Symmetry

35 pages, 5154 KiB

Open AccessArticle

A Monte Carlo Simulation Framework for Evaluating the Robustness and Applicability of Settlement Prediction Models in High-Speed Railway Soft Foundations

by Zhenyu Liu, Liyang Wang, Taifeng Li, Huiqin Guo, Feng Chen, Youming Zhao, Qianli Zhang and Tengfei Wang

Symmetry 2025, 17(7), 1113; https://doi.org/10.3390/sym17071113 (registering DOI) - 10 Jul 2025

Abstract

Accurate settlement prediction for high-speed railway (HSR) soft foundations remains challenging due to the irregular and dynamic nature of real-world monitoring data, often represented as non-equidistant and non-stationary time series (NENSTS). Existing empirical models lack clear applicability criteria under such conditions, resulting in [...] Read more.

Accurate settlement prediction for high-speed railway (HSR) soft foundations remains challenging due to the irregular and dynamic nature of real-world monitoring data, often represented as non-equidistant and non-stationary time series (NENSTS). Existing empirical models lack clear applicability criteria under such conditions, resulting in subjective model selection. This study introduces a Monte Carlo-based evaluation framework that integrates data-driven simulation with geotechnical principles, embedding the concept of symmetry across both modeling and assessment stages. Equivalent permeability coefficients (EPCs) are used to normalize soil consolidation behavior, enabling the generation of a large, statistically robust dataset. Four empirical settlement prediction models—Hyperbolic, Exponential, Asaoka, and Hoshino—are systematically analyzed for sensitivity to temporal features and resistance to stochastic noise. A symmetry-aware comprehensive evaluation index (CEI), constructed via a robust entropy weight method (REWM), balances multiple performance metrics to ensure objective comparison. Results reveal that while settlement behavior evolves asymmetrically with respect to EPCs over time, a symmetrical structure emerges in model suitability across distinct EPC intervals: the Asaoka method performs best under low-permeability conditions (EPC ≤ 0.03 m/d), Hoshino excels in intermediate ranges (0.03 < EPC ≤ 0.7 m/d), and the Exponential model dominates in highly permeable soils (EPC > 0.7 m/d). This framework not only quantifies model robustness under complex data conditions but also formalizes the notion of symmetrical applicability, offering a structured path toward intelligent, adaptive settlement prediction in HSR subgrade engineering. Full article

(This article belongs to the Section Engineering and Materials)

22 pages, 323 KiB

Open AccessArticle

A System of Parabolic Laplacian Equations That Are Interrelated and Radial Symmetry of Solutions

by Xingyu Liu

Symmetry 2025, 17(7), 1112; https://doi.org/10.3390/sym17071112 (registering DOI) - 10 Jul 2025

Abstract

We utilize the moving planes technique to prove the radial symmetry along with the monotonic characteristics of solutions for a system of parabolic Laplacian equations. In this system, the solutions of the two equations are interdependent, with the solution of one equation depending [...] Read more.

We utilize the moving planes technique to prove the radial symmetry along with the monotonic characteristics of solutions for a system of parabolic Laplacian equations. In this system, the solutions of the two equations are interdependent, with the solution of one equation depending on the function of the other. By use of the maximal regularity theory that has been established for fractional parabolic equations, we ensure the solvability of these systems. Our initial step is to formulate a narrow region principle within a parabolic cylinder. This principle serves as a theoretical basis for implementing the moving planes method. Following this, we focus our attention on parabolic systems with fractional Laplacian equations and deduce that the solutions are radial symmetric and monotonic when restricted to the unit ball. Full article

(This article belongs to the Special Issue Advance in Functional Equations, Second Edition)

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23 pages, 4119 KiB

Open AccessArticle

Cross-Scenario Interpretable Prediction of Coal Mine Water Inrush Probability: An Integrated Approach Driven by Gaussian Mixture Modeling with Manifold Learning and Metaheuristic Optimization

by Qiushuang Zheng and Changfeng Wang

Symmetry 2025, 17(7), 1111; https://doi.org/10.3390/sym17071111 (registering DOI) - 10 Jul 2025

Abstract

Predicting water inrush in coal mines faces significant challenges due to limited data, model generalization, and a lack of interpretability. Current approaches often neglect the inherent geometrical symmetries and structured patterns within the complex hydrological parameter space, rely on local parameter optimization, and [...] Read more.

