Symmetry

22 pages, 5367 KiB

Open AccessArticle

An Improved Bee Colony Optimization Algorithm Using a Sugeno–Takagi Interval Type-2 Fuzzy Logic System for the Optimal Design of Stable Autonomous Mobile Robot Controllers

by Leticia Amador-Angulo, Patricia Melin and Oscar Castillo

Symmetry 2025, 17(5), 789; https://doi.org/10.3390/sym17050789 (registering DOI) - 20 May 2025

Abstract

This study proposes an enhanced Sugeno–Takagi interval type-2 fuzzy logic system (SIT2FLS) to find the best values for two important parameters in Bee Colony Optimization (BCO). The aim of this study was to develop a stable controller for a mobile robot utilizing BCO [...] Read more.

This study proposes an enhanced Sugeno–Takagi interval type-2 fuzzy logic system (SIT2FLS) to find the best values for two important parameters in Bee Colony Optimization (BCO). The aim of this study was to develop a stable controller for a mobile robot utilizing BCO in the fuzzy controller and to determine the best membership functions (MFs) in a type-1 fuzzy logic system (T1FLS) for control. Another objective was to use an SIT2FLS to find the best

α

and

β

parameters for BCO to enhance the robot trajectory, which was evaluated through an analysis of the mean squared errors. Three types of perturbations were analyzed and simulated. The performance of the SIT2FLS-FBCO was evaluated and compared to that of the T1FLS-FBCO. In addition, a comparative study was performed to demonstrate that the improved BCO works well when there are disturbances affecting the controller. Finally, it was compared with the Mamdani approach, and an FBCO with an interval type-3 FLS was also developed. Full article

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

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29 pages, 2596 KiB

Open AccessArticle

Symmetry and Time-Delay-Driven Dynamics of Rumor Dissemination

by Cunlin Li, Zhuanting Ma, Lufeng Yang and Tajul Ariffin Masron

Symmetry 2025, 17(5), 788; https://doi.org/10.3390/sym17050788 (registering DOI) - 19 May 2025

Abstract

The dissemination of rumors can lead to significant economic damage and pose a grave threat to social harmony and the stability of people’s livelihoods. Consequently, curbing the dissemination of rumors is of paramount importance. The model in the text assumes that the population [...] Read more.

The dissemination of rumors can lead to significant economic damage and pose a grave threat to social harmony and the stability of people’s livelihoods. Consequently, curbing the dissemination of rumors is of paramount importance. The model in the text assumes that the population is homogeneous in terms of transmission behavior. This homogeneity is essentially a manifestation of translational symmetry. This paper undertakes a thorough examination of the impact of time delay on the dissemination of rumors within social networking services. We have developed a model for rumor dissemination, establishing the positivity and boundedness of its solutions, and identified the existence of an equilibrium point. The study further involved determining the critical threshold of the proposed model, accompanied by a comprehensive examination of its Hopf bifurcation characteristics. In the expression of the threshold

R_{0}

, the parameters appear in a symmetric form, reflecting the balance between dissemination and suppression mechanisms. Furthermore, detailed investigations were carried out to assess both the localized and global stability properties of the system’s equilibrium states. In stability analysis, the symmetry in the distribution of characteristic equation roots determines the system’s dynamic behavior. Through numerical simulations, we analyzed the potential impacts and theoretically examined the factors influencing rumor dissemination, thereby validating our theoretical analysis. An optimal control strategy was formulated, and three control variables were incorporated to describe the strategy. The optimization framework incorporates a specifically designed cost function that simultaneously accounts for infection reduction and resource allocation efficiency in control strategy implementation. The optimal control strategy proposed in the study involves a comparison between symmetric and asymmetric interventions. Symmetric control measures may prove inefficient, whereas asymmetric control demonstrates higher efficacy—highlighting a trade-off in symmetry considerations for optimization problems. Full article

(This article belongs to the Special Issue Advances in Mathematical Models and Partial Differential Equations: 2nd Edition)

57 pages, 2583 KiB

Open AccessReview

Heavy–Heavy and Heavy–Light Mesons in Cold Nuclear Matter

by J. J. Cobos-Martínez, Guilherme N. Zeminiani and Kazuo Tsushima

Symmetry 2025, 17(5), 787; https://doi.org/10.3390/sym17050787 (registering DOI) - 19 May 2025

Abstract

We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and [...] Read more.

We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and an effective Lagrangian. As demonstrated by the cases of pionic and kaonic atoms, studies of the meson–nucleus bound state can provide us with important information on chiral symmetry in a dense nuclear medium. In this review, we examine the mesons,

K, K^{*}, D, D^{*}, B, B^{*}, η, η^{'}, ϕ, η_{c}, J / ψ, η_{b}, Υ

, and

B_{c}

, where our emphasis is on the heavy mesons. In addition, we also present some new results for the

B_{c}

-nucleus bound states. Full article

(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)

28 pages, 2804 KiB

Open AccessArticle

Adaptive Network-Based Fuzzy Inference System Training Using Nine Different Metaheuristic Optimization Algorithms for Time-Series Analysis of Brent Oil Price and Detailed Performance Analysis

by Ebubekir Kaya, Ahmet Kaya and Ceren Baştemur Kaya

Symmetry 2025, 17(5), 786; https://doi.org/10.3390/sym17050786 (registering DOI) - 19 May 2025

Abstract

Brent oil holds a significant position in the global energy market, as oil prices in many regions are indexed to it. Therefore, forecasting the future price of Brent oil is of great importance. In recent years, artificial intelligence techniques have been widely applied [...] Read more.

Brent oil holds a significant position in the global energy market, as oil prices in many regions are indexed to it. Therefore, forecasting the future price of Brent oil is of great importance. In recent years, artificial intelligence techniques have been widely applied in modeling and prediction tasks. In this study, an Adaptive Neuro-Fuzzy Inference System (ANFIS), a well-established AI approach, was employed for the time-series forecasting of Brent oil prices. To ensure effective learning and improve prediction accuracy, ANFIS was trained using nine different metaheuristic algorithms: Artificial Bee Colony (ABC), Selfish Herd Optimizer (SHO), Biogeography-Based Optimization (BBO), Multi-Verse Optimizer (MVO), Teaching–Learning-Based Optimization (TLBO), Cuckoo Search (CS), Moth Flame Optimization (MFO), Marine Predator Algorithm (MPA), and Flower Pollination Algorithm (FPA). Symmetric training procedures were applied across all algorithms to ensure fair and consistent evaluation. The analyses were conducted on the lowest and highest daily, weekly, and monthly Brent oil prices. Mean squared error (MSE) was used as the primary performance metric. The results showed that all algorithms achieved effective prediction performance. Among them, BBO and TLBO demonstrated superior accuracy and stability, particularly in handling the complexities of Brent oil forecasting. This study contributes to the literature by combining ANFIS and metaheuristics within a symmetric framework of experimentation and evaluation. Full article

(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry)

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25 pages, 2904 KiB

Open AccessArticle

Modeling Academic Social Networks Using Covering and Matching in Intuitionistic Fuzzy Influence Graphs

by Waheed Ahmad Khan, Yusra Arooj and Hai Van Pham

Symmetry 2025, 17(5), 785; https://doi.org/10.3390/sym17050785 (registering DOI) - 19 May 2025

Abstract

Influence graphs are essential tools for analyzing interactions and relationships in social networks. However, real-world networks often involve uncertainty due to incomplete, vague, or dynamic information. The structure of influence graphs often exhibits natural symmetries, which play a crucial role in optimizing covering [...] Read more.

