Symmetry

25 pages, 1047 KiB

Open AccessArticle

Integrated Blockchain and Federated Learning for Robust Security in Internet of Vehicles Networks

by Zhikai He, Rui Xu, Binyu Wang, Qisong Meng, Qiang Tang, Li Shen, Zhen Tian and Jianyu Duan

Symmetry 2025, 17(7), 1168; https://doi.org/10.3390/sym17071168 - 21 Jul 2025

Viewed by 561

Abstract

The Internet of Vehicles (IoV) operates in an environment characterized by asymmetric security threats, where centralized vulnerabilities create a critical imbalance that can be disproportionately exploited by attackers. This study addresses this imbalance by proposing a symmetrical security framework that integrates Blockchain and [...] Read more.

The Internet of Vehicles (IoV) operates in an environment characterized by asymmetric security threats, where centralized vulnerabilities create a critical imbalance that can be disproportionately exploited by attackers. This study addresses this imbalance by proposing a symmetrical security framework that integrates Blockchain and Federated Learning (FL) to restore equilibrium in the Vehicle–Road–Cloud ecosystem. The evolution toward sixth-generation (6G) technologies amplifies both the potential of vehicle-to-everything (V2X) communications and its inherent security risks. The proposed framework achieves a delicate balance between robust security and operational efficiency. By leveraging blockchain’s symmetrical and decentralized distribution of trust, the framework ensures data and model integrity. Concurrently, the privacy-preserving approach of FL balances the need for collaborative intelligence with the imperative of safeguarding sensitive vehicle data. A novel Cloud Proxy Re-Encryption Offloading (CPRE-IoV) algorithm is introduced to facilitate efficient model updates. The architecture employs a partitioned blockchain and a smart contract-driven FL pipeline to symmetrically neutralize threats from malicious nodes. Finally, extensive simulations validate the framework’s effectiveness in establishing a resilient and symmetrically secure foundation for next-generation IoV networks. Full article

(This article belongs to the Section Computer)

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19 pages, 6699 KiB

Open AccessArticle

Research on Peak Characteristics of Turbulent Flow in Horizontal Annuli with Varying Curvatures Based on Numerical Simulation

by Panliang Liu, Yanchao Sun, Jinxiang Wang and Guohua Chang

Symmetry 2025, 17(7), 1167; https://doi.org/10.3390/sym17071167 - 21 Jul 2025

Viewed by 243

Abstract

Annular flow is a common flow configuration encountered in fields such as food engineering, energy and power engineering, and petroleum engineering. The annular space formed by the inner and outer pipes exhibits unique characteristics, with the distinct curvatures of the inner and outer [...] Read more.

Annular flow is a common flow configuration encountered in fields such as food engineering, energy and power engineering, and petroleum engineering. The annular space formed by the inner and outer pipes exhibits unique characteristics, with the distinct curvatures of the inner and outer pipes rendering the annulus fundamentally different from a circular pipe. The complexity of the annular structure complicates the rapid calculation of turbulent statistics in engineering practice, as modeling these statistics necessitates a comprehensive understanding of their peak characteristics. However, current research lacks a thorough understanding of the peak characteristics of turbulent flows in annuli with varying diameter ratios (the ratio of the inner tube’s diameter to the outer tube’s diameter) between the inner and outer pipes. To gain a deeper insight into the turbulent peak characteristics within annular flows, this study employs numerical simulation methods to investigate the first- and second-order turbulent statistics under different diameter ratios resulting from varying curvatures of the inner and outer pipes. These statistics encompass velocity distribution, the position and magnitude of maximum velocity, turbulence intensity, turbulent kinetic energy, and Reynolds stress. The research findings indicate that the contour plots of velocity, turbulence intensity, and turbulent kinetic energy distributions under different diameter ratio conditions exhibit central symmetry. The peaks of the first-order statistical quantities are located in the mainstream region of the annulus, and their positions gradually shift closer to the center of the annulus as the diameter ratio increases. For the second-order statistical quantities, peaks are observed near both the inner and outer walls, and their positions move closer to the walls as the diameter ratio rises. The peak values of turbulent characteristics show significant variations across different diameter ratios. Both the inner and outer wall surfaces exhibit peaks in their second-order statistical quantities. For instance, the maximum value of Reynolds stress near the inner tube is 101.4% of that near the outer tube, and the distance from the wall where the maximum Reynolds stress occurs near the inner tube is 97.2% of the corresponding distance near the outer tube. This study is of great significance for optimizing the diameter combination of the inner and outer pipes in annular configurations and for evaluating turbulent statistics. Full article

(This article belongs to the Section Mathematics)

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19 pages, 431 KiB

Open AccessArticle

The Detection of a Defect in a Dual-Coupling Optomechanical System

by Zhen Li and Ya-Feng Jiao

Symmetry 2025, 17(7), 1166; https://doi.org/10.3390/sym17071166 - 21 Jul 2025

Viewed by 277

Abstract

We provide an approach to detect a nitrogen-vacancy (NV) center, which might be a defect in a diamond nanomembrane, using a dual-coupling optomechanical system. The NV center modifies the energy-level structure of a dual-coupling optomechanical system through dressed states arising from its interaction [...] Read more.

We provide an approach to detect a nitrogen-vacancy (NV) center, which might be a defect in a diamond nanomembrane, using a dual-coupling optomechanical system. The NV center modifies the energy-level structure of a dual-coupling optomechanical system through dressed states arising from its interaction with the mechanical membrane. Thus, we study the photon blockade in the cavity of a dual-coupling optomechanical system in which an NV center is embedded in a single-crystal diamond nanomembrane. The NV center significantly influences the statistical properties of the cavity field. We systematically investigate how three key NV center parameters affect photon blockade: (i) its coupling strength to the mechanical membrane, (ii) transition frequency, and (iii) decay rate. We find that the NV center can shift, give rise to a new dip, and even suppress the original dip in a bare quadratic optomechanical system. In addition, we can amplify the effect of the NV center on photon statistics by adding a gravitational potential when the NV center has little effect on photon blockade. Therefore, our study provides a method to detect diamond nanomembrane defects in a dual-coupling optomechanical system. Full article

(This article belongs to the Section Physics)

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22 pages, 13310 KiB

Open AccessArticle

Dual-Domain Joint Learning Reconstruction Method (JLRM) Combined with Physical Process for Spectral Computed Tomography (SCT)

by Genwei Ma, Ping Yang and Xing Zhao

Symmetry 2025, 17(7), 1165; https://doi.org/10.3390/sym17071165 - 21 Jul 2025

Viewed by 216

Abstract

Spectral computed tomography (SCT) enables material decomposition, artifact reduction, and contrast enhancement, leveraging symmetry principles across its technical framework to enhance material differentiation and image quality. However, its nonlinear data acquisition process involving noise and scatter leads to a highly ill-posed inverse problem. [...] Read more.

