Symmetry

32 pages, 21341 KB

Open AccessArticle

Steady-State Response of Nonlinear Systems with Nonlinear Dissipative Elements Using a Bond Graph Symmetry

by Gilberto Gonzalez-Avalos, Luis Arthur Cleary-Balderas, Gerardo Ayala-Jaimes, José Aarón Padilla García and Christian E. Guzman-Ceballos

Symmetry 2026, 18(10), 1678; https://doi.org/10.3390/sym18101678 - 9 Oct 2026

Abstract

The analysis of nonlinear systems has always been a challenge. The structure of the mathematical model of a nonlinear physical system often does not allow us to identify how the elements that make up the system are related. A bond graph allows its [...] Read more.

The analysis of nonlinear systems has always been a challenge. The structure of the mathematical model of a nonlinear physical system often does not allow us to identify how the elements that make up the system are related. A bond graph allows its elements to be classified into fields in such a way that the relationship between them can be determined. This paper proposes a bond graph junction structure with an integral causality assignment for a class of nonlinear systems, through which a mathematical model can be derived. The class of nonlinear systems consists of products of functions of the state variables and nonlinear dissipative elements. The steady-state response of the system can be obtained from a bond graph with an assignment of derivative causality. Depending on the causal connections between the elements, solving a nonlinear algebraic equation is required to determine the contribution of nonlinear resistive elements to the steady state of the state variables. Therefore, a bond graph exhibits symmetry between the modeled system and its mathematical model. A case study is solved using the proposed methodology, and the steady-state response results are verified through bond graph simulation with integral causality. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Systems)

35 pages, 9448 KB

Open AccessArticle

Traveling-Wave-Based High-Speed Main Protection of Low-Frequency AC Submarine Cables with Analytical-Model-Based Offline Setting

by Cong Liu, Jiangyan Guo, Yiheng Xie, Ning Tong and Nan Yang

Symmetry 2026, 18(10), 1677; https://doi.org/10.3390/sym18101677 - 9 Oct 2026

Abstract

Long-distance low-frequency alternating-current (LFAC) submarine cables exhibit pronounced high-frequency attenuation and dispersion, while background components generated by the modular multilevel matrix converter (M3C) complicate fault-wavefront extraction. This study proposes a single-ended traveling-wave primary protection scheme combining a Bergeron numerical model, variational mode decomposition [...] Read more.

Long-distance low-frequency alternating-current (LFAC) submarine cables exhibit pronounced high-frequency attenuation and dispersion, while background components generated by the modular multilevel matrix converter (M3C) complicate fault-wavefront extraction. This study proposes a single-ended traveling-wave primary protection scheme combining a Bergeron numerical model, variational mode decomposition (VMD), and the Teager energy operator (TEO). The Bergeron model is used offline to calculate theoretical wavefront counts for different fault locations and fault resistances. The most adverse offline result determines a unified fixed wavefront-count threshold for online protection. After the startup criterion is triggered, the 1-mode backward traveling wave within a 2 ms window is differentiated and normalized. VMD decomposes the signal into multiple modal components, and two informative modes are selected based on their energy contribution, wavefront characterization capability, and performance in the presence of noise to reconstruct the traveling-wave feature signal. TEO then maps the reconstructed signal into an energy sequence, where local peaks mark wavefront arrivals. An internal fault is identified when the measured wavefront count reaches the fixed threshold. Case studies conducted in PSCAD/EMTDC show that the starting criterion detects abrupt changes for single-phase grounding faults at different locations, and the proposed protection correctly distinguishes the tested internal and reverse external faults. The scheme operates correctly for all tested internal fault locations, including faults with fault resistances of up to 300 Ω, and remains secure for the tested reverse external faults. Full article

(This article belongs to the Special Issue Symmetry in Digitalisation of Distribution Power System)

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43 pages, 3578 KB

Open AccessArticle

Symmetry-Based Reformulation of the Gravity Sensitivity Matrix for Efficient Regional-Scale Gravity Imaging

by José Carlos Ortiz-Alemán, Sebastián López-Juárez, Jhonatan Fernando Eulopa-Hernández, Carlos Couder-Castañeda, Diego Alfredo Padilla-Pérez, Pablo Alejandro Arizpe-Carreon and David Saucedo-Jiménez

Symmetry 2026, 18(10), 1676; https://doi.org/10.3390/sym18101676 - 9 Oct 2026

Abstract

Regional-scale gravity imaging is limited by the size of the sensitivity matrix: a direct three-dimensional formulation of the gravity operator requires on the order of

10^{13}

coefficients, making explicit storage infeasible on standard hardware. We exploit two symmetry properties of the gravitational [...] Read more.

