Next Issue
Volume 17, September
Previous Issue
Volume 17, July
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.3
2.2
Journals
Symmetry
Volume 17
Issue 8
share announcement

Symmetry, Volume 17, Issue 8 (August 2025) – 201 articles

Cover Story (view full-size image): The chemical properties of silver may be understood but its nuclear structure is far from being revealed. Ag isotopes exhibit characteristics of both spherical and deformed nuclei. The typical seniority scheme is unusually perturbed by a strong quadrupole–quadrupole interaction, leading to a puzzling arrangement of levels. A prominent feature challenging theoretical models is the J-1 anomaly expressed by the inversion of j and j-1 states. The authors systematically study the Ag structure by applying the IBFM-1 model based on symmetries found in the nuclear Hamiltonian. It is shown that odd-A Ag can be described as Cd cores coupled to a g9/2 proton hole. The authors hint that structure effects like the J-1 anomaly may have astrophysical impact: low-lying isomers in Ag nuclei can alter reaction rates and affect astrophysical processes. View this paper
  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
27 pages, 11562 KB  
Article
A Symmetry-Driven Hybrid Framework Integrating ITTAO and sLSTM-Attention for Air Quality Prediction
by Yanping Liu, Kunkun Zhang, Bohao Yu, Bin Liao, Fuhong Song and Chunju Tang
Symmetry 2025, 17(8), 1369; https://doi.org/10.3390/sym17081369 - 21 Aug 2025
Viewed by 458
Abstract
Air pollution poses a threat to public health, ecosystem stability, and sustainable development. Accurate air quality prediction is essential for environmental protection and achieving sustainability. This study proposes a symmetry-driven hybrid framework that integrates an Improved Triangulation Topology Aggregation Optimizer (ITTAO) with a [...] Read more.
Air pollution poses a threat to public health, ecosystem stability, and sustainable development. Accurate air quality prediction is essential for environmental protection and achieving sustainability. This study proposes a symmetry-driven hybrid framework that integrates an Improved Triangulation Topology Aggregation Optimizer (ITTAO) with a Stable Long Short-Term Memory (sLSTM) network and an attention mechanism to achieve high-precision air quality prediction. Three enhancement strategies are introduced to improve the optimization capability of the TTAO algorithm. Experiments with CEC2017 standard functions validate the ITTAO algorithm’s superior convergence and global search ability. ITTAO then optimizes the hyperparameters of the sLSTM-Attention model, resulting in the ITTAO-sLSTM-Attention model. Four air quality datasets from diverse regions in China verify the model’s performance, demonstrating that the proposed model outperforms seven swarm intelligence-optimized sLSTM-Attention models and six machine learning models. Compared to the LSTM model, ITTAO-sLSTM-Attention reduces RMSE by 23.47%, 13.23%, 19.69%, and 26.46% across four cities, confirming its enhanced accuracy and generalization. Finally, an interactive air quality prediction system based on the ITTAO-sLSTM-Attention model and PyQt is developed, offering a user-friendly tool for air quality prediction. Full article
(This article belongs to the Section Computer)
►▼ Show Figures

Figure 1

33 pages, 3689 KB  
Article
Research on a Multi-Agent Job Shop Scheduling Method Based on Improved Game Evolution
by Wei Xie, Bin Du, Jiachen Ma, Jun Chen and Xiangle Zheng
Symmetry 2025, 17(8), 1368; https://doi.org/10.3390/sym17081368 - 21 Aug 2025
Viewed by 386
Abstract
As the global manufacturing industry’s transformation accelerates toward being intelligent, “unmanned”, and low-carbon, manufacturing workshops face conflicts between production schedules and transportation tasks, leading to low efficiency and resource waste. This paper presents a multi-agent collaborative scheduling optimization method based on a hybrid [...] Read more.
As the global manufacturing industry’s transformation accelerates toward being intelligent, “unmanned”, and low-carbon, manufacturing workshops face conflicts between production schedules and transportation tasks, leading to low efficiency and resource waste. This paper presents a multi-agent collaborative scheduling optimization method based on a hybrid game–genetic framework to address issues like high AGV (Automated Guided Vehicle) idle rates, excessive energy consumption, and uncoordinated equipment scheduling. The method establishes a trinity system integrating distributed decision-making, dynamic coordination, and environment awareness. In this system, the multi-agent decision-making and collaboration process exhibits significant symmetry characteristics. All agents (machine agents, mobile agents, etc.) follow unified optimization criteria and interaction rules, forming a dynamically balanced symmetric scheduling framework in resource competition and collaboration, which ensures fairness and consistency among different agents in task allocation, path planning, and other links. An improved best-response dynamic algorithm is employed in the decision-making layer to solve the multi-agent Nash equilibrium, while the genetic optimization layer enhances the global search capability by encoding scheduling schemes and adjusting crossover/mutation probabilities using dynamic competition factors. The coordination pivot layer updates constraints in real time based on environmental sensing, forming a closed-loop optimization mechanism. Experimental results show that, compared with the traditional genetic algorithm (TGA) and particle swarm optimization (PSO), the proposed method reduces the maximum completion time by 54.5% and 44.4% in simple scenarios and 57.1% in complex scenarios, the AGV idling rate by 68.3% in simple scenarios and 67.5%/77.6% in complex scenarios, and total energy consumption by 15.7%/10.9% in simple scenarios and 25%/18.2% in complex scenarios. This validates the method’s effectiveness in improving resource utilization and energy efficiency, providing a new technical path for intelligent scheduling in manufacturing workshops. Meanwhile, its symmetric multi-agent collaborative framework also offers a reference for the application of symmetry in complex manufacturing system optimization. Full article
(This article belongs to the Section Computer)
►▼ Show Figures

Figure 1

18 pages, 1447 KB  
Article
Symmetry-Guided Surrogate-Assisted NSGA-II for Multi-Objective Optimization of Renewable Energy Systems
by Manuel J. C. S. Reis
Symmetry 2025, 17(8), 1367; https://doi.org/10.3390/sym17081367 - 21 Aug 2025
Viewed by 607
Abstract
In this study, we propose a novel hybrid metaheuristic framework that leverages symmetry awareness to enhance the performance of multi-objective optimization in renewable energy systems. Motivated by the repetitive and structured patterns commonly found in solar, wind, and demand profiles, we introduce a [...] Read more.
In this study, we propose a novel hybrid metaheuristic framework that leverages symmetry awareness to enhance the performance of multi-objective optimization in renewable energy systems. Motivated by the repetitive and structured patterns commonly found in solar, wind, and demand profiles, we introduce a symmetry-guided variant of the NSGA-II algorithm, enriched with a customized crossover operator that detects and exploits symmetrical patterns in candidate solutions. To further accelerate convergence and reduce computational cost, we integrate a surrogate modeling strategy using machine learning to approximate fitness evaluations in later generations. Our experimental evaluation, based on a synthetic dataset simulating one week (168 h) of operation in a hybrid solar–wind power system, incorporating realistic diurnal patterns in generation and demand, demonstrates the proposed method’s superiority over baseline NSGA-II in terms of solution diversity, convergence, and runtime efficiency. The results highlight the importance of integrating domain-specific structure—such as temporal symmetry—into the design of metaheuristics for sustainable energy applications. This approach opens new avenues for scalable, intelligent optimization in complex energy environments. Full article
(This article belongs to the Special Issue Applications of Symmetry/Asymmetry in Artificial Intelligence and Deep Metaheuristics)
►▼ Show Figures

