Symmetry

27 pages, 3758 KB

Open AccessArticle

Belief Entropy-Based MAGDM Algorithm Under Double Hierarchy Quantum-like Bayesian Networks and Its Application to Wastewater Reuse

by Juxiang Wang, Yaping Li, Xin Wang and Yanjun Wang

Symmetry 2025, 17(11), 2013; https://doi.org/10.3390/sym17112013 - 20 Nov 2025

Viewed by 356

Abstract

The traditional multi-attribute group decision-making (MAGDM) method easily ignores the interference effect among decision-makers (DMs), while quantum theory can effectively portray the uncertainty in the decision-making process and quantify the preference interference among DMs. The asymmetry of evaluation information in social networks can [...] Read more.

The traditional multi-attribute group decision-making (MAGDM) method easily ignores the interference effect among decision-makers (DMs), while quantum theory can effectively portray the uncertainty in the decision-making process and quantify the preference interference among DMs. The asymmetry of evaluation information in social networks can have a significant impact on decision-making. In this paper, a quantum MAGDM algorithm based on probabilistic linguistic term sets (PLTSs) and a quantum-like Bayesian network (QLBN) is proposed (PL-QLBN), utilizing quantum theory and social network concepts and introducing a novel method for calculating interference effects based on belief entropy. Firstly, a complete trust network is constructed based on the probabilistic linguistic trust transfer operator and the minimum path method. A trust aggregation method, considering interference effects, is proposed for the QLBN to determine the DM weights. Next, the attribute weights are calculated based on the entropy weight method. Then, a probabilistic linguistic MAGDM considering interference effects is proposed based on the QLBN. Finally, the feasibility and validity of the provided method are verified through Hefei City’s selection of wastewater reuse alternatives. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)

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42 pages, 18045 KB

Open AccessArticle

MSCSO: A Modified Sand Cat Swarm Optimization for Global Optimization and Multilevel Thresholding Image Segmentation

by Xuanqi Yuan, Zihao Zhu, Zhengxing Yang and Yongnian Zhang

Symmetry 2025, 17(11), 2012; https://doi.org/10.3390/sym17112012 - 20 Nov 2025

Cited by 3 | Viewed by 347

Abstract

To address the limitations of the original Sand Cat Swarm Optimization (SCSO) algorithm—such as static strategy selection, insufficient population diversity, and coarse boundary handling—this paper proposes a multi-strategy enhanced version, namely the Modified Sand Cat Swarm Optimization (MSCSO). The algorithm improves performance through [...] Read more.

To address the limitations of the original Sand Cat Swarm Optimization (SCSO) algorithm—such as static strategy selection, insufficient population diversity, and coarse boundary handling—this paper proposes a multi-strategy enhanced version, namely the Modified Sand Cat Swarm Optimization (MSCSO). The algorithm improves performance through three core strategies: (1) an adaptive strategy selection mechanism that dynamically adapts to different optimization phases; (2) an adaptive crossover–mutation strategy inspired by differential evolution, in which mutation vectors are generated with the guidance of the global best solution and updated via binomial crossover, thereby enhancing both population diversity and local search capability; and (3) a boundary control mechanism guided by the global best solution, which repairs out-of-bound solutions by relocating them between the global best and the boundary, thus preserving useful search information and avoiding oscillation near the limits. To validate the performance of MSCSO, extensive experiments were conducted on the CEC2020 and CEC2022 benchmark suites under 10- and 20-dimensional scenarios, where MSCSO was compared with seven algorithms, including Particle Swarm Optimization (PSO) and Gray Wolf Optimizer (GWO). The results demonstrate that MSCSO consistently outperforms its competitors on unimodal, multimodal, and hybrid functions. Notably, MSCSO achieved the best Friedman ranking across all dimensions. Ablation studies further confirm that the three proposed strategies exhibit strong synergy, collectively accelerating convergence and enhancing stability. In addition, MSCSO was applied to multilevel threshold image segmentation, where Otsu’s criterion was adopted as the objective function and experiments were conducted on five benchmark images with 4–10 thresholds. The results show that MSCSO achieves superior segmentation quality, significantly outperforming the comparison algorithms. Overall, this study demonstrates that MSCSO effectively balances exploration and exploitation without increasing computational complexity, providing not only a powerful tool for global optimization but also a reliable technique for engineering tasks such as multilevel threshold image segmentation. These findings highlight its strong theoretical significance and promising application potential. Full article

(This article belongs to the Special Issue Heuristic Search for Combinatorial Optimization Problems and Symmetry Applications)

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20 pages, 2026 KB

Open AccessArticle

Global Sensitivity and Mathematical Modeling for Zoonotic Lassa Virus Transmission and Disability in Critical Cases in the Light of Fractional Order Model

by Ibrahim Aldayel, Osamah AbdulAziz Aldayel and El Mehdi Farah

Symmetry 2025, 17(11), 2011; https://doi.org/10.3390/sym17112011 - 20 Nov 2025

Viewed by 351

Abstract

Lassa fever remains a significant zoonotic threat in West Africa, characterized by complex human-to-human and rodent-to-human transmission pathways and prolonged immune responses. Existing integer-order models often neglect the long-term memory and delayed recovery effects inherent to the disease. In this study, we develop [...] Read more.

Lassa fever remains a significant zoonotic threat in West Africa, characterized by complex human-to-human and rodent-to-human transmission pathways and prolonged immune responses. Existing integer-order models often neglect the long-term memory and delayed recovery effects inherent to the disease. In this study, we develop and analyze a fractional-order Caputo model for Lassa fever transmission incorporating disability feedback among recovered individuals. The model captures memory-dependent infection and recovery dynamics, offering a more realistic description of epidemic persistence. The model is symmetric when the fractional approach to unity where it recovers its classical ODE counterpart. Analytical results establish the positivity, boundedness, existence, and uniqueness of solutions, while Picard stability and contraction mapping confirm well-posedness within the fractional framework. A Grünwald–Letnikov discretization scheme is constructed for numerical simulation, validated under varying fractional orders (

λ \in [0.7, 1]

). The results reveal that decreasing the fractional order slows the infection decay rate and prolongs epidemic duration, highlighting the biological significance of memory effects. A global sensitivity analysis based on Latin Hypercube Sampling and Partial Rank Correlation Coefficients (LHS–PRCC) identifies the rodent-to-human transmission rate (

κ_{1}

), human-to-human transmission rate (

η_{1}

), and rodent interaction rate (

ξ_{r}

) as the most influential parameters. These findings provide critical insight into the control and management of Lassa fever through rodent population control, improved recovery rates, and early human intervention. The fractional-order formulation thus extends existing models both mathematically and epidemiologically by capturing delayed dynamics and disability-induced feedback mechanisms. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)

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18 pages, 353 KB

Open AccessArticle

Existence of Solutions to Symmetric Multivalued Functional Integral Equations with Illustrative Applications in Medicine and Logistics

by Marek T. Malinowski

Symmetry 2025, 17(11), 2010; https://doi.org/10.3390/sym17112010 - 20 Nov 2025

Viewed by 433

Abstract

This paper investigates functional integral equations with multivalued terms that appear symmetrically on both sides of the equation. We impose structural conditions on the coefficients that, while insufficient to ensure uniqueness, are adequate to guarantee the existence of at least one solution. We [...] Read more.

