Search Results (175)

Conservation laws are core concepts in dynamical system modeling and the study of physical symmetries. Although machine learning has achieved significant progress in discovering physical laws, existing methods often face challenges such as identifying only a single conserved quantity. To bridge this gap, we introduce OAC-Net. By embedding a gradient orthogonality penalty directly into the neural network’s objective function, OAC-Net enables the simultaneous discovery of multiple independent integrals of motion (IOM) directly from raw trajectory data. Unlike previous heuristic approaches, we prove that gradient orthogonality of real-analytic functions implies the functional independence of the learned integrals of motion. The proposed method is validated on several canonical dynamical systems, including the two-dimensional Kepler system. Experimental results show that OAC-Net efficiently and robustly identifies multiple independent integrals of motion, with the learned integrals of motion exhibiting strong correlations with their true physical values. Additionally, ablation studies confirm OAC-Net’s robustness to hyperparameters such as noise strength and orthogonal penalty coefficient. Our approach provides an effective framework for discovering multiple interpretable integrals of motion from complex trajectory data. Full article

Symmetric electromagnetic sensing architectures induce representation-space decompositions that organize how measured fields respond to rotations, reflections, and programmable configurations. This paper develops a symmetry-resolved framework for analyzing how local parameter sensitivity is distributed across irreducible sectors and how this distribution changes under tensor lifting. Character-weighted Reynolds projectors decompose the derivatives of first-, second-, and fourth-order observables into orthogonal isotypic components, whose relative weights are quantified through normalized entropy, effective-sector occupancy, and dominant-sector concentration. The formulation distinguishes algebraic sector accessibility, determined by induced representations and tensor-product fusion, from the sensitivity profile realized by a specific physical observation model. The framework is validated using a narrowband far-field electromagnetic model of a two-ring $C_4$-symmetric receiving array and is further examined through matched cyclic and dihedral array ensembles. The results reveal a robust redistribution of sensitivity under tensor lifting in the tested cyclic architectures, while the dihedral configurations exhibit a different, order-dependent behavior associated with their richer representation structure. These findings do not imply a universal increase in information or estimation performance; rather, they show that tensorization reorganizes the symmetry channels through which local sensitivity is expressed. The proposed framework provides a diagnostic tool for comparing and designing symmetry-aware antenna arrays, metasurfaces, reconfigurable intelligent surfaces, and related programmable sensing architectures. Full article

Mobile edge computing (MEC) must serve rapidly growing populations of latency-critical and energy-constrained devices, yet distributed offloading faces two coupled problems: learned multi-agent policies depend on the arbitrary numerical ordering of edge servers, which wastes training samples and treats physically equivalent configurations inconsistently, while short-horizon cost minimization overloads attractive servers and destabilizes their queues. This paper presents SEAL-MAC (Symmetry-Equivariant Lyapunov Multi-Agent Actor–Critic), a distributed learning framework that addresses both problems jointly. First, a symmetric resource-set actor with a mirror consistency regularizer enforces server relabeling equivariance of each user’s policy and invariance of its value and Lyapunov critics. Second, a load-symmetric Lyapunov–potential shaping mechanism augments drift-plus-penalty rewards with normalized load-balance signals, coupling queue stability, fairness, and strategic alignment. The shaped interaction is analyzed as a Lyapunov-shaped Markov potential game: exact under orthogonal congestion-separable conditions, and a Markov $\alpha$-potential game under heterogeneity or interference, yielding conditional finite-time $(ϵ+\alpha )$-Nash convergence and mean-square queue stability. Each device learns from local observations and $O\left(M\right)$ queue broadcasts without exchanging gradients or policies. In simulations with up to 200 users, SEAL-MAC reduces average delay by 9.0%, 95th-percentile delay by 11.8%, energy consumption by 10.6%, and the deadline-violation rate from 3.1% to 1.8% relative to the strongest Lyapunov baseline, halves the empirical one-step deviation gain of an identically shaped Ly-PPO agent (0.048 versus 0.098), and raises the Jain fairness index from 0.88 to 0.94. Full article

