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Symmetry

Symmetry is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences. Symmetry is published monthly online by MDPI.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within SCIE (Web of Science), Scopus, CAPlus / SciFinder, Inspec, Astrophysics Data System, and other databases.
Journal Rank: JCR - Q2 (Multidisciplinary Sciences) / CiteScore - Q1 (General Mathematics )
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 17.1 days after submission; acceptance to publication is undertaken in 2.8 days (median values for papers published in this journal in the first half of 2025).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Testimonials: See what our editors and authors say about Symmetry.

Impact Factor: 2.2 (2024); 5-Year Impact Factor: 2.1 (2024)

Imprint Information Journal Flyer Open Access ISSN: 2073-8994

Latest Articles

57 pages, 647 KiB

Open AccessArticle

A Unified Perspective on Poincaré and Galilei Relativity: II. General Relativity: A. Kinematics

by Christian Y. Cardall

Symmetry 2025, 17(8), 1245; https://doi.org/10.3390/sym17081245 (registering DOI) - 5 Aug 2025

Building on the first paper in this series (Paper I), a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting is further pursued through a consideration of the kinematics of general relativity, with the gravitational dynamics to be addressed separately. [...] Read more.

Building on the first paper in this series (Paper I), a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting is further pursued through a consideration of the kinematics of general relativity, with the gravitational dynamics to be addressed separately. The metric of the 5-dimensional affine spacetimes governed by the Bargmann groups considered in Paper I (central extensions of the Poincaré and Galilei groups) is generalized to curved spacetime by extending the usual 1 + 3 (traditionally `3 + 1’) formalism of general relativity on 4-dimensional spacetime to a 1 + 3 + 1 formalism, whose spacetime kinematics is shown to be consistent with that of the usual 1 + 3 formalism. Spacetime tensor laws governing the motion of an elementary classical material particle and the dynamics of a simple fluid are presented, along with their 1 + 3 + 1 decompositions; these reference the foliation of spacetime in a manner that partially reverts the Einstein perspective (accelerated fiducial observers, and geodesic material particles and fluid elements) to a Newton-like perspective (geodesic fiducial observers, and accelerated material particles and fluid elements subject to a gravitational force). These spacetime laws of motion for particles and fluids also suggest that a strong-field Galilei general relativity would involve a limit in which not only

c \to \infty

but also

G \to \infty

, such that

G / c^{2}

remains constant. Full article

(This article belongs to the Special Issue Recent Advance in Mathematical Physics II)

14 pages, 330 KiB

Open AccessArticle

Sharp Bounds on Hankel Determinants for Starlike Functions Defined by Symmetry with Respect to Symmetric Domains

by Alina Alb Lupaş, Adel Salim Tayyah and Janusz Sokół

Symmetry 2025, 17(8), 1244; https://doi.org/10.3390/sym17081244 (registering DOI) - 5 Aug 2025

This work investigates the behavior of the coefficients of analytic functions within certain subclasses characterized by inherent symmetric structures. By leveraging deep connections with functions exhibiting positive real part properties, the approach introduces a modern analytical framework that links the studied coefficients to [...] Read more.

This work investigates the behavior of the coefficients of analytic functions within certain subclasses characterized by inherent symmetric structures. By leveraging deep connections with functions exhibiting positive real part properties, the approach introduces a modern analytical framework that links the studied coefficients to those of auxiliary functions with regulated behavior. This connection allows for the derivation of sharp estimates and facilitates computational treatment. The proposed method builds upon certain classical and modern coefficient inequalities. The study focuses on obtaining precise bounds for specific determinant expressions associated with initial, inverse, and inverse logarithmic coefficients, all within a subclass of starlike functions exhibiting internal symmetry aligned with a recently introduced canonical structure. This symmetric perspective reveals how geometric properties can lead to refined quantitative outcomes that enhance contemporary analytic theory. Full article

(This article belongs to the Special Issue Functional Equations and Inequalities: Topics and Applications)

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29 pages, 1407 KiB

Open AccessArticle

Symmetry-Driven Two-Population Collaborative Differential Evolution for Parallel Machine Scheduling in Lace Dyeing with Probabilistic Re-Dyeing Operations

by Jing Wang, Jingsheng Lian, Youpeng Deng, Lang Pan, Huan Xue, Yanming Chen, Debiao Li, Xixing Li and Deming Lei

Symmetry 2025, 17(8), 1243; https://doi.org/10.3390/sym17081243 - 5 Aug 2025

In lace textile manufacturing, the dyeing process in parallel machine environments faces challenges from sequence-dependent setup times due to color family transitions, machine eligibility constraints based on weight capacities, and probabilistic re-dyeing operations arising from quality inspection failures, which often lead to increased [...] Read more.

