Symmetry

16 pages, 18584 KB

Open AccessArticle

A Framework for Nuclei and Overlapping Cytoplasm Segmentation with MaskDino and Hausdorff Distance

by Baocan Zhang, Xiaolu Jiang, Wei Zhao and Shixiao Xiao

Symmetry 2026, 18(2), 218; https://doi.org/10.3390/sym18020218 - 23 Jan 2026

Accurate segmentation of nuclei and cytoplasm in cervical cytology images plays a pivotal role in characterizing cellular morphology. The primary challenge is to precisely delineate boundaries within densely clustered cells, which is complicated by low-contrast edges and irregular morphologies. This paper introduces a [...] Read more.

Accurate segmentation of nuclei and cytoplasm in cervical cytology images plays a pivotal role in characterizing cellular morphology. The primary challenge is to precisely delineate boundaries within densely clustered cells, which is complicated by low-contrast edges and irregular morphologies. This paper introduces a novel framework combining MaskDino architecture with Hausdorff distance loss, enhanced by a two-phase training strategy. The method begins by employing MaskDino for precise nucleus segmentation. Building on this foundation, the framework then enhances cytoplasmic boundary detection in cellular clusters by incorporating a Hausdorff distance loss, with weight transfer initialization ensuring feature consistency across tasks.. The symmetry between the nucleus and cytoplasm servers as a key morphological indicator for cell assessment, and our method provides a reliable basis for such analysis. Extensive experiments demonstrate that our method achieves state-of-the-art cytoplasm segmentation results on the ISBI2014 dataset, with absolute improvements of 2.9% in DSC, 1.6% in TPRp and 2.0% in FNRo. The performance of nucleus segmentation is better than the average level. These results validate the proposed framework’s effectiveness for improving cervical cancer screening through robust cellular segmentation. Full article

(This article belongs to the Section Computer)

16 pages, 356 KB

Open AccessArticle

Delay Differential Equations with a Damping Term: Enhanced Criteria for Testing the Oscillatory Performance of Solutions

by Asma Al-Jaser, Osama Moaaz and Amira Essam

Symmetry 2026, 18(2), 217; https://doi.org/10.3390/sym18020217 - 23 Jan 2026

Abstract

The oscillatory characteristics of solutions to damped differential equations are examined in this study. Enhanced properties are obtained for positive solutions of the equation under examination. These properties are then utilized to derive criteria ensuring the oscillation of all solutions of the equation, [...] Read more.

The oscillatory characteristics of solutions to damped differential equations are examined in this study. Enhanced properties are obtained for positive solutions of the equation under examination. These properties are then utilized to derive criteria ensuring the oscillation of all solutions of the equation, based on the symmetry principle between positive and negative solutions. Several techniques are employed to establish oscillation criteria that encompass a broader range of cases of the equation under investigation. Through the new approach adopted in this study, criteria are obtained that refine and complement the related previous results. The findings are applied to Euler-type equations and are juxtaposed with prior results to illustrate their significance. Full article

(This article belongs to the Section Mathematics)

20 pages, 1369 KB

Open AccessArticle

Symmetry-Aware Interpretable Anomaly Alarm Optimization Method for Power Monitoring Systems Based on Hierarchical Attention Deep Reinforcement Learning

by Zepeng Hou, Qiang Fu, Weixun Li, Yao Wang, Zhengkun Dong, Xianlin Ye, Xiaoyu Chen and Fangyu Zhang

Symmetry 2026, 18(2), 216; https://doi.org/10.3390/sym18020216 - 23 Jan 2026

Abstract

With the rapid advancement of smart grids driven by renewable energy integration and the extensive deployment of supervisory control and data acquisition (SCADA) and phasor measurement units (PMUs), addressing the escalating alarm flooding via intelligent analysis of large-scale alarm data is pivotal to [...] Read more.

