Symmetry

19 pages, 8611 KB

Open AccessArticle

Pixel-Level Fuzzy Rule Attention Maps for Interpretable MRI Classification

by Tae-Wan Kim and Keun-Chang Kwak

Symmetry 2025, 17(12), 2187; https://doi.org/10.3390/sym17122187 - 18 Dec 2025

Viewed by 196

Although Artificial Intelligence (AI) has achieved notable performance, particularly in medicine, the structural opacity leading to the black-box phenomenon inhibits interpretability, thus necessitating a balance (Symmetry) between performance and transparency. Specifically, in the medical domain, effective diagnosis requires that high predictive performance be [...] Read more.

Although Artificial Intelligence (AI) has achieved notable performance, particularly in medicine, the structural opacity leading to the black-box phenomenon inhibits interpretability, thus necessitating a balance (Symmetry) between performance and transparency. Specifically, in the medical domain, effective diagnosis requires that high predictive performance be symmetrically counterbalanced by sufficient trust and explainability for clinical practice. Existing visualization techniques like Grad-CAM can highlight attention regions but provide limited insight into the reasoning process and often focus on irrelevant areas. To address this limitation, we propose a Fuzzy Attention Rule (FAR) model that extends fuzzy inference to MRI (Magnetic Resonance Imaging) image classification. The FAR model applies pixel-level fuzzy membership functions and logical operations (AND, OR, AND + OR, AND × OR) to generate rule-based attention maps, enabling explainable and convolution-free feature extraction. Experiments on Kaggle’s Brain MRI and Alzheimer’s MRI datasets show that FAR achieves comparable accuracy to Resnet50 while using far fewer parameters and significantly outperforming MLP. Quantitative and qualitative analyses confirm that FAR focuses more precisely on lesion regions than Grad-CAM. These results demonstrate that fuzzy logic can enhance both the explainability and reliability of medical AI systems without compromising performance. Full article

(This article belongs to the Special Issue Applications of Symmetry/Asymmetry in Artificial Intelligence and Deep Metaheuristics)

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18 pages, 309 KB

Open AccessArticle

Finite-Region Boundedness and Stabilization of 2D Continuous-Time Roesser Models

by Mariem Ghamgui and Driss Mehdi

Symmetry 2025, 17(12), 2186; https://doi.org/10.3390/sym17122186 - 18 Dec 2025

Viewed by 172

Abstract

This paper investigates the finite-region stability (FRS) and stabilization problems for 2D continuous-time systems described by a Roesser model. We first establish a novel set of FRS and finite-region boundedness (FRB) conditions, extending the

L_{2}

-based concept on finite-time stability from 1D [...] Read more.

This paper investigates the finite-region stability (FRS) and stabilization problems for 2D continuous-time systems described by a Roesser model. We first establish a novel set of FRS and finite-region boundedness (FRB) conditions, extending the

L_{2}

-based concept on finite-time stability from 1D systems to the 2D continuous domain with a new condition based on the generalized state vector of the 2D continuous-time system in contrast with the norm-based condition found in the literature. Sufficient conditions are then derived to guarantee that the system state remains within a predefined quadratic region over a finite-time horizon. Furthermore, the framework is extended to analyze FRB under two distinct classes of external disturbances. Finally, a complete procedure for state feedback stabilization is provided, with all sufficient conditions for FRS and stabilization expressed entirely in terms of numerically tractable Linear Matrix Inequalities (LMIs) enabling controller design that ensures closed-loop finite-region performance under both disturbance classes. The effectiveness and feasibility of the proposed approach are demonstrated through numerical examples. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Control Engineering)

26 pages, 4603 KB

Open AccessReview

Machine Learning-Enabled Quantification and Interpretation of Structural Symmetry Collapse in Cementitious Materials

by Taehwi Lee and Min Ook Kim

Symmetry 2025, 17(12), 2185; https://doi.org/10.3390/sym17122185 - 18 Dec 2025

Viewed by 225

Abstract

The mechanical and durability performance of cementitious materials is fundamentally governed by the symmetry, anisotropy, and hierarchical organization of their microstructures. Conventional experimental characterization—based on imaging, spectroscopy, and physical testing—often struggles to capture these multiscale spatial patterns and their nonlinear correlations with macroscopic [...] Read more.

The mechanical and durability performance of cementitious materials is fundamentally governed by the symmetry, anisotropy, and hierarchical organization of their microstructures. Conventional experimental characterization—based on imaging, spectroscopy, and physical testing—often struggles to capture these multiscale spatial patterns and their nonlinear correlations with macroscopic performance. Recent advances in machine learning (ML) provide unprecedented opportunities to interpret structural symmetry and anisotropy through data-driven analytics, computer vision, and physics-informed models. Furthermore, we summarize cases where symmetry-informed descriptors improve performance prediction accuracy in fiber- and nano-modified composites, demonstrating that ML-based symmetry analysis can substantially complement the limitations of conventional experimental-based characterization. We confirm that image-based models such as CNN and U-Net quantify the directionality and connectivity of pores and cracks, and that physically informative neural networks (PINNs) and heterogeneous data-based models enhance physical consistency and computational efficiency compared to conventional FEM and CFD. Finally, we present the conceptual and methodological foundation for developing AI-based microstructural symmetry analysis, aiming to go beyond simple prediction and establish a conceptual foundation for AI-driven cement design based on microstructure–performance causality. Full article

(This article belongs to the Special Issue Symmetry, Asymmetry and Other Patterns in Structural Engineering with Its Application)

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21 pages, 4855 KB

Open AccessArticle

A Fair Ensemble Clustering Method

by Yanqing Li, Ruixin Feng and Caiming Zhong

Symmetry 2025, 17(12), 2184; https://doi.org/10.3390/sym17122184 - 18 Dec 2025

Viewed by 189

Abstract

Ensemble clustering has become a widely used technique for improving robustness and accuracy by combining multiple clustering results. However, traditional ensemble clustering methods often fail to provide fair treatment between groups defined by sensitive attributes. Central to many ensemble methods is the symmetric [...] Read more.

Ensemble clustering has become a widely used technique for improving robustness and accuracy by combining multiple clustering results. However, traditional ensemble clustering methods often fail to provide fair treatment between groups defined by sensitive attributes. Central to many ensemble methods is the symmetric co-association matrix, which captures pairwise similarity between data points based on their co-occurrence across base clusterings. This paper introduces a fair ensemble clustering method based on the symmetric co-association matrix. The proposed method integrates fairness constraints into the objective function of the ensemble process, using the results from base clusterings that lack fairness considerations as input. The optimization is performed iteratively, and the final clustering results are represented directly by a label matrix obtained efficiently using a coordinate descent approach. By integrating fairness into the clustering process, the method avoids the need for post-processing to achieve fair results. Comprehensive experiments on both real-world and synthetic datasets validate the effectiveness and practicality of the proposed method. Full article

(This article belongs to the Special Issue Advances in Machine Learning and Symmetry/Asymmetry)

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22 pages, 5717 KB

Open AccessArticle

Flow and Heat Transfer in Porous Media Under Non-Standard Asymmetric Boundary Conditions

by Nasser Firouzi, Joy Djuansjah and Przemysław Podulka

Symmetry 2025, 17(12), 2183; https://doi.org/10.3390/sym17122183 - 18 Dec 2025

Viewed by 252

Abstract

This study investigates natural convection in porous media under non-standard asymmetric boundary conditions, focusing on flow and heat transfer. Numerical simulations were performed to analyze flow patterns, temperature distributions, and heat transfer for varying Rayleigh numbers, porosities, and internal heat generation rates. The [...] Read more.