Spectral computed tomography (SCT) enables material decomposition, artifact reduction, and contrast enhancement, leveraging symmetry principles across its technical framework to enhance material differentiation and image quality. However, its nonlinear data acquisition process involving noise and scatter leads to a highly ill-posed inverse problem. To address this, we propose a dual-domain iterative reconstruction network that combines joint learning reconstruction with physical process modeling, which also uses the symmetric complementary properties of the two domains for optimization. A dedicated physical module models the SCT forward process to ensure stability and accuracy, while a residual-to-residual strategy reduces the computational burden of model-based iterative reconstruction (MBIR). Our method, which won the AAPM DL-Spectral CT Challenge, achieves high-accuracy material decomposition. Extensive evaluations also demonstrate its robustness under varying noise levels, confirming the method’s generalizability. This integrated approach effectively combines the strengths of physical modeling, MBIR, and deep learning. Full article

(This article belongs to the Section Mathematics)

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10 pages, 278 KiB

Open AccessEditorial

Symmetry in Geometric Theory of Analytic Functions

by Alina Alb Lupaş

Symmetry 2025, 17(7), 1164; https://doi.org/10.3390/sym17071164 - 21 Jul 2025

Viewed by 270

Abstract

This Special Issue, titled “Symmetry in the Geometric Theory of Analytic Functions”, is addressed to researchers in the complex analysis domain [...] Full article

(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)

19 pages, 626 KiB

Open AccessArticle

A Strong Anonymous Privacy Protection Authentication Scheme Based on Certificateless IOVs

by Xiaohu He, Shan Gao, Hua Wang and Chuyan Wang

Symmetry 2025, 17(7), 1163; https://doi.org/10.3390/sym17071163 - 21 Jul 2025

Viewed by 214

Abstract

The Internet of Vehicles (IoVs) uses vehicles as the main carrier to communicate with other entities, promoting efficient transmission and sharing of traffic data. Using real identities for communication may leak private data, so pseudonyms are commonly used as identity credentials. However, existing [...] Read more.

The Internet of Vehicles (IoVs) uses vehicles as the main carrier to communicate with other entities, promoting efficient transmission and sharing of traffic data. Using real identities for communication may leak private data, so pseudonyms are commonly used as identity credentials. However, existing anonymous authentication schemes have limitations, including large vehicle storage demands, information redundancy, time-dependent pseudonym updates, and public–private key updates coupled with pseudonym changes. To address these issues, we propose a certificateless strong anonymous privacy protection authentication scheme that allows vehicles to autonomously generate and dynamically update pseudonyms. Additionally, the trusted authority transmits each entity’s partial private key via a session key, eliminating reliance on secure channels during transmission. Based on the elliptic curve discrete logarithm problem, the scheme’s existential unforgeability is proven in the random oracle model. Performance analysis shows that it outperforms existing schemes in computational cost and communication overhead, with the total computational cost reduced by 70.29–91.18% and communication overhead reduced by 27.75–82.55%, making it more suitable for privacy-sensitive and delay-critical IoV environments. Full article

(This article belongs to the Special Issue Applications Based on Symmetry in Applied Cryptography)

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30 pages, 10173 KiB

Open AccessArticle

Integrated Robust Optimization for Lightweight Transformer Models in Low-Resource Scenarios

by Hui Huang, Hengyu Zhang, Yusen Wang, Haibin Liu, Xiaojie Chen, Yiling Chen and Yuan Liang

Symmetry 2025, 17(7), 1162; https://doi.org/10.3390/sym17071162 - 21 Jul 2025

Viewed by 562

Abstract

With the rapid proliferation of artificial intelligence (AI) applications, an increasing number of edge devices—such as smartphones, cameras, and embedded controllers—are being tasked with performing AI-based inference. Due to constraints in storage capacity, computational power, and network connectivity, these devices are often categorized [...] Read more.

With the rapid proliferation of artificial intelligence (AI) applications, an increasing number of edge devices—such as smartphones, cameras, and embedded controllers—are being tasked with performing AI-based inference. Due to constraints in storage capacity, computational power, and network connectivity, these devices are often categorized as operating in resource-constrained environments. In such scenarios, deploying powerful Transformer-based models like ChatGPT and Vision Transformers is highly impractical because of their large parameter sizes and intensive computational requirements. While lightweight Transformer models, such as MobileViT, offer a promising solution to meet storage and computational limitations, their robustness remains insufficient. This poses a significant security risk for AI applications, particularly in critical edge environments. To address this challenge, our research focuses on enhancing the robustness of lightweight Transformer models under resource-constrained conditions. First, we propose a comprehensive robustness evaluation framework tailored for lightweight Transformer inference. This framework assesses model robustness across three key dimensions: noise robustness, distributional robustness, and adversarial robustness. It further investigates how model size and hardware limitations affect robustness, thereby providing valuable insights for robustness-aware model design. Second, we introduce a novel adversarial robustness enhancement strategy that integrates lightweight modeling techniques. This approach leverages methods such as gradient clipping and layer-wise unfreezing, as well as decision boundary optimization techniques like TRADES and SMART. Together, these strategies effectively address challenges related to training instability and decision boundary smoothness, significantly improving model robustness. Finally, we deploy the robust lightweight Transformer models in real-world resource-constrained environments and empirically validate their inference robustness. The results confirm the effectiveness of our proposed methods in enhancing the robustness and reliability of lightweight Transformers for edge AI applications. Full article

(This article belongs to the Section Mathematics)

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22 pages, 1805 KiB

Open AccessArticle

A Hybrid Semantic and Multi-Attention Mechanism Approach for Detecting Vulnerabilities in Smart Contract Code

by Zhenxiang He, Yanling Liu and Xiaohui Sun

Symmetry 2025, 17(7), 1161; https://doi.org/10.3390/sym17071161 - 21 Jul 2025

Viewed by 511

Abstract

Driven by blockchain technology, numerous industries are increasingly adopting smart contracts to enhance efficiency, reduce costs, and improve transparency. As a result, ensuring the security of smart contracts has become critical. Traditional detection methods often suffer from low efficiency, are prone to missing [...] Read more.