With the rapid advancement of smart grids driven by renewable energy integration and the extensive deployment of supervisory control and data acquisition (SCADA) and phasor measurement units (PMUs), addressing the escalating alarm flooding via intelligent analysis of large-scale alarm data is pivotal to safeguarding the safe and stable operation of power grids. To tackle these challenges, this study introduces a pioneering alarm optimization framework based on symmetry-driven crowdsourced active learning and interpretable deep reinforcement learning (DRL). Firstly, an anomaly alarm annotation method integrating differentiated crowdsourcing and active learning is proposed to mitigate the inherent asymmetry in data distribution. Secondly, a symmetrically structured DRL-based hierarchical attention deep Q-network is designed with a dual-path encoder to balance the processing of multi-scale alarm features. Finally, a SHAP-driven interpretability framework is established, providing global and local attribution to enhance decision transparency. Experimental results on a real-world power alarm dataset demonstrate that the proposed method achieves a Fleiss’ Kappa of 0.82 in annotation consistency and an F1-Score of 0.95 in detection performance, significantly outperforming state-of-the-art baselines. Additionally, the false positive rate is reduced to 0.04, verifying the framework’s effectiveness in suppressing alarm flooding while maintaining high recall. Full article

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

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33 pages, 5323 KB

Open AccessArticle

A Robust Constitutive Model for Clays over a Wide Range of Plasticity and Overconsolidation Ratio (OCR) with Symmetric, Continuous Curvature Control of a Teardrop Yield Surface

by Thammanun Chatwong, Nopanom Kaewhanam, Siwa Kaewplang, Nopakun Phonchamni, Sudsakorn Inthidech, Apichit Kampala and Sivarit Sultornsanee

Symmetry 2026, 18(2), 215; https://doi.org/10.3390/sym18020215 - 23 Jan 2026

Abstract

This study addresses a key limitation of conventional clay constitutive models, which often assume linear stress paths at low stress ratios and lack a systematic link between plasticity and yield surface shape. A symmetry-consistent bounding surface plasticity framework is proposed, introducing two shape [...] Read more.

This study addresses a key limitation of conventional clay constitutive models, which often assume linear stress paths at low stress ratios and lack a systematic link between plasticity and yield surface shape. A symmetry-consistent bounding surface plasticity framework is proposed, introducing two shape parameters, Ψ and Ω, to control curvature and scaling of the yield surface under low stress ratios. The formulation preserves a unified, smooth yield function with continuous gradients, ensuring compatibility with standard numerical integration schemes. To enhance practical applicability, a three-level calibration strategy is established, ranging from direct triaxial interpretation to empirical correlations based on oedometer-derived indices. Model performance is validated against experimental data for clays with varying plasticity, demonstrating improved representation of curved stress paths without increasing formulation complexity. The proposed approach provides a transparent and reproducible extension to existing frameworks, bridging the gap between theoretical consistency and engineering-oriented calibration. Full article

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

24 pages, 1452 KB

Open AccessArticle

Nonreciprocal Flow of Fluctuations, Populations and Correlations Between Doubly Coupled Bosonic Modes

by Zbigniew Ficek

Symmetry 2026, 18(2), 214; https://doi.org/10.3390/sym18020214 - 23 Jan 2026

Abstract

Interesting new correlations and unidirectional properties of two bosonic modes under the influence of the environment appear when the modes are mutually coupled through the simultaneously applied linear mode-hopping and nonlinear squeezing interactions. Under such double coupling, it is found that while the [...] Read more.

Interesting new correlations and unidirectional properties of two bosonic modes under the influence of the environment appear when the modes are mutually coupled through the simultaneously applied linear mode-hopping and nonlinear squeezing interactions. Under such double coupling, it is found that while the Hamiltonian of the system is clearly Hermitian, the dynamics of the quadrature components of the field operators can be attributed to the non-Hermicity of the system. This manifests through an asymmetric coupling between the quadrature components, which then leads to a variety of remarkable features. In particular, we identify how the emerging exceptional point controls the conversion of thermal states of the modes into single-mode classically or quantum-squeezed states. Furthermore, for reservoirs in squeezed states, we find that the two-photon correlations present in these reservoirs are responsible for unidirectional flow of populations and correlations among the modes and the flow can be controlled by appropriate tuning of the mutual orientation of the squeezed noise ellipses. In the course of analyzing these effects, we find that the flow of the population creates the first-order coherence between the modes which, on the other hand, rules out an enhancement of the two photon correlations responsible for entanglement between the modes. These results suggest new alternatives for the creation of single-mode squeezed fields and the potential applications for the controlled unidirectional transfer of population and correlations in bosonic chains. Full article