Figure 1

20 pages, 2239 KB  
Article
Lightweight Financial Fraud Detection Using a Symmetrical GAN-CNN Fusion Architecture
by Yiwen Yang, Chengjun Xu and Guisheng Tian
Symmetry 2025, 17(8), 1366; https://doi.org/10.3390/sym17081366 - 21 Aug 2025
Viewed by 622
Abstract
With the rapid development of information technology and the deep integration of the Internet platform, the scale and form of financial transactions continue to grow and expand, significantly improving users’ payment experience and life efficiency. However, financial transactions bring us convenience but also [...] Read more.
With the rapid development of information technology and the deep integration of the Internet platform, the scale and form of financial transactions continue to grow and expand, significantly improving users’ payment experience and life efficiency. However, financial transactions bring us convenience but also expose many security risks, such as money laundering activities, forged checks, and other financial fraud that occurs frequently, seriously threatening the stability and security of the financial system. Due to the imbalance between the proportion of normal and abnormal transactions in the data, most of the existing deep learning-based methods still have obvious deficiencies in learning small numbers sample classes, context modeling, and computational complexity control. To address these deficiencies, this paper proposes a symmetrical structure-based GAN-CNN model for lightweight financial fraud detection. The symmetrical structure can improve the feature extraction and fusion ability and enhance the model’s recognition effect for complex fraud patterns. Synthetic fraud samples are generated based on a GAN to alleviate category imbalance. Multi-scale convolution and attention mechanisms are designed to extract local and global transaction features, and adaptive aggregation and context encoding modules are introduced to improve computational efficiency. We conducted numerous replicate experiments on two public datasets, YelpChi and Amazon. The results showed that on the Amazon dataset with a 50% training ratio, compared with the CNN-GAN model, the accuracy of our model was improved by 1.64%, and the number of parameters was reduced by approximately 88.4%. Compared with the hybrid CNN-LSTM–attention model under the same setting, the accuracy was improved by 0.70%, and the number of parameters was reduced by approximately 87.6%. The symmetry-based lightweight architecture proposed in this work is novel in terms of structural design, and the experimental results show that it is both efficient and accurate in detecting imbalanced transactions. Full article
(This article belongs to the Section Computer)
►▼ Show Figures

Figure 1

31 pages, 2717 KB  
Article
PSO-Driven Scalable Dual-Adaptive PV Array Reconfiguration Under Partial Shading
by Özgür Karaduman and Koray Şener Parlak
Symmetry 2025, 17(8), 1365; https://doi.org/10.3390/sym17081365 - 21 Aug 2025
Viewed by 386
Abstract
Partial shading conditions cause current mismatches between series-connected panels in photovoltaic (PV) arrays, significantly reducing power efficiency. To mitigate this limitation, reconfiguration methods based on dynamically changing the electrical connections within the PV array have been proposed. In recent years, adaptive and dual-adaptive [...] Read more.
Partial shading conditions cause current mismatches between series-connected panels in photovoltaic (PV) arrays, significantly reducing power efficiency. To mitigate this limitation, reconfiguration methods based on dynamically changing the electrical connections within the PV array have been proposed. In recent years, adaptive and dual-adaptive PV connection structures, which particularly balance the line currents and aim to restore current symmetry under irregular shading conditions, have gained prominence due to their notable efficiency improvements. The dual nature of these structures inherently supports this symmetry by enabling balanced reconfigurations on both sides of the array. However, the dual-adaptive structure expands the solution space due to the exponential growth of the connection combinations with the increasing number of lines, and this makes real-time optimization difficult. In fact, this structure has been optimized with genetic algorithm (GA) before; however, the convergence time of GA exceeds acceptable limits in large arrays. In this study, a Particle Swarm Optimization (PSO) algorithm is applied to solve the dual-adaptive PV array reconfiguration problem. Particle Swarm Optimization (PSO) is a metaheuristic algorithm that utilizes swarm intelligence to efficiently explore large solution spaces. PSO’s fast convergence capability and low computational cost enable real-time applications by enabling optimization in acceptable times even for larger PV arrays. Simulation results reveal that PSO successfully manages the exponential growth in the solution space and significantly increases the real-time applicability of the reconfiguration process by effectively increasing the efficiency. In this respect, PSO is considered a powerful and practical solution for reconfiguration problems in large-scale PV arrays. Full article
(This article belongs to the Special Issue Symmetry in Green Technologies: Design, Optimization, and Applications)
►▼ Show Figures

Figure 1

30 pages, 3166 KB  
Article
Decarbonizing China’s Express Freight Market Using High-Speed Rail Services and Carbon Taxes: A Bi-Level Optimization Approach
by Lin Li
Symmetry 2025, 17(8), 1364; https://doi.org/10.3390/sym17081364 - 21 Aug 2025
Viewed by 581
Abstract
This study explores the potential for reducing CO2 emissions in China’s express freight sector by promoting a modal shift from air and road transport to high-speed rail (HSR) through the implementation of a carbon tax policy. A bi-level optimization model is employed [...] Read more.
This study explores the potential for reducing CO2 emissions in China’s express freight sector by promoting a modal shift from air and road transport to high-speed rail (HSR) through the implementation of a carbon tax policy. A bi-level optimization model is employed to analyze the decision-making processes of three key stakeholders: the government, HSR operators, and shippers. The government aims to maximize consumer surplus while reducing CO2 emissions through a carbon tax policy; HSR operators seek to maximize transportation profit; and shippers select the most efficient transportation mode based on cost and service considerations. A solution algorithm combining particle swarm optimization, the CPLEX solver, and a custom convergence procedure is designed to solve the bi-level programming model and determine the optimal carbon tax rate. The findings from the Beijing–Shanghai corridor case study indicate that a well-designed carbon tax policy, when integrated with robust HSR services, can effectively encourage a modal shift towards HSR. The extent of emission reduction is influenced by both the capacity of HSR infrastructure and the stringency of the carbon tax policy. This research highlights the importance of addressing asymmetries in transportation mode preferences and market demands. The integration of carbon tax policies with HSR services not only mitigates emissions but also promotes greater symmetry and efficiency within the transportation network. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Sustainable Transport and Logistics)
►▼ Show Figures

Figure 1

36 pages, 750 KB  
Article
Remarks on the Simple Equations Method (SEsM) for Obtaining Exact Solutions of Nonlinear Differential Equations: Selected Simple Equations
by Nikolay K. Vitanov and Kaloyan N. Vitanov
Symmetry 2025, 17(8), 1363; https://doi.org/10.3390/sym17081363 - 20 Aug 2025
Viewed by 1010
Abstract
We present a short review of the methodology and applications of the Simple Equations Method (SEsM) for obtaining exact solutions to nonlinear differential equations. The applications part of the review is focused on the simple equations used, with examples of the use of [...] Read more.
We present a short review of the methodology and applications of the Simple Equations Method (SEsM) for obtaining exact solutions to nonlinear differential equations. The applications part of the review is focused on the simple equations used, with examples of the use of the differential equations for exponential functions, for the function 1p+exp(qξ)r, for the function 1/coshn, and for the function tanhn. We list several propositions and theorems that are part of the SEsM methodology. We show how SEsM can lead to multisoliton solutions of integrable equations. Furthermore, we note that each exact solution to a nonlinear differential equation can, in principle, be obtained by the methodology of SEsM. The methodology of SEsM can be based on different simple equations. Numerous methods exist for obtaining exact solutions to nonlinear differential equations, which are based on the construction of a solution using certain known functions. Many of these methods are specific cases of SEsM, where the simple differential equation used in SEsM is the equation whose solution is the corresponding function used in these methodologies. We note that the exact solutions obtained by SEsM can be used as a basis for further research on exact solutions to corresponding differential equations by the application of methods that use the symmetries of the solved equation. Full article
(This article belongs to the Section Mathematics)
►▼ Show Figures