Predicting water inrush in coal mines faces significant challenges due to limited data, model generalization, and a lack of interpretability. Current approaches often neglect the inherent geometrical symmetries and structured patterns within the complex hydrological parameter space, rely on local parameter optimization, and struggle with interpretability, leading to insufficient predictive accuracy and engineering applicability under complex geological conditions. This study addresses these limitations by integrating Gaussian mixture modeling (GMM), manifold learning, and data augmentation to effectively capture multimodal hydrological data distributions and reveal their intrinsic symmetrical configurations and manifold structures, thereby reducing feature dimensionality. We then apply a whale optimization algorithm (WOA)-enhanced XGBoost model to forecast water inrush probabilities. Our model achieved an R² of 0.92, demonstrating a greater than 60% error reduction across various metrics. Validation at the Yangcheng Coal Mine confirmed that this balanced approach significantly enhances predictive accuracy, interpretability, and cross-scenario applicability. The synergy between high accuracy and transparency provides decision makers with reliable risk insights, enabling bidirectional validation with geological mechanisms and supporting the implementation of targeted, proactive safety measures. Full article

(This article belongs to the Section Mathematics)

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18 pages, 3719 KiB

Open AccessArticle

Energy-Efficient Bipedal Locomotion Through Parallel Actuation of Hip and Ankle Joints

by Prabhu Manoharan and Karthikeyan Palanisamy

Symmetry 2025, 17(7), 1110; https://doi.org/10.3390/sym17071110 (registering DOI) - 10 Jul 2025

Abstract

Achieving energy-efficient, human-like gait remains a major challenge in bipedal humanoid robotics, as traditional serial actuation architectures often lead to high instantaneous power peaks and uneven load distribution. This study addresses the lack of research on how mechanical symmetry, achieved through parallel actuation, [...] Read more.

Achieving energy-efficient, human-like gait remains a major challenge in bipedal humanoid robotics, as traditional serial actuation architectures often lead to high instantaneous power peaks and uneven load distribution. This study addresses the lack of research on how mechanical symmetry, achieved through parallel actuation, can improve power management in lower-limb joints. We developed a 14-degree-of-freedom (DOF) hip-sized bipedal robot model and conducted simulations comparing a conventional serial configuration—using single-DOF rotary actuators—with a novel parallel configuration that employs paired linear actuators at the hip pitch, hip roll, ankle pitch, and ankle roll joints. Simulation results over a standardized walking cycle show that the parallel configuration reduces peak hip-pitch power by 80.4% and peak ankle-pitch power by 53.5%. These findings demonstrate that incorporating actuator symmetry through parallel joint design significantly reduces actuator stress, improves load sharing, and enhances overall energy efficiency in bipedal locomotion. Full article

(This article belongs to the Section Engineering and Materials)

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32 pages, 2917 KiB

Open AccessArticle

Self-Adapting CPU Scheduling for Mixed Database Workloads via Hierarchical Deep Reinforcement Learning

by Suchuan Xing, Yihan Wang and Wenhe Liu

Symmetry 2025, 17(7), 1109; https://doi.org/10.3390/sym17071109 (registering DOI) - 10 Jul 2025

Abstract

Modern database systems require autonomous CPU scheduling frameworks that dynamically optimize resource allocation across heterogeneous workloads while maintaining strict performance guarantees. We present a novel hierarchical deep reinforcement learning framework augmented with graph neural networks to address CPU scheduling challenges in mixed database [...] Read more.