This study investigates natural convection in porous media under non-standard asymmetric boundary conditions, focusing on flow and heat transfer. Numerical simulations were performed to analyze flow patterns, temperature distributions, and heat transfer for varying Rayleigh numbers, porosities, and internal heat generation rates. The results indicate that increasing the Rayleigh number significantly enhances heat transfer, with Nusselt numbers ranging from 5.72 to 11.02 across all cases. Higher internal heat generation and porosity lead to more uniform temperature distributions and larger convection cells, with Nusselt numbers increasing by up to 16% compared to the base case. These findings demonstrate that non-uniform boundary conditions, such as linearly cooled sidewalls, have a significant effect on heat transfer in porous media, offering insights for improving thermal management in materials with complex boundary conditions. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in the Numerical Study of Heat Transfer and Fluid Flow)

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32 pages, 24136 KB

Open AccessArticle

A Study on the Deterioration of Atmospheric Conditions in Road Areas Based on the Equal-Pollution Model and Fluid Dynamics Simulations

by Chuan Lu, Lin Teng, Xueqi Wang, Chuanwei Du, Wenke Yan and Yan Wang

Symmetry 2025, 17(12), 2182; https://doi.org/10.3390/sym17122182 - 18 Dec 2025

Viewed by 254

Abstract

This study investigates the impact of roadside building development and vehicle exhaust emissions on atmospheric deterioration in urban highway areas. By integrating satellite-based building coverage data with an equal-pollution vehicle conversion method (based on human toxicity potential), we establish a computational fluid dynamics [...] Read more.

This study investigates the impact of roadside building development and vehicle exhaust emissions on atmospheric deterioration in urban highway areas. By integrating satellite-based building coverage data with an equal-pollution vehicle conversion method (based on human toxicity potential), we establish a computational fluid dynamics framework to simulate pollutant dispersion. Key results reveal the following: (1) Street canyon morphology, particularly its geometric symmetry, dominates diffusion patterns. Wide canyons (aspect ratio = 3.3) reduce CO accumulation by over 30% compared to deep canyons (aspect ratio = 0.3), highlighting the role of built form in regulating pollution distribution. (2) Under idealized conditions, photocatalytic pavement mitigates pollutant concentrations at human breathing height by 28.7–56.7%, demonstrating the potential of uniformly applied material solutions. These findings provide a validated theoretical basis for optimizing urban road design and evaluating environmental policies, with considerations for spatial layout and material treatment. Full article

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

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19 pages, 1657 KB

Open AccessArticle

From Mathematics to Art: Modelling the Pascal’s Triangle with Petri Nets

by David Mailland and Iwona Grobelna

Symmetry 2025, 17(12), 2181; https://doi.org/10.3390/sym17122181 - 18 Dec 2025

Viewed by 291

Abstract

Pascal’s triangle is a classical mathematical construct, historically studied for centuries, that organises binomial coefficients in a triangular array and serves as a cornerstone in combinatorics, algebra, and number theory. Herein, we propose to model it with Petri nets, a formal specification technique [...] Read more.

Pascal’s triangle is a classical mathematical construct, historically studied for centuries, that organises binomial coefficients in a triangular array and serves as a cornerstone in combinatorics, algebra, and number theory. Herein, we propose to model it with Petri nets, a formal specification technique derived from discrete event systems. A minimal Petri net is created that generates Pascal’s triangle under a simple arithmetic rule. Token counts in each place coincide with binomial coefficients, providing a direct combinatorial interpretation. Two other classical structures emerge from this model: by colouring tokens depending on their parity, the Sierpiński triangle appears; by routing tokens randomly at each branching, the binomial distribution arises, converging to a Gaussian limit as depth increases. As a result, a single Petri construction unifies three mathematical objects: Pascal’s Triangle, Sierpiński’s Triangle, and the Gaussian distribution. This connection illustrates the invaluable potential of Petri nets as unifying tools for modelling discrete mathematical structures and beyond. Full article

(This article belongs to the Special Issue Symmetry and Graph Theory, 2nd Edition)

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11 pages, 267 KB

Open AccessArticle

On the Characterization of the Unitary Cayley Graphs of the Upper Triangular Matrix Rings

by Waldemar Hołubowski, Bogdana Oliynyk and Viktoriia Solomko

Symmetry 2025, 17(12), 2180; https://doi.org/10.3390/sym17122180 - 18 Dec 2025

Viewed by 177

Abstract

There are several graphs naturally associated with rings. The unitary Cayley graph of a ring R is the graph with vertex set R, where two elements

x, y \in R

are adjacent if and only if

x - y

is a [...] Read more.

There are several graphs naturally associated with rings. The unitary Cayley graph of a ring R is the graph with vertex set R, where two elements

x, y \in R

are adjacent if and only if

x - y

is a unit of R. We show that the unitary Cayley graph

C_{T_{n} (F)}

of the ring

T_{n} (F)

of all upper triangular matrices over a finite field

F

is isomorphic to a semistrong product of a complete graph and the antipodal graph of a Hamming graph. In particular, when

| F | = 2

, the graph

C_{T_{n} (F)}

has a highly symmetric structure: it is the union of

2^{n - 1}

complete bipartite graphs. Moreover, we prove that the clique number and the chromatic number of

C_{T_{n} (F)}

are both equal to

| F |

, and we establish tight upper and lower bounds for the domination number of

C_{T_{n} (F)}

. Full article

(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)

10 pages, 232 KB

Open AccessArticle

Observing Ghost Entanglement Beyond Scattering Amplitudes in Quantum Electrodynamics

by Chiara Marletto and Vlatko Vedral

Symmetry 2025, 17(12), 2179; https://doi.org/10.3390/sym17122179 - 18 Dec 2025

Viewed by 186

Abstract

A fully local quantum account of the interactions experienced between charges requires us to use all four modes of the electromagnetic vector potential in the Lorenz gauge. However, it is frequently stated that only the two transverse modes of the vector potential are [...] Read more.

