Symmetry

12 pages, 2359 KiB

Open AccessArticle

Efficient Parallel Ray Tracing Algorithm for Electromagnetic Scattering in Inhomogeneous Plasma Using Graphic Processing Unit

by Yijing Wang, Xinbo He and Bing Wei

Symmetry 2025, 17(4), 627; https://doi.org/10.3390/sym17040627 - 21 Apr 2025

Abstract

This paper presents a parallel ray tracing (RT) algorithm based on a graphic processing unit (GPU) applied to electromagnetic scattering calculations in an inhomogeneous plasma to enhance the computational efficiency of the algorithm. The proposed algorithm utilizes a fourth-order Runge–Kutta method to solve [...] Read more.

This paper presents a parallel ray tracing (RT) algorithm based on a graphic processing unit (GPU) applied to electromagnetic scattering calculations in an inhomogeneous plasma to enhance the computational efficiency of the algorithm. The proposed algorithm utilizes a fourth-order Runge–Kutta method to solve the Haselgrove equation to track ray paths within the inhomogeneous plasma and implements parallel processing of the RT procedure using GPU. By independently assigning single threads to the rays originating from the vertices and the midpoints of each triangulated ray tube, a substantial number of rays are traced in parallel to reduce the algorithm runtime. The results indicate that the parallel RT algorithm based on GPU significantly enhances computation efficiency in inhomogeneous plasma while maintaining accuracy. Full article

(This article belongs to the Section Physics)

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25 pages, 6931 KiB

Open AccessArticle

Dynamic Evolution Method and Symmetric Consistency Analysis for Big Data-Oriented Software Architecture Based on Extended Bigraph

by Chaoze Lu and Qifeng Zou

Symmetry 2025, 17(4), 626; https://doi.org/10.3390/sym17040626 - 21 Apr 2025

Abstract

With the development of artificial intelligence technology, there are increasingly high requirements for processing big data systems. Big data systems have undergone rapid evolution in response to changing demands. Due to the complex structural connections and dispersed component positions of big data processing [...] Read more.

With the development of artificial intelligence technology, there are increasingly high requirements for processing big data systems. Big data systems have undergone rapid evolution in response to changing demands. Due to the complex structural connections and dispersed component positions of big data processing systems, traditional formal methods find it difficult to dynamically model their structure and position simultaneously. To address this issue, this study proposes a formal modeling framework that extends Bigraph to support the dynamic evolution of big data software architecture. This model is capable of verifying the symmetry consistency of structural connections and component positions in evolutionary systems and evaluating them through real-life case studies of banking big data systems. The results confirmed its correctness and practical feasibility. Full article

(This article belongs to the Section Computer)

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81 pages, 2075 KiB

Open AccessReview

A Comprehensive Review on Solving the System of Equations AX = C and XB = D

by Qing-Wen Wang, Zi-Han Gao and Jia-Le Gao

Symmetry 2025, 17(4), 625; https://doi.org/10.3390/sym17040625 - 21 Apr 2025

Abstract

This survey provides a review of the theoretical research on the classic system of matrix equations

A X = C

and

X B = D

, which has wide-ranging applications across fields such as control theory, optimization, image processing, and robotics. The paper [...] Read more.

This survey provides a review of the theoretical research on the classic system of matrix equations

A X = C

and

X B = D

, which has wide-ranging applications across fields such as control theory, optimization, image processing, and robotics. The paper discusses various solution methods for the system, focusing on specialized approaches, including generalized inverse methods, matrix decomposition techniques, and solutions in the forms of Hermitian, extreme rank, reflexive, and conjugate solutions. Additionally, specialized solving methods for specific algebraic structures, such as Hilbert spaces, Hilbert

C^{*}

-modules, and quaternions, are presented. The paper explores the existence conditions and explicit expressions for these solutions, along with examples of their application in color images. Full article

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

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24 pages, 6825 KiB

Open AccessArticle

Numerical Analysis on Cooling Performances for Connectors Using Immersion Cooling in Ultra-Fast Chargers for Electric Vehicles

by Seong-Guk Hwang, Moo-Yeon Lee and Beom-Seok Ko

Symmetry 2025, 17(4), 624; https://doi.org/10.3390/sym17040624 - 20 Apr 2025

Abstract

The increasing demand for ultra-fast charging in electric vehicles (EVs) necessitates advancements in thermal management strategies to mitigate Joule heating, which arises due to electrical resistance in charging connectors and cable cores. This study presents a numerical analysis of immersion cooling performance for [...] Read more.

The increasing demand for ultra-fast charging in electric vehicles (EVs) necessitates advancements in thermal management strategies to mitigate Joule heating, which arises due to electrical resistance in charging connectors and cable cores. This study presents a numerical analysis of immersion cooling performance for ultra-fast chargers under realistic charging conditions. The simulated results are validated by experiments with a maximum deviation of 5.5% at 600 A and 700 A currents. The novelty of this work lies in the consideration of a realistic charging cable length of 5 m, the evaluation of temperature characteristics in the charger connector, and the analysis of geometric symmetry in the charging cable and coolant configuration to ensure uniform heat distribution. Key operating conditions were systematically analyzed, including applied currents, ambient temperatures, coolant flow rates, cable core cross-sectional areas, and different types of coolants. Results indicate that increasing the applied current from 400 A to 800 A raised the connector temperature from 60.73 °C to 97.33 °C. As the ambient temperature increased from 20 °C to 50 °C, the connector temperature rose significantly from 42.71 °C to 74.99 °C, while the maximum cable core temperature increased from 65.26 °C to 100.61 °C. Increasing the cable core cross-sectional area from 20 mm² to 30 mm² reduced the connector temperature from 77.20 °C to 74.99 °C. Meanwhile, increasing the coolant flow rate from 2 LPM to 5 LPM had a negligible effect on the connector temperature. Among the three tested coolants, Novec 7500 exhibited the highest cooling efficiency, achieving the lowest contact temperature (74.76 °C) and the highest performance evaluation criteria (PEC) value of 3.8. This study provides valuable guidelines for enhancing symmetry-driven thermal management systems and demonstrates the potential of immersion cooling to improve efficiency, safety, and operational reliability in next-generation high-power EV chargers. Full article

(This article belongs to the Special Issue Symmetry in Power Systems and Thermal Engineering)

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27 pages, 2335 KiB

Open AccessArticle

Electroencephalogram-Based Familiar and Unfamiliar Face Perception Classification Underlying Event-Related Potential Analysis and Confident Learning

by Zhihan Zuo, Menglu Zhou, Zhihe Lyu and Yuchun Fang

Symmetry 2025, 17(4), 623; https://doi.org/10.3390/sym17040623 - 20 Apr 2025

Viewed by 47

Abstract

Electroencephalogram (EEG), as a kind of neurobiological signal, is an essential tool for studying human perception, yet its acquisition is often time-consuming and laborious. Accordingly, this paper presents the largest publicly available EEG dataset to date for familiar and unfamiliar face perception analysis [...] Read more.