This paper investigates functional integral equations with multivalued terms that appear symmetrically on both sides of the equation. We impose structural conditions on the coefficients that, while insufficient to ensure uniqueness, are adequate to guarantee the existence of at least one solution. We assumed mere continuity of the coefficients to establish a Peano-type existence theorem. The existence result was derived through the application of Schauder’s fixed-point theorem. We further highlighted that this finding for symmetric multivalued functional integral equations significantly informs the analysis of delayed multivalued functional equations, which is commonly utilized in modeling processes where both the present and past states of the system play a crucial role. To illustrate the applicability of the proposed frameworks, representative examples were formulated and numerically solved for each type of equation, highlighting potential use cases in medicine and logistics. Full article

(This article belongs to the Section Mathematics)

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20 pages, 3589 KB

Open AccessArticle

A Symmetry Analysis Method for Teaching Knowledge Graph Evolution Driven by Directed Attributed Graphs

by Qifeng Zou, Chaoze Lu and Yinan Sun

Symmetry 2025, 17(11), 2009; https://doi.org/10.3390/sym17112009 - 20 Nov 2025

Viewed by 423

Abstract

Entity symmetry in teaching knowledge graphs is a characteristic of knowledge semantic expression and association, which plays a crucial role in the composition of knowledge structure. However, the evolution of the teaching knowledge graph may disrupt the symmetry of the knowledge structure, leading [...] Read more.

Entity symmetry in teaching knowledge graphs is a characteristic of knowledge semantic expression and association, which plays a crucial role in the composition of knowledge structure. However, the evolution of the teaching knowledge graph may disrupt the symmetry of the knowledge structure, leading to the emergence of asymmetric phenomena and resulting in adverse effects on the subsequent search and representation of knowledge. Therefore, this article proposes a symmetry analysis method for the evolution of teaching knowledge graphs driven by directed attributed graphs. Firstly, a teaching knowledge graph model with directed attributed graphs is presented, on which the entity connection symmetry, entity center symmetry, and entity mirror symmetry of the teaching knowledge graph are defined. Then, the addition, replacement, and deletion of entity evolution rules that affect symmetry in the teaching knowledge graph model were characterized, and a teaching knowledge graph evolution algorithm based on directed attributed graph transformation was designed. On this basis, an in-depth analysis was conducted on the symmetry of the evolution of the teaching knowledge graph, which was disrupted and maintained. Finally, experiments verify that preserving or breaking symmetry has a significant impact on the connectivity and path complexity of knowledge graphs. In addition, a case study on the evolution of a Japanese major teaching knowledge graph with both symmetric and asymmetric transformations is provided to validate the feasibility and effectiveness of the proposed directed attributed graph driven symmetry analysis method for educational knowledge graph evolution. Full article

(This article belongs to the Section Computer)

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17 pages, 1179 KB

Open AccessArticle

Regret Psychology-Driven Information Propagation and Behavioral Adoption in Complex Social Networks

by Nana Li, Yajuan Cui, Yang Tian, Chenxi Hu, Xuzhen Zhu and Simin Hu

Symmetry 2025, 17(11), 2008; https://doi.org/10.3390/sym17112008 - 20 Nov 2025

Viewed by 498

Abstract

In recent years, information propagation on social networks has attracted extensive attention, with psychological characteristics of individuals exerting a significant influence on the diffusion process. Our study investigates the role of regret psychology and its impact on information spreading and behavioral adoption. We [...] Read more.

In recent years, information propagation on social networks has attracted extensive attention, with psychological characteristics of individuals exerting a significant influence on the diffusion process. Our study investigates the role of regret psychology and its impact on information spreading and behavioral adoption. We categorize individuals into regretful and non-regretful groups and introduce regret intensity together with the proportion of regretful individuals as dynamic variables. Based on this, we construct a two-layer interactive model consisting of a psychological layer and a behavioral layer. Then we establish the behavioral adoption model for the heterogeneous population and study the propagation characteristics of the regretful individuals on social networks. Furthermore, we derive the propagation dynamics using edge-based compartmental theory to examine the transmission mechanism. Numerical simulations, which coincide nicely with our theoretical analyses, reveal the crossover phenomena in phase transitions: as the regret threshold increases, adoption dynamics shift from second-order continuous to first-order discontinuous transitions. More importantly, for a given propagation probability, there exists an optimal regret threshold that maximizes the final adoption size. These findings highlight the crucial role of regret psychology in reshaping the propagation mechanism and provide a new theoretical perspective for understanding symmetry transformations and group heterogeneity in social contagion dynamics. Full article

(This article belongs to the Section Computer)

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22 pages, 4191 KB

Open AccessArticle

Influence of Adverse Pressure Gradient on the Drag Reduction Characteristics of Riblets

by Qiyue Ma, Peiqing Liu, Hao Guo, Fei Cui, Yankun Su and Chunpeng Li

Symmetry 2025, 17(11), 2007; https://doi.org/10.3390/sym17112007 - 20 Nov 2025

Viewed by 409

Abstract

The riblet surface is a passive turbulence drag reduction technology with promising aerospace application prospects. To investigate the drag reduction effects of riblets under flow conditions more representative of actual aircraft surfaces, this study establishes an adverse pressure gradient environment at moderate-to-high Reynolds [...] Read more.

The riblet surface is a passive turbulence drag reduction technology with promising aerospace application prospects. To investigate the drag reduction effects of riblets under flow conditions more representative of actual aircraft surfaces, this study establishes an adverse pressure gradient environment at moderate-to-high Reynolds numbers. Symmetrically arranged two testing plates with riblets’ surface and smooth surface, hot-wire anemometry is employed to measure the skin friction drag of both plates to get a direct measurement of the drag reduction rate. And the drag reduction mechanism is analyzed through burst events detection and coherent structure’s inclination angle. The measurement results indicate that the adverse pressure gradient itself leads to a reduction in wall friction, and the turbulent boundary layer velocity profile deviates from the standard logarithmic law, rendering the Clauser chart method unsuitable for estimating the friction velocity. The adverse pressure gradient contributes positively to the drag reduction rate of riblets, while the increase in Reynolds number in this experiment has no substantial effect. For the near wall structures, their asymmetrical movement of ejection and sweep and investigated by VITA. The significant decrease in burst frequency and increase in coherent structure inclination angle in the turbulent boundary layer over the riblet surface are identified as the primary reasons for reduced wall friction, with these changes being particularly pronounced under adverse pressure gradient conditions. Full article

(This article belongs to the Section Engineering and Materials)

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15 pages, 749 KB

Open AccessArticle

On the Solvability of Some Systems of Nonlinear Difference Equations

by Jawharah Ghuwayzi AL-Juaid

Symmetry 2025, 17(11), 2006; https://doi.org/10.3390/sym17112006 - 20 Nov 2025

Viewed by 274

Abstract

The aim of this paper is to find formulas for the solutions of the nonlinear system of difference equations related to symmetry [...] Read more.