A fully local quantum account of the interactions experienced between charges requires us to use all four modes of the electromagnetic vector potential in the Lorenz gauge. However, it is frequently stated that only the two transverse modes of the vector potential are “real” in that they contain photons that can actually be detected. The photons present in the other two modes, the scalar and the longitudinal, are considered unobservable and are referred to as “virtual particles” or “ghosts”. Here we argue that this view, which is rooted in standard quantum electrodynamics, is a consequence of assuming that charges are always dressed in such modes and that naked charges do not have an independent existence. In particular, we present a thought experiment where, assuming that naked charges can be independently manipulated, one can then measure the entanglement generated between a charge and the scalar modes. This entanglement is a direct function of the number of photons present in the scalar field. Our conclusion, therefore, is that the scalar quantum variables, under this assumption, would be as “real” as the transverse ones, where reality is defined by their ability to affect the charge. A striking consequence of this is that there is a critical value of charge beyond which we cannot detect its spatial superposition by local means. Full article

(This article belongs to the Section Physics)

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14 pages, 2471 KB

Open AccessArticle

Unmanned Aerial Vehicle Logistics Distribution Path Planning Based on Improved Grey Wolf Optimization Algorithm

by Wei-Qi Feng, Yong Yang, Lin-Feng Yang, Yu-Jie Fu and Kai-Jun Xu

Symmetry 2025, 17(12), 2178; https://doi.org/10.3390/sym17122178 - 18 Dec 2025

Viewed by 207

Abstract

Aiming to solve the bottlenecks of the traditional Grey Wolf Optimizer (GWO) in UAV three-dimensional path planning—including uneven initial population distribution, slow convergence speed, and proneness to local optima—this paper proposes an improved algorithm (CPS-GWO) that integrates the Kent chaotic map with Particle [...] Read more.

Aiming to solve the bottlenecks of the traditional Grey Wolf Optimizer (GWO) in UAV three-dimensional path planning—including uneven initial population distribution, slow convergence speed, and proneness to local optima—this paper proposes an improved algorithm (CPS-GWO) that integrates the Kent chaotic map with Particle Swarm Optimization (PSO) to mitigate these limitations. To enhance the diversity of the initial population, the Kent chaotic map is employed, as ergodicity ensures the symmetric distribution of the initial population, expanding search coverage; meanwhile, a nonlinear adaptive strategy is adopted to dynamically adjust the control parameter a, enabling flexible search behaviour. Furthermore, the grey wolf position update rule is optimized by incorporating the inertia weight and social learning mechanism of PSO, which strengthens the algorithm’s ability to balance exploration and exploitation. Additionally, a multi-objective comprehensive cost function is constructed, encompassing path length, collision penalty, height constraints, and path smoothness, to fully align with the practical demands of UAV path planning. To validate the performance of CPS-GWO, a three-dimensional urban simulation environment is established on the MATLAB platform. Comparative experiments with different population sizes are conducted, with the traditional GWO as the benchmark. The results demonstrate that, compared with the original GWO, (1) the average fitness of CPS-GWO is significantly reduced by 31.30–38.53%; (2) the path length is shortened by 15.62–22.12%; (3) path smoothness is improved by 43.44–51.52%; and (4) the fitness variance is only 9.58–12.16% of that of the traditional GWO, indicating notably enhanced robustness. Consequently, the proposed CPS-GWO effectively balances global exploration and local exploitation capabilities, thereby providing a novel technical solution for efficient path planning in UAV logistics and distribution under complex urban environments, which holds important engineering application value. Full article

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18 pages, 339 KB

Open AccessArticle

On a New Extension of the t-Transformation of Probability Measures

by Abdulmajeed Albarrak, Raouf Fakhfakh and Ghadah Alomani

Symmetry 2025, 17(12), 2177; https://doi.org/10.3390/sym17122177 - 17 Dec 2025

Viewed by 312

Abstract

This paper establishes a comprehensive analytical framework for a new transformation of probability measures, denoted by

T_{(a, t)}

, which unifies the classical t- and

T_{a}

-transformations in free probability. We derive the functional equation characterizing [...] Read more.

This paper establishes a comprehensive analytical framework for a new transformation of probability measures, denoted by

T_{(a, t)}

, which unifies the classical t- and

T_{a}

-transformations in free probability. We derive the functional equation characterizing

T_{(a, t)}

through the Cauchy–Stieltjes transform and explicitly show how it specializes to known deformations when

a = 0

or

t = 1

. Within the setting of Cauchy-Stieltjes kernel families, we prove structural symmetry and invariance properties of the transformation, demonstrating in particular that both the free Meixner family and the free analog of the Letac-Mora class remain invariant under

T_{(a, t)}

. Furthermore, we obtain several new limiting theorems that uncover symmetric relationships among fundamental free distributions, including the semicircular, Marchenko–Pastur, and free binomial laws. Full article

(This article belongs to the Section Mathematics)

23 pages, 361 KB

Open AccessArticle

BiHom–Lie Brackets and the Toda Equation

by Botong Gai, Chuanzhong Li, Jiacheng Sun, Shuanhong Wang and Haoran Zhu

Symmetry 2025, 17(12), 2176; https://doi.org/10.3390/sym17122176 - 17 Dec 2025

Viewed by 287

Abstract

We introduce a BiHom-type skew-symmetric bracket on general linear Lie algebra

G L (V)

built from two commuting inner automorphisms

α = A d_{ψ}

and

β = A d_{ϕ}

, with [...] Read more.

We introduce a BiHom-type skew-symmetric bracket on general linear Lie algebra

G L (V)

built from two commuting inner automorphisms

α = A d_{ψ}

and

β = A d_{ϕ}

, with

ψ, ϕ \in G L (V)

and integers

i, j

. We prove that

(G L (V), {[\cdot, \cdot]}_{(ψ, ϕ)}^{(i, j)}, α, β)

is a BiHom–Lie algebra, and we study the Lax equation obtained by replacing the commutator in the finite nonperiodic Toda lattice by this bracket. For the symmetric choice

ϕ = ψ

with

(i, j) = (0, 0)

, the deformed flow is equivariant under conjugation and becomes gauge-equivalent, via

\tilde{L} = ψ^{- 1} L ψ

, to a Toda-type Lax equation with a conjugated triangular projection. In particular, scalar deformations amount to a constant rescaling of time. On embedded

2 \times 2

blocks, we derive explicit trigonometric and hyperbolic formulae that make symmetry constraints (e.g., tracelessness) transparent. In the asymmetric hyperbolic case, we exhibit a trace obstruction showing that the right-hand side is generically not a commutator, which amounts to symmetry breaking of the isospectral property. We further extend the construction to the weakly coupled Toda lattice with an indefinite metric and provide explicit

2 \times 2

solutions via an inverse-scattering calculation, clarifying and correcting certain formulas in the literature. The classical Toda dynamics are recovered at special parameter values. Full article

(This article belongs to the Special Issue Symmetry in Integrable Systems and Soliton Theories)

25 pages, 6176 KB

Open AccessArticle

Audiovisual Brain Activity Recognition Based on Symmetric Spatio-Temporal–Frequency Feature Association Vectors

by Yang Xi, Lu Zhang, Chenxue Wu, Bingjie Shi and Cunzhen Li

Symmetry 2025, 17(12), 2175; https://doi.org/10.3390/sym17122175 - 17 Dec 2025

Viewed by 187

Abstract

The neural mechanisms of auditory and visual processing are not only a core research focus in cognitive neuroscience but also hold critical importance for the development of brain–computer interfaces, neurological disease diagnosis, and human–computer interaction technologies. However, EEG-based studies on classifying auditory and [...] Read more.

