Due to scheduled maintenance work on our servers, there may be short service disruptions on this website between 11:00 and 12:00 CEST on March 28th.
Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (295)

Search Parameters:
Keywords = symmetric difference localization

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
16 pages, 796 KB  
Article
The Effects of Selected Mechanical and Anthropometric Variables on Change-of-Direction Ability in National Team-Level Youth Basketball Players
by Áron Mészáros, Bence Kopper, Annamária Zsákai, József Horváth, Lukasz Trzaskoma and Tamás Szabó
Sports 2026, 14(4), 129; https://doi.org/10.3390/sports14040129 (registering DOI) - 25 Mar 2026
Abstract
Change-of-direction (COD) ability is a key determinant of performance in youth basketball, yet the relative contribution of braking, re-acceleration, trunk motion, and body composition remains unclear. Thirty-two male U18 national-team level players (17.6 ± 0.7 y; 194.8 ± 4.5 cm; 89.1 ± 9.4 [...] Read more.
Change-of-direction (COD) ability is a key determinant of performance in youth basketball, yet the relative contribution of braking, re-acceleration, trunk motion, and body composition remains unclear. Thirty-two male U18 national-team level players (17.6 ± 0.7 y; 194.8 ± 4.5 cm; 89.1 ± 9.4 kg) completed whole-body and segmental DEXA assessment, bilateral countermovement jump (CMJ) testing and a 505 agility test (505) instrumented with a local positioning system. Mean COD times were 2.36 ± 0.09 s (505) and 1.84 ± 0.08 s (303), with maximal deceleration (DcMax) of −7.26 ± 0.52 m·s−2. Paired t-tests showed no significant differences between right- and left-leg turns for any variable (all p > 0.25), indicating symmetrical COD performance. General linear models revealed that DcMax was the only consistent predictor of COD time (505: R2 = 0.53, F (7,24) = 3.91, p = 0.006, partial η2 = 0.31; 303: R2 = 0.49, F(9,22) = 2.34, p = 0.050, partial η2 = 0.34), with a smaller additional effect of approach speed for the 303 segment (p = 0.049). Body-composition indices and CMJ variables showed only weak, non-significant correlations with COD time (|r| < 0.30, p > 0.05), and neither centripetal force nor trunk angular speed was associated with performance. These findings indicate that high-intensity braking capacity, rather than muscle mass or jump power per se, is the primary mechanical determinant of COD in elite youth basketball, suggesting that deceleration-focused training should be prioritized in performance development. Full article
Show Figures

Figure 1

31 pages, 2615 KB  
Article
Zeroth-Order Riemannian Adaptive Regularized Proximal Quasi-Newton Optimization Method
by Yinpu Ma, Cunlin Li, Zhichao Wang and Qian Li
Axioms 2026, 15(3), 203; https://doi.org/10.3390/axioms15030203 - 10 Mar 2026
Viewed by 292
Abstract
Recently, the adaptive regularized proximal quasi-Newton (ARPQN) method has demonstrated a strong performance in solving composite optimization problems over the Stiefel manifold. However, its reliance on first-order information limits its applicability to scenarios where gradient and Hessian evaluations are unavailable or costly. In [...] Read more.
Recently, the adaptive regularized proximal quasi-Newton (ARPQN) method has demonstrated a strong performance in solving composite optimization problems over the Stiefel manifold. However, its reliance on first-order information limits its applicability to scenarios where gradient and Hessian evaluations are unavailable or costly. In this paper, we propose a zeroth-order adaptive regularized proximal quasi-Newton method (ZO-ARPQN) for black-box composite optimization over Riemannian manifolds, particularly the Stiefel and symmetric positive definite (SPD) manifolds. The proposed method estimates the Riemannian gradient and curvature information through randomized one-point finite-difference approximations and adaptively updates a regularized quasi-Newton matrix to capture the local manifold geometry. Theoretically, we established global convergence and complex analyses under mild assumptions. More importantly, by incorporating curvature-aware regularization and random perturbations in the proximal quasi-Newton framework, we proved that ZO-ARPQN can escape strict saddle points with a high probability. This guarantees convergence to a stationary point, even in the absence of explicit gradients. Extensive numerical experiments were conducted on manifold-constrained problems, including sparse PCA and robot stiffness tuning. These demonstrated that ZO-ARPQN shows a competitive convergence behavior compared with other state-of-the-art Riemannian optimization methods, while requiring only function evaluations. Full article
(This article belongs to the Section Geometry and Topology)
Show Figures