Electroencephalogram (EEG), as a kind of neurobiological signal, is an essential tool for studying human perception, yet its acquisition is often time-consuming and laborious. Accordingly, this paper presents the largest publicly available EEG dataset to date for familiar and unfamiliar face perception analysis (FUFP). The EEG signals of 66 channels were recorded from 8 participants, each exposed to 8 familiar faces (FFs) and 32 unfamiliar faces (UFs) randomly, repeated 20 times, yielding 6400 samples. Inspired by the inherent slight symmetry exhibited by the 2D position of EEG electrodes and EEG data, we employed five baseline machine learning methods, proving the feasibility of classifying familiarity through EEG. There are indeed neural features related to face familiarity in EEG signals. Event-related potential (ERP) analysis towards FFs and UF responses reveals that UFs induce larger N400 component amplitudes than FFs. Therefore, we propose a deep learning method based on ERP analysis and confident learning (ECL) for familiarity classification, which can effectively focus the model’s attention on more discriminative features and clean the data. Experimental results show that our model’s accuracy outperforms other existing familiarity classification models. We encourage researchers to utilize FUFP for algorithm tests and face perception analysis. Full article

(This article belongs to the Section Computer)

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56 pages, 16344 KiB

Open AccessArticle

Polyhedral Embeddings of Triangular Regular Maps of Genus g, 2⩽g⩽14, and Neighborly Spatial Polyhedra

by Jürgen Bokowski and Kevin H.

Symmetry 2025, 17(4), 622; https://doi.org/10.3390/sym17040622 - 19 Apr 2025

Viewed by 54

Abstract

This article provides a survey of polyhedral embeddings of triangular regular maps of genus g,

2 ⩽ g ⩽ 14

, and of neighborly spatial polyhedra. An old conjecture of Grünbaum from 1967, although disproved in 2000, lies behind this investigation. We [...] Read more.

This article provides a survey of polyhedral embeddings of triangular regular maps of genus g,

2 ⩽ g ⩽ 14

, and of neighborly spatial polyhedra. An old conjecture of Grünbaum from 1967, although disproved in 2000, lies behind this investigation. We discuss all duals of these polyhedra as well, whereby we accept, e.g., the Szilassi torus with its non-convex faces to be a dual of the Möbius torus. A numerical optimization approach by the second author for finding such embeddings was first applied to finding (unsuccessfully) a dual polyhedron of one of the 59 closed oriented surfaces with the complete graph of 12 vertices as their edge graph. The same method has been successfully applied for finding polyhedral embeddings of triangular regular maps of genus g,

2 ⩽ g ⩽ 14

. The effectiveness of the new method has led to ten additional new polyhedral embeddings of triangular regular maps and their duals. There do exist symmetrical polyhedral embeddings of all triangular regular maps with genus g,

2 ⩽ g ⩽ 14

, except in a single undecided case of genus 13. Among these results, there are three new Leonardo polyhedra, each with 156 vertices, 546 edges, and 364 triangular faces, based on the Hurwitz triplet of genus 14 with Conder notation R14.1, R14.2, and R14.3. Full article

(This article belongs to the Special Issue Symmetry in Combinatorial Structures)

39 pages, 10771 KiB

Open AccessArticle

A Data-Driven Methodology for Industrial Design Optimization and Consumer Preference Modeling: An Application of Computer-Aided Design in Sustainable Refrigerator Design Research

by Yu Chen, Haotian Liu, Jianwei Zhang and Jiang Wu

Symmetry 2025, 17(4), 621; https://doi.org/10.3390/sym17040621 - 19 Apr 2025

Viewed by 140

Abstract

Addressing the insufficient identification of key consumer requirements in refrigerator design and the current limitations in understanding the impacts and underlying mechanisms of product design on sustainability, this study develops an interdisciplinary methodological framework that synergizes industrial design principles with advanced computer-aided design [...] Read more.

Addressing the insufficient identification of key consumer requirements in refrigerator design and the current limitations in understanding the impacts and underlying mechanisms of product design on sustainability, this study develops an interdisciplinary methodological framework that synergizes industrial design principles with advanced computer-aided design techniques and deep neural network approaches. Initially, consumer decision preferences concerning essential product attributes and sustainability indicators are systematically elucidated through semi-structured interviews and multi-source data fusion, with a particular emphasis on user sensitivity to energy efficiency ratings, based on a high-quality sample of 303 respondents. Subsequently, a latent diffusion model alongside a ControlNet architecture is employed to intelligently generate design solutions, followed by comprehensive multi-attribute optimization screening using an integrated decision-making model. The empirical evidence reveals that the synergistic interplay between functional rationality and design coordination plays a critical role in determining the overall competitiveness of the design solutions. Furthermore, by incorporating established industrial design practices, prototypes of mini desktop and vehicle-mounted multifunctional refrigerators—derived from neural network-generated design features—are developed and assessed. Finally, a nonlinear predictive mapping model is constructed to delineate the relationship between industrial design characteristics and consumer appeal. The experimental results show that the proposed support vector regression model achieves a root mean square error of 0.0719 and a coefficient of determination of 0.8480, significantly outperforming the Bayesian regularization backpropagation neural network baseline. These findings validate the model’s predictive accuracy and its applicability in small-sample, high-dimensional, and nonlinear industrial design scenarios. This research provides a data-driven, intelligent analytical approach that bridges industrial design with computer-aided design, thereby optimizing product market competitiveness and sustainable consumer value while promoting both theoretical innovation and practical advancements in sustainable design practices. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Computer-Aided Industrial Design)

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15 pages, 386 KiB

Open AccessArticle

Parameter Estimation in Multifactor Uncertain Differential Equation with Symmetry Analysis for Stock Prediction

by Jiashuo Zhang, Tingqing Ye, Xiaoya Xu, Yang Liu and Haoran Zheng

Symmetry 2025, 17(4), 620; https://doi.org/10.3390/sym17040620 - 19 Apr 2025

Viewed by 175

Abstract

Multifactor uncertain differential equations (MUDEs) are effective tools to model dynamic systems under multi-source noise. With the widespread use of MUDEs, parameter estimation as the bridge between the observed data and the MUDE becomes increasingly important. Thus, how to estimate unknown parameters in [...] Read more.

