Symmetry

28 pages, 3528 KB

Open AccessArticle

Sustainable Urban Mobility: Leveraging Generative AI for Symmetry-Aware Traffic Light Optimization

by Pedro C. Santana-Mancilla, Antonio Guerrero-Ibáñez, Juan Contreras-Castillo, Jesús García-Mancilla and Luis Anido-Rifón

Symmetry 2025, 17(12), 2083; https://doi.org/10.3390/sym17122083 (registering DOI) - 4 Dec 2025

Abstract

Urban intersections are critical nodes where traffic congestion and energy inefficiency converge. Traditional signal control systems often optimize either mobility or sustainability, creating an asymmetry between flow efficiency and environmental impact. This study introduces a symmetry-aware generative optimization framework that leverages Generative Artificial [...] Read more.

Urban intersections are critical nodes where traffic congestion and energy inefficiency converge. Traditional signal control systems often optimize either mobility or sustainability, creating an asymmetry between flow efficiency and environmental impact. This study introduces a symmetry-aware generative optimization framework that leverages Generative Artificial Intelligence (GAI) to balance both dimensions. Using the microscopic simulator SUMO, we modeled a signalized intersection in Colima, Mexico, under five control strategies: Fixed Time (baseline), GPT-4o, GPT-5 Thinking, Gemini 2.5 Pro, and DeepSeek V3. Each Large Language Model (LLM) received structured simulation data and generated new phase-duration configurations to minimize queue length, travel time, and CO₂ emissions while improving average speed. Step-level performance was evaluated using descriptive statistics, and Wilcoxon signed-rank tests paired with Holm–Bonferroni correction. Results show that all LLM-based controllers significantly outperformed the Fixed Time baseline (adjusted p ≤ 4.8 × 10⁻⁶), with large effect sizes (|dz| ≈ 1.5–2.6). GPT-5 achieved the strongest performance, reducing queue size by ≈ 44%, CO₂ emissions by ≈ 17%, and increasing average speed by ≈ 58%. The results validate the feasibility of symmetry-aware generative reasoning for sustainable traffic optimization and establish a reproducible methodological framework applicable to future AI-driven urban mobility systems. Full article

(This article belongs to the Special Issue Symmetry-Aware Generative AI: Emerging Trends and Applications in Intelligent Transportation Systems)

26 pages, 1170 KB

Open AccessArticle

Bayesian-Optimized Learning on Heterogeneous Multipartite Graphs: A Framework for Multi-Level Relational Data

by Tuba Koç, Mehmet Ali Cengiz and Haydar Koç

Symmetry 2025, 17(12), 2082; https://doi.org/10.3390/sym17122082 (registering DOI) - 4 Dec 2025

Abstract

Real-world systems frequently exhibit hierarchical multipartite graph structures, yet existing graph neural network (GNN) approaches lack systematic frameworks for hyperparameter optimization in heterogeneous multi-level architectures, limiting their practical applicability. This study proposes a Bayesian optimization framework specifically designed for heterogeneous GNNs operating on [...] Read more.

Real-world systems frequently exhibit hierarchical multipartite graph structures, yet existing graph neural network (GNN) approaches lack systematic frameworks for hyperparameter optimization in heterogeneous multi-level architectures, limiting their practical applicability. This study proposes a Bayesian optimization framework specifically designed for heterogeneous GNNs operating on three-level graph structures, addressing the computational challenges of configuring partition-aware architecture. Four GNN architectures—Graph Convolutional Networks (GCNs), Graph Attention Networks (GATs), Graph Isomorphism Networks (GINs), and GraphSAGE—were systematically evaluated using Gaussian Process-based Bayesian hyperparameter optimization with inter-partition message-passing mechanisms. The framework was validated on the TIMSS 2023 dataset (10,000 students, 789 schools, 25 countries), demonstrating that Bayesian-optimized GraphSAGE achieved the highest explained variance (R² = 0.6187, RMSE = 71.73, MAE = 64.32) compared to seven baseline methods. Bayesian optimization substantially improved model performance, revealing that two-layer architectures optimally capture cross-partition dependencies in three-level structures. GNNExplainer was used to identify the most influential student-level features learned by the model, providing explanatory insight into how the model represents individual characteristics. The optimization framework is broadly applicable to other heterogeneous and multi-level graph settings; however, the empirical findings, such as the optimal architecture depth, are specific to hierarchical graphs with structural properties like the TIMSS topology. Full article

(This article belongs to the Section Mathematics)

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19 pages, 3283 KB

Open AccessArticle

Sculpting Chaos: Task-Specific Robotic Control with a Novel Hopfield System and False Attractors

by Faiza Zaamoune and Christos Volos

Symmetry 2025, 17(12), 2081; https://doi.org/10.3390/sym17122081 (registering DOI) - 4 Dec 2025

Abstract

This study introduces a novel robotic control paradigm, “chaos redirection,” which utilizes a single chaotic Hopfield Neural Network (HNN). We introduce “false attractors” synthetic trajectories created by applying controlled temporal shifts to the HNN’s state variables. This method allows a single chaotic source [...] Read more.