Figure 1

20 pages, 21647 KB  
Article
Spatial Orthogonal and Boundary-Aware Network for Rotated and Elongated-Target Detection
by Yong Liu, Zhengbiao Jing, Yinghong Chang and Donglin Jing
Algorithms 2026, 19(3), 206; https://doi.org/10.3390/a19030206 - 9 Mar 2026
Viewed by 165
Abstract
In recent years, the refinement of bounding box representations has emerged as a major research focus in remote sensing. Nevertheless, mainstream detection algorithms typically ignore the disruptive impacts induced by the diverse morphologies and arbitrary orientations of high-aspect-ratio aerial objects throughout model training, [...] Read more.
In recent years, the refinement of bounding box representations has emerged as a major research focus in remote sensing. Nevertheless, mainstream detection algorithms typically ignore the disruptive impacts induced by the diverse morphologies and arbitrary orientations of high-aspect-ratio aerial objects throughout model training, thereby giving rise to several critical technical challenges: (1) Anisotropic information distribution: Target features are highly concentrated in one spatial dimension but sparse in the other, with significant feature differences across bounding box parameters, breaking the symmetry of feature distribution. (2) Missing high-quality positive samples: IoU-based assignment strategies fail to adequately capture the symmetric structural characteristics of elongated targets, resulting in incomplete coverage of critical features. (3) Loss function gradient instability: Small deviations in large-aspect-ratio bounding boxes cause drastic loss value fluctuations, as the asymmetric gradient changes hinder stable optimization directions during training. To address the challenges, we propose a Spatial Orthogonal and Boundary-Aware Network (SOBA-Net) for rotated and elongated target detection, leveraging symmetry-aware designs to enhance feature representation. Specifically, spatial staggered convolutions are constructed to fuse local and directional contextual features, effectively modeling long-range symmetric information across multiple spatial scales and reducing background noise interference. Secondly, the designed Symmetric-Constrained Label Assignment (SC-LA) introduces an IoU-weighted function, ensuring high-quality samples with symmetric structural features are classified as positive samples. Ultimately, the designed Gradient Dynamic Equilibrium Loss Function mitigates the problem of unstable gradients associated with high-aspect-ratio objects by enforcing symmetrical gradient regulation across samples with negligible localization deviations. Comprehensive evaluations across three representative remote sensing benchmarks—DOTA, UCAS-AOD, and HRSC2016—sufficiently corroborate the superiority of symmetry-aware enhancement schemes, which boast straightforward implementation and efficient inference deployment. Full article
(This article belongs to the Special Issue Advances in Deep Learning-Based Data Analysis)
Show Figures

Figure 1

29 pages, 4566 KB  
Article
Post-Experimental Analysis of the Light-Harvesting Protein–Pigment Complex Present in Green Sulfur Bacteria: An Approach in Quantum Biology
by Francisco Delgado and Estela Delgado-Ceballos
Symmetry 2026, 18(2), 373; https://doi.org/10.3390/sym18020373 - 17 Feb 2026
Viewed by 366
Abstract
Quantum biology is a multidiscipline which analyses possible critical aspects of life that could be based on the macroscopic expression of quantum phenomena. The high efficiency of light energy harvesting in green sulfur bacteria during photosynthesis is associated with entanglement and tunneling effects [...] Read more.
Quantum biology is a multidiscipline which analyses possible critical aspects of life that could be based on the macroscopic expression of quantum phenomena. The high efficiency of light energy harvesting in green sulfur bacteria during photosynthesis is associated with entanglement and tunneling effects in the Fenna–Mathew–Olson complex. This has been studied to assess itscontribution, when conducting the light energy captured by the chlorosome, to the reaction center, where it is transformed into chemical energy. This work analyses, in the quantum domain, the coherence and entanglement between those two components associated with a general non-localized absorption spectrum in the pigments serving as input antennas. This study first imposes a more symmetric structure on the absorption spectrum, revealing certain relations which, when it is partially broken and parametrized on the most feasible pigments, displays a characteristic spectrum associated with the nature of the bacteria studied, in terms of their habitat and evolutionary survival. Finally, a brief insight analysis of similarities and differences in the protein sequence of the complex is conducted to trace possible traits relating them to some of the previous quantum features and suggesting some responsible positions within the FMO protein sequence. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Models)
Show Figures