The aim of this paper is to find formulas for the solutions of the nonlinear system of difference equations related to symmetry

P_{n + 1} = \frac{T_{n} T_{n - 2}}{- P_{n - 3} - T_{n}}, T_{n + 1} = \frac{P_{n} P_{n - 2}}{\pm T_{n - 3} \pm P_{n}},

where the initial conditions

P_{- 3}, P_{- 2}, P_{- 1}, P_{0}, T_{- 3}, T_{- 2}, T_{- 1}

, and

T_{0}

are arbitrary real numbers. Moreover, the theoretical results are verified through several numerical examples, which are simulated and graphically illustrated using mathematical programs. Full article

(This article belongs to the Special Issue Advances in Nonlinear Systems and Symmetry/Asymmetry)

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32 pages, 768 KB

Open AccessArticle

Asymptotic Analysis of Generalized Logistic Affiliation Network Models with Node Attributes

by Yifan Fan, Lin Luo and Si Chen

Symmetry 2025, 17(11), 2005; https://doi.org/10.3390/sym17112005 - 19 Nov 2025

Viewed by 381

Abstract

Affiliation networks, with their bipartite structure and non-binary features, pose unique challenges due to their complex relationships and diverse node attributes. These challenges differ from those in symmetric one-mode networks. To address them, we propose a generalized logistic affiliation network model. Despite the [...] Read more.

Affiliation networks, with their bipartite structure and non-binary features, pose unique challenges due to their complex relationships and diverse node attributes. These challenges differ from those in symmetric one-mode networks. To address them, we propose a generalized logistic affiliation network model. Despite the structural asymmetry, the model incorporates node attributes and includes parameters for actor activeness, event popularity, and symmetric patterns in actor–event interactions. We study the theoretical properties of this model under an asymptotic framework, where the number of actors and events grows to infinity. Using maximum likelihood estimation, we show that the estimators for degree heterogeneity and node homophily converge to multivariate normal distributions under mild conditions. To validate the model and our theory, we conduct experiments on both simulated data and a movie-rating dataset. Full article

(This article belongs to the Section Mathematics)

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32 pages, 33001 KB

Open AccessArticle

Two Novel Sparse Models for Support Vector Machines

by Shuanghong Qu, Renato De Leone and Min Huang

Symmetry 2025, 17(11), 2004; https://doi.org/10.3390/sym17112004 - 19 Nov 2025

Viewed by 430

Abstract

Based on the Support Vector Machine (SVM) and Twin Parametric Margin SVM (TPMSVM), this paper proposes two sparse models, named Sparse SVM (SSVM) and Sparse TPMSVM (STPMSVM). The study aims to achieve high sparsity, rapid prediction, and strong generalization capability by transforming the [...] Read more.

Based on the Support Vector Machine (SVM) and Twin Parametric Margin SVM (TPMSVM), this paper proposes two sparse models, named Sparse SVM (SSVM) and Sparse TPMSVM (STPMSVM). The study aims to achieve high sparsity, rapid prediction, and strong generalization capability by transforming the classical quadratic programming problems (QPPs) into linear programming problems (LPPs). The core idea stems from a clear geometric motivation: introducing an

ℓ_{1}

-norm penalty on the dual variables to break the inherent rotational symmetry of the traditional

ℓ_{2}

-norm on the normal vector. Through a theoretical reformulation using the Karush–Kuhn–Tucker (KKT) conditions, we achieve a transformation from explicit symmetry-breaking to implicit structural constraints—the

ℓ_{1}

penalty term does not appear explicitly in the final objective function, while the sparsity-inducing effect is fundamentally encoded within the objective functions and their constraints. Ultimately, the derived linear programming models naturally yield highly sparse solutions. Extensive experiments are conducted on multiple synthetic datasets under various noise conditions, as well as on 20 publicly available benchmark datasets. Results demonstrate that the two sparse models achieve significant sparsity at the support vectors level—on the benchmark datasets, SSVM, and STPMSVM reduce the number of support vectors by an average of 56.21% compared with conventional SVM, while STPMSVM achieves an average reduction of 39.11% compared with TPMSVM—thereby greatly improving prediction efficiency. Notably, SSVM maintains accuracy comparable to conventional SVM under low-noise conditions while attaining extreme sparsity and prediction efficiency. In contrast, STPMSVM offers enhanced robustness to noise and maintains a better balance between sparsity and accuracy, preserving the desirable properties of TPMSVM while improving prediction efficiency and robustness. Full article

(This article belongs to the Section Mathematics)

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24 pages, 9658 KB

Open AccessArticle

Research on Dynamic Characteristics and Seismic Response of Suspen-Dome Structures Accounting for the Influence of Substructure Stiffness: Shaking Table Test and Numerical Analysis

by Zetao Zhao, Suduo Xue and Xiongyan Li

Symmetry 2025, 17(11), 2003; https://doi.org/10.3390/sym17112003 - 19 Nov 2025

Viewed by 334

Abstract

This paper examines the dynamic characteristics and seismic responses of suspen-dome structures, incorporating the influence of substructures, using the Lanzhou Olympic Sports Center Comprehensive Gymnasium with a symmetric suspen-dome roof as a case study. A scaled test model with a 1:20 ratio was [...] Read more.

This paper examines the dynamic characteristics and seismic responses of suspen-dome structures, incorporating the influence of substructures, using the Lanzhou Olympic Sports Center Comprehensive Gymnasium with a symmetric suspen-dome roof as a case study. A scaled test model with a 1:20 ratio was developed, and a novel approach to simplifying the complex substructures of the prototype structure within the scaled model was proposed. The accuracy of this method was validated. Subsequently, both an overall numerical model and a simplified numerical model (excluding substructures) were constructed. Their natural frequencies and seismic responses were compared. Additionally, the impact of substructure stiffness on dynamic characteristics and seismic responses investigated. The findings reveal that substructures decrease the natural frequencies of the suspen-dome structure while amplifying its seismic responses. The maximum relative error of the natural frequencies between the overall model and the simplified numerical model is as high as 25.9%; and the maximum relative difference in acceleration, displacement and strain between the two models can reach 0.71 g, 1.27 mm and 181.6 με, respectively. Thus, the inclusion of substructure effects is critical in the seismic analysis of suspen-dome structures. Moreover, as substructure stiffness decreases, the natural frequencies of the suspen-dome structure are reduced, and the vibration mode shifts from superstructure deformation to cooperative deformation involving both the superstructure and substructure. Finally, variations in substructure stiffness influence the constraints on the superstructure or the fundamental frequency of the overall structure, and consequently, the seismic responses of the suspen-dome structure. Thus, when performing seismic analyses, it is essential to design appropriate substructure stiffness and consider the specific characteristics of the building site. Full article

(This article belongs to the Section Engineering and Materials)

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21 pages, 1921 KB

Open AccessArticle

Enhanced Skin Lesion Segmentation via Attentive Reverse-Attention U-Net

by Buket Toptaş

Symmetry 2025, 17(11), 2002; https://doi.org/10.3390/sym17112002 - 19 Nov 2025

Viewed by 612

Abstract

Accurate identification and segmentation of skin lesions are essential for the early diagnosis of skin cancer. Symmetry is an important diagnostic cue in clinical practice, as malignant lesions often exhibit asymmetric patterns in shape, color, and texture. Therefore, incorporating symmetry-based features into automated [...] Read more.