This study introduces a novel robotic control paradigm, “chaos redirection,” which utilizes a single chaotic Hopfield Neural Network (HNN). We introduce “false attractors” synthetic trajectories created by applying controlled temporal shifts to the HNN’s state variables. This method allows a single chaotic source to be sculpted into distinct, task-specific behaviors for autonomous robots. We apply this framework to three applications: area cleaning, systematic search, and security patrol. Quantitative, statistically validated analysis demonstrates the successful generation of functionally distinct behaviors, including high-frequency, confined re-visitation for security patrols; maximized exploratory efficiency for search tasks; and high-entropy, non-repetitive paths for thorough cleaning. Our findings establish this as a robust and computationally efficient framework for applications requiring unpredictable, yet structured, behavior. Full article

(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits III)

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17 pages, 270 KB

Open AccessArticle

Symmetric Structures in Mock-Lie Algebras: The Quasi-Centroid and Its Matrix Representations up to Dimension 5

by Keli Zheng, Yue Zhu, Wei Shan and Ying Guo

Symmetry 2025, 17(12), 2080; https://doi.org/10.3390/sym17122080 (registering DOI) - 4 Dec 2025

Abstract

Symmetric structures are key in non-associative algebras. A Mock-Lie algebra, defined by commutativity and the Jacobi identity, shows strong algebraic symmetry. This paper studies the quasi-centroid, which captures the symmetry of linear operators commuting with the algebra’s product. We define the quasi-centroid and [...] Read more.

Symmetric structures are key in non-associative algebras. A Mock-Lie algebra, defined by commutativity and the Jacobi identity, shows strong algebraic symmetry. This paper studies the quasi-centroid, which captures the symmetry of linear operators commuting with the algebra’s product. We define the quasi-centroid and set its condition for linear endomorphisms under the bracket operation. We classify matrix representations of quasi-centroids for all Mock-Lie algebras of dimensions 2 to 5 by computing matrices and analyzing coefficient relations. These results provide a foundation for further structural study. We also show that in each case, the centroid is strictly contained in the quasi-centroid, confirming proper containment for all these algebras. Full article

(This article belongs to the Special Issue Symmetry in Lie Groups and Lie Algebras)

23 pages, 808 KB

Open AccessArticle

Leader–Follower Consensus of Switched Multi-Agent Systems Under Distributed Event-Triggered Scheme

by Jia Zheng, Xiuling Li, Tongchao Wang, Hongying Wang and Jiaxuan Sun

Symmetry 2025, 17(12), 2079; https://doi.org/10.3390/sym17122079 - 4 Dec 2025

Abstract

This paper proposes an event-triggered distributed switching strategy, which solves the consensus problem of switching multi-agent systems. By introducing an event-triggering mechanism, the exchange signals of each agent are updated only at discrete trigger moments, thereby reducing communication and computing loads. The design [...] Read more.

This paper proposes an event-triggered distributed switching strategy, which solves the consensus problem of switching multi-agent systems. By introducing an event-triggering mechanism, the exchange signals of each agent are updated only at discrete trigger moments, thereby reducing communication and computing loads. The design of the trigger conditions takes into account the error between the follower and its neighbor states to ensure consensus is reached. By constructing multiple Lyapunov functions and using loop functions related to event triggering, the conservativeness of multiple Lyapunov function methods is relaxed. It is shown that the closed-loop system achieves exponential leader—follower consensus even when all subsystems are unstable, while strictly excluding Zeno behavior. Numerical simulations verify the effectiveness of the proposed method. Full article

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20 pages, 3401 KB

Open AccessArticle

Dynamic Optimization of Multi-Echelon Supply Chain Inventory Policies Under Disruptive Scenarios: A Deep Reinforcement Learning Approach

by Xiaonong Lu, Hongzhe Wang, Zhanglin Peng, Chen Liao and Chunyan Liu

Symmetry 2025, 17(12), 2078; https://doi.org/10.3390/sym17122078 - 4 Dec 2025

Abstract

Addressing two types of supply chain disruptions—frequent short-duration disruptions (e.g., minor natural disasters) and infrequent long-duration disruptions (e.g., geopolitical conflicts, public health crises)—while considering their impact on logistics capacity, this paper proposes a multi-echelon inventory management optimization framework based on the Proximal Policy [...] Read more.