Graphical abstract

29 pages, 5633 KB  
Article
Study on Spatial Effects of Non-Symmetric Cable-Stayed Bridges Under Operational Loads
by Xiaogang Li, Qin Wang, Peng Ding, Minglin Zhou, Xiaohu Chen and Shanxing Xiang
Buildings 2026, 16(4), 821; https://doi.org/10.3390/buildings16040821 - 17 Feb 2026
Viewed by 291
Abstract
Addressing the issues of the complex mechanical responses and significant spatial effects of asymmetric large-span cable-stayed steel box girder bridges with shared public-rail traffic under operational loads (live load, static wind, and structural temperature differences), this paper uses the Lijiatuo Yangtze River Double-Line [...] Read more.
Addressing the issues of the complex mechanical responses and significant spatial effects of asymmetric large-span cable-stayed steel box girder bridges with shared public-rail traffic under operational loads (live load, static wind, and structural temperature differences), this paper uses the Lijiatuo Yangtze River Double-Line Bridge on Chongqing Metro Line 18 as the engineering background to construct multi-scale finite element models for the entire bridge and the closure segment, and validates them against GNSS displacement and strain monitoring data from the actual bridge. The study shows that the spatiotemporal asymmetry of operational live loads induces significant lateral bias effects in the main bridge, resulting in reverse displacements in the mid-span section, and with stress distributions characterized by “oscillation in the side spans and concentration in the mid-span.” The study also shows that, under static wind loads, the bridge’s lateral displacement approximately increases linearly with wind speed, and the mid-span response is higher than that of the side spans, showing significant spatial sensitivity to wind loads. Finally, the study shows that, although the system temperature difference causes small overall displacements, it still induces symmetrical lateral deformations and local stress concentrations near the closure segment. Local refined analyses further reveal the displacement distribution mechanism of the closure segment under operational loads. The health monitoring data agree well with the simulation results, validating the reliability of the numerical model. The research systematically reveals the spatial mechanical behavior of such bridges under operational loads, providing theoretical basis and engineering references for the design optimization and safety monitoring of similar asymmetric cable-stayed bridges. Full article
(This article belongs to the Section Building Structures)
Show Figures

Figure 1

27 pages, 36275 KB  
Article
Symmetry-Guided AB-Dynamic Feature Refinement Network for Weakly Supervised Shadow Removal
by Yiming Shao, Zhijia Zhang and Minmin Yang
Symmetry 2026, 18(2), 330; https://doi.org/10.3390/sym18020330 - 11 Feb 2026
Viewed by 259
Abstract
Shadow removal aims to restore photometric, chromatic, and structural consistency between shadowed and non-shadowed image regions. Although weakly supervised shadow removal methods reduce the reliance on densely paired training data, they still struggle to fully exploit appearance priors from non-shadow regions. As a [...] Read more.
Shadow removal aims to restore photometric, chromatic, and structural consistency between shadowed and non-shadowed image regions. Although weakly supervised shadow removal methods reduce the reliance on densely paired training data, they still struggle to fully exploit appearance priors from non-shadow regions. As a result, their shadow removal outputs often appear unnatural, exhibiting color shifts and loss of fine texture details. To address this issue, we propose an ab-dynamic feature refinement network (AB-DFRNet) for weakly supervised shadow removal that more effectively exploits structural and chromatic symmetry during training. A high-frequency information enhancement (HFIE) module is introduced into the shadow generation subnet to extract and enhance high-frequency components via frequency separation and dense convolutions, thereby facilitating the learning of fine structural symmetry and enriching pseudo-shadow details. In the removal subnet, a dual-attention adaptive fusion (DAAF) module combines global and local attention mechanisms to adaptively recalibrate channel-wise and spatial features, improving multi-scale feature integration. Furthermore, a chrominance-only consistency (COC) loss is designed to minimize differences between the a and b channels of restored regions and their non-shadow references in the Lab color space. This additional color refinement constraint encourages a symmetric distribution of chromatic information and helps the refinement network produce more natural shadow-removed results. Extensive experiments are conducted on three benchmark datasets: ISTD, SRD, and Video Shadow Removal. The results confirm the effectiveness of AB-DFRNet, demonstrating competitive quantitative performance and noticeably better visual quality compared with existing weakly supervised shadow removal methods. Full article
(This article belongs to the Section Computer)
Show Figures

