Search Results (14)

To address the uncertainty of the measurement noise covariance matrix in vehicle state estimation, this paper proposes a symmetry-aware extended Kalman filter optimized by a chaotic-gradient strategy. The symmetry-aware concept is introduced from the approximate mirror symmetry of vehicle lateral dynamics under left and right steering excitations. Under identical road adhesion and vehicle operating conditions, the yaw-rate and sideslip-angle responses should exhibit balanced statistical characteristics for positive and negative lateral motions. However, a fixed measurement noise covariance matrix may break this balance and lead to direction-dependent estimation bias or delayed convergence. To improve the statistical consistency of the estimation process, the proposed method adaptively tunes the measurement noise covariance matrix according to the innovation covariance mismatch. A chaotic search mechanism is first used to enhance global exploration, and a variable-step gradient method is then applied to refine the local optimal solution. Through the iterative combination of chaotic traversal and gradient-based refinement, the proposed observer improves the balance between model prediction and measurement correction under stochastic disturbances. The effectiveness of the proposed method is verified through CarSim and MATLAB/Simulink co-simulation. The results show that, compared with EKF, UKF, and AEKF benchmark observers, the proposed CG_EKF provides more accurate estimation of vehicle yaw rate and sideslip angle. Full article

Background/Objectives: A marked anteroposterior gradient of nasal fossa pneumatisation over the posterior maxillary alveolar base has been documented at the second premolar level, yet whether this gradient extends to the second upper molar (M2)—the primary site for posterior implant rehabilitation—remains uncharacterised. We aimed to quantify this gradient by classifying pneumatisation patterns above the maxillary alveolar base at M2 (Type 1: pure antral; Type 2: antral with palatine recess; Type 3: Big Nose pattern with combined antral and nasal involvement), assess bilateral symmetry and sex distribution, and compare findings with published second premolar data. Methods: A retrospective study was conducted on 165 cone-beam computed tomography scans (330 sides) from a Romanian population. Patterns were classified as Type 1 (pure antral), Type 2 (antral with palatine recess), or Type 3 (Big Nose pattern). Bilateral symmetry was assessed using Cohen’s kappa, and sex differences using Fisher’s exact test. Results: Type 1 was observed in 93.3% of sides, Type 2 in 4.2%, and Type 3 in 2.4%. Bilateral symmetry was 98.8% (kappa = 0.904), with all Type 3 cases occurring bilaterally. No significant sex difference was found (p = 0.363), although Type 3 showed a non-significant male predominance (OR = 4.55; p = 0.305). The Big Nose pattern was 6.8-fold less prevalent at M2 than at the second premolar level. Conclusions: A 6.8-fold reduction in Big Nose prevalence from the second premolar (16.2%) to M2 (2.4%) confirms a pronounced anteroposterior gradient in nasal fossa involvement over the posterior maxillary alveolar base—the central finding of this study. At M2, the maxillary sinus dominates exclusively in 97.6% of sides, rendering standard sinus floor elevation highly predictable. The invariable bilaterality of the Big Nose pattern at M2 supports contralaterally symmetrical surgical planning. These findings provide a gradient-based clinical framework: nasal-floor-aware augmentation planning is essential anteriorly (premolar region), whereas standard sinus augmentation protocols are reliably applicable at M2. Full article

Abnormal gait associated with neuromuscular and musculoskeletal disorders represents a growing clinical burden, particularly in aging populations. This study presents a modular, low-cost Smart Rehabilitation Walker (SRW) that integrates multimodal sensing and real-time haptic feedback to enable simultaneous gait monitoring and corrective intervention in both clinical and home environments. The system combines force-sensing resistors for bilateral load symmetry assessment, inertial measurement units for fall detection, and surface electromyography (sEMG) for neuromuscular activity monitoring within a closed-loop assistive feedback architecture. A 15-day pilot study involving ten individuals with rheumatoid arthritis and clinically observed neurological gait abnormalities demonstrated measurable improvements in gait biomechanics. The Force Symmetry Index (FSI), calculated using the Robinson symmetry metric, decreased from an average of 0.9691 to 0.2019, corresponding to a 79.26% average reduction in inter-limb load asymmetry. Concurrently, sEMG measurements showed a substantial increase in neuromuscular activation (ΔEMG = 4.28), with statistical analysis confirming a significant improvement across participants (paired t-test: t(9) = 13.58, p < 0.001). To model rehabilitation trajectories, a nonlinear predictive framework based on Gaussian Process Regression achieved high predictive accuracy (R² ≈ 0.9, with a mean RMSE of 0.0385), while providing uncertainty-aware trend estimation. Validation using an independent amyotrophic lateral sclerosis gait dataset further demonstrated the transferability of the analytical pipeline. These results highlight the potential of sensor-enabled assistive walkers as scalable platforms for quantitative gait rehabilitation, adaptive feedback, and long-term mobility monitoring. Full article