Modern database systems require autonomous CPU scheduling frameworks that dynamically optimize resource allocation across heterogeneous workloads while maintaining strict performance guarantees. We present a novel hierarchical deep reinforcement learning framework augmented with graph neural networks to address CPU scheduling challenges in mixed database environments comprising Online Transaction Processing (OLTP), Online Analytical Processing (OLAP), vector processing, and background maintenance workloads. Our approach introduces three key innovations: first, a symmetric two-tier control architecture where a meta-controller allocates CPU budgets across workload categories using policy gradient methods while specialized sub-controllers optimize process-level resource allocation through continuous action spaces; second, graph neural network-based dependency modeling that captures complex inter-process relationships and communication patterns while preserving inherent symmetries in database architectures; and third, meta-learning integration with curiosity-driven exploration enabling rapid adaptation to previously unseen workload patterns without extensive retraining. The framework incorporates a multi-objective reward function balancing Service Level Objective (SLO) adherence, resource efficiency, symmetric fairness metrics, and system stability. Experimental evaluation through high-fidelity digital twin simulation and production deployment demonstrates substantial performance improvements: 43.5% reduction in p99 latency violations for OLTP workloads and 27.6% improvement in overall CPU utilization, with successful scaling to 10,000 concurrent processes maintaining sub-3% scheduling overhead. This work represents a significant advancement toward truly autonomous database resource management, establishing a foundation for next-generation self-optimizing database systems with implications extending to broader orchestration challenges in cloud-native architectures. Full article

(This article belongs to the Section Computer)

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30 pages, 34072 KiB

Open AccessArticle

ARE-PaLED: Augmented Reality-Enhanced Patch-Level Explainable Deep Learning System for Alzheimer’s Disease Diagnosis from 3D Brain sMRI

by Chitrakala S and Bharathi U

Symmetry 2025, 17(7), 1108; https://doi.org/10.3390/sym17071108 - 10 Jul 2025

Abstract

Structural magnetic resonance imaging (sMRI) is a vital tool for diagnosing neurological brain diseases. However, sMRI scans often show significant structural changes only in limited brain regions due to localised atrophy, making the identification of discriminative features a key challenge. Importantly, the human [...] Read more.

Structural magnetic resonance imaging (sMRI) is a vital tool for diagnosing neurological brain diseases. However, sMRI scans often show significant structural changes only in limited brain regions due to localised atrophy, making the identification of discriminative features a key challenge. Importantly, the human brain exhibits inherent bilateral symmetry, and deviations from this symmetry—such as asymmetric atrophy—are strong indicators of early Alzheimer’s disease (AD). Patch-based methods help capture local brain changes for early AD diagnosis, but they often struggle with fixed-size limitations, potentially missing subtle asymmetries or broader contextual cues. To address these limitations, we propose a novel augmented reality (AR)-enhanced patch-level explainable deep learning (ARE-PaLED) system. It includes an adaptive multi-scale patch extraction network (AMPEN) to adjust patch sizes based on anatomical characteristics and spatial context, as well as an informative patch selection algorithm (IPSA) to identify discriminative patches, including those reflecting asymmetry patterns associated with AD; additionally, an AR module is proposed for future immersive explainability, complementing the patch-level interpretation framework. Evaluated on 1862 subjects from the ADNI and AIBL datasets, the framework achieved an accuracy of 92.5% (AD vs. NC) and 85.9% (AD vs. MCI). The proposed ARE-PaLED demonstrates potential as an interpretable and immersive diagnostic aid for sMRI-based AD diagnosis, supporting the interpretation of model predictions for AD diagnosis. Full article

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23 pages, 1501 KiB

Open AccessArticle

Special Basis for Efficient Numerical Solutions of Differential Equations: Application to the Energy Transfer Equation

by Fahir Talay Akyildiz and Fehaid Salem Alshammari

Symmetry 2025, 17(7), 1107; https://doi.org/10.3390/sym17071107 - 9 Jul 2025

Abstract

We introduce a novel family of compactly supported basis functions, termed Legendre Delta-Shaped Functions (LDSFs), constructed using the eigenfunctions of the Legendre differential equation. We begin by proving that LDSFs form a basis for a Haar space. We then demonstrate that interpolation using [...] Read more.