Accurate identification and segmentation of skin lesions are essential for the early diagnosis of skin cancer. Symmetry is an important diagnostic cue in clinical practice, as malignant lesions often exhibit asymmetric patterns in shape, color, and texture. Therefore, incorporating symmetry-based features into automated analysis can enhance segmentation reliability and improve diagnostic accuracy. However, automated lesion segmentation faces significant challenges, including blurred boundaries, low-contrast lesions, and heterogeneous backgrounds. To address these challenges, we propose a hybrid deep neural network model that enhances the traditional U-Net architecture with an integrated reverse-attention module embedded within its skip connections. This innovation sharpens feature extraction in ambiguous regions, boosting segmentation accuracy, particularly in complex areas. The model employs a multifaceted loss function approach—encompassing binary cross entropy, dice, Tversky, and compound losses—to effectively manage data imbalances while preserving lesion boundary details. Experimental validation on the ISIC2018 and PH² datasets demonstrates the model’s efficacy, achieving dice similarity coefficients of 88.71% and 93.41% and mean intersection over union values of 87.68% and 90.78%, respectively. These results underscore the potential of our approach for clinical applications. Full article

(This article belongs to the Section Computer)

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26 pages, 2894 KB

Open AccessArticle

Cross-Scale Symmetry-Aware Causal Spatiotemporal Modeling with Adaptive Fusion and Region-Knowledge Transfer

by Xueyu Xu, Wenyuan Sun, Ratneswary Rasiah, Rongqing Lu and Yun Zheng

Symmetry 2025, 17(11), 2001; https://doi.org/10.3390/sym17112001 - 19 Nov 2025

Cited by 1 | Viewed by 556

Abstract

Accurate forecasting in heterogeneous spatiotemporal environments requires models that are both generalizable and interpretable, while also preserving cross-scale symmetry between temporal and spatial patterns. Existing deep learning approaches often struggle with limited adaptability to data-scarce regions and lack transparency in capturing cross-scale causal [...] Read more.

Accurate forecasting in heterogeneous spatiotemporal environments requires models that are both generalizable and interpretable, while also preserving cross-scale symmetry between temporal and spatial patterns. Existing deep learning approaches often struggle with limited adaptability to data-scarce regions and lack transparency in capturing cross-scale causal factors. To address these challenges, we propose a novel framework, Cross-Scale Symmetry-Aware Causal Spatiotemporal Modeling with Adaptive Fusion and Region-Knowledge Transfer, which integrates three key innovations. First, a Dynamic Spatio-Temporal Fusion Framework (DSTFF) leverages frequency-aware temporal transformations and adaptive graph attention to capture complex multi-scale dependencies, ensuring temporal–spatial symmetry in representation learning. Second, a Region-Knowledge Enhanced Transfer Learning (RKETL) mechanism distills knowledge across regions through teacher–student distillation, graph-based embeddings, and meta-learning initialization, thereby maintaining structural symmetry between data-rich and data-scarce regions. Third, a Multi-Granularity Causal Inference Prediction Module (MCIPM) uncovers cross-scale causal structures and supports counterfactual reasoning, providing causal symmetry across daily, weekly, and monthly horizons. Comprehensive experiments on multi-regional logistics datasets from China and the U.S. validate the effectiveness of our approach. Across six diverse Chinese regions, our method consistently outperforms state-of-the-art baselines (e.g., PatchTST, TimesNet, FEDformer), reducing MAE by 18.5% to 27.4%. On the U.S. Freight dataset, our model achieves significant performance gains with stable long-horizon accuracy, confirming its strong cross-domain generalization. Few-shot experiments further demonstrate that with only 5% of training data, our framework surpasses the best baseline trained with 20% data. Robustness analyses under input perturbations and uncertainty quantification show that the model maintains low error variance and produces well-calibrated prediction intervals. Furthermore, interpretability is concretely realized through MCIPM, which visualizes the learned causal graphs and quantifies each regional factor’s contribution to forecasting outcomes. This causal interpretability enables transparent understanding of how temporal spatial dynamics interact across scales, supporting actionable decision-making in logistics management and policy planning. Overall, this work contributes a unified spatiotemporal learning framework that leverages symmetry principles across scales and regions to enhance interpretability, transferability, and forecasting accuracy. Full article

(This article belongs to the Section Computer)

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22 pages, 8755 KB

Open AccessArticle

Symmetrical Pulse Shape Optimization for Low-Complexity RedCap Devices in Industrial Multipath Channels

by Anna Orlova, Sergey Zavjalov, Aleksandra Chekireva, Alexandra Kuznetsova, Ilya Lavrenyuk, Sergey Makarov and Ge Dong

Symmetry 2025, 17(11), 2000; https://doi.org/10.3390/sym17112000 - 19 Nov 2025

Viewed by 449

Abstract

Wireless communications in industrial environments are challenged by severe multipath propagation, which causes significant signal distortion. Conventional mitigation techniques, such as complex equalizers, are unsuitable as they contradict the stringent low-power and low-complexity requirements of Reduced Capability (RedCap) devices. This paper introduces a [...] Read more.

Wireless communications in industrial environments are challenged by severe multipath propagation, which causes significant signal distortion. Conventional mitigation techniques, such as complex equalizers, are unsuitable as they contradict the stringent low-power and low-complexity requirements of Reduced Capability (RedCap) devices. This paper introduces a novel method for optimizing single-carrier pulse shapes under a distortion constraint to combat multipath propagation. The performance was evaluated through simulations in MATLAB 2023b using a ray-traced warehouse model. The results show that the proposed optimal pulses achieve a significant reduction in Error Vector Magnitude (EVM) (up to 40% in non-line-of-sight scenarios) compared to conventional root-raised cosine (RRC) pulses, while adhering to the 20 MHz RedCap bandwidth requirement. Furthermore, this performance is attainable with a low-complexity scaling equalizer. EVM degradation under Doppler shift is estimated and the pilot period required to maintain the target distortion level is specified. The resulting bit rate of approximately 2.9 Mbps supports industrial sensor networks and low-definition video streaming, confirming the approach’s suitability for resource-constrained industrial applications. Full article

(This article belongs to the Section Engineering and Materials)

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31 pages, 1924 KB

Open AccessArticle

Two-Stage Robust Optimal Configuration of Multi-Energy Microgrid Considering Tiered Carbon Trading and Demand Response

by Xinxin Xu and Yanli Du

Symmetry 2025, 17(11), 1999; https://doi.org/10.3390/sym17111999 - 19 Nov 2025

Viewed by 620

Abstract

To further explore the potential of CO₂ emission reduction and optimize the cost of microgrids, a two-stage robust optimization configuration method for multi-energy microgrids is proposed, considering uncertainty, tiered carbon trading, and demand response. The model incorporates power-to-gas (P2G) and carbon capture [...] Read more.

To further explore the potential of CO₂ emission reduction and optimize the cost of microgrids, a two-stage robust optimization configuration method for multi-energy microgrids is proposed, considering uncertainty, tiered carbon trading, and demand response. The model incorporates power-to-gas (P2G) and carbon capture and storage (CCS) technologies to enhance renewable energy utilization and reduce carbon emissions. A tiered carbon trading mechanism is introduced to penalize high emissions, while incentive-based demand response is employed to adjust load profiles and improve economic performance. The optimization model is formulated as a two-stage robust problem: the outer stage minimizes annual investment and maintenance costs, while the inner stage identifies the worst-case scenario under uncertainties. The model is solved using the Column-and-Constraint Generation (C&CG) algorithm and implemented in MATLAB R2022b with the Gourbi solver. Simulation results demonstrate that the proposed approach reduces carbon emissions by up to 31.9% and total costs by 3.28% compared to conventional configurations, while increasing the penetration of renewable energy. This study provides practical reference for the low-carbon and economic planning of microgrids with P2G and CCS integration. Full article

(This article belongs to the Section Mathematics)

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32 pages, 2523 KB

Open AccessArticle

Hybrid Nanofluid Flow and Heat Transfer in Inclined Porous Cylinders: A Coupled ANN and Numerical Investigation of MHD and Radiation Effects

by Muhammad Fawad Malik, Reem Abdullah Aljethi, Syed Asif Ali Shah and Sidra Yasmeen

Symmetry 2025, 17(11), 1998; https://doi.org/10.3390/sym17111998 - 18 Nov 2025

Viewed by 616

Abstract

This study investigates the thermal characteristics of two hybrid nanofluids, single-walled carbon nanotubes with titanium dioxide (

S W C N T - T i O_{2}

) and multi-walled carbon nanotubes with copper (

M W C N T - C u

[...] Read more.