Influence graphs are essential tools for analyzing interactions and relationships in social networks. However, real-world networks often involve uncertainty due to incomplete, vague, or dynamic information. The structure of influence graphs often exhibits natural symmetries, which play a crucial role in optimizing covering and matching strategies by decreasing redundancy and enhancing efficiency. Traditional influence graph models struggle to address such complexities. To address this gap, we present the novel concepts of covering and matching in intuitionistic fuzzy influence graphs (IFIGs) for modeling academic social networks. These graphs incorporate degrees of membership and non-membership to better reflect uncertainty in influence patterns. Thus, the main aim of this study is to initiate the concepts of covering and matching within the IFIG paradigm and provide its application in social networks. Initially, we establish some basic terms related to covering and matching with illustrative examples. We also investigate complete and complete bipartite IFIGs. To verify the practicality of this study, student interactions across subjects are analyzed using strong paths and strong independent sets. The proposed model is then evaluated using the TOPSIS method to rank participants based on their influence. Moreover, a comparative study is conducted to demonstrate that the proposed model not only handles uncertainty effectively but also performs better than the existing approaches. Full article

(This article belongs to the Section Mathematics)

17 pages, 3728 KiB

Open AccessArticle

Short-Term Solar Photovoltaic Power Prediction Utilizing the VMD-BKA-BP Neural Network

by Yuanquan Sun, Zhongli Wang, Jiahui Wang and Qiuhua Li

Symmetry 2025, 17(5), 784; https://doi.org/10.3390/sym17050784 (registering DOI) - 19 May 2025

Abstract

Photovoltaic (PV) power generation is characterized by high stochasticity, symmetry in daily power generation and low predictive accuracy. Enhancing the precision of power forecasting is crucial for improving symmetrical economic operation of the power grid. Due to Back-Propagation (BP) neural network prediction, there [...] Read more.

Photovoltaic (PV) power generation is characterized by high stochasticity, symmetry in daily power generation and low predictive accuracy. Enhancing the precision of power forecasting is crucial for improving symmetrical economic operation of the power grid. Due to Back-Propagation (BP) neural network prediction, there are problems such as difficulty in choosing network structure and high data requirements. A hybrid photovoltaic power forecasting model is introduced, utilizing the black-winged kite optimization algorithm (BKA) method to optimize the number of decompositions and maximum number of iterations in variational mode decomposition (VMD), as well as the critical parameters in the BP neural network. Initially, SHAP (Shapley Additive exPlanations) analysis identifies the primary factors used to serve as inputs for the K-means++ clustering of similar days, with the dataset segmented into samples of analogous days to reduce the asymmetric stochasticity of PV generation. Subsequently, the highly correlated features and PV power across different weather scenarios are decomposed using VMD, and a BKA-BP neural network prediction model is developed for each subcomponent. Ultimately, the predicted values are reconstructed through superimposition to yield the final prediction outcomes. The simulation findings indicate that VMD-BKA-BP neural network ensemble prediction model significantly enhances the short-term prediction accuracy of photovoltaic power relative to alternative models. This prediction model can be used in the future to optimize power dispatch and improve grid stability. Full article

(This article belongs to the Special Issue Applications Based on Symmetry in Machine Learning and Data Mining)

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25 pages, 6255 KiB

Open AccessArticle

Threat Intelligence Named Entity Recognition Based on Segment-Level Information Extraction and Similar Semantic Space Construction

by Long Chen, Hongli Deng, Jun Zhang, Bochuan Zheng and Rui Jiang

Symmetry 2025, 17(5), 783; https://doi.org/10.3390/sym17050783 (registering DOI) - 19 May 2025

Abstract

Threat intelligence is crucial for the early detection of network security threats, and named entity recognition (NER) plays a critical role in this process. However, traditional NER models based on sequence tagging primarily focus on word-level information for single-token entities, which leads to [...] Read more.

Threat intelligence is crucial for the early detection of network security threats, and named entity recognition (NER) plays a critical role in this process. However, traditional NER models based on sequence tagging primarily focus on word-level information for single-token entities, which leads to the inefficient extraction of multi-token entities in intelligence texts. Moreover, traditional NER models provide only a single semantic representation of intelligence texts, meaning that polysemous entities in intelligence texts cannot be effectively classified. To address these problems, this paper proposes a novel model based on segment-level information extraction and similar semantic space construction (SSNER). First, SSNER retrains the traditional BERT model based on a threat intelligence corpus and modifies BERT’s mask mechanism to extract the segment-level word embedding so that the ability of the SSNER to recognize multi-token entities is enhanced. Second, SSNER designs a similar semantic space construction method, which obtains compound semantic representations with symmetrical properties by filtering out the set of similar words and integrating them using self-attention to generate more accurate labels for the polysemous entities. The experimental results on two datasets, DNRTI and Bridges, indicate that SSNER outperforms both baseline and related models. In particular, SSNER achieves an F1-score of 96.02% on the Bridges dataset, exceeding the previous best model by approximately 1.46%. Full article

(This article belongs to the Section Computer)

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17 pages, 1082 KiB

Open AccessArticle

FedOPCS: An Optimized Poisoning Countermeasure for Non-IID Federated Learning with Privacy-Preserving Stability

by Fenhua Bai, Yinqi Zhao, Tao Shen, Kai Zeng, Xiaohui Zhang and Chi Zhang

Symmetry 2025, 17(5), 782; https://doi.org/10.3390/sym17050782 (registering DOI) - 19 May 2025

Abstract

Federated learning (FL), as a distributed machine learning framework, enables multiple participants to jointly train models without sharing data, thereby ensuring data privacy and security. However, FL systems still struggle to escape the typical poisoning threat launched by Byzantine nodes. The current defence [...] Read more.