We introduce a novel family of compactly supported basis functions, termed Legendre Delta-Shaped Functions (LDSFs), constructed using the eigenfunctions of the Legendre differential equation. We begin by proving that LDSFs form a basis for a Haar space. We then demonstrate that interpolation using classical Legendre polynomials is a special case of interpolation with the proposed Legendre Delta-Shaped Basis Functions (LDSBFs). To illustrate the potential of LDSBFs, we apply the corresponding series to approximate a rectangular pulse. The results reveal that Gibbs oscillations decay rapidly, resulting in significantly improved accuracy across smooth regions. This example underscores the effectiveness and novelty of our approach. Furthermore, LDSBFs are employed within the collocation framework to solve Poisson-type equations and systems of nonlinear differential equations arising in energy transfer problems. We also derive new error bounds for interpolation polynomials in a special case, expressed in both the discrete (L₂) norm and the Sobolev (H_p) norm. To validate the proposed method, we compare our results with those obtained using the Legendre pseudospectral method. Numerical experiments confirm that our approach is accurate, efficient, and highly competitive with existing techniques. Full article

40 pages, 5065 KiB

Open AccessFeature PaperReview

Electroexcitation of Nucleon Resonances and Emergence of Hadron Mass

by Patrick Achenbach, Daniel S. Carman, Ralf W. Gothe, Kyungseon Joo, Victor I. Mokeev and Craig D. Roberts

Symmetry 2025, 17(7), 1106; https://doi.org/10.3390/sym17071106 (registering DOI) - 9 Jul 2025

Abstract

Developing an understanding of phenomena driven by the emergence of hadron mass (EHM) is one of the most challenging problems in the Standard Model. This discussion focuses on the impact of results on nucleon resonance (

N^{*}

) electroexcitation amplitudes (or [...] Read more.

Developing an understanding of phenomena driven by the emergence of hadron mass (EHM) is one of the most challenging problems in the Standard Model. This discussion focuses on the impact of results on nucleon resonance (

N^{*}

) electroexcitation amplitudes (or

γ_{v} p N^{*}

electrocouplings) obtained from experiments during the 6 GeV era in Hall B at Jefferson Lab on understanding EHM. Analyzed using continuum Schwinger function methods (CSMs), these results have revealed new pathways for the elucidation of EHM. A good description of the

Δ (1232) 3 / 2^{+}

,

N (1440) 1 / 2^{+}

, and

Δ (1600) 3 / 2^{+}

electrocouplings, achieved by CSM analyses that express a realistic dressed quark mass function, sheds light on the strong interaction dynamics underlying EHM. Extensions to

N^{*}

studies for higher-mass states are outlined, as well as experimental results anticipated in the 12 GeV era at Jefferson Lab and those that would be enabled by a further increase in the beam energy to 22 GeV. Full article

(This article belongs to the Special Issue The Symmetry of QCD Matter and Functional QCD Approaches)

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22 pages, 2171 KiB

Open AccessArticle

A Multi-Objective Method for Enhancing the Seismic Resilience of Urban Water Distribution Networks

by Li Long, Ziang Pan, Huaping Yang, Yong Yang and Feiyu Liu

Symmetry 2025, 17(7), 1105; https://doi.org/10.3390/sym17071105 - 9 Jul 2025

Abstract

Enhancing the seismic resilience of urban water distribution networks (WDNs) requires the improvement of both earthquake resistance and rapid recovery capabilities within the system. This paper proposes a multi-objective method to enhance the seismic resilience of the WDNs, focusing on system restoration capabilities [...] Read more.

