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Symmetry
Volume 17
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Symmetry, Volume 17, Issue 5 (May 2025) – 171 articles

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27 pages, 10195 KiB  
Article
WIGformer: Wavelet-Based Illumination-Guided Transformer
by Wensheng Cao, Tianyu Yan, Zhile Li and Jiongyao Ye
Symmetry 2025, 17(5), 798; https://doi.org/10.3390/sym17050798 - 20 May 2025
Abstract
Low-light image enhancement remains a challenging task in computer vision due to the complex interplay of noise, asymmetrical artifacts, illumination non-uniformity, and detail preservation. Existing methods such as traditional histogram equalization, gamma correction, and Retinex-based approaches often struggle to balance contrast improvement and [...] Read more.
Low-light image enhancement remains a challenging task in computer vision due to the complex interplay of noise, asymmetrical artifacts, illumination non-uniformity, and detail preservation. Existing methods such as traditional histogram equalization, gamma correction, and Retinex-based approaches often struggle to balance contrast improvement and naturalness preservation. Deep learning methods such as CNNs and transformers have shown promise, but face limitations in modeling multi-scale illumination and long-range dependencies. To address these issues, we propose WIGformer, a novel wavelet-based illumination-guided transformer framework for low-light image enhancement. The proposed method extends the single-stage Retinex theory to explicitly model noise in both reflectance and illumination components. It introduces a wavelet illumination estimator with a Wavelet Feature Enhancement Convolution (WFEConv) module to capture multi-scale illumination features and an illumination feature-guided corruption restorer with an Illumination-Guided Enhanced Multihead Self-Attention (IGEMSA) mechanism. WIGformer leverages the symmetry properties of wavelet transforms to achieve multi-scale illumination estimation, ensuring balanced feature extraction across different frequency bands. The IGEMSA mechanism integrates adaptive feature refinement and illumination guidance to suppress noise and artifacts while preserving fine details. The same mechanism allows us to further exploit symmetrical dependencies between illumination and reflectance components, enabling robust and natural enhancement of low-light images. Extensive experiments on the LOL-V1, LOL-V2-Real, and LOL-V2-Synthetic datasets demonstrate that WIGformer achieves state-of-the-art performance and outperforms existing methods, with PSNR improvements of up to 26.12 dB and an SSIM score of 0.935. The qualitative results demonstrate WIGformer’s superior capability to not only restore natural illumination but also maintain structural symmetry in challenging conditions, preserving balanced luminance distributions and geometric regularities that are characteristic of properly exposed natural scenes. Full article
(This article belongs to the Section Computer)
19 pages, 754 KiB  
Article
Closed Forms and Structural Properties of Lucas Matrices Derived from Tridiagonal Toeplitz Matrices
by Fikri Koken and Muaz Aksoy
Symmetry 2025, 17(5), 797; https://doi.org/10.3390/sym17050797 - 20 May 2025
Abstract
This study investigates the closed forms of Lucas matrices, with a particular emphasis on the nth powers of the tridiagonal symmetric Toeplitz matrix S4(x,y), whose entries are associated with Lucas numbers Ln. [...] Read more.
This study investigates the closed forms of Lucas matrices, with a particular emphasis on the nth powers of the tridiagonal symmetric Toeplitz matrix S4(x,y), whose entries are associated with Lucas numbers Ln. The analysis extends Filipponi’s foundational work by examining distinct cases of ordered pairs (x,y), thereby determining the precise conditions under which S4(x,y) qualifies as a Fibonacci–Lucas matrix. Furthermore, it identifies specific conditions under which S4(x,y) can be classified as any Fibonacci–Lucas matrix. These findings contribute to the theoretical framework of Fibonacci–Lucas matrices and provide novel insights into their structural properties. Full article
(This article belongs to the Section Mathematics)
24 pages, 1733 KiB  
Article
ProFusion: Multimodal Prototypical Networks for Few-Shot Learning with Feature Fusion
by Jia Zhao, Ziyang Cao, Huiling Wang, Xu Wang and Yingzhou Chen
Symmetry 2025, 17(5), 796; https://doi.org/10.3390/sym17050796 - 20 May 2025
Abstract
Existing few-shot learning models leverage vision-language pre-trained models to alleviate the data scarcity problem. However, such models usually process visual and text information separately, which causes still inherent disparities between cross-modal features. Therefore, we propose the ProFusion model, which leverages multimodal pre-trained models [...] Read more.
Existing few-shot learning models leverage vision-language pre-trained models to alleviate the data scarcity problem. However, such models usually process visual and text information separately, which causes still inherent disparities between cross-modal features. Therefore, we propose the ProFusion model, which leverages multimodal pre-trained models and prototypical networks to construct multiple prototypes. Specifically, ProFusion generates image and text prototypes symmetrically using the visual encoder and text encoder, while integrating visual and text information through the fusion module to create more expressive multimodal feature fusion prototypes. Additionally, we introduce the alignment module to ensure consistency between image and text prototypes. During inference, ProFusion calculates the similarity of test images to the three types of prototypes separately and applies a weighted sum to generate the final prediction. Experiments demonstrate that ProFusion performs outstanding classification tasks on 15 benchmark datasets. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Computer Vision and Graphics)
34 pages, 589 KiB  
Article
Anisotropic Four-Dimensional Spaces of Real Numbers
by Maksut M. Abenov, Mars B. Gabbassov, Tolybay Z. Kuanov and Berik I. Tuleuov
Symmetry 2025, 17(5), 795; https://doi.org/10.3390/sym17050795 - 20 May 2025
Abstract
This article constructs all the anisotropic spaces of four-dimensional numbers in which the commutative and associative operations of addition and multiplication are defined. In this case, so-called “zero divisors” appear in these spaces. The structures of zero divisors in each space are described [...] Read more.
This article constructs all the anisotropic spaces of four-dimensional numbers in which the commutative and associative operations of addition and multiplication are defined. In this case, so-called “zero divisors” appear in these spaces. The structures of zero divisors in each space are described and their properties are investigated. It is shown that there are two types of zero divisors and they form a two-dimensional subspace of the four-dimensional space. A space of 4 × 4 matrices is constructed that is isomorphic to the space of four-dimensional numbers. The concept of the spectrum of a four-dimensional number is introduced and a bijective mapping between four-dimensional numbers and their spectra is constructed. Thanks to this, methods for solving linear and quadratic equations in four-dimensional spaces are developed. It is proven that a quadratic equation in a four-dimensional space generally has four roots. The concept of the spectral norm is introduced in the space of four-dimensional numbers and the equivalence of the spectral norm to the Euclidean norm is proved. Full article
(This article belongs to the Section Mathematics)
16 pages, 1509 KiB  
Article
A Reliable Deep Learning Model for ECG Interpretation: Mitigating Overconfidence and Direct Uncertainty Quantification
by Xuedong Li, Qingxiao Zheng, Shibin Zhang, Shipeng Fu, Yingke Chen and Ke Ye
Symmetry 2025, 17(5), 794; https://doi.org/10.3390/sym17050794 - 20 May 2025
Abstract
Electrocardiogram (ECG) interpretation using deep learning models holds immense potential for improving cardiac diagnosis. However, existing models often suffer from overconfident predictions and lack the capability to directly quantify uncertainty, leading to unreliable clinical guidance. To address this challenge, we propose a model [...] Read more.