Multifactor uncertain differential equations (MUDEs) are effective tools to model dynamic systems under multi-source noise. With the widespread use of MUDEs, parameter estimation as the bridge between the observed data and the MUDE becomes increasingly important. Thus, how to estimate unknown parameters in a MUDE under a multi-source noise environment is a challenge. To address this, this paper innovatively proposes a moment method to estimate the unknown parameters in a MUDE and illustrates two numerical examples to show the process of estimating parameters. Furthermore, since the system or environment is complex and constantly changing, the parameters in the MUDE are not constants but time-varying functions in many cases. Therefore, parameter estimation for time-varying functions is another challenge. In order to deal with this, this paper develops a method of parameter estimation for time-varying functions in the MUDE based on the moment method. As an application, this method of parameter estimation for time-varying functions is used to model China Merchants Bank stock. Full article

(This article belongs to the Special Issue Symmetry Applications in Uncertain Differential Equations)

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18 pages, 283 KiB

Open AccessArticle

A System of Coupled Matrix Equations with an Application over the Commutative Quaternion Ring

by Xiao-Quan Chen, Long-Sheng Liu, Xiao-Xiao Ma and Qian-Wen Long

Symmetry 2025, 17(4), 619; https://doi.org/10.3390/sym17040619 - 18 Apr 2025

Viewed by 63

Abstract

In this paper, we study the necessary and sufficient conditions for a system of matrix equations to have a solution and a Hermitian solution. As an application, we establish the necessary and sufficient conditions for a classical matrix system to have a reducible [...] Read more.

In this paper, we study the necessary and sufficient conditions for a system of matrix equations to have a solution and a Hermitian solution. As an application, we establish the necessary and sufficient conditions for a classical matrix system to have a reducible solution. Finally, we present an algorithm, along with two concrete examples to validate the main conclusions. Full article

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

14 pages, 259 KiB

Open AccessArticle

Existence, Uniqueness and Stability Analysis for Generalized Φ-Caputo Fractional Boundary Value Problems

by Ozlem Batit Ozen

Symmetry 2025, 17(4), 618; https://doi.org/10.3390/sym17040618 - 18 Apr 2025

Viewed by 46

Abstract

This study investigates solutions of a class of boundary value problems involving the

Φ

-Caputo fractional derivative and the p-Laplacian operator. Through the application of fixed-point theory, we confirm the existence and uniqueness of solutions to nonlinear

Φ

-Caputo fractional differential equations [...] Read more.

This study investigates solutions of a class of boundary value problems involving the

Φ

-Caputo fractional derivative and the p-Laplacian operator. Through the application of fixed-point theory, we confirm the existence and uniqueness of solutions to nonlinear

Φ

-Caputo fractional differential equations with the p-Laplacian operator. Moreover, we have demonstrated that this problem is stable in the framework of Ulam–Hyers stability. Our findings enhance the theoretical understanding of fractional differential equations and have potential applications in various scientific and engineering fields. In addition, an illustrative example is provided to support the key insights derived from this research. Full article

(This article belongs to the Special Issue Nonlinear Differential and Integral Equations and Their Infinite Systems)

27 pages, 7107 KiB

Open AccessArticle

CBACA-YOLOv5: A Symmetric and Asymmetric Attention-Driven Detection Framework for Citrus Leaf Disease Identification

by Jiaxian Zhu, Jiahong Chen, Huiyang He, Weihua Bai and Teng Zhou

Symmetry 2025, 17(4), 617; https://doi.org/10.3390/sym17040617 - 18 Apr 2025

Viewed by 76

Abstract

The citrus industry plays a pivotal role in modern agriculture. With the expansion of citrus plantations, the intelligent detection and prevention of diseases and pests have become essential for advancing smart agriculture. Traditional citrus leaf disease identification methods primarily rely on manual observation, [...] Read more.

The citrus industry plays a pivotal role in modern agriculture. With the expansion of citrus plantations, the intelligent detection and prevention of diseases and pests have become essential for advancing smart agriculture. Traditional citrus leaf disease identification methods primarily rely on manual observation, which is often time-consuming, labor-intensive, and prone to inaccuracies due to inherent asymmetries in disease manifestations. This work introduces CBACA-YOLOv5, an enhanced YOLOv5s-based detection algorithm designed to effectively capture the symmetric and asymmetric features of common citrus leaf diseases. Specifically, the model integrates the convolutional block attention module (CBAM), which symmetrically enhances feature extraction across spatial and channel dimensions, significantly improving the detection of small and occluded targets. Additionally, we incorporate coordinate attention (CA) mechanisms into the YOLOv5s C3 module, explicitly addressing asymmetrical spatial distributions of disease features. The CARAFE upsampling module further optimizes feature fusion symmetry, enhancing the extraction efficiency and accelerating the network convergence. Experimental findings demonstrate that CBACA-YOLOv5 achieves an accuracy of 96.1% and a mean average precision (mAP) of 92.1%, and improvements of 0.6% and 2.3%, respectively, over the baseline model. The proposed CBACA-YOLOv5 model exhibits considerable robustness and reliability in detecting citrus leaf diseases under diverse and asymmetrical field conditions, thus holding substantial promise for practical integration into intelligent agricultural systems. Full article

(This article belongs to the Section Computer)

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26 pages, 6637 KiB

Open AccessArticle

Hybrid Cybersecurity for Asymmetric Threats: Intrusion Detection and SCADA System Protection Innovations

by Abdulmohsen Almalawi, Shabbir Hassan, Adil Fahad, Arshad Iqbal and Asif Irshad Khan

Symmetry 2025, 17(4), 616; https://doi.org/10.3390/sym17040616 - 18 Apr 2025

Viewed by 88

Abstract

Supervisory control and data acquisition (SCADA) systems are vulnerable to cyberattacks; hence, cybersecurity is a major concern. Hybrid methodologies using advanced machine learning (ML) may increase intrusion detection and system security. The intrusion detection algorithms have little adaptability, high false-positive rates for novel [...] Read more.