Figure 1

35 pages, 2418 KB  
Article
A Theoretical Proposal to Localize and Determine the Amount of Methane, Ammonia and Carbon Dioxide in Nano-Cages of Water Clathrate Through the Space Infrared Spectroscopic Observations
by Azzedine Lakhlifi, Pierre R. Dahoo and Mustapha Meftah
Methane 2026, 5(1), 9; https://doi.org/10.3390/methane5010009 - 5 Feb 2026
Viewed by 330
Abstract
This paper investigates the different relaxation channels of a single symmetric top NH3 and a spherical top CH4 molecule trapped at low temperature in a clathrate hydrate nano-cage in the infrared absorption domain of their vibrational degrees of freedom. The approach [...] Read more.
This paper investigates the different relaxation channels of a single symmetric top NH3 and a spherical top CH4 molecule trapped at low temperature in a clathrate hydrate nano-cage in the infrared absorption domain of their vibrational degrees of freedom. The approach utilizes the Born–Oppenheimer approximation and the extended site inclusion model applied to CO2 in a previous work, which was based on pairwise atom–atom effective interaction potentials. The calculations show that trapping the methane or ammonia molecule is energetically more favorable in a type sI clathrate structure than in an sII one, and entropic considerations show that methane can be released much more easily than ammonia from clathrate hydrate nano-cages. In the small (s) and large (l) nano-cages with the sI structure, the CH4 molecule exhibits a more or less perturbed rotational motion, while the NH3 molecule shows a strongly hindered orientational motion that tends to a three-dimension librational motion (oscillation motion) around its orientational equilibrium configuration. The calculated orientational energy level schemes are quite different from those of the molecular free rotation. In the static field inside the cage, degenerate ν3 and ν4 vibrational modes of methane and ammonia molecules are shifted and split. Moreover, for ammonia molecules, the ν1 and ν2 modes are shifted, and the inversion motion is no longer allowed. The non-radiative and radiative relaxation channels of CH4, NH3 and CO2 in clathrate nano-cages are discussed with reference to the matrix isolation spectroscopic results. Upon laser excitation, then, from the energy levels calculated for the different degrees of freedom, NH3 and CO2 are expected to fluoresce, while for CH4, non-radiative relaxation should lead to evaporation at the surface of clathrates. Experimental setups are suggested to localize and study these species underneath ice surfaces on distant planets or planetesimals from mobile detectors such as drones or CubeSats equipped with appropriate laser sources and telescopes with 2D imaging detectors. Full article
Show Figures

Figure 1

15 pages, 6161 KB  
Article
Differential Expression and Analysis of TBX3 Gene in Skin Tissues of Dun Mongolian Horses with and Without Bider Markings
by Tana An and Manglai Dugarjaviin
Animals 2026, 16(2), 297; https://doi.org/10.3390/ani16020297 - 18 Jan 2026
Viewed by 402
Abstract
(1) Background: The dun coat color, a wild-type phenotype in horses characterized by pigment dilution and primitive markings, is regulated by TBX3. This study explored the expression and localization of TBX3 in the Bider marking (a primitive mark unique to the shoulder [...] Read more.
(1) Background: The dun coat color, a wild-type phenotype in horses characterized by pigment dilution and primitive markings, is regulated by TBX3. This study explored the expression and localization of TBX3 in the Bider marking (a primitive mark unique to the shoulder of horses); (2) Methods: We compared skin tissues from Bider-marked and non-Bider dun Mongolian horses. Samples were collected from the Bider area (dark-colored/light-colored shoulder), dorsal midline, and croup. Histological staining, qRT-PCR, and Western blotting were used to analyze pigment distribution and TBX3 expression at mRNA and protein levels; (3) Results: Histology revealed asymmetric pigment deposition in hair shafts from light-colored areas of both Bider and non-Bider horses, whereas dark areas showed symmetric distribution. qRT-PCR and Western blotting showed TBX3 expression was significantly higher in the shoulder of non-Bider horses compared to Bider horses. Conversely, Bider horses exhibited higher TBX3 levels in all other sampled areas. Immunohistochemistry localized TBX3 protein to the epidermis and hair follicle bulbs in both groups; (4) Conclusions: In dun Mongolian horses, TBX3 expression differences between dark and light skin areas correlate with Bider markings. TBX3 is implicated in this specific pigment marking, though its upstream regulation requires further study. These findings provide key insights into the mechanism behind Bider marking formation. Full article
(This article belongs to the Special Issue Advances in Genetic Variability and Selection of Equines)
Show Figures