(This article belongs to the Special Issue Symmetry and Nonlinearity in Optics)

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25 pages, 1079 KB

Open AccessArticle

Anisotropic Preferred Reference Frames for Relativistic Quantum Information Systems

by Timothy Ganesan, Zeeshan Yousaf and M. Z. Bhatti

Symmetry 2026, 18(2), 213; https://doi.org/10.3390/sym18020213 - 23 Jan 2026

Abstract

Two novel spacetimes are introduced in this work as anisotropic preferred reference frames tailored for applications in relativistic quantum information systems. The resulting anisotropic geometry arises intrinsically from the underlying algebraic structure of spin matrices rather than being imposed through external prescriptions, background [...] Read more.

Two novel spacetimes are introduced in this work as anisotropic preferred reference frames tailored for applications in relativistic quantum information systems. The resulting anisotropic geometry arises intrinsically from the underlying algebraic structure of spin matrices rather than being imposed through external prescriptions, background fields, or perturbative approximations. The associated Lorentz factors, symmetry group structure and metric-preserving transformations are systematically analyzed within the context of relativistic quantum information theory. Full article

(This article belongs to the Section Mathematics)

24 pages, 5388 KB

Open AccessArticle

A New Hyperchaotic Map and Its Manifold of Conditional Symmetry

by Zhenxin Hu, Chunbiao Li, Xiaolong Qi, Ioannis P. Antoniades and Christos Volos

Symmetry 2026, 18(2), 212; https://doi.org/10.3390/sym18020212 - 23 Jan 2026

Abstract

In this work, the polarity balance of a novel two-dimensional hyperchaotic map is considered, and thus the corresponding manifold of conditional symmetry is coined. The unique map has a simple structure but provides direct 2-D offset boosting, which brings the possibility for the [...] Read more.

In this work, the polarity balance of a novel two-dimensional hyperchaotic map is considered, and thus the corresponding manifold of conditional symmetry is coined. The unique map has a simple structure but provides direct 2-D offset boosting, which brings the possibility for the construction of conditional symmetry by introducing an absolute value function. The corresponding evolution of the discrete sequences from the system is verified by the circuit implementation based on the microcontroller of CH32V307. The pseudorandom data from the map increases its adaptability for applications in information security. The hyperchaotic sequence-injected Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Sparrow Search Algorithm (SSA) show their improved performance in the optimization algorithm. Robot path planning experiments confirm that all three algorithms exhibit superior convergence performance, global search capability, and path smoothness compared with the original algorithms. Full article

(This article belongs to the Section Engineering and Materials)

18 pages, 4791 KB

Open AccessArticle

Research on Structural Design and Plugging Laws of Knot Temporary Plugging Agent

by Jianjun Xue, Qiang Sun, Ran Wei, Weiqing Li, Leilei Yu, Wei Wang and Yongsheng Liu

Symmetry 2026, 18(2), 211; https://doi.org/10.3390/sym18020211 - 23 Jan 2026

Abstract

Horizontal wellbore temporary plugging and diversion fracturing serves as a critical technical approach for the economical and efficient development of unconventional oil and gas reservoirs. A degradable knot temporary plugging agent (TPA) offers distinct advantages for perforation plugging in horizontal wellbore; however, existing [...] Read more.

Horizontal wellbore temporary plugging and diversion fracturing serves as a critical technical approach for the economical and efficient development of unconventional oil and gas reservoirs. A degradable knot temporary plugging agent (TPA) offers distinct advantages for perforation plugging in horizontal wellbore; however, existing research remains limited, and the influence of knot TPA parameters on perforation temporary plugging mechanisms has not been clearly elucidated. This study employs a CFD-DBCM coupled model to conduct numerical simulations of temporary plugging with a knot TPA. The simulation is validated through visualized temporary plugging experiments, followed by an optimization analysis focusing on the flank length and structural configurations of the knot TPA. Research indicates that, when the flank is less than 1.6 times the central diameter, its plugging capacity is significantly compromised. Once the flank exceeds 1.6 times the central diameter, the total plugging performance of the knot TPA improves to a certain extent, and the temporary plugging capacity for the upper perforations increases particularly significantly. When flank lengths are identical, a knot TPA with uniformly distributed four flanks exhibits superior plugging performance compared to configurations featuring only single or double flanks. Given formation heterogeneity, a temporary plugging simulation analysis of the combined knot TPA was conducted. The results indicate that employing a combined knot TPA achieves a higher valid plugging rate compared to using only one type of knot TPA, with valid plugging accounting for the majority of cases. Field application of knot TPA was conducted in the fracturing stage of an oil well in Zhejiang, and the changes in on-site data verified the effectiveness of the temporary plugging technique of knot TPA. Full article