Supervisory control and data acquisition (SCADA) systems are vulnerable to cyberattacks; hence, cybersecurity is a major concern. Hybrid methodologies using advanced machine learning (ML) may increase intrusion detection and system security. The intrusion detection algorithms have little adaptability, high false-positive rates for novel threats, and restricted feature extraction. SCADA systems are subject to sophisticated attacks. This study’s hybrid autoencoder-hybrid ResNet–long short-term memory (LSTM) (HAE–HRL) architecture includes deep feature extraction, anomaly detection, and sequential analysis. This framework uses these three methods to improve threat detection. AI can scan massive amounts of data and find patterns humans and traditional systems miss. The hybrid approach gives defenders an unequal edge. Autoencoders identify anomalies, convolutional neural networks (CNNs) extract features, and hybrid ResNet–LSTM learns temporal patterns. Cyber risks are correctly classified using this method. With SCADA security and intrusion detection, the model may considerably enhance network abnormality and hostile activity detection. According to experimental tests, HAE–HRL reduces false positives and improves detection accuracy, making it a robust cybersecurity solution. Full article

(This article belongs to the Special Issue Advanced Studies of Symmetry/Asymmetry in Cybersecurity)

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21 pages, 8075 KiB

Open AccessArticle

Finite Element Analysis-Based Assessment of Damage Parameters for Ultra-Low-Cycle Fatigue Behavior of Structural Steels

by Ivan Milojević, Mirsad Tarić, Dardan Klimenta, Bojana Grujić, Darius Andriukaitis, Saša Jovanović and Miloš Čolović

Symmetry 2025, 17(4), 615; https://doi.org/10.3390/sym17040615 - 18 Apr 2025

Viewed by 84

Abstract

Steel structures subjected to earthquakes or extreme cyclic loadings may undergo extensive damage and fractures due to ultra-low-cycle fatigue (ULCF). Although assessments of damage initiation and evolution parameters have been carried out for some steels exposed to low-cycle fatigue, so far, these parameters [...] Read more.

Steel structures subjected to earthquakes or extreme cyclic loadings may undergo extensive damage and fractures due to ultra-low-cycle fatigue (ULCF). Although assessments of damage initiation and evolution parameters have been carried out for some steels exposed to low-cycle fatigue, so far, these parameters for structural steels exposed to ULCF have neither been sufficiently studied nor quantified. Accordingly, this paper provides the results of finite element analysis (FEA) concerning the ULCF behaviors of S355 and S690 steel specimens. Calibration of the damage parameters is performed in SIMULIA Abaqus 6.11 FEA software using a direct cyclic algorithm and available experimental data. Kliman’s model for the hysteresis energy of cyclic loading is used to analytically verify the damage parameters. In addition, available experimental data were obtained from cyclic axial strain tests on S355 and S690 steel specimens according to the ASTM International standard E606/E606M-21. Finally, the non-linear Chaboche–Lemaitre (C–L) combined isotropic–kinematic hardening model is used for the characterization of the ULCF behavior of S355 steel in a simple cylindrical bar. It is found that the two damage initiation parameters are 5.0 and −0.8, the first damage initiation parameter is dominant when modeling the number of cycles to failure, and the second damage initiation parameter is a material constant. Full article

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

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30 pages, 2062 KiB

Open AccessArticle

Reliability Estimation of Stress–Strength Model for Multi-Component System Based on Lomax Distribution Using the Survival Signature

by Jiaojiao Guo, Tian Guo, Jialin Su, Jianhui Li and Xiaogang Liu

Symmetry 2025, 17(4), 614; https://doi.org/10.3390/sym17040614 - 18 Apr 2025

Viewed by 61

Abstract

In this paper, the stress–strength reliability of complex systems with diverse component types is investigated based on the theoretical framework of survival signatures. Assuming that both the strength and stress of components of the same type follow the Lomax distribution, the maximum likelihood [...] Read more.

In this paper, the stress–strength reliability of complex systems with diverse component types is investigated based on the theoretical framework of survival signatures. Assuming that both the strength and stress of components of the same type follow the Lomax distribution, the maximum likelihood estimation (MLE), maximum spacing estimation (MSPE), and Bayesian estimation for the stress–strength model are derived under the condition that components of the same type have common scale parameters. Subsequently, the 95% Bootstrap-p and Highest Posterior Density confidence intervals for the stress–strength reliability were derived using Monte Carlo simulation. Additionally, since stress cycles are represented by a Poisson process, a dynamic stress–strength model for the system subjected to periodic stresses over the interval

(0, t]

was developed, together with an approximate computational algorithm for this model. Finally, a simulation experiment was conducted using a system consisting of a total of nine components of three different types to analyze these estimation methods. The findings reveal that MLE exhibits the lowest estimation error, registering merely 0.001 in the case of small-sized samples. Compared with the previous two methods, Bayesian estimation has a relatively larger error. However, in the case of large samples, the error is 0.0112. In addition, the performance and accuracy of the dynamic model were verified through the proposed algorithm. The results indicate that compared with the static model at

t = 0

, the error of the algorithm is 0.0464. Overall, the model evaluation results are satisfactory. Full article

(This article belongs to the Section Computer)

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26 pages, 1779 KiB

Open AccessArticle

Multi-Ship Collision Avoidance in Inland Waterways Using Actor–Critic Learning with Intrinsic and Extrinsic Rewards

by Shaojun Gan, Ziqi Zhang, Yanxia Wang and Dejun Wang

Symmetry 2025, 17(4), 613; https://doi.org/10.3390/sym17040613 - 18 Apr 2025

Viewed by 81

Abstract

Inland waterway navigation involves complex traffic conditions with frequent multi-ship encounters. Benefiting from its straightforward structure and robust adaptability, reinforcement learning has found applications in navigation. This article proposes a deep actor–critic collision avoidance model which is based on the weighted summation of [...] Read more.

Inland waterway navigation involves complex traffic conditions with frequent multi-ship encounters. Benefiting from its straightforward structure and robust adaptability, reinforcement learning has found applications in navigation. This article proposes a deep actor–critic collision avoidance model which is based on the weighted summation of intrinsic reward and extrinsic reward, overcoming the sparsity of the reward function in navigation tasks. For the proposed algorithm, the extrinsic reward considers factors of collision risk, economic reward, and penalties for violating collision avoidance rules, while the intrinsic reward explores the novelty of agent states. The optimization of the own ship’s actions is achieved through the utilization of a weighted summation of these two types of rewards, providing valuable guidance for decision-making in a symmetrical interaction framework. To validate the performance of the proposed multi-ship collision avoidance model, simulations of both two-ship encounters and complex multi-ship scenarios involving dynamic and static obstacles are conducted. The following conclusions can be drawn: (1) The proposed model could provide effective decisions for ship navigation in inland waterways, maintaining symmetrical coordination between vessels. (2) The hybrid reward mechanism successfully guides ship behavior in collision avoidance scenarios. Full article

(This article belongs to the Section Engineering and Materials)

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25 pages, 2121 KiB

Open AccessArticle

Lie Group Intrinsic Mean Feature Detectors for Real-Time Industrial Surface Defect Detection

by Chengjun Xu, Jingqian Shu, Zhenghan Wang and Jialin Wang

Symmetry 2025, 17(4), 612; https://doi.org/10.3390/sym17040612 - 18 Apr 2025

Viewed by 96

Abstract

In the actual industrial production environment, the surface defects of products are subtle, and the number of different types of defect data samples is also quite small. Most deep learning models rely on a large number of training samples and parameters to achieve [...] Read more.