Federated learning (FL), as a distributed machine learning framework, enables multiple participants to jointly train models without sharing data, thereby ensuring data privacy and security. However, FL systems still struggle to escape the typical poisoning threat launched by Byzantine nodes. The current defence measures almost all rely on the anomaly detection of local gradients in a plaintext state, which not only weakens privacy protection but also allows malicious clients to upload malicious ciphertext gradients once they are encrypted, which thus easily evade existing screenings. At the same time, mainstream aggregation algorithms are generally based on the premise that “each client’s data satisfy an independent and identically distributed (IID)”, which is obviously difficult to achieve in real scenarios where large-scale terminal devices hold their own data. Symmetry in data distribution and model updates across clients is crucial for achieving robust and fair aggregation, yet non-IID data and adversarial attacks disrupt this balance. To address these challenges, we propose FedOPCS, an optimized poisoning countermeasure for non-IID FL algorithms with privacy-preserving stability by introducing three key innovations: Conditional Generative Adversarial Network (CGAN)-based data augmentation with conditional variables to simulate global distribution, a dynamic weight adjustment mechanism with homomorphic encryption, and two-stage anomaly detection combining gradient analysis and model performance evaluation. Extensive experiments on MNIST and CIFAR-10 show that, in the model poisoning and mixed poisoning environments, FedOPCS outperforms the baseline methods by 11.4% and 4.7%, respectively, while maintaining the same efficiency as FedAvg. FedOPCS therefore offers a privacy-preserving, Byzantine-robust, and communication-efficient solution for future heterogeneous FL deployments. Full article

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19 pages, 289 KiB

Open AccessArticle

The Radial Symmetry and Monotonicity of Solutions of Fractional Parabolic Equations in the Unit Ball

by Xingyu Liu

Symmetry 2025, 17(5), 781; https://doi.org/10.3390/sym17050781 (registering DOI) - 19 May 2025

Abstract

We use the method of moving planes to prove the radial symmetry and monotonicity of solutions of fractional parabolic equations in the unit ball. Since the fractional Laplacian operator is a linear operator, we investigate the maximal regularity of nonlocal parabolic fractional Laplacian [...] Read more.

We use the method of moving planes to prove the radial symmetry and monotonicity of solutions of fractional parabolic equations in the unit ball. Since the fractional Laplacian operator is a linear operator, we investigate the maximal regularity of nonlocal parabolic fractional Laplacian equations in the unit ball. The maximal regularity of nonlocal parabolic fractional Laplacian equations guarantees the existence of solutions in the unit ball. Based on these conditions, we first establish a maximum principle in a parabolic cylinder, and the principles provide a starting position to apply the method of moving planes. Then, we consider the fractional parabolic equations and derive the radial symmetry and monotonicity of solutions in the unit ball. Full article

(This article belongs to the Special Issue Symmetry and Applications of Differential Geometry to the Differential Equations of Mathematical Physics)

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31 pages, 6017 KiB

Open AccessArticle

LGNet: A Symmetric Dual-Branch Lightweight Model for Remote Sensing Scene Classification Based on Lie Group Feature Extraction and Cross-Attention Mechanism

by Haoyang Zeng, Shaopu Zou, Chunlian Yao and Chengjun Xu

Symmetry 2025, 17(5), 780; https://doi.org/10.3390/sym17050780 (registering DOI) - 18 May 2025

Abstract

Existing remote sensing scene classification (RSSC) models mainly rely on convolutional neural networks (CNNs) to extract high-level features from remote sensing images, while neglecting the importance of low-level features. To address this, we propose a novel RSSC framework, LGNet, a lightweight model with [...] Read more.

Existing remote sensing scene classification (RSSC) models mainly rely on convolutional neural networks (CNNs) to extract high-level features from remote sensing images, while neglecting the importance of low-level features. To address this, we propose a novel RSSC framework, LGNet, a lightweight model with a symmetric dual-branch architecture that combines Lie group-based feature extraction with an innovative multi-dimensional cross-attention mechanism. By utilizing the Lie group feature covariance matrix in one branch, the model captures the low-level features of the image while extracting the high-level semantic information using CNNs in the parallel branch. The dynamic fusion of these multi-scale features using the attention mechanism optimizes the classification accuracy and computational efficiency. Extensive experiments on three standard datasets (AID, UC Merced, and NWPU-RESISC45) show that LGNet outperforms current state-of-the-art models, providing superior classification performance with significantly fewer parameters. Verified on publicly available challenging datasets, LGNet achieves a classification accuracy of 96.50% with 4.71M parameters on AID. Compared with other state-of-the-art models, it has certain advantages regarding classification accuracy and parameter count. These results highlight the efficiency and effectiveness of LGNet in complex remote sensing scenarios, making it a promising solution for large-scale high-resolution remote sensing images (HRSSI) tasks. Full article

(This article belongs to the Section Computer)

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21 pages, 11005 KiB

Open AccessArticle

Shape-Aware Dynamic Alignment Network for Oriented Object Detection in Aerial Images

by Linsen Zhu, Donglin Jing, Baiyu Lu, Dong Zheng, Shuaixing Ren and Zhili Chen

Symmetry 2025, 17(5), 779; https://doi.org/10.3390/sym17050779 (registering DOI) - 17 May 2025

Viewed by 64

Abstract

The field of remote sensing target detection has experienced rapid development in recent years, demonstrating significant value in various applications. However, general detection algorithms still face many key challenges when dealing with directional target detection: firstly, conventional networks struggle to accurately represent features [...] Read more.

The field of remote sensing target detection has experienced rapid development in recent years, demonstrating significant value in various applications. However, general detection algorithms still face many key challenges when dealing with directional target detection: firstly, conventional networks struggle to accurately represent features of rotated targets, particularly in modeling the slender shape characteristics of high-aspect-ratio targets; secondly, the mismatch between the static label allocation strategy and the feature space of dynamic rotating targets leads to bias in training sample selection under extreme-aspect-ratio scenarios. To address these issues, this paper proposes a single-stage Shape-Aware Dynamic Alignment Network (SADA-Net) that collaboratively enhances detection accuracy through feature representation optimization and adaptive label matching. The network’s design philosophy demonstrates greater flexibility and complementarity than that of previous models. Specifically, a Dynamic Refined Rotated Convolution Module (DRRCM) is designed to achieve rotation-adaptive feature alignment. An Anchor-Refined Feature Alignment Module (ARFAM) is further constructed to correct feature-to-spatial misalignment. In addition, a Shape-Aware Quality Assessment (SAQA) strategy is proposed to optimize sample matching quality based on target shape information. Experiment results demonstrate that SADA-Net achieves excellent performance comparable to state-of-the-art methods on three widely used remote sensing datasets (i.e., HRSC2016, DOTA, and UCAS-AOD). Full article

(This article belongs to the Section Mathematics)

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26 pages, 1969 KiB

Open AccessArticle

Dynamic Responseof Complex Defect near Anisotropic Bi-Material Interface by Incident Out-Plane Wave

by Huanan Xu, Caizhu Yang, Yonghui Wang, Guoguan Lan and Faqiang Qiu

Symmetry 2025, 17(5), 778; https://doi.org/10.3390/sym17050778 (registering DOI) - 17 May 2025

Viewed by 59

Abstract

The Dynamic response of two cavities, an elliptical inclusion and a linear crack near anisotropic bi-material interface, was explored analytically by incident out-plane waves in the current work. Firstly, the media is divided into two half spaces (an elastic anisotropic half space with [...] Read more.