Driven by blockchain technology, numerous industries are increasingly adopting smart contracts to enhance efficiency, reduce costs, and improve transparency. As a result, ensuring the security of smart contracts has become critical. Traditional detection methods often suffer from low efficiency, are prone to missing complex vulnerabilities, and have limited accuracy. Although deep learning approaches address some of these challenges, issues with both accuracy and efficiency remain in current solutions. To overcome these limitations, this paper proposes a symmetry-inspired solution that harmonizes bidirectional and generative semantic patterns. First, we generate distinct feature extraction segments for different vulnerabilities. We then use the Bidirectional Encoder Representations from Transformers (BERT) module to extract original semantic features from these segments and the Generative Pre-trained Transformer (GPT) module to extract generative semantic features. Finally, the two sets of semantic features are fused using a multi-attention mechanism and input into a classifier for result prediction. Our method was tested on three datasets, achieving F1 scores of 93.33%, 93.65%, and 92.31%, respectively. The results demonstrate that our approach outperforms most existing methods in smart contract detection. Full article

(This article belongs to the Section Computer)

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19 pages, 1142 KiB

Open AccessArticle

Matching Concepts of m-Polar Fuzzy Incidence Graphs

by Dilara Akter Mitu, Weihua Yang, Abid Ali, Tanmoy Mahapatra, Gohar Ali and Ioan-Lucian Popa

Symmetry 2025, 17(7), 1160; https://doi.org/10.3390/sym17071160 - 20 Jul 2025

Viewed by 246

Abstract

The m-Polar Fuzzy Incidence Graph (m-PFIG) is an extension of the m-Polar Fuzzy Graph (m-PFG), which provides information on how vertices affect edges. This study explores the concept of matching within both bipartite and general m-polar [...] Read more.

The m-Polar Fuzzy Incidence Graph (m-PFIG) is an extension of the m-Polar Fuzzy Graph (m-PFG), which provides information on how vertices affect edges. This study explores the concept of matching within both bipartite and general m-polar fuzzy incidence graphs (m-PFIGs). It extends various results and theorems from fuzzy graph theory to the framework of m-PFIGs. This research investigates various operations within m-PFIGs, including augmenting paths, matching principal numbers, and the relationships among them. It focuses on identifying the most suitable employees for specific roles and achieving optimal outcomes, particularly in situations involving internal conflicts within an organization. To address fuzzy maximization problems involving vertex–incidence pairs, this study outlines key properties of maximum matching principal numbers in m-PFIGs. Ultimately, the matching concept is applied to attain these maximum principal values, demonstrating its effectiveness, particularly in bipartite m-PFIG scenarios. Full article

(This article belongs to the Special Issue Symmetry and Graph Theory, 2nd Edition)

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25 pages, 1507 KiB

Open AccessArticle

DARN: Distributed Adaptive Regularized Optimization with Consensus for Non-Convex Non-Smooth Composite Problems

by Cunlin Li and Yinpu Ma

Symmetry 2025, 17(7), 1159; https://doi.org/10.3390/sym17071159 - 20 Jul 2025

Viewed by 271

Abstract

This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to [...] Read more.

This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to enforce strong convexity of weakly convex objectives and ensure subproblem well-posedness; (2) a consensus update based on doubly stochastic matrices, guaranteeing asymptotic convergence of agent states to a global consensus point; and (3) an innovative adaptive regularization mechanism that dynamically adjusts regularization strength using local function value variations to balance stability and convergence speed. Theoretical analysis demonstrates that the algorithm maintains strict monotonic descent under non-convex and non-smooth conditions by constructing a mixed time-scale Lyapunov function, achieving a sublinear convergence rate. Notably, we prove that the projection-based update rule for regularization parameters preserves lower-bound constraints, while spectral decay properties of consensus errors and perturbations from local updates are globally governed by the Lyapunov function. Numerical experiments validate the algorithm’s superiority in sparse principal component analysis and robust matrix completion tasks, showing a 6.6% improvement in convergence speed and a 51.7% reduction in consensus error compared to fixed-regularization methods. This work provides theoretical guarantees and an efficient framework for distributed non-convex optimization in heterogeneous networks. Full article

(This article belongs to the Section Mathematics)

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26 pages, 487 KiB

Open AccessArticle

Biquadratic Tensors: Eigenvalues and Structured Tensors

by Liqun Qi and Chunfeng Cui

Symmetry 2025, 17(7), 1158; https://doi.org/10.3390/sym17071158 - 20 Jul 2025

Cited by 1 | Viewed by 216

Abstract

The covariance tensors in statistics and Riemann curvature tensor in relativity theory are both biquadratic tensors that are weakly symmetric, but not symmetric in general. Motivated by this, in this paper, we consider nonsymmetric biquadratic tensors and extend M-eigenvalues to nonsymmetric biquadratic tensors [...] Read more.

The covariance tensors in statistics and Riemann curvature tensor in relativity theory are both biquadratic tensors that are weakly symmetric, but not symmetric in general. Motivated by this, in this paper, we consider nonsymmetric biquadratic tensors and extend M-eigenvalues to nonsymmetric biquadratic tensors by symmetrizing these tensors. We present a Gershgorin-type theorem for biquadratic tensors, and show that (strictly) diagonally dominated biquadratic tensors are positive semi-definite (definite). We introduce Z-biquadratic tensors, M-biquadratic tensors, strong M-biquadratic tensors,

B_{0}

-biquadratic tensors, and B-biquadratic tensors. We show that M-biquadratic tensors and symmetric

B_{0}

-biquadratic tensors are positive semi-definite, and that strong M-biquadratic tensors and symmetric B-biquadratic tensors are positive definite. A Riemannian Limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method for computing the smallest M-eigenvalue of a general biquadratic tensor is presented. Numerical results are reported. Full article

(This article belongs to the Section Mathematics)

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16 pages, 278 KiB

Open AccessArticle

Maximal Norms of Orthogonal Projections and Closed-Range Operators

by Salma Aljawi, Cristian Conde, Kais Feki and Shigeru Furuichi

Symmetry 2025, 17(7), 1157; https://doi.org/10.3390/sym17071157 - 19 Jul 2025

Viewed by 280

Abstract

Using the Dixmier angle between two closed subspaces of a complex Hilbert space

H

, we establish the necessary and sufficient conditions for the operator norm of the sum of two orthogonal projections,

P_{W_{1}}

and

P_{W_{2}}

, onto closed [...] Read more.

Using the Dixmier angle between two closed subspaces of a complex Hilbert space

H

, we establish the necessary and sufficient conditions for the operator norm of the sum of two orthogonal projections,

P_{W_{1}}

and

P_{W_{2}}

, onto closed subspaces

W_{1}

and

W_{2}

, to attain its maximum, namely

∥ P_{W_{1}} + P_{W_{2}} ∥ = 2 .