Figure 1

29 pages, 425 KB  
Article
Analysis of Solutions to Nonlocal Tensor Kirchhoff–Carrier-Type Problems with Strong and Weak Damping, Multiple Mixed Time-Varying Delays, and Logarithmic-Term Forcing
by Aziz Belmiloudi
Symmetry 2026, 18(1), 172; https://doi.org/10.3390/sym18010172 - 16 Jan 2026
Viewed by 249
Abstract
In this contribution, we propose and study long-time behaviors of a new class of N-dimensional delayed Kirchhoff–Carrier-type problems with variable transfer coefficients involving a logarithmic nonlinearity. We take into account the dependence of diffusion and damping coefficients on the position and direction, [...] Read more.
In this contribution, we propose and study long-time behaviors of a new class of N-dimensional delayed Kirchhoff–Carrier-type problems with variable transfer coefficients involving a logarithmic nonlinearity. We take into account the dependence of diffusion and damping coefficients on the position and direction, as well as the presence of different types of delays. This class of nonlocal anisotropic and nonlinear wave-type equations with multiple time-varying mixed delays and dampings, of a fairly general form, containing several arbitrary functions and free parameters, is of the following form: 2ut2div(K(σuL2(Ω)2)Aσ(x)u)+M(uL2(Ω)2)udiv(ζ(t)Aσ(x)ut)+d0(t)ut+Dr(x,t;ut)=G(u), where u(x,t) is the state function, M and K are the nonlocal Kirchhoff operators and the nonlinear operator G(u) corresponds to a logarithmic source term. The symmetric tensor Aσ describes the anisotropic behavior and processes of the system, and the operator Dr represents the multiple time-varying mixed delays related to velocity ut. Our problem, which encompasses numerous equations already studied in the literature, is relevant to a wide range of practical and concrete applications. It not only considers anisotropy in diffusion, but it also assumes that the strong damping can be totally anisotropic (a phenomenon that has received very little mathematical attention in the literature). We begin with the reformulation of the problem into a nonlinear system coupling a nonlocal wave-type equation with ordinary differential equations, with the help of auxiliary functions. Afterward, we study the local existence and some necessary regularity results of the solutions by using the Faedo–Galerkin approximation, combining some energy estimates and the logarithmic Sobolev inequality. Next, by virtue of the potential well method combined with the Nehari manifold, conditions for global in-time existence are given. Finally, subject to certain conditions, the exponential decay of global solutions is established by applying a perturbed energy method. Many of the obtained results can be extended to the case of other nonlinear source terms. Full article
(This article belongs to the Section Mathematics)
23 pages, 5058 KB  
Article
Research on State of Health Assessment of Lithium-Ion Batteries Using Actual Measurement Data Based on Hybrid LSTM–Transformer Model
by Hanyu Zhang and Jifei Wang
Symmetry 2026, 18(1), 169; https://doi.org/10.3390/sym18010169 - 16 Jan 2026
Cited by 1 | Viewed by 478
Abstract
An accurate assessment of the state of health (SOH) of lithium-ion batteries (LIBs) is crucial for ensuring the safety and reliability of energy storage systems and electric vehicles. However, existing methods face challenges: physics-based models are computationally complex, traditional data-driven methods rely heavily [...] Read more.
An accurate assessment of the state of health (SOH) of lithium-ion batteries (LIBs) is crucial for ensuring the safety and reliability of energy storage systems and electric vehicles. However, existing methods face challenges: physics-based models are computationally complex, traditional data-driven methods rely heavily on manual feature engineering, and single models lack the ability to capture both local and global degradation patterns. To address these issues, this paper proposes a novel hybrid LSTM–Transformer model for LIB SOH estimation using actual measurement data. The model integrates Long Short-Term Memory (LSTM) networks to capture local temporal dependencies with the Trans-former architecture to model global degradation trends through self-attention mechanisms. Experimental validation was conducted using eight 18650 Nickel Cobalt Manganese (NCM) LIBs subjected to 750 charge–discharge cycles under room temperature conditions. Sixteen statistical features were extracted from voltage and current data during constant current–constant voltage (CC-CV) phases, with feature selection based on the Pearson correlation coefficient and maximum information coefficient analysis. The proposed LSTM–Transformer model demonstrated superior performance compared to the standalone LSTM and Transformer models, achieving a mean absolute error (MAE) as low as 0.001775, root mean square error (RMSE) of 0.002147, and mean absolute percentage error (MAPE) of 0.196% for individual batteries. Core features including cumulative charge (CC Q), charging time, and voltage slope during the constant current phase showed a strong correlation with the SOH (absolute PCC > 0.8). The hybrid model exhibited excellent generalization across different battery cells with consistent error distributions and nearly overlapping prediction curves with actual SOH trajectories. The symmetrical LSTM–Transformer hybrid architecture provides an accurate, robust, and generalizable solution for LIB SOH assessment, effectively overcoming the limitations of traditional methods while offering potential for real-time battery management system applications. This approach enables health feature learning without manual feature engineering, representing an advancement in data-driven battery health monitoring. Full article
(This article belongs to the Section Engineering and Materials)
Show Figures