Regional-scale gravity imaging is limited by the size of the sensitivity matrix: a direct three-dimensional formulation of the gravity operator requires on the order of

10^{13}

coefficients, making explicit storage infeasible on standard hardware. We exploit two symmetry properties of the gravitational sensitivity kernel: translational invariance, giving the operator a Block Toeplitz with Toeplitz Blocks (BTTB) structure, and central symmetry, halving the number of unique kernel evaluations, to reformulate the Linear Back-Projection (LBP) adjoint operator as depth-wise two-dimensional convolutions. With finite-support truncation at cutoff radius

R_{\max}

, memory requirements drop from terabyte-scale dense arrays to compact per-layer kernels. We implement and benchmark two equivalent backends: an OpenMP spatial-domain stencil and an FFT convolution via BTTB circulant embedding. For a production-scale model (

701 \times 401 \times 512

cells,

R_{\max} = 150

), the stencil completed the LBP computation in 7187 s on one thread and 354 s on 32 threads (

S_{32} = 20.29

), while the FFT backend required 13.8 s; both agree to within an invariant checksum (

3.3464 \times 10^{10}

). Applied to Bouguer gravity data over the Chicxulub impact crater, northern Yucatán Peninsula, the raw LBP amplitudes were calibrated to physical density contrasts through a two-parameter rescaling solved in closed form as a box-constrained convex quadratic program and cross-validated against an independent simulated-annealing search, reducing the RMS misfit from

27.3

to

5.3

mGal (an

81 %

reduction). The resulting model shows density patterns consistent with the crater’s known structural organization. As a single-pass adjoint method, LBP does not resolve the non-uniqueness of the gravity inverse problem, and the model is interpreted for regional structure rather than for pointwise density values; the formulation extends directly to iterative regularized inversion. Full article

(This article belongs to the Section A: Computer Science)

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28 pages, 6090 KB

Open AccessArticle

The Socio-Economic Asymmetry Index (SEA): A Framework for Identifying Vulnerability–Exposure Mismatch in Flood-Prone Agricultural Landscapes

by Patiwat Littidej, Jiradech Majandang, Benjamabhorn Pumhirunroj and Donald Slack

Symmetry 2026, 18(10), 1675; https://doi.org/10.3390/sym18101675 - 9 Oct 2026

Abstract

Flood risk studies in Southeast Asia often treat physical exposure and socio-economic vulnerability as separate issues. That approach misses something important: in many places, socio-economic factors matter more than physical exposure in deciding who gets hit hardest. This study introduces the Socio-Economic Asymmetry [...] Read more.

Flood risk studies in Southeast Asia often treat physical exposure and socio-economic vulnerability as separate issues. That approach misses something important: in many places, socio-economic factors matter more than physical exposure in deciding who gets hit hardest. This study introduces the Socio-Economic Asymmetry Index (SEA), a ratio-based tool designed to measure how much socio-economic vulnerability outweighs physical exposure. The framework was tested across 63,010 sampling points in the Upper Chi River Basin, northeastern Thailand. Six composite indices were built from satellite and land-use data: the Net Economic Loss Index (NELI), Income Loss Sensitivity Index (ILSI), Adaptation Cost Index (ACI), Community Economic Resilience Index (CERI), Maladaptive Development Risk Index (MDRI), and Composite Risk Index (CRI). Random Forest and SHAP analyses were then used to see how each component shaped flood outcomes. Results show that about 25% of the study area falls into High or Very High Asymmetry, with SEA values above 0.478. ACI had the strongest positive correlation with SEA (r = 0.808), followed by NELI (r = 0.788) and flood frequency (r = 0.786), while CERI showed a strong negative correlation (r = −0.707). This suggests that community resilience does help buffer socio-economic asymmetry. Using flood frequency as an external target, an SEA greater than 0.608 emerged as the best cutoff point (AUC = 0.988, sensitivity = 0.972, specificity = 0.962). K-means clustering identified four community types: High Asymmetry (9.5%), Moderate Asymmetry (37.4%), Low Asymmetry (16.2%), and Resilient (36.8%). Each type needs its own management strategy. The SEA framework offers a practical way to direct socio-economic interventions in flood-prone areas, supporting SDGs 11, 13, and 15. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Remote Sensing and Applications)