These conditions are expressed in terms of the geometric relationship and symmetry between the ranges of the projections. We apply these results to orthogonal projections associated with a closed-range operator via its Moore–Penrose inverse. Additionally, for any bounded operator T with closed range in

H

, we derive sufficient conditions ensuring

∥ T T^{†} + T^{†} T ∥ = 2,

where

T^{†}

denotes the Moore–Penrose inverse of T. This work highlights how symmetry between operator ranges and their algebraic structure governs norm extremality and extends a recent finite-dimensional result to the general Hilbert space setting. Full article

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

14 pages, 1344 KiB

Open AccessArticle

Approximate Solutions of the Fisher–Kolmogorov Equation in an Analytic Domain of the Complex Plane

by Victor Orlov and Alexander Chichurin

Symmetry 2025, 17(7), 1156; https://doi.org/10.3390/sym17071156 - 19 Jul 2025

Viewed by 167

Abstract

The paper oresents the analytical construction of approximate solutions to the generalized Fisher–Kolmogorov equation in the complex domain. The existence and uniqueness of such solutions are established within an analytic domanin of the complex plane. The study employs techniques from complex function theory [...] Read more.

The paper oresents the analytical construction of approximate solutions to the generalized Fisher–Kolmogorov equation in the complex domain. The existence and uniqueness of such solutions are established within an analytic domanin of the complex plane. The study employs techniques from complex function theory and introduces a modified version of the Cauchy majorant method. The principal innovation of the proposed approach, as opposed to the classical method, lies in constructing the majorant for the solution of the equation rather than for its right-hand side. A formula for calculating the analyticity radius is derived, which guarantees the absence of a movable singular point of algebraic type for the solutions under consideration. Special exact periodic solutions are found in elementary functions. Theoretical results are verified by numerical study. Full article

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

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24 pages, 824 KiB

Open AccessArticle

MMF-Gait: A Multi-Model Fusion-Enhanced Gait Recognition Framework Integrating Convolutional and Attention Networks

by Kamrul Hasan, Khandokar Alisha Tuhin, Md Rasul Islam Bapary, Md Shafi Ud Doula, Md Ashraful Alam, Md Atiqur Rahman Ahad and Md. Zasim Uddin

Symmetry 2025, 17(7), 1155; https://doi.org/10.3390/sym17071155 - 19 Jul 2025

Viewed by 505

Abstract

Gait recognition is a reliable biometric approach that uniquely identifies individuals based on their natural walking patterns. It is widely used to recognize individuals who are challenging to camouflage and do not require a person’s cooperation. The general face-based person recognition system often [...] Read more.

Gait recognition is a reliable biometric approach that uniquely identifies individuals based on their natural walking patterns. It is widely used to recognize individuals who are challenging to camouflage and do not require a person’s cooperation. The general face-based person recognition system often fails to determine the offender’s identity when they conceal their face by wearing helmets and masks to evade identification. In such cases, gait-based recognition is ideal for identifying offenders, and most existing work leverages a deep learning (DL) model. However, a single model often fails to capture a comprehensive selection of refined patterns in input data when external factors are present, such as variation in viewing angle, clothing, and carrying conditions. In response to this, this paper introduces a fusion-based multi-model gait recognition framework that leverages the potential of convolutional neural networks (CNNs) and a vision transformer (ViT) in an ensemble manner to enhance gait recognition performance. Here, CNNs capture spatiotemporal features, and ViT features multiple attention layers that focus on a particular region of the gait image. The first step in this framework is to obtain the Gait Energy Image (GEI) by averaging a height-normalized gait silhouette sequence over a gait cycle, which can handle the left–right gait symmetry of the gait. After that, the GEI image is fed through multiple pre-trained models and fine-tuned precisely to extract the depth spatiotemporal feature. Later, three separate fusion strategies are conducted, and the first one is decision-level fusion (DLF), which takes each model’s decision and employs majority voting for the final decision. The second is feature-level fusion (FLF), which combines the features from individual models through pointwise addition before performing gait recognition. Finally, a hybrid fusion combines DLF and FLF for gait recognition. The performance of the multi-model fusion-based framework was evaluated on three publicly available gait databases: CASIA-B, OU-ISIR D, and the OU-ISIR Large Population dataset. The experimental results demonstrate that the fusion-enhanced framework achieves superior performance. Full article

(This article belongs to the Special Issue Symmetry and Its Applications in Image Processing)

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33 pages, 2297 KiB

Open AccessArticle

Orthogonal-Constrained Graph Non-Negative Matrix Factorization for Clustering

by Wen Li, Junjian Zhao and Yasong Chen

Symmetry 2025, 17(7), 1154; https://doi.org/10.3390/sym17071154 - 19 Jul 2025

Viewed by 285

Abstract

We propose a novel approach for clustering problem, which refers to as Graph Regularized Orthogonal Subspace Non Negative Matrix Factorization (GNMFOS). This type of model introduces both graph regularization and orthogonality as penalty terms into the objective function. It not only obtains the [...] Read more.

We propose a novel approach for clustering problem, which refers to as Graph Regularized Orthogonal Subspace Non Negative Matrix Factorization (GNMFOS). This type of model introduces both graph regularization and orthogonality as penalty terms into the objective function. It not only obtains the uniqueness of matrix decomposition but also improves the sparsity of decomposition and reduces computational complexity. Most importantly, using the idea of iteration under weak orthogonality, we construct an auxiliary function for the algorithm and obtain convergence proof to compensate for the lack of convergence proof in similar models. The experimental results show that compared with classical models such as GNMF and NMFOS, our algorithm significantly improves clustering performance and the quality of reconstructed images. Full article

(This article belongs to the Section Mathematics)

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32 pages, 907 KiB

Open AccessArticle

A New Exponentiated Power Distribution for Modeling Censored Data with Applications to Clinical and Reliability Studies

by Kenechukwu F. Aforka, H. E. Semary, Sidney I. Onyeagu, Harrison O. Etaga, Okechukwu J. Obulezi and A. S. Al-Moisheer

Symmetry 2025, 17(7), 1153; https://doi.org/10.3390/sym17071153 - 18 Jul 2025

Viewed by 1025

Abstract

This paper presents the exponentiated power shanker (EPS) distribution, a fresh three-parameter extension of the standard Shanker distribution with the ability to extend a wider class of data behaviors, from right-skewed and heavy-tailed phenomena. The structural properties of the distribution, namely complete and [...] Read more.