Electrocardiogram (ECG) interpretation using deep learning models holds immense potential for improving cardiac diagnosis. However, existing models often suffer from overconfident predictions and lack the capability to directly quantify uncertainty, leading to unreliable clinical guidance. To address this challenge, we propose a model for uncertainty-aware ECG interpretation. The model employs a deep convolutional architecture with max-pooling residual modules to capture both local and global spatiotemporal features from raw ECG signals. The architectural design respects the symmetry inherent in ECG waveforms—such as periodicity and morphological consistency across cardiac cycles—enabling the network to extract clinically relevant features more effectively. Then, unlike conventional models that rely on softmax-based probability outputs, our approach parameterizes class distributions using the Dirichlet distribution, while Subjective Logic translates these parameters into interpretable belief masses and uncertainty scores. We evaluate the model on the PhysioNet Challenge 2017 dataset, our model achieves an accuracy of 86.12%, an F1 score of 83.14%, a Precision-Recall Area Under the Curve (PR-AUC) of 85.25%, and a Receiver Operating Characteristic Area Under the Curve (ROC-AUC) of 92.87%—outperforming baseline models in three out of four metrics. Critically, the model reduces overconfidence to 0.59% (compared to 12–22% in softmax-based baselines), aligning prediction confidence with true accuracy. By progressively increasing the uncertainty threshold u, the model dynamically filters low-confidence predictions, leading to consistently improved performance—reaching up to 93.59% accuracy, 93.22% F1 score, 89.17% PR-AUC, and 95.10% ROC-AUC at u = 0.1. These results validate the model’s capacity for reliable ECG interpretation while leveraging physiological signal symmetry for enhanced feature extraction. Full article
(This article belongs to the Section Computer)
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19 pages, 6004 KiB  
Article
Remote Sensing Image Change Detection Based on Dynamic Adaptive Context Attention
by Yong Xie, Yixuan Wang, Xin Wang, Yin Tan and Qin Qin
Symmetry 2025, 17(5), 793; https://doi.org/10.3390/sym17050793 - 20 May 2025
Abstract
Although some progress has been made in deep learning-based remote sensing image change detection, the complexity of scenes and the diversity of changes in remote sensing images lead to challenges related to background interference. For instance, remote sensing images typically contain numerous background [...] Read more.
Although some progress has been made in deep learning-based remote sensing image change detection, the complexity of scenes and the diversity of changes in remote sensing images lead to challenges related to background interference. For instance, remote sensing images typically contain numerous background regions, while the actual change regions constitute only a small proportion of the overall image. To address these challenges in remote sensing image change detection, this paper proposes a Dynamic Adaptive Context Attention Network (DACA-Net) based on an exchanging dual encoder–decoder (EDED) architecture. The core innovation of DACA-Net is the development of a novel Dynamic Adaptive Context Attention Module (DACAM), which learns attention weights and automatically adjusts the appropriate scale according to the features present in remote sensing images. By fusing multi-scale contextual features, DACAM effectively captures information regarding changes within these images. In addition, DACA-Net adopts an EDED architectural design, where the conventional convolutional modules in the EDED framework are replaced by DACAM modules. Unlike the original EDED architecture, DACAM modules are embedded after each encoder unit, enabling dynamic recalibration of T1/T2 features and cross-temporal information interaction. This design facilitates the capture of fine-grained change features at multiple scales. This architecture not only facilitates the extraction of discriminative features but also promotes a form of structural symmetry in the processing pipeline, contributing to more balanced and consistent feature representations. To validate the applicability of our proposed method in real-world scenarios, we constructed an Unmanned Aerial Vehicle (UAV) remote sensing dataset named the Guangxi Beihai Coast Nature Reserves (GBCNR). Extensive experiments conducted on three public datasets and our GBCNR dataset demonstrate that the proposed DACA-Net achieves strong performance across various evaluation metrics. For example, it attains an F1 score (F1) of 72.04% and a precision(P) of 66.59% on the GBCNR dataset, representing improvements of 3.94% and 4.72% over state-of-the-art methods such as semantic guidance and spatial localization network (SGSLN) and bi-temporal image Transformer (BIT), respectively. These results verify that the proposed network significantly enhances the ability to detect critical change regions and improves generalization performance. Full article
(This article belongs to the Section Computer)
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18 pages, 1890 KiB  
Article
Symmetry-Entropy-Constrained Matrix Fusion for Dynamic Dam-Break Emergency Planning
by Shuai Liu, Dewei Yang, Hao Hu and Junping Wang
Symmetry 2025, 17(5), 792; https://doi.org/10.3390/sym17050792 - 20 May 2025
Abstract
Existing studies on ontology evolution lack automated mechanisms to balance semantic coherence and adaptability under real-time uncertainties, particularly in resolving spatiotemporal asymmetry and multidimensional coupling imbalances in dam-break scenarios. Traditional methods such as WordNet’s tree symmetry and FrameNet’s frame symmetry fail to formalize [...] Read more.
Existing studies on ontology evolution lack automated mechanisms to balance semantic coherence and adaptability under real-time uncertainties, particularly in resolving spatiotemporal asymmetry and multidimensional coupling imbalances in dam-break scenarios. Traditional methods such as WordNet’s tree symmetry and FrameNet’s frame symmetry fail to formalize dynamic adjustments through quantitative metrics, leading to path dependency and delayed responses. This study addresses this gap by introducing a novel symmetry-entropy-constrained matrix fusion algorithm, which integrates algebraic direct sum operations and Hadamard product with entropy-driven adaptive weighting. The original contribution lies in the symmetry entropy metric, which quantifies structural deviations during fusion to systematically balance semantic stability and adaptability. This work formalizes ontology evolution as a symmetry-driven optimization process. Experimental results demonstrate that shared concepts between ontologies (s = 3) reduce structural asymmetry by 25% compared to ontologies (s = 1), while case studies validate the algorithm’s ability to reconcile discrepancies between theoretical models and practical challenges in evacuation efficiency and crowd dynamics. This advancement promotes the evolution of traditional emergency management systems towards an adaptive intelligent form. Full article
(This article belongs to the Section Mathematics)
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10 pages, 1543 KiB  
Article
Synthesis, Structural Characterization, EPR Analysis and Antimicrobial Activity of a Copper(II) Thiocyanate Complex Based on 3,7-Di(3-pyridyl)-1,5-dioxa-3,7-diazacyclooctane
by Wei Qian, Zibo Wang, Jingfeng Xia, Hongxia Wang, Shuling Dong, Shuai Lou, Ping Ding and Li Li
Symmetry 2025, 17(5), 791; https://doi.org/10.3390/sym17050791 - 20 May 2025
Abstract
The reaction of bipyridine 3,7-di(3-pyridyl)-1,5-dioxa-3,7-diazacyclooctane (L) with copper thiocyanate produces a discrete metallamacrocycle [Cu(L)(SCN)2(DMF)]2 (1). In complex 1, two cis-coordinated ligands combine with two copper ions to form an unabridged 24-membered macrocycle. Each copper ion is five-coordinated [...] Read more.