The neural mechanisms of auditory and visual processing are not only a core research focus in cognitive neuroscience but also hold critical importance for the development of brain–computer interfaces, neurological disease diagnosis, and human–computer interaction technologies. However, EEG-based studies on classifying auditory and visual brain activities largely overlook the in-depth utilization of spatial distribution patterns and frequency-specific characteristics inherent in such activities. This paper proposes an analytical framework that constructs symmetrical spatio-temporal–frequency feature association vectors to represent brain activities by computing EEG microstates across multiple frequency bands and brain functional connectivity networks. Then we construct an Adaptive Tensor Fusion Network (ATFN) that leverages feature association vectors to recognize brain activities related to auditory, visual, and audiovisual processing. The ATFN includes a feature fusion and selection module based on differential feature enhancement, a feature encoding module enhanced with attention mechanisms, and a classifier based on a multilayer perceptron to achieve the efficient recognition of audiovisual brain activities. The feature association vectors are then processed by the Adaptive Tensor Fusion Network (ATFN) to efficiently recognize different types of audiovisual brain activities. The results show that the classification accuracy for auditory, visual, and audiovisual brain activity reaches 96.97% using the ATFN, demonstrating that the proposed symmetric spatio-temporal–frequency feature association vectors effectively characterize visual, auditory, and audiovisual brain activities. The symmetrical spatio-temporal–frequency feature association vectors establish a computable mapping that captures the intrinsic correlations among temporal, spatial, and frequency features, offering a more interpretable method to represent brain activities. The proposed ATFN provides an effective recognition framework for brain activity, with a potential application for brain–computer interfaces and neurological disease diagnosis. Full article

(This article belongs to the Special Issue Symmetry in Deep Learning Networks and Its Applications in the Real World)

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23 pages, 9243 KB

Open AccessArticle

Asymmetric Spatial–Frequency Fusion Network for Infrared and Visible Object Detection

by Jing Liu, Jing Gao, Xiaoyong Liu, Junjie Tao, Jun Ma, Chaoping Guo, Peijun Shi and Pan Li

Symmetry 2025, 17(12), 2174; https://doi.org/10.3390/sym17122174 - 17 Dec 2025

Viewed by 267

Abstract

Infrared and visible image fusion-based object detection is critical for robust environmental perception under adverse conditions, yet existing methods still suffer from insufficient modeling of modality discrepancies and limited adaptivity in their fusion mechanisms. This work proposes an asymmetric spatial–frequency fusion network, AsyFusionNet. [...] Read more.

Infrared and visible image fusion-based object detection is critical for robust environmental perception under adverse conditions, yet existing methods still suffer from insufficient modeling of modality discrepancies and limited adaptivity in their fusion mechanisms. This work proposes an asymmetric spatial–frequency fusion network, AsyFusionNet. The network adopts an asymmetric dual-branch backbone that extends the RGB branch to P5 while truncating the infrared branch at P4, thereby better aligning with the physical characteristics of the two modalities, enhancing feature complementarity, and enabling fine-grained modeling of modality differences. On top of this backbone, a local–global attention fusion (LGAF) module is introduced to model local and global attention in parallel and reorganize them through lightweight convolutions, achieving joint spatial–channel selective enhancement. Modality-specific feature enhancement is further realized via a hierarchical attention module (HAM) in the RGB branch, which employs dynamic kernel selection to emphasize multi-level texture details, and a fourier spatial spectral modulation (FS2M) module in the infrared branch, which more effectively captures global thermal radiation patterns. Extensive experiments on the

M^{3}

FD and VEDAI datasets demonstrate that AsyFusionNet attains

86.3 %

and

54.1 %

{mAP}_{50}

, respectively, surpassing the baseline by

8.8

and

6.4

points (approximately

11.4 %

and

13.4 %

relative gains) while maintaining real-time inference speed. Full article

(This article belongs to the Section Computer)

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23 pages, 2909 KB

Open AccessArticle

A Symmetry-Aware Hierarchical Graph-Mamba Network for Spatio-Temporal Road Damage Detection

by Zichun Tian, Xiaokang Shao, Yuqi Bai, Qianyun Zhang, Zhuxuanzi Wang and Yingrui Ji

Symmetry 2025, 17(12), 2173; https://doi.org/10.3390/sym17122173 - 17 Dec 2025

Viewed by 334

Abstract

The prompt and precise detection of road damage is vital for effective infrastructure management, forming the foundation for intelligent transportation systems and cost-effective pavement maintenance. While current convolutional neural network (CNN)-based methodologies have made progress, they are fundamentally limited by treating damages as [...] Read more.

The prompt and precise detection of road damage is vital for effective infrastructure management, forming the foundation for intelligent transportation systems and cost-effective pavement maintenance. While current convolutional neural network (CNN)-based methodologies have made progress, they are fundamentally limited by treating damages as independent, isolated entities, thereby ignoring the intrinsic spatial symmetry and topological organization inherent in complex damage patterns like alligator cracking. This conceptual asymmetry in modeling leads to two major deficiencies: “context blindness,” which overlooks essential structural interrelations, and “temporal inconsistency” in video analysis, resulting in unstable, flickering predictions. To address this, we propose a Spatio-Temporal Graph Mamba You-Only-Look-Once (STG-Mamba-YOLO) network, a novel architecture that introduces a symmetry-informed, hierarchical reasoning process. Our approach explicitly models and integrates contextual dependencies across three levels to restore a holistic and consistent structural representation. First, at the pixel level, a Mamba state-space model within the YOLO backbone enhances the modeling of long-range spatial dependencies, capturing the elongated symmetry of linear cracks. Second, at the object level, an intra-frame damage Graph Network enables explicit reasoning over the topological symmetry among damage candidates, effectively reducing false positives by leveraging their relational structure. Third, at the sequence level, a Temporal Graph Mamba module tracks the evolution of this damage graph, enforcing temporal symmetry across frames to ensure stable, non-flickering results in video streams. Comprehensive evaluations on multiple public benchmarks demonstrate that our method outperforms existing state-of-the-art approaches. STG-Mamba-YOLO shows significant advantages in identifying intricate damage topologies while ensuring robust temporal stability, thereby validating the effectiveness of our symmetry-guided, multi-level contextual fusion paradigm for structural health monitoring. Full article

(This article belongs to the Special Issue Applications of Symmetry/Asymmetry in Structural Dynamics and Structural Health Monitoring)

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36 pages, 1582 KB

Open AccessArticle

A Deep Random Forest Model with Symmetry Analysis for Hyperspectral Image Data Classification Based on Feature Importance

by Jie Lian, Wei Feng, Qing Wang, Yuhang Dong, Gabriel Dauphin and Jian Bai

Symmetry 2025, 17(12), 2172; https://doi.org/10.3390/sym17122172 - 17 Dec 2025

Viewed by 191

Abstract

Hyperspectral imagery (HSI), as a core data carrier in remote sensing, plays a crucial role in many fields. Still, it also faces numerous challenges, including the curse of dimensionality, noise interference, and small samples. These problems severely affect the generalization ability and classification [...] Read more.