26 pages, 13866 KB

Open AccessArticle

Interpretable Causal Structure Learning for Multivariate Air Quality Forecasting: An Integrated Evolutionary-Cognitive Approach

by Xiaoqian Liu, Jun Yang, Yingjun Zhang, Liang Fan and Qianxia Ma

Symmetry 2026, 18(10), 1674; https://doi.org/10.3390/sym18101674 - 9 Oct 2026

Abstract

Accurate Air Quality Index (AQI) forecasting is essential for public health protection and sustainable urban planning. Existing data-driven forecasting models often provide limited interpretability of pollutant interactions, while conventional Fuzzy Cognitive Map (FCM) learning algorithms may struggle to optimize causal weights effectively. To [...] Read more.

Accurate Air Quality Index (AQI) forecasting is essential for public health protection and sustainable urban planning. Existing data-driven forecasting models often provide limited interpretability of pollutant interactions, while conventional Fuzzy Cognitive Map (FCM) learning algorithms may struggle to optimize causal weights effectively. To address these limitations, this study proposes IGWO-FCM, an evolutionary-cognitive framework that integrates an Improved Grey Wolf Optimizer (IGWO) with FCMs for interpretable causal structure learning and AQI forecasting under uncertainty. The framework employs FCMs to represent pollutant interactions and feedback mechanisms, and introduces a hierarchical transformation operator and adaptive learning strategy to enhance causal weight optimization. On a real-world urban AQI dataset comprising 744 hourly records and six pollutants, as well as two public benchmarks, IGWO-FCM achieves the lowest MAE and RMSE among the compared FCM learning algorithms for five of the six pollutants, reducing these errors by up to 29.6% and 40.2%, respectively, relative to the strongest baseline. These results demonstrate the predictive performance of IGWO-FCM and its potential to provide interpretable insights into pollutant interactions for AQI forecasting. Full article

(This article belongs to the Section A: Computer Science)

20 pages, 1147 KB

Open AccessArticle

Focal and Generalized Focal Geometry Associated with Rotational Hypersurfaces in

E^{4}

by Sezgin Büyükkütük, Ilim Kişi and Günay Öztürk

Symmetry 2026, 18(10), 1673; https://doi.org/10.3390/sym18101673 - 9 Oct 2026

Abstract

This paper investigates focal and generalized focal geometry associated with rotational hypersurfaces in the four-dimensional Euclidean space

E^{4}

. Explicit parametrizations are derived for several classes of rotational hypersurfaces, including toroidal and special Monge-type structures. The corresponding focal hypersurfaces are constructed and [...] Read more.

This paper investigates focal and generalized focal geometry associated with rotational hypersurfaces in the four-dimensional Euclidean space

E^{4}

. Explicit parametrizations are derived for several classes of rotational hypersurfaces, including toroidal and special Monge-type structures. The corresponding focal hypersurfaces are constructed and their geometric properties are analyzed through the computation of shape operators, Gaussian curvature, and mean curvature. Conditions for degeneracy, flatness, and minimality are determined. In addition, generalized focal hypersurfaces defined via principal curvature-dependent offsets are introduced and examined. The results provide explicit geometric descriptions and curvature characterizations that extend classical focal constructions from

E^{3}

to higher-dimensional hypersurface geometry, while highlighting the role of rotational symmetry in the structure and degeneracy of focal hypersurfaces. Full article

(This article belongs to the Section B: Mathematics)

24 pages, 4032 KB

Open AccessArticle

Grid-Forming Static Power Generator with Coordinated Control of Two-Stage Converters

by Xiaoming Luan, Guangyao Qiao, Yixuan Wang, Zhiyong Yu, Yundan Cheng, Yifeng Lin, Qi Chen, Yunfei Xu and Xianzhe Bao

Symmetry 2026, 18(10), 1672; https://doi.org/10.3390/sym18101672 - 9 Oct 2026

Abstract

Grid-forming (GFM) control is an important technical solution for addressing the declining voltage-support capability and inertia level of modern power systems. By integrating a high-voltage directly connected grid-side converter with supercapacitors, the grid-forming static power generator (GFM-SPG) can provide active- and reactive-power support [...] Read more.