This study investigates the thermal characteristics of two hybrid nanofluids, single-walled carbon nanotubes with titanium dioxide (

S W C N T - T i O_{2}

) and multi-walled carbon nanotubes with copper (

M W C N T - C u

), as they flow over an inclined, porous, and longitudinally stretched cylindrical surface with kerosene as the base fluid. The model takes into consideration all of the consequences of magnetohydrodynamic (MHD) effects, thermal radiation, and Arrhenius-like energy of activation. The outcomes of this investigation hold practical significance for energy storage systems, nuclear reactor heat exchangers, electronic cooling devices, biomedical hyperthermia treatments, oil and gas transport processes, and aerospace thermal protection technologies. The proposed hybrid ANN–numerical framework provides an effective strategy for optimizing the thermal performance of hybrid nanofluids in advanced thermal management and energy systems. A set of coupled ordinary differential equations is created by applying similarity transformations to the governing nonlinear partial differential equations that reflect conservation of mass, momentum, energy, and species concentration. The boundary value problem solver bvp4c, which is based in MATLAB (R2020b), is used to solve these equations numerically. The findings demonstrate that, in comparison to the

M W C N T - C u / k e r o s e n e

nanofluid, the

S W C N T - T i O_{2}

/kerosene hybrid nanofluid improves the heat transfer rate (Nusselt number) by up to

23.6 %

. When a magnetic field is applied, velocity magnitudes are reduced by almost

15 %

, and the temperature field is enhanced by around

12 %

when thermal radiation is applied. The impact of important dimensionless variables, such as the cylindrical surface’s inclination angle, the medium’s porosity, the magnetic field’s strength, the thermal radiation parameter, the curvature ratio, the activation energy, and the volume fraction of nanoparticles, is investigated in detail using a parametric study. According to the comparison findings, at the same flow and thermal boundary conditions, the

S W C N T - T i O_{2}

/kerosene hybrid nanofluid performs better thermally than its

M W C N T - C u

/kerosene counterpart. These results offer important new information for maximizing heat transfer in engineering systems with hybrid nanofluids and inclined porous geometries under intricate physical conditions. With its high degree of agreement with numerical results, the ANN model provides a computationally effective stand-in for real-time thermal system optimization. Full article

(This article belongs to the Special Issue Integral/Differential Equations and Symmetry)

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21 pages, 18140 KB

Open AccessArticle

Effect of Formation Flight on Flight Endurance Performance of Solar-Powered UAV

by Cili Qiang and Zhijin Wang

Symmetry 2025, 17(11), 1997; https://doi.org/10.3390/sym17111997 - 18 Nov 2025

Viewed by 390

Abstract

Traditional solar-powered unmanned aerial vehicles (SUAVs) universally adopt ultra-high aspect ratio designs to enhance aerodynamic efficiency, which unfortunately leads to significant issues such as reduced structural reliability and poor resistance to atmospheric disturbances. In contrast, SUAVs with low aspect ratios suffer from inferior [...] Read more.

Traditional solar-powered unmanned aerial vehicles (SUAVs) universally adopt ultra-high aspect ratio designs to enhance aerodynamic efficiency, which unfortunately leads to significant issues such as reduced structural reliability and poor resistance to atmospheric disturbances. In contrast, SUAVs with low aspect ratios suffer from inferior aerodynamic efficiency, making it challenging to achieve long-endurance flight. This study addresses the endurance performance of low-aspect-ratio SUAVs by proposing and demonstrating a formation flight strategy to improve their cruise efficiency. To investigate the endurance characteristics of SUAVs, an energy model was established, encompassing solar cell power generation, battery energy storage, avionics, and propulsion systems. Computational fluid dynamics (CFD) simulations and surrogate modeling techniques were employed to develop a proxy model correlating formation parameters with lift and drag characteristics. Using this surrogate model, the formation parameters were optimized to minimize cruise power consumption. Energy simulations were subsequently conducted for both solo and formation flight scenarios. The results indicate that the optimized formation configuration achieved a 15% increase in maximum lift-to-drag ratio. Energy simulation results indicate that the endurance performance of SUAVs under formation flight is enhanced by 92.7%, 43.3%, and 18.8% at latitudes of 45° N, 50° N, and 60° N, respectively. These findings confirm the feasibility of using formation flight to enable sustained operation for small SUAVs. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Dynamics and Control of Biomimetic Robots)

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19 pages, 2873 KB

Open AccessArticle

High-Performance Sensorless Control of Induction Motors via ANFIS and NPC Inverter Topology

by Zina Boussada, Bassem Omri and Mouna Ben Hamed

Symmetry 2025, 17(11), 1996; https://doi.org/10.3390/sym17111996 - 18 Nov 2025

Viewed by 503

Abstract

This paper presents a high-performance sensorless control strategy for induction motors using an Adaptive Neuro-Fuzzy Inference System (ANFIS) for rotor speed estimation, eliminating the need for mechanical sensors. The ANFIS approach leverages stator voltages and currents, reducing costs and complexity. The motor is [...] Read more.

This paper presents a high-performance sensorless control strategy for induction motors using an Adaptive Neuro-Fuzzy Inference System (ANFIS) for rotor speed estimation, eliminating the need for mechanical sensors. The ANFIS approach leverages stator voltages and currents, reducing costs and complexity. The motor is controlled via Indirect Stator Field Orientation Control (ISFOC) with a three-level Neutral–Point–Clamped (NPC) inverter employing Space Vector Modulation (SVM). Symmetry in the motor’s magnetic structure and SVM’s switching patterns enhances control precision, stability, and efficiency while minimizing harmonic distortion. Simulation results validate the proposed ANFIS-based estimator’s superior performance compared to a MRAS-based Luenberger observer under various operating conditions, demonstrating accurate speed tracking and robustness against load disturbances. Full article

(This article belongs to the Section Engineering and Materials)

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27 pages, 17561 KB

Open AccessArticle

Symmetry-Inspired Design and Full-Coverage Path Planning for a Multi-Arm NDT Robot on a Reactor Pressure Vessel

by Maocheng Hong, Zhengyang Zhao, Jianxiang Jiang, Xiaoyang Zhao, Jingli Yan, Huaidong Chen and Xiaobing Zhang

Symmetry 2025, 17(11), 1995; https://doi.org/10.3390/sym17111995 - 18 Nov 2025

Viewed by 443

Abstract

Regular ultrasonic full-coverage inspection of reactor pressure vessels (RPVs) is critical to ensuring the safe operation of nuclear power plants. However, due to the extreme operating conditions and complex internal geometry of RPVs, most existing inspection technologies face significant challenges in achieving convenient [...] Read more.