The reaction of bipyridine 3,7-di(3-pyridyl)-1,5-dioxa-3,7-diazacyclooctane (L) with copper thiocyanate produces a discrete metallamacrocycle [Cu(L)(SCN)2(DMF)]2 (1). In complex 1, two cis-coordinated ligands combine with two copper ions to form an unabridged 24-membered macrocycle. Each copper ion is five-coordinated with two nitrogens from separate ligands, two nitrogens from thiocyanates and one oxygen from the dimethylformamide (DMF) solvent. Complex 1 has been characterized using single-crystal X-ray diffraction, optical and thermal analyses and antimicrobial activity measurements. The solid electron paramagnetic resonance (EPR) analysis of complex 1 yielded a characteristic structural g factor value of 2.147. In addition, the thermal analysis established that the complex is thermally stable at up to 176 °C. The antimicrobial activity measurements demonstrated that both the ligand and complex 1 exhibit an inhibitory effect on two strains, where the complex exhibits a significantly greater inhibition relative to that of the free ligand (p < 0.05). Full article
(This article belongs to the Section Chemistry: Symmetry/Asymmetry)
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10 pages, 222 KiB  
Article
Maximum Colored Cuts in Edge-Colored Complete k-Partite Graphs and Complete Graphs
by Huawen Ma
Symmetry 2025, 17(5), 790; https://doi.org/10.3390/sym17050790 - 20 May 2025
Abstract
The Maximum Colored Cut problem aims to seek a bipartition of the vertex set of a graph, maximizing the number of colors in the crossing edges. It is a classical Max-Cut problem if the host graph is rainbow. Let [...] Read more.
The Maximum Colored Cut problem aims to seek a bipartition of the vertex set of a graph, maximizing the number of colors in the crossing edges. It is a classical Max-Cut problem if the host graph is rainbow. Let mcc(G) denote the maximum number of colors in a cut of an edge-colored graph G. Let Ck be a cycle of length k; we say G is PC-Ck-free if G contains no properly colored Ck. We say G is a p-edge-colored graph if there exist p colors in G. In this paper, we first show that if G is a PC-C3-free p-edge-colored complete 4-partite graph, then mcc(G)=p. Let k≥3 be an integer. Then, we show that if G is a PC-C4-free p-edge-colored complete k-partite graph, then mcc(G)≥min{p−1,15p/16}. Finally, for a p-edge-colored complete graph G, we prove that mcc(G)≥p−1 if G is PC-C4-free, and mcc(G)≥min{p−6,7p/8} if G is PC-C5-free and p≥7. Full article
(This article belongs to the Special Issue Advances in Graph Theory Ⅱ)
22 pages, 5367 KiB  
Article
An Improved Bee Colony Optimization Algorithm Using a Sugeno–Takagi Interval Type-2 Fuzzy Logic System for the Optimal Design of Stable Autonomous Mobile Robot Controllers
by Leticia Amador-Angulo, Patricia Melin and Oscar Castillo
Symmetry 2025, 17(5), 789; https://doi.org/10.3390/sym17050789 - 20 May 2025
Abstract
This study proposes an enhanced Sugeno–Takagi interval type-2 fuzzy logic system (SIT2FLS) to find the best values for two important parameters in Bee Colony Optimization (BCO). The aim of this study was to develop a stable controller for a mobile robot utilizing BCO [...] Read more.
This study proposes an enhanced Sugeno–Takagi interval type-2 fuzzy logic system (SIT2FLS) to find the best values for two important parameters in Bee Colony Optimization (BCO). The aim of this study was to develop a stable controller for a mobile robot utilizing BCO in the fuzzy controller and to determine the best membership functions (MFs) in a type-1 fuzzy logic system (T1FLS) for control. Another objective was to use an SIT2FLS to find the best α and β parameters for BCO to enhance the robot trajectory, which was evaluated through an analysis of the mean squared errors. Three types of perturbations were analyzed and simulated. The performance of the SIT2FLS-FBCO was evaluated and compared to that of the T1FLS-FBCO. In addition, a comparative study was performed to demonstrate that the improved BCO works well when there are disturbances affecting the controller. Finally, it was compared with the Mamdani approach, and an FBCO with an interval type-3 FLS was also developed. Full article
(This article belongs to the Special Issue Theory and Applications on the Recent Extensions of Ordinary Fuzzy Sets)
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29 pages, 2593 KiB  
Article
Symmetry and Time-Delay-Driven Dynamics of Rumor Dissemination
by Cunlin Li, Zhuanting Ma, Lufeng Yang and Tajul Ariffin Masron
Symmetry 2025, 17(5), 788; https://doi.org/10.3390/sym17050788 - 19 May 2025
Abstract
The dissemination of rumors can lead to significant economic damage and pose a grave threat to social harmony and the stability of people’s livelihoods. Consequently, curbing the dissemination of rumors is of paramount importance. The model in the text assumes that the population [...] Read more.
The dissemination of rumors can lead to significant economic damage and pose a grave threat to social harmony and the stability of people’s livelihoods. Consequently, curbing the dissemination of rumors is of paramount importance. The model in the text assumes that the population is homogeneous in terms of transmission behavior. This homogeneity is essentially a manifestation of translational symmetry. This paper undertakes a thorough examination of the impact of time delay on the dissemination of rumors within social networking services. We have developed a model for rumor dissemination, establishing the positivity and boundedness of its solutions, and identified the existence of an equilibrium point. The study further involved determining the critical threshold of the proposed model, accompanied by a comprehensive examination of its Hopf bifurcation characteristics. In the expression of the threshold R0, the parameters appear in a symmetric form, reflecting the balance between dissemination and suppression mechanisms. Furthermore, detailed investigations were carried out to assess both the localized and global stability properties of the system’s equilibrium states. In stability analysis, the symmetry in the distribution of characteristic equation roots determines the system’s dynamic behavior. Through numerical simulations, we analyzed the potential impacts and theoretically examined the factors influencing rumor dissemination, thereby validating our theoretical analysis. An optimal control strategy was formulated, and three control variables were incorporated to describe the strategy. The optimization framework incorporates a specifically designed cost function that simultaneously accounts for infection reduction and resource allocation efficiency in control strategy implementation. The optimal control strategy proposed in the study involves a comparison between symmetric and asymmetric interventions. Symmetric control measures may prove inefficient, whereas asymmetric control demonstrates higher efficacy—highlighting a trade-off in symmetry considerations for optimization problems. Full article
(This article belongs to the Special Issue Advances in Mathematical Models and Partial Differential Equations: 2nd Edition)
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57 pages, 2571 KiB  
Review
Heavy–Heavy and Heavy–Light Mesons in Cold Nuclear Matter
by J. J. Cobos-Martínez, Guilherme N. Zeminiani and Kazuo Tsushima
Symmetry 2025, 17(5), 787; https://doi.org/10.3390/sym17050787 (registering DOI) - 19 May 2025
Abstract
We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and [...] Read more.