In lace textile manufacturing, the dyeing process in parallel machine environments faces challenges from sequence-dependent setup times due to color family transitions, machine eligibility constraints based on weight capacities, and probabilistic re-dyeing operations arising from quality inspection failures, which often lead to increased tardiness. To tackle this multi-constrained problem, a stochastic integer programming model is formulated to minimize total estimated tardiness. A novel symmetry-driven two-population collaborative differential evolution (TCDE) algorithm is then proposed. It features two symmetrically complementary subpopulations that achieve a balance between global exploration and local exploitation. One subpopulation employs chaotic parameter adaptation through a logistic map for symmetrically enhanced exploration, while the other adjusts parameters based on population diversity and convergence speed to facilitate symmetry-aware exploitation. Moreover, it also incorporates a symmetrical collaborative mechanism that includes the periodic migration of top individuals between subpopulations, along with elite-set guidance, to enhance both population diversity and convergence efficiency. Extensive computational experiments were conducted on 21 small-scale (optimally validated via CVX) and 15 large-scale synthetic datasets, as well as 21 small-scale (similarly validated) and 20 large-scale industrial datasets. These experiments demonstrate that TCDE significantly outperforms state-of-the-art comparative methods. Ablation studies also further verify the critical role of its symmetry-based components, with computational results confirming its superiority in solving the considered problem. Full article

(This article belongs to the Special Issue Meta-Heuristics for Manufacturing Systems Optimization, 3rd Edition)

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20 pages, 29354 KiB

Open AccessArticle

Two-Dimensional Reproducing Kernel-Based Interpolation Approximation for Best Regularization Parameter in Electrical Tomography Algorithm

by Fanpeng Dong and Shihong Yue

Symmetry 2025, 17(8), 1242; https://doi.org/10.3390/sym17081242 - 5 Aug 2025

The regularization parameter plays an important role in regularization-based electrical tomography (ET) algorithms, but the existing methods generally cannot determine the parameter. Moreover, these methods are not real-time since a thorough search must be performed for the best parameter. To address the issue, [...] Read more.

The regularization parameter plays an important role in regularization-based electrical tomography (ET) algorithms, but the existing methods generally cannot determine the parameter. Moreover, these methods are not real-time since a thorough search must be performed for the best parameter. To address the issue, a reproducing kernel-based interpolation approximation method is proposed to efficiently estimate the best regularization parameter from a group of representative samples. The optimization and generation of the new method have been verified by theoretical analysis and experimental demonstration. The theoretical evaluation is conducted in a Hilbert space with a known reproducing kernel, and its symmetry ensures the uniqueness of the interpolation. And experimental validation is carried out using both simulated and actual models, each with a range of distinct features. Results indicate that the new method can approximately find the best regularization parameter. Consequently, when using the regularization parameter, the new method can effectively improve both the spatial resolution and steadiness of ET imaging process. Full article

(This article belongs to the Section Computer)

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13 pages, 265 KiB

Open AccessArticle

On LRS Space-Times Admitting Conformal Motions

by Ragab M. Gad, Awatif Al-Jedani and Shahad T. Alsulami

Symmetry 2025, 17(8), 1241; https://doi.org/10.3390/sym17081241 - 5 Aug 2025

In this paper, we study the conformal symmetry for locally rotationally symmetric Bianchi type I space-time. New exact conformal solutions of Einstein’s field equations for this space-time were obtained. The space-time geometry of these solutions is found to be non-vacuum, conformally flat, and [...] Read more.

In this paper, we study the conformal symmetry for locally rotationally symmetric Bianchi type I space-time. New exact conformal solutions of Einstein’s field equations for this space-time were obtained. The space-time geometry of these solutions is found to be non-vacuum, conformally flat, and shear-free. We show that in order for LRS Bianchi type I space-time to admit a conformal vector field it must reduce to the FRW space-time. Some physical and kinematic properties of the obtained conformal solutions are also discussed. Full article

(This article belongs to the Section Mathematics)

25 pages, 3418 KiB

Open AccessReview

Review on the Theoretical and Practical Applications of Symmetry in Thermal Sciences, Fluid Dynamics, and Energy

by Nattan Roberto Caetano

Symmetry 2025, 17(8), 1240; https://doi.org/10.3390/sym17081240 - 5 Aug 2025

This literature review explores the role of symmetry in thermal sciences, fluid dynamics, and energy applications, emphasizing the theoretical and practical implications. Symmetry is a fundamental tool for simplifying complex problems, enhancing computational efficiency, and improving system design across multiple engineering and physics [...] Read more.