Figure 1

20 pages, 1301 KB  
Article
Divide-and-Merge Parallel Hierarchical Ensemble DNNs with Local Knowledge Augmentation
by Zhibin Jiang, Shuai Dong, Kaining Liu, Jie Zhou and Xiongtao Zhang
Symmetry 2025, 17(8), 1362; https://doi.org/10.3390/sym17081362 - 20 Aug 2025
Viewed by 403
Abstract
Traditional deep neural networks (DNNs) often suffer from a time-consuming training process, which is restricted by accumulation of excessive network layers and a large amount of parameters. More neural units are required to be stacked to achieve desirable performance. Specifically, when dealing with [...] Read more.
Traditional deep neural networks (DNNs) often suffer from a time-consuming training process, which is restricted by accumulation of excessive network layers and a large amount of parameters. More neural units are required to be stacked to achieve desirable performance. Specifically, when dealing with large-scale datasets, a single DNN can hardly obtain the best performance on the available limited computing resources. To address the issues above, in this paper, a novel Parallel Hierarchical Ensemble Deep Neural Network (PH-E-DNN) is proposed to improve accuracy and efficiency of the deep network. Firstly, the fuzzy C-means algorithm (FCM) is adopted so that the large-scale dataset is separated into several small data partitions. As a benefit of the fuzzy partitioning of the FCM, several sub-models can be obtained through learning their respective data partitions and isolating them from the others. Secondly, the prediction results of each sub-model in the current level are used as the discriminative knowledge appended to original regional subsets, and predictions from each level symmetrically augment inputs for the next level. In the PH-E-DNN architecture, predictions from each level symmetrically augment inputs for the next level, creating a symmetrical flow of discriminative knowledge across the hierarchical structure. Finally, multiple regional subsets are merged to form a global augmented dataset, while multi-level parallel sub-models are stacked to organize a large-scale deep ensemble network. More importantly, only the multiple DNNs in the last level are ensembled to generate the decision result of the proposed PH-E-DNN. Extensive experiments demonstrate that the PH-E-DNN is superior to some traditional and deep learning models, only requiring a few parameters to be set, which demonstrates its efficiency and flexibility. Full article
(This article belongs to the Special Issue Advances in Neural Network/Deep Learning and Symmetry/Asymmetry)
►▼ Show Figures

Figure 1

17 pages, 5026 KB  
Article
Numerical Investigation on Thermally Induced Self-Excited Thermoacoustic Oscillations in the Pipelines of Cryogenic Storage Systems
by Liu Liu, Cong Zhuo, Yongqing Liu and Geng Chen
Symmetry 2025, 17(8), 1361; https://doi.org/10.3390/sym17081361 - 20 Aug 2025
Viewed by 370
Abstract
Spacecraft and satellites are equipped with cryogenic storage systems to maintain instruments and engines at optimal operating temperatures. However, in cryogenic storage tanks, the steep temperature gradient along the pipeline (arising from sections inside and outside the tank) may induce instability in stored [...] Read more.
Spacecraft and satellites are equipped with cryogenic storage systems to maintain instruments and engines at optimal operating temperatures. However, in cryogenic storage tanks, the steep temperature gradient along the pipeline (arising from sections inside and outside the tank) may induce instability in stored gases such as helium or hydrogen, leading to large-amplitude, self-excited thermoacoustic oscillations, known as Taconis oscillations. Taconis oscillations not only cause structural damage to pipelines, jeopardizing the safety of the cryogenic storage system, but also produce significant heat leakage and boil-off losses of cryogens. This study employs computational fluid dynamics (CFD) to simulate Taconis oscillations within a U-shaped cryogenic helium pipeline. The flow dynamics and acoustic field characteristics of the cryogenic helium pipeline are first analyzed. Fast Fourier transform and wavelet transform are employed to characterize the Taconis oscillations. A subsequent parametric study investigates the influence of the location and magnitude of temperature gradients on the dynamic behavior of Taconis oscillations. Simulation results reveal that the onset temperature gradient is at a minimum when the temperature gradient is applied at one-quarter of the cryogenic pipeline. To prevent the occurrence of Taconis oscillations, the transition between the warm and cold sections should be away from one-quarter of the cryogenic helium pipe. Moreover, increasing the temperature gradient leads to the emergence of multiple oscillation modes and an upward shift in their natural frequencies. This research gives deeper insights into the dynamics of thermally induced thermoacoustic oscillations in cryogenic pipelines, providing guidelines for improving the efficiency and safety of cryogenic storage systems in aerospace engineering. Full article
(This article belongs to the Section Engineering and Materials)
►▼ Show Figures

Figure 1

20 pages, 764 KB  
Article
Black Hole Solution in f(R,G) Gravitational Theory Coupled with Scalar Field
by G. G. L. Nashed and A. Eid
Symmetry 2025, 17(8), 1360; https://doi.org/10.3390/sym17081360 - 20 Aug 2025
Viewed by 489
Abstract
In this work, we explore a class of spherically symmetric black hole (BH) solutions within the framework of modified gravity, focusing on a non-ghost-free f(R,G) theory coupled to a scalar field. We present a novel black hole geometry [...] Read more.
In this work, we explore a class of spherically symmetric black hole (BH) solutions within the framework of modified gravity, focusing on a non-ghost-free f(R,G) theory coupled to a scalar field. We present a novel black hole geometry that arises as a deformation of the Schwarzschild solution and analyze its physical and thermodynamic properties. Our results show that the model satisfies stability conditions, with the Ricci scalar R, as well as its first and second derivatives, remaining positive throughout the spacetime. The solution admits multiple horizons and exhibits strong curvature singularities compared to those in general relativity. Furthermore, it supports a non-trivial scalar field potential. A comprehensive thermodynamic analysis is performed, including evaluations of the entropy, temperature, heat capacity, and quasi-local energy. We find that the black hole exhibits thermodynamic stability within certain ranges of model parameters. In addition, we investigate geodesic deviation and derive the conditions necessary for stability within the f(R,G) gravitational framework. Full article
(This article belongs to the Section Physics)
►▼ Show Figures