The mathematical representation of discrete signals is classically governed by linear basis transforms, such as the Discrete Fourier Transform (DFT), which treat spectral projection as a rigid, deterministic geometric operation. Under this paradigm, signal compression and thresholding rely on heuristic error metrics like the Minimum Mean Squared Error (MMSE). To mathematically axiomatize these fundamental operations, this paper reformulates computational basis transforms through the lens of Cooperative Game Theory. By defining discrete signal reconstruction as a Grand Coalition of orthogonal frequency players, we establish a strict mathematical isomorphism between functional analysis and cooperative game theory. We prove that the spectral energy assigned to each frequency coefficient is exactly its Shapley Value and that classical MMSE minimization is mathematically equivalent to maximizing the retained Shapley payout. Furthermore, we extend this framework to physical hardware and linear shift-invariant (LSI) systems, modeling 8-bit quantization and the Modulation Transfer Function (MTF) as sub-additive “economic taxes” on the coalition. Finally, by intentionally violating the Shapley Symmetry Axiom to mimic the Contrast Sensitivity Function (CSF) of the human visual system, we propose a fundamentally new mathematical basis: the Perceptual Game-Theoretic Transform (PGTT). Unlike classical methods that rely on post hoc quantization for signal compression, the PGTT acts as an inherently efficient transform that structurally guarantees sub-Nyquist computational complexity and dynamic range reallocation prior to physical hardware saturation. Full article

To address the challenge of simultaneously achieving broadband absorption, multi-mechanism tunability, and angular stability in terahertz multifunctional devices, this paper proposes a MoS₂/VO₂ composite terahertz metamaterial absorber based on an asymmetric multi-nested C-shaped structure. The device adopts a three-layer configuration consisting of a MoS₂/VO₂ composite plane–SiO₂ dielectric–Au reflector layer. Unlike conventional symmetric structures, which are limited by selection rules and symmetry-protected dark modes that hinder the excitation of higher-order resonances, this design effectively breaks structural symmetry protection through geometric asymmetry. This induces strong mode hybridization between originally orthogonal dark and bright modes, enabling broadband high absorption exceeding 96.7% across the 1.88–3.52 THz frequency range (61% RBW). Notably, the device demonstrates synergistic tuning advantages: the macroscopic on/off switching of broadband absorption characteristics via the phase transition of VO₂, combined with fine blind-spot compensation and enhancement in absorption peaks using the electrical tunability of MoS₂. Furthermore, thanks to its sub-wavelength unit cell design, the structure maintains excellent performance stability over a wide incident angle range from 0° to 60°. This study reveals a synergistic enhancement mechanism combining the asymmetric unit cell and hybrid materials, providing a systematic physical solution for resolving the trade-off between bandwidth extension and dynamic reconfigurability. Full article

Lightweight polylactic acid (PLA LW) is a thermally activated foaming filament in which print temperature governs the extent of in situ gas expansion. This dual role, as a microstructural design parameter and a primary source of performance variability, motivates the three-phase, multi-factorial experimental program reported here. FDM-printed specimens of three infill topologies were investigated: orthogonal Cubic, hierarchical Subdivision Cubic (Sub-Cubic), and Gyroid triply periodic minimal surface (TPMS), each representing a distinct crystallographic symmetry class. A total of 504 specimens were fabricated across eight print temperatures (190–260 °C), three flow rate settings (70%, 80%, 100%), and four infill ratios (10%, 20%, 40%, 60%) and tested under quasi-static tensile and Charpy impact loading, with six replicates per condition distributed across two independent batches. One-way ANOVA confirmed a strong temperature effect on ultimate tensile strength (UTS) in Phase 1 (F(7,40) = 22.37, p < 0.001), while the Gyroid is uniquely temperature-sensitive in Phase 2 at 70% flow rate (F(1,8) = 14.30, p = 0.005) compared to the Cubic and Sub-Cubic, which exhibit no significant temperature effect in the 230–240 °C window. The Gyroid at 240 °C and 70% flow rate achieved the highest specific strength among Phase 2 configurations (20.9 MPa·cm³/g); Phase 3 demonstrated that Gyroid-specific strength decreases monotonically with the infill ratio, reaching 15.4, 12.3, and 8.8 MPa·cm³/g at 10%, 40%, and 60% infill, respectively. Cubic infill at 230 °C and 80% flow rate delivered the most reproducible performance (CV_UTS = 3.3%), while Sub-Cubic at the same condition combined high specific strength (20.5 MPa·cm³/g) with low variability (CV_UTS = 4.3%); both observations are quantified through a symmetry robustness index and a symmetry consistency indicator. Macrographic fractography supported geometry-controlled fracture: Cubic specimens fracture along layer interface mirror planes or ±45° shear planes depending on the thermal regime, while Gyroid specimens exhibit multi-plane, curvature-deflected fracture with no preferred crack propagation direction. These results indicate that geometric symmetry class is an important organizing factor for the mechanical response of FDM-printed PLA LW structures within the investigated parameter space. Full article