Hyperspectral imagery (HSI), as a core data carrier in remote sensing, plays a crucial role in many fields. Still, it also faces numerous challenges, including the curse of dimensionality, noise interference, and small samples. These problems severely affect the generalization ability and classification accuracy of traditional machine learning and deep learning algorithms. Existing solutions suffer from bottlenecks such as unknown cost matrices and excessive computational overhead. And ensemble learning fails to fully exploit the deep semantic features and feature importance relationships of high-dimensional data. To address these issues, this paper proposes a dual ensemble classification framework (DRF-FI) based on feature importance analysis and a deep random forest. This method integrates feature selection and two-layer ensemble learning. First, it identifies discriminative spectral bands through feature importance quantification. Then, it constructs a balanced training subset through random oversampling. Finally, it integrates four different ensemble strategies. Experimental results on three benchmark hyperspectral datasets demonstrate that DRF-FI exhibits outstanding performance across multiple datasets, particularly excelling in handling highly imbalanced data. Compared to traditional random forests, the proposed method achieves stable improvements in both overall accuracy (OA) and average accuracy (AA). On specific datasets, OA and AA were enhanced by up to 0.84% and 1.24%, respectively. This provides an effective solution to the class imbalance problem in hyperspectral images. Full article

(This article belongs to the Section Computer)

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26 pages, 8438 KB

Open AccessArticle

LLM-WPFNet: A Dual-Modality Fusion Network for Large Language Model-Empowered Wind Power Forecasting

by Xuwen Zheng, Yongliang Luo and Yahui Shan

Symmetry 2025, 17(12), 2171; https://doi.org/10.3390/sym17122171 - 17 Dec 2025

Viewed by 328

Abstract

Wind power forecasting is critical to grid stability and renewable energy integration. However, existing deep learning methods struggle to incorporate semantic domain knowledge from textual information, exhibit limited generalization with scarce training data, and require high computational costs for extensive fine-tuning. Large language [...] Read more.

Wind power forecasting is critical to grid stability and renewable energy integration. However, existing deep learning methods struggle to incorporate semantic domain knowledge from textual information, exhibit limited generalization with scarce training data, and require high computational costs for extensive fine-tuning. Large language models (LLMs) offer a promising solution through their semantic representations, few-shot learning capabilities, and multimodal processing abilities. This paper proposes LLM-WPFNet, a dual-modality fusion framework that integrates frozen pre-trained LLMs with time-series analysis for wind power forecasting. The key insight is encoding temporal patterns as structured textual prompts to enable semantic guidance from frozen LLMs without fine-tuning. LLM-WPFNet employs two parallel encoding branches to extract complementary features from time series and textual prompts, unified through asymmetric multi-head attention fusion that enables selective semantic knowledge transfer from frozen LLM embeddings to enhance temporal representations. By maintaining the LLM frozen, our method achieves computational efficiency while leveraging robust semantic representations. Extensive experiments on four wind farm datasets (36–200 MW) across five prediction horizons (1–24 h) demonstrate that LLM-WPFNet consistently outperforms state-of-the-art baselines by 11% in MAE and RMSE. Notably, with only 10% of training data, it achieves a 17.6% improvement over the best baseline, validating its effectiveness in both standard and data-scarce scenarios. These results highlight the effectiveness and robustness of the dual-modality fusion design in predicting wind power under complex real-world conditions. Full article

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23 pages, 11512 KB

Open AccessArticle

Realizing Fuel Conservation and Safety for Emerging Mixed Traffic Flows: The Mechanism of Pulse and Glide Under Signal Coordination

by Ayinigeer Wumaierjiang, Jinjun Sun, Hongang Li, Wei Dai and Chongshuo Xu

Symmetry 2025, 17(12), 2170; https://doi.org/10.3390/sym17122170 - 17 Dec 2025

Viewed by 158

Abstract

Pulse and glide (PnG) has limited application in urban traffic flows, particularly in emerging mixed traffic flows comprising connected and automated vehicles (CAVs) and human-driven vehicles (HDVs), as well as at signalized intersections. In light of this, green wave coordination is applied to [...] Read more.

Pulse and glide (PnG) has limited application in urban traffic flows, particularly in emerging mixed traffic flows comprising connected and automated vehicles (CAVs) and human-driven vehicles (HDVs), as well as at signalized intersections. In light of this, green wave coordination is applied to the urban network of multiple signalized intersections. Under perception asymmetries, HDVs lack environmental perception capabilities, while CAVs are equipped with perception sensors of varying performance. CAVs could activate the PnG mode and set its average speed based on signal phase and safety status, enabling assessment of fuel savings and safety. The findings reveal that (i) excluding idling fuel consumption, when the traffic volume is low and market penetration rate (MPR) of CAVs exceeds 70%, CAVs could significantly reduce regional average fuel consumption by up to 8.8%. (ii) Compared to HDVs, CAVs could achieve a fuel saving rate (FSR) ranging from 7.1% to 50%. In low-traffic-volume conditions, CAVs with greater detection ranges could swiftly activate the PnG mode to achieve fuel savings, while in higher-traffic-volume conditions, more precise sensing aids effectiveness. (iii) the PnG mode could ensure safety for CAVs and HDVs, with CAVs equipped with highly precise sensing exhibiting particularly robust safety performance. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Intelligent Transportation System)

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24 pages, 3751 KB

Open AccessArticle

Machine Learning Framework for Automated Transistor-Level Analogue and Digital Circuit Synthesis

by Rajkumar Sarma, Dhiraj Kumar Singh, Moataz Kadry Nasser Sediek and Conor Ryan

Symmetry 2025, 17(12), 2169; https://doi.org/10.3390/sym17122169 - 17 Dec 2025

Viewed by 284

Abstract

Transistor-level Integrated Circuit (IC) design is fundamental to modern electronics, yet it remains one of the most expertise-intensive and time-consuming stages of chip development. As circuit complexity continues to rise, the need to automate this low-level design process has become critical to sustaining [...] Read more.

Transistor-level Integrated Circuit (IC) design is fundamental to modern electronics, yet it remains one of the most expertise-intensive and time-consuming stages of chip development. As circuit complexity continues to rise, the need to automate this low-level design process has become critical to sustaining innovation and productivity across the semiconductor industry. This study presents a fully automated methodology for transistor-level IC design using a novel framework that integrates Grammatical Evolution (GE) with Cadence SKILL code. Beyond automation, the framework explicitly examines how symmetry and asymmetry shape the evolutionary search space and resulting circuit structures. To address the time-consuming and expertise-intensive nature of conventional integrated circuit design, the framework automates the synthesis of both digital and analogue circuits without requiring prior domain knowledge. A specialised attribute grammar (AG) evolves circuit topology and sizing, with performance assessed by a multi-objective fitness function. Symmetry is analysed at three levels: (i) domain-level structural dualities (e.g., NAND/NOR mirror topologies and PMOS/NMOS exchanges), (ii) objective-level symmetries created by logic threshold settings, and (iii) representational symmetries managed through grammatical constraints that preserve valid connectivity while avoiding redundant isomorphs. Validation was carried out on universal logic gates (NAND and NOR) at multiple logic thresholds, as well as on a temperature sensor. Under stricter thresholds, the evolved logic gates display emergent duality, converging to mirror-image transistor configurations; relaxed thresholds increase symmetric plateaus and slow convergence. The evolved logic gates achieve superior performance over conventional Complementary Metal–Oxide–Semiconductor (CMOS), Transmission Gate Logic (TGL), and Gate Diffusion Input (GDI) implementations, demonstrating lower power consumption, a reduced Power–Delay Product (PDP), and fewer transistors. Similarly, the evolved temperature sensor exhibits improved sensitivity, reduced power, and Integral Nonlinearity (INL), and a smaller area compared to the conventional Proportional to Absolute Temperature (PTAT) or “gold” circuit, without requiring resistors. The analogue design further demonstrates beneficial asymmetry in device roles, breaking canonical structures to achieve higher performance. Across all case studies, the evolved designs matched or outperformed their manually designed counterparts, demonstrating that this GE-based approach provides a scalable and effective path toward fully automated, symmetry-aware integrated circuit synthesis. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Evolutionary Algorithms)