(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2025)

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27 pages, 5002 KB

Open AccessArticle

A Robust Meta-Learning-Based Map-Matching Method for Vehicle Navigation in Complex Environments

by Fei Meng and Jiale Zhao

Symmetry 2026, 18(1), 210; https://doi.org/10.3390/sym18010210 - 22 Jan 2026

Abstract

Map matching is a fundamental technique for aligning noisy GPS trajectory data with digital road networks and constitutes a key component of Intelligent Transportation Systems (ITS) and Location-Based Services (LBS). Nevertheless, existing approaches still suffer from notable limitations in complex environments, particularly urban [...] Read more.

Map matching is a fundamental technique for aligning noisy GPS trajectory data with digital road networks and constitutes a key component of Intelligent Transportation Systems (ITS) and Location-Based Services (LBS). Nevertheless, existing approaches still suffer from notable limitations in complex environments, particularly urban and urban-like scenarios characterized by heterogeneous GPS noise and sparse observations, including inadequate adaptability to dynamically varying noise, unavoidable trade-offs between real-time efficiency and matching accuracy, and limited generalization capability across heterogeneous driving behaviors. To overcome these challenges, this paper presents a Meta-learning-driven Progressive map-Matching (MPM) method with a symmetry-aware design, which integrates a two-layer pattern-mining-based noise-robust meta-learning mechanism with a dynamic weight adjustment strategy. By explicitly modeling topological symmetry in road networks, symmetric trajectory patterns, and symmetric noise variation characteristics, the proposed method effectively enhances prior knowledge utilization, accelerates online adaptation, and achieves a more favorable balance between accuracy and computational efficiency. Extensive experiments on two real-world datasets demonstrate that MPM consistently outperforms state-of-the-art methods, achieving up to 10–15% improvement in matching accuracy while reducing online matching latency by over 30% in complex urban environments. Furthermore, the symmetry-aware design significantly improves robustness against asymmetric interference, thereby providing a reliable and scalable solution for high-precision map matching in complex and dynamic traffic environments. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Data Mining, Optimization Algorithms, and System Control for Intelligent Transportation Systems)

32 pages, 1195 KB

Open AccessArticle

A Hybrid Hesitant Fuzzy DEMATEL-Entropy Weight Variation Coefficient Method for Low-Carbon Automotive Supply Chain Risk Assessment

by Ying Xiang, Shaoqian Ji, Long Guo, Liangkun Guo, Rui Xu and Zhiming Guo

Symmetry 2026, 18(1), 209; https://doi.org/10.3390/sym18010209 - 22 Jan 2026

Abstract

In the context of a low-carbon economy, automotive parts supply chains face multifaceted risks, making an effective supply chain risk assessment model a crucial means of ensuring supply chain stability. Traditional evaluation methods struggle to comprehensively and accurately identify all influencing factors and [...] Read more.