In the actual industrial production environment, the surface defects of products are subtle, and the number of different types of defect data samples is also quite small. Most deep learning models rely on a large number of training samples and parameters to achieve high-precision defect detection. At the same time, the edge computing layer in the actual industrial environment may also encounter transmission delays and insufficient resources. Training a proper model for a specific type of surface defect while simultaneously satisfying the real-time accuracy of defect detection is still a challenging task. To effectively deal with the above challenges, we propose an edge-cloud computing defect detection model based on the intrinsic mean feature detector in the Lie Group space. The modules in the model adopt a symmetrical structure, which can extract related features more effectively. Different from existing models, this model utilizes the Lie Group space intrinsic mean feature as a metric to characterize the essential attributes of different types of surface defects. In addition, we propose an intrinsic mean attention mechanism in the Lie Group manifold space that is easy to implement at the edge service layer without increasing the number of model parameters, thereby enhancing the detection performance of tiny surface defects. Extensive experiments on three publicly available and challenging datasets reveal the superiority of our model in terms of detection accuracy, real-time detection, number of parameters, and computational performance. In addition, our proposed model also shows competitiveness and advantages compared with state-of-the-art models. Full article

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14 pages, 9746 KiB

Open AccessArticle

A Two-Stage Welding Control System Combining Rule-Based and Data-Driven Vision

by Mingtian Ma, Hong Lu, Zidong Wu, Yongquan Zhang, He Huang, Weijie Dong, Zhi Liu, Zhangjie Li and Yongjie He

Symmetry 2025, 17(4), 611; https://doi.org/10.3390/sym17040611 - 18 Apr 2025

Viewed by 99

Abstract

With the development of welding automation and intelligence, computer vision-based welding process monitoring technologies have become increasingly applied. However, interference factors such as welding fumes, spatter, and intense arc light in the welding environment significantly affect the performance of existing welding monitoring and [...] Read more.

With the development of welding automation and intelligence, computer vision-based welding process monitoring technologies have become increasingly applied. However, interference factors such as welding fumes, spatter, and intense arc light in the welding environment significantly affect the performance of existing welding monitoring and control technologies. To address this issue, this paper proposes a novel method for extracting molten pool dimensions that integrates rule-based and data-driven vision approaches and introduces a welding speed control system that considers the stability of the welding process. The goal of this study is to develop a method that not only monitors the molten pool’s size but also evaluates its stability. In this system, the first stage improves the accuracy of molten pool recognition and dimension extraction through an enhanced method, while the second stage introduces a speed adjustment factor based on welding stability to achieve stable control of welding speed. Experimental results demonstrate that the proposed method shows high adaptability and extraction accuracy under various interference conditions. The welding speed control strategy significantly enhances the stability and symmetry of the welding process, with performance improvements of approximately 45% in stability compared to the conventional method. This leads to an overall improvement in weld quality. Full article

(This article belongs to the Special Issue Symmetry and Its Applications in Automation and Control Systems)

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32 pages, 2699 KiB

Open AccessArticle

Dynamic Marketing Uplift Modeling: A Symmetry-Preserving Framework Integrating Causal Forests with Deep Reinforcement Learning for Personalized Intervention Strategies

by Jiyuan Wang, Yutong Tan, Bingying Jiang, Bi Wu and Wenhe Liu

Symmetry 2025, 17(4), 610; https://doi.org/10.3390/sym17040610 - 17 Apr 2025

Viewed by 189

Abstract

Traditional marketing uplift models suffer from a fundamental limitation: they typically operate under static assumptions that fail to capture the temporal dynamics of customer responses to marketing interventions. This paper introduces a novel framework that combines causal forest algorithms with deep reinforcement learning [...] Read more.

Traditional marketing uplift models suffer from a fundamental limitation: they typically operate under static assumptions that fail to capture the temporal dynamics of customer responses to marketing interventions. This paper introduces a novel framework that combines causal forest algorithms with deep reinforcement learning to dynamically model marketing uplift effects. Our approach enables the real-time identification of heterogeneous treatment effects across customer segments while simultaneously optimizing intervention strategies through an adaptive learning mechanism. The key innovations of our framework include the following: (1) a counterfactual simulation environment that emulates diverse customer response patterns; (2) an adaptive reward mechanism that captures both immediate and long-term intervention outcomes; and (3) a dynamic policy optimization process that continually refines targeting strategies based on evolving customer behaviors. Empirical evaluations on both simulated and real-world marketing campaign data demonstrate that our approach significantly outperforms traditional static uplift models, achieving up to a 27% improvement in targeting efficiency and an 18% increase in the return on marketing investment. The framework leverages inherent symmetries in customer-intervention interactions, where balanced and symmetric reward structures ensure fair optimization across diverse customer segments. The proposed framework addresses the limitations of existing methods by effectively modeling the dynamic and heterogeneous nature of customer responses to marketing interventions, providing marketers with a powerful tool for implementing personalized and adaptive campaign strategies. Full article

(This article belongs to the Section Mathematics)

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22 pages, 3302 KiB

Open AccessArticle

Path Planning of Mobile Robot Based on Dual-Layer Fuzzy Control and Improved Genetic Algorithm

by Yangxin Teng, Tingping Feng, Changlin Song, Junmin Li, Simon X. Yang and Hongjun Zhu

Symmetry 2025, 17(4), 609; https://doi.org/10.3390/sym17040609 - 17 Apr 2025

Cited by 1 | Viewed by 173

Abstract

This study addresses the dual challenges of complex road environments and diverse task-safety requirements in mobile-robot path planning by proposing an innovative method that integrates a dual-layer fuzzy control system with an improved genetic algorithm. Initially, an expert system-based dual-layer fuzzy control system [...] Read more.