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24 pages, 1614 KB

Open AccessArticle

Platform-Targeted Technology Investment and Sales Mode Selection Considering Asymmetry of Power Structures

by Hua Zhang

Symmetry 2025, 17(12), 2168; https://doi.org/10.3390/sym17122168 - 16 Dec 2025

Viewed by 189

Abstract

In the current digital competition environment, e-commerce platforms have increased their investment in targeted advertising, improving advertising efficiency while also influencing the choice of product sales modes. This study aims to deeply explore the investment made by platforms in targeted technology and the [...] Read more.

In the current digital competition environment, e-commerce platforms have increased their investment in targeted advertising, improving advertising efficiency while also influencing the choice of product sales modes. This study aims to deeply explore the investment made by platforms in targeted technology and the impact of the choice of sales modes under the asymmetry of power structures. Based on game theory and optimization theory, we develop a decision-making model for targeted technology investments and sales mode selection. Through equilibrium analysis and numerical simulation, the results show that (1) targeted advertising leads to price increases, a reduction in advertising investment, and a decline in demand. Additionally, targeted advertising boosts the seller’s profit while negatively affecting the profit of the other party. (2) When in platform-led sales mode, if the unit advertising cost is low, the platform favors the resale mode; otherwise, it opts for the agency mode. When in manufacturer-led sales mode, regardless of the advertising mode, if the unit advertising cost is low, the manufacturer prefers the agency mode; otherwise, it selects the resale mode. (3) Under different power structures, the conditions and scope for platform-targeted technology investments were provided, and for different advertising models, suggestions were provided for the sales mode selection of the platform and the manufacturer. Full article

(This article belongs to the Section Mathematics)

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18 pages, 7001 KB

Open AccessArticle

Numerical Study of Symmetry in Tunneling-Induced Soil Arch

by Haoran Meng, Yao Li, Houxian Chen, Xuchao Du, Xingli Chen, Haoyu Zhang and Francisco López-Almansa

Symmetry 2025, 17(12), 2167; https://doi.org/10.3390/sym17122167 - 16 Dec 2025

Viewed by 217

Abstract

This paper addresses the issue of stress redistribution in surrounding soil during the construction of shallow-buried, large-section loess tunnels. Using the Luochuan Tunnel as a case study, we employ the FLAC 3D numerical simulation method to investigate the effects of advanced pipe roof [...] Read more.

This paper addresses the issue of stress redistribution in surrounding soil during the construction of shallow-buried, large-section loess tunnels. Using the Luochuan Tunnel as a case study, we employ the FLAC 3D numerical simulation method to investigate the effects of advanced pipe roof support on the stability of the surrounding soil. The results demonstrate that advanced pipe umbrella reduces the stress release amplitude at the vault by 50% compared to the unsupported condition, due to a “pre-support-load bearing mechanism”, while promoting orderly stress recovery. The “longitudinal beam effect” and “transverse arch effect” of soils effectively suppress the plastic zone area of the surrounding soil from 413.3 m² (unsupported) to 95.0 m², achieving a reduction exceeding 77%. Furthermore, the pipe umbrella support facilitates the formation of a more efficient “active soil arch”, which exhibits distinct symmetrical characteristics. The arch’s stress distribution and spatial structure both follow symmetrical patterns, significantly enhancing the self-stabilizing capacity of the surrounding soil. As a result, the height of the stress release zone at the tunnel excavation face and the surrounding soil stability areas is reduced by 45.9% and 63.3%, respectively, compared to the unsupported condition. This study also establishes a Pasternak elastic foundation beam model that accounts for the spatiotemporal effects of support, elucidating the mechanism of pipe umbrella support and providing a theoretical foundation for the design and construction risk control of shallow large-section loess tunnels. Full article

(This article belongs to the Special Issue Asymmetry and Symmetry in Infrastructure)

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18 pages, 4375 KB

Open AccessArticle

Gauge Transformation Effects of Nonlocal Potentials in the Strong-Field Approximation for Complex Molecules

by Shuning Gao, Shuang Wu, Jun Wang and Lanhai He

Symmetry 2025, 17(12), 2166; https://doi.org/10.3390/sym17122166 - 16 Dec 2025

Viewed by 187

Abstract

In ultrafast science, the strong-field approximation (SFA) provides a powerful framework to describe high-order harmonic generation (HHG) and related phenomena. Meanwhile, within the current ab initio theoretical framework, the use of nonlocal potentials in calculating multi-electron molecular wave functions is almost unavoidable. We [...] Read more.

In ultrafast science, the strong-field approximation (SFA) provides a powerful framework to describe high-order harmonic generation (HHG) and related phenomena. Meanwhile, within the current ab initio theoretical framework, the use of nonlocal potentials in calculating multi-electron molecular wave functions is almost unavoidable. We find that when such wave functions are directly applied to compute transition dipole moments for correcting SFA, it introduces a fundamental gauge transformation problem. Specifically, the nonlocal potential contributes an additional gauge-dependent phase function to the dipole operator, which directly modifies the phase of the transition dipole. As a consequence, the saddle-point equations acquire an entirely different structure compared to the standard SFA, leading to a splitting of the conventional short and long classical trajectories in HHG into multiple distinct quantum trajectories. Here, “complex molecules” refers to multi-center molecular systems whose nonlocal electronic structure leads to gauge-dependent strong-field responses. Our analysis highlights that the validity of gauge in-variation cannot be assumed universally in SFA framework. Our approach combines the molecular strong-field approximation with gauge transformation analysis, incorporating nonlocal pseudopotentials, saddle-point equations, and multi-center recombination effects. Full article

(This article belongs to the Section Physics)

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18 pages, 1082 KB

Open AccessArticle

Exploration of Time-Dependent Dispersion and Nonlinearity Management in Stabilization and Transition of Localized Structures in Nonlinear Optical Media

by Zeyneb Taibi, Houria Chaachoua Sameut, Meruyert Zhassybayeva, P. Sakthivinayagam and Nurzhan Serikbayev

Symmetry 2025, 17(12), 2165; https://doi.org/10.3390/sym17122165 - 16 Dec 2025

Viewed by 191

Abstract

In this work, we study a generalised high-order nonlinear Schrödinger equation with time-dependent coefficients, embracing a wide range of physical influences. By employing the Darboux transformation, we construct explicit breather and rogue wave solutions, illustrating how the spectral parameter governs waveform transitions. In [...] Read more.