Grid-forming (GFM) control is an important technical solution for addressing the declining voltage-support capability and inertia level of modern power systems. By integrating a high-voltage directly connected grid-side converter with supercapacitors, the grid-forming static power generator (GFM-SPG) can provide active- and reactive-power support to high-voltage power grids. This paper investigates a GFM-SPG with a two-stage converter topology and proposes a coordinated control strategy for the two-stage converters. The transient response characteristics of the GFM-SPG are classified into three operating regions, and the effects of key control parameters are analyzed to establish basic parameter design guidelines. To simultaneously enhance grid inertial support and transient voltage-support capability, a variable inertia time-constant control strategy is further proposed. Under normal operating conditions, a relatively large inertia time constant is adopted to provide inertial support, whereas a small inertia time constant is employed during voltage ride-through to enable rapid phase synchronization and prioritize reactive-power support. The proposed control strategy is validated through electromagnetic transient simulations and hardware-in-the-loop (HIL) experiments. The results demonstrate that the two-stage GFM-SPG can achieve stable DC-bus voltage regulation and provide effective inertia and transient voltage support under different grid operating conditions. Full article

(This article belongs to the Special Issue Structural Evolution and Key Supporting Technologies of Power Systems with an Ultra-High Proportion of Renewable Energy Integration)

38 pages, 3729 KB

Open AccessArticle

Progressive Asymmetry Damage Behavior and Macro–Micro-Scale Coupled Constitutive Modeling of Sandstone with Intersecting Fractures Under Freeze–Thaw Cycles and Loading

by Yanhai Zhao and Yanyu Wang

Symmetry 2026, 18(10), 1671; https://doi.org/10.3390/sym18101671 - 9 Oct 2026

Abstract

To investigate the progressive asymmetry damage characteristics of intersecting fracture rock under the coupled effect of freeze–thaw cycles and loading, nuclear magnetic resonance tests were conducted on intact, single fracture, and intersecting fracture sandstone under freeze–thaw cycles. Uniaxial and triaxial compression tests were [...] Read more.

To investigate the progressive asymmetry damage characteristics of intersecting fracture rock under the coupled effect of freeze–thaw cycles and loading, nuclear magnetic resonance tests were conducted on intact, single fracture, and intersecting fracture sandstone under freeze–thaw cycles. Uniaxial and triaxial compression tests were conducted to investigate the mechanical behavior and failure characteristics of fractured rock, while the effects of freeze–thaw cycles on pore structure evolution, microscopic damage, and mechanical degradation were further evaluated. The results showed that the intersecting fracture rock was more sensitive to microscopic damage caused by freeze–thaw cycles. As external loading was applied, the initiation stress and peak stress of the intersecting fracture rock were the lowest of the three rock types, and the failure mode changed from shear failure to tensile failure. Based on damage localization theory and fracture mechanics, the expansion of macro-fissures in the rock were found to be equivalent to the growth process of crack clusters at the tip, and a progressive damage constitutive model considering the coupled effect of freeze–thaw cycles and loading was developed. This model was able to reproduce the main characteristics of the mechanical response and damage evolution of intersecting fracture rock. It provides a potential reference for understanding the mechanical behavior engineering rock in cold regions. Full article

(This article belongs to the Section F: Engineering and Materials)

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1 pages, 128 KB

Open AccessRetraction

RETRACTED: Zhu et al. Research on Fouling Shellfish on Marine Aquaculture Cages Detection Technology Based on an Improved Symmetric Faster R-CNN Detection Algorithm. Symmetry 2025, 17, 2107

by Pengshuai Zhu, Hao Li, Junhua Chen and Chengjun Guo

Symmetry 2026, 18(10), 1670; https://doi.org/10.3390/sym18101670 - 9 Oct 2026

Abstract

The journal retracts the article titled “Research on Fouling Shellfish on Marine Aquaculture Cages Detection Technology Based on an Improved Symmetric Faster R-CNN Detection Algorithm” [...] Full article

30 pages, 2626 KB

Open AccessArticle

A GRU-Augmented Kalman Filter for State Estimation in Systems with Colored Noise

by Haihua Xie

Symmetry 2026, 18(10), 1669; https://doi.org/10.3390/sym18101669 - 8 Oct 2026

Abstract

Although the Kalman filter is optimal for linear Gaussian systems, its performance degrades in practical scenarios when noise is colored rather than white. Additionally, the Kalman filter requires substantial domain knowledge to derive parametric forms. To overcome these limitations, this paper proposes a [...] Read more.