The Dynamic response of two cavities, an elliptical inclusion and a linear crack near anisotropic bi-material interface, was explored analytically by incident out-plane waves in the current work. Firstly, the media is divided into two half spaces (an elastic anisotropic half space with a circular cavity and a linear crack, and an elastic isotropic half space containing an elliptical cavity and an elliptical inclusion). With the help of the image principle, the complex function method is then used to derive the wave fields in each half space. Combined with Green’s functions approach, the relevant Green’s functions developed in the “crack creation” and “conjunction of two half spaces” procedures are derived sequentially. Subsequently, based on the “conjunction” technique, undetermined anti-plane forces are applied to the horizontal surfaces of two half spaces to maintain the continuity criteria of the interface. A series of Fredholm integral equations isobtained and then solved by utilizing the direct discrete technique. Dynamic stress concentration of two elliptical cavities and an elliptical inclusion is mainly considered graphically to discuss the interaction between two half spaces. Finally, a parametric study on the dynamic stress concentration factor (DSCF) was given to show the influence of different parameters on the interaction. Full article

(This article belongs to the Section Mathematics)

46 pages, 850 KiB

Open AccessArticle

Advancing Tensor Theories

by Pierros Ntelis

Symmetry 2025, 17(5), 777; https://doi.org/10.3390/sym17050777 (registering DOI) - 16 May 2025

Viewed by 27

Abstract

This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that unifies diverse tensor indices, and explore its transformation [...] Read more.

This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that unifies diverse tensor indices, and explore its transformation properties. Using fractional derivatives, we provide a geometrical interpretation of these generalised tensors, revealing new insights into its structure. Additionally, we forge a deep connection between tensor and category theories, integrating sets, tensors, categories, and functors with extensions like partial differentiation and integration. This synthesis yields original constructs—setorial tensors, categorial tensors, and functorial tensors—which open uncharted pathways in mathematical analysis. Our contributions not only extend prior research but also significantly enhance tensor theory, category theory, set theory, logic, topology, algebraic geometry, foundations, and philosophy, with potential applications spanning physics, geometry, and beyond. Full article

(This article belongs to the Special Issue Advances in Topology and Algebraic Geometry)

21 pages, 911 KiB

Open AccessArticle

Competition in Bike-Sharing: Effects of Discount Incentives and Comfort Level

by Lishuang Bian, Qizhou Hu, Xiaoyu Wu, Xin Zhang and Minjia Tan

Symmetry 2025, 17(5), 776; https://doi.org/10.3390/sym17050776 - 16 May 2025

Viewed by 23

Abstract

This paper investigates the competition between two types of bike-sharing services, particularly at bus stops, subway stations, and residential areas. Two types of shared bicycle travel choice models are constructed. A shared bicycle operator attracts users by implementing discount incentives, and the comfort [...] Read more.

This paper investigates the competition between two types of bike-sharing services, particularly at bus stops, subway stations, and residential areas. Two types of shared bicycle travel choice models are constructed. A shared bicycle operator attracts users by implementing discount incentives, and the comfort levels of riding the two types of shared bicycles are different. The equilibrium fares, potential user demand, and operator profits under joint profit maximization, price competition, and potential user demand competition scenarios are derived, and the competitive results under the three scenarios are compared. The results show that, in the potential user demand competition, the difference in potential demand between the two operators is largest; in the joint profit maximization scenario involving shared bicycle operators, the difference in potential user demand is smallest. In all competitive scenarios, higher operating costs and costs in lowering comfort loss for the shared bicycle operators will increase fares; the substitution level between the two types of shared bicycles has a positive impact on potential user demand, and the higher the substitution level, the better the effect of discounts in attracting users. Full article

(This article belongs to the Section Engineering and Materials)

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22 pages, 3105 KiB

Open AccessArticle

High Impedance Fault Line Detection Based on Current Traveling Wave Spectrum Symmetry Driving for New Distribution Network

by Maner Xiao, Jupeng Zeng, Zehua Zhou, Qiming Zhang, Li Deng and Feiyu Peng

Symmetry 2025, 17(5), 775; https://doi.org/10.3390/sym17050775 - 16 May 2025

Viewed by 19

Abstract

Challenges are brought to high impedance fault (HIF) line selection in traditional distribution networks by the fault signals with short windows and weak characteristics provided by new energy power sources. A new method driven by the symmetry of current traveling wave spectrum is [...] Read more.

Challenges are brought to high impedance fault (HIF) line selection in traditional distribution networks by the fault signals with short windows and weak characteristics provided by new energy power sources. A new method driven by the symmetry of current traveling wave spectrum is proposed in this paper. Frequency-domain features are extracted by using Pisarenko spectral decomposition, and the differences in amplitude, frequency, and polarity between faulted and healthy feeders are analyzed. A similarity matrix is constructed with the help of Manhattan distance, and an improved density-based spatial clustering of application with noise (DBSCAN) clustering is adopted to achieve intelligent fault line selection. Experimental results show that compared with the steady state component method and the transient component method, the accuracy of this method is increased to 97.5%, with an improvement of more than 12.5%. Quantitative thresholds are replaced by qualitative spectrum differences, and this method is not affected by weak signals, thus solving the problem of threshold setting caused by the access of new energy. The accuracy of this method under different fault types, phases, and resistances is verified by simulation, ensuring easy engineering implementation. Full article

(This article belongs to the Section Engineering and Materials)

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19 pages, 933 KiB

Open AccessArticle

Revisiting the Contact Model with Diffusion Beyond the Conventional Methods

by Roberto da Silva, Eliseu Venites Filho, Henrique A. Fernandes and Paulo F. Gomes

Symmetry 2025, 17(5), 774; https://doi.org/10.3390/sym17050774 - 16 May 2025

Viewed by 12

Abstract

The contact process is a nonequilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the effects of particle mobility and diffusion on criticality have [...] Read more.

The contact process is a nonequilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the effects of particle mobility and diffusion on criticality have been preliminarily explored, they remain poorly understood in many aspects. In this work, we examine how the critical rate of the model varies with the probability of particle mobility. By analyzing different stochastic evolutions of the system, we employ two modern approaches: (1) Random Matrix Theory (RMT): By building on the success of RMT, particularly Wishart-like matrices, in studying statistical physics of systems with up-down symmetry via magnetization dynamics [R. da Silva, IJMPC 2022], we demonstrate its applicability to models with an absorbing state; (2) Optimized Temporal Power Laws: By using short-time dynamics, we optimize power laws derived from ensemble-averaged evolutions of the system. Both methods consistently reveal that the critical rate decays with mobility according to a simple Belehradek function. Additionally, a straightforward mean-field analysis supports the decay of the critical parameter with mobility, although it predicts a simpler linear dependence. We also demonstrate that the more sophisticated pair approximation mean-field model developed by ben-Avraham and Köhler aligns closely with the Belehradek function, precisely matching our lattice simulation results. Full article

(This article belongs to the Section Mathematics)

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17 pages, 8321 KiB

Open AccessArticle

Flexible Piezoresistive Sensor with High Stability Based on GO@PDMS-PU Porous Structure

by Qingfang Zhang, Yi Li, Xingyu Wang, Xiaoyu Zhang, Shuyi Liu, Hengyi Yuan, Xiaodong Yang, Da Li, Zeping Jin, Yujian Zhang, Yutong Liu and Zhengmai Bian

Symmetry 2025, 17(5), 773; https://doi.org/10.3390/sym17050773 - 16 May 2025

Viewed by 13

Abstract

In recent years, flexible piezoresistive sensors based on polydimethylsiloxane (PDMS) matrix materials have developed rapidly, showing broad application prospects in fields such as human motion monitoring, electronic skin, and intelligent robotics. However, achieving a balance between structural durability and fabrication simplicity remains challenging. [...] Read more.