In this work, we study a generalised high-order nonlinear Schrödinger equation with time-dependent coefficients, embracing a wide range of physical influences. By employing the Darboux transformation, we construct explicit breather and rogue wave solutions, illustrating how the spectral parameter governs waveform transitions. In these dynamics, dispersion determines stability and symmetry, nonlinearity influences the peak amplitude and width, and third-order dispersion introduces asymmetry and drift in the wave profile. We have demonstrated that stabilization, destabilization and shifting of the centre of the localization, or drifting towards the soliton in space or even temporal directions, can be possible by manoeuvring the spectral parameter relating dispersion and nonlinearity in optical fibre. Manoeuvring the spectral parameter relates the dispersion

a_{1} (t)

and nonlinearity from 100 t to 0.1 t leads to the stabilization of the soliton by a notable decrease in the amplitude for two hundred folds. The results reveal that the inclusion of higher-order term functions as a control mechanism for managing instability and localisation in nonlinear optical fibre systems, offering promising prospects for future developments in nonlinear optics. Full article

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17 pages, 2991 KB

Open AccessArticle

Simulation of Seismic Wave Attenuation and Dispersion in Fractured Medium and Analysis of Its Influencing Factors

by Zhentao Wang, Fanchang Zhang, Genyang Tang and Yanxiao He

Symmetry 2025, 17(12), 2164; https://doi.org/10.3390/sym17122164 - 16 Dec 2025

Viewed by 229

Abstract

The simulation of seismic wave attenuation and dispersion in a fractured medium and the analysis of the influencing factors have an important guiding role for fracture detection and characterization. In this paper, for the fractured medium saturated with fluid, the finite element numerical [...] Read more.

The simulation of seismic wave attenuation and dispersion in a fractured medium and the analysis of the influencing factors have an important guiding role for fracture detection and characterization. In this paper, for the fractured medium saturated with fluid, the finite element numerical simulation method of the Lamé–Navier and Navier–Stokes equations is investigated and compared with the numerical simulation method based on Biot’s equation. Biot’s method is more suitable for simulating fractured media at the mesoscopic scale, whereas for microscopic media, the Lamé–Navier and Navier–Stokes equations demonstrate distinct advantages. Meanwhile, the numerical simulation method is employed to analyze the influencing factors of connectivity of symmetrical fractures, effective compression length of seismic waves, and fluid viscosity. This analysis further elucidates the mechanisms and change characteristics of seismic wave attenuation and dispersion, providing theoretical guidance for the detection of fractures and fluids. Full article

(This article belongs to the Section Engineering and Materials)

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30 pages, 1497 KB

Open AccessArticle

A New Flexible Integrated Linear–Weibull Lifetime Model: Analytical Characterization and Real-Data Studies

by Isyaku Muhammad, Mustapha Muhammad, Zeineb Klai, Badamasi Abba and Zoalnoon Ahmed Abeid Allah Saad

Symmetry 2025, 17(12), 2163; https://doi.org/10.3390/sym17122163 - 16 Dec 2025

Viewed by 196

Abstract

In this work, we introduce a new four-parameter distribution, called the integrated linear–Weibull (ILW) model, constructed by embedding a dynamic linear component within the Weibull framework. The ILW distribution is capable of capturing a wide variety of symmetric and asymmetric density shapes and [...] Read more.

In this work, we introduce a new four-parameter distribution, called the integrated linear–Weibull (ILW) model, constructed by embedding a dynamic linear component within the Weibull framework. The ILW distribution is capable of capturing a wide variety of symmetric and asymmetric density shapes and accommodates diverse failure-rate behaviors. We derive several of its key mathematical and statistical properties, including moments, extropy, cumulative residual entropy, order statistics, and their asymptotic forms. The mean residual life function and its reciprocal relationship with the failure rate are also obtained. An algorithm for generating random samples from the ILW distribution is provided, and model identifiability is examined numerically through the Kullback–Leibler divergence. Parameter estimation is carried out via maximum likelihood, and a simulation study is conducted to assess the accuracy of the estimators; the results show improvements in estimator performance as sample size increases. Finally, three real datasets involving failure-time observations and one describing hydrological and epidemiological data are analyzed to demonstrate the practical usefulness of the ILW model. In these applications, the proposed model exhibits competitive or superior performance relative to several existing lifetime distributions based on standard model selection criteria and goodness-of-fit measures. Full article

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24 pages, 11779 KB

Open AccessArticle

Aircraft Trajectory Tracking via Geometric Prior-Guided Keypoint Detection in SMR

by Xiaoyan Wang, Jiangyan Ji, Mingmin Wu, Peng Li, Xiangli Wang, Zhaowen Tong and Zhixiang Huang

Symmetry 2025, 17(12), 2162; https://doi.org/10.3390/sym17122162 - 16 Dec 2025

Viewed by 199

Abstract

Detecting aircraft in Airport Surface Movement Radar (SMR) imagery presents a unique challenge rooted in the conflict between object symmetry and data asymmetry. While aircraft possess strong structural symmetry, their radar signatures are often sparse, incomplete, and highly asymmetric, leading to target loss [...] Read more.

Detecting aircraft in Airport Surface Movement Radar (SMR) imagery presents a unique challenge rooted in the conflict between object symmetry and data asymmetry. While aircraft possess strong structural symmetry, their radar signatures are often sparse, incomplete, and highly asymmetric, leading to target loss and position jitter in traditional detection algorithms. To overcome this, we introduce SWCR-YOLO, a keypoint detection framework designed to learn and enforce the target’s implicit structural symmetry from its imperfect radar representation. Our model reconstructs a stable aircraft pose by localizing four keypoints (nose, tail, wingtips) that define its symmetric axes. Based on YOLOv11n, SWCR-YOLO incorporates a MultiScaleStem module and wavelet transforms to effectively extract features from the sparse, asymmetric scatter points, while a Multi-Scale Convolutional Attention (MSCA) module refines salient information. Crucially, training is guided by a Geometric Regularized Keypoint Loss (GRKLoss), which introduces a symmetry-based prior by imposing angular constraints on the keypoints to ensure physically plausible pose estimations. Our symmetry-aware approach, on a real-world SMR dataset, achieves an mAP50 of 88.2% and reduces the trajectory root mean square error by 51.8% compared to MTD-CFAR pipeline methods, from 8.235 m to 3.968 m, demonstrating its effectiveness in handling asymmetric data for robust object tracking. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Image Processing and Computer Vision)

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22 pages, 50111 KB

Open AccessArticle

Kernel Adaptive Swin Transformer for Image Restoration

by Zhen Ni, Jingyu Wang, Aniruddha Bhattacharjya and Le Yan

Symmetry 2025, 17(12), 2161; https://doi.org/10.3390/sym17122161 - 15 Dec 2025

Viewed by 411

Abstract

In this modern era, attention has been devoted to blind super-resolution design, which improves image restoration performance by combining self-attention networks and explicitly introducing degradation information. This paper proposes a novel model called Kernel Adaptive Swin Transformer (KAST) to address the ill-posedness in [...] Read more.