We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and an effective Lagrangian. As demonstrated by the cases of pionic and kaonic atoms, studies of the meson–nucleus bound state can provide us with important information on chiral symmetry in a dense nuclear medium. In this review, we examine the mesons, K,K∗,D,D∗,B,B∗,η,η′,ϕ,ηc,J/ψ,ηb,Υ, and Bc, where our emphasis is on the heavy mesons. In addition, we also present some new results for the Bc-nucleus bound states. Full article
(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)
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28 pages, 2804 KiB  
Article
Adaptive Network-Based Fuzzy Inference System Training Using Nine Different Metaheuristic Optimization Algorithms for Time-Series Analysis of Brent Oil Price and Detailed Performance Analysis
by Ebubekir Kaya, Ahmet Kaya and Ceren Baştemur Kaya
Symmetry 2025, 17(5), 786; https://doi.org/10.3390/sym17050786 - 19 May 2025
Abstract
Brent oil holds a significant position in the global energy market, as oil prices in many regions are indexed to it. Therefore, forecasting the future price of Brent oil is of great importance. In recent years, artificial intelligence techniques have been widely applied [...] Read more.
Brent oil holds a significant position in the global energy market, as oil prices in many regions are indexed to it. Therefore, forecasting the future price of Brent oil is of great importance. In recent years, artificial intelligence techniques have been widely applied in modeling and prediction tasks. In this study, an Adaptive Neuro-Fuzzy Inference System (ANFIS), a well-established AI approach, was employed for the time-series forecasting of Brent oil prices. To ensure effective learning and improve prediction accuracy, ANFIS was trained using nine different metaheuristic algorithms: Artificial Bee Colony (ABC), Selfish Herd Optimizer (SHO), Biogeography-Based Optimization (BBO), Multi-Verse Optimizer (MVO), Teaching–Learning-Based Optimization (TLBO), Cuckoo Search (CS), Moth Flame Optimization (MFO), Marine Predator Algorithm (MPA), and Flower Pollination Algorithm (FPA). Symmetric training procedures were applied across all algorithms to ensure fair and consistent evaluation. The analyses were conducted on the lowest and highest daily, weekly, and monthly Brent oil prices. Mean squared error (MSE) was used as the primary performance metric. The results showed that all algorithms achieved effective prediction performance. Among them, BBO and TLBO demonstrated superior accuracy and stability, particularly in handling the complexities of Brent oil forecasting. This study contributes to the literature by combining ANFIS and metaheuristics within a symmetric framework of experimentation and evaluation. Full article
(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry)
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25 pages, 2909 KiB  
Article
Modeling Academic Social Networks Using Covering and Matching in Intuitionistic Fuzzy Influence Graphs
by Waheed Ahmad Khan, Yusra Arooj and Hai Van Pham
Symmetry 2025, 17(5), 785; https://doi.org/10.3390/sym17050785 - 19 May 2025
Abstract
Influence graphs are essential tools for analyzing interactions and relationships in social networks. However, real-world networks often involve uncertainty due to incomplete, vague, or dynamic information. The structure of influence graphs often exhibits natural symmetries, which play a crucial role in optimizing covering [...] Read more.
Influence graphs are essential tools for analyzing interactions and relationships in social networks. However, real-world networks often involve uncertainty due to incomplete, vague, or dynamic information. The structure of influence graphs often exhibits natural symmetries, which play a crucial role in optimizing covering and matching strategies by decreasing redundancy and enhancing efficiency. Traditional influence graph models struggle to address such complexities. To address this gap, we present the novel concepts of covering and matching in intuitionistic fuzzy influence graphs (IFIGs) for modeling academic social networks. These graphs incorporate degrees of membership and non-membership to better reflect uncertainty in influence patterns. Thus, the main aim of this study is to initiate the concepts of covering and matching within the IFIG paradigm and provide its application in social networks. Initially, we establish some basic terms related to covering and matching with illustrative examples. We also investigate complete and complete bipartite IFIGs. To verify the practicality of this study, student interactions across subjects are analyzed using strong paths and strong independent sets. The proposed model is then evaluated using the TOPSIS method to rank participants based on their influence. Moreover, a comparative study is conducted to demonstrate that the proposed model not only handles uncertainty effectively but also performs better than the existing approaches. Full article
(This article belongs to the Section Mathematics)
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17 pages, 3728 KiB  
Article
Short-Term Solar Photovoltaic Power Prediction Utilizing the VMD-BKA-BP Neural Network
by Yuanquan Sun, Zhongli Wang, Jiahui Wang and Qiuhua Li
Symmetry 2025, 17(5), 784; https://doi.org/10.3390/sym17050784 - 19 May 2025
Abstract
Photovoltaic (PV) power generation is characterized by high stochasticity, symmetry in daily power generation and low predictive accuracy. Enhancing the precision of power forecasting is crucial for improving symmetrical economic operation of the power grid. Due to Back-Propagation (BP) neural network prediction, there [...] Read more.
Photovoltaic (PV) power generation is characterized by high stochasticity, symmetry in daily power generation and low predictive accuracy. Enhancing the precision of power forecasting is crucial for improving symmetrical economic operation of the power grid. Due to Back-Propagation (BP) neural network prediction, there are problems such as difficulty in choosing network structure and high data requirements. A hybrid photovoltaic power forecasting model is introduced, utilizing the black-winged kite optimization algorithm (BKA) method to optimize the number of decompositions and maximum number of iterations in variational mode decomposition (VMD), as well as the critical parameters in the BP neural network. Initially, SHAP (Shapley Additive exPlanations) analysis identifies the primary factors used to serve as inputs for the K-means++ clustering of similar days, with the dataset segmented into samples of analogous days to reduce the asymmetric stochasticity of PV generation. Subsequently, the highly correlated features and PV power across different weather scenarios are decomposed using VMD, and a BKA-BP neural network prediction model is developed for each subcomponent. Ultimately, the predicted values are reconstructed through superimposition to yield the final prediction outcomes. The simulation findings indicate that VMD-BKA-BP neural network ensemble prediction model significantly enhances the short-term prediction accuracy of photovoltaic power relative to alternative models. This prediction model can be used in the future to optimize power dispatch and improve grid stability. Full article
(This article belongs to the Special Issue Applications Based on Symmetry in Machine Learning and Data Mining)
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25 pages, 6255 KiB  
Article
Threat Intelligence Named Entity Recognition Based on Segment-Level Information Extraction and Similar Semantic Space Construction
by Long Chen, Hongli Deng, Jun Zhang, Bochuan Zheng and Rui Jiang
Symmetry 2025, 17(5), 783; https://doi.org/10.3390/sym17050783 - 19 May 2025
Abstract
Threat intelligence is crucial for the early detection of network security threats, and named entity recognition (NER) plays a critical role in this process. However, traditional NER models based on sequence tagging primarily focus on word-level information for single-token entities, which leads to [...] Read more.
