Symmetry

23 pages, 1623 KB

Open AccessArticle

Integral and Numerical Formulations for Seeking the Period of Non-Conservative Nonlinear Oscillator With/Without the First Integral

by Chein-Shan Liu, Chia-Cheng Tsai and Chih-Wen Chang

Symmetry 2025, 17(9), 1584; https://doi.org/10.3390/sym17091584 - 22 Sep 2025

Viewed by 137

Abstract

For a non-conservative nonlinear oscillator (NCNO) having a periodic solution, the existence of the first integral is a certain symmetry of the nonlinear dynamical system, which signifies the balance of kinetic energy and potential energy. A first-order nonlinear ordinary differential equation (ODE) is [...] Read more.

For a non-conservative nonlinear oscillator (NCNO) having a periodic solution, the existence of the first integral is a certain symmetry of the nonlinear dynamical system, which signifies the balance of kinetic energy and potential energy. A first-order nonlinear ordinary differential equation (ODE) is used to derive the first integral, which, equipped with a right-end boundary condition, can determine an implicit potential function for computing the period by an exact integral formula. However, the integrand is singular, which renders a less accurate value of the period. A generalized integral conservation law endowed with a weight function is constructed, which is proved to be equivalent to the exact integral formula. Minimizing the error to satisfy the periodicity conditions, the optimal initial value of the weight function is determined. Two non-iterative methods are developed by integrating three first-order ODEs or two first-order ODEs to compute the period. Very accurate value of the period can be observed upon testing five examples. For the NCNO without having the first integral, the integral-type period formula is derived. Four examples belong to the Liénard equation, involving the van der Pol equation, are evaluated by the proposed iterative method to determine the oscillatory amplitude and period. For the case with one or more limit cycles, the amplitude and period can be estimated very accurately. For the NCNO of a broad type with or without having the first integral, the present paper features a solid theoretical foundation and contributes integral-type formulations for the determination of the oscillatory period. The development of new numerical algorithms and extensive validation across a diverse set of examples is given. Full article

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34 pages, 35098 KB

Open AccessArticle

Numerical Study of Asymmetry in Blast Pressure Propagation and Rock Damage Under Eccentric Decoupled Charges

by Pin Wang, Anping Huang, Xiaolin Zheng and Shuting Zhou

Symmetry 2025, 17(9), 1583; https://doi.org/10.3390/sym17091583 - 22 Sep 2025

Viewed by 208

Abstract

The eccentric decoupled charge (EDC) is widely used in blasting engineering, but the combined effects of decoupling ratio, coupling medium, and explosive position (eccentricity coefficient) on blast pressure propagation and rock damage remain insufficiently understood. In this study, the RHT material model in [...] Read more.

The eccentric decoupled charge (EDC) is widely used in blasting engineering, but the combined effects of decoupling ratio, coupling medium, and explosive position (eccentricity coefficient) on blast pressure propagation and rock damage remain insufficiently understood. In this study, the RHT material model in LS-DYNA is calibrated using fracture patterns from laboratory tests, and a series of cubic single-hole numerical models is established to examine the influence of charging parameters on pressure evolution and rock damage. The results show that EDC blasting generates a clear eccentricity effect in pressure propagation: the coupled side exhibits a higher peak pressure and faster loading, while the decoupled side experiences delayed wave arrival and lower peak pressure. This asymmetry intensifies with increasing decoupling ratio and eccentricity coefficient. Pressure decay follows a nonlinear power function, with attenuation in the axial direction being greater than in the radial direction. The total damage volume decreases with increasing decoupling ratio, but the eccentricity of the damage pattern becomes more evident, especially in the crushed zone. Different coupling media influence this effect: air/sand coupling readily produces eccentricity effects, while water coupling requires a larger decoupling ratio to do so. From an energy perspective, the evolving asymmetry in fracture behavior is closely linked to the redistribution of internal energy between the coupled and decoupled sides, as governed by the charging configuration. Full article

(This article belongs to the Special Issue Symmetry, Asymmetry and Nonlinearity in Geomechanics)

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27 pages, 4212 KB

Open AccessArticle

Artificial Neural Network Modeling of Darcy–Forchheimer Nanofluid Flow over a Porous Riga Plate: Insights into Brownian Motion, Thermal Radiation, and Activation Energy Effects on Heat Transfer

by Zafar Abbas, Aljethi Reem Abdullah, Muhammad Fawad Malik and Syed Asif Ali Shah

Symmetry 2025, 17(9), 1582; https://doi.org/10.3390/sym17091582 - 22 Sep 2025

Viewed by 142

Abstract

Nanotechnology has become a transformative field in modern science and engineering, offering innovative approaches to enhance conventional thermal and fluid systems. Heat and mass transfer phenomena, particularly fluid motion across various geometries, play a crucial role in industrial and engineering processes. The inclusion [...] Read more.

Nanotechnology has become a transformative field in modern science and engineering, offering innovative approaches to enhance conventional thermal and fluid systems. Heat and mass transfer phenomena, particularly fluid motion across various geometries, play a crucial role in industrial and engineering processes. The inclusion of nanoparticles in base fluids significantly improves thermal conductivity and enables advanced phase-change technologies. The current work examines Powell–Eyring nanofluid’s heat transmission properties on a stretched Riga plate, considering the effects of magnetic fields, porosity, Darcy–Forchheimer flow, thermal radiation, and activation energy. Using the proper similarity transformations, the pertinent governing boundary-layer equations are converted into a set of ordinary differential equations (ODEs), which are then solved using the boundary value problem fourth-order collocation (BVP4C) technique in the MATLAB program. Tables and graphs are used to display the outcomes. Due to their significance in the industrial domain, the Nusselt number and skin friction are also evaluated. The velocity of the nanofluid is shown to decline with a boost in the Hartmann number, porosity, and Darcy–Forchheimer parameter values. Moreover, its energy curves are increased by boosting the values of thermal radiation and the Biot number. A stronger Hartmann number M decelerates the flow (thickening the momentum boundary layer), whereas increasing the Riga forcing parameter Q can locally enhance the near-wall velocity due to wall-parallel Lorentz forcing. Visual comparisons and numerical simulations are used to validate the results, confirming the durability and reliability of the suggested approach. By using a systematic design technique that includes training, testing, and validation, the fluid dynamics problem is solved. The model’s performance and generalization across many circumstances are assessed. In this work, an artificial neural network (ANN) architecture comprising two hidden layers is employed. The model is trained with the Levenberg–Marquardt scheme on reliable numerical datasets, enabling enhanced prediction capability and computational efficiency. The ANN demonstrates exceptional accuracy, with regression coefficients

R \approx 1.0

and the best validation mean squared errors of

8.52 \times 10^{- 10}

,

7.91 \times 10^{- 9}

, and

1.59 \times 10^{- 8}

for the Powell–Eyring, heat radiation, and thermophoresis models, respectively. The ANN-predicted velocity, temperature, and concentration profiles show good agreement with numerical findings, with only minor differences in insignificant areas, establishing the ANN as a credible surrogate for quick parametric assessment and refinement in magnetohydrodynamic (MHD) nanofluid heat transfer systems. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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13 pages, 286 KB

Open AccessArticle

Categories of Harmonic Functions in the Symmetric Unit Disk Linked to the Bessel Function

by Naci Taşar, Fethiye Müge Sakar, Basem Frasin and Ibtisam Aldawish

Symmetry 2025, 17(9), 1581; https://doi.org/10.3390/sym17091581 - 22 Sep 2025

Viewed by 136

Abstract

Here in this paper, we establish the basic inclusion relations among the harmonic class

HF (σ, η)

with the classes

S_{HF}^{*}

of starlike harmonic functions and

K_{HF}

of convex harmonic functions defined in open symmetric unit disk [...] Read more.