This literature review explores the role of symmetry in thermal sciences, fluid dynamics, and energy applications, emphasizing the theoretical and practical implications. Symmetry is a fundamental tool for simplifying complex problems, enhancing computational efficiency, and improving system design across multiple engineering and physics domains. Thermal and fluid processes are applied in several modern energy use technologies, essentially involving the complex, multidimensional interaction of fluid mechanics and thermodynamics, such as renewable energy applications, combustion diagnostics, or Computational Fluid Dynamics (CFD)-based optimization, where symmetry is highly considered to simplify geometric parameters. Indeed, the interconnection between experimental analysis and the numerical simulation of processes is an important field. Symmetry operates as a unifying principle, its presence determining everything from the stability of turbulent flows to the efficiency of nuclear reactors, revealing hidden patterns that transcend scales and disciplines. Rotational invariance in pipelines; rotors of hydraulic, thermal, and wind turbines, and in many other cases, for instance, not only lowers computational cost but also guarantees that solutions validated in the laboratory can be effectively scaled up to industrial applications, demonstrating its crucial role in bridging theoretical concepts and real-world implementation. Thus, a wide range of symmetry solutions is exhibited in this research area, the results of which contribute to the development of science and fast information for decision making in industry. In this review, essential findings from prominent research were synthesized, highlighting how symmetry has been conceptualized and applied in these contexts. Full article

(This article belongs to the Special Issue Symmetry in Thermal Fluid Sciences and Energy Applications)

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15 pages, 2255 KiB

Open AccessArticle

Nonnormalized Field Statistics in Coupled Reverberation Chambers

by Angelo Gifuni, Anett Kenderes and Giuseppe Grassini

Symmetry 2025, 17(8), 1239; https://doi.org/10.3390/sym17081239 - 5 Aug 2025

In this work, we show the probability density functions (PDFs) and cumulative density functions (CDFs) of the nonnormalized field components and the associated powers received inside coupled reverberation chambers (CRCs), considering two canonical cases of single electrically small coupling apertures (ESCAs). These two [...] Read more.

In this work, we show the probability density functions (PDFs) and cumulative density functions (CDFs) of the nonnormalized field components and the associated powers received inside coupled reverberation chambers (CRCs), considering two canonical cases of single electrically small coupling apertures (ESCAs). These two cases involve one-dimensional (1D) and two-dimensional (2D) single electrically small CAs, respectively. We achieve normalized statistics from the nonnormalized ones for both field components and associated powers. We show that the comparison of the mean square values (MSVs) of the nonnormalized PDFs of the field components to the mean values (MVs) of the related nonnormalized PDFs of the powers is a proper method to corroborate the accuracy of the same achieved theoretical distributions, when they are achieved in an independent way. The achieved theoretical results are also validated by measurements. Moreover, for the sake of completeness and rigor of published results, we show two useful cases of the results from the measurements using two electrically large CAs. Full article

(This article belongs to the Special Issue Symmetric/Asymmetric Analysis and Design of Microwave Circuits/Antennas)

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16 pages, 3826 KiB

Open AccessArticle

Surface Resistivity Imaging for Drilling Columnar Cores

by Qi Ran, Qiang Lai, Benjian Zhang, Yuyu Wu, Jun Tang and Zhe Wu

Symmetry 2025, 17(8), 1238; https://doi.org/10.3390/sym17081238 - 5 Aug 2025

The resistivity imaging system is specifically designed for the precise measurement of resistivity distributions within drilled columnar core samples. Its coaxial symmetric configuration enables the non-destructive characterization of electrical properties, with broad applications in oil and gas exploration, reservoir evaluation, and geological research. [...] Read more.