Addressing two types of supply chain disruptions—frequent short-duration disruptions (e.g., minor natural disasters) and infrequent long-duration disruptions (e.g., geopolitical conflicts, public health crises)—while considering their impact on logistics capacity, this paper proposes a multi-echelon inventory management optimization framework based on the Proximal Policy Optimization (PPO) algorithm. Unlike traditional inventory control models with simplistic assumptions, this study integrates factors such as the frequency, duration, and impact of disruptions into the inventory optimization process. It is designed to coordinate replenishment decisions at the warehouse while reacting to local retailer states. Since retailers share the same cost parameters and demand dynamics, their decision problems are structurally symmetric, which allows us to use a shared policy across retailers and thus keep the learning model compact and scalable. Numerical experiments compare the PPO policy with classical inventory heuristics under various network sizes and disruption types. The results show that PPO consistently achieves lower total costs than the benchmarks, and its relative advantage becomes more pronounced under severe or longer disruptions. These findings suggest that modern policy-gradient methods, combined with simple forms of structural symmetry, can provide an effective and scalable tool for managing disrupted multi-echelon supply chains. Full article

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19 pages, 4544 KB

Open AccessArticle

Research on Multi-View Phase Shift and Highlight Region Treatment for Large Curved Parts Measurement

by Ronggui Song, Xiaofo Liu, Chen Luo and Yijun Zhou

Symmetry 2025, 17(12), 2077; https://doi.org/10.3390/sym17122077 - 4 Dec 2025

Abstract

For large curved parts with complex surfaces, which often exhibit both symmetry and asymmetry in their geometric features, the multi-view combined with the phase shift method and highlight regions treatment method has been proposed and applied to the online measurement system. The hardware [...] Read more.

For large curved parts with complex surfaces, which often exhibit both symmetry and asymmetry in their geometric features, the multi-view combined with the phase shift method and highlight regions treatment method has been proposed and applied to the online measurement system. The hardware components of the measuring system include a self-designed multi-vision platform and a multi-view three-dimensional measurement platform composed of rotating platform, robot and linear guide rail. The overall calibration of the system was conducted to guarantee the effectiveness of the measurement point cloud splicing of each viewing angle. And the system integrates the three-dimensional measurement technology of multi vision combined with the phase shift method and online measure system to realize full coverage and high-precision measurement of the impeller—addressing both its inherent symmetry (regular blade arrangement) and local asymmetry (irregular edge details)—and controls the relative error of the measured size and the actual size within 1%. In addition, the highlight regions treatment method has also been proposed. By adjusting the camera’s exposure time to change the light intensity of the captured images, images under different exposures and their valid pixels are obtained, thereby facilitating the synthesis of a composite image free of highlight phenomena. Experimental results demonstrate that the proposed method can achieve full-coverage measurement of the measured object and effective measurement of highlight regions. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Dynamics of Mechanical and Structural Engineering)

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19 pages, 3037 KB

Open AccessArticle

Simulation Method Improvement of Confined Concrete Box Steel Arch Supports in Soft Rock Tunnels

by Xiangxiang Wang, Shuling Huang, Xiuli Ding, Yuting Zhang, Dengxue Liu and Gang Han

Symmetry 2025, 17(12), 2076; https://doi.org/10.3390/sym17122076 - 4 Dec 2025

Abstract

The confined concrete box steel arch support—composed of box steel and core concrete with a geometrically symmetric double-chamber cross-section—is an innovative solution for effective deformation control in soft rock tunnels. To address the longstanding challenge of balancing accuracy and efficiency in numerical simulations [...] Read more.