Enhancing the seismic resilience of urban water distribution networks (WDNs) requires the improvement of both earthquake resistance and rapid recovery capabilities within the system. This paper proposes a multi-objective method to enhance the seismic resilience of the WDNs, focusing on system restoration capabilities while comprehensively considering the hydraulic recovery index, maintenance time, and maintenance cost. The method utilizes a random simulation approach to generate various damage scenarios for the WDN, considering pipe leakage, pipe bursts, and variations in node flow resulting from changes in water pressure. It characterizes the functions of the WDN through hydraulic service satisfaction and quantifies system resilience using a performance response function. Additionally, it determines the optimal dispatch strategy for emergency repair teams and the optimal emergency repair sequence for earthquake-damaged networks using a genetic algorithm. Furthermore, a comprehensive computational platform has been developed to systematically analyze and optimize seismic resilience strategies for WDNs. The feasibility of the proposed method is demonstrated through an example involving the WDN in Xi’an City. The results indicate that the single-objective seismic resilience improvement method based on the hydraulic recovery index is the most effective for enhancing the seismic resilience of the WDN. In contrast, the multi-objective method proposed in this article reduces repair time by 17.9% and repair costs by 3.4%, while only resulting in a 0.2% decrease in the seismic resilience of the WDN. This method demonstrates the most favorable comprehensive restoration effect, and the success of our method in achieving a symmetrically balanced restoration outcome demonstrates its value. The proposed methodology and software can provide both theoretical frameworks and technical support for urban WDN administrators. Full article

(This article belongs to the Section Engineering and Materials)

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20 pages, 2516 KiB

Open AccessArticle

Visual Attention Fusion Network (VAFNet): Bridging Bottom-Up and Top-Down Features in Infrared and Visible Image Fusion

by Yaochen Liu, Yunke Wang and Zixuan Jing

Symmetry 2025, 17(7), 1104; https://doi.org/10.3390/sym17071104 - 9 Jul 2025

Abstract

Infrared and visible image fusion aims to integrate useful information from the source image to obtain a fused image that not only has excellent visual perception but also promotes the performance of the subsequent object detection task. However, due to the asymmetry between [...] Read more.

Infrared and visible image fusion aims to integrate useful information from the source image to obtain a fused image that not only has excellent visual perception but also promotes the performance of the subsequent object detection task. However, due to the asymmetry between image fusion and object detection tasks, obtaining superior visual effects while facilitating object detection tasks remains challenging in real-world applications. Addressing this issue, we propose a novel visual attention fusion network for infrared and visible image fusion (VAFNet), which can bridge bottom-up and top-down features to achieve high-quality visual perception while improving the performance of object detection tasks. The core idea is that bottom-up visual attention is utilized to extract multi-layer bottom-up features for ensuring superior visual perception, while top-down visual attention determines object attention signals related to object detection tasks. Then, a bidirectional attention integration mechanism is designed to naturally integrate two forms of attention into the fused image. Experiments on public and collection datasets demonstrate that VAFNet not only outperforms seven state-of-the-art (SOTA) fusion methods in qualitative and quantitative evaluation but also has advantages in facilitating object detection tasks. Full article

(This article belongs to the Special Issue Symmetry in Next-Generation Intelligent Information Technologies)

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27 pages, 392 KiB

Open AccessArticle

Non-Autonomous Soliton Hierarchies

by Maciej Błaszak, Krzysztof Marciniak and Błażej M. Szablikowski

Symmetry 2025, 17(7), 1103; https://doi.org/10.3390/sym17071103 - 9 Jul 2025

Abstract

A formalism for the systematic construction of integrable non-autonomous deformations of soliton hierarchies is presented. The theory is formulated as an initial value problem (IVP) for an associated Frobenius integrability condition on a Lie algebra. It is shown that this IVP has a [...] Read more.

A formalism for the systematic construction of integrable non-autonomous deformations of soliton hierarchies is presented. The theory is formulated as an initial value problem (IVP) for an associated Frobenius integrability condition on a Lie algebra. It is shown that this IVP has a formal solution, and within the framework of two particular subalgebras of the hereditary Lie algebra, the explicit forms of this formal solution are derived. Finally, this formalism is applied to the Korteveg-de Vries, dispersive water waves and Ablowitz–Kaup–Newell–Segur soliton hierarchies. The zero-curvature representations and Hamiltonian structures of the considered non-autonomous soliton hierarchies are also provided. Full article

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

23 pages, 5304 KiB

Open AccessArticle

Improvement and Optimization of Underwater Image Target Detection Accuracy Based on YOLOv8

by Yisong Sun, Wei Chen, Qixin Wang, Tianzhong Fang and Xinyi Liu

Symmetry 2025, 17(7), 1102; https://doi.org/10.3390/sym17071102 - 9 Jul 2025

Abstract

The ocean encompasses the majority of the Earth’s surface and harbors substantial energy resources. Nevertheless, the intricate and asymmetrically distributed underwater environment renders existing target detection performance inadequate. This paper presents an enhanced YOLOv8s approach for underwater robot object detection to address issues [...] Read more.