In recent years, flexible piezoresistive sensors based on polydimethylsiloxane (PDMS) matrix materials have developed rapidly, showing broad application prospects in fields such as human motion monitoring, electronic skin, and intelligent robotics. However, achieving a balance between structural durability and fabrication simplicity remains challenging. Traditional methods for preparing PDMS flexible substrates with high porosity and high stability often require complex, costly processes. Breaking through the constraints of conventional material systems, this study innovatively combines the high elasticity of polydimethylsiloxane (PDMS) with the stochastically distributed porous topology of a sponge-derived biotemplate through biomimetic templating replication technology, fabricating a heterogeneous composite system with an architecturally asymmetric spatial network. After 5000 loading cycles, uncoated samples experienced a thickness reduction of 7.0 mm, while PDMS-coated samples showed minimal thickness changes (2.0–3.0 mm), positively correlated with curing agent content (5:1 to 20:1). The 5:1 ratio sample demonstrated exceptional mechanical stability. As evidenced, the PDMS film-encapsulated architecturally asymmetric spatial network demonstrates superior stress dissipation efficacy, effectively mitigating stress concentration phenomena inherent to symmetric configurations that induce matrix fracture, thereby achieving optimal mechanical stability. Compared to the pre-test resistance distribution of 10–248 Ω, after 5000 cyclic loading cycles, the uncoated samples exhibited a narrowed resistance range of 10–50 Ω, while PDMS-coated samples maintained a broader resistance range (10–240 Ω) as the curing agent ratio increased (from 20:1 to 5:1), demonstrating that increasing the curing agent ratio helps maintain conductive network stability. The 5:1 ratio sample displayed the lowest resistance variation rate attenuation—only 3% after 5000 cycles (vs. 80% for uncoated samples)—and consistently minimal attenuation at all stages, validating superior electrical stability. Under 0–6 kPa pressure, the 5:1 ratio device maintained a linear sensitivity of 0.157 kPa⁻¹, outperforming some existing works. Human motion monitoring experiments further confirmed its reliable signal output. Furthermore, the architecturally asymmetric spatial network of the device enables superior conformability to complex curvilinear geometries, leveraging its structural anisotropy to achieve seamless interfacial adaptation. By synergistically optimizing material composition and structural design, this study provides a novel technical method for developing highly durable flexible electronic devices. Full article

(This article belongs to the Section Engineering and Materials)

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36 pages, 2061 KiB

Open AccessArticle

A Symmetric Dual-Drive Text Matching Model Based on Dynamically Gated Sparse Attention Feature Distillation with a Faithful Semantic Preservation Strategy

by Peng Jiang and Xiaodong Cai

Symmetry 2025, 17(5), 772; https://doi.org/10.3390/sym17050772 - 15 May 2025

Viewed by 97

Abstract

A new text matching model based on dynamic gated sparse attention feature distillation with a faithful semantic preservation strategy is proposed to address the fact that text matching models are susceptible to interference from weakly relevant information and that they find it difficult [...] Read more.

A new text matching model based on dynamic gated sparse attention feature distillation with a faithful semantic preservation strategy is proposed to address the fact that text matching models are susceptible to interference from weakly relevant information and that they find it difficult to obtain key features that are faithful to the original semantics, resulting in a decrease in accuracy. Compared to the traditional attention mechanism, with its high computational complexity and difficulty in discarding weakly relevant features, this study designs a new dynamic gated sparse attention feature distillation method based on dynamic gated sparse attention, aiming to obtain key features. Weakly relevant features are obtained through the synergy of dynamic gated sparse attention, a gradient inversion layer, a SoftMax function, and projection theorem literacy. Among these, sparse attention enhances weakly correlated feature capture through multimodal dynamic fusion with adaptive compression. Then, the projection theorem is used to identify and discard the noisy features in the hidden layer information to obtain the key features. This feature distillation strategy, in which the semantic information of the original text is decomposed into key features and noise features, forms an orthogonal decomposition symmetry in the semantic space. A new variety of faithful semantic preservation strategies is designed to make the key features faithful to the original semantic information. This strategy introduces an interval loss function and calculates the angle between the key features and the original hidden layer information with the help of cosine similarity in order to ensure that the features reflect the semantics of the original text. This can further update the iterative key features and thus improve the accuracy. The strategy builds a feature fidelity verification mechanism with a symmetric core of bidirectional considerations of semantic accuracy and correspondence to the original text. The experimental results show that the accuracies are 89.10% and 95.01% in the English datasets MRPC and Scitail, respectively; 87.8% in the Chinese dataset PAWX; and 80.32% and 80.27% in the Ant Gold dataset, respectively. Meanwhile, the accuracies in the KUAKE-QTR dataset and Macro-F1 are 70.10% and 68.08%, respectively, which are better than other methods. Full article

(This article belongs to the Section Mathematics)

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33 pages, 1460 KiB

Open AccessArticle

A Novel Approach in 3D Model Reconstruction from Engineering Drawings Based on Symmetric Adjacency Matrices Using DXF Files and Genetic Algorithm

by Predrag Mitić, Vladimir Kočović, Milan Mišić, Miladin Stefanović, Aleksandar Đorđević, Marko Pantić and Damir Projović

Symmetry 2025, 17(5), 771; https://doi.org/10.3390/sym17050771 - 15 May 2025

Viewed by 77

Abstract

The application of CAD/CAM technologies in modern production has revolutionized manufacturing processes, leading to significant improvements in precision, efficiency, and flexibility. These technologies enable the design and manufacturing of complex geometries with high accuracy, reducing errors and material waste. CAD/CAM integration streamlines workflows, [...] Read more.

The application of CAD/CAM technologies in modern production has revolutionized manufacturing processes, leading to significant improvements in precision, efficiency, and flexibility. These technologies enable the design and manufacturing of complex geometries with high accuracy, reducing errors and material waste. CAD/CAM integration streamlines workflows, enhances productivity, and facilitates rapid prototyping, accelerating the time-to-market for new products. Additionally, it supports customization and scalability in production, allowing for cost-effective small-batch and large-scale manufacturing. Without a 3D model of the product, it is not possible to use the advantages of applying advanced CAD/CAM technologies. Recognizing 3D models from engineering drawings is essential for modern production, especially for outsourcing companies in fluctuating market conditions, where the production process is organized with 2D workshop drawings on paper. This paper proposes a novel methodology for reconstructing 3D models from 2D engineering drawings, specifically those in DXF file format, leveraging a genetic algorithm. A core component of this approach is the representation of the 2D drawing as a symmetric adjacency matrix. This matrix serves as the foundational data structure for the genetic algorithm, enabling the evolutionary process to effectively optimize the 3D reconstruction. The experimental evaluation, conducted on multiple engineering drawing test cases (including both polyhedral and cylindrical geometries), demonstrated consistent convergence of the proposed GA-based method toward topologically valid and geometrically accurate 3D wireframe models. The approach achieved successful reconstruction in all cases, with fitness scores ranging from 1.1 to 112.2 depending on model complexity, and average execution times from 2 to 100 seconds. These results confirm the method’s robustness, scalability, and applicability in real-world CAD environments, while establishing a new direction for topology-driven 3D reconstruction using evolutionary computation. Full article

(This article belongs to the Special Issue Symmetry in Process Optimization)

21 pages, 411 KiB

Open AccessArticle

Full-Duplex Relaying Systems with Massive MIMO: Equal Gain Approach

by Meng Wang, Boying Zhao, Wenqing Li, Meng Jin and Si-Nian Jin

Symmetry 2025, 17(5), 770; https://doi.org/10.3390/sym17050770 - 15 May 2025

Viewed by 56

Abstract

In this paper, the uplink spectral efficiency performance of a massive MIMO system based on full-duplex relay communication is investigated in Rician fading channels. The relay station is equipped with a large number of antennas, while multiple source and destination nodes are located [...] Read more.