The resistivity imaging system is specifically designed for the precise measurement of resistivity distributions within drilled columnar core samples. Its coaxial symmetric configuration enables the non-destructive characterization of electrical properties, with broad applications in oil and gas exploration, reservoir evaluation, and geological research. By integrating a ring return electrode and full-circumference electrode arrays, the system can acquire core-scale resistivity data in conductive media environments. The self-developed imaging software employs advanced processing algorithms—including depth correction, amplitude normalization, and image enhancement—to transform raw resistivity measurements into high-resolution surface imaging maps. Experimental results demonstrate that the system can resolve features such as cracks with a minimum width of 0.5 mm and pores with a minimum inner diameter of 0.4 mm in granite core, providing a novel technical approach for the fine-scale characterization of core materials. Full article

(This article belongs to the Special Issue Symmetry in Civil Transportation Engineering—2nd Edition)

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39 pages, 8108 KiB

Open AccessArticle

PSMP: Category Prototype-Guided Streaming Multi-Level Perturbation for Online Open-World Object Detection

by Shibo Gu, Meng Sun, Zhihao Zhang, Yuhao Bai and Ziliang Chen

Symmetry 2025, 17(8), 1237; https://doi.org/10.3390/sym17081237 - 5 Aug 2025

Inspired by the human ability to learn continuously and adapt to changing environments, researchers have proposed Online Open-World Object Detection (OLOWOD). This emerging paradigm faces the challenges of detecting known categories, discovering unknown ones, continuously learning new categories, and mitigating catastrophic forgetting. To [...] Read more.

Inspired by the human ability to learn continuously and adapt to changing environments, researchers have proposed Online Open-World Object Detection (OLOWOD). This emerging paradigm faces the challenges of detecting known categories, discovering unknown ones, continuously learning new categories, and mitigating catastrophic forgetting. To address these challenges, we propose Category Prototype-guided Streaming Multi-Level Perturbation, PSMP, a plug-and-play method for OLOWOD. PSMP, comprising semantic-level, enhanced data-level, and enhanced feature-level perturbations jointly guided by category prototypes, operates at different representational levels to collaboratively extract latent knowledge across tasks and improve adaptability. In addition, PSMP constructs the “contrastive tension” based on the relationships among category prototypes. This mechanism inherently leverages the symmetric structure formed by class prototypes in the latent space, where prototypes of semantically similar categories tend to align symmetrically or equidistantly. By guiding perturbations along these symmetric axes, the model can achieve more balanced generalization between known and unknown categories. PSMP requires no additional annotations, is lightweight in design, and can be seamlessly integrated into existing OWOD methods. Extensive experiments show that PSMP achieves an improvement of approximately 1.5% to 3% in mAP for known categories compared to conventional online training methods while significantly increasing the Unknown Recall (UR) by around 4.6%. Full article

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

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31 pages, 1755 KiB

Open AccessArticle

Two-Stage Distributionally Robust Optimization for an Asymmetric Loss-Aversion Portfolio via Deep Learning

by Xin Zhang, Shancun Liu and Jingrui Pan

Symmetry 2025, 17(8), 1236; https://doi.org/10.3390/sym17081236 - 4 Aug 2025

In portfolio optimization, investors often overlook asymmetric preferences for gains and losses. We propose a distributionally robust two-stage portfolio optimization (DR-TSPO) model, which is suitable for scenarios where the loss reference point is adaptively updated based on prior decisions. For analytical convenience, we [...] Read more.

In portfolio optimization, investors often overlook asymmetric preferences for gains and losses. We propose a distributionally robust two-stage portfolio optimization (DR-TSPO) model, which is suitable for scenarios where the loss reference point is adaptively updated based on prior decisions. For analytical convenience, we further reformulate the DR-TSPO model as an equivalent second-order cone programming counterpart. Additionally, we develop a deep learning-based constraint correction algorithm (DL-CCA) trained directly on problem descriptions, which enhances computational efficiency for large-scale non-convex distributionally robust portfolio optimization. Our empirical results obtained using global market data demonstrate that during COVID-19, the DR-TSPO model outperformed traditional two-stage optimization in reducing conservatism and avoiding extreme losses. Full article

(This article belongs to the Section Computer)

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18 pages, 3407 KiB

Open AccessArticle

Graph Convolutional Network with Multi-View Topology for Lightweight Skeleton-Based Action Recognition

by Liangliang Wang, Xu Zhang and Chuang Zhang

Symmetry 2025, 17(8), 1235; https://doi.org/10.3390/sym17081235 - 4 Aug 2025

Skeleton-based action recognition is an important subject in deep learning. Graph Convolutional Networks (GCNs) have demonstrated strong performance by modeling the human skeleton as a natural topological graph, representing the connections between joints. However, most existing methods rely on non-adaptive topologies or insufficiently [...] Read more.