Figure 1

19 pages, 588 KB  
Article
Influence of Bilateral Upper Limb Morphological Asymmetry on Grip Strength Related to Gender in Non-Athlete University Students
by Stefan Alecu, Gheorghe Adrian Onea, Dana Badau, Adela Badau and Florentina Nechita
Symmetry 2026, 18(1), 122; https://doi.org/10.3390/sym18010122 - 8 Jan 2026
Cited by 1 | Viewed by 528
Abstract
Bilateral morphological asymmetry of the upper limbs may influence grip strength even in semi-active young adults. Understanding this relationship is important for identifying early neuromuscular imbalances with implications for ergonomics and rehabilitation. This study aimed to examine associations between upper limb anthropometric characteristics [...] Read more.
Bilateral morphological asymmetry of the upper limbs may influence grip strength even in semi-active young adults. Understanding this relationship is important for identifying early neuromuscular imbalances with implications for ergonomics and rehabilitation. This study aimed to examine associations between upper limb anthropometric characteristics and grip strength in non-athlete students, considering gender and manual dominance. The sample included 192 healthy university students (110 females, 82 males; mean age 19.92 ± 1.4 years) without prior sports training. Thirteen bilateral anthropometric parameters of the upper limbs were assessed, including hand and palm dimensions, segmental lengths, and arm and forearm circumferences, along with grip strength measured by dynamometry in two positions: arm extended and arm flexed at 90°. Statistical analysis revealed significant differences in forearm length, arm and forearm circumferences, and grip strength (p < 0.001). The dominant limb consistently demonstrated higher grip strength, with mean differences of approximately 2 kg. Male participants showed higher absolute values for all morphological and functional variables, whereas stronger correlations between distal upper-limb morphology and grip strength were observed in females. These findings indicate that, despite largely symmetric skeletal dimensions, moderate functional asymmetries exist and grip strength is influenced primarily by local muscular development rather than overall limb size. Full article
(This article belongs to the Special Issue Symmetry Application in Motor Control in Sports and Rehabilitation)
Show Figures