This paper presents the exponentiated power shanker (EPS) distribution, a fresh three-parameter extension of the standard Shanker distribution with the ability to extend a wider class of data behaviors, from right-skewed and heavy-tailed phenomena. The structural properties of the distribution, namely complete and incomplete moments, entropy, and the moment generating function, are derived and examined in a formal manner. Maximum likelihood estimation (MLE) techniques are used for estimation of parameters, as well as a Monte Carlo simulation study to account for estimator performance across varying sample sizes and parameter values. The EPS model is also generalized to a regression paradigm to include covariate data, whose estimation is also conducted via MLE. Practical utility and flexibility of the EPS distribution are demonstrated through two real examples: one for the duration of repairs and another for HIV/AIDS mortality in Germany. Comparisons with some of the existing distributions, i.e., power Zeghdoudi, power Ishita, power Prakaamy, and logistic-Weibull, are made through some of the goodness-of-fit statistics such as log-likelihood, AIC, BIC, and the Kolmogorov–Smirnov statistic. Graphical plots, including PP plots, QQ plots, TTT plots, and empirical CDFs, further confirm the high modeling capacity of the EPS distribution. Results confirm the high goodness-of-fit and flexibility of the EPS model, making it a very good tool for reliability and biomedical modeling. Full article

(This article belongs to the Section Mathematics)

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22 pages, 7609 KiB

Open AccessArticle

Generalizable Potential Supplier Recommendation Under Small-Sized Datasets via Adaptive Feature Perception Model

by Qinglong Wu, Lingling Tang, Zhisen Chen and Xiaochen Zhang

Symmetry 2025, 17(7), 1152; https://doi.org/10.3390/sym17071152 - 18 Jul 2025

Viewed by 286

Abstract

Precisely deciding potential suppliers enables companies to engage with high-caliber partners that fulfill their strategic development requirements, bolster their core competitiveness, and foster sustainable market growth. To mitigate the challenges enterprises face in selecting appropriate suppliers, a recommendation method for potential suppliers tailored [...] Read more.

Precisely deciding potential suppliers enables companies to engage with high-caliber partners that fulfill their strategic development requirements, bolster their core competitiveness, and foster sustainable market growth. To mitigate the challenges enterprises face in selecting appropriate suppliers, a recommendation method for potential suppliers tailored to a small-sized dataset is proposed. This approach employs an enhanced Graph Convolutional Neural Network (GCNN) to resolve the accuracy deficiencies in supplier recommendations within a limited dataset. Initially, a supply preference network is created to ascertain the topological relationship between the company and its suppliers. Subsequently, the GCNN is enhanced through dual-path refinements in network structure and loss function, culminating in the adaptive feature perception model. Thereafter, the adaptive feature perception model is employed to adaptively learn the topological relationship and extract the company’s procurement preference vector from the trained model. A matching approach is employed to produce a recommended supplier list for the company. A case study involving 143 publicly listed companies is presented, revealing that the proposed method markedly enhances the accuracy of potential supplier recommendations on a small-sized dataset, thereby offering a dependable and efficient approach for enterprises to effectively evaluate potential suppliers with limited data. Full article

(This article belongs to the Section Computer)

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24 pages, 1571 KiB

Open AccessArticle

HE/MPC-Based Scheme for Secure Computing LCM/GCD and Its Application to Federated Learning

by Xin Liu, Xinyuan Guo, Dan Luo, Lanying Liang, Wei Ye, Yuchen Zhang, Baohua Zhang, Yu Gu and Yu Guo

Symmetry 2025, 17(7), 1151; https://doi.org/10.3390/sym17071151 - 18 Jul 2025

Viewed by 350

Abstract

Federated learning promotes the development of cross-domain intelligent applications under the premise of protecting data privacy, but there are still problems of sensitive parameter information leakage of multi-party data temporal alignment and resource scheduling process, and traditional symmetric encryption schemes suffer from low [...] Read more.

Federated learning promotes the development of cross-domain intelligent applications under the premise of protecting data privacy, but there are still problems of sensitive parameter information leakage of multi-party data temporal alignment and resource scheduling process, and traditional symmetric encryption schemes suffer from low efficiency and poor security. To this end, in this paper, based on the modified NTRU-type multi-key fully homomorphic encryption scheme, an asymmetric algorithm, a secure computation scheme of multi-party least common multiple and greatest common divisor without full set under the semi-honest model is proposed. Participants strictly follow the established process. Nevertheless, considering that malicious participants may engage in poisoning attacks such as tampering with or uploading incorrect data to disrupt the protocol process and cause incorrect results, a scheme against malicious spoofing is further proposed, which resists malicious spoofing behaviors and not all malicious attacks, to verify the correctness of input parameters or data through hash functions and zero-knowledge proof, ensuring it can run safely and stably. Experimental results show that our semi-honest model scheme improves the efficiency by 39.5% and 45.6% compared to similar schemes under different parameter conditions, and it is able to efficiently process small and medium-sized data in real time under high bandwidth; although there is an average time increase of 1.39 s, the anti-malicious spoofing scheme takes into account both security and efficiency, achieving the design expectations. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Cryptography and Cyber Security)

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21 pages, 5616 KiB

Open AccessArticle

Symmetry-Guided Dual-Branch Network with Adaptive Feature Fusion and Edge-Aware Attention for Image Tampering Localization

by Zhenxiang He, Le Li and Hanbin Wang

Symmetry 2025, 17(7), 1150; https://doi.org/10.3390/sym17071150 - 18 Jul 2025

Viewed by 335

Abstract

When faced with diverse types of image tampering and image quality degradation in real-world scenarios, traditional image tampering localization methods often struggle to balance boundary accuracy and robustness. To address these issues, this paper proposes a symmetric guided dual-branch image tampering localization network—FENet [...] Read more.

When faced with diverse types of image tampering and image quality degradation in real-world scenarios, traditional image tampering localization methods often struggle to balance boundary accuracy and robustness. To address these issues, this paper proposes a symmetric guided dual-branch image tampering localization network—FENet (Fusion-Enhanced Network)—that integrates adaptive feature fusion and edge attention mechanisms. This method is based on a structurally symmetric dual-branch architecture, which extracts RGB semantic features and SRM noise residual information to comprehensively capture the fine-grained differences in tampered regions at the visual and statistical levels. To effectively fuse different features, this paper designs a self-calibrating fusion module (SCF), which introduces a content-aware dynamic weighting mechanism to adaptively adjust the importance of different feature branches, thereby enhancing the discriminative power and expressiveness of the fused features. Furthermore, considering that image tampering often involves abnormal changes in edge structures, we further propose an edge-aware coordinate attention mechanism (ECAM). By jointly modeling spatial position information and edge-guided information, the model is guided to focus more precisely on potential tampering boundaries, thereby enhancing its boundary detection and localization capabilities. Experiments on public datasets such as Columbia, CASIA, and NIST16 demonstrate that FENet achieves significantly better results than existing methods. We also analyze the model’s performance under various image quality conditions, such as JPEG compression and Gaussian blur, demonstrating its robustness in real-world scenarios. Experiments in Facebook, Weibo, and WeChat scenarios show that our method achieves average F1 scores that are 2.8%, 3%, and 5.6% higher than those of existing state-of-the-art methods, respectively. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Image Processing and Computer Vision Using Embedded Systems)