In the context of a low-carbon economy, automotive parts supply chains face multifaceted risks, making an effective supply chain risk assessment model a crucial means of ensuring supply chain stability. Traditional evaluation methods struggle to comprehensively and accurately identify all influencing factors and their interrelationships in automotive parts supply chains. This article constructs an evaluation model based on the principle of symmetry. The “structural symmetry” is determined by the ratio of the completeness of risk dimension coverage in the indicator system to the precision of indicators, while “fusion symmetry” refers to the degree of equilibrium in information contribution during the fusion of subjective and objective weights. First, Fault Tree Analysis (FTA) and the Delphi method are adopted to establish a risk evaluation index system, whereby structural symmetry is ensured by the equilibrium between the completeness of risk dimension coverage and the accuracy of indicators in the index system. Second, drawing on the symmetric fusion principle, this study proposes a hybrid evaluation approach integrating hesitant fuzzy DEMATEL with entropy weight-coefficient of variation (HDEC), and the fusion symmetry is guaranteed by the balanced integration of subjective and objective weight information. Finally, a case study of an automotive parts supply chain enterprise quantitatively assesses and ranks risk factors, with corresponding countermeasures proposed. The symmetry-guided HDEC method achieves high accuracy, identifying indicator–causal relationships. Compared with the traditional entropy-weighted AHP algorithm, the Pearson correlation coefficient is 0.8566, and Spearman’s rank correlation coefficient is 0.88, indicating strong weight correlation and robust stability. The integration of mathematical symmetry enhances the model’s theoretical rigor, which aligns with symmetry-oriented optimization research. Full article

23 pages, 3120 KB

Open AccessArticle

Adaptive Coordinated Control for Yaw and Roll Stability of Distributed-Drive Commercial Vehicles

by Shaodan Na, Licheng Huang and Lianghong Wu

Symmetry 2026, 18(1), 208; https://doi.org/10.3390/sym18010208 - 22 Jan 2026

Abstract

Distributed-drive commercial vehicles are prone to skidding or rolling over when operating on low-friction roads or negotiating tight curves. To address this issue, this paper proposes a control strategy based on Adaptive Model Predictive Control (AMPC) to coordinate yaw and roll stability of [...] Read more.

Distributed-drive commercial vehicles are prone to skidding or rolling over when operating on low-friction roads or negotiating tight curves. To address this issue, this paper proposes a control strategy based on Adaptive Model Predictive Control (AMPC) to coordinate yaw and roll stability of distributed-drive commercial vehicles. By analyzing the improved

β - \dot{β}

phase-plane boundary and the roll stability threshold, this study identifies the yaw rate, sideslip angle, and predicted lateral load transfer rate (PLTR) as key indicators for vehicle stability assessment. The AMPC controller employs these metrics to dynamically adjust the control weights associated with yaw and roll stability in real time, thereby calculating the required additional yaw moment, which is applied through optimal torque distribution among all four wheels to achieve coordinated control. Finally, experiments are conducted on a Simulink-TruckSim co-simulation platform to assess the performance of AMPC. Compared with the conventional MPC method, the proposed approach achieves obvious improvements in both roll and yaw stability under sinusoidal and fishhook operating conditions. Full article

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19 pages, 621 KB

Open AccessArticle

The Hubble Tension in Light of the Symmetry of Scale Invariance

by Frédéric Courbin and André Maeder

Symmetry 2026, 18(1), 207; https://doi.org/10.3390/sym18010207 - 22 Jan 2026

Abstract

When the expansion rate of the Universe at recombination is used to infer the present expansion rate

H_{0}

, the value derived in the

Λ

CDM model,

H_{0} = 67.4

km s

^{- 1}

Mpc

^{- 1}

, is [...] Read more.

When the expansion rate of the Universe at recombination is used to infer the present expansion rate

H_{0}

, the value derived in the

Λ

CDM model,

H_{0} = 67.4

km s

^{- 1}

Mpc

^{- 1}

, is about in 6

σ

tension with the value measured locally,

H_{0} = 74

km s

^{- 1}

Mpc

^{- 1}

. In this work, we consider instead the expansion history in the context of the symmetry of scale-invariant vacuum (SIV model). We first perform two major cosmological tests: the Hubble diagram for type-Ia supernovae and the fundamental relation between

H_{0}

, the age of the Universe, and the total density of matter,

Ω_{m}

. This allows us to constrain

Ω_{m}

in SIV, with both tests giving the best agreement for

Ω_{m}

= 0.20. We then study the physical connections of the dynamical and thermal states of the Universe at recombination with the present Hubble constant,

H_{0}

, and the present temperature, T, in the

Λ

CDM and SIV contexts. We find that, in SIV, the properties at recombination may be conveyed to the present ones (