The ocean encompasses the majority of the Earth’s surface and harbors substantial energy resources. Nevertheless, the intricate and asymmetrically distributed underwater environment renders existing target detection performance inadequate. This paper presents an enhanced YOLOv8s approach for underwater robot object detection to address issues of subpar image quality and low recognition accuracy. The precise measures are enumerated as follows: initially, to address the issue of model parameters, we optimized the ninth convolutional layer by substituting certain conventional convolutions with adaptive deformable convolution DCN v4. This modification aims to more effectively capture the deformation and intricate features of underwater targets, while simultaneously decreasing the parameter count and enhancing the model’s ability to manage the deformation challenges presented by underwater images. Furthermore, the Triplet Attention module is implemented to augment the model’s capacity for detecting multi-scale targets. The integration of low-level superficial features with high-level semantic features enhances the feature expression capability. The original CIoU loss function was ultimately substituted with Shape IoU, enhancing the model’s performance. In the underwater robot grasping experiment, the system shows particular robustness in handling radial symmetry in marine organisms and reflection symmetry in artificial structures. The enhanced algorithm attained a mean Average Precision (mAP) of 87.6%, surpassing the original YOLOv8s model by 3.4%, resulting in a marked enhancement of the object detection model’s performance and fulfilling the real-time detection criteria for underwater robots. Full article

(This article belongs to the Special Issue Computer Vision, Pattern Recognition, Machine Learning, and Symmetry, 2nd Edition)

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20 pages, 922 KiB

Open AccessArticle

Distributed Time Delay Models: An Alternative to Fractional Calculus-Based Models for Fractional Behavior Modeling

by Jocelyn Sabatier

Symmetry 2025, 17(7), 1101; https://doi.org/10.3390/sym17071101 - 9 Jul 2025

Abstract

This paper illustrates that distributed time delay models can exhibit fractional behaviors, addressing the limitations of fractional calculus-based models outlined in the introduction. Given the extensive results generated by these models, they present a compelling alternative to fractional models. The demonstration is done [...] Read more.

This paper illustrates that distributed time delay models can exhibit fractional behaviors, addressing the limitations of fractional calculus-based models outlined in the introduction. Given the extensive results generated by these models, they present a compelling alternative to fractional models. The demonstration is done both in discrete time and in continuous time. The two cases yield fractional behavior within a defined time/frequency range. To conclude and using two examples, the article highlights that modeling fractional behaviors using distributed delay systems allows for coherent physical interpretations, which a fractional model representation struggles to achieve. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

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18 pages, 301 KiB

Open AccessArticle

Casorati-Type Inequalities for Submanifolds in S-Space Forms with Semi-Symmetric Connection

by Md Aquib

Symmetry 2025, 17(7), 1100; https://doi.org/10.3390/sym17071100 - 9 Jul 2025

Abstract

The primary aim of this paper is to establish two sharp geometric inequalities concerning submanifolds of S-space forms equipped with semi-symmetric metric connections (SSMCs). Specifically, we derive new inequalities involving the generalized normalized

δ

-Casorati curvatures [...] Read more.

The primary aim of this paper is to establish two sharp geometric inequalities concerning submanifolds of S-space forms equipped with semi-symmetric metric connections (SSMCs). Specifically, we derive new inequalities involving the generalized normalized

δ

-Casorati curvatures

δ_{c} (t; q_{1} + q_{2} - 1)

and

{\hat{δ}}_{c} (t; q_{1} + q_{2} - 1)

for bi-slant submanifolds. The cases in which equality holds are thoroughly examined, offering a deeper understanding of the geometric structure underlying such submanifolds. In addition, we present several immediate applications that highlight the relevance of our findings, and we support the article with illustrative examples. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology, 4th Edition)

21 pages, 2471 KiB

Open AccessArticle

Attention-Based Mask R-CNN Enhancement for Infrared Image Target Segmentation

by Liang Wang and Kan Ren

Symmetry 2025, 17(7), 1099; https://doi.org/10.3390/sym17071099 - 9 Jul 2025

Abstract

Image segmentation is an important method in the field of image processing, while infrared (IR) image segmentation is one of the challenges in this field due to the unique characteristics of IR data. Infrared imaging utilizes the infrared radiation emitted by objects to [...] Read more.