Threat intelligence is crucial for the early detection of network security threats, and named entity recognition (NER) plays a critical role in this process. However, traditional NER models based on sequence tagging primarily focus on word-level information for single-token entities, which leads to the inefficient extraction of multi-token entities in intelligence texts. Moreover, traditional NER models provide only a single semantic representation of intelligence texts, meaning that polysemous entities in intelligence texts cannot be effectively classified. To address these problems, this paper proposes a novel model based on segment-level information extraction and similar semantic space construction (SSNER). First, SSNER retrains the traditional BERT model based on a threat intelligence corpus and modifies BERT’s mask mechanism to extract the segment-level word embedding so that the ability of the SSNER to recognize multi-token entities is enhanced. Second, SSNER designs a similar semantic space construction method, which obtains compound semantic representations with symmetrical properties by filtering out the set of similar words and integrating them using self-attention to generate more accurate labels for the polysemous entities. The experimental results on two datasets, DNRTI and Bridges, indicate that SSNER outperforms both baseline and related models. In particular, SSNER achieves an F1-score of 96.02% on the Bridges dataset, exceeding the previous best model by approximately 1.46%. Full article
(This article belongs to the Section Computer)
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17 pages, 1082 KiB  
Article
FedOPCS: An Optimized Poisoning Countermeasure for Non-IID Federated Learning with Privacy-Preserving Stability
by Fenhua Bai, Yinqi Zhao, Tao Shen, Kai Zeng, Xiaohui Zhang and Chi Zhang
Symmetry 2025, 17(5), 782; https://doi.org/10.3390/sym17050782 - 19 May 2025
Abstract
Federated learning (FL), as a distributed machine learning framework, enables multiple participants to jointly train models without sharing data, thereby ensuring data privacy and security. However, FL systems still struggle to escape the typical poisoning threat launched by Byzantine nodes. The current defence [...] Read more.
Federated learning (FL), as a distributed machine learning framework, enables multiple participants to jointly train models without sharing data, thereby ensuring data privacy and security. However, FL systems still struggle to escape the typical poisoning threat launched by Byzantine nodes. The current defence measures almost all rely on the anomaly detection of local gradients in a plaintext state, which not only weakens privacy protection but also allows malicious clients to upload malicious ciphertext gradients once they are encrypted, which thus easily evade existing screenings. At the same time, mainstream aggregation algorithms are generally based on the premise that “each client’s data satisfy an independent and identically distributed (IID)”, which is obviously difficult to achieve in real scenarios where large-scale terminal devices hold their own data. Symmetry in data distribution and model updates across clients is crucial for achieving robust and fair aggregation, yet non-IID data and adversarial attacks disrupt this balance. To address these challenges, we propose FedOPCS, an optimized poisoning countermeasure for non-IID FL algorithms with privacy-preserving stability by introducing three key innovations: Conditional Generative Adversarial Network (CGAN)-based data augmentation with conditional variables to simulate global distribution, a dynamic weight adjustment mechanism with homomorphic encryption, and two-stage anomaly detection combining gradient analysis and model performance evaluation. Extensive experiments on MNIST and CIFAR-10 show that, in the model poisoning and mixed poisoning environments, FedOPCS outperforms the baseline methods by 11.4% and 4.7%, respectively, while maintaining the same efficiency as FedAvg. FedOPCS therefore offers a privacy-preserving, Byzantine-robust, and communication-efficient solution for future heterogeneous FL deployments. Full article
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19 pages, 289 KiB  
Article
The Radial Symmetry and Monotonicity of Solutions of Fractional Parabolic Equations in the Unit Ball
by Xingyu Liu
Symmetry 2025, 17(5), 781; https://doi.org/10.3390/sym17050781 - 19 May 2025
Abstract
We use the method of moving planes to prove the radial symmetry and monotonicity of solutions of fractional parabolic equations in the unit ball. Since the fractional Laplacian operator is a linear operator, we investigate the maximal regularity of nonlocal parabolic fractional Laplacian [...] Read more.
We use the method of moving planes to prove the radial symmetry and monotonicity of solutions of fractional parabolic equations in the unit ball. Since the fractional Laplacian operator is a linear operator, we investigate the maximal regularity of nonlocal parabolic fractional Laplacian equations in the unit ball. The maximal regularity of nonlocal parabolic fractional Laplacian equations guarantees the existence of solutions in the unit ball. Based on these conditions, we first establish a maximum principle in a parabolic cylinder, and the principles provide a starting position to apply the method of moving planes. Then, we consider the fractional parabolic equations and derive the radial symmetry and monotonicity of solutions in the unit ball. Full article
(This article belongs to the Special Issue Symmetry and Applications of Differential Geometry to the Differential Equations of Mathematical Physics)
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31 pages, 6017 KiB  
Article
LGNet: A Symmetric Dual-Branch Lightweight Model for Remote Sensing Scene Classification Based on Lie Group Feature Extraction and Cross-Attention Mechanism
by Haoyang Zeng, Shaopu Zou, Chunlian Yao and Chengjun Xu
Symmetry 2025, 17(5), 780; https://doi.org/10.3390/sym17050780 - 18 May 2025
Viewed by 194
Abstract
Existing remote sensing scene classification (RSSC) models mainly rely on convolutional neural networks (CNNs) to extract high-level features from remote sensing images, while neglecting the importance of low-level features. To address this, we propose a novel RSSC framework, LGNet, a lightweight model with [...] Read more.
Existing remote sensing scene classification (RSSC) models mainly rely on convolutional neural networks (CNNs) to extract high-level features from remote sensing images, while neglecting the importance of low-level features. To address this, we propose a novel RSSC framework, LGNet, a lightweight model with a symmetric dual-branch architecture that combines Lie group-based feature extraction with an innovative multi-dimensional cross-attention mechanism. By utilizing the Lie group feature covariance matrix in one branch, the model captures the low-level features of the image while extracting the high-level semantic information using CNNs in the parallel branch. The dynamic fusion of these multi-scale features using the attention mechanism optimizes the classification accuracy and computational efficiency. Extensive experiments on three standard datasets (AID, UC Merced, and NWPU-RESISC45) show that LGNet outperforms current state-of-the-art models, providing superior classification performance with significantly fewer parameters. Verified on publicly available challenging datasets, LGNet achieves a classification accuracy of 96.50% with 4.71M parameters on AID. Compared with other state-of-the-art models, it has certain advantages regarding classification accuracy and parameter count. These results highlight the efficiency and effectiveness of LGNet in complex remote sensing scenarios, making it a promising solution for large-scale high-resolution remote sensing images (HRSSI) tasks. Full article
(This article belongs to the Section Computer)
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21 pages, 11005 KiB  
Article
Shape-Aware Dynamic Alignment Network for Oriented Object Detection in Aerial Images
by Linsen Zhu, Donglin Jing, Baiyu Lu, Dong Zheng, Shuaixing Ren and Zhili Chen
Symmetry 2025, 17(5), 779; https://doi.org/10.3390/sym17050779 - 17 May 2025
Viewed by 103
Abstract
The field of remote sensing target detection has experienced rapid development in recent years, demonstrating significant value in various applications. However, general detection algorithms still face many key challenges when dealing with directional target detection: firstly, conventional networks struggle to accurately represent features [...] Read more.