This study addresses the dual challenges of complex road environments and diverse task-safety requirements in mobile-robot path planning by proposing an innovative method that integrates a dual-layer fuzzy control system with an improved genetic algorithm. Initially, an expert system-based dual-layer fuzzy control system is developed. The first layer translates complex road conditions and obstacles into road-safety levels, while the second layer combines these with task-safety levels to generate fitness weights for the genetic algorithm. Furthermore, road-safety factors are incorporated into the genetic algorithm’s fitness function to enhance safety considerations in path planning. The algorithm implementation incorporates Bernoulli chaotic mapping, Gaussian operators, and Symmetrical Sigmoid operators to optimize the selection, crossover, and mutation processes, significantly boosting the algorithm’s global search capability and efficiency. Experimental results indicate that the proposed method reduces path distance by up to 5.9% and decreases the number of turns by up to 85.7%, demonstrating superior universality and robustness across various comparative experiments. This research contributes to resolving the issues posed by complex road environments and varying task-safety requirements in mobile-robot path planning. Full article

(This article belongs to the Section Engineering and Materials)

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17 pages, 9440 KiB

Open AccessArticle

RACFME: Object Tracking in Satellite Videos by Rotation Adaptive Correlation Filters with Motion Estimations

by Xiongzhi Wu, Haifeng Zhang, Chao Mei, Jiaxin Wu and Han Ai

Symmetry 2025, 17(4), 608; https://doi.org/10.3390/sym17040608 - 16 Apr 2025

Viewed by 98

Abstract

Video satellites provide high-temporal-resolution remote sensing images that enable continuous monitoring of the ground for applications such as target tracking and airport traffic detection. In this paper, we address the problems of object occlusion and the tracking of rotating objects in satellite videos [...] Read more.

Video satellites provide high-temporal-resolution remote sensing images that enable continuous monitoring of the ground for applications such as target tracking and airport traffic detection. In this paper, we address the problems of object occlusion and the tracking of rotating objects in satellite videos by introducing a rotation-adaptive tracking algorithm for correlation filters with motion estimation (RACFME). Our algorithm proposes the following improvements over the KCF method: (a) A rotation-adaptive feature enhancement module (RA) is proposed to obtain the rotated image block by affine transformation combined with the target rotation direction prior, which overcomes the disadvantage of HOG features lacking rotation adaptability, improves tracking accuracy while ensuring real-time performance, and solves the problem of tracking failure due to insufficient valid positive samples when tracking rotating targets. (b) Based on the correlation between peak response and occlusion, an occlusion detection method for vehicles and ships in satellite video is proposed. (c) Motion estimations are achieved by combining Kalman filtering with motion trajectory averaging, which solves the problem of tracking failure in the case of object occlusion. The experimental results show that the proposed RACFME algorithm can track a moving target with a 95% success score, and the RA module and ME both play an effective role. Full article

(This article belongs to the Special Issue Advances in Image Processing with Symmetry/Asymmetry)

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21 pages, 1371 KiB

Open AccessArticle

Developing a New Approach for Assessing and Improving Business Excellence: Integrating Fuzzy Analytic Hierarchical Process and Constraint Programming Model

by Tijana Petrović, Danijela Tadić, Dragan Marinković, Goran Đurić and Nikola Komatina

Symmetry 2025, 17(4), 607; https://doi.org/10.3390/sym17040607 - 16 Apr 2025

Viewed by 94

Abstract

This study introduces a novel two-stage model for assessing and enhancing business excellence based on the EFQM framework. The Fuzzy Analytic Hierarchy Process (FAHP) is used in the first stage to calculate the weight vectors of criteria and sub-criteria, incorporating uncertainty through triangular [...] Read more.

This study introduces a novel two-stage model for assessing and enhancing business excellence based on the EFQM framework. The Fuzzy Analytic Hierarchy Process (FAHP) is used in the first stage to calculate the weight vectors of criteria and sub-criteria, incorporating uncertainty through triangular fuzzy numbers (TFNs). In the second stage, the OR-Tools CP-SAT solver is used to solve the selection and improvement of sub-criteria as a multidimensional knapsack problem with mixed min/max constraints. In this way, a new and enhanced model for evaluating business excellence is presented—one that takes into account the company’s current capabilities and circumstances while also providing management with a starting point for enhancing business performance. The model is validated using data from a manufacturing company in central Serbia. The findings suggest that improvement efforts should not be symmetrically distributed across all EFQM criteria and sub-criteria. Instead, an asymmetric approach provides efficient resource allocation while maximizing business excellence improvements. This study emphasizes the balance or symmetry between subjective decision-makers’ assessments and mathematically based optimization, demonstrating the practical applicability of the proposed method in strategic decision-making under resource constraints. Full article

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

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17 pages, 281 KiB

Open AccessArticle

Fuzzy Double Yang Transform and Its Application to Fuzzy Parabolic Volterra Integro-Differential Equation

by Atanaska Georgieva, Slav I. Cholakov, Maria Vasileva and Yordanka Gudalova

Symmetry 2025, 17(4), 606; https://doi.org/10.3390/sym17040606 - 16 Apr 2025

Viewed by 94

Abstract

This article introduces a new fuzzy double integral transformation called fuzzy double Yang transformation. We review some of the main properties of the transformation and find the conditions for its existence. We prove the theorems for partial derivatives and fuzzy unitary convolution. All [...] Read more.

This article introduces a new fuzzy double integral transformation called fuzzy double Yang transformation. We review some of the main properties of the transformation and find the conditions for its existence. We prove the theorems for partial derivatives and fuzzy unitary convolution. All of the new results are applied to find an analytical solution to the fuzzy parabolic Volterra integro-differential equation (FPVIDE) with a suitably selected memory kernel. In addition, a numerical example is provided to illustrate how the proposed method might be helpful for solving FPVIDE utilizing symmetric triangular fuzzy numbers. Compared with other symmetric transforms, we conclude that our new approach is simpler and needs less calculations. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)

16 pages, 13982 KiB

Open AccessArticle

Exploring Chaos in Fractional Order Systems: A Study of Constant and Variable-Order Dynamics

by Reem Allogmany, Nada A. Almuallem, Reima Daher Alsemiry and Mohamed A. Abdoon

Symmetry 2025, 17(4), 605; https://doi.org/10.3390/sym17040605 - 16 Apr 2025

Viewed by 142

Abstract

Fractional calculus generalizes well-known differentiation and integration to noninteger orders, allowing a more accurate framework for modeling complex dynamical behaviors. The application of fractional-order systems is quite wide in engineering, biology, and physics because they inherently capture the memory effects and long-range dependencies. [...] Read more.