Figure 1

17 pages, 3396 KB  
Article
A Direct Discrete Recurrent Neural Network with Integral Noise Tolerance and Fuzzy Integral Parameters for Discrete Time-Varying Matrix Problem Solving
by Chenfu Yi, Jie Chen and Ling Li
Symmetry 2025, 17(8), 1359; https://doi.org/10.3390/sym17081359 - 20 Aug 2025
Viewed by 381
Abstract
Discrete time-varying matrix problems are prevalent in scientific and engineering fields, and their efficient solution remains a key research objective. Existing direct discrete recurrent neural network models exhibit limitations in noise resistance and are prone to accuracy degradation in complex noise environments. To [...] Read more.
Discrete time-varying matrix problems are prevalent in scientific and engineering fields, and their efficient solution remains a key research objective. Existing direct discrete recurrent neural network models exhibit limitations in noise resistance and are prone to accuracy degradation in complex noise environments. To overcome these deficiencies, this paper proposes a fuzzy integral direct discrete recurrent neural network (FITDRNN) model. The FITDRNN model incorporates an integral term to counteract noise interference and employs a fuzzy logic system for dynamic adjustment of the integral parameter magnitude, thereby further enhancing its noise resistance. Theoretical analysis, combined with numerical experiments and robotic arm trajectory tracking experiments, verifies the convergence and noise resistance of the proposed FITDRNN model. Full article
(This article belongs to the Section Mathematics)
►▼ Show Figures

Figure 1

23 pages, 4588 KB  
Article
Discrete Memristor-Based Hyperchaotic Map and Its Analog Circuit Implementation
by Haiwei Sang, Zongyun Yang, Xianzhou Liu, Qiao Wang and Xiong Yu
Symmetry 2025, 17(8), 1358; https://doi.org/10.3390/sym17081358 - 19 Aug 2025
Viewed by 486
Abstract
In this paper, control parameters are incorporated into the absolute discrete memristor (A-DM) map proposed by Bao, and its dynamic characteristics are analyzed. Subsequently, the A-DM is introduced into the traditional sine map via parallel coupling to construct a new sine A-DM hyperchaotic [...] Read more.
In this paper, control parameters are incorporated into the absolute discrete memristor (A-DM) map proposed by Bao, and its dynamic characteristics are analyzed. Subsequently, the A-DM is introduced into the traditional sine map via parallel coupling to construct a new sine A-DM hyperchaotic map (SAHM). The dynamics of SAHM are investigated using Lyapunov exponent spectra and bifurcation diagrams, with additional analysis on its multi-stability and symmetry properties. Circuit simulations successfully realize the attractors corresponding to SAHM under typical parameters. Evaluations of SAHM’s complexity, performance comparisons, and its application to pseudorandom number generators (PRNG) demonstrate that SAHM is well-suited for secure encryption scenarios. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Chaos Theory and Application)
►▼ Show Figures

Figure 1

16 pages, 3664 KB  
Article
Water, Heat, Vapor Migration, and Frost Heaving Mechanism of Unsaturated Silty Clay During a Unidirectional Freezing Process
by Dengzhou Li and Hanghang Wang
Symmetry 2025, 17(8), 1357; https://doi.org/10.3390/sym17081357 - 19 Aug 2025
Viewed by 325
Abstract
Infrastructure development in permafrost regions continues to face growing challenges from frost heaves and thaw settlement. The traditional frost heave theory considers that soil freezing is caused by the migration of liquid water in the soil; however, existing engineering practice shows that the [...] Read more.
Infrastructure development in permafrost regions continues to face growing challenges from frost heaves and thaw settlement. The traditional frost heave theory considers that soil freezing is caused by the migration of liquid water in the soil; however, existing engineering practice shows that the migration of water vapor during the freezing process cannot be neglected. Based on the hydrothermal–air migration theory of unsaturated soils and their frost heave mechanism, this study established a coupled hydrothermal–air frost heave model for unsaturated silty clay under unidirectional freezing conditions. The computational model was verified through indoor modelling tests. The entire process of water vapor migration, moisture accumulation, and condensation-induced ice formation in unsaturated silty clay was comprehensively reproduced by numerical simulation. The results showed that the moisture field is redistributed during the freezing process of unsaturated soil. The increase in volumetric ice content in the frozen zone is due mainly to the migration of water vapor. Liquid water and water vapor in the unfrozen zone migrate towards the freezing edge driven by the temperature gradient, where they accumulate, leading to a decrease in the unsaturated pore space and a decrease in the equivalent vapor content. This study’s results can provide theoretical support for frost damage prevention in unsaturated silty clay in permafrost regions. Full article
►▼ Show Figures

Figure 1

26 pages, 6608 KB  
Article
Sim-Geometry Modal Decomposition (SGMD)-Based Optimization Strategy for Hybrid Battery and Supercapacitor Energy Storage Frequency Regulation
by Yongling He, Zhengquan Zuo, Kang Shen, Jun Gao, Qiuyu Chen, Jianqun Liu and Haoyu Liu
Symmetry 2025, 17(8), 1356; https://doi.org/10.3390/sym17081356 - 19 Aug 2025
Viewed by 476
Abstract
This study examines the issue of wind power smoothing in renewable-energy-grid integration scenarios. Under the “dual-carbon” policy initiative, large-scale renewable energy integration (particularly wind power) has become a global focus. However, the intermittency and uncertainty of wind power output exacerbate grid power fluctuations, [...] Read more.
This study examines the issue of wind power smoothing in renewable-energy-grid integration scenarios. Under the “dual-carbon” policy initiative, large-scale renewable energy integration (particularly wind power) has become a global focus. However, the intermittency and uncertainty of wind power output exacerbate grid power fluctuations, posing challenges to power system stability. Consequently, smoothing strategies for wind power energy storage systems are desperately needed to improve operational economics and grid stability. According to current research, single energy storage technologies are unable to satisfy both the system-level economic operating requirements and high-frequency power fluctuation compensation at the same time, resulting in a trade-off between economic efficiency and precision of frequency regulation. Therefore, hybrid energy storage technologies have emerged as a key research focus in wind power energy storage. This study employs the SE-SGMD method, utilizing the distinct characteristics of lithium batteries and supercapacitors to decompose frequency regulation commands into low- and high-frequency components via frequency separation strategies, thereby controlling the output of supercapacitors and lithium batteries, respectively. Additionally, the GA-GWO algorithm is applied to optimize energy-storage-system configuration, with experimental validation conducted. The theoretical contributions of this study include the following: (1) introducing the SE-SGMD frequency separation strategy into hybrid energy storage systems, overcoming the performance limitations of single energy storage devices, and (2) developing a power allocation mechanism on the basis of the inherent properties of energy storage devices. In terms of methodological innovation, the designed hybrid GA-GWO algorithm achieves a balance between optimization accuracy and efficiency. Compared to PSO-DE and GWO-PSO, the GA-GWO energy storage system demonstrates improvements of 21.10% and 17.47% in revenue, along with reductions of 6.26% and 12.57% in costs, respectively. Full article
(This article belongs to the Special Issue Navigating New Horizons: Symmetry and Advances in the Integration and Active Support of Large-Scale Renewable Energy)
►▼ Show Figures