Intensive care units (ICUs) generate heterogeneous data streams, including structured electronic health records, physiological time series, and medical imaging, that describe the same patient state through different observational forms. Effective multimodal learning in this setting requires a principled balance between representation-level symmetry and architectural asymmetry. Clinically corresponding patient states should exhibit cross-modal representational symmetry, whereas each modality retains intrinsic asymmetry in dimensionality, temporal resolution, noise characteristics, and missingness. This study proposes a modality-specific sparse autoencoder framework for efficient multimodal ICU representation learning under this symmetry–asymmetry principle. Separate sparse encoders are assigned to each modality to preserve the modality-dependent structure while suppressing redundant latent activity through adaptive gating. Representation-level symmetry is encouraged through a sparsity-aware contrastive objective that aligns paired latent embeddings across modalities only on active informative dimensions. To further model inter-patient dependencies, the framework incorporates a graph neural network (GNN) whose message-passing operations respect modality-specific sparsity patterns. Experimental results indicate that the proposed framework improves predictive performance and computational efficiency relative to conventional multimodal baselines, while also exhibiting stronger robustness under missing-modality conditions and more selective latent representations. Overall, the method provides an effective and clinically relevant multimodal learning strategy for ICU decision support while offering a measurable symmetry-aware and asymmetry-preserving formulation for heterogeneous medical data. Full article

Cross-institutional collaborative fraud detection is essential for combating increasingly sophisticated financial fraud, yet privacy regulations and data silos severely constrain knowledge sharing among institutions. This study aims to develop a privacy-preserving framework that enables effective collaborative fraud detection while protecting raw data, with particular emphasis on exploiting symmetry properties in federated architectures and graph topology analysis. We propose an Adaptive Federated Graph Attention Network (FedGAT), which employs spatio-temporal graph attention mechanisms to capture topological structures and dynamic fraud patterns within institutional transaction networks. The framework introduces a symmetric similarity matrix derived from graph topological features, where the symmetry property ($s_{ij}=s_{ji}$) ensures consistent and unbiased measurement of structural relationships between any pair of institutions. Based on this symmetric similarity metric, an adaptive weighted aggregation mechanism is designed for cross-institutional parameter fusion, enabling balanced knowledge transfer that respects the symmetric collaborative relationship among participating institutions. The symmetric information exchange protocol between local institutions and the central server further guarantees equitable contribution and benefit distribution throughout the federated learning process. The framework is evaluated on the Elliptic Bitcoin transaction dataset and the IEEE-CIS fraud detection dataset, with recall rate and false positive rate as primary performance metrics. Results show that FedGAT achieves a recall of 0.85 and a false-positive rate of 0.038 in single-institution detection, representing approximately 40% and 70% improvements over existing methods, respectively. In collaborative detection across five virtual institutions, the symmetry-aware adaptive aggregation mechanism enables all participants to achieve performance gains exceeding 15% while completely eliminating negative transfer effects observed in simple averaging approaches. This work contributes a novel symmetry-based federated learning framework that balances privacy protection with detection performance, advancing the literature on cross-institutional financial risk management. Full article

This paper develops a rigorous mathematical and computational framework for four-dimensional chess defined on the discrete hypercubic lattice $\{1,\dots , 8{\}}^4$. We formalize piece movement using displacement sets in ${\mathbb{Z}}^4$, define adjacency via the Chebyshev metric, and analyze the resulting move graphs for rooks, bishops, knights, queens, and kings. We establish exact mobility formulas, parity invariants, and connectivity properties, consolidating known product-graph results for rooks and kings while introducing a boundary-sensitive analysis of the four-dimensional knight verified by exhaustive enumeration. The mathematical framework is complemented by a fully implemented 4D chess engine and interactive visualization environment rendering all 64 (z,w)-slices of the hypercube simultaneously. The system supports full move legality, generalized special rules, multi-king checkmate detection, and reproducible state enumeration. Performance measurements and exploratory branching-factor estimates are obtained through reproducible random playouts using the publicly available implementation. We contextualize this ruleset within existing work on move graphs on ${\mathbb{Z}}_n^m$, higher-dimensional leapers, spectral properties of grid graphs, toroidal analogs, and multidimensional visualization. Exploratory qualitative feedback (N = 18) is included to examine whether the visualization design is interpretable and navigable in practice, providing feasibility-oriented observations on how slice-based 4D projection and layered board rendering are perceived by non-expert users in an exploratory context. Together, the mathematical results, implemented engine, and visualization form a coherent foundation for the study of strategy, complexity, and human interaction in four-dimensional game systems. The framework provides a basis for future investigations into spectral analysis of move graphs, symmetry-aware search, hierarchical planning, and educational applications in high-dimensional geometry. Full article