In this paper, the uplink spectral efficiency performance of a massive MIMO system based on full-duplex relay communication is investigated in Rician fading channels. The relay station is equipped with a large number of antennas, while multiple source and destination nodes are located at both ends of the transceiver. Each source and destination node is equipped with a single antenna. The relay station adopts Maximum Ratio Combining/Maximum Ratio Transmission (MRC/MRT) and Equal Gain Combining/Equal Gain Transmission (EGC/EGT) schemes to perform linear preprocessing on the received signals. Approximate expressions for uplink spectral efficiency under both MRC/MRT and EGC/EGT schemes are derived, and the effects of antenna number, signal-to-noise ratio (SNR), and loop interference on spectral efficiency are analyzed. In addition, the impact of full-duplex and half-duplex modes on system performance is compared, and a hybrid relay scheme is proposed to maximize the total spectral efficiency by dynamically switching between full-duplex and half-duplex modes based on varying levels of loop interference. Finally, a novel power allocation scheme is proposed to maximize energy efficiency under given total spectral efficiency and peak power constraints at both the relay and source nodes. The results show that the impact of loop interference can be eliminated by using a massive receive antenna array, leading to the disappearance of inter-pair interference and noise. Under these conditions, the spectral efficiency of the system can be improved up to

2 N

times, while the transmission power of the user and relay nodes can be reduced to

1 / N_{rx}

and

1 / N_{tx}

, respectively. Full article

(This article belongs to the Section Engineering and Materials)

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31 pages, 9659 KiB

Open AccessArticle

Full-Element Analysis of Side-Channel Leakage Dataset on Symmetric Cryptographic Advanced Encryption Standard

by Weifeng Liu, Wenchang Li, Xiaodong Cao, Yihao Fu, Juping Wu, Jian Liu, Aidong Chen, Yanlong Zhang, Shuo Wang and Jing Zhou

Symmetry 2025, 17(5), 769; https://doi.org/10.3390/sym17050769 - 15 May 2025

Viewed by 62

Abstract

The application of deep learning in side-channel analysis faces critical challenges arising from dispersed public datasets—i.e., datasets collected from heterogeneous sources and platforms with varying formats, labeling schemes, and sampling settings—and insufficient sample distribution uniformity, characterized by imbalanced class distributions and long-tailed label [...] Read more.

The application of deep learning in side-channel analysis faces critical challenges arising from dispersed public datasets—i.e., datasets collected from heterogeneous sources and platforms with varying formats, labeling schemes, and sampling settings—and insufficient sample distribution uniformity, characterized by imbalanced class distributions and long-tailed label samples. This paper presents a systematic analysis of symmetric cryptographic AES side-channel leakage datasets, examining how these issues impact the performance of deep learning-based side-channel analysis (DL-SCA) models. We analyze over 10 widely used datasets, including DPA Contest and ASCAD, and highlight key inconsistencies via visualization, statistical metrics, and model performance evaluations. For instance, the DPA_v4 dataset exhibits extreme label imbalance with a long-tailed distribution, while the ASCAD datasets demonstrate missing leakage features. Experiments conducted using CNN and Transformer models show that such imbalances lead to high accuracy for a few labels (e.g., label 14 in DPA_v4) but also extremely poor accuracy (<0.5%) for others, severely degrading generalization. We propose targeted improvements through enhanced data collection protocols, training strategies, and feature alignment techniques. Our findings emphasize that constructing balanced datasets covering the full key space is vital to achieving robust and generalizable DL-SCA performance. This work contributes both empirical insights and methodological guidance for standardizing the design of side-channel datasets. Full article

(This article belongs to the Special Issue Applications Based on Symmetry and Asymmetry in Deep Learning and Artificial Intelligence Methods)

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45 pages, 14000 KiB

Open AccessArticle

Automated Eye Disease Diagnosis Using a 2D CNN with Grad-CAM: High-Accuracy Detection of Retinal Asymmetries for Multiclass Classification

by Sameh Abd El-Ghany, Mahmood A. Mahmood and A. A. Abd El-Aziz

Symmetry 2025, 17(5), 768; https://doi.org/10.3390/sym17050768 - 15 May 2025

Viewed by 66

Abstract

Eye diseases (EDs), including glaucoma, diabetic retinopathy, and cataracts, are major contributors to vision loss and reduced quality of life worldwide. These conditions not only affect millions of individuals but also impose a significant burden on global healthcare systems. As the population ages [...] Read more.

Eye diseases (EDs), including glaucoma, diabetic retinopathy, and cataracts, are major contributors to vision loss and reduced quality of life worldwide. These conditions not only affect millions of individuals but also impose a significant burden on global healthcare systems. As the population ages and lifestyle changes increase the prevalence of conditions like diabetes, the incidence of EDs is expected to rise, further straining diagnostic and treatment resources. Timely and accurate diagnosis is critical for effective management and prevention of vision loss, as early intervention can significantly slow disease progression and improve patient outcomes. However, traditional diagnostic methods rely heavily on manual analysis of fundus imaging, which is labor-intensive, time-consuming, and subject to human error. This underscores the urgent need for automated, efficient, and accurate diagnostic systems that can handle the growing demand while maintaining high diagnostic standards. Current approaches, while advancing, still face challenges such as inefficiency, susceptibility to errors, and limited ability to detect subtle retinal asymmetries, which are critical early indicators of disease. Effective solutions must address these issues while ensuring high accuracy, interpretability, and scalability. This research introduces a 2D single-channel convolutional neural network (CNN) based on ResNet101-V2 architecture. The model integrates gradient-weighted class activation mapping (Grad-CAM) to highlight retinal asymmetries linked to EDs, thereby enhancing interpretability and detection precision. Evaluated on retinal Optical Coherence Tomography (OCT) datasets for multiclass classification tasks, the model demonstrated exceptional performance, achieving accuracy rates of 99.90% for four-class tasks and 99.27% for eight-class tasks. By leveraging patterns of retinal symmetry and asymmetry, the proposed model improves early detection and simplifies the diagnostic workflow, offering a promising advancement in the field of automated eye disease diagnosis. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric in Deep Computer Vision and Generative Modeling)

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20 pages, 328 KiB

Open AccessArticle

Semilocal Convergence Domain of a Chandrasekhar Integral Equation

by Eulalia Martínez and Arleen Ledesma

Symmetry 2025, 17(5), 767; https://doi.org/10.3390/sym17050767 - 15 May 2025

Viewed by 51

Abstract

In this study, we discuss the semilocal convergence analysis of a fourth-order iterative method in Banach spaces. We assume the Fréchet derivative satisfies the Lipschitz continuity condition, obtains suitable recurrence relations, and determines the domain of convergence under appropriate initial estimates. In addition, [...] Read more.