Figure 1

22 pages, 4344 KB  
Article
CGAP-HBSA: A Source Camera Identification Framework Under Few-Shot Conditions
by Yifan Hu, Zhiqiang Wen, Aofei Chen and Lini Wu
Symmetry 2026, 18(1), 71; https://doi.org/10.3390/sym18010071 - 31 Dec 2025
Viewed by 329
Abstract
Source camera identification relies on sensor noise features to distinguish between different devices, but large-scale sample labeling is time-consuming and labor-intensive, making it difficult to implement in real-world applications. The noise residuals generated by different camera sensors exhibit statistical asymmetry, and the structured [...] Read more.
Source camera identification relies on sensor noise features to distinguish between different devices, but large-scale sample labeling is time-consuming and labor-intensive, making it difficult to implement in real-world applications. The noise residuals generated by different camera sensors exhibit statistical asymmetry, and the structured patterns within these residuals also show local symmetric relationships. Together, these features form the theoretical foundation for camera source identification. To address the problem of limited labeled data under few-shot conditions, this paper proposes a Cross-correlation Guided Augmentation and Prediction with Hybrid Bidirectional State-Space Model Attention (CGAP-HBSA) framework, based on the aforementioned symmetry-related theoretical foundation. The method extracts symmetric correlation structures from unlabeled samples and converts them into reliable pseudo-labeled samples. Furthermore, the HBSA network jointly models symmetric structures and asymmetric variations in camera fingerprints using a bidirectional SSM module and a hybrid attention mechanism, thereby enhancing long-range spatial modeling capabilities and recognition robustness. In the Dresden dataset, the proposed method achieves an identification accuracy for the 5-shot camera source identification task that is only 0.02% lower than the current best-performing method under few-shot conditions, MDM-CPS, and outperforms other classical few-shot camera source identification methods. In the 10-shot task, the method improves by at least 0.3% compared to MDM-CPS. In the Vision dataset, the method improves the identification accuracy in the 5-shot camera source identification task by at least 6% compared to MDM-CPS, and in the 10-shot task, it improves by at least 3% over the best-performing MDM-CPS method. Experimental results demonstrate that the proposed method achieves competitive or superior performance in both 5-shot and 10-shot settings. Additional robustness experiments further confirm that the HBSA network maintains strong performance even under image compression and noise contamination conditions. Full article
Show Figures

Figure 1

25 pages, 1090 KB  
Article
Evaluating Large Language Models on Chinese Zero Anaphora: A Symmetric Winograd-Style Minimal-Pair Benchmark
by Zimeng Li, Yichen Qiao, Xiaoran Chen and Shuangshuang Chen
Symmetry 2026, 18(1), 47; https://doi.org/10.3390/sym18010047 - 26 Dec 2025
Viewed by 602
Abstract
This study investigates how large language models (LLMs) handle Chinese zero anaphora under symmetric minimal-pair conditions designed to neutralize shallow syntactic cues. We construct a Winograd-style benchmark of carefully controlled sentence pairs that require semantic interpretation, pragmatic inference, discourse tracking, and commonsense reasoning [...] Read more.
This study investigates how large language models (LLMs) handle Chinese zero anaphora under symmetric minimal-pair conditions designed to neutralize shallow syntactic cues. We construct a Winograd-style benchmark of carefully controlled sentence pairs that require semantic interpretation, pragmatic inference, discourse tracking, and commonsense reasoning rather than structural heuristics. Using GPT-4, ChatGLM-4, and LLaMA-3 under zero-shot, one-shot, and few-shot prompting, we assess both accuracy and the reasoning traces generated through a standardized Chain-of-Thought diagnostic. Results show that all models perform consistently on items solvable through local cues but display systematic asymmetric errors on 19 universally misinterpreted sentences that demand deeper discourse reasoning. Analysis of these failures reveals weaknesses in semantic role differentiation, topic-chain maintenance, logical-relation interpretation, pragmatic inference, and long-distance dependency tracking. These findings suggest that while LLMs perform well on simpler tasks, they still face challenges in interpreting contextually omitted arguments in Chinese. The study provides a new controlled evaluation resource, an interpretable error analysis framework, and evidence of differences in symmetric versus asymmetric reasoning behaviors in LLMs. Future research could expand the current benchmark to longer discourse contexts, incorporate multi-modal or knowledge-grounded cues, and explore fine-tuning LLMs on discourse data, helping clarify whether asymmetric patterns stem from deeper reasoning challenges or from interactions between models and the evaluation format. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Natural Language Processing)
Show Figures