Although the Kalman filter is optimal for linear Gaussian systems, its performance degrades in practical scenarios when noise is colored rather than white. Additionally, the Kalman filter requires substantial domain knowledge to derive parametric forms. To overcome these limitations, this paper proposes a data-driven filtering method that operates in the presence of colored noise and with partial information without requiring exact prior knowledge. We propose CKFNet, a novel real-time filtering framework that integrates a linear state-space model under colored noise with a gated recurrent unit. The network replaces the traditional Kalman gain computation, enabling the model to implicitly learn noise statistics from data and adapt to colored noise dynamics. Experiments across various colored noise conditions and model mismatch scenarios show that CKFNet outperforms baseline methods in most tested scenarios, and remains robust where model-based filters degrade. The results indicate that CKFNet effectively combines the interpretability and efficiency of state-space models with the adaptive learning capability of neural networks, offering a reliable filtering solution under realistic noise assumptions. Full article

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14 pages, 1100 KB

Open AccessArticle

Fractional Integral Contractions in Symmetric S-Metric Spaces with Lucas Polynomial Spectral Collocation

by Mohamed Gamal, Maryam A. Alghamdi and Youssri Hassan Youssri

Symmetry 2026, 18(10), 1668; https://doi.org/10.3390/sym18101668 - 8 Oct 2026

Abstract

This study introduces a novel class of fractional integral contractions within the framework of symmetric S-metric spaces. By embedding a Riemann–Liouville fractional integral (

RLFI

) operator into an integral-type contractive condition, we offer a versatile extension of classical fixed point principles. [...] Read more.

This study introduces a novel class of fractional integral contractions within the framework of symmetric S-metric spaces. By embedding a Riemann–Liouville fractional integral (

RLFI

) operator into an integral-type contractive condition, we offer a versatile extension of classical fixed point principles. Assuming suitable properties for the associated locally bounded and locally integrable function, we prove the existence and uniqueness of a fixed point for self-mappings on symmetric complete S-metric spaces, demonstrating that the corresponding Picard iterative sequence converges to this unique point. Notably, setting the fractional order to unity recovers the classical integral-type contractive condition. To showcase the practical utility of this theoretical framework, we develop a numerical spectral collocation method for solving related fractional differential equations. Utilizing Lucas polynomials as basis functions alongside Riemann equidistant collocation nodes, we transform continuous equations into discrete algebraic systems. The established fixed point theorems provide the analytical foundation for the convergence of the iterative algorithms used to solve these nonlinear systems. We present a comprehensive algorithm, derive rigorous error bounds, and provide numerical examples with tabular and graphical illustrations that confirm the spectral accuracy and exponential convergence rates of the proposed methodology. Full article

(This article belongs to the Special Issue Functional Analysis and Fixed Points)

11 pages, 242 KB

Open AccessArticle

On Gaussian Family of Generalized Fibonacci Polynomials

by Canan Çakıcı, Neşe Ömür and Sibel Koparal

Symmetry 2026, 18(10), 1667; https://doi.org/10.3390/sym18101667 - 7 Oct 2026

Abstract

In this paper, we define Gaussian generalized Fibonacci polynomials as a new member of the family of Gaussian polynomials. We examine in detail the fundamental algebraic and structural properties of these polynomials, which are defined using matrix properties, and present the Binet-type formula [...] Read more.

In this paper, we define Gaussian generalized Fibonacci polynomials as a new member of the family of Gaussian polynomials. We examine in detail the fundamental algebraic and structural properties of these polynomials, which are defined using matrix properties, and present the Binet-type formula and recurrence relations. Furthermore, we give some identities involving these polynomials. Finally, we derive generating and exponential generating functions of these polynomials. Full article

(This article belongs to the Special Issue Symmetries in Algebraic Combinatorics and Their Applications)

21 pages, 1144 KB

Open AccessArticle

Dynamic Topology-Preserving Multi-Label Class-Incremental Learning

by Weiwei Shi and Yilin Xu

Symmetry 2026, 18(10), 1666; https://doi.org/10.3390/sym18101666 - 7 Oct 2026

Abstract

To address the insufficient stability of the feature space in class-incremental learning, this paper proposes a Dynamic Topology-Preserving Multi-Label Class-Incremental Learning (DTP-MLCIL) method. Specifically, a Neural Gas (NG) network is introduced to construct and maintain an adaptive topological skeleton of the feature space [...] Read more.