Image segmentation is an important method in the field of image processing, while infrared (IR) image segmentation is one of the challenges in this field due to the unique characteristics of IR data. Infrared imaging utilizes the infrared radiation emitted by objects to produce images, which can supplement the performance of visible-light images under adverse lighting conditions to some extent. However, the low spatial resolution and limited texture details in IR images hinder the achievement of high-precision segmentation. To address these issues, an attention mechanism based on symmetrical cross-channel interaction—motivated by symmetry principles in computer vision—was integrated into a Mask Region-Based Convolutional Neural Network (Mask R-CNN) framework. A Bottleneck-enhanced Squeeze-and-Attention (BNSA) module was incorporated into the backbone network, and novel loss functions were designed for both the bounding box (Bbox) regression and mask prediction branches to enhance segmentation performance. Furthermore, a dedicated infrared image dataset was constructed to validate the proposed method. The experimental results demonstrate that the optimized model achieves higher segmentation accuracy and better segmentation performance compared to the original network and other mainstream segmentation models on our dataset, demonstrating how symmetrical design principles can effectively improve complex vision tasks. Full article

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

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21 pages, 7528 KiB

Open AccessArticle

A Fine-Tuning Method via Adaptive Symmetric Fusion and Multi-Graph Aggregation for Human Pose Estimation

by Yinliang Shi, Zhaonian Liu, Bin Jiang, Tianqi Dai and Yuanfeng Lian

Symmetry 2025, 17(7), 1098; https://doi.org/10.3390/sym17071098 - 9 Jul 2025

Abstract

Human Pose Estimation (HPE) aims to accurately locate the positions of human key points in images or videos. However, the performance of HPE is often significantly reduced in practical application scenarios due to environmental interference. To address this challenge, we propose a ladder [...] Read more.

Human Pose Estimation (HPE) aims to accurately locate the positions of human key points in images or videos. However, the performance of HPE is often significantly reduced in practical application scenarios due to environmental interference. To address this challenge, we propose a ladder side-tuning method for the Vision Transformer (ViT) pre-trained model based on multi-path feature fusion to improve the accuracy of HPE in highly interfering environments. First, we extract the global features, frequency features and multi-scale spatial features through the ViT pre-trained model, the discrete wavelet convolutional network and the atrous spatial pyramid pooling network (ASPP). By comprehensively capturing the information of the human body and the environment, the ability of the model to analyze local details, textures, and spatial information is enhanced. In order to efficiently fuse these features, we devise an adaptive symmetric feature fusion strategy, which dynamically adjusts the intensity of feature fusion according to the similarity among features to achieve the optimal fusion effect. Finally, a multi-graph feature aggregation method is developed. We construct graph structures of different features and deeply explore the subtle differences among the features based on the dual fusion mechanism of points and edges to ensure the information integrity. The experimental results demonstrate that our method achieves 4.3% and 4.2% improvements in the AP metric on the MS COCO dataset and a custom high-interference dataset, respectively, compared with the HRNet. This highlights its superiority for human pose estimation tasks in both general and interfering environments. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Computer Vision and Graphics)

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22 pages, 2009 KiB

Open AccessArticle

Transient Analysis of a Continuous-Service Markovian Queueing Model with Offline and Online Customers

by Ramupillai Sudhesh, Paulsamy Balakrishnan and Ratchaga Dass Sebasthi Priya

Symmetry 2025, 17(7), 1097; https://doi.org/10.3390/sym17071097 - 9 Jul 2025

Abstract

This study examines a single-server Markovian queueing system featuring continuous service and an infinite number of customers at both ends—namely, offline and online clients. Offline customers are conventional clients who arrive at the system following a Poisson process, while online customers are assumed [...] Read more.