Figure 1

21 pages, 2847 KB  
Article
Modeling and Solving Two-Sided Disassembly Line Balancing Problem Under Partial Disassembly of Parts
by Shuwei Wang, Huaizi Wang, Jia Liu, Guofeng Xu and Guoxun Xu
Symmetry 2026, 18(1), 4; https://doi.org/10.3390/sym18010004 - 19 Dec 2025
Viewed by 394
Abstract
In two-sided disassembly lines, stations are symmetrically arranged on both sides of the conveyor, which is suitable for large-sized waste products. During the disassembly process, evenly assigning parts to workstations while satisfying various constraints and optimizing some disassembly objectives is a challenging task. [...] Read more.
In two-sided disassembly lines, stations are symmetrically arranged on both sides of the conveyor, which is suitable for large-sized waste products. During the disassembly process, evenly assigning parts to workstations while satisfying various constraints and optimizing some disassembly objectives is a challenging task. Therefore, this study deals with a two-sided partial disassembly line balancing problem, and a multi-objective mathematical model for this problem is built. While satisfying various constraints, four objectives, namely, the hazard index, profit, smoothness index, and demand index, are optimized. Due to the NP-hard nature of the problem, an improved discrete whale optimization algorithm is proposed. According to the characteristics of the feasible solutions, an encoding method based on a one-dimensional integer array is designed, which can effectively decrease the memory space and simplify the design of neighbor structures. In the three stages of encircling prey, random wandering, and bubble-net attacking, based on the search features of each stage, different neighbor operators and search strategies are designed to enhance the local exploitation and global exploration capabilities. Finally, the performance of the proposed algorithm was tested against other algorithms for different types of instances and a disassembly case. The results show that the proposed algorithm can not only solve various types of disassembly line balancing problems but also shows superior performance. Full article
(This article belongs to the Section Mathematics)
Show Figures

Figure 1

14 pages, 2471 KB  
Article
Unmanned Aerial Vehicle Logistics Distribution Path Planning Based on Improved Grey Wolf Optimization Algorithm
by Wei-Qi Feng, Yong Yang, Lin-Feng Yang, Yu-Jie Fu and Kai-Jun Xu
Symmetry 2025, 17(12), 2178; https://doi.org/10.3390/sym17122178 - 18 Dec 2025
Cited by 2 | Viewed by 472
Abstract
Aiming to solve the bottlenecks of the traditional Grey Wolf Optimizer (GWO) in UAV three-dimensional path planning—including uneven initial population distribution, slow convergence speed, and proneness to local optima—this paper proposes an improved algorithm (CPS-GWO) that integrates the Kent chaotic map with Particle [...] Read more.
Aiming to solve the bottlenecks of the traditional Grey Wolf Optimizer (GWO) in UAV three-dimensional path planning—including uneven initial population distribution, slow convergence speed, and proneness to local optima—this paper proposes an improved algorithm (CPS-GWO) that integrates the Kent chaotic map with Particle Swarm Optimization (PSO) to mitigate these limitations. To enhance the diversity of the initial population, the Kent chaotic map is employed, as ergodicity ensures the symmetric distribution of the initial population, expanding search coverage; meanwhile, a nonlinear adaptive strategy is adopted to dynamically adjust the control parameter a, enabling flexible search behaviour. Furthermore, the grey wolf position update rule is optimized by incorporating the inertia weight and social learning mechanism of PSO, which strengthens the algorithm’s ability to balance exploration and exploitation. Additionally, a multi-objective comprehensive cost function is constructed, encompassing path length, collision penalty, height constraints, and path smoothness, to fully align with the practical demands of UAV path planning. To validate the performance of CPS-GWO, a three-dimensional urban simulation environment is established on the MATLAB platform. Comparative experiments with different population sizes are conducted, with the traditional GWO as the benchmark. The results demonstrate that, compared with the original GWO, (1) the average fitness of CPS-GWO is significantly reduced by 31.30–38.53%; (2) the path length is shortened by 15.62–22.12%; (3) path smoothness is improved by 43.44–51.52%; and (4) the fitness variance is only 9.58–12.16% of that of the traditional GWO, indicating notably enhanced robustness. Consequently, the proposed CPS-GWO effectively balances global exploration and local exploitation capabilities, thereby providing a novel technical solution for efficient path planning in UAV logistics and distribution under complex urban environments, which holds important engineering application value. Full article
Show Figures

Figure 1

Back to TopTop