The confined concrete box steel arch support—composed of box steel and core concrete with a geometrically symmetric double-chamber cross-section—is an innovative solution for effective deformation control in soft rock tunnels. To address the longstanding challenge of balancing accuracy and efficiency in numerical simulations of such supports, this study proposes an improved simulation method. Specifically, a compression-bending yield criterion for the steel–concrete composite structure was derived based on the plane section assumption and full-section plasticity criterion. This criterion was then embedded into a pile element via Fish programming to develop an improved pile element, enabling accurate simulation of the bending moment–axial force coupling effect. Verification results demonstrate that the derived yield criterion precisely captures the axial force–bending moment coupling behavior of the confined concrete box section. Numerical simulation data exhibit excellent consistency with the theoretical m-n curve, with the maximum deviation in yield axial force and bending moment not exceeding 10%. Compared with the solid element model, the improved pile element model shows differences of less than 6%, 13%, and 21% in key indicators of surrounding rock stress, deformation, and plastic zone, respectively—meeting engineering accuracy requirements. Notably, the mesh count of the improved model is only 5.5% of that of the solid element model, achieving over a 40-fold increase in computational efficiency. Furthermore, this study identifies section type and section size as the dominant parameters governing surrounding rock stability, providing valuable insights for the design and numerical simulation optimization of soft-rock tunnel support systems. Full article

(This article belongs to the Special Issue Geotechnical and Geological Engineering with Emphasis on Symmetry: Methods, Theories, and Applications)

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14 pages, 313 KB

Open AccessArticle

On Self-Approximation of the Riemann Zeta Function in Short Intervals

by Aidas Balčiūnas, Antanas Laurinčikas and Darius Šiaučiūnas

Symmetry 2025, 17(12), 2075; https://doi.org/10.3390/sym17122075 - 3 Dec 2025

Abstract

The Riemann hypothesis (RH) says that all zeros of the Riemann zeta function

ζ (s)

,

s = σ + i t

, in the strip

{s \in C : 0 < σ < 1}

lie on the line [...] Read more.

The Riemann hypothesis (RH) says that all zeros of the Riemann zeta function

ζ (s)

,

s = σ + i t

, in the strip

{s \in C : 0 < σ < 1}

lie on the line

σ = 1 / 2

. There are many equivalents of RH in various terms. In this paper, we propose equivalents of RH in terms of self-approximation, i.e., of the approximation of

ζ (s)

by

ζ (s + i τ)

,

τ \in R

, in the interval

τ \in [T, T + U]

with

T^{η} ⩽ U ⩽ T

,

η = 1273 / 4033

. We show that the RH is equivalent to the positivity of lower density and (with some exception for the accuracy of approximation) the density of the set of approximating shifts

ζ (s + i τ)

. For the proof, a probabilistic approach and mean square estimates for

ζ (s)

in short intervals are applied. Full article

(This article belongs to the Section Mathematics)

43 pages, 3902 KB

Open AccessArticle

Uncovering Symmetric and Asymmetric Deterioration Patterns in Maryland’s Steel Bridges Through Time-Series Clustering and Principal Component Analysis

by Soroush Piri, Zeinab Bandpey, Mehdi Shokouhian and Ruel Sabellano

Symmetry 2025, 17(12), 2074; https://doi.org/10.3390/sym17122074 - 3 Dec 2025

Abstract

This study analyzes long-term deterioration patterns in 1378 Maryland steel bridges using annual Bridge Health Index (BHI) records from 1995–2021. Missing observations were addressed through linear interpolation combined with forward/backward filling, after which feature-wise z-score standardization was applied to ensure comparability across annual [...] Read more.

This study analyzes long-term deterioration patterns in 1378 Maryland steel bridges using annual Bridge Health Index (BHI) records from 1995–2021. Missing observations were addressed through linear interpolation combined with forward/backward filling, after which feature-wise z-score standardization was applied to ensure comparability across annual trajectories. Euclidean K-means clustering (k-means++ initialization, 10 restarts) was implemented to identify deterioration archetypes, with K = 6 selected using the elbow method and the silhouette coefficient. Cluster-internal stability was evaluated using bridge-level Root Mean Squared Error (RMSE), and uncertainty in median deterioration profiles was quantified using 2000-iteration percentile-based bootstrap confidence intervals. To interpret structural and contextual drivers within each group, Principal Component Analysis (PCA) was performed on screened and standardized geometric, structural, and traffic-related attributes. Results revealed strong imbalance in cluster membership (757, 503, 35, 33, 44, and 6 bridges), reflecting substantial diversity in long-term BHI behavior. Cluster-median RMSE values ranged from 2.69 to 22.66, while wide confidence bands in smaller clusters highlighted elevated uncertainty due to limited sample size. PCA indicated that span length, deck width, truck percentage, and projected future ADT were the most influential differentiators of deteriorating clusters, while stable clusters were distinguished by consistently high BHI component values and limited geometric complexity. Missing rehabilitation records prevented definitive attribution of U-shaped or recovering trajectories to specific intervention events. Overall, this study establishes a scalable, statistically supported framework for deterioration-trajectory profiling and provides actionable insight for proactive inspection scheduling, rehabilitation prioritization, and long-term asset management planning for state-level bridge networks. Full article