To address the insufficient stability of the feature space in class-incremental learning, this paper proposes a Dynamic Topology-Preserving Multi-Label Class-Incremental Learning (DTP-MLCIL) method. Specifically, a Neural Gas (NG) network is introduced to construct and maintain an adaptive topological skeleton of the feature space through the Competitive Hebbian Learning (CHL) algorithm, thereby approximating and tracking the underlying feature distribution at the manifold geometry level. Based on this topological representation, an anti-forgetting node loss is designed to constrain the consistency between current features and the historical topology from both node-position and topological-connectivity perspectives, thereby reinforcing regions that encode previously acquired knowledge. Furthermore, a max-min loss is introduced to proactively organize the feature space of newly emerging classes, encouraging new class representations to remain well separated from historical regions while forming compact intra-class clusters. By explicitly preserving the geometric stability of the feature space, the proposed method effectively alleviates structural drift and topological distortion during the incremental learning process. Comprehensive experimental evaluations demonstrate the effectiveness of the proposed method. Full article

(This article belongs to the Section A: Computer Science)

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21 pages, 516 KB

Open AccessArticle

On the Convergence of ILC for Hilfer Fractional-Order Systems with Initial State Errors

by Sabu Sunmitha, Devaraj Vivek and Abdulah A. Alghamdi

Symmetry 2026, 18(10), 1665; https://doi.org/10.3390/sym18101665 - 7 Oct 2026

Abstract

This paper addresses tracking control for nonlinear Hilfer fractional-order systems (HFOS) with initial state errors. To enhance tracking performance over repeated operations, a closed-loop

D^{α, β}

-type and first-order

{PD}^{α, β}

-type iterative learning control strategy is proposed. By [...] Read more.

This paper addresses tracking control for nonlinear Hilfer fractional-order systems (HFOS) with initial state errors. To enhance tracking performance over repeated operations, a closed-loop

D^{α, β}

-type and first-order

{PD}^{α, β}

-type iterative learning control strategy is proposed. By employing the

(1 - γ, λ)

-norm in conjunction with Hölder’s inequality and Young’s inequality, sufficient conditions are derived to guarantee the convergence of the proposed learning algorithm. It is shown that, under the derived convergence conditions, the tracking error converges to zero as the iteration number increases. Finally, numerical examples are presented to validate the theoretical results and demonstrate the convergence and tracking performance of the proposed control schemes. Full article

(This article belongs to the Section B: Mathematics)

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18 pages, 11803 KB

Open AccessArticle

PR-YOLOv8s: A Lightweight Improved YOLOv8s for Printed Circuit Board Micro-Defect Detection

by Miao Wang, Wanyi Zhang, Tengteng Wang and Qian Du

Symmetry 2026, 18(10), 1664; https://doi.org/10.3390/sym18101664 - 7 Oct 2026

Abstract

Printed Circuit Boards (PCBs) are core components in electronics manufacturing. Six types of micro-defects, such as missing holes, mouse-bites and open circuits, may easily cause complete device failure. The original YOLOv8 employs only the P3/P4/P5 multi-scale detection heads, leading to severe loss of [...] Read more.