Skeleton-based action recognition is an important subject in deep learning. Graph Convolutional Networks (GCNs) have demonstrated strong performance by modeling the human skeleton as a natural topological graph, representing the connections between joints. However, most existing methods rely on non-adaptive topologies or insufficiently expressive representations. To address these limitations, we propose a Multi-view Topology Refinement Graph Convolutional Network (MTR-GCN), which is efficient, lightweight, and delivers high performance. Specifically: (1) We propose a new spatial topology modeling approach that incorporates two views. A dynamic view fuses joint information from dual streams in a pairwise manner, while a static view encodes the shortest static paths between joints, preserving the original connectivity relationships. (2) We propose a new MultiScale Temporal Convolutional Network (MSTC), which is efficient and lightweight. (3) Furthermore, we introduce a new temporal topology strategy by modeling temporal frames as a graph, which strengthens the extraction of temporal features. By modeling the human skeleton as both a spatial and a temporal graph, we reveal a topological symmetry between space and time within the unified spatio-temporal framework. The proposed model achieves state-of-the-art performance on several benchmark datasets, including NTU RGB + D (XSub: 92.8%, XView: 96.8%), NTU RGB + D 120 (XSub: 89.6%, XSet: 90.8%), and NW-UCLA (95.7%), demonstrating the effectiveness of our GCN module, TCN module, and overall architecture. Full article

(This article belongs to the Section Computer)

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23 pages, 5966 KiB

Open AccessArticle

Study on Mechanism and Constitutive Modelling of Secondary Anisotropy of Surrounding Rock of Deep Tunnels

by Kang Yi, Peilin Gong, Zhiguo Lu, Chao Su and Kaijie Duan

Symmetry 2025, 17(8), 1234; https://doi.org/10.3390/sym17081234 - 4 Aug 2025

Crack initiation, propagation, and slippage serve as the key mesoscopic mechanisms contributing to the deterioration of deep tunnel surrounding rocks. In this study, a secondary anisotropy of deep tunnels surrounding rocks was proposed: The axial-displacement constraint of deep tunnels forces cracks in the [...] Read more.

Crack initiation, propagation, and slippage serve as the key mesoscopic mechanisms contributing to the deterioration of deep tunnel surrounding rocks. In this study, a secondary anisotropy of deep tunnels surrounding rocks was proposed: The axial-displacement constraint of deep tunnels forces cracks in the surrounding rock to initiate, propagate, and slip in planes parallel to the tunnel axial direction. These cracks have no significant effect on the axial strength of the surrounding rock but significantly reduce the tangential strength, resulting in the secondary anisotropy. First, the secondary anisotropy was verified by a hybrid stress–strain controlled true triaxial test of sandstone specimens, a CT 3D (computed tomography three-dimensional) reconstruction of a fractured sandstone specimen, a numerical simulation of heterogeneous rock specimens, and field borehole TV (television) images. Subsequently, a novel SSA (strain-softening and secondary anisotropy) constitutive model was developed to characterise the secondary anisotropy of the surrounding rock and developed using C++ into a numerical form that can be called by FLAC^3D (Fast Lagrangian Analysis of Continua in 3 Dimensions). Finally, effects of secondary anisotropy on a deep tunnel surrounding rock were analysed by comparing the results calculated by the SSA model and a uniform strain-softening model. The results show that considering the secondary anisotropy, the extent of strain-softening of the surrounding rock was mitigated, particularly the axial strain-softening. Moreover, it reduced the surface displacement, plastic zone, and dissipated plastic strain energy of the surrounding rock. The proposed SSA model can precisely characterise the objectively existent secondary anisotropy, enhancing the accuracy of numerical simulations for tunnels, particularly for deep tunnels. Full article

(This article belongs to the Section Engineering and Materials)

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15 pages, 712 KiB

Open AccessArticle

Extracting Correlations in Arbitrary Diagonal Quantum States via Weak Couplings and Auxiliary Systems

by Hui Li, Chao Zheng, Yansong Li and Xian Lu

Symmetry 2025, 17(8), 1233; https://doi.org/10.3390/sym17081233 - 4 Aug 2025

In this work, we introduce a novel method to extract correlations in diagonal quantum states in multi-particle quantum systems, addressing a significant limitation of traditional approaches that require prior knowledge of the density matrices of quantum states. Instead of relying on classical information [...] Read more.