In this study, we discuss the semilocal convergence analysis of a fourth-order iterative method in Banach spaces. We assume the Fréchet derivative satisfies the Lipschitz continuity condition, obtains suitable recurrence relations, and determines the domain of convergence under appropriate initial estimates. In addition, the uniqueness domain for the solution and the error bounds are obtained. Next, several numerical examples, one which includes a Chandrasekhar integral equation, are carried out to apply the theoretical findings for semilocal convergence. Then, a final overview is provided. Full article

(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry II)

19 pages, 329 KiB

Open AccessArticle

Analyzing Network Stability via Symmetric Structures and Domination Integrity in Signed Fuzzy Graphs

by Chakaravarthy Sankar, Chandran Kalaivani, Perumal Chellamani and Gangatharan Venkat Narayanan

Symmetry 2025, 17(5), 766; https://doi.org/10.3390/sym17050766 - 15 May 2025

Viewed by 78

Abstract

The concept of domination is introduced within the context of signed fuzzy graphs (signed-FGs), along with examples, as a novel metric to evaluate graph stability under varying conditions. This metric particularly focuses on dominant sets and integrity measures, providing a well-rounded approach to [...] Read more.

The concept of domination is introduced within the context of signed fuzzy graphs (signed-FGs), along with examples, as a novel metric to evaluate graph stability under varying conditions. This metric particularly focuses on dominant sets and integrity measures, providing a well-rounded approach to assessing the structural stability of signed- FGs. The necessity of fulfilling the domination integrity condition in evaluating the performance of signed-FGs is highlighted through a discussion on its formulation and an analysis of its upper and lower bounds. An algorithm for identifying strong arcs and classifying them is presented, along with an algorithm for identifying signed fuzzy trees. Furthermore, the role of symmetry in signed-FGs is explored, revealing that symmetrical structures often correspond to higher domination integrity, thus contributing to the improved stability and predictability of the graphs. The paper also establishes important connections with classical graph varieties, such as complete graphs and their variations, demonstrating that changes in domination integrity increase with certain parameters. Additionally, real-life scenarios where these concepts are applicable serve to complement the theoretical results. The case study findings illustrate the significance of domination integrity in practical contexts by emphasizing various instances where it can be determined and utilized. Such instances include identifying independent dominant sets in path and cycle diagrams, as well as estimating the lower bounds of domination integrity in these structures. The estimation of domination integrity using block graph methods is underscored as crucial for enhancing the efficiency of signed-FG applications. Full article

(This article belongs to the Section Mathematics)

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23 pages, 3716 KiB

Open AccessArticle

A Study on Dual-Mode Hybrid Dynamics Finite Element Algorithm for Human Soft Tissue Deformation Simulation

by Lei Guo, Xin Guo and Feiya Lv

Symmetry 2025, 17(5), 765; https://doi.org/10.3390/sym17050765 - 15 May 2025

Viewed by 81

Abstract

The simulation of human soft tissue deformation is a key issue in the research of surgical simulators. The most mathematically accurate model for soft tissue behavior is the finite element model (FEM), being the most widely adopted numerical approach for nonlinear continuum mechanics [...] Read more.

The simulation of human soft tissue deformation is a key issue in the research of surgical simulators. The most mathematically accurate model for soft tissue behavior is the finite element model (FEM), being the most widely adopted numerical approach for nonlinear continuum mechanics equations. The total Lagrangian explicit dynamics (TLED) model is a nonlinear FEM that could simulate the nonlinear deformation of soft tissues accurately and in real time. However, the main problems faced by this method are the high computational cost and the real-time performance of the simulation. Therefore, the linear FEM is used for ensuring computational efficiency and real-time performance of the simulation, though it is inadequate for capturing true biomechanical behavior. Consequently, we have to solve the problems of real-time performance and computational efficiency of nonlinear finite elements in simulating soft tissue deformation. To address this computational challenge, we propose a Dual-Mode Hybrid Dynamics Finite Element Algorithm (DHD-FEA). First, we divide the deformed soft tissues into the surgical area and the non-surgical area. Then, the TLED nonlinear FEM is applied to the simulation of soft tissue deformation in the surgical area, ensuring the accuracy of the simulation effect. Simultaneously, the simulation of soft tissue deformation in the non-surgical area using the linear FEM improves the real-time performance of the simulation and reduces the overall computational cost. Numerical results demonstrate that the error rate in the simulation of the DHD-FEA is lower than that of the complete linear FEM, and the computational efficiency is higher than that of the TLED. Therefore, the DHD-FEA not only ensures the accuracy of soft tissue simulation in the surgical area but also reduces the computational cost. Full article

(This article belongs to the Special Issue Simulation and Modelling in Natural Sciences, Biomedicine and Engineering III)

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25 pages, 1286 KiB

Open AccessArticle

Solving Fractional Stochastic Differential Equations via a Bilinear Time-Series Framework

by Rami Alkhateeb, Ma’mon Abu Hammad, Basma AL-Shutnawi, Nabil Laiche and Zouaoui Chikr El Mezouar

Symmetry 2025, 17(5), 764; https://doi.org/10.3390/sym17050764 - 15 May 2025

Viewed by 83

Abstract

This paper introduces a novel numerical approach for solving fractional stochastic differential equations (FSDEs) using bilinear time-series models, driven by the Caputo–Katugampola (C-K) fractional derivative. The C-K operator generalizes classical fractional derivatives by incorporating an additional parameter, enabling the enhanced modeling of memory [...] Read more.

This paper introduces a novel numerical approach for solving fractional stochastic differential equations (FSDEs) using bilinear time-series models, driven by the Caputo–Katugampola (C-K) fractional derivative. The C-K operator generalizes classical fractional derivatives by incorporating an additional parameter, enabling the enhanced modeling of memory effects and hereditary properties in stochastic systems. The primary contribution of this work is the development of an efficient numerical framework that combines bilinear time-series discretization with the C-K derivative to approximate solutions for FSDEs, which are otherwise analytically intractable due to their nonlinear and memory-dependent nature. We rigorously analyze the impact of fractional-order dynamics on system behavior. The bilinear time-series framework provides a computationally efficient alternative to traditional methods, leveraging multiplicative interactions between past observations and stochastic innovations to model complex dependencies. A key advantage of our approach is its flexibility in handling both stochasticity and fractional-order effects, making it suitable for applications in a famous nuclear physics model. To validate the method, we conduct a comparative analysis between exact solutions and numerical approximations, evaluating convergence properties under varying fractional orders and discretization steps. Our results demonstrate robust convergence, with simulations highlighting the superior accuracy of the C-K operator over classical fractional derivatives in preserving system dynamics. Additionally, we provide theoretical insights into the stability and error bounds of the discretization scheme. Using the changes in the number of simulations and the operator parameters of Caputo–Katugampola, we can extract some properties of the stochastic fractional differential model, and also note the influence of Brownian motion and its formulation on the model, the main idea posed in our contribution based on constructing the fractional solution of a proposed fractional model using known bilinear time series illustrated by application in nuclear physics models. Full article

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15 pages, 256 KiB

Open AccessArticle

Lie Group Classification for a Reduced Burgers System

by Christodoulos Sophocleous and Rita Tracinà

Symmetry 2025, 17(5), 763; https://doi.org/10.3390/sym17050763 - 14 May 2025

Viewed by 87

Abstract

We consider a variable coefficient Burgers system in two spatial variables. A similarity mapping is used to reduce the number of independent variables. Lie symmetry analysis is applied to the reduced system. We present the equivalence groups for this system and the complete [...] Read more.