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6 pages, 132 KiB

Open AccessEditorial

Research on Fuzzy Logic and Mathematics with Applications II

by Saeid Jafari

Symmetry 2025, 17(7), 1149; https://doi.org/10.3390/sym17071149 - 18 Jul 2025

Viewed by 216

Abstract

The notion of a non-rigid fuzzy set was introduced by Lotfi A [...] Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

21 pages, 2308 KiB

Open AccessArticle

Forgery-Aware Guided Spatial–Frequency Feature Fusion for Face Image Forgery Detection

by Zhenxiang He, Zhihao Liu and Ziqi Zhao

Symmetry 2025, 17(7), 1148; https://doi.org/10.3390/sym17071148 - 18 Jul 2025

Cited by 1 | Viewed by 466

Abstract

The rapid development of deepfake technologies has led to the widespread proliferation of facial image forgeries, raising significant concerns over identity theft and the spread of misinformation. Although recent dual-domain detection approaches that integrate spatial and frequency features have achieved noticeable progress, they [...] Read more.

The rapid development of deepfake technologies has led to the widespread proliferation of facial image forgeries, raising significant concerns over identity theft and the spread of misinformation. Although recent dual-domain detection approaches that integrate spatial and frequency features have achieved noticeable progress, they still suffer from limited sensitivity to local forgery regions and inadequate interaction between spatial and frequency information in practical applications. To address these challenges, we propose a novel forgery-aware guided spatial–frequency feature fusion network. A lightweight U-Net is employed to generate pixel-level saliency maps by leveraging structural symmetry and semantic consistency, without relying on ground-truth masks. These maps dynamically guide the fusion of spatial features (from an improved Swin Transformer) and frequency features (via Haar wavelet transforms). Cross-domain attention, channel recalibration, and spatial gating are introduced to enhance feature complementarity and regional discrimination. Extensive experiments conducted on two benchmark face forgery datasets, FaceForensics++ and Celeb-DFv2, show that the proposed method consistently outperforms existing state-of-the-art techniques in terms of detection accuracy and generalization capability. The future work includes improving robustness under compression, incorporating temporal cues, extending to multimodal scenarios, and evaluating model efficiency for real-world deployment. Full article

(This article belongs to the Section Computer)

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14 pages, 465 KiB

Open AccessArticle

Quantum W-Type Entanglement in Photonic Systems with Environmental Decoherence

by Kamal Berrada and Smail Bougouffa

Symmetry 2025, 17(7), 1147; https://doi.org/10.3390/sym17071147 - 18 Jul 2025

Viewed by 349

Abstract

Preserving quantum entanglement in multipartite systems under environmental decoherence is a critical challenge for quantum information processing. In this work, we investigate the dynamics of W-type entanglement in a system of three photons, focusing on the effects of Markovian and non-Markovian decoherence regimes. [...] Read more.

Preserving quantum entanglement in multipartite systems under environmental decoherence is a critical challenge for quantum information processing. In this work, we investigate the dynamics of W-type entanglement in a system of three photons, focusing on the effects of Markovian and non-Markovian decoherence regimes. Using the lower bound of concurrence (LBC) as a measure of entanglement, we analyze the time evolution of the LBC for photons initially prepared in a W state under the influence of dephasing noise. We explore the dependence of entanglement dynamics on system parameters such as the dephasing angle and refractive-index difference, alongside environmental spectral properties. Our results, obtained within experimentally feasible parameter ranges, reveal how the enhancement of entanglement preservation can be achieved in Markovian and non-Markovian regimes according to the system parameters. These findings provide valuable insights into the robustness of W-state entanglement in tripartite photonic systems and offer practical guidance for optimizing quantum protocols in noisy environments. Full article

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24 pages, 7960 KiB

Open AccessArticle

Creep Behavior and Deformation Mechanism of Aluminum Alloy: Integrating Multiscale Simulation and Experiments

by Weizheng Lu, Jianguo Wu, Jiajun Liu, Xiaoai Yi, Qiyue Zhang, Yang Chen, Jia Li and Qihong Fang

Symmetry 2025, 17(7), 1146; https://doi.org/10.3390/sym17071146 - 17 Jul 2025

Viewed by 324

Abstract

Aluminum (Al) alloys exhibit exceptional mechanical properties, seeing widespread use in various industrial fields. Here, we use a multiscale simulation method combining phase field method, dislocation dynamics, and crystal plasticity finite element method to reveal the evolution law of precipitates, the interaction mechanism [...] Read more.

Aluminum (Al) alloys exhibit exceptional mechanical properties, seeing widespread use in various industrial fields. Here, we use a multiscale simulation method combining phase field method, dislocation dynamics, and crystal plasticity finite element method to reveal the evolution law of precipitates, the interaction mechanism between dislocations and precipitates, and the grain-level creep deformation mechanism in 7A09 Al alloy under creep loading. The phase field method indicates that Al alloys tend to form fewer but larger precipitates during the creep process, under the dominant effect of stress-assisted Ostwald ripening. The dynamic equilibrium process of precipitate is not only controlled by classical diffusion mechanisms, but also closely related to the local strain field induced by dislocations and the elastic interaction between precipitates. Dislocation dynamics simulations indicate that the appearance of multiple dislocation loops around the precipitate during the creep process is the main dislocation creep deformation mechanism. A crystal plasticity finite element model is established based on experimental characterization to investigate the macroscopic creep mechanism. The dislocation climb is hindered by grain boundaries during creep, and high-density dislocation bands are formed around specific grains, promoting non-uniform plastic strain and leading to strong strain gradients. This work provides fundamental insights into understanding creep behavior and deformation mechanism of Al alloy for deep-sea environments. Full article

(This article belongs to the Section Engineering and Materials)

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14 pages, 3371 KiB

Open AccessArticle

A Symmetry-Driven Broadband Circularly Polarized Magnetoelectric Dipole Antenna with Bandpass Filtering Response

by Xianjing Lin, Zuhao Jiang, Miaowang Zeng and Zengpei Zhong

Symmetry 2025, 17(7), 1145; https://doi.org/10.3390/sym17071145 - 17 Jul 2025

Viewed by 239

Abstract

This paper presents a symmetry-driven broadband circularly polarized magnetoelectric dipole antenna with bandpass filtering response, where the principle of symmetry is strategically employed to enhance both radiation and filtering performance. The antenna’s circular polarization is achieved through a symmetrical arrangement of two orthogonally [...] Read more.