In this modern era, attention has been devoted to blind super-resolution design, which improves image restoration performance by combining self-attention networks and explicitly introducing degradation information. This paper proposes a novel model called Kernel Adaptive Swin Transformer (KAST) to address the ill-posedness in image super-resolution and the resulting irregular difficulties in restoration, including asymmetrical degradation problems. KAST introduces four key innovations: (1) local degradation-aware modeling, (2) parallel attention-based feature fusion, (3) log-space continuous position bias, and (4) comprehensive validation on diverse datasets. The model captures degraded information in different regions of low-resolution images, effectively encodes and distinguishes these degraded features using self-attention mechanisms, and accurately restores image details. The proposed approach innovatively integrates degraded features with image features through a parallel attention fusion strategy, enhancing the network’s ability to capture pixel relationships and achieving denoising, deblurring, and high-resolution image reconstruction. Experimental results demonstrate that our model performs well on multiple datasets, effectively verifying the effectiveness of the proposed method. Full article

(This article belongs to the Section Computer)

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29 pages, 3775 KB

Open AccessArticle

Blockchain-Based Batch Authentication and Symmetric Group Key Agreement in MEC Environments

by Yun Deng, Jing Zhang, Jin Liu and Jinyong Li

Symmetry 2025, 17(12), 2160; https://doi.org/10.3390/sym17122160 - 15 Dec 2025

Viewed by 273

Abstract

To address the high computational and communication overheads and the limited edge security found in many existing batch verification methods for Mobile Edge Computing (MEC), this paper presents a blockchain-based batch authentication and symmetric group key agreement protocol. A core feature of this [...] Read more.

To address the high computational and communication overheads and the limited edge security found in many existing batch verification methods for Mobile Edge Computing (MEC), this paper presents a blockchain-based batch authentication and symmetric group key agreement protocol. A core feature of this protocol is the establishment of a shared symmetric key among all authenticated participants. This symmetry in key distribution is fundamental for enabling secure and efficient broadcast or multicast communication within the MEC group. The protocol introduces a chameleon hash function built on elliptic curves, allowing smart mobile devices (SMDs) to generate lightweight signatures. The edge server (ES) then performs efficient large-scale batch authentication using an aggregate signature technique. Considering the need for secure and independent communication between SMDs and ES, the protocol further establishes a one-to-one session key agreement mechanism and uses a Merkle tree to verify session key correctness. Formal verification with ProVerif2.05 tool confirms the protocol’s security and multiple protection properties. Experimental results show that, compared with the CPPBA, ECCAS, and LBVP schemes, the protocol improves computational efficiency of batch authentication by 0.94%, 67.20%, and 49.53%, respectively. For group key agreement, the protocol achieves a 35.26% improvement in computational efficiency over existing schemes. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Embedded Systems)

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31 pages, 7089 KB

Open AccessArticle

Performance Analysis of a MIMO System Under Realistic Conditions Using 3GPP Channel Model

by Nikolaos Mouziouras, Andreas Tsormpatzoglou and Constantinos T. Angelis

Symmetry 2025, 17(12), 2159; https://doi.org/10.3390/sym17122159 - 15 Dec 2025

Viewed by 279

Abstract

In recent years, the scientific community has increasingly focused on state-of-the-art techniques, such as MIMO and mmWave transmission, aimed at enhancing the performance of telecommunication channels both quantitatively and qualitatively through various approaches. These efforts often rely on channel models designed to more [...] Read more.

In recent years, the scientific community has increasingly focused on state-of-the-art techniques, such as MIMO and mmWave transmission, aimed at enhancing the performance of telecommunication channels both quantitatively and qualitatively through various approaches. These efforts often rely on channel models designed to more accurately represent real-world conditions, thereby ensuring that the results are objective and practically applicable. In the present study, we employ one of the most scientifically reliable system- level simulators, Vienna SLS Simulator, to evaluate the performance of a wireless channel that we configure based on the latest standards (3GPP TR 36.873). We take into account the well-known non-symmetrical behavior of mMIMOs, where m stands for microwave MIMOs, in wireless communication systems and analyze the resulting changes in key performance metrics including average cell throughput, average user spectral efficiency and signal-to-interference-plus-noise ratio (SINR). We vary specific parameters such as transmission power, antenna polarization, ratio of indoor to outdoor users, and others with the aim of validating or challenging existing scientific assumptions. Particular attention is given to studying how variations in the aforementioned factors affect channel geometry and spatial uniformity, emphasizing the role of antenna geometry, polarization and user distribution in shaping channel asymmetries in mmWave MU-MIMO systems. Overall, this study provides insights into designing more balanced and efficient wireless systems in realistic urban environments. Full article

(This article belongs to the Special Issue Exploring Symmetry in Wireless Communication)

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29 pages, 11637 KB

Open AccessArticle

Scene Heatmap-Guided Adaptive Tiling and Dual-Model Collaboration-Based Object Detection in Ultra-Wide-Area Remote Sensing Images

by Fuwen Hu, Yeda Li, Jiayu Zhao and Chunping Min

Symmetry 2025, 17(12), 2158; https://doi.org/10.3390/sym17122158 - 15 Dec 2025

Viewed by 241

Abstract

This work addresses computational inefficiency in ultra-wide-area remote sensing image (RSI) object detection. Traditional homogeneous tiling strategies enforce computational symmetry by processing all image regions uniformly, ignoring the intrinsic spatial asymmetry of target distribution where target-dense coexist with vast target-sparse areas (e.g., deserts, [...] Read more.

This work addresses computational inefficiency in ultra-wide-area remote sensing image (RSI) object detection. Traditional homogeneous tiling strategies enforce computational symmetry by processing all image regions uniformly, ignoring the intrinsic spatial asymmetry of target distribution where target-dense coexist with vast target-sparse areas (e.g., deserts, farmlands), thereby wasting computational resources. To overcome symmetry mismatch, we propose a heat-guided adaptive blocking and dual-model collaboration (HAB-DMC) framework. First, a lightweight EfficientNetV2 classifies initial 1024 × 1024 tiles into semantic scenes (e.g., airports, forests). A target-scene relevance metric converts scene probabilities into a heatmap, identifying high-attention regions (HARs, e.g., airports) and low-attention regions (LARs, e.g., forests). HARs undergo fine-grained tiling (640 × 640 with 20% overlap) to preserve small targets, while LARs use coarse tiling (1024 × 1024) to minimize processing. Crucially, a dual-model strategy deploys: (1) a high-precision LSK-RTDETR-base detector (with Large Selective Kernel backbone) for HARs to capture multi-scale features, and (2) a streamlined LSK-RTDETR-lite detector for LARs to accelerate inference. Experiments show 23.9% faster inference on 30k-pixel images and reduction in invalid computations by 72.8% (from 50% to 13.6%) versus traditional methods, while maintaining competitive mAP (74.2%). The key innovation lies in repurposing heatmaps from localization tools to dynamic computation schedulers, enabling system-level efficiency for Ultra-Wide-Area RSIs. Full article

(This article belongs to the Topic Image Processing, Signal Processing and Their Applications)

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Symmetry, Volume 17, Issue 12 (December 2025) – 174 articles

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