T = 2.726

and

H_{0}

at

z = 0

) without any tension, indicating

H_{0} = 74

km s

^{- 1}

Mpc

^{- 1}

in spite of the anchoring on the CMB. This is due to the slightly different expansion and temperature histories of the two cosmological models. Importantly, this happens to occur for

Ω_{m}

= 0.20, as constrained in SIV with supernovae and cosmic age. This suggests that the Hubble tension currently found between

H_{0}

values in the early and late Universe may simply be the result of

Λ C D M

ignoring the small but still measurable effects of scale invariance. Full article

(This article belongs to the Special Issue Demystifying the Dark Sector of the Cosmos in the Lab: Astrophysical Ingredients in Laboratory Searches near the Quantum Limit)

12 pages, 247 KB

Open AccessArticle

Matrices of Tangents and Cotangents and Their Associated Integer Matrices

by Michał Różański and Roman Wituła

Symmetry 2026, 18(1), 206; https://doi.org/10.3390/sym18010206 - 22 Jan 2026

Abstract

In this paper, we consider certain special sine, tangent, and cotangent symmetric matrices, along with their associated integer matrices. We present interesting relationships that connect these matrices. Relevant examples of the corresponding matrices are also provided, along with several intriguing problems. A separate [...] Read more.

In this paper, we consider certain special sine, tangent, and cotangent symmetric matrices, along with their associated integer matrices. We present interesting relationships that connect these matrices. Relevant examples of the corresponding matrices are also provided, along with several intriguing problems. A separate section includes proofs of the main theorems, which we believe are noteworthy in their own right. Full article

(This article belongs to the Section Mathematics)

15 pages, 1377 KB

Open AccessArticle

Symmetry Breaking on a Chessboard: 50 Years After Eigen’s and Winkler’s “Laws of the Game”

by Antonella D’Elia and Savino Longo

Symmetry 2026, 18(1), 205; https://doi.org/10.3390/sym18010205 - 22 Jan 2026

Abstract

This paper analyses several mathematical games developed 50 years ago by Manfred Eigen and Ruthild Winkler in their famous book “Laws of the Game: How the Principles of Nature Govern Chance,” published for the first time in German in 1975. These games are [...] Read more.

This paper analyses several mathematical games developed 50 years ago by Manfred Eigen and Ruthild Winkler in their famous book “Laws of the Game: How the Principles of Nature Govern Chance,” published for the first time in German in 1975. These games are intended to represent the essential aspects of chemical selection processes via symmetry breaking in biological systems. Special attention is paid to games that model biochemical kinetics, in which a chessboard is used to represent different types of substrates. The time-dependent statistical outcomes of several games are studied by Monte Carlo techniques. Analytical stochastic models applied to these games relate game rules to partial differential equation problems with appropriate initial and boundary conditions: rationalizing their outcomes, they confirm the intuitions of the original authors and add new insights. The potential impact of game-based models on current research on biological homochirality is discussed. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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24 pages, 2902 KB

Open AccessArticle

Research on Prolonged Violation Behavior Recognition in Construction Sites Based on Artificial Intelligence

by Kai Yu, Zhenyue Wang, Lujie Zhou, Xuesong Yang, Zhaoxiang Mu and Tianyu Wang

Symmetry 2026, 18(1), 204; https://doi.org/10.3390/sym18010204 - 22 Jan 2026

Abstract

Prolonged violation behavior is characterized by sustained temporal presence, slow action changes, and similarity to normal behavior. Due to the complex construction environment, intelligent recognition algorithms face significant challenges. This paper proposes an improved YOLOv8-based model, DGEA-YOLOv8, to address these issues, using “playing [...] Read more.

Prolonged violation behavior is characterized by sustained temporal presence, slow action changes, and similarity to normal behavior. Due to the complex construction environment, intelligent recognition algorithms face significant challenges. This paper proposes an improved YOLOv8-based model, DGEA-YOLOv8, to address these issues, using “playing with mobile phones” as a case study. The model integrates the DCNv3 module in the backbone to enhance behavior deformation adaptability and the GELAN module to improve lightweight performance and global perception in resource-limited environments. An ECA attention mechanism is added to enhance small target detection, while the ASPP module boosts multi-scale perception. ByteTrack is incorporated for continuous tracking of prolonged violation behavior in construction scenarios. Experimental results show that DGEA-YOLOv8 achieves 94.5% mAP50, a 2.95% improvement over the YOLOv8s baseline, with better data capture rates and lower ID change rates compared to algorithms like Deepsort and Strongsort. A construction-specific dataset of over 3000 images verifies the model’s effectiveness. From the perspective of data symmetry, the proposed model demonstrates strong capability in addressing asymmetric feature distributions and behavioral imbalance inherent in prolonged violations, restoring spatiotemporal consistency in detection. In conclusion, DGEA-YOLOv8 provides a precise, efficient, and adaptive solution for recognizing prolonged violation behaviors in construction sites. Full article