In this work, we introduce a novel method to extract correlations in diagonal quantum states in multi-particle quantum systems, addressing a significant limitation of traditional approaches that require prior knowledge of the density matrices of quantum states. Instead of relying on classical information processing, our method is based on weak couplings and ancillary systems, eliminating the need for classical communication, optimization, and complex calculations. The concept of mutually unbiased bases is intrinsically linked to symmetry, as it entails the uniform distribution of quantum states across distinct bases. Within the framework of our theoretical model, mutually unbiased bases are employed to facilitate weak measurements and to function as the post-selected states. To quantify the correlations in the initial state, we employ the trace distance between the initial state and the product of its marginal states, and illustrate the feasibility and effectiveness of our approach. We generalize the approach to accommodate high-dimensional multi-particle systems for potential applications in quantum information processing and quantum networks. Full article

(This article belongs to the Topic Quantum Systems and Their Applications)

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20 pages, 1644 KiB

Open AccessArticle

A Symmetric Multi-Scale Convolutional Transformer Network for Plant Disease Image Classification

by Chuncheng Xu and Tianjin Yang

Symmetry 2025, 17(8), 1232; https://doi.org/10.3390/sym17081232 - 4 Aug 2025

Plant disease classification is critical for effective crop management. Recent advances in deep learning, especially Vision Transformers (ViTs), have shown promise due to their strong global feature modeling capabilities. However, ViTs often overlook local features and suffer from feature extraction degradation during patch [...] Read more.

Plant disease classification is critical for effective crop management. Recent advances in deep learning, especially Vision Transformers (ViTs), have shown promise due to their strong global feature modeling capabilities. However, ViTs often overlook local features and suffer from feature extraction degradation during patch merging as channels increase. To address these issues, we propose PLTransformer, a hybrid model designed to symmetrically capture both global and local features. We design a symmetric multi-scale convolutional module that combines two different-scale receptive fields to simultaneously extract global and local features so that the model can better perceive multi-scale disease morphologies. Additionally, we propose an overlap-attentive channel downsampler that utilizes inter-channel attention mechanisms during spatial downsampling, effectively preserving local structural information and mitigating semantic loss caused by feature compression. On the PlantVillage dataset, PLTransformer achieves 99.95% accuracy, outperforming DeiT (96.33%), Twins (98.92%), and DilateFormer (98.84%). These results demonstrate its superiority in handling multi-scale disease features. Full article

(This article belongs to the Section Computer)

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28 pages, 6199 KiB

Open AccessArticle

Dual Chaotic Diffusion Framework for Multimodal Biometric Security Using Qi Hyperchaotic System

by Tresor Lisungu Oteko and Kingsley A. Ogudo

Symmetry 2025, 17(8), 1231; https://doi.org/10.3390/sym17081231 - 4 Aug 2025

The proliferation of biometric technology across various domains including user identification, financial services, healthcare, security, law enforcement, and border control introduces convenience in user identity verification while necessitating robust protection mechanisms for sensitive biometric data. While chaos-based encryption systems offer promising solutions, many [...] Read more.

The proliferation of biometric technology across various domains including user identification, financial services, healthcare, security, law enforcement, and border control introduces convenience in user identity verification while necessitating robust protection mechanisms for sensitive biometric data. While chaos-based encryption systems offer promising solutions, many existing chaos-based encryption schemes exhibit inherent shortcomings including deterministic randomness and constrained key spaces, often failing to balance security robustness with computational efficiency. To address this, we propose a novel dual-layer cryptographic framework leveraging a four-dimensional (4D) Qi hyperchaotic system for protecting biometric templates and facilitating secure feature matching operations. The framework implements a two-tier encryption mechanism where each layer independently utilizes a Qi hyperchaotic system to generate unique encryption parameters, ensuring template-specific encryption patterns that enhance resistance against chosen-plaintext attacks. The framework performs dimensional normalization of input biometric templates, followed by image pixel shuffling to permutate pixel positions before applying dual-key encryption using the Qi hyperchaotic system and XOR diffusion operations. Templates remain encrypted in storage, with decryption occurring only during authentication processes, ensuring continuous security while enabling biometric verification. The proposed system’s framework demonstrates exceptional randomness properties, validated through comprehensive NIST Statistical Test Suite analysis, achieving statistical significance across all 15 tests with p-values consistently above 0.01 threshold. Comprehensive security analysis reveals outstanding metrics: entropy values exceeding 7.99 bits, a key space of