The field of remote sensing target detection has experienced rapid development in recent years, demonstrating significant value in various applications. However, general detection algorithms still face many key challenges when dealing with directional target detection: firstly, conventional networks struggle to accurately represent features of rotated targets, particularly in modeling the slender shape characteristics of high-aspect-ratio targets; secondly, the mismatch between the static label allocation strategy and the feature space of dynamic rotating targets leads to bias in training sample selection under extreme-aspect-ratio scenarios. To address these issues, this paper proposes a single-stage Shape-Aware Dynamic Alignment Network (SADA-Net) that collaboratively enhances detection accuracy through feature representation optimization and adaptive label matching. The network’s design philosophy demonstrates greater flexibility and complementarity than that of previous models. Specifically, a Dynamic Refined Rotated Convolution Module (DRRCM) is designed to achieve rotation-adaptive feature alignment. An Anchor-Refined Feature Alignment Module (ARFAM) is further constructed to correct feature-to-spatial misalignment. In addition, a Shape-Aware Quality Assessment (SAQA) strategy is proposed to optimize sample matching quality based on target shape information. Experiment results demonstrate that SADA-Net achieves excellent performance comparable to state-of-the-art methods on three widely used remote sensing datasets (i.e., HRSC2016, DOTA, and UCAS-AOD). Full article
(This article belongs to the Section Mathematics)
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26 pages, 6013 KiB  
Article
Dynamic Responseof Complex Defect near Anisotropic Bi-Material Interface by Incident Out-Plane Wave
by Huanan Xu, Caizhu Yang, Yonghui Wang, Guoguan Lan and Faqiang Qiu
Symmetry 2025, 17(5), 778; https://doi.org/10.3390/sym17050778 - 17 May 2025
Viewed by 93
Abstract
The Dynamic response of two cavities, an elliptical inclusion and a linear crack near anisotropic bi-material interface, was explored analytically by incident out-plane waves in the current work. Firstly, the media is divided into two half spaces (an elastic anisotropic half space with [...] Read more.
The Dynamic response of two cavities, an elliptical inclusion and a linear crack near anisotropic bi-material interface, was explored analytically by incident out-plane waves in the current work. Firstly, the media is divided into two half spaces (an elastic anisotropic half space with a circular cavity and a linear crack, and an elastic isotropic half space containing an elliptical cavity and an elliptical inclusion). With the help of the image principle, the complex function method is then used to derive the wave fields in each half space. Combined with Green’s functions approach, the relevant Green’s functions developed in the “crack creation” and “conjunction of two half spaces” procedures are derived sequentially. Subsequently, based on the “conjunction” technique, undetermined anti-plane forces are applied to the horizontal surfaces of two half spaces to maintain the continuity criteria of the interface. A series of Fredholm integral equations isobtained and then solved by utilizing the direct discrete technique. Dynamic stress concentration of two elliptical cavities and an elliptical inclusion is mainly considered graphically to discuss the interaction between two half spaces. Finally, a parametric study on the dynamic stress concentration factor (DSCF) was given to show the influence of different parameters on the interaction. Full article
(This article belongs to the Section Mathematics)
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46 pages, 846 KiB  
Article
Advancing Tensor Theories
by Pierros Ntelis
Symmetry 2025, 17(5), 777; https://doi.org/10.3390/sym17050777 - 16 May 2025
Viewed by 36
Abstract
This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that unifies diverse tensor indices, and explore its transformation [...] Read more.
This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that unifies diverse tensor indices, and explore its transformation properties. Using fractional derivatives, we provide a geometrical interpretation of these generalised tensors, revealing new insights into its structure. Additionally, we forge a deep connection between tensor and category theories, integrating sets, tensors, categories, and functors with extensions like partial differentiation and integration. This synthesis yields original constructs—setorial tensors, categorial tensors, and functorial tensors—which open uncharted pathways in mathematical analysis. Our contributions not only extend prior research but also significantly enhance tensor theory, category theory, set theory, logic, topology, algebraic geometry, foundations, and philosophy, with potential applications spanning physics, geometry, and beyond. Full article
(This article belongs to the Special Issue Advances in Topology and Algebraic Geometry)
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21 pages, 911 KiB  
Article
Competition in Bike-Sharing: Effects of Discount Incentives and Comfort Level
by Lishuang Bian, Qizhou Hu, Xiaoyu Wu, Xin Zhang and Minjia Tan
Symmetry 2025, 17(5), 776; https://doi.org/10.3390/sym17050776 - 16 May 2025
Viewed by 33
Abstract
This paper investigates the competition between two types of bike-sharing services, particularly at bus stops, subway stations, and residential areas. Two types of shared bicycle travel choice models are constructed. A shared bicycle operator attracts users by implementing discount incentives, and the comfort [...] Read more.
This paper investigates the competition between two types of bike-sharing services, particularly at bus stops, subway stations, and residential areas. Two types of shared bicycle travel choice models are constructed. A shared bicycle operator attracts users by implementing discount incentives, and the comfort levels of riding the two types of shared bicycles are different. The equilibrium fares, potential user demand, and operator profits under joint profit maximization, price competition, and potential user demand competition scenarios are derived, and the competitive results under the three scenarios are compared. The results show that, in the potential user demand competition, the difference in potential demand between the two operators is largest; in the joint profit maximization scenario involving shared bicycle operators, the difference in potential user demand is smallest. In all competitive scenarios, higher operating costs and costs in lowering comfort loss for the shared bicycle operators will increase fares; the substitution level between the two types of shared bicycles has a positive impact on potential user demand, and the higher the substitution level, the better the effect of discounts in attracting users. Full article
(This article belongs to the Section Engineering and Materials)
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22 pages, 3105 KiB  
Article
High Impedance Fault Line Detection Based on Current Traveling Wave Spectrum Symmetry Driving for New Distribution Network
by Maner Xiao, Jupeng Zeng, Zehua Zhou, Qiming Zhang, Li Deng and Feiyu Peng
Symmetry 2025, 17(5), 775; https://doi.org/10.3390/sym17050775 - 16 May 2025
Viewed by 29
Abstract
Challenges are brought to high impedance fault (HIF) line selection in traditional distribution networks by the fault signals with short windows and weak characteristics provided by new energy power sources. A new method driven by the symmetry of current traveling wave spectrum is [...] Read more.