Background/Objectives: Exercise-induced fatigue is a fundamental component of running performance and training, yet it is also implicated in altered movement mechanics and increased injury risk. While numerous studies have examined fatigue-related biomechanical changes during running, findings remain fragmented across biomechanical domains and fatigue modalities. The purpose of this systematic review was to synthesize contemporary evidence on the effects of fatigue on lower-limb biomechanics during running and to interpret the potential injury relevance of these adaptations. Methods: A systematic literature search was conducted in PubMed, Scopus, and Web of Science for original empirical studies published between January 2010 and December 2025. Eligible studies involved human participants performing running or running-related tasks, applied an explicit fatigue protocol, and reported quantitative lower-limb biomechanical outcomes. Study selection followed PRISMA 2020 guidelines. Data extraction included participant characteristics, fatigue protocols, biomechanical measures, instrumentation, and key findings. Methodological quality was assessed using the Cochrane Risk of Bias 2 (RoB-2) tool. Due to substantial methodological heterogeneity, findings were synthesized narratively. Results: Twenty-four studies met the inclusion criteria. Across studies, fatigue consistently altered spatiotemporal parameters, joint kinematic and kinetic variables, spring-mass behavior, impact loading, coordination variability, neuromuscular output, and inter-limb symmetry. Common adaptations included increased ground contact time, reduced ankle joint power and stiffness, increased joint range of motion, elevated impact loading, and greater movement variability. These changes reflected reduced mechanical efficiency and a redistribution of mechanical load from distal to proximal joints, particularly toward the knee and hip. Similar fatigue-related biomechanical patterns were observed in both laboratory-based and real-world endurance running conditions. Conclusions: Exercise-induced fatigue produces systematic and injury-relevant alterations in lower-limb biomechanics during running. These adaptations may preserve short-term performance but create mechanical conditions associated with increased susceptibility to overuse and non-contact injuries. Integrating fatigue-aware biomechanical assessment, neuromuscular conditioning, and individualized load management strategies may help mitigate adverse fatigue-related adaptations. Full article

Map matching is a fundamental technique for aligning noisy GPS trajectory data with digital road networks and constitutes a key component of Intelligent Transportation Systems (ITS) and Location-Based Services (LBS). Nevertheless, existing approaches still suffer from notable limitations in complex environments, particularly urban and urban-like scenarios characterized by heterogeneous GPS noise and sparse observations, including inadequate adaptability to dynamically varying noise, unavoidable trade-offs between real-time efficiency and matching accuracy, and limited generalization capability across heterogeneous driving behaviors. To overcome these challenges, this paper presents a Meta-learning-driven Progressive map-Matching (MPM) method with a symmetry-aware design, which integrates a two-layer pattern-mining-based noise-robust meta-learning mechanism with a dynamic weight adjustment strategy. By explicitly modeling topological symmetry in road networks, symmetric trajectory patterns, and symmetric noise variation characteristics, the proposed method effectively enhances prior knowledge utilization, accelerates online adaptation, and achieves a more favorable balance between accuracy and computational efficiency. Extensive experiments on two real-world datasets demonstrate that MPM consistently outperforms state-of-the-art methods, achieving up to 10–15% improvement in matching accuracy while reducing online matching latency by over 30% in complex urban environments. Furthermore, the symmetry-aware design significantly improves robustness against asymmetric interference, thereby providing a reliable and scalable solution for high-precision map matching in complex and dynamic traffic environments. Full article