Here in this paper, we establish the basic inclusion relations among the harmonic class

HF (σ, η)

with the classes

S_{HF}^{*}

of starlike harmonic functions and

K_{HF}

of convex harmonic functions defined in open symmetric unit disk U. Moreover, we investigate inclusion connections for the harmonic classes

T N_{HF} (ϱ)

and

T Q_{HF} (ϱ)

of harmonic functions by applying the operator

Λ

associated with the Bessel function. Furthermore, several special cases of the main results are obtained for the particular case

σ = 0

. Full article

(This article belongs to the Special Issue Applications of Special Functions in Complex Analysis and Their Symmetries)

17 pages, 1039 KB

Open AccessArticle

A Federated Intrusion Detection System for Edge Environments Using Multi-Index Hashing and Attention-Based KNN

by Ying Liu, Xing Liu, Hao Yu, Bowen Guo and Xiao Liu

Symmetry 2025, 17(9), 1580; https://doi.org/10.3390/sym17091580 - 22 Sep 2025

Viewed by 402

Abstract

Edge computing offers low-latency and distributed processing for IoT applications but poses new security challenges, due to limited resources and decentralized data. Intrusion detection systems (IDSs) are essential for real-time threat monitoring, yet traditional IDS frameworks often struggle in edge environments, failing to [...] Read more.

Edge computing offers low-latency and distributed processing for IoT applications but poses new security challenges, due to limited resources and decentralized data. Intrusion detection systems (IDSs) are essential for real-time threat monitoring, yet traditional IDS frameworks often struggle in edge environments, failing to meet efficiency requirements. This paper presents an efficient intrusion detection framework that integrates spatiotemporal hashing, federated learning, and fast K-nearest neighbor (KNN) retrieval. A hashing neural network encodes network traffic into compact binary codes, enabling low-overhead similarity comparison via Hamming distance. To support scalable retrieval, multi-index hashing is applied for sublinear KNN searching. Additionally, we propose an attention-guided federated aggregation strategy that dynamically adjusts client contributions, reducing communication costs. Our experiments on benchmark datasets demonstrate that our method achieves competitive detection accuracy with significantly lower computational, memory, and communication overhead, making it well-suited for edge-based deployment. Full article

(This article belongs to the Section Computer)

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17 pages, 1671 KB

Open AccessArticle

Early-Stage Prediction of Steel Weight in Industrial Buildings Using Neural Networks

by Johnny Setiawan, Ridho Bayuaji, Mohammad Arif Rohman and Delima Canny Valentine Simarmata

Symmetry 2025, 17(9), 1579; https://doi.org/10.3390/sym17091579 - 22 Sep 2025

Viewed by 200

Abstract

In industrial building projects, steel is the main material used to create sturdy structures that have large open spaces without many columns in the center of the building. To estimate the cost of constructing a building before it enters the detailed design stage, [...] Read more.

In industrial building projects, steel is the main material used to create sturdy structures that have large open spaces without many columns in the center of the building. To estimate the cost of constructing a building before it enters the detailed design stage, engineers and stakeholders must have the right tools and guidelines. Steel is an important construction material used at high volumes in industrial buildings, and it plays a significant role in determining the total cost of a project. This study develops and evaluates an artificial neural network (ANN) model based on multilayer perceptron (MLP) to predict the weight of steel structures in industrial buildings. The data collected include actual projects from 180 industrial building projects, using parameters that influence the weight of steel. The findings show that the ANN method can accurately estimate the weight of steel at an early stage in the building project, even before the detailed design phase. It was found that ANN has the ability to predict the weight of steel for industrial buildings with an excellent degree of accuracy, with a coefficient of correlation (R²) of 94.85% and prediction accuracy (PA) of 94.23%. This indicates that the relationship between the independent and dependent variables of the developed models is good and the predicted values from the forecast model fit with the real-life data. Full article

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

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18 pages, 3433 KB

Open AccessArticle

Mathematical Modelling of Electrode Geometries in Electrostatic Fog Harvesters

by Egils Ginters and Patriks Voldemars Ginters

Symmetry 2025, 17(9), 1578; https://doi.org/10.3390/sym17091578 - 21 Sep 2025

Viewed by 246

Abstract

This paper presents a comparative mathematical analysis of electrode configurations used in active fog water harvesting systems based on electrostatic ionization. The study begins with a brief overview of fog formation and typology. It also addresses the global relevance of fog as a [...] Read more.

This paper presents a comparative mathematical analysis of electrode configurations used in active fog water harvesting systems based on electrostatic ionization. The study begins with a brief overview of fog formation and typology. It also addresses the global relevance of fog as a decentralized water resource. It also outlines the main methods and collector designs currently employed for fog water capture, both passive and active. The core of the work involves solving the Laplace equation for various electrode geometries to compute electrostatic field distributions and analyze field line density patterns as a proxy for potential water collection efficiency. The evaluated configurations include centered rod–cylinder, symmetric parallel multi-rod, and asymmetric wire–plate layouts, with emphasis on identifying spatial regions of high field line convergence. These regions are interpreted as likely trajectories of charged droplets under Coulombic force influence. The modeling approach enables preliminary assessment of design efficiency without relying on time-consuming droplet-level simulations. The results serve as a theoretical foundation prior to the construction of electrode layouts in the portable HygroCatch experimental harvester and provide insight into how field structure correlates with fog water harvesting performance. Full article

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

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17 pages, 1133 KB

Open AccessArticle

Spatio-Temporal Recursive Method for Traffic Flow Interpolation

by Gang Wang, Yuhao Mao, Xu Liu, Haohan Liang and Keqiang Li

Symmetry 2025, 17(9), 1577; https://doi.org/10.3390/sym17091577 - 21 Sep 2025

Viewed by 248

Abstract

Traffic data sequence imputation plays a crucial role in maintaining the integrity and reliability of transportation analytics and decision-making systems. With the proliferation of sensor technologies and IoT devices, traffic data often contain missing values due to sensor failures, communication issues, or data [...] Read more.