10^{320}

, negligible correlation coefficients (<

10^{- 2}

), and robust differential attack resistance with an NPCR of 99.60% and a UACI of 33.45%. Empirical evaluation, on standard CASIA Face and Iris databases, demonstrates practical computational efficiency, achieving average encryption times of 0.50913s per user template for 256 × 256 images. Comparative analysis against other state-of-the-art encryption schemes verifies the effectiveness and reliability of the proposed scheme and demonstrates our framework’s superior performance in both security metrics and computational efficiency. Our findings contribute to the advancement of biometric template protection methodologies, offering a balanced performance between security robustness and operational efficiency required in real-world deployment scenarios. Full article

(This article belongs to the Special Issue New Advances in Symmetric Cryptography)

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20 pages, 547 KiB

Open AccessArticle

An Efficient Spectral Method for a Class of Asymmetric Functional-Order Diffusion–Wave Equations Using Generalized Chelyshkov Wavelets

by Quan H. Do and Hoa T. B. Ngo

Symmetry 2025, 17(8), 1230; https://doi.org/10.3390/sym17081230 - 4 Aug 2025

Asymmetric functional-order (variable-order) fractional diffusion–wave equations (FO-FDWEs) introduce considerable computational challenges, as the fractional order of the derivatives can vary spatially or temporally. To overcome these challenges, a novel spectral method employing generalized fractional-order Chelyshkov wavelets (FO-CWs) is developed to efficiently solve such [...] Read more.

Asymmetric functional-order (variable-order) fractional diffusion–wave equations (FO-FDWEs) introduce considerable computational challenges, as the fractional order of the derivatives can vary spatially or temporally. To overcome these challenges, a novel spectral method employing generalized fractional-order Chelyshkov wavelets (FO-CWs) is developed to efficiently solve such equations. In this approach, the Riemann–Liouville fractional integral operator of variable order is evaluated in closed form via a regularized incomplete Beta function, enabling the transformation of the governing equation into a system of algebraic equations. This wavelet-based spectral scheme attains extremely high accuracy, yielding significantly lower errors than existing numerical techniques. In particular, numerical results show that the proposed method achieves notably improved accuracy compared to existing methods under the same number of basis functions. Its strong convergence properties allow high precision to be achieved with relatively few wavelet basis functions, leading to efficient computations. The method’s accuracy and efficiency are demonstrated on several practical diffusion–wave examples, indicating its suitability for real-world applications. Furthermore, it readily applies to a wide class of fractional partial differential equations (FPDEs) with spatially or temporally varying order, demonstrating versatility for diverse applications. Full article

(This article belongs to the Topic Numerical Methods for Partial Differential Equations)

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16 pages, 457 KiB

Open AccessArticle

Examples for BPS Solitons Destabilized by Quantum Effects

by Willem J. Meyer and Herbert Weigel

Symmetry 2025, 17(8), 1229; https://doi.org/10.3390/sym17081229 - 4 Aug 2025

We investigate serval models for two scalar fields in one space dimension with topologically stable solitons that are constructed from BPS equations. The asymptotic behavior of these solitons fully determines their classical energies. A particular feature of the considered models is that there [...] Read more.

We investigate serval models for two scalar fields in one space dimension with topologically stable solitons that are constructed from BPS equations. The asymptotic behavior of these solitons fully determines their classical energies. A particular feature of the considered models is that there are several translationally invariant ground states that we call primary and secondary vacua. The former are those that are asymptotically assumed by the solitons. Solitons that occupy a secondary vacuum in finite but eventually large portions of space are classically degenerate. Thus the quantum contributions to the energies are decisive for the energetically favored soliton. While some of these solitons were constructed previously, we, for the first time, compute the leading (one-loop) quantum contribution their energies. In all cases considered we find that this contribution is not bounded from below and that it is the more negative the larger the region is in which the soliton approaches a secondary vacuum. This corroborates the conjecture, earlier inferred from the Shifman-Voloshin soliton, that the availability of secondary vacua destabilizes these solitons on the quantum level. Full article

(This article belongs to the Section Physics)

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18 pages, 761 KiB

Open AccessArticle

A Priori Sample Size Determination for Estimating a Location Parameter Under a Unified Skew-Normal Distribution

by Cong Wang, Weizhong Tian and Jingjing Yang

Symmetry 2025, 17(8), 1228; https://doi.org/10.3390/sym17081228 - 4 Aug 2025

The a priori procedure (APP) is concerned with determining appropriate sample sizes to ensure that sample statistics to be obtained are likely to be good estimators of corresponding population parameters. Previous researchers have shown how to compute a priori confidence interval means or [...] Read more.