(This article belongs to the Section Computer)

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21 pages, 4135 KB

Open AccessArticle

Numerical Modeling of Wind-Induced Deformation in Eastern Red Cedar Tree Forms Using Fluid–Structure Interaction Analysis

by Ahmet Ayaz and Mahdi Tabatabaei Malazi

Symmetry 2026, 18(1), 203; https://doi.org/10.3390/sym18010203 - 21 Jan 2026

Abstract

This research aims to investigate wind-induced effects numerically in full-scale Eastern Red Cedar tree (ERCT) forms under various wind speeds. A total of 72 model cases were carefully analyzed for variations in crown lengths (CLs), canopy diameters (CDs), bole lengths (BLs), and trunk [...] Read more.

This research aims to investigate wind-induced effects numerically in full-scale Eastern Red Cedar tree (ERCT) forms under various wind speeds. A total of 72 model cases were carefully analyzed for variations in crown lengths (CLs), canopy diameters (CDs), bole lengths (BLs), and trunk diameters (TDs) at wind speeds ranging from 15 m/s to 30 m/s. The realizable k–ε turbulence model is employed to resolve the flow region and obtain drag force (FD), velocity, and pressure distributions within the computational fluid domain. The resulting aerodynamic loads are then transferred to ERCT models using a one-way fluid–structure interaction (one-way FSI) approach to predict deformation, stress, and strain in the solid zone. The accuracy of these findings was validated by comparing drag coefficient (C_D) results with those from previously conducted studies. Research results reveal that wind speed and the geometric dimensions of the tree notably influence the FD, deformation, strain, and stress experienced by the tree. When wind speed rises from 15 to 30 m/s, the amount of FD, deformation, strain, and stress increases on the ERCT. The present research helps improve the understanding of tree patterns impacted by wind, which is essential for urban design and planning. It provides guidance on how to choose and arrange necessary real trees for efficient windbreaks and comfortable surroundings in life. Full article

(This article belongs to the Special Issue Symmetry in Computational Fluid Dynamics)

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24 pages, 883 KB

Open AccessArticle

SDA-Net: A Symmetric Dual-Attention Network with Multi-Scale Convolution for MOOC Dropout Prediction

by Yiwen Yang, Chengjun Xu and Guisheng Tian

Symmetry 2026, 18(1), 202; https://doi.org/10.3390/sym18010202 - 21 Jan 2026

Abstract

With the rapid development of Massive Open Online Courses (MOOCs), high dropout rates have become a major challenge, limiting the quality of online education and the effectiveness of targeted interventions. Although existing MOOC dropout prediction methods have incorporated deep learning and attention mechanisms [...] Read more.

With the rapid development of Massive Open Online Courses (MOOCs), high dropout rates have become a major challenge, limiting the quality of online education and the effectiveness of targeted interventions. Although existing MOOC dropout prediction methods have incorporated deep learning and attention mechanisms to improve predictive performance to some extent, they still face limitations in modeling differences in course difficulty and learning engagement, capturing multi-scale temporal learning behaviors, and controlling model complexity. To address these issues, this paper proposes a MOOC dropout prediction model that integrates multi-scale convolution with a symmetric dual-attention mechanism, termed SDA-Net. In the feature modeling stage, the model constructs a time allocation ratio matrix (MRatio), a resource utilization ratio matrix (SRatio), and a relative group-level ranking matrix (Rank) to characterize learners’ behavioral differences in terms of time investment, resource usage structure, and relative performance, thereby mitigating the impact of course difficulty and individual effort disparities on prediction outcomes. Structurally, SDA-Net extracts learning behavior features at different temporal scales through multi-scale convolution and incorporates a symmetric dual-attention mechanism composed of spatial and channel attention to adaptively focus on information highly correlated with dropout risk, enhancing feature representation while maintaining a relatively lightweight architecture. Experimental results on the KDD Cup 2015 and XuetangX public datasets demonstrate that SDA-Net achieves more competitive performance than traditional machine learning methods, mainstream deep learning models, and attention-based approaches on major evaluation metrics; in particular, it attains an accuracy of 93.7% on the KDD Cup 2015 dataset and achieves an absolute improvement of 0.2 percentage points in Accuracy and 0.4 percentage points in F1-Score on the XuetangX dataset, confirming that the proposed model effectively balances predictive performance and model complexity. Full article