Traffic data sequence imputation plays a crucial role in maintaining the integrity and reliability of transportation analytics and decision-making systems. With the proliferation of sensor technologies and IoT devices, traffic data often contain missing values due to sensor failures, communication issues, or data processing errors. It is necessary to effectively interpolate these missing parts to ensure the correctness of downstream work. Compared with other data, the monitoring data of traffic flow shows significant temporal and spatial correlations. However, most methods have not fully integrated the correlations of these types. In this work, we introduce the Temporal–Spatial Fusion Neural Network (TSFNN), a framework designed to address missing data recovery in transportation monitoring by jointly modeling spatial and temporal patterns. The architecture incorporates a temporal component, implemented with a Recurrent Neural Network (RNN), to learn sequential dependencies, alongside a spatial component, implemented with a Multilayer Perceptron (MLP), to learn spatial correlations. For performance validation, the model was benchmarked against several established methods. Using real-world datasets with varying missing-data ratios, TSFNN consistently delivered more accurate interpolations than all baseline approaches, highlighting the advantage of combining temporal and spatial learning within a single framework. Full article

(This article belongs to the Section Computer)

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23 pages, 3485 KB

Open AccessArticle

MSGS-SLAM: Monocular Semantic Gaussian Splatting SLAM

by Mingkai Yang, Shuyu Ge and Fei Wang

Symmetry 2025, 17(9), 1576; https://doi.org/10.3390/sym17091576 - 20 Sep 2025

Viewed by 436

Abstract

With the iterative evolution of SLAM (Simultaneous Localization and Mapping) technology in the robotics domain, the SLAM paradigm based on three-dimensional Gaussian distribution models has emerged as the current state-of-the-art technical approach. This research proposes a novel MSGS-SLAM system (Monocular Semantic Gaussian Splatting [...] Read more.

With the iterative evolution of SLAM (Simultaneous Localization and Mapping) technology in the robotics domain, the SLAM paradigm based on three-dimensional Gaussian distribution models has emerged as the current state-of-the-art technical approach. This research proposes a novel MSGS-SLAM system (Monocular Semantic Gaussian Splatting SLAM), which innovatively integrates monocular vision with three-dimensional Gaussian distribution models within a semantic SLAM framework. Our approach exploits the inherent spherical symmetries of isotropic Gaussian distributions, enabling symmetric optimization processes that maintain computational efficiency while preserving geometric consistency. Current mainstream three-dimensional Gaussian semantic SLAM systems typically rely on depth sensors for map reconstruction and semantic segmentation, which not only significantly increases hardware costs but also limits the deployment potential of systems in diverse scenarios. To overcome this limitation, this research introduces a depth estimation proxy framework based on Metric3D-V2, which effectively addresses the inherent deficiency of monocular vision systems in depth information acquisition. Additionally, our method leverages architectural symmetries in indoor environments to enhance semantic understanding through symmetric feature matching. Through this approach, the system achieves robust and efficient semantic feature integration and optimization without relying on dedicated depth sensors, thereby substantially reducing the dependency of three-dimensional Gaussian semantic SLAM systems on depth sensors and expanding their application scope. Furthermore, this research proposes a keyframe selection algorithm based on semantic guidance and proxy depth collaborative mechanisms, which effectively suppresses pose drift errors accumulated during long-term system operation, thereby achieving robust global loop closure correction. Through systematic evaluation on multiple standard datasets, MSGS-SLAM achieves comparable technical performance to existing three-dimensional Gaussian model-based semantic SLAM systems across multiple key performance metrics including ATE RMSE, PSNR, and mIoU. Full article

(This article belongs to the Section Engineering and Materials)

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14 pages, 356 KB

Open AccessArticle

The Charmed Meson Spectrum Using One-Loop Corrections to the One-Gluon Exchange Potential

by André Capelo-Astudillo, Telmo Aguilar, Marlon Conde-Correa, Álvaro Duenas-Vidal, Pablo G. Ortega and Jorge Segovia

Symmetry 2025, 17(9), 1575; https://doi.org/10.3390/sym17091575 - 20 Sep 2025

Viewed by 158

Abstract

We investigate the charmed meson spectrum using a constituent quark model (CQM) with one-loop corrections applied to the one-gluon exchange (OGE) potential. The study aims to understand if the modified version of our CQM sufficiently account for the charmed meson spectrum observed experimentally, [...] Read more.

We investigate the charmed meson spectrum using a constituent quark model (CQM) with one-loop corrections applied to the one-gluon exchange (OGE) potential. The study aims to understand if the modified version of our CQM sufficiently account for the charmed meson spectrum observed experimentally, without invoking exotic quark and gluon configurations such as hybrid mesons or tetraquarks. Within this model, charmed mesons’ masses are computed, comparing theoretical predictions to experimental data. The results, within uncertainties, suggest that our theoretical framework generally reproduces mass splittings and level ordering observed for charmed mesons. Particularly, large discrepancies between theory and experiment found in P-wave states are, at least, significantly ameliorated by incorporating higher-order interaction terms. Therefore, the findings emphasize that while the traditional quark model is limited in fully describing charmed mesons, enhanced potential terms may bridge the gap with experimental observations. The study contributes a framework for predicting excited charmed meson states for future experimental validation. Full article

(This article belongs to the Section Physics)

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26 pages, 365 KB

Open AccessArticle

Exact Solutions of Maxwell Vacuum Equations in Petrov Homogeneous Non-Null Spaces

by Valery V. Obukhov

Symmetry 2025, 17(9), 1574; https://doi.org/10.3390/sym17091574 - 20 Sep 2025

Viewed by 144

Abstract

The classification of exact solutions of Maxwell vacuum equations for pseudo-Riemannian spaces with spatial symmetry (homogeneous non-null spaces in Petrov) in the presence of electromagnetic fields invariant with respect to the action of the group of space motions is summarized. A new classification [...] Read more.

The classification of exact solutions of Maxwell vacuum equations for pseudo-Riemannian spaces with spatial symmetry (homogeneous non-null spaces in Petrov) in the presence of electromagnetic fields invariant with respect to the action of the group of space motions is summarized. A new classification method is used, common to all homogeneous zero spaces of Petrov. The method is based on the use of canonical reper vectors and on the use of a new approach to the systematization of solutions. The classification results are presented in a form more convenient for further use. Using the previously made refinement of the classification of Petrov spaces, the classification of exact solutions of Maxwell vacuum equations for spaces with the group of motions

G_{3} (V I I I)

is completed. Full article

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

24 pages, 344 KB

Open AccessArticle

Novel Weighted Dynamic Hardy-Type Inequalities in the Framework of Delta Conformable Calculus on Time Scales

by Haytham M. Rezk, Ahmed R. El-Saeed, Mohamed Mousa and Karim A. Mohamed

Symmetry 2025, 17(9), 1573; https://doi.org/10.3390/sym17091573 - 19 Sep 2025

Viewed by 181

Abstract

This work presents new results concerning weighted Hardy-type inequalities within the framework of delta conformable fractional integrals on arbitrary time scales. The proposed approach unifies the treatment of inequalities across continuous and discrete domains, enabling the derivation of original forms in both settings. [...] Read more.