Figure 1

18 pages, 299 KB  
Article
A Mirsky-Type Unitarily Invariant Norm Inequality for Dual Quaternion Matrices and Its Applications
by Jin Zhong and Ping Zhong
Symmetry 2025, 17(8), 1355; https://doi.org/10.3390/sym17081355 - 19 Aug 2025
Viewed by 364
Abstract
In this paper, we present a Mirsky-type unitarily invariant norm inequality for dual quaternion matrices, which can be regarded as a singular value perturbation theorem for dual quaternion matrices. By using this unitarily invariant norm inequality, we obtain some other unitarily invariant norm [...] Read more.
In this paper, we present a Mirsky-type unitarily invariant norm inequality for dual quaternion matrices, which can be regarded as a singular value perturbation theorem for dual quaternion matrices. By using this unitarily invariant norm inequality, we obtain some other unitarily invariant norm inequalities for dual quaternion matrices, including the low-rank approximation problem, eigenvalue perturbation theorem and polar decomposition. Some inequalities for the difference between singular values and eigenvalues of two dual quaternion matrices under the Frobenius norm are extended. Full article
(This article belongs to the Special Issue Exploring Symmetry in Dual Quaternion Matrices and Matrix Equations)
28 pages, 2049 KB  
Article
Joint Optimization of Delivery Time, Quality, and Cost for Complex Product Supply Chain Networks Based on Symmetry Analysis
by Peng Dong, Weibing Chen, Kewen Wang and Enze Gong
Symmetry 2025, 17(8), 1354; https://doi.org/10.3390/sym17081354 - 19 Aug 2025
Viewed by 444
Abstract
Products with complex structures are structurally intricate and involve multiple professional fields and engineering construction elements, making it difficult for a single contractor to independently develop and manufacture such complex structural products. Therefore, during the research, development, and production of complex products, collaboration [...] Read more.
Products with complex structures are structurally intricate and involve multiple professional fields and engineering construction elements, making it difficult for a single contractor to independently develop and manufacture such complex structural products. Therefore, during the research, development, and production of complex products, collaboration between manufacturers and suppliers is essential to ensure the smooth completion of projects. In this process, a complex supply chain network is often formed to achieve collaborative cooperation among all project participants. Within such a complex supply chain network, issues such as delayed delivery, poor product quality, or low resource utilization by any participant may trigger the bullwhip effect. This, in turn, can negatively impact the delivery cycle, product cost, and quality of the entire complex product, causing it to lose favorable competitive positions such as quality advantages and delivery advantages in fierce market competition. Therefore, this paper firstly explores the mechanism of complex product manufacturing and the supply network of complex product manufacturing, in order to grasp the inherent structure of complex product manufacturing with a focus on identifying symmetrical properties among supply chain nodes. Secondly, a complex product supply chain network model is constructed with the Graphical Evaluation and Review Technique (GERT), incorporating symmetry constraints to reflect balanced resource allocation and mutual dependencies among symmetrical nodes. Then, from the perspective of supply chain, we focus on identifying the shortcomings of supply chain suppliers and optimizing the management cost of the whole supply chain in order to improve the quality of complex products, delivery level, and cost saving level. This study constructs a Restricted Grey GERT (RG-GERT) network model with constrained outputs, integrates moment-generating functions and Mason’s Formula to derive transfer functions, and employs a hybrid algorithm (genetic algorithm combined with non-linear programming) to solve the multi-objective optimization problem (MOOP) for joint optimization of delivery time, quality, and cost. Empirical analysis is conducted using simulated data from Y Company’s aerospace equipment supply chain, covering interval parameters such as delivery time [5–30 days], cost [40,000–640,000 CNY], and quality [0.85–1.0], validated with industry-specific constraints. Empirical analysis using Y Company’s aerospace supply chain data shows that the model achieves a maximum customer satisfaction of 0.96, with resource utilization efficiency of inefficient suppliers improved by 15–20% (p < 0.05) after secondary optimization. Key contributions include (1) integrating symmetry analysis to simplify network modeling; (2) extending GERT with grey parameters for non-probabilistic uncertainty; (3) developing a two-stage optimization framework linking customer satisfaction and resource efficiency. Full article
(This article belongs to the Section Computer)
►▼ Show Figures

Figure 1

22 pages, 10127 KB  
Article
Ensemble-Based Susceptibility Modeling with Predictive Symmetry Optimization: A Case Study from Mount Tai, China
by Zhuang Zhao, Bin Chen, Pan Liu, Xiong Duan, Zhonglin Ji, Changjuan Feng, Xin Tan, Yixin Zhang and Fuhai Cui
Symmetry 2025, 17(8), 1353; https://doi.org/10.3390/sym17081353 - 19 Aug 2025
Viewed by 409
Abstract
Accurate prediction of geological hazard susceptibility forms the foundation of effective risk management, yet small-sample constraints often limit model generalization. In order to address this issue, this study applied an ensemble method based on predictive symmetry quantification, using Mount Tai, China, as a [...] Read more.
Accurate prediction of geological hazard susceptibility forms the foundation of effective risk management, yet small-sample constraints often limit model generalization. In order to address this issue, this study applied an ensemble method based on predictive symmetry quantification, using Mount Tai, China, as a test case. Thirteen influencing factors were integrated using six machine learning algorithms—Logistic Regression (LR), Multilayer Perceptron (MLP), Random Forest (RF), Gradient Boosting Decision Tree (GBDT), eXtreme Gradient Boosting (XGB), and Support Vector Machine (SVM)—trained on 34 hazard sites. Symmetry breaking in model outputs was quantified, and XGB and MLP, which showed the lowest correlation (0.59), were selected for dynamic weighted integration. Symmetry-adjusted weighting counteracts bias from individual models. For hyperparameter tuning, grid search was employed, while SHapley Additive exPlanations (SHAP) was used to quantify factor contributions. The performance of each model was evaluated using AUC and AP metrics. The key results show that all base models performed robustly (AUC > 0.8), with XGB showing high consistency (AUC = 0.927), and the performance of the symmetry-optimized ensemble (MLP + XGB) exceeded that of all the individual models (AUC = 0.964). The dominant drivers of Geohazards included elevation, slope, the topographic wetness index, and road adjacency, with high-susceptibility zones clustered in southeastern high-altitude terrain, central mountains, and road-intensive north-central sectors. The approach presented here provides an ensemble method based on predictive symmetry quantification that is effective under the constraints of small sample sizes. Full article
(This article belongs to the Section Computer)
►▼ Show Figures

Figure 1

17 pages, 7815 KB  
Article
Design and Analysis of Memristive Electromagnetic Radiation in a Hopfield Neural Network
by Zhimin Gu, Bin Hu, Hongxin Zhang, Xiaodan Wang, Yaning Qi and Min Yang
Symmetry 2025, 17(8), 1352; https://doi.org/10.3390/sym17081352 - 19 Aug 2025
Viewed by 449
Abstract
This study introduces a memristive Hopfield neural network (M-HNN) model to investigate electromagnetic radiation impacts on neural dynamics in complex electromagnetic environments. The proposed framework integrates a magnetic flux-controlled memristor into a three-neuron Hopfield architecture, revealing significant alterations in network dynamics through comprehensive [...] Read more.
This study introduces a memristive Hopfield neural network (M-HNN) model to investigate electromagnetic radiation impacts on neural dynamics in complex electromagnetic environments. The proposed framework integrates a magnetic flux-controlled memristor into a three-neuron Hopfield architecture, revealing significant alterations in network dynamics through comprehensive nonlinear analysis. Numerical investigations demonstrate that memristor-induced electromagnetic effects induce distinctive phenomena, including coexisting attractors, transient chaotic states, symmetric bifurcation diagrams and attractor structures, and constant chaos. The proposed system can generate more than 12 different attractors and extends the chaotic region. Compared with the chaotic range of the baseline Hopfield neural network (HNN), the expansion amplitude reaches 933%. Dynamic characteristics are systematically examined using phase trajectory analysis, bifurcation mapping, and Lyapunov exponent quantification. Experimental validation via a DSP-based hardware implementation confirms the model’s operational feasibility and consistency with numerical predictions, establishing a reliable platform for electromagnetic–neural interaction studies. Full article
(This article belongs to the Topic A Real-World Application of Chaos Theory)
►▼ Show Figures