Regular ultrasonic full-coverage inspection of reactor pressure vessels (RPVs) is critical to ensuring the safe operation of nuclear power plants. However, due to the extreme operating conditions and complex internal geometry of RPVs, most existing inspection technologies face significant challenges in achieving convenient and efficient full-coverage traversal detection. To address these limitations, this study proposes a novel nondestructive inspection robot equipped with four symmetrically arranged inspection arms for comprehensive RPV ultrasonic inspection. By considering the structural symmetry and motion characteristics of the inspection arms, a corresponding kinematic analysis is conducted, resulting in a precise kinematic model that enables real-time computation of both forward and inverse kinematic solutions with high accuracy. Furthermore, an adaptive full-coverage inspection method is developed by leveraging the vessel’s axisymmetric geometry and by partitioning the RPV into seven distinct detection zones, allowing the four inspection arms to independently complete inspections across the maximum number of zones, thereby significantly enhancing both detection coverage and operational efficiency. Experiments demonstrated the practical feasibility of the proposed robotic system and validated the effectiveness of the full-coverage inspection method. Full article

(This article belongs to the Section Engineering and Materials)

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28 pages, 9191 KB

Open AccessArticle

Intelligent Q&A System for Welding Processes Based on a Symmetric KG-DB Hybrid-RAG Strategy

by Shuxia Ye, Liwen Cai, Yongwei Zhang, Xiaoqi Xin, Bo Jiang and Liang Qi

Symmetry 2025, 17(11), 1994; https://doi.org/10.3390/sym17111994 - 18 Nov 2025

Viewed by 555

Abstract

This paper pioneers the use of the symmetrical Hybrid-RAG strategy in the ship welding process domain, addressing the problems of fragmented, unstructured knowledge storage, as well as the limitations of traditional Retrieval-Augmented Generation (RAG), particularly high retrieval noise and low accuracy when answering [...] Read more.

This paper pioneers the use of the symmetrical Hybrid-RAG strategy in the ship welding process domain, addressing the problems of fragmented, unstructured knowledge storage, as well as the limitations of traditional Retrieval-Augmented Generation (RAG), particularly high retrieval noise and low accuracy when answering complex procedural queries. This study proposes an intelligent three-stage symmetric “Generate–Retrieve–Generate” framework for the ship welding process (SWP-Chat), supported by dual retrieval engines: a Neo4j knowledge graph for symbolic reasoning and a vector database for semantic retrieval. Unlike approaches that rely solely on LLM-based process planning, SWP-Chat uses the LLM to generate a logical form, then executes Cypher queries on Neo4j, enabling transparent traceability, precise entity–relation constraints, and deterministic retrieval. Meanwhile, the vector channel supplements unstructured or contextual welding information to enhance semantic coverage. To further improve efficiency, principal component analysis (PCA) was employed for vector dimensionality reduction, reducing average retrieval latency by 31% while retaining more than 95% variance. In addition, an explainable structural–confidence fusion formula integrates evidence from both engines to produce auditable and trustworthy industrial responses. Experimental evaluation demonstrates that the framework achieves an F1 score of 79.35%, greatly surpassing typical RAG systems. Full article

(This article belongs to the Section Computer)

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12 pages, 290 KB

Open AccessArticle

A Broader Perspective on the Phenomenology of Quantum-Gravity-Induced Infrared/Ultraviolet Mixing

by Giovanni Amelino-Camelia

Symmetry 2025, 17(11), 1993; https://doi.org/10.3390/sym17111993 - 18 Nov 2025

Viewed by 324

Abstract

I revisit some arguments that motivate infrared/ultraviolet (IR/UV) mixing, a mechanism such that ultraviolet quantum-gravity structures produce novel features also in a far-infrared regime. On the conceptual side, I highlight in particular an apparently general connection between IR/UV mixing and departures from the [...] Read more.

I revisit some arguments that motivate infrared/ultraviolet (IR/UV) mixing, a mechanism such that ultraviolet quantum-gravity structures produce novel features also in a far-infrared regime. On the conceptual side, I highlight in particular an apparently general connection between IR/UV mixing and departures from the standard relativistic symmetries of classical spacetimes. In addition to its conceptual appeal, interest in IR/UV mixing has also been driven by the availability of some opportunities for experimental testing, and my main focus is on phenomenological models of IR/UV mixing that can provide guidance to the experimental efforts. While usually each formulation of IR/UV mixing is investigated within an isolated research program, some parts of my analysis point to possible connections among different formulations and with other quantum-gravity studies. Full article

(This article belongs to the Special Issue Lorentz Invariance Violation and Space–Time Symmetry Breaking)

50 pages, 1742 KB

Open AccessReview

A Review of Pavement Performance Deterioration Modeling: Influencing Factors and Techniques

by Benjamin G. Famewo and Mehdi Shokouhian

Symmetry 2025, 17(11), 1992; https://doi.org/10.3390/sym17111992 - 18 Nov 2025

Cited by 1 | Viewed by 2245

Abstract

Accurate modeling of pavement performance is vital to maintaining safe, reliable, and sustainable transportation infrastructure. This review synthesizes current approaches to pavement deterioration modeling, with emphasis on key influencing factors, performance indicators, and methodologies employed within Pavement Management Systems (PMS). Primary deterioration drivers, [...] Read more.

Accurate modeling of pavement performance is vital to maintaining safe, reliable, and sustainable transportation infrastructure. This review synthesizes current approaches to pavement deterioration modeling, with emphasis on key influencing factors, performance indicators, and methodologies employed within Pavement Management Systems (PMS). Primary deterioration drivers, including traffic loading and environmental stressors, are analyzed for their impact on degradation patterns. Performance indicators such as the Pavement Surface Evaluation and Rating (PASER), Pavement Condition Index (PCI), and International Roughness Index (IRI) are evaluated for their effectiveness in capturing pavement condition and guiding maintenance decisions. Modeling techniques are broadly categorized into deterministic, probabilistic, and intelligent (machine learning–based) frameworks to illustrate the evolution of predictive approaches. Across these approaches, the notion of symmetry can be interpreted as the balance and consistency achieved between model assumptions, input variables, and predicted pavement behavior, while asymmetry represents deviations caused by uncertainty, variability, and nonlinearity inherent in real-world conditions. Recognizing these symmetrical and asymmetrical relationships helps unify different modeling paradigms and provides insight into how each framework handles equilibrium between accuracy, complexity, and interpretability. The review also highlights persistent challenges in data availability, quality, and standardization. Notably, the increasing adoption of machine learning reflects its capacity to handle high-dimensional and spatiotemporal datasets. Recommendations are proposed to improve the robustness, scalability, and transparency of future deterioration models, thereby enhancing their role in data-driven, resilient, and cost-effective pavement management strategies. Full article

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

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13 pages, 1077 KB

Open AccessArticle

Fabry–Perot Spin Resonances in Rashba–Ferromagnet Hall Geometry Enabling Tunable Spin Currents

by Jinki Hong and Sangsu Kim

Symmetry 2025, 17(11), 1991; https://doi.org/10.3390/sym17111991 - 17 Nov 2025

Viewed by 334

Abstract

Spin–orbit interaction enables the generation and manipulation of spin currents without external magnetic fields, providing opportunities for spin–orbitronic devices. Here, we theoretically investigate a two-dimensional Rashba channel embedded in a Hall geometry with ferromagnetic probes. We demonstrate that symmetry breaking in this configuration [...] Read more.