Accurate point-cloud registration is a fundamental task in intelligent 3D perception systems, including autonomous robotics, indoor digital twins, augmented reality, smart sensing, and scene-level spatial understanding. However, reliable registration in structured indoor environments remains challenging because repetitive architectural layouts, extensive planar regions, limited overlap, and rotational symmetries often weaken local geometric distinctiveness and lead to ambiguous correspondences. In addition, appearance inconsistency caused by illumination changes, exposure variation, and sensor-dependent color responses further degrades the reliability of cross-view matching. To address these issues, this paper presents MaCSE-Reg, an indoor registration method that combines explicit Manhattan-axis modeling with independent multi-color-space point-wise encoding. Rather than proposing a wholly new multi-modal paradigm, MaCSE-Reg builds on prior geometry–color fusion studies and focuses on two under-emphasized design choices for structured indoor scenes: (i) dominant orthogonal axes estimated from surface normals, regularized by an axis-consistency objective and gated by an axis-confidence score, and (ii) complementary RGB, Lab, and HSV representations learned through independent point-wise encoders for illumination-tolerant appearance matching. Geometric, structural, and color-aware features are adaptively fused, and a learnable multi-modal matching formulation is used to refine correspondences before weighted Procrustes pose estimation. Experiments on standard indoor registration benchmarks demonstrate that MaCSE-Reg improves registration robustness and pose accuracy under low-overlap conditions, repetitive structures, and illumination variations. The results support the value of this specific structural–appearance combination for intelligent indoor 3D perception while remaining complementary to existing geometry–color registration frameworks. Full article

Malignant pleural mesothelioma (MPM) is an aggressive pleural tumor associated with asbestos exposure. Poor clinical outcome of MPM is often driven by late-stage diagnosis due to non-specific clinical presentation, similarity to pleural lesions (e.g., inflammatory changes, metastatic adenocarcinoma), and limitations of current diagnostic methods. We employed Fourier transform infrared (FTIR) spectroscopy combined with convolutional neural networks (CNNs) to analyze formalin-fixed paraffin-embedded (FFPE) pleural tissue samples from patients with MPM, metastatic adenocarcinoma, pleural inflammation, and normal (healthy) pleura. Glycan analysis of FFPE normal pleura and MPM was performed using ultra-high-performance liquid chromatography (UPLC) and mass spectrometry (MS). Our FTIR-spectral analysis uncovered a strong spectral fingerprint of MPM that was especially apparent in the region typical for C-O and C-C stretches as well as local symmetry region typical for deformation vibrations of CH₂ and C-OH groups, all appearing in carbohydrates. Our orthogonal validation of these findings through a targeted glycomics approach using UPLC confirmed that the MPM N-glycome exhibits a distinct fingerprint that distinguishes it from normal pleural tissue. Through utilization of MS for identifying the exact structures of differentially expressed N-glycan peaks, we also identified two high-mannose N-glycan structures that show a specific biomarker potential for MPM and need to be examined in future studies. Full article