Figure 1

21 pages, 1192 KB  
Article
Video Stabilization Algorithm Based on View Boundary Synthesis
by Wenchao Shan, Hejing Zhao, Xin Li, Qian Huang, Chuanxu Jiang, Yiming Wang, Ziqi Chen and Yao Tong
Symmetry 2025, 17(8), 1351; https://doi.org/10.3390/sym17081351 - 19 Aug 2025
Viewed by 558
Abstract
Video stabilization is a critical technology for enhancing visual content quality in dynamic shooting scenarios, especially with the widespread adoption of mobile photography devices and Unmanned Aerial Vehicle (UAV) platforms. While traditional digital stabilization algorithms can improve frame stability by modeling global motion [...] Read more.
Video stabilization is a critical technology for enhancing visual content quality in dynamic shooting scenarios, especially with the widespread adoption of mobile photography devices and Unmanned Aerial Vehicle (UAV) platforms. While traditional digital stabilization algorithms can improve frame stability by modeling global motion trajectories, they often suffer from excessive cropping or boundary distortion, leading to a significant loss of valid image regions. To address this persistent challenge, we propose the View Out-boundary Synthesis Algorithm (VOSA), a symmetry-aware spatio-temporal consistency framework. By leveraging rotational and translational symmetry principles in motion dynamics, VOSA realizes optical flow field extrapolation through an encoder–decoder architecture and an iterative boundary extension strategy. Experimental results demonstrate that VOSA enhances conventional stabilization by increasing content retention by 6.3% while maintaining a 0.943 distortion score, outperforming mainstream methods in dynamic environments. The symmetry-informed design resolves stability–content conflicts and outperforms mainstream methods in dynamic environments, establishing a new paradigm for full-frame stabilization. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Image Processing and Computer Vision)
►▼ Show Figures

Figure 1

24 pages, 1981 KB  
Article
A Lightweight Batch Authenticated Key Agreement Scheme Based on Fog Computing for VANETs
by Lihui Li, Huacheng Zhang, Song Li, Jianming Liu and Chi Chen
Symmetry 2025, 17(8), 1350; https://doi.org/10.3390/sym17081350 - 18 Aug 2025
Viewed by 338
Abstract
In recent years, fog-based vehicular ad hoc networks (VANETs) have become a hot research topic. Due to the inherent insecurity of open wireless channels between vehicles and fog nodes, establishing session keys through authenticated key agreement (AKA) protocols is critically important for securing [...] Read more.
In recent years, fog-based vehicular ad hoc networks (VANETs) have become a hot research topic. Due to the inherent insecurity of open wireless channels between vehicles and fog nodes, establishing session keys through authenticated key agreement (AKA) protocols is critically important for securing communications. However, existing AKA schemes face several critical challenges: (1) When a large number of vehicles initiate AKA requests within a short time window, existing schemes that process requests one by one individually incur severe signaling congestion, resulting in significant quality of service degradation. (2) Many AKA schemes incur excessive computational and communication overheads due to the adoption of computationally intensive cryptographic primitives (e.g., bilinear pairings and scalar multiplications on elliptic curve groups) and unreasonable design choices, making them unsuitable for the low-latency requirements of VANETs. To address these issues, we propose a lightweight batch AKA scheme based on fog computing. In our scheme, when a group of vehicles requests AKA sessions with the same fog node within the set time interval, the fog node aggregates these requests and, with assistance from the traffic control center, establishes session keys for all vehicles by a round of operations. It has significantly reduced the operational complexity of the entire system. Moreover, our scheme employs Lagrange interpolation and lightweight cryptographic tools, thereby significantly reducing both computational and communication overheads. Additionally, our scheme supports conditional privacy preservation and includes a revocation mechanism for malicious vehicles. Security analysis demonstrates that the proposed scheme meets the security and privacy requirements of VANETs. Performance evaluation indicates that our scheme outperforms existing state-of-the-art solutions in terms of efficiency. Full article
(This article belongs to the Special Issue Applications Based on Symmetry in Applied Cryptography)
►▼ Show Figures

Figure 1

22 pages, 3075 KB  
Article
Synthesizing Olfactory Understanding: Multimodal Language Models for Image–Text Smell Matching
by Sergio Esteban-Romero, Iván Martín-Fernández, Manuel Gil-Martín and Fernando Fernández-Martínez
Symmetry 2025, 17(8), 1349; https://doi.org/10.3390/sym17081349 - 18 Aug 2025
Viewed by 512
Abstract
Olfactory information, crucial for human perception, is often underrepresented compared to visual and textual data. This work explores methods for understanding smell descriptions within a multimodal context, where scent information is conveyed indirectly through text and images. We address the challenges of the [...] Read more.
Olfactory information, crucial for human perception, is often underrepresented compared to visual and textual data. This work explores methods for understanding smell descriptions within a multimodal context, where scent information is conveyed indirectly through text and images. We address the challenges of the Multimodal Understanding of Smells in Texts and Images (MUSTI) task by proposing novel approaches that leverage language-specific models and state-of-the-art multimodal large language models (MM-LLMs). Our core contribution is a multimodal framework using language-specific encoders for text and image data. This allows for a joint embedding space that explores the semantic symmetry between smells, texts, and images to identify olfactory-related connections shared across the modalities. While ensemble learning with language-specific models achieved good performance, MM-LLMs demonstrated exceptional potential. Fine-tuning a quantized version of the Qwen-VL-Chat model achieved a state-of-the-art macro F1-score of 0.7618 on the MUSTI task. This highlights the effectiveness of MM-LLMs in capturing task requirements and adapting to specific formats. Full article
(This article belongs to the Section Computer)
►▼ Show Figures

Figure 1

28 pages, 2339 KB  
Article
Biomechanical Effects of Lower Limb Asymmetry During Running: An OpenSim Computational Study
by Andreea Maria Mănescu, Carmen Grigoroiu, Neluța Smîdu, Corina Claudia Dinciu, Iulius Radulian Mărgărit, Adrian Iacobini and Dan Cristian Mănescu
Symmetry 2025, 17(8), 1348; https://doi.org/10.3390/sym17081348 - 18 Aug 2025
Cited by 2 | Viewed by 768
Abstract
Symmetry and asymmetry significantly influence running biomechanics, performance, and injury risk. Given the practical, ethical, and methodological constraints inherent in human-subject studies, computational modeling emerges as a valuable alternative for exploring biomechanical asymmetries in detail. This study systematically evaluated the mechanical effects of [...] Read more.
Symmetry and asymmetry significantly influence running biomechanics, performance, and injury risk. Given the practical, ethical, and methodological constraints inherent in human-subject studies, computational modeling emerges as a valuable alternative for exploring biomechanical asymmetries in detail. This study systematically evaluated the mechanical effects of lower limb imbalance during running using a simulation-based musculoskeletal framework in OpenSim. A total of 130 simulations were performed, incorporating controlled asymmetries in limb strength, stride length, and ground reaction forces (±5% and ±10%), to quantify alterations in joint moments, ground reaction forces (GRF), and muscular activation patterns. Results demonstrated clear biomechanical deviations under asymmetric conditions. Vertical ground reaction forces (GRF) decreased on the weaker limb and increased on the stronger limb, with peak knee joint moments rising by up to 20% under pronounced asymmetry. Muscle activation in major lower limb muscles, including the gastrocnemius and quadriceps, increased substantially on the stronger side, reflecting compensatory mechanical loading. These findings highlight the negative consequences of uneven limb loading and support the use of computational modeling to guide personalized training, rehabilitation, and injury prevention strategies. Full article
(This article belongs to the Special Issue Advances in Biomechanics and Sport Sciences: Exploring Symmetry and Asymmetry in Human Movement)
►▼ Show Figures

