medical research and treatment to move forward, helping healthcare systems cooperate more effectively. Full article
(This article belongs to the Special Issue Exploring Symmetry in Wireless Communication)
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21 pages, 7084 KiB  
Article
Chinese Paper-Cutting Style Transfer via Vision Transformer
by Chao Wu, Yao Ren, Yuying Zhou, Ming Lou and Qing Zhang
Entropy 2025, 27(7), 754; https://doi.org/10.3390/e27070754 - 15 Jul 2025
Viewed by 332
Abstract
Style transfer technology has seen substantial attention in image synthesis, notably in applications like oil painting, digital printing, and Chinese landscape painting. However, it is often difficult to generate migrated images that retain the essence of paper-cutting art and have strong visual appeal [...] Read more.
Style transfer technology has seen substantial attention in image synthesis, notably in applications like oil painting, digital printing, and Chinese landscape painting. However, it is often difficult to generate migrated images that retain the essence of paper-cutting art and have strong visual appeal when trying to apply the unique style of Chinese paper-cutting art to style transfer. Therefore, this paper proposes a new method for Chinese paper-cutting style transformation based on the Transformer, aiming at realizing the efficient transformation of Chinese paper-cutting art styles. Specifically, the network consists of a frequency-domain mixture block and a multi-level feature contrastive learning module. The frequency-domain mixture block explores spatial and frequency-domain interaction information, integrates multiple attention windows along with frequency-domain features, preserves critical details, and enhances the effectiveness of style conversion. To further embody the symmetrical structures and hollowed hierarchical patterns intrinsic to Chinese paper-cutting, the multi-level feature contrastive learning module is designed based on a contrastive learning strategy. This module maximizes mutual information between multi-level transferred features and content features, improves the consistency of representations across different layers, and thus accentuates the unique symmetrical aesthetics and artistic expression of paper-cutting. Extensive experimental results demonstrate that the proposed method outperforms existing state-of-the-art approaches in both qualitative and quantitative evaluations. Additionally, we created a Chinese paper-cutting dataset that, although modest in size, represents an important initial step towards enriching existing resources. This dataset provides valuable training data and a reference benchmark for future research in this field. Full article
(This article belongs to the Section Multidisciplinary Applications)
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27 pages, 14879 KiB  
Article
Research on AI-Driven Classification Possibilities of Ball-Burnished Regular Relief Patterns Using Mixed Symmetrical 2D Image Datasets Derived from 3D-Scanned Topography and Photo Camera
by Stoyan Dimitrov Slavov, Lyubomir Si Bao Van, Marek Vozár, Peter Gogola and Diyan Minkov Dimitrov
Symmetry 2025, 17(7), 1131; https://doi.org/10.3390/sym17071131 - 15 Jul 2025
Viewed by 348
Abstract
The present research is related to the application of artificial intelligence (AI) approaches for classifying surface textures, specifically regular reliefs patterns formed by ball burnishing operations. A two-stage methodology is employed, starting with the creation of regular reliefs (RRs) on test parts by [...] Read more.
The present research is related to the application of artificial intelligence (AI) approaches for classifying surface textures, specifically regular reliefs patterns formed by ball burnishing operations. A two-stage methodology is employed, starting with the creation of regular reliefs (RRs) on test parts by ball burnishing, followed by 3D topography scanning with Alicona device and data preprocessing with Gwyddion, and Blender software, where the acquired 3D topographies are converted into a set of 2D images, using various virtual camera movements and lighting to simulate the symmetrical fluctuations around the tool-path of the real camera. Four pre-trained convolutional neural networks (DenseNet121, EfficientNetB0, MobileNetV2, and VGG16) are used as a base for transfer learning and tested for their generalization performance on different combinations of synthetic and real image datasets. The models were evaluated by using confusion matrices and four additional metrics. The results show that the pretrained VGG16 model generalizes the best regular reliefs textures (96%), in comparison with the other models, if it is subjected to transfer learning via feature extraction, using mixed dataset, which consist of 34,037 images in following proportions: non-textured synthetic (87%), textured synthetic (8%), and real captured (5%) images of such a regular relief. Full article
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17 pages, 1331 KiB  
Article
A Neural Network Training Method Based on Distributed PID Control
by Kun Jiang
Symmetry 2025, 17(7), 1129; https://doi.org/10.3390/sym17071129 - 14 Jul 2025
Viewed by 288
Abstract
In the previous article, we introduced a neural network framework based on symmetric differential equations. This novel framework exhibits complete symmetry, endowing it with perfect mathematical properties. While we have examined some of the system’s mathematical characteristics, a detailed discussion of the network [...] Read more.
In the previous article, we introduced a neural network framework based on symmetric differential equations. This novel framework exhibits complete symmetry, endowing it with perfect mathematical properties. While we have examined some of the system’s mathematical characteristics, a detailed discussion of the network training methodology has not yet been presented. Drawing on the principles of the traditional backpropagation algorithm, this study proposes an alternative training approach that utilizes differential equation signal propagation instead of chain rule derivation. This approach not only preserves the effectiveness of training but also offers enhanced biological interpretability. The foundation of this methodology lies in the system’s reversibility, which stems from its inherent symmetry—a key aspect of our research. However, this method alone is insufficient for effective neural network training. To address this, we further introduce a distributed Proportional–Integral–Derivative (PID) control approach, emphasizing its implementation within a closed system. By incorporating this method, we achieved both faster training speeds and improved accuracy. This approach not only offers novel insights into neural network training but also extends the scope of research into control methodologies. To validate its effectiveness, we apply this method to the MNIST (Modified National Institute of Standards and Technology database) and Fashion-MNIST, demonstrating its practical utility. Full article
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14 pages, 4522 KiB  
Article
A Wideband Circularly Polarized Metasurface Antenna with High Gain Using Characteristic Mode Analysis
by Zijie Li, Yuechen Liu, Mengfei Zhao, Weihua Zong and Shi He
Electronics 2025, 14(14), 2818; https://doi.org/10.3390/electronics14142818 - 13 Jul 2025
Viewed by 414
Abstract
This paper proposes a novel high-gain, wideband, circularly polarized (CP) metasurface (MTS) antenna. The antenna is composed of a centrally symmetric MTS and a slot-coupled feeding network. Through characteristic mode analysis (CMA), parasitic patches and mode-suppressing patches are added around the MTS to [...] Read more.
This paper proposes a novel high-gain, wideband, circularly polarized (CP) metasurface (MTS) antenna. The antenna is composed of a centrally symmetric MTS and a slot-coupled feeding network. Through characteristic mode analysis (CMA), parasitic patches and mode-suppressing patches are added around the MTS to enhance the desired modes and suppress the unwanted modes. Subsequently, a feeding network that merges a ring slot with an L-shaped microstrip line is utilized to excite two orthogonal modes with a 90° phase difference, thereby achieving CP and high-gain radiation. Finally, a prototype with dimensions of 0.9λ0 × 0.9λ0 × 0.05λ0 is fabricated and tested. The measured results demonstrate an impedance bandwidth (IBW) of 39.5% (4.92–7.37 GHz), a 3 dB axial ratio bandwidth (ARBW) of 33.1% (5.25–7.33 GHz), and a peak gain of 9.4 dBic at 6.9 GHz. Full article
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