This study examines a single-server Markovian queueing system featuring continuous service and an infinite number of customers at both ends—namely, offline and online clients. Offline customers are conventional clients who arrive at the system following a Poisson process, while online customers are assumed to be endlessly present in the system. All service times are exponentially and identically distributed and independent. Utilizing generating functions and Laplace transform techniques, this study derives exact analytical expressions for the system size probabilities in both transient and steady states. Furthermore, it evaluates key performance measures for each state and provides graphical representations to illustrate the system’s dynamics, thereby enriching the understanding of its operational behavior. This work contributes to the advancement of priority-based queueing models and proposes a novel framework applicable to hybrid service architectures in contemporary digital ecosystems. Full article

(This article belongs to the Section Mathematics)

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15 pages, 295 KiB

Open AccessArticle

Neutrosophic Quadruple Metric Spaces

by Memet Şahin and Arif Sarıoğlan

Symmetry 2025, 17(7), 1096; https://doi.org/10.3390/sym17071096 - 8 Jul 2025

Abstract

Instead of measuring the distance between two points with a positive real number, determining the degree to which the distance between these two points is close, not close, or uncertain allows for more detailed measurement. Recently, researchers have overcome this grading problem by [...] Read more.

Instead of measuring the distance between two points with a positive real number, determining the degree to which the distance between these two points is close, not close, or uncertain allows for more detailed measurement. Recently, researchers have overcome this grading problem by using probability distribution functions, along with fuzzy, intuitionistic fuzzy, and neutrosophic sets. This study pioneers neutrosophic quadruple metric spaces as a powerful new tool for quantifying distances under complex, multi-dimensional uncertainty. It provides a comprehensive mathematical structure, including topology, convergence theory, and completeness, and handles both symmetric and asymmetric cases, generalising previous neutrosophic metric results. For this purpose, neutrosophic quadruple metric spaces were derived from neutrosophic metric spaces in order to better model situations involving uncertainty. Also, we generalised the findings obtained with the neutrosophic metric to the quadruple neutrosophic metric. Full article

(This article belongs to the Special Issue Theory and Applications on the Recent Extensions of Ordinary Fuzzy Sets)

20 pages, 49600 KiB

Open AccessArticle

An Improved Symmetric Network with Feature Difference and Receptive Field for Change Detection

by Botao Zhang, Yixuan Wang, Jia Lu and Qin Wang

Symmetry 2025, 17(7), 1095; https://doi.org/10.3390/sym17071095 - 8 Jul 2025

Abstract

Change detection (CD) is essential for Earth observation tasks, as it identifies alterations in specific geographic areas over time. The advancement of deep learning has significantly improved the accuracy of CD. However, encoder–decoder architectures often struggle to effectively capture temporal differences. Encoders may [...] Read more.

Change detection (CD) is essential for Earth observation tasks, as it identifies alterations in specific geographic areas over time. The advancement of deep learning has significantly improved the accuracy of CD. However, encoder–decoder architectures often struggle to effectively capture temporal differences. Encoders may lose critical spatial details, while decoders can introduce bias due to inconsistent receptive fields across layers. To address these limitations, this paper proposes an enhanced symmetric network, termed FDRF (feature difference and receptive field), which incorporates two novel components: the multibranch feature difference extraction (MFDE) module and the adaptive ensemble decision (AED) module. MFDE independently extracts differential features from bitemporal images at each encoder layer, using multiscale fusion to retain image content and improve the quality of feature difference modeling. AED assigns confidence weights to predictions from different decoder layers based on their receptive field sizes and then combines them adaptively to reduce scale-related bias. To validate the effectiveness and robustness of FDRF, experiments were conducted on five public datasets (SYSU, LEVIR-CD, WHU, NJDS, and CLCD), as well as a UAV-based dataset collected from two national coastal nature reserves in Guangxi Beihai, China. The results demonstrate that FDRF consistently outperforms existing methods in accuracy and robustness across diverse scenarios. Full article

(This article belongs to the Section Computer)

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