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Symmetry

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

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All Articles (18,267)

  • Article
  • Open Access

Takagi–Sugeno–Kang (TSK) fuzzy classifiers have achieved notable success in pattern recognition and data mining due to their combination of approximation capability and model interpretability. However, existing TSK classifiers predominantly rely on batch training, which becomes impractical in streaming environments characterized by continuous sample arrival, limited memory, and evolving data distributions. To address these challenges, this paper proposes the Online Adaptive TSK (OA-TSK) fuzzy classifier with an incremental–decremental update protocol for non-stationary data streams. First, we develop the Decremental Adaptive TSK Fuzzy Classifier (DA-TSK), whose update procedure applies the Sherman–Morrison formula to a symmetric rank-one downdate, enabling precise sample removal while maintaining exact equivalence to batch least-squares retraining. Building upon DA-TSK and our prior Dynamic Incremental Adaptive TSK Fuzzy Classifier (DIA-TSK), we then propose OA-TSK, which integrates incremental and decremental updates within a sliding-window mechanism to achieve continuous adaptation with bounded memory. The key theoretical contribution is that, in exact arithmetic, OA-TSK produces at every time step the same ridge-regularized least-squares solution as batch retraining on the active window. To further handle severe shifts in the input distribution, which can cause fixed rule centers to become poorly aligned with newly arriving samples, we propose Online Adaptive TSK with Antecedent Reclustering (OA-A-TSK), which incorporates an adaptive antecedent reclustering mechanism. Comprehensive experiments on synthetic and real-world data streams demonstrate that OA-TSK achieves classification accuracy comparable to that of ridge-regularized batch retraining while substantially reducing per-sample computational complexity. An analysis of average ranks shows that OA-TSK and OA-A-TSK rank among the top-performing methods across diverse drift scenarios while preserving the intrinsic interpretability of TSK fuzzy systems.

Symmetry

21 October 2026

Architecture of the OA-A-TSK online learning framework. The Gaussian MFs receive the input feature vector 
  
    
      
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, and dashed arrows represent the antecedent reclustering mechanism triggered by a severe imbalance among the mean normalized firing strengths of the rules.
  • Article
  • Open Access

Background and Aim: Goalkeeper performance relies on bilateral upper-limb function. In amputee football, unilateral upper-limb absence asymmetrically reduces the defendable area, creating a task-specific biomechanical constraint. This study aimed to examine goal-direction patterns relative to the goalkeeper’s missing-arm side and their associations with shot characteristics. Methods: We analyzed 474 goals from 115 matches (35 teams) in the 2021 European Championship and 2022 World Cup. Video recordings were coded by three analysts (Cohen’s Kappa = 0.94). Logistic regression with cluster-robust standard errors was applied to 431 goals, accounting for within-match tactical clustering. The outcome was shot direction toward the goalkeeper’s missing-arm side. Results: Approximately 52.9% of goals targeted the missing-arm side. Shot zone was the strongest predictor: center shots (OR = 0.39, 95% CI: 0.21–0.76, FDR-adjusted p = 0.012) and opposite-side shots (OR = 0.18, 95% CI: 0.08–0.40, FDR-adjusted p = 0.001) showed 61% and 82% reduced likelihood, respectively, compared to same-side shots. High shots were twice as likely as low shots to target the missing-arm side (OR = 2.06, 95% CI: 1.32–3.21, FDR-adjusted p = 0.009). These may be consistent with trajectory-dependent differences in the challenges faced by goalkeepers with anatomical asymmetry. Conclusions: Shot zone and height were associated with goal-direction patterns relative to the goalkeeper’s missing-arm side. Because only scored goals were analyzed, these findings do not establish greater scoring vulnerability on the missing-arm side or deliberate tactical exploitation of anatomical asymmetry.

Symmetry

21 October 2026

(A) Spatial segmentation of the playing field into nine zones. (B) Division of the goal into six zones. (C) Goalkeeper’s missing arm versus intact arm side with functional division of the goalmouth. (D) Categorization of shooting zone: same side, opposite side, and center.
  • Article
  • Open Access

The thermal runaway propagation in lithium-ion battery modules poses a serious threat to the safety of electric vehicles and energy storage systems. This study experimentally evaluated the thermal propagation suppression performance of five insulating materials: polyimide foam, nano-porous silica aerogel, ceramic fiber, pre-oxidized fiber aerogel, and mica sheet on 4 Ah ternary pouch cell modules. Thermal runaway was triggered in Cell 1 via an external short circuit (30C), and propagation behavior was characterized in terms of temperature evolution, propagation time, mass loss, and microstructural analysis. The results indicated that aerogel-based materials exhibited excellent thermal insulation performance. For the nano-porous silica aerogel, the temperature difference between its front and back surfaces reached as high as 484 °C, while the temperature rise of the adjacent cell was kept below 107 °C, thereby completely blocking propagation. The module mass loss was only 17.63 g, corresponding to a material loss rate of 0.67%. Pre-oxidized fiber aerogel also effectively suppressed propagation, albeit with a slightly higher material loss rate of 2.20%. In contrast, ceramic fiber and mica sheets only partially delayed thermal runaway propagation, as the adjacent cells still exhibited cracking and electrolyte leakage. Polyimide foam failed to prevent thermal runaway propagation, only extending the total propagation time from 424 s to 678 s (an increase of 60%) before being completely burned. Microstructural SEM analysis revealed that the aerogel materials suffered only slight fiber fracture, whereas the ceramic fiber underwent severe structural damage, the mica sheets displayed cracks and melting, and the polyimide foam was completely combusted. Taken together, these findings suggest that nano-porous silica aerogel is the preferred material for blocking thermal runaway in lithium-ion batteries, offering practical guidance for the thermal safety design of battery systems.

Symmetry

21 October 2026

Experimental test platform.
  • Article
  • Open Access

Transparent curved surfaces of glass packaging bottles produce structural responses that can obscure local appearance asymmetries associated with defects, complicating their segmentation across different scales and shapes. To address these challenges, we propose DFSR-Net, a glass bottle defect segmentation network. A Differential Context Modulation Module combines local differential responses with multiscale context to enhance weak anomalies while suppressing interference from normal bottle structures. A Key-Node Sparse Graph Propagation module uses key-node selection and restricted neighborhood aggregation to limit irrelevant cross-layer propagation and selectively transfer informative defect features. In the decoder, Dual-Receptive-Field Spatial Selection adaptively integrates local details and broader context, while Dual-Statistic Directional Calibration calibrates height- and width-wise spatial responses to improve region completeness and boundary representation. Experiments on the public Bottle Body dataset and the self-collected industrial glass bottle defect dataset show that DFSR-Net achieves mean Intersection over Union values of 81.08% and 80.14%. DFSR-Net also achieves a single-image processing speed of 74.3 FPS while maintaining high segmentation accuracy, suggesting potential for online glass bottle defect inspection.

Symmetry

21 October 2026

Overall architecture of DFSR-Net. DCMM, KSGP, DRSS, and DSDC are integrated to perform encoder feature enhancement, selective cross-layer propagation, receptive-field adaptation, and spatial response calibration, respectively.

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Symmetry - ISSN 2073-8994