Microservice architecture has become a foundational component of modern distributed systems due to its modularity, scalability, and deployment flexibility. However, the increasing complexity and dynamic nature of service interactions have introduced substantial challenges in accurately detecting runtime anomalies. Existing methods often rely on multiple monitoring metrics, which introduce redundancy and noise while increasing the complexity of data collection and model design. This paper proposes a novel spatiotemporal anomaly detection framework that integrates Dynamic Graph Neural Networks (D-GNN) combined with Long Short-Term Memory (LSTM) networks to model both the structural dependencies and temporal evolution of microservice behaviors. Unlike traditional approaches, our method uses only CPU utilization as the sole monitoring metric, leveraging its high observability and strong correlation with service performance. From a symmetry perspective, normal microservice behaviors exhibit approximately symmetric spatiotemporal patterns: structurally similar services tend to share similar CPU trajectories, and recurring workload cycles induce quasi-periodic temporal symmetries in utilization signals. Runtime anomalies can therefore be interpreted as symmetry-breaking events that create localized structural and temporal asymmetries in the service graph. The proposed framework is explicitly designed to exploit such symmetry properties: the D-GNN component respects permutation symmetry on the microservice graph while embedding the evolving structural context of each service, and the LSTM module captures shift-invariant temporal trends in CPU usage to highlight asymmetric deviations over time. Experiments conducted on real-world microservice datasets demonstrate that the proposed method delivers excellent performance, achieving 98 percent accuracy and 98 percent F1-score. Compared to baseline methods such as DeepTraLog, which achieves 0.93 precision, 0.978 recall, and 0.954 F1-score, our approach performs competitively, achieving 0.980 precision, 0.980 recall, and 0.980 F1-score. Our results indicate that a single-metric, symmetry-aware spatiotemporal modeling approach can achieve competitive performance without the complexity of multi-metric inputs, providing a lightweight and robust solution for real-time anomaly detection in large-scale microservice environments. Full article

We recast cooperative localization and scheduling in heterogeneous multi-agent systems through the lens of symmetry and symmetry breaking. On the geometric side, the Fisher Information Matrix (FIM) objective is invariant to rigid Euclidean transformations of the global frame, while its maximization admits symmetric optimal sensor formations; on the algorithmic side, heterogeneity and task constraints break permutation symmetry across agents, requiring policies that are sensitive to role asymmetries. We model communication as a random graph and quantify structural symmetry via topology metrics (average path length, clustering, betweenness) and graph automorphism-related indices, connecting these to estimation uncertainty. We then design a hybrid reward for reinforcement learning (RL) that is equivariant to agent relabeling within roles yet intentionally introduces asymmetry through distance/FIM terms to avoid degenerate symmetric configurations with poor observability. Simulations show that (i) symmetry-aware, FIM-optimized path planning reduces localization error versus symmetric but non-informative placements; and (ii) controlled symmetry breaking in policy learning improves robustness and data rate–reward trade-offs over baselines. Our results position symmetry/asymmetry as first-class design principles that unify estimation-theoretic invariances with learning-based coordination in complex heterogeneous networks. Under DDPG training, the total data rate (SDR) reaches $6.63\pm 0.97$ and the average reward per step (ARPS) is $-80.70\pm 6.94$, representing improvements of approximately $11.8\%$ over the baseline $(5.93\pm 3.51)$ and $11.1\%$ over SAC $(5.97\pm 2.66)$, respectively. The network’s mean shortest-path length is $L=1.721$, and the average betweenness centrality of the coordination nodes is ≈0.098. Moreover, the FIM-optimized path-planning strategy achieves the lowest localization error among all evaluated policies. Full article

The aim of sequential recommendation (SR) is to predict a user’s next interaction by analyzing their historical behavioral sequences. The proposed framework leverages the inherent symmetry in user behavior patterns, where temporal and spectral representations exhibit complementary structures that can be harmonized for robust recommendation. Conventional SR methods predominantly utilize implicit feedback (e.g., clicks and views) as model inputs, whereby observed interactions are treated as positive instances, while unobserved ones are considered negative samples. However, the inherent randomness and diversity in user behaviors inevitably introduce noise into such implicit feedback, potentially compromising the accuracy of recommendations. Recent studies have explored noise mitigation through two primary approaches: temporal-domain methods that reweight interactions to distill clean samples for comprehensive user preference modeling, and frequency-domain techniques that purify item embeddings to reduce the propagation of noise. While temporal approaches excel in sample refinement, frequency-based methods demonstrate superior capability in learning noise-resistant representations through spectral analysis. Motivated by the desire to synergize these complementary advantages, we propose SR-DFN, a novel framework that systematically addresses noise interference through coordinated time–frequency processing. Self-guided sample purification is implemented in the temporal domain of our architecture via adaptive interaction weighting, effectively distilling behaviorally significant patterns. The refined sequence is then transformed into the frequency domain, where learnable spectral filters operate to further attenuate residual noise components while preserving essential preference signals. Drawing on the convolution theorem’s revelation regarding frequency-domain operations capturing behavioral periodicity, we critically examine conventional position encoding schemes and propose an efficient parameterization strategy that eliminates redundant positional embeddings without compromising temporal awareness. Comprehensive experiments conducted on four real-world benchmark datasets demonstrate SR-DFN’s superior performance over state-of-the-art baselines, with ablation studies validating the effectiveness of our dual-domain denoising mechanism. Our findings suggest that coordinated time–frequency processing offers a principled solution for noise-resilient sequential recommendation while challenging conventional assumptions about positional encoding requirements in spectral-based approaches. The symmetry principles underlying our dual-domain approach demonstrate how the balanced processing of temporal and frequency domains can achieve superior noise resilience. Full article