Challenges are brought to high impedance fault (HIF) line selection in traditional distribution networks by the fault signals with short windows and weak characteristics provided by new energy power sources. A new method driven by the symmetry of current traveling wave spectrum is proposed in this paper. Frequency-domain features are extracted by using Pisarenko spectral decomposition, and the differences in amplitude, frequency, and polarity between faulted and healthy feeders are analyzed. A similarity matrix is constructed with the help of Manhattan distance, and an improved density-based spatial clustering of application with noise (DBSCAN) clustering is adopted to achieve intelligent fault line selection. Experimental results show that compared with the steady state component method and the transient component method, the accuracy of this method is increased to 97.5%, with an improvement of more than 12.5%. Quantitative thresholds are replaced by qualitative spectrum differences, and this method is not affected by weak signals, thus solving the problem of threshold setting caused by the access of new energy. The accuracy of this method under different fault types, phases, and resistances is verified by simulation, ensuring easy engineering implementation. Full article
(This article belongs to the Section Engineering and Materials)
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19 pages, 933 KiB  
Article
Revisiting the Contact Model with Diffusion Beyond the Conventional Methods
by Roberto da Silva, Eliseu Venites Filho, Henrique A. Fernandes and Paulo F. Gomes
Symmetry 2025, 17(5), 774; https://doi.org/10.3390/sym17050774 - 16 May 2025
Viewed by 17
Abstract
The contact process is a nonequilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the effects of particle mobility and diffusion on criticality have [...] Read more.
The contact process is a nonequilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the effects of particle mobility and diffusion on criticality have been preliminarily explored, they remain poorly understood in many aspects. In this work, we examine how the critical rate of the model varies with the probability of particle mobility. By analyzing different stochastic evolutions of the system, we employ two modern approaches: (1) Random Matrix Theory (RMT): By building on the success of RMT, particularly Wishart-like matrices, in studying statistical physics of systems with up-down symmetry via magnetization dynamics [R. da Silva, IJMPC 2022], we demonstrate its applicability to models with an absorbing state; (2) Optimized Temporal Power Laws: By using short-time dynamics, we optimize power laws derived from ensemble-averaged evolutions of the system. Both methods consistently reveal that the critical rate decays with mobility according to a simple Belehradek function. Additionally, a straightforward mean-field analysis supports the decay of the critical parameter with mobility, although it predicts a simpler linear dependence. We also demonstrate that the more sophisticated pair approximation mean-field model developed by ben-Avraham and Köhler aligns closely with the Belehradek function, precisely matching our lattice simulation results. Full article
(This article belongs to the Section Mathematics)
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17 pages, 8321 KiB  
Article
Flexible Piezoresistive Sensor with High Stability Based on GO@PDMS-PU Porous Structure
by Qingfang Zhang, Yi Li, Xingyu Wang, Xiaoyu Zhang, Shuyi Liu, Hengyi Yuan, Xiaodong Yang, Da Li, Zeping Jin, Yujian Zhang, Yutong Liu and Zhengmai Bian
Symmetry 2025, 17(5), 773; https://doi.org/10.3390/sym17050773 - 16 May 2025
Viewed by 17
Abstract
In recent years, flexible piezoresistive sensors based on polydimethylsiloxane (PDMS) matrix materials have developed rapidly, showing broad application prospects in fields such as human motion monitoring, electronic skin, and intelligent robotics. However, achieving a balance between structural durability and fabrication simplicity remains challenging. [...] Read more.
In recent years, flexible piezoresistive sensors based on polydimethylsiloxane (PDMS) matrix materials have developed rapidly, showing broad application prospects in fields such as human motion monitoring, electronic skin, and intelligent robotics. However, achieving a balance between structural durability and fabrication simplicity remains challenging. Traditional methods for preparing PDMS flexible substrates with high porosity and high stability often require complex, costly processes. Breaking through the constraints of conventional material systems, this study innovatively combines the high elasticity of polydimethylsiloxane (PDMS) with the stochastically distributed porous topology of a sponge-derived biotemplate through biomimetic templating replication technology, fabricating a heterogeneous composite system with an architecturally asymmetric spatial network. After 5000 loading cycles, uncoated samples experienced a thickness reduction of 7.0 mm, while PDMS-coated samples showed minimal thickness changes (2.0–3.0 mm), positively correlated with curing agent content (5:1 to 20:1). The 5:1 ratio sample demonstrated exceptional mechanical stability. As evidenced, the PDMS film-encapsulated architecturally asymmetric spatial network demonstrates superior stress dissipation efficacy, effectively mitigating stress concentration phenomena inherent to symmetric configurations that induce matrix fracture, thereby achieving optimal mechanical stability. Compared to the pre-test resistance distribution of 10–248 Ω, after 5000 cyclic loading cycles, the uncoated samples exhibited a narrowed resistance range of 10–50 Ω, while PDMS-coated samples maintained a broader resistance range (10–240 Ω) as the curing agent ratio increased (from 20:1 to 5:1), demonstrating that increasing the curing agent ratio helps maintain conductive network stability. The 5:1 ratio sample displayed the lowest resistance variation rate attenuation—only 3% after 5000 cycles (vs. 80% for uncoated samples)—and consistently minimal attenuation at all stages, validating superior electrical stability. Under 0–6 kPa pressure, the 5:1 ratio device maintained a linear sensitivity of 0.157 kPa−1, outperforming some existing works. Human motion monitoring experiments further confirmed its reliable signal output. Furthermore, the architecturally asymmetric spatial network of the device enables superior conformability to complex curvilinear geometries, leveraging its structural anisotropy to achieve seamless interfacial adaptation. By synergistically optimizing material composition and structural design, this study provides a novel technical method for developing highly durable flexible electronic devices. Full article
(This article belongs to the Section Engineering and Materials)
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36 pages, 2061 KiB  
Article
A Symmetric Dual-Drive Text Matching Model Based on Dynamically Gated Sparse Attention Feature Distillation with a Faithful Semantic Preservation Strategy
by Peng Jiang and Xiaodong Cai
Symmetry 2025, 17(5), 772; https://doi.org/10.3390/sym17050772 - 15 May 2025
Viewed by 104
Abstract
A new text matching model based on dynamic gated sparse attention feature distillation with a faithful semantic preservation strategy is proposed to address the fact that text matching models are susceptible to interference from weakly relevant information and that they find it difficult [...] Read more.
A new text matching model based on dynamic gated sparse attention feature distillation with a faithful semantic preservation strategy is proposed to address the fact that text matching models are susceptible to interference from weakly relevant information and that they find it difficult to obtain key features that are faithful to the original semantics, resulting in a decrease in accuracy. Compared to the traditional attention mechanism, with its high computational complexity and difficulty in discarding weakly relevant features, this study designs a new dynamic gated sparse attention feature distillation method based on dynamic gated sparse attention, aiming to obtain key features. Weakly relevant features are obtained through the synergy of dynamic gated sparse attention, a gradient inversion layer, a SoftMax function, and projection theorem literacy. Among these, sparse attention enhances weakly correlated feature capture through multimodal dynamic fusion with adaptive compression. Then, the projection theorem is used to identify and discard the noisy features in the hidden layer information to obtain the key features. This feature distillation strategy, in which the semantic information of the original text is decomposed into key features and noise features, forms an orthogonal decomposition symmetry in the semantic space. A new variety of faithful semantic preservation strategies is designed to make the key features faithful to the original semantic information. This strategy introduces an interval loss function and calculates the angle between the key features and the original hidden layer information with the help of cosine similarity in order to ensure that the features reflect the semantics of the original text. This can further update the iterative key features and thus improve the accuracy. The strategy builds a feature fidelity verification mechanism with a symmetric core of bidirectional considerations of semantic accuracy and correspondence to the original text. The experimental results show that the accuracies are 89.10% and 95.01% in the English datasets MRPC and Scitail, respectively; 87.8% in the Chinese dataset PAWX; and 80.32% and 80.27% in the Ant Gold dataset, respectively. Meanwhile, the accuracies in the KUAKE-QTR dataset and Macro-F1 are 70.10% and 68.08%, respectively, which are better than other methods. Full article
(This article belongs to the Section Mathematics)
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33 pages, 6054 KiB  
Article
A Novel Approach in 3D Model Reconstruction from Engineering Drawings Based on Symmetric Adjacency Matrices Using DXF Files and Genetic Algorithm
by Predrag Mitić, Vladimir Kočović, Milan Mišić, Miladin Stefanović, Aleksandar Ðorđević, Marko Pantić and Damir Projović
Symmetry 2025, 17(5), 771; https://doi.org/10.3390/sym17050771 - 15 May 2025
Viewed by 91
Abstract
The application of CAD/CAM technologies in modern production has revolutionized manufacturing processes, leading to significant improvements in precision, efficiency, and flexibility. These technologies enable the design and manufacturing of complex geometries with high accuracy, reducing errors and material waste. CAD/CAM integration streamlines workflows, [...] Read more.