(This article belongs to the Special Issue Application of Symmetry in Civil Infrastructure Asset Management)

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21 pages, 439 KB

Open AccessArticle

Learning Student Knowledge States from Multi-View Question–Skill Networks

by Jiawei Li, Dan Xiang, Chunlin Li, Shun Mao, Yuhuan Chen, Miao Sun, Wei He, Yuanfei Deng and Chengli Sun

Symmetry 2025, 17(12), 2073; https://doi.org/10.3390/sym17122073 - 3 Dec 2025

Abstract

Accurately modeling students’ evolving knowledge states is a core challenge in intelligent education systems. Existing knowledge tracing methods often rely on single-view representations, limiting their ability to capture high-order dependencies among questions and underlying skills. In this paper, we propose a Multi-View Question–Skill [...] Read more.

Accurately modeling students’ evolving knowledge states is a core challenge in intelligent education systems. Existing knowledge tracing methods often rely on single-view representations, limiting their ability to capture high-order dependencies among questions and underlying skills. In this paper, we propose a Multi-View Question–Skill Network (MVQSN), which constructs complementary relational views from readily available data to model student knowledge states comprehensively. Specifically, we first build a question–skill bipartite graph capturing direct question–skill associations, a skill complementarity view where edges represent synergistic relationships between skills derived from co-occurrence patterns, and a question co-response view that captures hierarchical question–question associations emerging from the hierarchical patterns of aggregated student responses. Each view is independently encoded using graph neural networks, producing view-specific student knowledge embeddings. To enhance representation consistency across views while preserving unique view information, we employ a multi-view contrastive learning module that aligns embeddings from different views. The aligned embeddings are then fused through an attention-guided mechanism, generating a unified and expressive student knowledge state representation. Finally, the unified embeddings are fed into a prediction layer to estimate students’ future performance. We conduct extensive experiments on three publicly available datasets, demonstrating that MVQSN significantly outperforms state-of-the-art baselines in prediction performance. Full article

(This article belongs to the Section Computer)

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15 pages, 319 KB

Open AccessArticle

Irreducible Generalized Restricted Representations of

g (∆_{2})

by Sherali S. Ibraev, Larissa Kainbayeva, Gulzat M. Yensebayeva, Anar A. Ibrayeva, Manat Z. Parmenova, Gulnur K. Yeshmurat and Nabat A. Abuova

Symmetry 2025, 17(12), 2072; https://doi.org/10.3390/sym17122072 - 3 Dec 2025

Abstract

Generalized restricted representations were introduced to facilitate the study of representations of modular Lie algebras that lack a restricted structure. At present, generalized restricted representations are defined for Lie algebras of the Cartan type and for contragredient Lie algebras over fields of positive [...] Read more.

Generalized restricted representations were introduced to facilitate the study of representations of modular Lie algebras that lack a restricted structure. At present, generalized restricted representations are defined for Lie algebras of the Cartan type and for contragredient Lie algebras over fields of positive characteristic. Classifications of irreducible generalized restricted representations have been obtained for both classes of Lie algebras. However, irreducible generalized restricted representations with non-restricted highest weights, as well as their dimensions, remain largely unexplored. For contragredient Lie algebras, the dimensions of such representations are known only in the case of a three-dimensional simple algebra over a field of characteristic 2. In this paper, we study irreducible generalized restricted representations of the ten-dimensional simple contragredient Lie algebra

g (∆_{2})

with a Cartan matrix of

∆_{2} = (\begin{matrix} 0 & 1 \\ 1 & 1 \end{matrix})

over an algebraically closed field of characteristic

p = 2 .