Spin–orbit interaction enables the generation and manipulation of spin currents without external magnetic fields, providing opportunities for spin–orbitronic devices. Here, we theoretically investigate a two-dimensional Rashba channel embedded in a Hall geometry with ferromagnetic probes. We demonstrate that symmetry breaking in this configuration leads to experimentally accessible electrical signals, such as open-circuit voltages and short-circuit currents. By analyzing the mirror symmetry of the system, we identified the FM magnetization configurations that maximize these signals. These signals arise from two distinct mechanisms: the Edelstein spin density and spin interference generated by multiple reflections at the Rashba–ferromagnet interfaces. Importantly, the interference is governed solely by the spin-precessional phase, with orbital contributions canceled out. By tuning the channel width, the interference produces Fabry–Perot resonances that allow controllable enhancement of these electrical signals. The resulting Hall responses is well within the range of experimentally reported spin Hall angles, confirming their experimental feasibility. Our results highlight how coherent spin interference, combined with the Edelstein effect, provides a controllable pathway for spin current engineering. Full article

(This article belongs to the Section Physics)

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32 pages, 11603 KB

Open AccessArticle

Leveraging the Symmetry Between Active Dual-Steering-Wheel MPC and Passive Air Bearing for Ground-Based Satellite Hovering Tests

by Xiao Zhang, Zhen Zhao, Zainan Jiang, Zhigang Xu and Yonglin Tian

Symmetry 2025, 17(11), 1990; https://doi.org/10.3390/sym17111990 - 17 Nov 2025

Viewed by 394

Abstract

Satellite hovering missions involve an active propulsion phase for precise maneuvering and a subsequent passive dynamics phase wherein the satellite responds to external forces, such as from a manipulator. Therefore, a ground-testing method capable of seamlessly integrating these operational regimes is required. This [...] Read more.

Satellite hovering missions involve an active propulsion phase for precise maneuvering and a subsequent passive dynamics phase wherein the satellite responds to external forces, such as from a manipulator. Therefore, a ground-testing method capable of seamlessly integrating these operational regimes is required. This paper presents a novel methodology that leverages the symmetry between active wheel-driven control and passive air-bearing dynamics to establish a unified testing platform. A mathematical model is established for the dual independent steering-wheel drive system, and an error model for tracking both the translational (position) trajectory and the rotational (attitude) trajectory of the satellite during hovering is derived. Based on this, a Model Predictive Control (MPC) scheme is designed to generate optimal driving speeds and steering angles for the wheels, ensuring accurate trajectory tracking while explicitly adhering to their driving and steering constraints. Furthermore, our work involves the integrated design of a gravity-compensated platform and its steering wheels, incorporating design methods to enhance air-bearing safety and a seamless switching method to maintain test continuity by minimizing transient disturbances. Experiments demonstrate that this integrated platform delivers both high-precision satellite trajectory tracking and high-fidelity passive air-bearing micro-gravity simulation for the active and passive phases of a satellite hovering mission. Full article

(This article belongs to the Section Engineering and Materials)

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24 pages, 4016 KB

Open AccessArticle

Settlement Prediction of Preloading Method Based on SSA-BP Neural Network with Consideration of Asymmetric Settlement Behavior

by Xinye Wu, Zhiwei Wang, Haixu Duan, Yuxiang Gan, Shenghui Chen, Man Li, Xu Zhao and Enpu Xu

Symmetry 2025, 17(11), 1989; https://doi.org/10.3390/sym17111989 - 17 Nov 2025

Viewed by 422

Abstract

This study focuses on the East Channel Project (Xiang’an South Road—Airport Expressway Section). The project is in the South Port Harbor Bay area. The area has highly complex and asymmetrical geology. Construction faces multiple challenges: tight schedule, overlapping pipeline operations, and large-scale foundation [...] Read more.

This study focuses on the East Channel Project (Xiang’an South Road—Airport Expressway Section). The project is in the South Port Harbor Bay area. The area has highly complex and asymmetrical geology. Construction faces multiple challenges: tight schedule, overlapping pipeline operations, and large-scale foundation treatment needs. To tackle these, the project uses the plastic drainage board surcharge preloading method for ground improvement. This technique needs continuous settlement deformation monitoring. The monitoring aims to spot potential asymmetric trends and fix the best unloading time. Traditional settlement prediction methods have limits. So, this study develops an intelligent prediction model (SSA-BP). It combines the Sparrow Search Algorithm (SSA) with the BP neural network. The model uses SSA’s strong global search ability to optimize the BP network’s initial weights and thresholds. This effectively avoids local minima and improves prediction stability. Comparative experiments with other optimization algorithms (Particle Swarm Optimization PSO, Grey Wolf Optimizer GWO, and Differential Evolution DE) show that the SSA-BP model has better convergence accuracy and robustness. Field monitoring data validation indicates the model’s prediction error is stably between −3.4% and 3.2%. It surpasses traditional methods like the three-point and hyperbolic methods. The study’s key innovation is introducing an asymmetry-aware view. It analyzes settlement’s morphological evolution and predictability under surcharge preloading. The SSA-BP model can identify both symmetric and asymmetric deformation patterns well. It offers a new computational tool to understand asymmetry breaking in geotechnical systems. Moreover, the model can accurately predict settlement behavior in real time. This provides dynamic construction decision-making guidance and effective cost control. This research shows that intelligent algorithms have great potential. They can reveal complex geotechnical systems’ inherent laws and promote foundation engineering’s intelligentization. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Operations Research)

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23 pages, 4433 KB

Open AccessReview

Autonomous Multirotor UAV Docking and Charging: A Comprehensive Review of Systems, Mechanisms, and Emerging Technologies

by Alen Šćuric, Nino Krznar, Antonia Penđer, Ivan Štedul and Denis Kotarski

Symmetry 2025, 17(11), 1988; https://doi.org/10.3390/sym17111988 - 17 Nov 2025

Viewed by 3372

Abstract

Multirotor Unmanned Aerial Vehicles (UAVs), characterized by their inherently symmetrical propulsion configurations, are increasingly applied across diverse domains, yet their endurance remains fundamentally constrained by the high energy demand of flight. Autonomous docking and charging systems have emerged as practical solutions, enabling UAVs [...] Read more.