Printed Circuit Boards (PCBs) are core components in electronics manufacturing. Six types of micro-defects, such as missing holes, mouse-bites and open circuits, may easily cause complete device failure. The original YOLOv8 employs only the P3/P4/P5 multi-scale detection heads, leading to severe loss of shallow fine-grained features of PCB micro-defects. Although the vanilla P2 shallow detection head supplements fine-grained features, background noise from PCB silkscreen and copper cladding triggers oscillating upward drift of validation-set DFL and weakens model generalization. To tackle this problem, this study proposes PR-YOLOv8s for general PCB micro-defect detection. Taking the self-optimized P2 detection head as the core innovation, we reconstruct the shallow detection branch by optimizing network structure and training strategy. Shared convolution reduces redundant parameters. Depthwise separable convolution cuts inference cost in regression branches. Label smoothing is utilized for loss regularization to suppress training oscillation of the original P2 head. Furthermore, CBAM attention and RepDepthconv re-parameterized separable convolution are integrated to build RD-CBAM, a unified feature enhancement module. It suppresses background interference, enhances defect representation and reduces computational overhead to balance accuracy, stability and lightweight performance. Ablation and comparative experiments are implemented under unified hyperparameters, with performance evaluated via loss curves, quantitative metrics and normalized confusion matrices. Results verify that the optimized P2 head dominates performance gain and fully eliminates the upward drift of DFL. The proposed model achieves 98.45% precision, 98.87% recall, 99.30% mAP50 and 81.04% mAP50-95. Its mAP50-95 rises by about 19 percentage points over baseline YOLOv8s, outperforming recent real-time detectors including YOLOv9-s, YOLOv10-s, RT-DETR-R18, and YOLO-NAS-S. With high precision and real-time inference, PR-YOLOv8s is applicable to industrial PCB inspection and pre-competition defect screening for college electronics competitions, possessing practical value for both industrial deployment and higher-education practice. Although the added P2 head and attention module introduce a moderate computational overhead (GFLOPs increase by approximately 10% and parameters by less than 1% over the baseline YOLOv8s), the accuracy gain is substantial and far outweighs this cost. Full article

(This article belongs to the Section A: Computer Science)

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69 pages, 2687 KB

Open AccessReview

Photovoltaic Cooling Technologies: Current Developments, Technical Barriers, and Future Perspectives

by Ihsan Okta Harmailil, Sakhr M. Sultan, Masita Mohammad, Ahmad Fazlizan, Ahmad Fudholi and Tso Chih Ping

Symmetry 2026, 18(10), 1663; https://doi.org/10.3390/sym18101663 - 5 Oct 2026

Abstract

Solar energy has become one of the most promising renewable energy sources owing to its wide availability and relatively low initial cost for energy conversion. Among the various technologies, photovoltaic (PV) systems represent one of the most effective approaches for harnessing solar energy [...] Read more.

Solar energy has become one of the most promising renewable energy sources owing to its wide availability and relatively low initial cost for energy conversion. Among the various technologies, photovoltaic (PV) systems represent one of the most effective approaches for harnessing solar energy through the photovoltaic effect. Nevertheless, a key limitation affecting the large-scale deployment of PV systems is their sensitivity to operating temperature. Heat accumulation can reduce electrical performance, accelerate degradation, and create spatial temperature non-uniformity across the module surface. In this context, thermal symmetry refers to a balanced and spatially uniform temperature distribution across comparable regions of a PV module; improved thermal symmetry can reduce local hot spots and thermal gradients that adversely affect reliability. Existing literature on PV cooling places insufficient emphasis on the standardization of critical parameters required to evaluate and compare different cooling techniques under consistent operating conditions. Therefore, this study reviews recent advancements in passive, active, and hybrid PV cooling and proposes a common comparison framework covering temperature reduction, electrical performance, auxiliary energy consumption, net energy benefit, economic considerations, environmental requirements, climate suitability, maintenance, scalability, and technology maturity. Particular attention is given to the distinction between gross performance improvement and net benefit in active cooling systems, for which pumps and fans may consume part of the additional generated energy. The analysis indicates that PV cooling technologies still face critical challenges, including high costs, maintenance demands, incomplete reporting of parasitic energy use, and reduced or variable performance under extreme environmental conditions. The review concludes with recommendations for standardized testing, climate-adaptive design, improved thermal uniformity, and transparent reporting of net system performance. Full article

(This article belongs to the Section F: Engineering and Materials)

15 pages, 3838 KB

Open AccessArticle

A Sylvester-Type Matrix Equation over the Dual Quaternion Algebra and Its Application

by Chen Li and Qing-Wen Wang

Symmetry 2026, 18(10), 1662; https://doi.org/10.3390/sym18101662 - 5 Oct 2026

Abstract

The Sylvester-type equation has applications in many fields, such as control theory, scientific computing, and signal processing. However, research on the Sylvester-type equation over dual quaternions remains limited. In this paper, using generalized inverses and matrix rank, we provide necessary and sufficient conditions [...] Read more.