This paper presents a symmetry-driven broadband circularly polarized magnetoelectric dipole antenna with bandpass filtering response, where the principle of symmetry is strategically employed to enhance both radiation and filtering performance. The antenna’s circular polarization is achieved through a symmetrical arrangement of two orthogonally placed metallic ME dipoles combined with a phase delay line, creating balanced current distributions for optimal CP characteristics. The design further incorporates symmetrical parasitic elements—a pair of identical inverted L-shaped metallic structures placed perpendicular to the ground plane at −45° relative to the ME dipoles—which introduce an additional CP resonance through their mirror-symmetric configuration, thereby significantly broadening the axial ratio bandwidth. The filtering functionality is realized through a combination of symmetrical modifications: grid slots etched in the metallic ground plane and an open-circuited stub loaded on the microstrip feed line work in tandem to create two radiation nulls in the upper stopband, while the inherent symmetrical properties of the ME dipoles naturally produce a radiation null in the lower stopband. This comprehensive symmetry-based approach results in a well-balanced bandpass filtering response across a wide operating bandwidth. Experimental validation through prototype measurement confirms the effectiveness of the symmetric design with compact dimensions of 0.96

λ_{0}

× 0.55

λ_{0}

× 0.17

λ_{0}

(

λ_{0}

is the wavelength at the lowest operating frequency), demonstrating an impedance bandwidth of 66.4% (2.87–5.05 GHz), an AR bandwidth of 31.9% (3.32–4.58 GHz), an average passband gain of 5.5 dBi, and out-of-band suppression levels of 11.5 dB and 26.8 dB at the lower and upper stopbands, respectively, along with good filtering performance characterized by a gain-suppression index (GSI) of 0.93 and radiation skirt index (RSI) of 0.58. The proposed antenna is suitable for satellite communication terminals requiring wide AR bandwidth and strong interference rejection in L/S-bands. Full article

(This article belongs to the Special Issue Symmetry Study in Electromagnetism: Topics and Advances)

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26 pages, 2989 KiB

Open AccessArticle

Studying Homoclinic Chaos in a Class of Piecewise Smooth Oscillators: Melnikov’s Approach, Symmetry Results, Simulations and Applications to Generating Antenna Factors Using Approximation and Optimization Techniques

by Nikolay Kyurkchiev, Tsvetelin Zaevski, Anton Iliev, Vesselin Kyurkchiev and Asen Rahnev

Symmetry 2025, 17(7), 1144; https://doi.org/10.3390/sym17071144 - 17 Jul 2025

Viewed by 289

Abstract

In this paper, we provide a novel extended mixed differential model that is appealing to users because of its numerous free parameters. The motivation of this research arises from the opportunity for a general investigation of some outstanding classical and novel dynamical models. [...] Read more.

In this paper, we provide a novel extended mixed differential model that is appealing to users because of its numerous free parameters. The motivation of this research arises from the opportunity for a general investigation of some outstanding classical and novel dynamical models. The higher energy levels known in the literature can be governed by appropriately added correction factors. Furthermore, the different applications of the considered model can be achieved only after a proper parameter calibration. All these necessitate the use of diverse optimization and approximation techniques. The proposed extended model is especially useful in the important field of decision making, namely the antenna array theory. This is due to the possibility of generating high-order Melnikov polynomials. The work is a natural continuation of the authors’ previous research on the topic of chaos generation via the term

{x | x |}^{a - 1}

. Some specialized modules for investigating the dynamics of the proposed oscillators are provided. Last but not least, the so-defined dynamical model can be of interest for scientists and practitioners in the area of antenna array theory, which is an important part of the decision-making field. The stochastic control of oscillations is also the subject of our consideration. The underlying distributions we use may be symmetric, asymmetric or strongly asymmetric. The same is true for the mass in the tails, too. As a result, the stochastic control of the oscillations we purpose may exhibit a variety of possible behaviors. In the final section, we raise some important issues related to the methodology of teaching Master’s and PhD students. Full article

(This article belongs to the Section Mathematics)

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32 pages, 6510 KiB

Open AccessArticle

Multiphysics Finite Element Analysis and Optimization of Load-Bearing Frame for Pure Electric SUVs

by Yingshuai Liu, Chenxing Liu, Xueming Gao and Jianwei Tan

Symmetry 2025, 17(7), 1143; https://doi.org/10.3390/sym17071143 - 17 Jul 2025

Viewed by 439

Abstract

With the increasing environmental pollution and resource consumption caused by automobiles, a lightweight design of automobiles is the best solution at present. In this paper, the load-bearing frame of pure electric SUVs is taken as the research object. The finite element analysis method [...] Read more.

With the increasing environmental pollution and resource consumption caused by automobiles, a lightweight design of automobiles is the best solution at present. In this paper, the load-bearing frame of pure electric SUVs is taken as the research object. The finite element analysis method is used to analyze the strength, stiffness and modal performance of the load-bearing frame, and the material selection of the frame is optimized according to the analysis results to achieve a lightweight design. First, a three-dimensional model of the pure electric SUV frame is established using SolidWorks software 2019 and then imported into ANSYS 2024 R1 Workbench for meshing and material property definition. Then, through finite element static analysis, the various force conditions of the frame under three typical working conditions of full-load bending, full-load braking and full-load turning are simulated; the stress distribution and deformation of the frame under different working conditions are confirmed; and the strength and stiffness performance of the frame are evaluated. After the above analysis, a modal analysis of the frame is carried out, and the natural frequency and vibration mode of the frame are finally obtained. According to the analysis results, the material replacement method is selected to optimize the lightweight design of the frame. The results show that the weight of the frame is significantly reduced after material optimization, while still meeting the strength, stiffness and modal performance requirements. This article provides a certain reference value for the lightweight design of pure electric SUV frames in the future. Full article

(This article belongs to the Special Issue Advanced Materials, Structures, Symmetrical Design and Mechanism in Mechanical Engineering, 2nd Edition)

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18 pages, 1709 KiB

Open AccessArticle

Fluid and Dynamic Analysis of Space–Time Symmetry in the Galloping Phenomenon

by Jéssica Luana da Silva Santos, Andreia Aoyagui Nascimento and Adailton Silva Borges

Symmetry 2025, 17(7), 1142; https://doi.org/10.3390/sym17071142 - 17 Jul 2025

Viewed by 352

Abstract

Energy generation from renewable sources has increased exponentially worldwide, particularly wind energy, which is converted into electricity through wind turbines. The growing demand for renewable energy has driven the development of horizontal-axis wind turbines with larger dimensions, as the energy captured is proportional [...] Read more.