Graph neural networks (GNNs) have shown great advantages in collaborative filtering recommender systems due to their capacity to model user–item relationships through information propagation. However, traditional GNN-based recommenders often fail to distinguish nodes with the same local structure, leading to identical representations after propagation. Some studies address this issue by introducing positional encoding. However, most existing positional encoding approaches break the permutation and orthogonal symmetries of graph representations and degrade generalization ability. To address this limitation, we propose EPCF (equivariant positional collaborative filtering), a novel GNN model for collaborative filtering that introduces an equivariant propagation mechanism for Laplacian positional features. The proposed mechanism preserves equivariance of positional features under orthogonal transformations while maintaining the permutation equivariance inherent to graphs, which can improve generalization. The equivariant positional features are further leveraged to guide node embedding propagation. Our experiments on real-world datasets show that EPCF achieves better average performance than the evaluated baselines, achieving average improvements of 7.01% in Recall@20 and 1.17% in area under the curve (AUC) over the strongest baselines. Furthermore, integrating EPCF as a plug-in mechanism into five different GNN backbone models achieves improvements of 23.13% in Recall@20 and 2.14% in AUC across five datasets, demonstrating its generalization capability. Full article

Spectral fidelity is critical for accurate hyperspectral image (HSI) processing. A key characteristic of HSI data is the strong correlation between spectral bands, which manifests as structured symmetry in spectral covariance matrices. While global low-rank tensor decompositions leverage this spectral structure, they often neglect the significant spatial heterogeneity present in real-world scenes. To address this limitation, we propose a Region-Aware 3D Tensor Decomposition (RA-3DTD) framework that balances global spectral consistency with local spatial adaptation. Our approach first performs residual energy-based region detection to identify complex regions within the hyperspectral cube, and then applies localized Higher-Order Orthogonal Iteration (HOOI) specifically to those regions requiring enhanced detail preservation. This two-phase design incorporates global low-rank constraints with local spatial processing, improving denoising accuracy. Extensive experiments on four benchmark datasets (Pavia_80, Indian Pines, Salinas, and Pavia University) demonstrate the effectiveness of our method compared to five leading model-based baselines including BM3D, LRMR, NLR, LRTD, and FastHyDe. Our approach achieves a 1.33 dB increase in PSNR over a leading model-based competitor (FastHyDe) in complex urban scenes while maintaining strong structure fidelity as measured by SSIM and SAM metrics. Full article

Internal diameter atmospheric plasma spraying (ID-APS) commonly employs an inherently inclined nozzle configuration to overcome geometric interference in confined cylindrical components. This non-orthogonal deposition condition breaks the symmetry of the plasma jet and produces asymmetric thickness distributions, making uniform coating formation difficult to control using conventional models developed for planar or external spraying. In this study, a kinematic-based mathematical model was developed from experimentally measured single-path deposition data obtained under representative internal spraying conditions. A skew-normal formulation was introduced to describe the asymmetric cross-sectional profile, and a superposition framework was established to relate kinematics and geometric constraints to coating quality metrics, including mean thickness, profile uniformity, flatness, and lateral distance. The effects of kinematic parameters and workpiece geometric characteristics were systematically analyzed, and the resulting model was implemented on an internal cylindrical surface to predict spatial thickness evolution. Experimental validation was conducted at both macroscopic and microscopic scales through surface reconstruction and cross-sectional microscopy, confirming that the proposed approach can capture the main features of coating buildup and provide reliable estimates of thickness uniformity. The developed framework offers a practical tool for process design and quality control in ID-APS, reducing dependence on empirical parameter tuning and enabling more consistent thickness control on internal surfaces. Full article

Reconstructing building models from urban SAR tomography (TomoSAR) point clouds is often constrained by limited resolution, low positioning accuracy in elevation, as well as data incompleteness and artifacts caused by microwave imaging mechanisms. These challenges seriously restrict the extraction of high-accuracy building models with structural details from TomoSAR point clouds. This paper proposes a refined urban building modeling method that effectively utilizes structural priors, including directionality, orthogonality, and potential symmetry. First, a piecewise fitting strategy integrated with density-based segmentation is employed to iteratively estimate the main directions of the buildings and capture finer geometric variations of complex façade footprints than simple-plane approximations. Second, a roof extraction algorithm combining an adaptive Doug-las–Peucker approach with symmetry evaluation and constraints is developed to regularize roof outlines and repair data defects. Crucially, to handle extreme cases where roof data are entirely missing, a novel building width estimation method based on building shadow analysis is proposed. Experiments conducted on the SARMV3D-1.0 and SARMV3D-3.0 point cloud datasets demonstrate that the proposed method significantly enhances reconstruction accuracy and geometric fidelity in urban regions compared to state-of-the-art approaches. Full article