This work presents new results concerning weighted Hardy-type inequalities within the framework of delta conformable fractional integrals on arbitrary time scales. The proposed approach unifies the treatment of inequalities across continuous and discrete domains, enabling the derivation of original forms in both settings. The obtained results exhibit symmetry with classical inequalities, and several integral and discrete inequalities arise as special cases. These findings extend and generalize known results and enrich the theory of integral inequalities in fractional and dynamic calculus, providing a versatile platform for further developments in symmetric and weighted inequality analysis. Full article

(This article belongs to the Section Mathematics)

26 pages, 6893 KB

Open AccessArticle

Angle-of-Attack, Induced Attitude Evolution in a Coupled Crater, and Plugging Penetration of Thin Concrete Targets

by Zheng Tao, Wenbin Li, Wei Zhu, Junjie Xu and Jihua Yan

Symmetry 2025, 17(9), 1572; https://doi.org/10.3390/sym17091572 - 19 Sep 2025

Viewed by 138

Abstract

To address the limitations of existing models that typically treat crater formation and shear plugging as independent processes and only consider angle of attack effects during the initial crater phase, this study proposes a dynamic shear _plugging model for projectile penetration into thin [...] Read more.

To address the limitations of existing models that typically treat crater formation and shear plugging as independent processes and only consider angle of attack effects during the initial crater phase, this study proposes a dynamic shear _plugging model for projectile penetration into thin concrete targets. The model is built upon the improved three-stage penetration theory and cavity expansion principles, and introduces a coupled cratering, plugging mechanism that captures the simultaneous interaction between these stages. A differential surface force approach is employed to describe the asymmetric stress distribution on the projectile nose under non-zero angle of attack conditions, while free surface effects are incorporated to refine local stress predictions. A series of validation experiments was performed with 30 mm rigid projectiles penetrating 27 MPa concrete slabs under different impact velocities and initial angles of attack. The results show that the proposed model achieves prediction errors of less than 20% for both residual velocity and exit attitude angle, significantly outperforming classical models such as those of Duan and Liu, which tend to underestimate post-impact deflection by treating cratering and plugging separately. Based on this validated framework, parametric studies were conducted to examine the effects of the initial inclination, impact velocity, and target thickness on the evolution of projectile attitude and angle of attack. The findings demonstrate that the dynamic shear plugging mechanism exerts a critical regulatory influence on projectile deflection during thin target penetration. This work, therefore, not only resolves the directional reversal issue inherent in earlier theories but also provides theoretical support for the engineering design of concrete protective structures subjected to angular impact conditions. Full article

(This article belongs to the Special Issue Symmetry, Asymmetry and Nonlinearity in Geomechanics)

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23 pages, 5585 KB

Open AccessArticle

NURBS Morphing Optimization of Drag and Lift in a Coupe-Class Vehicle Using Symmetry-Plane Comparison of Aerodynamic Performance

by Sohaib Guendaoui, Abdeslam El Akkad, Ahmed El Khalfi, Sorin Vlase and Marin Marin

Symmetry 2025, 17(9), 1571; https://doi.org/10.3390/sym17091571 - 19 Sep 2025

Viewed by 228

Abstract

This study presents a morphing Non-Uniform Rational B-Spline (NURBS) optimization method for enhancing sports car aerodynamics, with performance evaluation conducted in the vehicle’s symmetry plane. The morphing approach enables precise, smooth deformations of rear-end and spoiler geometries while preserving shape continuity, allowing controlled [...] Read more.

This study presents a morphing Non-Uniform Rational B-Spline (NURBS) optimization method for enhancing sports car aerodynamics, with performance evaluation conducted in the vehicle’s symmetry plane. The morphing approach enables precise, smooth deformations of rear-end and spoiler geometries while preserving shape continuity, allowing controlled aerodynamic modifications suitable for comparative analysis. Flow simulations were carried out in ANSYS Fluent 2022 using the Reynolds-Averaged Navier–Stokes (RANS) equations with the standard k-ε turbulence model, selected for its stability and accuracy in predicting boundary-layer evolution, wake behavior, and flow separation in external automotive flows. Three configurations were assessed: the baseline model, a spoiler-equipped version, and two NURBS-morphed designs. The symmetry-plane evaluation ensured bilateral balance across all variants, enabling direct comparison of drag and lift performance. The results show that the proposed morphing strategy achieved notable lift reduction and favorable drag-to-lift ratios while maintaining manufacturability. The findings demonstrate that combining NURBS-based morphing with symmetry-plane aerodynamic assessment offers an efficient, reliable framework for vehicle aerodynamic optimization, bridging geometric flexibility with robust computational evaluation. Full article

(This article belongs to the Section Mathematics)

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14 pages, 2875 KB

Open AccessArticle

Laterality, Shot Direction and Spatial Asymmetry in Decisive Penalty Kicks: Evidence from Elite Men’s Football

by Pablo Cidre-Fuentes, Manuel Alberto González-Harcevnicow and Iván Prieto-Lage

Symmetry 2025, 17(9), 1570; https://doi.org/10.3390/sym17091570 - 19 Sep 2025

Viewed by 285

Abstract

Penalty shootouts often decide major football tournaments, making the analysis of spatial symmetry and shot patterns crucial for performance optimization. This study analyzed 212 decisive penalty kicks in elite men’s football to explore spatial patterns and asymmetries in execution, as well as their [...] Read more.

Penalty shootouts often decide major football tournaments, making the analysis of spatial symmetry and shot patterns crucial for performance optimization. This study analyzed 212 decisive penalty kicks in elite men’s football to explore spatial patterns and asymmetries in execution, as well as their relationship with performance effectiveness. An observational methodology was used, combining temporal pattern detection (T-patterns) and chi-square tests to examine associations between contextual, spatial, and outcome-related variables. Results showed that the most frequently targeted area was left-down (28.3%), with a success rate of 71.7%. Additionally, central zones exhibited particularly high accuracy (ranging from 88.9% to 100%) despite their low usage frequency. Differences were also observed in the distribution of shots between left- and right-footed players, both in frequency and effectiveness, although these were not significant. The findings suggest the presence of strategic tendencies and functional spatial asymmetries, which may have implications for specialized training in high-pressure scenarios. These insights can guide targeted training strategies for both kickers and goalkeepers and encourage further research on decision-making and spatial behavior under extreme pressure. Full article

(This article belongs to the Special Issue Symmetry Application in Motor Control in Sports and Rehabilitation)

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14 pages, 357 KB

Open AccessArticle

Existence of Mild Solutions for the Generalized Anti-Periodic Boundary Value Problem to the Fractional Hybird Differential Equations with p(t)-Laplacian Operator

by Jinxiu Liu, Guanghao Jiang and Tengfei Shen

Symmetry 2025, 17(9), 1569; https://doi.org/10.3390/sym17091569 - 19 Sep 2025

Viewed by 121

Abstract

The main objective of this work is to discuss the generalized anti-periodic boundary conditions of the generalized Caputo fractional differential equations with

p (t)

-Laplacian operators. By applying the Schaefer fixed point theorem, the existence of mild solutions to this problem [...] Read more.