Energy generation from renewable sources has increased exponentially worldwide, particularly wind energy, which is converted into electricity through wind turbines. The growing demand for renewable energy has driven the development of horizontal-axis wind turbines with larger dimensions, as the energy captured is proportional to the area swept by the rotor blades. In this context, the dynamic loads typically observed in wind turbine towers include vibrations caused by rotating blades at the top of the tower, wind pressure, and earthquakes (less common). In offshore wind farms, wind turbine towers are also subjected to dynamic loads from waves and ocean currents. Vortex-induced vibration can be an undesirable phenomenon, as it may lead to significant adverse effects on wind turbine structures. This study presents a two-dimensional transient model for a rigid body anchored by a torsional spring subjected to a constant velocity flow. We applied a coupling of the Fourier pseudospectral method (FPM) and immersed boundary method (IBM), referred to in this study as IMERSPEC, for a two-dimensional, incompressible, and isothermal flow with constant properties—the FPM to solve the Navier–Stokes equations, and IBM to represent the geometries. Computational simulations, solved at an aspect ratio of

ϕ = 4.0

, were analyzed, considering Reynolds numbers ranging from

R e = 150

to Re = 1000 when the cylinder is stationary, and

R e = 250

when the cylinder is in motion. In addition to evaluating vortex shedding and Strouhal number, the study focuses on the characterization of space–time symmetry during the galloping response. The results show a spatial symmetry breaking in the flow patterns, while the oscillatory motion of the rigid body preserves temporal symmetry. The numerical accuracy suggested that the IMERSPEC methodology can effectively solve complex problems. Moreover, the proposed IMERSPEC approach demonstrates notable advantages over conventional techniques, particularly in terms of spectral accuracy, low numerical diffusion, and ease of implementation for moving boundaries. These features make the model especially efficient and suitable for capturing intricate fluid–structure interactions, offering a promising tool for analyzing wind turbine dynamics and other similar systems. Full article

(This article belongs to the Special Issue Symmetry in Fluid Mechanics: New Challenges in Fluid–Structure Interaction)

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11 pages, 255 KiB

Open AccessArticle

New Sufficient Conditions for p-Valent Functions

by Mamoru Nunokawa, Janusz Sokół and Edyta Trybucka

Symmetry 2025, 17(7), 1141; https://doi.org/10.3390/sym17071141 - 16 Jul 2025

Viewed by 171

Abstract

A function that is holomorphic in a set E, in the complex plane, is called p-valent in E if, for every complex number, w, the equation f (z) = w has, at most, p roots in E. [...] Read more.

A function that is holomorphic in a set E, in the complex plane, is called p-valent in E if, for every complex number, w, the equation f (z) = w has, at most, p roots in E. In this paper, we established some sufficient conditions for holomorphic functions in the unit disk |z| < 1 to be at most p-valent in the unit disk or p-valent or p-valent starlike in the unit disk. Full article

(This article belongs to the Section Mathematics)

19 pages, 2632 KiB

Open AccessArticle

Data-Driven Attack Detection Mechanism Against False Data Injection Attacks in DC Microgrids Using CNN-LSTM-Attention

by Chunxiu Li, Xinyu Wang, Xiaotao Chen, Aiming Han and Xingye Zhang

Symmetry 2025, 17(7), 1140; https://doi.org/10.3390/sym17071140 - 16 Jul 2025

Viewed by 329

Abstract

This study presents a novel spatio-temporal detection framework for identifying False Data Injection (FDI) attacks in DC microgrid systems from the perspective of cyber–physical symmetry. While modern DC microgrids benefit from increasingly sophisticated cyber–physical symmetry network integration, this interconnected architecture simultaneously introduces significant [...] Read more.

This study presents a novel spatio-temporal detection framework for identifying False Data Injection (FDI) attacks in DC microgrid systems from the perspective of cyber–physical symmetry. While modern DC microgrids benefit from increasingly sophisticated cyber–physical symmetry network integration, this interconnected architecture simultaneously introduces significant cybersecurity vulnerabilities. Notably, FDI attacks can effectively bypass conventional Chi-square detector-based protection mechanisms through malicious manipulation of communication layer data. To address this critical security challenge, we propose a hybrid deep learning framework that synergistically combines: Convolutional Neural Networks (CNN) for robust spatial feature extraction from power system measurements; Long Short-Term Memory (LSTM) networks for capturing complex temporal dependencies; and an attention mechanism that dynamically weights the most discriminative features. The framework operates through a hierarchical feature extraction process: First-level spatial analysis identifies local measurement patterns; second-level temporal analysis detects sequential anomalies; attention-based feature refinement focuses on the most attack-relevant signatures. Comprehensive simulation studies demonstrate the superior performance of our CNN-LSTM-Attention framework compared to conventional detection approaches (CNN-SVM and MLP), with significant improvements across all key metrics. Namely, the accuracy, precision, F1-score, and recall could be improved by at least 7.17%, 6.59%, 2.72% and 6.55%. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Applied Machine Learning and Neural Networks for Hybrid Energy Ship Power System)

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21 pages, 733 KiB

Open AccessArticle

A Secure and Privacy-Preserving Approach to Healthcare Data Collaboration

by Amna Adnan, Firdous Kausar, Muhammad Shoaib, Faiza Iqbal, Ayesha Altaf and Hafiz M. Asif

Symmetry 2025, 17(7), 1139; https://doi.org/10.3390/sym17071139 - 16 Jul 2025

Viewed by 795

Abstract

Combining a large collection of patient data and advanced technology, healthcare organizations can excel in medical research and increase the quality of patient care. At the same time, health records present serious privacy and security challenges because they are confidential and can be [...] Read more.

Combining a large collection of patient data and advanced technology, healthcare organizations can excel in medical research and increase the quality of patient care. At the same time, health records present serious privacy and security challenges because they are confidential and can be breached through networks. Even traditional methods with federated learning are used to share data, patient information might still be at risk of interference while updating the model. This paper proposes the Privacy-Preserving Federated Learning with Homomorphic Encryption (PPFLHE) framework, which strongly supports secure cooperation in healthcare and at the same time providing symmetric privacy protection among participating institutions. Everyone in the collaboration used the same EfficientNet-B0 architecture and training conditions and keeping the model symmetrical throughout the network to achieve a balanced learning process and fairness. All the institutions used CKKS encryption symmetrically for their models to keep data concealed and stop any attempts at inference. Our federated learning process uses FedAvg on the server to symmetrically aggregate encrypted model updates and decrease any delays in our server communication. We attained a classification accuracy of 83.19% and 81.27% when using the APTOS 2019 Blindness Detection dataset and MosMedData CT scan dataset, respectively. Such findings confirm that the PPFLHE framework is generalizable among the broad range of medical imaging methods. In this way, patient data are kept secure while encouraging medical research and treatment to move forward, helping healthcare systems cooperate more effectively. Full article

(This article belongs to the Special Issue Exploring Symmetry in Wireless Communication)

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Symmetry, Volume 17, Issue 7 (July 2025) – 193 articles

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