We consider a variable coefficient Burgers system in two spatial variables. A similarity mapping is used to reduce the number of independent variables. Lie symmetry analysis is applied to the reduced system. We present the equivalence groups for this system and the complete Lie group classification. Lie symmetries are employed to reduce the system into ordinary differential equations. In certain cases, we derive exact solutions. A special case of the system admits a hidden symmetry. Furthermore, a differential substitution is applied to this special system that enables us to construct additional exact solutions. Full article

(This article belongs to the Section Mathematics)

14 pages, 262 KiB

Open AccessArticle

The Fractional-Order Effect Induced by Space–Time Order Mismatch in Operator Differential Equations

by Yajun Yin, Tianyi Zhou, Ruiheng Jiang, Xiaobin Yu and Chaoqian Luo

Symmetry 2025, 17(5), 762; https://doi.org/10.3390/sym17050762 - 14 May 2025

Viewed by 142

Abstract

This paper reports an interesting phenomenon in which fractional-order effects can be induced by the mismatch of the differential orders of space and time; that is, fractional-order effects can be induced by space–time symmetry breakage. Classical mathematical equations can be transformed into differential [...] Read more.

This paper reports an interesting phenomenon in which fractional-order effects can be induced by the mismatch of the differential orders of space and time; that is, fractional-order effects can be induced by space–time symmetry breakage. Classical mathematical equations can be transformed into differential equations of undetermined operators. We confirmed that the presence of fractional-order operator solutions in operator differential equations is contingent upon the mismatch of differential orders of space and time, which can induce both fractional operators in the time domain and fractional operators in the space domain. The introduction of symmetry breakage and operators of space and time offers novel insights into understanding nonlocal phenomena within the space–time continuum. Full article

(This article belongs to the Section Mathematics)

29 pages, 7785 KiB

Open AccessArticle

Data Value Assessment in Digital Economy Based on Backpropagation Neural Network Optimized by Genetic Algorithm

by Xujiang Qin, Qi He, Xin Zhang and Xiang Yang

Symmetry 2025, 17(5), 761; https://doi.org/10.3390/sym17050761 - 14 May 2025

Viewed by 135

Abstract

As a new form of economic activity driven by data resources and digital technologies, the digital economy underscores the strategic significance of data as a core production factor. This growing importance necessitates accurate and robust valuation methods. Data valuation poses core modeling challenges [...] Read more.

As a new form of economic activity driven by data resources and digital technologies, the digital economy underscores the strategic significance of data as a core production factor. This growing importance necessitates accurate and robust valuation methods. Data valuation poses core modeling challenges due to its nonlinear nature and the instability of neural networks, including gradient vanishing, parameter sensitivity, and slow convergence. To overcome these challenges, this study proposes a genetic algorithm-optimized BP (GA-BP) model, enhancing the efficiency and accuracy of data valuation. The BP neural network employs a symmetrical architecture, with neurons organized in layers and information transmitted symmetrically during both forward and backward propagation. Similarly, the genetic algorithm maintains a symmetric evolutionary process, featuring symmetric operations in both crossover and mutation. The empirical data used in this study are sourced from the Shanghai Data Exchange, comprising 519 data samples. Based on this dataset, the model incorporates 9 primary indicators and 21 secondary indicators to comprehensively assess data value, optimizing network weights and thresholds through the genetic algorithm. Experimental results show that the GA-BP model outperforms the traditional BP network in terms of mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (R²), achieving a 47.6% improvement in prediction accuracy. Furthermore, GA-BP exhibits faster convergence and greater stability. When compared to other models such as long short-term memory (LSTM), convolutional neural networks (CNNs), and optimization-based BP variants like particle swarm optimization BP (PSO-BP) and whale optimization algorithm BP (WOA-BP), GA-BP demonstrates superior generalization and robustness. This approach provides valuable insights into the commercialization of data assets. Full article

(This article belongs to the Topic Intelligent Optimization Algorithm: Theory and Applications)

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23 pages, 5411 KiB

Open AccessArticle

Numerical Study on the Heat Transfer Characteristics of a Hybrid Direct–Indirect Oil Cooling System for Electric Motors

by Jung-Su Park, Le Duc Tai and Moo-Yeon Lee

Symmetry 2025, 17(5), 760; https://doi.org/10.3390/sym17050760 - 14 May 2025

Viewed by 146

Abstract

Direct liquid cooling technology has the potential to enhance the thermal management performance of electric motors with continuously increasing energy density. However, direct liquid cooling technology has practical limitations for full-scale commercialization. In addition, the conventionally used indirect liquid cooling imposes higher thermal [...] Read more.

Direct liquid cooling technology has the potential to enhance the thermal management performance of electric motors with continuously increasing energy density. However, direct liquid cooling technology has practical limitations for full-scale commercialization. In addition, the conventionally used indirect liquid cooling imposes higher thermal resistance to cope with the increased thermal management performance of high power density electric motors. Therefore, this study proposes a hybrid direct–indirect oil cooling system as a next-generation cooling strategy for the enhanced thermal management of high power density electric motors. The heat transfer characteristics, including maximum winding, stator and motor housing temperatures, heat transfer coefficient, friction factor, pressure drop, and performance evaluation criteria (PEC), are investigated for different spray hole diameters, coolant oil volume flow rates, and motor heat loss levels. The computational model was validated with experimental results within a 5% error developed to evaluate heat transfer characteristics. The results show that spray hole diameter significantly influences cooling performance, with a larger diameter (1.7 mm) reducing hydraulic resistance while causing a slight increase in motor temperatures. The coolant oil volume flow rate has a major impact on heat dissipation, with an increase from 10 to 20 L/minute (LPM) reducing winding, stator, and housing temperatures by 22.05%, 22.70% and 24.02%, respectively. However, higher flow rates also resulted in an increased pressure drop, emphasizing the importance of the selection of a suitable volume flow rate based on the trade-off between cooling performance and energy consumption. Despite the increase in motor heat loss level from 2.6 kW to 8 kW, the hybrid direct–indirect oil cooling system effectively maintained all motor component temperatures below the critical threshold of 180 °C, confirming its suitability for high-performance electric motors. These findings contribute to the development and commercialization of the proposed next-generation cooling strategy for high power density electric motors for ensuring thermal stability and operational efficiency. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Advanced Research for Efficient Electric Vehicles)

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