We provide a complete classification of the irreducible generalized restricted

g (∆_{2})

modules and their dimensions (Theorem 1). These modules are parameterized by the fundamental weights

ω_{1}

and

ω_{2}

and by elements of the finite field

F_{2^{s}}

. Full article

(This article belongs to the Special Issue Symmetries in Algebraic Combinatorics and Their Applications)

25 pages, 5477 KB

Open AccessArticle

Three-Dimensional UAV Trajectory Planning Based on Improved Sparrow Search Algorithm

by Yong Yang, Li Sun, Yujie Fu, Weiqi Feng and Kaijun Xu

Symmetry 2025, 17(12), 2071; https://doi.org/10.3390/sym17122071 - 3 Dec 2025

Abstract

Whether an unmanned aerial vehicle (UAV) can complete its mission successfully is determined by trajectory planning. Reasonable and efficient UAV trajectory planning in 3D environments is a complex global optimization problem, in which numerous constraints need to be considered carefully, including mountainous terrain, [...] Read more.

Whether an unmanned aerial vehicle (UAV) can complete its mission successfully is determined by trajectory planning. Reasonable and efficient UAV trajectory planning in 3D environments is a complex global optimization problem, in which numerous constraints need to be considered carefully, including mountainous terrain, obstacles, no-fly zones, safety altitude, smoothness, flight distance, and so on. Generally speaking, symmetry characteristics from the starting point to the endpoint can be concluded from the potential spatial multiple trajectories. Aiming at the deficiencies of the Sparrow Search Algorithm (SSA) in 3D symmetric trajectory planning such as population diversity and local optimization, the sine–cosine function and the Lévy flight strategy are combined, and the Improved Sparrow Search Algorithm (ISSA) is proposed, which can find a better solution in a shorter time by dynamically adjusting the search step size and increasing the occasional large step jumps so as to increase the symmetry balance of the global search and the local development. In order to verify the effectiveness of the improved algorithm, ISSA is simulated and compared with the Sparrow Search Algorithm (SSA), Particle Swarm Algorithm (PSO), Gray Wolf Algorithm (GWO) and Whale Optimization Algorithm (WOA) in the same environment. The results show that the ISSA algorithm outperforms the comparison algorithms in key indexes such as convergence speed, path cost, obstacle avoidance safety, and path smoothness, and can meet the requirement of obtaining a higher-quality flight path in a shorter number of iterations. Full article

(This article belongs to the Section Computer)

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26 pages, 5797 KB

Open AccessArticle

ASGT-Net: A Multi-Modal Semantic Segmentation Network with Symmetric Feature Fusion and Adaptive Sparse Gating

by Wendie Yue, Kai Chang, Xinyu Liu, Kaijun Tan and Wenqian Chen

Symmetry 2025, 17(12), 2070; https://doi.org/10.3390/sym17122070 - 3 Dec 2025

Abstract

In the field of remote sensing, accurate semantic segmentation is crucial for applications such as environmental monitoring and urban planning. Effective fusion of multi-modal data is a key factor in improving land cover classification accuracy. To address the limitations of existing methods, such [...] Read more.

In the field of remote sensing, accurate semantic segmentation is crucial for applications such as environmental monitoring and urban planning. Effective fusion of multi-modal data is a key factor in improving land cover classification accuracy. To address the limitations of existing methods, such as inadequate feature fusion, noise interference, and insufficient modeling of long-range dependencies, this paper proposes ASGT-Net, an enhanced multi-modal fusion network. The network adopts an encoder-decoder architecture, with the encoder featuring a symmetric dual-branch structure based on a ResNet50 backbone and a hierarchical feature extraction framework. At each layer, Adaptive Weighted Fusion (AWF) modules are introduced to dynamically adjust the feature contributions from different modalities. Additionally, this paper innovatively introduces an alternating mechanism of Learnable Sparse Attention (LSA) and Adaptive Gating Fusion (AGF): LSA selectively activates salient features to capture critical spatial contextual information, while AGF adaptively gates multi-modal data flows to suppress common conflicting noise. These mechanisms work synergistically to significantly enhance feature integration, improve multi-scale representation, and reduce computational redundancy. Experiments on the ISPRS benchmark datasets (Vaihingen and Potsdam) demonstrate that ASGT-Net outperforms current mainstream multi-modal fusion techniques in both accuracy and efficiency. Full article

(This article belongs to the Section Computer)

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19 pages, 25779 KB

Open AccessArticle

UAVEdit-NeRFDiff: Controllable Region Editing for Large-Scale UAV Scenes Using Neural Radiance Fields and Diffusion Models

by Chenghong Ye, Xueyun Chen, Zhihong Chen, Zhenyu Sun, Shaojie Wu and Wenqin Deng

Symmetry 2025, 17(12), 2069; https://doi.org/10.3390/sym17122069 - 3 Dec 2025

Abstract

The integration of Neural Radiance Field (NeRF)-based 3D reconstruction with text-guided diffusion models enables flexible editing of real-world scenes. However, for large-scale UAV-captured scenes, existing methods struggle to achieve strong semantic consistency (e.g., in local editing) and suffer from cross-view inconsistency, primarily due [...] Read more.