Discussion of consciousness and artificial intelligence has hitherto focused on the question of whether a large language model (LLM) exhibits signs of consciousness or understanding. This paper proposes to redirect attention elsewhere: not to the model itself, but to the orchestrating layer that governs the model—the backend, understood here as the collection of mechanisms (context management, retrieval, evaluation, planning, and tool-use control) that structure the model’s operation. We argue that the backend performs a function functionally analogous to the role of consciousness in the human brain: it stabilizes generative processes, directs attention, maintains context, and mitigates the entropic disintegration of thought. Consciousness fulfills this function through the phenomenal layer—qualia—which creates a persistent subjective “inner canvas”, used here as a metaphor for a more general multimodal phenomenal space. The backend fulfills it only algorithmically, without phenomenal quality. We further show that computation is an informationally conservative process in the sense of Shannon’s Data Processing Inequality (DPI), and therefore cannot increase Shannon information, even though it may yield novel or pragmatically useful recombinations of existing information. We conclude by proposing the hypothesis that consciousness constitutes a phenomenon orthogonal to computation—not an emergent property of complexity, but a qualitative leap into a different dimension. This hypothesis, which builds on the author’s prior work in this Special Issue and in Symmetry, is presented as a conceptual contribution rather than a formal theory, and may have implications for how future artificial intelligence research conceptualizes the limits of computational architectures. Full article

The interaction between light and chiral plasmonic metasurfaces provides a powerful mechanism for controlling polarization states at the nanoscale. Utilizing displacement Talbot lithography for large-area fabrication, we characterized the chiroptical response by measuring the evolution of Stokes parameters to quantify phase retardation between orthogonal polarization components. To elucidate the underlying physical mechanism, we employ a hybrid finite element method and rigorous coupled-wave analysis approach to investigate the behavior of the far-field and local-field configurations. Our results reveal that the phase shift is highly sensitive to symmetry-breaking features, where the interplay between different modes dictates the overall circular dichroism signal. Furthermore, the analysis of local field plots suggests specific contributions of plasmonic modes to the chiroptical response. We conclude that the phase shift effects, characterized via Stokes parameters and modal analysis, provide a robust metric for engineering chiroptical properties in these systems. This work establishes a fundamental framework for developing compact polarization-control elements and enhances the understanding of phase-modulated light-matter interactions in chiral plasmonic metasurfaces. Full article

Knowledge graph completion (KGC) is commonly studied under static settings, whereas real-world knowledge graphs evolve continuously with newly emerging entities, relations, and facts. In continual knowledge graph completion (CKGC), the model is required to absorb newly arrived knowledge while retaining historical prediction ability. A central difficulty is that incremental knowledge is heterogeneous: some information reflects reusable cross-session schema regularities, whereas other information corresponds to volatile session-specific factual updates. Existing CKGC methods usually model these signals within a single adaptation stream, which can increase interference during sequential learning. To address this issue, we propose a schema–session decoupled adaptation framework for session-aware CKGC. Specifically, the framework introduces a shared Schema-LoRA to accumulate reusable schema knowledge across sessions and a session-specific Session-LoRA to capture local instance-level updates in each session. To further improve adaptation stability, Orthogonal Gradient Projection and Session-EWC are applied to the instance-adaptation branch to reduce harmful gradient interference and excessive parameter drift during current-session training. In addition, we adopt a two-stage retrieve–rerank inference pipeline that combines lightweight candidate retrieval with language model reranking to balance effectiveness and efficiency. Experimental results on both static and continual KGC benchmarks show that the proposed framework achieves competitive static performance and improves top-rank prediction and final averaged performance over observed sessions under the session-aware CKGC protocol. From a functional-symmetry perspective, Schema-LoRA and Session-LoRA act as two additive adaptation branches around the frozen backbone, separately modeling reusable schema regularity and evolving factual variation. These findings suggest that schema–session decoupling is an effective design choice for session-aware continual knowledge graph completion. Full article