The main objective of this work is to discuss the generalized anti-periodic boundary conditions of the generalized Caputo fractional differential equations with

p (t)

-Laplacian operators. By applying the Schaefer fixed point theorem, the existence of mild solutions to this problem is obtained, which generalizes and enriches the anti-periodic boundary value problem of Caputo fractional hybrid differential equations. Finally, a numerical example is given to verify our main results. The anti-periodic boundary value condition imparts a form of symmetric inversion with respect to the original state, so it exhibits an anti-symmetric structural feature. Full article

(This article belongs to the Section Mathematics)

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21 pages, 314 KB

Open AccessArticle

Synthesis of Index Difference Graph Structures for Cryptographic Implementation

by A. Netto Mertia and M. Sudha

Symmetry 2025, 17(9), 1568; https://doi.org/10.3390/sym17091568 - 19 Sep 2025

Viewed by 212

Abstract

Cryptography stands out as a scientific methodology for safeguarding communication against unauthorized access. This article proposes a newly formulated graph termed the Index Difference Graph (IDG). The proposed graph model serves as the secret key in the encryption process. Furthermore, we present a [...] Read more.

Cryptography stands out as a scientific methodology for safeguarding communication against unauthorized access. This article proposes a newly formulated graph termed the Index Difference Graph (IDG). The proposed graph model serves as the secret key in the encryption process. Furthermore, we present a new graph-based algorithm, the Index Difference Modular Cryptographic (IDMC) Algorithm, and analyze it using centipede and path graphs. The goal of this graph-based approach is to increase the encryption rate while maintaining computational efficiency. This research investigates different types of index difference graphs and analyzes the time and space complexity of the algorithm. IDMC exhibits a lower collision probability, thereby enhancing encryption security. When employing a graph that admits an Index Difference Graph structure in the cryptographic algorithm, both the sender and receiver must be aware of the graph’s precise structure, as this strengthens the robustness of the cryptographic key. The application of the index difference centipede graph

P_{n} ⊙ 2 k_{1}

in cryptography, examined through the IDMC algorithm, demonstrates exceptionally high brute-force resistance estimated at approximately

2.6 \times 10^{39}

for smaller instances with

n \leq 7

and escalating to

6.93 \times 10^{163}

for larger graphs with

n \geq 20

. This resistance underscores the algorithm’s efficiency and cryptographic resilience. Full article

(This article belongs to the Section Computer)

35 pages, 1103 KB

Open AccessArticle

Improving the Performance of Constructed Neural Networks with a Pre-Train Phase

by Ioannis G. Tsoulos, Vasileios Charilogis and Dimitrios Tsalikakis

Symmetry 2025, 17(9), 1567; https://doi.org/10.3390/sym17091567 - 19 Sep 2025

Viewed by 280

Abstract

A multitude of problems in the contemporary literature are addressed using machine learning models, the most widespread of which are artificial neural networks. Furthermore, in recent years, evolutionary techniques have emerged that identify both the architecture of artificial neural networks and their corresponding [...] Read more.

A multitude of problems in the contemporary literature are addressed using machine learning models, the most widespread of which are artificial neural networks. Furthermore, in recent years, evolutionary techniques have emerged that identify both the architecture of artificial neural networks and their corresponding parameters. Among these techniques, one can also identify the artificial neural networks being constructed, in which the structure and parameters of the neural network are effectively identified using Grammatical Evolution. In this work, a pre-training stage is introduced in which an artificial neural network with a fixed number of parameters is trained using some optimization technique such as the genetic algorithms used here. The final result of this additional phase is a trained artificial neural network, which is introduced into the genetic population used by Grammatical Evolution in the second phase. In this way, finding the overall minimum of the error function will be significantly accelerated, making the second phase method more efficient. The current work was applied to many classification and regression problems found in the related literature, and it was compared against other methods used for neural network training as well as against the original method used to construct neural networks. Full article

(This article belongs to the Special Issue Symmetry in Data Sciences and Machine Learning for Multidisciplinary Research)

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22 pages, 2780 KB

Open AccessArticle

Symmetry and Skewness in Weibull Modeling: Optimal Grouping for Parameter Estimation in Fertilizer Granule Strength

by Wojciech Przystupa, Paweł Kurasiński and Norbert Leszczyński

Symmetry 2025, 17(9), 1566; https://doi.org/10.3390/sym17091566 - 18 Sep 2025

Viewed by 210

Abstract

This study investigates Weibull distribution modeling for data under grouped observations. Two data grouping methods (equal-width and optimal) were compared for estimating parameters of the Weibull distribution using maximum likelihood estimation (MLE) in each case. Methodologically, our contribution is twofold: First, we derive [...] Read more.

This study investigates Weibull distribution modeling for data under grouped observations. Two data grouping methods (equal-width and optimal) were compared for estimating parameters of the Weibull distribution using maximum likelihood estimation (MLE) in each case. Methodologically, our contribution is twofold: First, we derive the correct Fisher information matrix for grouped data in the two-parameter Weibull and use it to compute optimal interval boundaries. Second, we derive maximum likelihood estimators for data grouped under these optimal intervals. The fit of the assumed distributions was evaluated using chi-squared goodness-of-fit tests. We also calculated Asymptotic Relative Efficiency (ARE) to compare the precision of parameter estimates across different grouping approaches. Optimal boundaries yielded systematically higher ARE than equal-width grouping in 100% of comparisons for the shape parameter

c

. Gains for the scale parameter

b

were smaller and occurred in about 62% of cases. Optimal grouping also produced generally higher chi-squared

(χ^{2})

goodness-of-fit p-values than equal-width grouping, indicating a better fit. From a symmetry standpoint, the Weibull distribution is inherently asymmetric, with the degree of asymmetry governed by the shape parameter

c

. We show that the choice of grouping affects the estimate of

c

and, thus, the inferred skewness, further explaining why optimally designed intervals yield both higher precision and a more faithful representation of failure behavior. Full article

(This article belongs to the Section Mathematics)

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25 pages, 2383 KB

Open AccessArticle

Application of the Finite Element Method in Stress and Strain Analysis of Spherical Tank for Fluid Storage

by Halima Onalla S. Ali, Vladimir Dedić, Jelena Živković, Nenad Todić and Radovan Petrović

Symmetry 2025, 17(9), 1565; https://doi.org/10.3390/sym17091565 - 18 Sep 2025

Viewed by 217

Abstract

Symmetry plays a key role in the study of stress and strain analysis of spherical tanks, as described in detail in the main text. The inherent geometric symmetry of a spherical tank–being uniform in all directions from its center–allows for significant simplification of [...] Read more.