Fractional calculus generalizes well-known differentiation and integration to noninteger orders, allowing a more accurate framework for modeling complex dynamical behaviors. The application of fractional-order systems is quite wide in engineering, biology, and physics because they inherently capture the memory effects and long-range dependencies. Out of these, fractional jerk chaotic systems have gained attention regarding their applications in secure communication, signal processing, and control systems. This work develops a comparative analysis of a fractional jerk system that includes constant- and variable-order derivatives to contribute to chaos–stability analysis. Additionally, this study uncovers novel chaotic behaviors, further expanding our understanding of complex dynamical systems. The results yield new insights into using variable-order dynamics to enable chaotic systems to better adapt to real applications. Full article

(This article belongs to the Special Issue Symmetry and Its Applications in Partial Differential Equations)

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16 pages, 1110 KiB

Open AccessArticle

Modeling the Digestion Process by a Distributed Delay Differential System

by Junli Liu, Zhenghua Guo and Hui Guo

Symmetry 2025, 17(4), 604; https://doi.org/10.3390/sym17040604 - 16 Apr 2025

Viewed by 68

Abstract

We modified the work of Wang and Zou, where both the costs and benefits of fear effects were considered, and a constant time delay was used to represent the biomass conversion time from prey to predator. In our work, we assumed that the [...] Read more.

We modified the work of Wang and Zou, where both the costs and benefits of fear effects were considered, and a constant time delay was used to represent the biomass conversion time from prey to predator. In our work, we assumed that the digestion delay is not a constant, but rather follows a specific distribution. The delay was modeled using a general kernel function, and a more general functional response function was also employed. Then, we established an integral–differential model with distributed time delays. We show that there exists a delay-dependent threshold that determines the system’s dynamics and the presence of coexistence equilibrium. In the absence of coexistence equilibrium, both populations tend toward extinction, or only the prey population survives. Conversely, when coexistence equilibrium exists, the system persists. Four kernel functions were considered to explore the effect of fear levels and time delays on population dynamics. We found that an increase in the fear level of the prey may alter the system dynamics from periodic oscillations to stability. Furthermore, our findings indicate that a fear effect-related functional response has great influence in shaping the model’s dynamics. These results indicate that ignoring time delay or fear effects, or the inappropriate use of kernel functions, may lead to inaccurate prediction results of the model. We want to point out that, when we investigate a pair of purely imaginary roots of the characteristic equation at the coexistence equilibrium, we just need to consider one of them due to the symmetry. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry of Differential Equations in Biomathematics)

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23 pages, 3249 KiB

Open AccessArticle

Process Optimization and Performance Characterization of Preparing 4A Molecular Sieves from Coal Gangue

by Dongpeng Zhang, Laiyang Zhu, Tiantian Ma, Xiwen Liang, Nie Sun and Fei Liu

Symmetry 2025, 17(4), 603; https://doi.org/10.3390/sym17040603 - 16 Apr 2025

Viewed by 87

Abstract

Coal mining and washing processes generate substantial amounts of coal gangue, posing significant environmental challenges. Coal gangue as a solid waste is rich in SiO₂ and Al₂O₃, with the SiO₂/Al₂O₃ molar ratio closely [...] Read more.

Coal mining and washing processes generate substantial amounts of coal gangue, posing significant environmental challenges. Coal gangue as a solid waste is rich in SiO₂ and Al₂O₃, with the SiO₂/Al₂O₃ molar ratio closely aligned with the ideal composition of 4A molecular sieves. In this study, through a synergistic pretreatment process involving low-temperature oxidation and hydrochloric acid leaching, the Fe₂O₃ content in coal gangue was reduced from 7.8 wt% to 1.1 wt%, markedly enhancing raw material purity. The alkali fusion–hydrothermal synthesis parameters were optimized via orthogonal experiments—calcination (750 °C, 2 h), aging (60 °C, 2 h), and crystallization (95 °C, 6 h) to maintain cubic symmetry, yielding highly crystalline 4A zeolite. Characterization via XRD, calcium ion adsorption capacity, SEM, and FTIR elucidated the regulatory mechanism of calcination on kaolinite phase transformation and the critical role of alkali fusion in activating silicon–aluminum component release. The as-synthesized zeolite exhibited a cubic morphology, high crystallinity, and sharp diffraction peaks consistent with the 4A zeolite phase. The pH of the zero point charge (pH_ZPC) of the 4A molecular sieve is 6.13. The 4A molecular sieve has symmetry-driven adsorption sites, and the adsorption of Cu²⁺ follows a monolayer adsorption mechanism (Langmuir model, R² = 0.997) with an average standard enthalpy change of 38.96 ± 4.47 kJ/mol and entropy change of 0.1277 ± 0.0148 kJ/mol, adhering to pseudo-second-order kinetics (R² = 0.999). The adsorption process can be divided into two stages. This study provides theoretical and technical insights into the high-value utilization of coal gangue. Full article

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

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16 pages, 5797 KiB

Open AccessArticle

Feature Symmetry Fusion Remote Sensing Detection Network Based on Spatial Adaptive Selection

by Heng Xiao, Donglin Jing, Fujun Zhao and Shaokang Zha

Symmetry 2025, 17(4), 602; https://doi.org/10.3390/sym17040602 - 16 Apr 2025

Viewed by 152

Abstract

This paper proposes a spatially adaptive feature fine fusion network consisting of a Fast Convolution Decomposition Sequence (FCDS) and a Spatial Selection Mechanism (SSM). Firstly, in FCDS, a large kernel convolution decomposition operation is used to break down dense convolution kernels into small [...] Read more.

This paper proposes a spatially adaptive feature fine fusion network consisting of a Fast Convolution Decomposition Sequence (FCDS) and a Spatial Selection Mechanism (SSM). Firstly, in FCDS, a large kernel convolution decomposition operation is used to break down dense convolution kernels into small convolutions with gradually increasing hole rates, forming a continuous kernel sequence to obtain finer scale features. This approach significantly reduces the number of parameters, improves network inference efficiency, and preserves the spatial feature expression ability of the network. Notably, the decomposed convolution kernel sequence adopts a symmetric dilation rate increment strategy, maintaining symmetry constraints in kernel weight distribution while expanding receptive fields. On this basis, the spatial selection mechanism is utilized to enhance the key features and background differences of the target location in the feature map, dynamically allocate weights to different fine scale feature maps, and improve the adaptive ability of multi-scale domains. This mechanism employs symmetric attention weight allocation (symmetric channel attention + spatial attention) to establish complementary symmetric response patterns across feature maps in both channel and spatial dimensions. Numerous experiments have shown that our method achieves higher performance with 81.64%, 91.34%, 91.20%mAP on three commonly used remote sensing target datasets (DOTA, UCAS AOD, HRSC2016) compared to existing advanced detection networks. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Object Detection)

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10 pages, 250 KiB

Open AccessArticle

Jensen–Jessen Inequality for Convex Maps

by Zdzisław Otachel

Symmetry 2025, 17(4), 601; https://doi.org/10.3390/sym17040601 - 16 Apr 2025

Viewed by 73

Abstract

In this paper, some vector inequalities for convex maps are proved. The obtained results refer to the famous Jensen inequality and generalize further classical inequalities of Jessen and McShane. In addition, the Hahn–Banach theorems with sublinear and convex maps are considered and used [...] Read more.