Figure 1

19 pages, 1846 KB  
Article
Numerical–ANN Framework for Thermal Analysis of MHD Water-Based Prandtl Nanofluid Flow over a Stretching Sheet Using Bvp4c
by Syed Asif Ali Shah, Fehaid Salem Alshammari, Muhammad Fawad Malik and Saira Batool
Symmetry 2025, 17(8), 1347; https://doi.org/10.3390/sym17081347 - 18 Aug 2025
Viewed by 510
Abstract
The main goal of this study is to create a computational solver that analyzes the effects of magnetohydrodynamics (MHD) on heat radiation in Cu–water-based Prandtl nanofluid flow using artificial neural networks. Copper nanoparticles are utilized to boost the water-based fluid’s thermal effect. [...] Read more.
The main goal of this study is to create a computational solver that analyzes the effects of magnetohydrodynamics (MHD) on heat radiation in Cu–water-based Prandtl nanofluid flow using artificial neural networks. Copper nanoparticles are utilized to boost the water-based fluid’s thermal effect. This study primarily focuses on heat transfer over a horizontal sheet, exploring different scenarios by varying key factors such as the magnetic field and thermal radiation properties. The mathematical model is formulated using partial differential equations (PDEs), which are then transformed into a corresponding set of ordinary differential equations (ODEs) through appropriate similarity transformations. The bvp4c solver is then used to simulate the numerical behavior. The effects of relevant parameters on the temperature, velocity, skin friction, and local Nusselt number profiles are examined. It is discovered that the parameters of the Prandtl fluid have a considerable impact. The local skin friction and the local Nusselt number are improved by increasing these parameters. The dataset is split into 70% training, 15% validation, and 15% testing. The ANN model successfully predicts skin friction and Nusselt number profiles, showing good agreement with numerical simulations. This hybrid framework offers a robust predictive approach for heat management systems in industrial applications. This study provides important insights for researchers and engineers aiming to comprehend flow characteristics and their behavior and to develop accurate predictive models. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Thermal Management)
►▼ Show Figures

Figure 1

5 pages, 197 KB  
Editorial
Special Issue: Chiral Symmetry in Physics
by Dubravko Klabučar
Symmetry 2025, 17(8), 1346; https://doi.org/10.3390/sym17081346 - 18 Aug 2025
Viewed by 388
Abstract
The study of symmetry principles has consistently provided excellent guidance in the search to understand the fundamental laws of nature [...] Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
23 pages, 2709 KB  
Article
Fusion of k-Means and Local Search Approach: An Improved Angular Bisector Insertion Algorithm for Solving the Traveling Salesman Problem
by Xiangfei Zeng, Jeng-Shyang Pan, Shu-Chuan Chu, Rui Wang, Xianquan Luo and Jiaqian Huang
Symmetry 2025, 17(8), 1345; https://doi.org/10.3390/sym17081345 - 18 Aug 2025
Viewed by 613
Abstract
The Angular Bisector Insertion Constructive Heuristic Algorithm (ABIA), though effective for small-scale TSPs, suffers from reduced solution quality and high computational complexity in larger instances due to the degradation of its geometric properties. To address this, two enhanced variants—k-ABIA and k-ABIA-3opt—are proposed. k-ABIA [...] Read more.
The Angular Bisector Insertion Constructive Heuristic Algorithm (ABIA), though effective for small-scale TSPs, suffers from reduced solution quality and high computational complexity in larger instances due to the degradation of its geometric properties. To address this, two enhanced variants—k-ABIA and k-ABIA-3opt—are proposed. k-ABIA employs k-means clustering to decompose large-scale problems into subgroups, each solved via ABIA, with designed inter-cluster connections to reduce global search cost. k-ABIA-3opt further integrates 3-opt local search and ATSP-specific refinement strategies to avoid local optima. Both algorithms were benchmarked against GA, AACO-LST, and the original ABIA on instances ranging from 100 to 1200 nodes, considering solution quality, stability, runtime, and ATSP performance. k-ABIA-3opt achieved the best overall solution quality, with a total deviation of 28.75%, outperforming AACO-LST (44.86%) and ABIA (144.93%). Meanwhile, k-ABIA, with its O(n2) complexity and low constant overhead, was the fastest, solving 1000-node problems within seconds on standard hardware. Both variants exhibit strong robustness due to minimal stochasticity. For ATSP, k-ABIA-3opt further incorporates directed graph-specific optimization strategies, yielding the best solution quality among all tested algorithms. In summary, k-ABIA-3opt is well-suited for scenarios demanding high-quality solutions within tight time constraints, while k-ABIA provides an efficient option for rapid large-scale TSP solving. Together, they offer scalable and effective solutions for both symmetric and asymmetric TSP instances. Full article
(This article belongs to the Section Computer)
►▼ Show Figures

Figure 1

27 pages, 1363 KB  
Article
FSTGAT: Financial Spatio-Temporal Graph Attention Network for Non-Stationary Financial Systems and Its Application in Stock Price Prediction
by Ze-Lin Wei, Hong-Yu An, Yao Yao, Wei-Cong Su, Guo Li, Saifullah, Bi-Feng Sun and Mu-Jiang-Shan Wang
Symmetry 2025, 17(8), 1344; https://doi.org/10.3390/sym17081344 - 17 Aug 2025
Viewed by 1038
Abstract
Accurately predicting stock prices is crucial for investment and risk management, but the non-stationarity of the financial market and the complex correlations among stocks pose challenges to traditional models (ARIMA, LSTM, XGBoost), resulting in difficulties in effectively capturing dynamic patterns and limited prediction [...] Read more.
Accurately predicting stock prices is crucial for investment and risk management, but the non-stationarity of the financial market and the complex correlations among stocks pose challenges to traditional models (ARIMA, LSTM, XGBoost), resulting in difficulties in effectively capturing dynamic patterns and limited prediction accuracy. To this end, this paper proposes the Financial Spatio-Temporal Graph Attention Network (FSTGAT), with the following core innovations: temporal modelling through gated causal convolution to avoid future information leakage and capture long- and short-term fluctuations; enhanced spatial correlation learning by adopting the Dynamic Graph Attention Mechanism (GATv2) that incorporates industry information; designing the Multiple-Input-Multiple-Output (MIMO) architecture of industry grouping for the simultaneous learning of intra-group synergistic and inter-group influence; symmetrically fusing spatio-temporal modules to construct a hierarchical feature extraction framework. Experiments in the commercial banking and metals sectors of the New York Stock Exchange (NYSE) show that FSTGAT significantly outperforms the benchmark model, especially in high-volatility scenarios, where the prediction error is reduced by 45–69%, and can accurately capture price turning points. This study confirms the potential of graph neural networks to model the structure of financial interconnections, providing an effective tool for stock forecasting in non-stationary markets, and its forecasting accuracy and industry correlation capturing ability can support portfolio optimization, risk management improvement and supply chain decision guidance. Full article
(This article belongs to the Section Computer)
►▼ Show Figures