The a priori procedure (APP) is concerned with determining appropriate sample sizes to ensure that sample statistics to be obtained are likely to be good estimators of corresponding population parameters. Previous researchers have shown how to compute a priori confidence interval means or locations for normal and skew-normal distributions. However, two critical limitations persist in the literature: (1) While numerous skewed models have been proposed, the APP equations for location parameters have only been formally established for the basic skew-normal distributions. (2) Even within this fundamental framework, the APPs for sample size determinations in estimating locations are constructed on samples of specifically dependent observations having multivariate skew-normal distributions jointly. Our work addresses these limitations by extending a priori reasoning to the more comprehensive unified skew-normal (SUN) distribution. The SUN family not only encompasses multiple existing skew-normal models as special cases but also enables broader practical applications through its capacity to model mixed skewness patterns and diverse tail behaviors. In this paper, we establish APP equations for determining the required sample sizes and set up confidence intervals for the location parameter in the one-sample case, as well as for the difference in locations in matched pairs and two independent samples, assuming independent observations from the SUN family. This extension addresses a critical gap in the literature and offers a valuable contribution to the field. Simulation studies support the equations presented, and two applications involve real data sets for illustrations of our main results. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines, Fourth Edition)

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17 pages, 462 KiB

Open AccessArticle

Fingerprint-Based Secure Query Scheme for Databases over Symmetric Mirror Servers

by Yu Zhang, Rui Zhu, Yin Li and Wenjv Hu

Symmetry 2025, 17(8), 1227; https://doi.org/10.3390/sym17081227 - 4 Aug 2025

The Karp and Rabin (KR) fingerprint is a special hash-like function widely utilized for efficient string matching. Recently, Sharma et al.leveraged its linear and symmetric properties to facilitate private database queries. However, their approach mainly protects encrypted or secret-shared databases rather than public [...] Read more.

The Karp and Rabin (KR) fingerprint is a special hash-like function widely utilized for efficient string matching. Recently, Sharma et al.leveraged its linear and symmetric properties to facilitate private database queries. However, their approach mainly protects encrypted or secret-shared databases rather than public databases, where only the query privacy is required. In this paper, we focus explicitly on privacy-preserving queries over public read-only databases. We propose a novel fingerprint-based keyword query scheme using the distributed point function (DPF), which effectively hides users’ data access patterns across two symmetric mirror servers. Moreover, we provide a rigorous analysis of the false positive probability inherent in fingerprinting and discuss strategies for its minimization. Our scheme achieves efficiency close to plaintext methods, significantly reducing deployment complexity. Full article

(This article belongs to the Section Computer)

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18 pages, 3091 KiB

Open AccessArticle

Construction of Typical Scenarios for Multiple Renewable Energy Plant Outputs Considering Spatiotemporal Correlations

by Yuyue Zhang, Yan Wen, Nan Wang, Zhenhua Yuan, Lina Zhang and Runjia Sun

Symmetry 2025, 17(8), 1226; https://doi.org/10.3390/sym17081226 - 3 Aug 2025

A high-quality set of typical scenarios is significant for power grid planning. Existing construction methods for typical scenarios do not account for the spatiotemporal correlations among renewable energy plant outputs, failing to adequately reflect the distribution characteristics of original scenarios. To address the [...] Read more.

A high-quality set of typical scenarios is significant for power grid planning. Existing construction methods for typical scenarios do not account for the spatiotemporal correlations among renewable energy plant outputs, failing to adequately reflect the distribution characteristics of original scenarios. To address the issues mentioned above, this paper proposes a construction method for typical scenarios considering spatiotemporal correlations, providing high-quality typical scenarios for power grid planning. Firstly, a symmetric spatial correlation matrix and a temporal autocorrelation matrix are defined, achieving quantitative representation of spatiotemporal correlations. Then, distributional differences between typical and original scenarios are quantified from multiple dimensions, and a scenario reduction model considering spatiotemporal correlations is established. Finally, the genetic algorithm is improved by incorporating adaptive parameter adjustment and an elitism strategy, which can efficiently obtain high-quality typical scenarios. A case study involving five wind farms and fourteen photovoltaic plants in Belgium is presented. The rate of error between spatial correlation matrices of original and typical scenario sets is lower than 2.6%, and the rate of error between temporal autocorrelations is lower than 2.8%. Simulation results demonstrate that typical scenarios can capture the spatiotemporal correlations of original scenarios. Full article

(This article belongs to the Special Issue New Power System and Symmetry)

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