In this paper, some vector inequalities for convex maps are proved. The obtained results refer to the famous Jensen inequality and generalize further classical inequalities of Jessen and McShane. In addition, the Hahn–Banach theorems with sublinear and convex maps are considered and used to prove the theorem on the support of certain convex maps. Full article

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

12 pages, 370 KiB

Open AccessArticle

Explanation of the Mass Pattern of the Low-Lying Scalar Nonet

by Mihail Chizhov, Emanuil Chizhov, Momchil Naydenov and Daniela Kirilova

Symmetry 2025, 17(4), 600; https://doi.org/10.3390/sym17040600 - 15 Apr 2025

Viewed by 111

Abstract

The aim of this work is to propose an explanation of the inverse mass hierarchy of the low-lying nonet of the scalar mesons in the framework of the massless Nambu–Jona-Lasinio

U_{R} (3) \times U_{L} (3)

quark model. [...] Read more.

The aim of this work is to propose an explanation of the inverse mass hierarchy of the low-lying nonet of the scalar mesons in the framework of the massless Nambu–Jona-Lasinio

U_{R} (3) \times U_{L} (3)

quark model. The proposed explanation is based on symmetry principles. The collective meson states are described via quark–antiquark pairs, whose condensates lead simultaneously to spontaneous breaking of chiral and flavour symmetry. It is shown that, due to flavour symmetry breaking, two iso-doublets of

K_{0}^{*} (700)

mesons play the role of Goldstone bosons. It is also proven that there exists a solution with degenerate masses of the

a_{0} (980)

and

f_{0} (980)

mesons and a zero mass of the

f_{0} (500)

meson. Full article

(This article belongs to the Special Issue Symmetry in Hadron Physics)

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23 pages, 8147 KiB

Open AccessArticle

Traffic Volume Estimation Based on Spatiotemporal Correlation Adaptive Graph Convolutional Network

by Sheng Ding, Fei Yan and Yingmin Yi

Symmetry 2025, 17(4), 599; https://doi.org/10.3390/sym17040599 - 15 Apr 2025

Viewed by 162

Abstract

Traffic volume estimation is a fundamental task in Intelligent Transportation Systems (ITS). The highly unbalanced and asymmetric spatiotemporal distribution of traffic flow combined with the sparse and uneven deployment of sensors pose significant challenges for accurate estimation. To address these issues, this paper [...] Read more.

Traffic volume estimation is a fundamental task in Intelligent Transportation Systems (ITS). The highly unbalanced and asymmetric spatiotemporal distribution of traffic flow combined with the sparse and uneven deployment of sensors pose significant challenges for accurate estimation. To address these issues, this paper proposes a novel traffic volume estimation framework. It combines a dynamic adjacency matrix Graph Convolutional Network (GCN) with a multi-scale transformer structure to capture spatiotemporal correlation. First, an adaptive speed-flow correlation module captures global road correlations based on historical speed patterns. Second, a dynamic recurrent graph convolution network is used to capture both short- and long-range correlations between roads. Third, a multi-scale transformer module models the short-term fluctuations and long-term trends of traffic volume at multiple scales, capturing temporal correlations. Finally, the output layer fuses spatiotemporal correlations to estimate the global road traffic volume at the current time. Experiments on the PEMS-BAY dataset in California show that the proposed model outperforms the baseline models and achieves good estimation results with only 30% sensor coverage. Ablation and hyperparameter experiments validate the effectiveness of each component of the model. Full article

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

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19 pages, 5667 KiB

Open AccessArticle

Content-Symmetrical Multidimensional Transpose of Image Sequences for the High Efficiency Video Coding (HEVC) All-Intra Configuration

by Tamer Shanableh

Symmetry 2025, 17(4), 598; https://doi.org/10.3390/sym17040598 - 15 Apr 2025

Viewed by 159

Abstract

Enhancing the quality of video coding whilst maintaining compliance with the syntax of video coding standards is challenging. In the literature, many solutions have been proposed that apply mainly to two-pass encoding, bitrate control algorithms, and enhancements of locally decoded images in the [...] Read more.

Enhancing the quality of video coding whilst maintaining compliance with the syntax of video coding standards is challenging. In the literature, many solutions have been proposed that apply mainly to two-pass encoding, bitrate control algorithms, and enhancements of locally decoded images in the motion-compensation loop. This work proposes a pre- and post-coding solution using the content-symmetrical multidimensional transpose of raw video sequences. The content-symmetrical multidimensional transpose results in images composed of slices of the temporal domain whilst preserving the video content. Such slices have higher spatial homogeneity at the expense of reducing the temporal resemblance. As such, an all-intra configuration is an excellent choice for compressing such images. Prior to displaying the decoded images, a content-symmetrical multidimensional transpose is applied again to restore the original form of the input images. Moreover, we propose a lightweight two-pass encoding solution in which we apply systematic temporal subsampling on the multidimensional transposed image sequences prior to the first-pass encoding. This noticeably reduces the complexity of the encoding process of the first pass and gives an indication as to whether or not the proposed solution is suitable for the video sequence at hand. Using the HEVC video codec, the experimental results revealed that the proposed solution results in a lower percentage of coding unit splits in comparison to regular HEVC coding without the multidimensional transpose of image sequences. This finding supports the claim of there being increasing spatial coherence as a result of the proposed solution. Additionally, using four quantization parameters, and in comparison to regular HEVC encoding, the resulting BD rate is −15.12%, which indicates a noticeable bitrate reduction. The BD-PSNR, on the other hand, was 1.62 dB, indicating an enhancement in the quality of the decoded images. Despite all of these benefits, the proposed solution has limitations, which are also discussed in the paper. Full article

(This article belongs to the Section Computer)

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Symmetry, Volume 17, Issue 4 (April 2025) – 154 articles

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