Figure 1

26 pages, 2471 KB  
Article
Fault-Tolerant Tracking Observer-Based Controller Design for DFIG-Based Wind Turbine Affected by Stator Inter-Turn Short Circuit
by Yossra Sayahi, Moez Allouche, Mariem Ghamgui, Sandrine Moreau, Fernando Tadeo and Driss Mehdi
Symmetry 2025, 17(8), 1343; https://doi.org/10.3390/sym17081343 - 17 Aug 2025
Viewed by 484
Abstract
This paper introduces a novel strategy for the diagnosis and fault-tolerant control (FTC) of inter-turn short-circuit (ITSC) faults in the stator windings of Doubly Fed Induction Generator (DFIG)-based wind turbines. ITSC faults are among the most common electrical issues in rotating machines: early [...] Read more.
This paper introduces a novel strategy for the diagnosis and fault-tolerant control (FTC) of inter-turn short-circuit (ITSC) faults in the stator windings of Doubly Fed Induction Generator (DFIG)-based wind turbines. ITSC faults are among the most common electrical issues in rotating machines: early detection is therefore essential to reduce maintenance costs and prevent severe damage to the wind turbine system. To address this, a Fault Detection and Diagnosis (FDD) approach is proposed to identify and assess the severity of ITSC faults in the stator windings. A state-space model of the DFIG under ITSC fault conditions is first developed in the (d,q) reference frame. Based on this model, an Unknown Input Observer (UIO) structured using Takagi–Sugeno (T-S) fuzzy models is designed to estimate the fault level. To mitigate the impact of the fault and ensure continued operation under degraded conditions, a T-S fuzzy fault-tolerant controller is synthesized. This controller enables natural decoupling and optimal power extraction across a wide range of rotor speed variations. Since the effectiveness of the FTC relies on accurate fault information, a Proportional-Integral Observer (PIO) is employed to estimate the ITSC fault level. The proposed diagnosis and compensation strategy is validated through simulations performed on a 3 kW wind turbine system, demonstrating its efficiency and robustness. Full article
(This article belongs to the Special Issue Symmetry, Fault Detection, and Diagnosis in Automatic Control Systems)
►▼ Show Figures

Figure 1

16 pages, 1879 KB  
Article
Parameter-Gain Accelerated ZNN Model for Solving Time-Variant Nonlinear Inequality-Equation Systems and Application on Tracking Symmetrical Trajectory
by Yihui Lei, Longyi Xu and Jialiang Chen
Symmetry 2025, 17(8), 1342; https://doi.org/10.3390/sym17081342 - 17 Aug 2025
Viewed by 379
Abstract
Time-variant nonlinear problems have always been a kind of complex research object in the field of control. The accuracy and efficiency of settling time-variant nonlinear inequality-equation (NIE) systems are often affected by the nonlinearity degree of the systems, and there are currently no [...] Read more.
Time-variant nonlinear problems have always been a kind of complex research object in the field of control. The accuracy and efficiency of settling time-variant nonlinear inequality-equation (NIE) systems are often affected by the nonlinearity degree of the systems, and there are currently no complete algorithms to settle the time-variant NIE systems effectively. To settle this class of complex systems effectively, time-variant NIE systems are first equivalently transformed into a time-variant equation by introducing a nonnegative variable. Then, through the idea of zeroing neural network (ZNN) and the role of time-variant parameter-gain functions, a parameter-gain accelerated ZNN (PGAZNN) model is proposed to solve time-variant NIE systems. Theoretically, the stability of the proposed PGAZNN model is proved by strict mathematical analysis. In addition, the PGAZNN model can achieve fixed-time convergence, and the upper-bound of convergence time is estimated. Finally, numerical simulation example and symmetry trajectory tracking are given to verify the validity and correctness of the proposed PGAZNN model. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Intelligent Control and Computing)
►▼ Show Figures

Figure 1

24 pages, 1377 KB  
Review
Statistical Analysis and Mechanisms of Aircraft Electrical Power System Failures Under Redundant Symmetric Architecture: A Review
by Zhaoyang Zeng, Jinkai Wang, Qingyu Zhu, Changqi Qu and Xiaochun Fang
Symmetry 2025, 17(8), 1341; https://doi.org/10.3390/sym17081341 - 17 Aug 2025
Viewed by 594
Abstract
The aircraft power supply system plays a crucial role in maintaining the stability and safety of airborne avionics. With the evolution toward more electric and all-electric aircraft, its architecture increasingly adopts symmetrical configurations, such as dual-redundant paths and three-phase balanced outputs. However, these [...] Read more.
The aircraft power supply system plays a crucial role in maintaining the stability and safety of airborne avionics. With the evolution toward more electric and all-electric aircraft, its architecture increasingly adopts symmetrical configurations, such as dual-redundant paths and three-phase balanced outputs. However, these symmetry-based designs are often disrupted by diverse fault mechanisms encountered in complex operational environments. This review contributes a comprehensive and structured analysis of how such fault events lead to symmetry-breaking phenomena across different subsystems, including generators, converters, controllers, and distribution networks. Unlike previous reviews that treat faults in isolation, this study emphasizes the underlying physical mechanisms and hierarchical fault propagation characteristics, revealing how structural coupling and multi-physics interactions give rise to failure modes. The paper concludes by outlining future research directions in symmetry-aware fault modeling and intelligent maintenance strategies, aiming to address the growing complexity and reliability demands of next-generation aircraft. Full article
(This article belongs to the Special Issue Symmetry in Fault Detection and Diagnosis for Dynamic Systems)
►▼ Show Figures

Figure 1

24 pages, 333 KB  
Article
Is Gravity Truly Balanced? A Historical–Critical Journey Through the Equivalence Principle and the Genesis of Spacetime Geometry
by Jaume de Haro and Emilio Elizalde
Symmetry 2025, 17(8), 1340; https://doi.org/10.3390/sym17081340 - 16 Aug 2025
Viewed by 448
Abstract
We present a novel derivation of the spacetime metric generated by matter, without invoking Einstein’s field equations. For static sources, the metric arises from a relativistic formulation of D’Alembert’s principle, where the inertial force is treated as a real dynamical entity that exactly [...] Read more.
We present a novel derivation of the spacetime metric generated by matter, without invoking Einstein’s field equations. For static sources, the metric arises from a relativistic formulation of D’Alembert’s principle, where the inertial force is treated as a real dynamical entity that exactly compensates gravity. This leads to a conformastatic metric whose geodesic equation—parametrized by proper time—reproduces the relativistic version of Newton’s second law for free fall. To extend the description to moving matter—uniformly or otherwise—we apply a Lorentz transformation to the static metric. The resulting non-static metric accounts for the motion of the sources and, remarkably, matches the weak-field limit of general relativity as obtained from the linearized Einstein equations in the de Donder (or Lorenz) gauge. This approach—at least at Solar System scales, where gravitational fields are weak—is grounded in a new dynamical interpretation of the Equivalence Principle. It demonstrates how gravity can emerge from the relativistic structure of inertia, without postulating or solving Einstein’s equations. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2025)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-201
Previous Issue
Next Issue
Back to TopTop