Symmetry plays a key role in the study of stress and strain analysis of spherical tanks, as described in detail in the main text. The inherent geometric symmetry of a spherical tank–being uniform in all directions from its center–allows for significant simplification of finite element models. This radial symmetry means that the stress and strain fields under uniform internal pressure are also symmetrical, reducing the computational domain to a small, representative portion of the tank rather than the entire structure. By using these symmetry principles, the study not only ensures the accuracy of its predictions but also achieves a high degree of computational efficiency, making complex engineering problems easier and more accessible. The application of symmetry, therefore, is not just a theoretical concept but a practical tool that underlies the methodology and success of this analysis. This study investigates the mechanical behavior of a spherical tank subjected to internal fluid pressure, utilizing the finite element method (FEM) as a primary analytical tool. Spherical tanks are widely used for the storage of various fluids, including liquefied natural gas (LNG), compressed gases, and water. Their design is critical to ensure structural integrity and safety. This research aims to provide a comprehensive stress and strain analysis of a typical spherical tank, focusing on the hoop and meridian stresses, and their distribution across the tank’s geometry. A 3D finite element model of a spherical tank will be developed using commercial FEA software. The model will incorporate realistic material properties (e.g., steel alloy) and boundary conditions that simulate the support structure and internal fluid pressure. The analysis will consider both linear elastic and potentially non-linear material responses to explore the tank’s behavior under various operational and overpressure scenarios. The primary objectives of this study are as follows: (1) determine the maximum principal stresses and strains within the tank wall, (2) analyze the stress concentration at critical points, such as support connections and nozzle penetrations, and (3) validate the FEM results against classical analytical solutions for thin-walled spherical pressure vessels. The findings will provide valuable insights into the structural performance of these tanks, highlighting potential areas of concern and offering a robust numerical approach for design optimization and safety assessment. This research demonstrates the power and utility of FEM in engineering design, offering a more detailed and accurate analysis than traditional analytical methods. Full article

(This article belongs to the Section Mathematics)

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16 pages, 15063 KB

Open AccessArticle

Numerical Simulation of 3D Full Hydraulic Jumps Using a GPU-Based SPH Model

by Jinbo Lin, Runzhen Wu, Yingchao Ma, Zhenglin Tian, Dongbin He, Jian Zheng and Lei Li

Symmetry 2025, 17(9), 1564; https://doi.org/10.3390/sym17091564 - 18 Sep 2025

Viewed by 209

Abstract

Hydraulic jumps typically exhibit a distinct symmetry under ideal boundary conditions and are characterized by a sudden change in flow depth and velocity. They are commonly employed in a diverse array of water management systems to dissipate excess energy due to their high [...] Read more.

Hydraulic jumps typically exhibit a distinct symmetry under ideal boundary conditions and are characterized by a sudden change in flow depth and velocity. They are commonly employed in a diverse array of water management systems to dissipate excess energy due to their high energy dissipation rate, strong adaptability to geological conditions and tailwater variation, small fluctuation in tailwater, and low cost of maintenance. In this study, a GPU-based Smoothed Particle Hydrodynamics (SPH) model of 3D hydraulic jumps is established. Numerical simulation of three 3D symmetric full hydraulic jumps with large Froude numbers are carried out, and satisfactory agreements are shown with a largest

L_{2}

error of 0.442 between the numerical free surface and experimental data. The model can reliably reproduce the free surface, jump the toe position, and jump the skimming flow. The analysis of the model efficiency shows that a maximum GPU acceleration of 12, which is equivalent to the theoretical maximum speedups, against parallel CPU can be achieved with a common GPU device. Furthermore, the energy dissipation in the stilling basin of a real sluice gate is investigated by the model. Therefore, the SPH model is a powerful tool for investigating the complex and large-scale 3D full hydraulic jumps for similar hydraulic engineering with the same boundary condition. Full article

(This article belongs to the Section Computer)

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13 pages, 909 KB

Open AccessArticle

An Innovated Vibration Equation for Longitudinal Plate by Using the Symmetric and Asymmetric Spectral Decomposition

by Jun Yin, Chuanping Zhou, Changyong Chu, Huipeng Chen and Fan Yang

Symmetry 2025, 17(9), 1563; https://doi.org/10.3390/sym17091563 - 18 Sep 2025

Viewed by 154

Abstract

Thick wall structures involving longitudinal wave are typically utilized in aerospace engineering, nuclear power engineering, precision transmission device design, and pressure vessels design. Consequently, developing sophisticated dynamic models for thick plates is of paramount importance. However, the commonly used longitudinal vibration equation is [...] Read more.

Thick wall structures involving longitudinal wave are typically utilized in aerospace engineering, nuclear power engineering, precision transmission device design, and pressure vessels design. Consequently, developing sophisticated dynamic models for thick plates is of paramount importance. However, the commonly used longitudinal vibration equation is of the second order, which is regarded as a plane stress problem. Its dispersion curve is a straight line, which cannot describe the actual dispersion in the plate. In this paper, the spectral analysis of Navier equation describing three-dimensional elasto-dynamics is carried out by using the symmetric and asymmetric spectral decomposition theory of differential operators and introducing the concept of virtual differential operators. The infinite product operator series describing longitudinal vibration are truncated into fourth order. The governing equation of longitudinal vibration consists of a fourth-order wave equation and a second-order wave equation. Owing to the fact that no a priori assumptions were introduced during the derivation of its dynamic equations, the proposed plate dynamic model boasts higher precision and is applicable across a broader frequency spectrum and for plates with greater thicknesses. This is a breakthrough in the longitudinal vibration equation of plates. Full article

(This article belongs to the Section Mathematics)

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10 pages, 238 KB

Open AccessArticle

Smoothness of the Solution of a Boundary Value Problem for Degenerate Elliptic Equations

by Perizat Beisebay, Yerbulat Akzhigitov, Talgat Akhazhanov, Gulmira Kenzhebekova and Dauren Matin

Symmetry 2025, 17(9), 1562; https://doi.org/10.3390/sym17091562 - 18 Sep 2025

Viewed by 207

Abstract

This paper investigates boundary value problems for a class of elliptic equations exhibiting uniform and non-uniform degeneracy, including cases of non-monotonic degeneration. A key objective is to identify conditions on the coefficients under which solutions maintain ultimate smoothness, even in the presence of [...] Read more.