The Sylvester-type equation has applications in many fields, such as control theory, scientific computing, and signal processing. However, research on the Sylvester-type equation over dual quaternions remains limited. In this paper, using generalized inverses and matrix rank, we provide necessary and sufficient conditions for the solvability of the dual quaternion matrix equation

A X + B Y C + Z D = E

. When the solvability conditions are satisfied, the general expression of the solution is derived. Subsequently, a numerical example is presented to verify the obtained results. Finally, based on these results, an application in color image encryption and decryption is provided. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2026)

25 pages, 1294 KB

Open AccessArticle

Optimizing Domain-Specific RAG Architectures for Low-Resource Languages: An Ablation Study for Institutional Knowledge Assistants in Turkish Higher Education

by Samet Diri, Ayhan Gültekin, Kerem Kartal, Hamdi Yılmaz and Ömer Faruk Gerzeli

Symmetry 2026, 18(10), 1661; https://doi.org/10.3390/sym18101661 - 4 Oct 2026

Abstract

In higher education, hallucination-free information retrieval is critical for navigating complex institutional legislation. This study develops a highly accurate, production-ready Retrieval-Augmented Generation (RAG) architecture tailored to Turkish, a morphologically rich, low-resource language. We evaluate the pipeline using an expert-curated dataset of 846 canonical [...] Read more.

In higher education, hallucination-free information retrieval is critical for navigating complex institutional legislation. This study develops a highly accurate, production-ready Retrieval-Augmented Generation (RAG) architecture tailored to Turkish, a morphologically rich, low-resource language. We evaluate the pipeline using an expert-curated dataset of 846 canonical question–answer pairs derived from real-world student inquiries. Rigorous statistical testing reveals that while top embedding models achieve comparable, statistically indistinguishable retrieval accuracy, BAAI/bge-m3 demonstrates robust representational symmetry by maintaining identical document rankings across normalized distance metrics. Challenging common literature assumptions, our architectural ablation shows that dense retrieval alone is highly sufficient; hybrid (dense + sparse) fusion yields no meaningful accuracy gain when indices are constructed over equivalent text. At the generation layer, an efficiently sized 9-billion-parameter model matches or surpasses the response quality of much larger models—a ranking confirmed via repeated-run significance testing—while operating 3.9 times faster than a 32-billion-parameter counterpart and 2.5 times faster than an 8-billion-parameter alternative. Finally, we demonstrate that the latency benefits of INT8 Scalar Quantization are highly scale-dependent, accelerating retrieval in small-scale micro-benchmarks but increasing end-to-end latency at larger index scales. Ultimately, this study establishes that optimizing a production RAG system relies on selecting highly aligned, efficient components rather than maximizing architectural complexity or parameter count. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Natural Language Processing)

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18 pages, 1010 KB

Open AccessArticle

Cellular Automaton Model and Simulation of Throat Area in Railway Passenger Station Based on Lagrange Coordinate System

by Hui Xie, Yongsheng Qian, Junwei Zeng and Yang Cui

Symmetry 2026, 18(10), 1660; https://doi.org/10.3390/sym18101660 - 3 Oct 2026

Abstract

With the rapid development of high-speed rail and passenger-dedicated lines, the load in the throat area of railway passenger stations is increasing. Asymmetric characteristics, including turnout resource competition and dynamic assignment of arrival–departure tracks, are notably pronounced in the throat area; nevertheless, there [...] Read more.

With the rapid development of high-speed rail and passenger-dedicated lines, the load in the throat area of railway passenger stations is increasing. Asymmetric characteristics, including turnout resource competition and dynamic assignment of arrival–departure tracks, are notably pronounced in the throat area; nevertheless, there is a lack of adequate research addressing these issues. This paper took the Lagrange coordinate system as the foundation and adopted the multi-dimensional cellular automaton and classical NaSch model. Treating trains as a one-dimensional continuous medium, we proposed a cellular automaton model for train operations in the throat area of a railway passenger terminal. The improved cellular automaton inherited the core vehicle update rules of the NaSch model, and its stochastic rules were adapted and simplified to match the practical operating features of railway station throat areas. Considering stop time, departure interval, and mixed-traffic ratio as three influencing factors, the simulation analyzed the average delay time of three speed types of trains in the throat area and the respective impacts of these factors on the throat area through capacity. The results showed that this model can depict the running status of the train in the throat area realistically and can provide a theoretical basis for subsequent research and analysis. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Intelligent Transportation)

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