(This article belongs to the Section Computer)

35 pages, 1361 KB

Open AccessArticle

A Fuzzy-SNA Computational Framework for Quantifying Intimate Relationship Stability and Social Network Threats

by Ning Wang and Xiangzhi Kong

Symmetry 2026, 18(1), 201; https://doi.org/10.3390/sym18010201 - 21 Jan 2026

Abstract

Intimate relationship stability is fundamental to human wellbeing, yet its quantitative assessment faces dual challenges: the inherent subjectivity of psychological constructs and the complexity of social ecosystems. Symmetry, as a fundamental structural feature of social interaction, plays a pivotal role in shaping relational [...] Read more.

Intimate relationship stability is fundamental to human wellbeing, yet its quantitative assessment faces dual challenges: the inherent subjectivity of psychological constructs and the complexity of social ecosystems. Symmetry, as a fundamental structural feature of social interaction, plays a pivotal role in shaping relational dynamics. To address these limitations, this study proposes an innovative computational framework that integrates Fuzzy Set Theory with Social Network Analysis (SNA). The framework consists of two complementary components: (1) a psychologically grounded fuzzy assessment model that employs differentiated membership functions to transform discrete subjective ratings into continuous and interpretable relationship quality indices and (2) an enhanced Fuzzy C-Means (FCM) threat detection model that utilizes Weighted Mahalanobis Distance to accurately identify and cluster potential interference sources within social networks. Empirical validation using a simulated dataset—comprising typical characteristic samples from 10 couples—demonstrates that the proposed framework not only generates interpretable relationship diagnostics by correcting biases associated with traditional averaging methods, but also achieves high precision in threat identification. The results indicate that stable relationships exhibit greater symmetry in partner interactions, whereas threatened nodes display structural and behavioural asymmetry. This study establishes a rigorous mathematical paradigm—“Subjective Fuzzification → Multidimensional Feature Engineering → Intelligent Clustering”—for relationship science, thereby advancing the field from descriptive analysis toward data-driven, quantitative evaluation and laying a foundation for systematic assessment of relational health. Full article

(This article belongs to the Section Mathematics)

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23 pages, 5096 KB

Open AccessReview

A Review of Hyperon Physics at BESIII Experiment

by Ruoyu Zhang and Xiongfei Wang

Symmetry 2026, 18(1), 200; https://doi.org/10.3390/sym18010200 - 21 Jan 2026

Abstract

The BESIII Collaboration has collected large data samples from

e^{+} e^{-}

collisions at center-of-mass energies ranging from 1.84 to 4.95 GeV, which include the world’s largest charmonium sample, consisting of 10 billion

J / ψ

and 3 billion [...] Read more.

The BESIII Collaboration has collected large data samples from

e^{+} e^{-}

collisions at center-of-mass energies ranging from 1.84 to 4.95 GeV, which include the world’s largest charmonium sample, consisting of 10 billion

J / ψ

and 3 billion

ψ (3686)

events. These high-statistics datasets enable BESIII to carry out a wide range of studies in hyperon physics. In this article, we review the major achievements of the BESIII Collaboration in this field, which can be broadly categorized into four areas: hyperon polarization and

C P

violation, rare hyperon decays, hyperon pair production, and hyperon–nucleon interactions. Full article

(This article belongs to the Collection Symmetry/Asymmetry in Baryon Decay: Polarization, Hyperon Asymmetry Parameters and CP Violation)

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