Multirotor Unmanned Aerial Vehicles (UAVs), characterized by their inherently symmetrical propulsion configurations, are increasingly applied across diverse domains, yet their endurance remains fundamentally constrained by the high energy demand of flight. Autonomous docking and charging systems have emerged as practical solutions, enabling UAVs to recharge or replace batteries without human intervention. This paper provides a structured review of current approaches, offering a systematic categorization of UAV docking platforms into fixed and mobile systems, followed by an analysis of positioning and landing strategies, charging mechanisms, and modular docking concepts. Advances in vision-based guidance and sensor fusion are highlighted as key enablers of precise and reliable autonomous recovery. Contact-based charging and wireless power transfer are compared, with their benefits and limitations outlined. In addition to charging solutions, the paper presents a dedicated review of mechanisms that enable automated battery swapping, increasingly recognized as a complementary pathway to extend mission duration. By synthesizing state-of-the-art research and implementations, this study identifies key technological trends, persisting challenges, and future directions toward scalable, fully autonomous ecosystems capable of long-duration operations. Full article

(This article belongs to the Special Issue Applications Based on Symmetry in Control Systems and Robotics)

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26 pages, 1323 KB

Open AccessArticle

Secure and Energy-Aware Cryptographic Framework for IoT-Enabled UAV Systems

by Dauriya Zhaxygulova, Maksim Iavich, Saule Rakhmetullina and Kuanysh Alipbayev

Symmetry 2025, 17(11), 1987; https://doi.org/10.3390/sym17111987 - 17 Nov 2025

Viewed by 809

Abstract

The rapid convergence of the Internet of Things (IoT), quantum computing, and artificial intelligence (AI) has amplified the urgency for lightweight yet resilient data protection mechanisms, particularly within unmanned aerial vehicles (UAV). Traditional cryptographic approaches, while mathematically secure, often fail to reconcile the [...] Read more.

The rapid convergence of the Internet of Things (IoT), quantum computing, and artificial intelligence (AI) has amplified the urgency for lightweight yet resilient data protection mechanisms, particularly within unmanned aerial vehicles (UAV). Traditional cryptographic approaches, while mathematically secure, often fail to reconcile the competing requirements of robustness, computational efficiency, and energy sustainability when deployed on resource-constrained platforms such as drones. To address this gap, this paper proposes a novel hybrid lightweight cryptographic model that strategically integrates symmetric and asymmetric primitives in a dual-layer design. The model leverages the efficiency of lightweight authenticated encryption for high-throughput data protection, while incorporating elliptic-curve and lattice-based key exchange mechanisms to ensure both forward secrecy and post-quantum resilience. Experimental evaluation demonstrates that the proposed scheme achieves superior performance compared to conventional methods, offering reduced computational overhead, lower energy consumption, and enhanced resistance to cyber threats. Crucially, the model maintains high levels of confidentiality, integrity, and authenticity while extending operational endurance, making it particularly well-suited for next-generation UAV operating within the broader IoT ecosystem. Full article

(This article belongs to the Section Mathematics)

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17 pages, 5065 KB

Open AccessArticle

Multi-Scale Investigation on Strength, Fracture Behavior, and Microstructure of Cemented Tailings Backfill Under Varying Mix Proportions

by Wenhai Liang, Haosen Wang, Jinsheng Xin, Liu Yang, Yunpeng Kou, Zaihai Wu and Baoshan Zhan

Symmetry 2025, 17(11), 1986; https://doi.org/10.3390/sym17111986 - 17 Nov 2025

Viewed by 444

Abstract

This study systematically investigates the mechanical behavior and failure mechanisms of cemented tailings backfill (CTB) prepared from classified and unclassified tailings across cement-to-tailings (C/T) ratios of 1:8, 1:6, and 1:4 and slurry concentrations of 60%, 65%, and 70%. Specimens were evaluated by uniaxial [...] Read more.

This study systematically investigates the mechanical behavior and failure mechanisms of cemented tailings backfill (CTB) prepared from classified and unclassified tailings across cement-to-tailings (C/T) ratios of 1:8, 1:6, and 1:4 and slurry concentrations of 60%, 65%, and 70%. Specimens were evaluated by uniaxial compression (UCS) tests, failure mode observation, and SEM. The results show that increasing C/T and concentration markedly enhances compressive strength: the maximum 28-day UCS reached 5.38 MPa under unclassified tailings, C/T = 1:4, 70%. Moreover, unclassified tailings exhibited a later-age strength gain of 244.9%, far exceeding the 58.5% observed for classified tailings. Failure modes evolve from brittle splitting to shear-dominated behavior as mixes densify, reflecting a transition from near-symmetric early-age stress/microstructural fields to asymmetric localized failure (symmetry breaking). SEM reveals that higher binder ratios and concentrations promote C-(A)-S-H-dominated gel formation, improved ITZ continuity, and reduced apparent porosity, thereby restraining microcrack initiation and coalescence. These findings elucidate the micro-to-macro mechanisms governing CTB strength and failure and provide field-relevant guidance for mix optimization and safe, efficient underground backfilling. Full article

(This article belongs to the Section Engineering and Materials)

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18 pages, 1493 KB

Open AccessArticle

Hamel’s Formalism and Variational Integrators of the Hydrodynamic Chaplygin Sleigh

by Li-Li Xia and Jun-Hua Zhang

Symmetry 2025, 17(11), 1985; https://doi.org/10.3390/sym17111985 - 17 Nov 2025

Viewed by 385

Abstract

Modeling of dynamic systems with nonholonomic constraints usually involves constraint multipliers. Consequently, the dynamic equations in the laboratory coordinate system have a complex form, and as a result, the corresponding numerical algorithms need to be improved in terms of both efficiency and accuracy. [...] Read more.

Modeling of dynamic systems with nonholonomic constraints usually involves constraint multipliers. Consequently, the dynamic equations in the laboratory coordinate system have a complex form, and as a result, the corresponding numerical algorithms need to be improved in terms of both efficiency and accuracy. This paper addresses establishing the mathematical model of the hydrodynamic sleigh in the Hamel framework. Firstly, the Lie symmetry and the Noether theorem conserved quantities of classic Chaplygin sleigh in which the inertial frame is reviewed. Based on the symmetries and the nonholonomic constraints, the frame of the sleigh can be directly realized in the algebraic space. Based on the mutual coupling mechanism between the fluid and the sleigh in a potential flow environment, the reduced equations in the moving frame are proposed in nonintegrable constraint distributions. The corresponding Hamel integrator is constructed based on the discrete variational principle. For the sleigh model in potential flow, the Hamel integrator is used to verify the feasibility of parameter control based on rotation angles and mass distribution, and to obtain the dynamic characteristics of the sleigh blade with both a rotational offset and translational offset. Numerical results indicate that the modeling method in the Hamel framework provides a more concise and efficient approach for exploring the dynamic behavior of the hydrodynamic sleigh. Full article

(This article belongs to the Section Physics)

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21 pages, 391 KB

Open AccessArticle

Dirac Factorization, Partial/Ordinary Differential Equations and Fractional Calculus

by Giuseppe Dattoli, Emanuele Di Palma and Alessandro Curcio

Symmetry 2025, 17(11), 1984; https://doi.org/10.3390/sym17111984 - 17 Nov 2025

Viewed by 371

Abstract

The Dirac factorization method (DFM) is the key feature of the present investigation. It is addressed to the relevant use in diverse fields of research, regarding, e.g., the handling of pseudo-operators arising in quantum mechanics and fractional calculus. We explore the role that [...] Read more.

The Dirac factorization method (DFM) is the key feature of the present investigation. It is addressed to the relevant use in diverse fields of research, regarding, e.g., the handling of pseudo-operators arising in quantum mechanics and fractional calculus. We explore the role that the factorization plays in a classical context too, including the study of d’Alembert and Laplace equations. Its strong entanglement with the Cauchy–Riemann conditions and with complex analysis is discussed. We complete our study with the extension of DFM to second-order ordinary differential equations, to classical analytical mechanics, and to higher-order partial differential equations. Full article

(This article belongs to the Special Issue Symmetry in Beam–Plasma Physics)

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