The application of CAD/CAM technologies in modern production has revolutionized manufacturing processes, leading to significant improvements in precision, efficiency, and flexibility. These technologies enable the design and manufacturing of complex geometries with high accuracy, reducing errors and material waste. CAD/CAM integration streamlines workflows, enhances productivity, and facilitates rapid prototyping, accelerating the time-to-market for new products. Additionally, it supports customization and scalability in production, allowing for cost-effective small-batch and large-scale manufacturing. Without a 3D model of the product, it is not possible to use the advantages of applying advanced CAD/CAM technologies. Recognizing 3D models from engineering drawings is essential for modern production, especially for outsourcing companies in fluctuating market conditions, where the production process is organized with 2D workshop drawings on paper. This paper proposes a novel methodology for reconstructing 3D models from 2D engineering drawings, specifically those in DXF file format, leveraging a genetic algorithm. A core component of this approach is the representation of the 2D drawing as a symmetric adjacency matrix. This matrix serves as the foundational data structure for the genetic algorithm, enabling the evolutionary process to effectively optimize the 3D reconstruction. The experimental evaluation, conducted on multiple engineering drawing test cases (including both polyhedral and cylindrical geometries), demonstrated consistent convergence of the proposed GA-based method toward topologically valid and geometrically accurate 3D wireframe models. The approach achieved successful reconstruction in all cases, with fitness scores ranging from 1.1 to 112.2 depending on model complexity, and average execution times from 2 to 100 s. These results confirm the method’s robustness, scalability, and applicability in real-world CAD environments, while establishing a new direction for topology-driven 3D reconstruction using evolutionary computation. Full article
(This article belongs to the Special Issue Symmetry in Process Optimization)
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21 pages, 411 KiB  
Article
Full-Duplex Relaying Systems with Massive MIMO: Equal Gain Approach
by Meng Wang, Boying Zhao, Wenqing Li, Meng Jin and Si-Nian Jin
Symmetry 2025, 17(5), 770; https://doi.org/10.3390/sym17050770 - 15 May 2025
Viewed by 63
Abstract
In this paper, the uplink spectral efficiency performance of a massive MIMO system based on full-duplex relay communication is investigated in Rician fading channels. The relay station is equipped with a large number of antennas, while multiple source and destination nodes are located [...] Read more.
In this paper, the uplink spectral efficiency performance of a massive MIMO system based on full-duplex relay communication is investigated in Rician fading channels. The relay station is equipped with a large number of antennas, while multiple source and destination nodes are located at both ends of the transceiver. Each source and destination node is equipped with a single antenna. The relay station adopts Maximum Ratio Combining/Maximum Ratio Transmission (MRC/MRT) and Equal Gain Combining/Equal Gain Transmission (EGC/EGT) schemes to perform linear preprocessing on the received signals. Approximate expressions for uplink spectral efficiency under both MRC/MRT and EGC/EGT schemes are derived, and the effects of antenna number, signal-to-noise ratio (SNR), and loop interference on spectral efficiency are analyzed. In addition, the impact of full-duplex and half-duplex modes on system performance is compared, and a hybrid relay scheme is proposed to maximize the total spectral efficiency by dynamically switching between full-duplex and half-duplex modes based on varying levels of loop interference. Finally, a novel power allocation scheme is proposed to maximize energy efficiency under given total spectral efficiency and peak power constraints at both the relay and source nodes. The results show that the impact of loop interference can be eliminated by using a massive receive antenna array, leading to the disappearance of inter-pair interference and noise. Under these conditions, the spectral efficiency of the system can be improved up to 2N times, while the transmission power of the user and relay nodes can be reduced to 1/Nrx and 1/Ntx, respectively. Full article
(This article belongs to the Section Engineering and Materials)
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31 pages, 9659 KiB  
Article
Full-Element Analysis of Side-Channel Leakage Dataset on Symmetric Cryptographic Advanced Encryption Standard
by Weifeng Liu, Wenchang Li, Xiaodong Cao, Yihao Fu, Juping Wu, Jian Liu, Aidong Chen, Yanlong Zhang, Shuo Wang and Jing Zhou
Symmetry 2025, 17(5), 769; https://doi.org/10.3390/sym17050769 - 15 May 2025
Viewed by 76
Abstract
The application of deep learning in side-channel analysis faces critical challenges arising from dispersed public datasets—i.e., datasets collected from heterogeneous sources and platforms with varying formats, labeling schemes, and sampling settings—and insufficient sample distribution uniformity, characterized by imbalanced class distributions and long-tailed label [...] Read more.
The application of deep learning in side-channel analysis faces critical challenges arising from dispersed public datasets—i.e., datasets collected from heterogeneous sources and platforms with varying formats, labeling schemes, and sampling settings—and insufficient sample distribution uniformity, characterized by imbalanced class distributions and long-tailed label samples. This paper presents a systematic analysis of symmetric cryptographic AES side-channel leakage datasets, examining how these issues impact the performance of deep learning-based side-channel analysis (DL-SCA) models. We analyze over 10 widely used datasets, including DPA Contest and ASCAD, and highlight key inconsistencies via visualization, statistical metrics, and model performance evaluations. For instance, the DPA_v4 dataset exhibits extreme label imbalance with a long-tailed distribution, while the ASCAD datasets demonstrate missing leakage features. Experiments conducted using CNN and Transformer models show that such imbalances lead to high accuracy for a few labels (e.g., label 14 in DPA_v4) but also extremely poor accuracy (<0.5%) for others, severely degrading generalization. We propose targeted improvements through enhanced data collection protocols, training strategies, and feature alignment techniques. Our findings emphasize that constructing balanced datasets covering the full key space is vital to achieving robust and generalizable DL-SCA performance. This work contributes both empirical insights and methodological guidance for standardizing the design of side-channel datasets. Full article
(This article belongs to the Special Issue Applications Based on Symmetry and Asymmetry in Deep Learning and Artificial Intelligence Methods)
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