The integration of Neural Radiance Field (NeRF)-based 3D reconstruction with text-guided diffusion models enables flexible editing of real-world scenes. However, for large-scale UAV-captured scenes, existing methods struggle to achieve strong semantic consistency (e.g., in local editing) and suffer from cross-view inconsistency, primarily due to the globally free generative behavior and the lack of scene continuity constraints in diffusion models. To address these issues, we propose the UAVEdit-NeRFDiff framework, which ensures the maintenance of overall symmetry by restricting the editing operations to the target region. First, we leverage both visual priors and semantic masks to achieve semantically consistent editing for key views, and then design Optimal Editing Propagation (OEP) and Progressive Inheritance Propagation (PIP) methods to achieve cross-view geometric consistency propagation for Single-View-Dependent Regions (SVDRs) and Multi-View-Dependent Regions (MVDRs). Finally, experiments on diverse editing tasks demonstrate our method’s superiority in semantic alignment, cross-view consistency, and visual fidelity on UAV scenes, with promising applications in weather and disaster scenario simulations. On the proposed TDB metric, our approach delivers more than 50% improvement over prior methods. To the best of our knowledge, this is the first text–visual bimodal-guided diffusion editing framework for NeRF-reconstructed UAV-captured scenes, offering a practical and effective route for related research. Full article

(This article belongs to the Section Engineering and Materials)

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30 pages, 11175 KB

Open AccessArticle

Urban High-Rise Building Asymmetric Settlement Induced by Subsurface Geological Anomalies: A Case Analysis of Mechanisms and Mitigation Strategies

by Xuedong Cui

Symmetry 2025, 17(12), 2068; https://doi.org/10.3390/sym17122068 - 3 Dec 2025

Abstract

Urban geological complexities induce asymmetric differential settlement of high-rise buildings, threatening structural stability and necessitating sustainable remediation. This study combines field monitoring with geotechnical simulations to diagnose karst void-induced foundation failures in the Zhongyi Park Wangfu Community (Guizhou karst urban area), proposing a [...] Read more.

Urban geological complexities induce asymmetric differential settlement of high-rise buildings, threatening structural stability and necessitating sustainable remediation. This study combines field monitoring with geotechnical simulations to diagnose karst void-induced foundation failures in the Zhongyi Park Wangfu Community (Guizhou karst urban area), proposing a low-carbon grouting strategy for subsurface spatial reinforcement. Key findings include the following: (1) Field monitoring identified significant asymmetric settlement and lateral displacement of the structure, primarily caused by the presence of voids in the strata and piles not founded on bedrock. (2) Theoretical modeling reveals that geotechnical properties of soil at the pile tip and along the pile shaft are the most critical factors controlling settlement magnitude, with larger cavity heights further intensifying the asymmetric deformation. (3) A novel grouting lifting strategy was implemented, involving layered reinforcement of weak soil above the pile end and grout-based compaction to generate controlled uplift force, targeting the mitigation of asymmetric settlement. (4) Post-intervention monitoring confirmed the strategy’s effectiveness, achieving a final deviation of only 2 cm in compliance with national standards (with asymmetric characteristics effectively controlled), while utilizing environmentally sustainable materials. Full article

(This article belongs to the Section Engineering and Materials)

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23 pages, 10451 KB

Open AccessArticle

Two-Degree-of-Freedom Digital RST Controller Synthesis for Robust String-Stable Vehicle Platoons

by Ali Maarouf, Irfan Ahmad and Yasser Bin Salamah

Symmetry 2025, 17(12), 2067; https://doi.org/10.3390/sym17122067 - 3 Dec 2025

Abstract

Cooperative and Autonomous Vehicle (CAV) platoons offer significant potential for improving road safety, traffic efficiency, and energy consumption, but maintaining precise inter-vehicle spacing and synchronized velocity under disturbances while ensuring string stability remains challenging. This paper presents a fully decentralized two-layer architecture for [...] Read more.