This paper investigates boundary value problems for a class of elliptic equations exhibiting uniform and non-uniform degeneracy, including cases of non-monotonic degeneration. A key objective is to identify conditions on the coefficients under which solutions maintain ultimate smoothness, even in the presence of degeneracy. The analysis is grounded in several fundamental aspects of symmetry. Structural symmetry is reflected in the formulation of the differential operators; functional symmetry emerges in the properties of the associated weighted Sobolev spaces; and spectral symmetry plays a critical role in the behavior of the eigenvalues and eigenfunctions used to characterize solutions. By employing localization techniques, a priori estimates, and spectral theory, we establish new coefficient conditions ensuring smoothness in both semi-periodic and Dirichlet boundary settings. Moreover, we prove the boundedness and compactness of certain weighted operators, whose definitions and properties are tightly linked to underlying symmetries in the problem’s formulation. These results are not only of theoretical importance but also bear practical implications for numerical methods and models where symmetry principles influence solution regularity and operator behavior. Full article

(This article belongs to the Section Mathematics)

24 pages, 2616 KB

Open AccessArticle

Symmetric Affix–Context Co-Attention: A Dual-Gating Framework for Robust POS Tagging in Low-Resource MRLs

by Yuan Qi, Samat Ali and Alim Murat

Symmetry 2025, 17(9), 1561; https://doi.org/10.3390/sym17091561 - 18 Sep 2025

Viewed by 296

Abstract

Part-of-speech (POS) tagging in low-resource, morphologically rich languages (LRLs/MRLs) remains challenging due to extensive affixation, high out-of-vocabulary (OOV) rates, and pervasive polysemy. We propose MRL-POS, a unified Transformer-CRF framework that dynamically selects informative affix features and integrates them with deep contextual embeddings via [...] Read more.

Part-of-speech (POS) tagging in low-resource, morphologically rich languages (LRLs/MRLs) remains challenging due to extensive affixation, high out-of-vocabulary (OOV) rates, and pervasive polysemy. We propose MRL-POS, a unified Transformer-CRF framework that dynamically selects informative affix features and integrates them with deep contextual embeddings via a novel dual-gating co-attention mechanism. First, a Dynamic Affix Selector adaptively adjusts n-gram ranges and frequency thresholds based on word length to ensure high-precision affix segmentation. Second, the Affix–Context Co-Attention Module employs two gating functions that conditionally amplify contextual dimensions with affix cues and vice versa, enabling robust disambiguation of complex and ambiguous forms. Third, Layer-Wise Attention Pooling aggregates multi-layer XLM-RoBERTa representations, emphasizing those most relevant for morphological and syntactic tagging. Evaluations on Uyghur, Kyrgyz, and Uzbek show that MRL-POS achieves an average F₁ of 84.10%, OOV accuracy of 84.24%, and Poly-F₁ of 72.14%, outperforming strong baselines by up to 8 F₁ points. By explicitly modeling the symmetry between morphological affix cues and sentence-level context through a dual-gating co-attention mechanism, MRL-POS achieves a balanced fusion that both preserves local structure and captures global dependencies. Interpretability analyses confirm that 89.1% of the selected affixes align with linguistic expectations. This symmetric design not only enhances robustness in low-resource and agglutinative settings but also offers a general paradigm for symmetry-aware sequence labeling tasks. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry Studies in Data Mining & Machine Learning of Large Language Models)

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18 pages, 5562 KB

Open AccessArticle

Symmetry-Aware Face Illumination Enhancement via Pixel-Adaptive Curve Mapping

by Jieqiong Yang, Yumeng Lu, Jiaqi Liu and Jizheng Yi

Symmetry 2025, 17(9), 1560; https://doi.org/10.3390/sym17091560 - 18 Sep 2025

Viewed by 286

Abstract

Face recognition under uneven illumination conditions presents significant challenges, as asymmetric shadows often obscure facial features while overexposed regions lose critical texture details. To address this problem, a novel symmetry-aware illumination enhancement method named face shadow detection network (FSDN) is proposed, which features [...] Read more.

Face recognition under uneven illumination conditions presents significant challenges, as asymmetric shadows often obscure facial features while overexposed regions lose critical texture details. To address this problem, a novel symmetry-aware illumination enhancement method named face shadow detection network (FSDN) is proposed, which features a nested U-Net architecture combined with Gaussian convolution. This method enables precise illumination intensity maps for the given face images through higher-order quadratic enhancement curves, effectively extending the low-light dynamic range while preserving essential facial symmetry. Comprehensive evaluations on the Extended Yale B and CMU-PIE datasets demonstrate the superiority of the proposed FSDN over conventional approaches, achieving structural similarity (SSIM) indices of 0.48 and 0.59, respectively, along with remarkably low face recognition error rates of 1.3% and 0.2%, respectively. The key innovation of this work lies in its simultaneous optimization of illumination uniformity and facial symmetry preservation, thereby significantly improving face analysis reliability under challenging lighting conditions. Full article

(This article belongs to the Section Computer)

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21 pages, 4354 KB

Open AccessArticle

Migration and Removal of Microplastics in a Dual-Cone Mini-Hydrocyclone

by Yiwei Dai, Xinjun Yang, Jiyun Du, Wei Yu, Dongxiang Wang and Fangyang Yuan

Symmetry 2025, 17(9), 1559; https://doi.org/10.3390/sym17091559 - 17 Sep 2025

Viewed by 247

Abstract

In this study, we analyzed the migration and removal of microplastics (MPs) using a dual-cone mini-hydrocyclone, thereby addressing the research gaps in flow mechanisms and separation efficiency for low-density MPs. We constructed and experimentally verified a numerical model. We discussed the velocity distribution [...] Read more.

In this study, we analyzed the migration and removal of microplastics (MPs) using a dual-cone mini-hydrocyclone, thereby addressing the research gaps in flow mechanisms and separation efficiency for low-density MPs. We constructed and experimentally verified a numerical model. We discussed the velocity distribution of the flow field and the effects of the feed flow rate, feed MP volume fraction, and density on the distribution of MPs. The flow field analysis demonstrated maximum axial velocity at the cylindrical axis and peak tangential/radial velocities in the large cone section, promoting MP enrichment along the axis. The separation efficiency was improved with higher feed flow rates (e.g., 78.56% at 10 m/s for 50 μm MPs) but decreased with an increase in the MP volume fraction due to particle collisions. The MPs with densities below water demonstrated near-complete separation (98.51%), whereas those larger than water density exhibited minimal efficiency. The MPs are concentrated in the large and small cone axes, with density differences that significantly affect the migration patterns. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Fluid Mechanics)

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10 pages, 919 KB

Open AccessArticle

Understanding Weightbearing Symmetries During Crawling in Typically Developing Infants and Infants with Limb Loss

by Mark D. Geil, Jill Cannoy, Emma Stockwell, Colleen Coulter, Megan Knapp, Lyle Blackwelder, Lucas Northway and Austin Brown

Symmetry 2025, 17(9), 1558; https://doi.org/10.3390/sym17091558 - 17 Sep 2025

Viewed by 827

Abstract

Crawling is an almost universal stage of locomotor development in infants; however, it is difficult to quantify using typical motion analysis techniques. The crawling stage therefore has underutilized potential to assess development and detect deviations or abnormalities. This study measured longitudinal weightbearing asymmetries [...] Read more.