This study presents a framework for designing symmetry-aware cooperative controllers to synchronize two SCARA LS3-B401S robots, ensuring precision, adaptability, and fault tolerance in flexible manufacturing environments. Four control strategies—Proportional–Integral–Derivative (PID), Adaptive Sliding Mode Control (ASMC), Adaptation-Enabled Neural Network (ANN), and Inverse-Dynamics with Disturbance Observer (ID-DO)—were evaluated through high-fidelity MATLAB/Simulink simulations (fixed 1 ms step size, ode4 solver), using dynamic SolidWorks 2022 models validated under realistic perturbations, including ±0.0005 rad sensor noise and ±5% mass variation. Among the strategies, the ANN controller—implemented as an 8-10-4 multi-layer perceptron—achieved the highest performance, consistently reducing trajectory errors by over 99%, maintaining symmetry deviations below 0.001 rad, and recovering from ±0.08 rad disturbances in 0.12 s. Its stabilization time averaged 0.247 s across joints, and energy consumption dropped to 0.01 J/s, representing a 98% improvement over PID. Despite a higher computational load (12.5 MFLOPS, 2.80 ms per iteration), GPU acceleration brought execution times below 1.4 ms, ensuring compliance with industrial 5 ms control cycles. These results establish a scalable foundation for next-generation multi-robot systems, with planned physical validation on SCARA LS3-B401S robots equipped with high-resolution encoders and advanced processors. By leveraging symmetry-driven coordination ($S=I$), the proposed framework supports resilient, sustainable, and high-precision manufacturing, aligned with the goals of Industry 5.0. Full article

Background and Objectives: Facial symmetry is a key component of facial beauty and attractiveness. However, perfect symmetry is rare, and slight asymmetries, also known as natural asymmetries, are common and contribute to the uniqueness of each face. The perception of facial asymmetry varies among individuals and can be influenced by several factors. This study aimed to investigate the self-perception of dento-facial asymmetry among a sample of Romanian individuals, focusing on their awareness, the extent to which it bothers them, and their desire for correction. Materials and Methods: A cross-sectional analytical study was conducted with 283 participants from Romania between January and February 2024. Participants completed a questionnaire designed to assess their self-perception of facial asymmetry and socio-demographic characteristics. The questionnaire included 10 questions on self-perception of facial asymmetry and 8 questions on socio-demographic data. Statistical analysis was performed using SPSS 26.0, and the Pearson Chi-square test was used for comparative analysis. Results: The sample was predominantly female (75.3%) with an average age of 32.24 years. Most participants were from urban areas (80.6%) and had university degrees (58.7%). About 28.7% of participants observed facial asymmetry, with dental asymmetry being the most frequently reported, followed by asymmetries in the eyebrows and eyelids. The right side of the face was more commonly perceived as asymmetric. Although 24.4% of participants were bothered by their asymmetry, 39.2% expressed a desire to correct it. Conclusions: One-third of participants identified dento-facial asymmetry, with the dental level being the most reported. A significant portion of participants expressed a desire to correct their asymmetries, highlighting the importance of understanding self-perception in the context of facial aesthetics. This study underscores the subjective nature of facial asymmetry perception and the varying thresholds for what is considered bothersome or in need of correction. Full article

Participants from across the age span participate in water fitness sessions. This challenges instructors to create proper exercise prescriptions. The aim of this study was to understand the effect of age on force production and symmetry during water exercises. Twenty-six women were categorized into two groups: (i) young adult (n = 13; 23.61 ± 1.15 years) and (ii) older (n = 13; 67.38 ± 3.48 years). Women performed a horizontal upper limbs adduction during an incremental protocol comprising four music cadences increased every 30 s (105, 120, 135, and 150 b∙min⁻¹). A differential pressure system composed of two sensors was used to measure the in-water force and to estimate the symmetry index. Young adults showed higher in-water forces (43–67 N) when compared with their older counterparts (31–55 N). No differences were observed between groups for the symmetry index. The cadences of 105–120 and 120–135 lead to different in-water force of the dominant limb in both groups, while the force of the non-dominant limb showed mix-findings. In conclusion, water fitness instructors should be aware that the same music cadence may trigger different kinetic behaviors in different ages, but without impairing symmetry when exercising at 120–135 b∙min⁻¹. Full article