Cooperative and Autonomous Vehicle (CAV) platoons offer significant potential for improving road safety, traffic efficiency, and energy consumption, but maintaining precise inter-vehicle spacing and synchronized velocity under disturbances while ensuring string stability remains challenging. This paper presents a fully decentralized two-layer architecture for homogeneous platoons whose identical vehicle dynamics and information flow produce an inherent symmetrical system structure. Operating under a predecessor-following topology with a constant time headway policy, the upper layer generates a smooth velocity reference based on local spacing and relative-velocity errors, while the lower layer employs a two-degree-of-freedom (2-DOF) digital RST controller designed through discrete-time pole placement and sensitivity-function shaping. The 2-DOF structure enables independent tuning of tracking and disturbance-rejection dynamics and provides a computationally lightweight solution suitable for embedded automotive platforms. The paper develops a stability analysis demonstrating internal stability and

L_{2}

string stability within this symmetrical closed-loop architecture. Simulations confirm string-stable behavior with attenuated spacing and velocity errors across the platoon during aggressive leader maneuvers and under input disturbances. The proposed method yields smooth control effort, fast transient recovery, and accurate spacing regulation, offering a robust and scalable control strategy for real-time longitudinal motion control in connected and automated vehicle platoons. Full article

(This article belongs to the Section Engineering and Materials)

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16 pages, 318 KB

Open AccessArticle

Efficient Traceable Oblivious Transfer Schemes with Aceess Control

by Weiwei Liu, Yankang Zhang, Kunhao Yang and Binghao Fu

Symmetry 2025, 17(12), 2066; https://doi.org/10.3390/sym17122066 - 3 Dec 2025

Abstract

In light of the rapid advancement of information technology, data privacy and security have emerged as critical societal concerns. There is an urgent need for the effective implementation of data access control and traceability mechanisms regarding the management of sensitive information.To address this [...] Read more.

In light of the rapid advancement of information technology, data privacy and security have emerged as critical societal concerns. There is an urgent need for the effective implementation of data access control and traceability mechanisms regarding the management of sensitive information.To address this issue, this paper presents an efficient traceable Oblivious Transfer with Access Control (AC-TOT) scheme that integrates traceability and access control mechanisms, with its core design rooted in cryptographic symmetry principles—specifically leveraging the symmetric properties of bilinear pairings to achieve consistent bidirectional verification of security parameters between protocol participants. Our scheme could ensure that only authorized users can access services from the server in a privacy-preserving manner, with the server being aware solely of the number of accessible services while remaining oblivious to their specific content. Furthermore, the scheme permits recipients to access services without undergoing identity verification, thereby mitigating the risk of personal information disclosure. The security analysis demonstrates that the proposed scheme effectively prevents user abuse and enables the sender to trace improper behaviors. Full article

(This article belongs to the Section Mathematics)

19 pages, 4029 KB

Open AccessArticle

Hyperspectral Image Compression Method Based on Spatio-Spectral Joint Feature Extraction and Attention Mechanism

by Yan Zhang and Huachao Xiao

Symmetry 2025, 17(12), 2065; https://doi.org/10.3390/sym17122065 - 3 Dec 2025

Abstract

Traditional hyperspectral image compression methods often struggle to achieve high compression ratios while maintaining satisfactory reconstructed image quality under low-bitrate conditions. With the progressive development of deep learning, it has demonstrated significant advantages in lossy image compression research. Compared to visible light images, [...] Read more.

Traditional hyperspectral image compression methods often struggle to achieve high compression ratios while maintaining satisfactory reconstructed image quality under low-bitrate conditions. With the progressive development of deep learning, it has demonstrated significant advantages in lossy image compression research. Compared to visible light images, hyperspectral images possess rich spectral information. When directly applying visible light image compression models to hyperspectral image compression, the spectral information of hyperspectral images is overlooked, making it difficult to achieve optimal compression performance. In this paper, we combine the characteristics of hyperspectral images by extracting spatial and spectral features and performing fusion-based encoding and decoding to achieve end-to-end lossy compression of hyperspectral images. The structures of the encoding end and the decoding end are in symmetry. Additionally, attention mechanism is incorporated to enhance reconstruction quality. The proposed model is compared with the latest hyperspectral image compression standard algorithms to validate its effectiveness. Experimental results show that, under the same image quality, the proposed method reduces the bpp (bits per pixel) by 4.67% compared to CCSDS123.0-B-2 on the Harvard hyperspectral dataset while also decreasing the spectral angle loss by 13.68%, achieving better performance. Full article

(This article belongs to the Special Issue Symmetry and Its Applications in Computer Vision)

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