Crawling is an almost universal stage of locomotor development in infants; however, it is difficult to quantify using typical motion analysis techniques. The crawling stage therefore has underutilized potential to assess development and detect deviations or abnormalities. This study measured longitudinal weightbearing asymmetries in typically developing (TD) crawling children and compared this population to children with limb loss or limb differences (LLD) using a pressure-sensing mat. The LLD group bore significantly more weight using their arms vs. their legs than the TD group (p < 0.001), but even in cases of unilateral limb loss, bilateral weightbearing symmetry was similar to TD, controlling for body mass and age (p = 0.570). As children in the TD group developed and gained body mass, their weight shifted significantly to their left side (η² = 0.050) and away from their arms and toward their legs (η² = 0.255). The results provide insight into the biomechanical development of TD infant crawling, and the ways in which an atypically developing population manages weightbearing during crawling. The establishment of symmetry data will be useful, as crawling can serve as an opportunity for earlier detection of neuromotor conditions such as cerebral palsy. Furthermore, insight into the crawling patterns of children with limb loss and limb difference can inform prosthetic prescription and the need to consider a missing weight shift toward the legs as children develop. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Biomechanics and Gait Mechanics)

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30 pages, 987 KB

Open AccessArticle

Combining Constructed Artificial Neural Networks with Parameter Constraint Techniques to Achieve Better Generalization Properties

by Ioannis G. Tsoulos, Vasileios Charilogis and Dimitrios Tsalikakis

Symmetry 2025, 17(9), 1557; https://doi.org/10.3390/sym17091557 - 17 Sep 2025

Viewed by 327

Abstract

This study presents a novel hybrid approach combining grammatical evolution with constrained genetic algorithms to overcome key limitations in automated neural network design. The proposed method addresses two critical challenges: the tendency of grammatical evolution to converge to suboptimal architectures due to local [...] Read more.

This study presents a novel hybrid approach combining grammatical evolution with constrained genetic algorithms to overcome key limitations in automated neural network design. The proposed method addresses two critical challenges: the tendency of grammatical evolution to converge to suboptimal architectures due to local optima, and the common overfitting problems in evolved networks. Our solution employs grammatical evolution for initial architecture generation while implementing a specialized genetic algorithm that simultaneously optimizes network parameters within dynamically adjusted bounds. The genetic component incorporates innovative penalty mechanisms in its fitness function to control neuron activation patterns and prevent overfitting. Comprehensive testing across 53 diverse datasets shows our method achieves superior performance compared to traditional optimization techniques, with an average classification error of 21.18% vs. 36.45% for ADAM, while maintaining better generalization capabilities. The constrained optimization approach proves particularly effective in preventing premature convergence, and the penalty system successfully mitigates overfitting even in complex, high-dimensional problems. Statistical validation confirms these improvements are significant (p <

1.1 \times 10^{- 8}

) and consistent across multiple domains, including medical diagnosis, financial prediction, and physical system modeling. This work provides a robust framework for automated neural network construction that balances architectural innovation with parameter optimization while addressing fundamental challenges in evolutionary machine learning. Full article

(This article belongs to the Special Issue Applications of Symmetry/Asymmetry in Artificial Intelligence and Deep Metaheuristics)

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19 pages, 1662 KB

Open AccessArticle

Kernel Mean p-Power Loss-Enhanced Robust Hammerstein Adaptive Filter and Its Performance Analysis

by Yan Liu, Chuanliang Tu, Yong Liu, Yu Chen, Chenggan Wen and Banghui Yin

Symmetry 2025, 17(9), 1556; https://doi.org/10.3390/sym17091556 - 17 Sep 2025

Viewed by 187

Abstract

Hammerstein adaptive filters (HAFs) are widely used for nonlinear system identification due to their structural simplicity and modeling effectiveness. However, their performance can degrade significantly in the presence of impulsive disturbance or other more complex non-Gaussian noise, which are common in real-world scenarios. [...] Read more.

Hammerstein adaptive filters (HAFs) are widely used for nonlinear system identification due to their structural simplicity and modeling effectiveness. However, their performance can degrade significantly in the presence of impulsive disturbance or other more complex non-Gaussian noise, which are common in real-world scenarios. To address this limitation, this paper proposes a robust HAF algorithm based on the kernel mean p-power error (KMPE) criterion. By extending the p-power loss into the kernel space, KMPE preserves its symmetry while providing enhanced robustness against non-Gaussian noise in adaptive filter design. In addition, random Fourier features are employed to flexibly and efficiently model the nonlinear component of the system. A theoretical analysis of steady-state excess mean square error is presented, and our simulation results validate the superior robustness and accuracy of the proposed method over the classical HAF and its robust variants. Full article

(This article belongs to the Section Computer)

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30 pages, 14149 KB

Open AccessArticle

Heterogeneous Group Adaptive Defense Model Based on Symmetry-Breaking and Skin Effect

by Yunzhuo Ma, Peng Yu, Meijuan Li and Xue-Bo Chen

Symmetry 2025, 17(9), 1555; https://doi.org/10.3390/sym17091555 - 17 Sep 2025

Viewed by 231

Abstract

Collective intelligence systems have demonstrated considerable potential in dynamic adversarial environments due to their distributed, self-organizing, and highly robust characteristics. The crux of an efficacious defense lies in establishing a dynamically adjustable, non-uniform defense structure through the differentiation of internal member roles. The [...] Read more.

Collective intelligence systems have demonstrated considerable potential in dynamic adversarial environments due to their distributed, self-organizing, and highly robust characteristics. The crux of an efficacious defense lies in establishing a dynamically adjustable, non-uniform defense structure through the differentiation of internal member roles. The proposed model is a heterogeneous-swarm adaptive-defense model based on symmetry breaking and skin effect. The model draws from symmetry theory, incorporating the skin effect of conductor currents and the hierarchical structural characteristics of biological groups, such as starlings. The construction of a radially symmetric dynamic hierarchical swarm structure is achieved by assigning different types of individuals with distinct safety radius preferences. Secondly, the principle of symmetry breaking is employed to establish a phase transition mechanism from radial symmetry to directed defense, thereby achieving an adaptive barrier formation algorithm. This algorithm enables the defensive group to assess threat characteristics and dynamically adjust defense resource deployment. The simulation results obtained from this study validate the phase transition process from continuous rotational symmetry to directed defense. This process demonstrates the barrier formation mechanism and ensures the safety and integrity of the core units within the group. Full article

(This article belongs to the Section Computer)

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