Search Results (551)

Conventional Pancharatnam–Berry (PB) phase metasurfaces operate within the two-dimensional SU(2) polarization space of the electric field, fundamentally limiting holographic multiplexing to two independent channels. Here, we propose and numerically demonstrate a four-channel holographic metasurface exploiting the recently discovered Riemann–Silberstein (RS) geometric phase arising from SU(4) polarization evolution in the full electromagnetic field space. The RS vector Ψ = E + icB unifies electric and magnetic fields into a four-dimensional polarization state space. By engineering bianisotropic Huygens meta-atoms with independently controllable electric-dipole orientation angle α and magnetic-dipole orientation angle ψ, four geometric-phase channels—labeled by the joint spin eigenstates |σ,κ⟩∈{|+,+⟩,|+,−⟩,|−,+⟩,|−,−⟩}—are simultaneously addressed from a single aperture. We develop the complete SU(4) transfer-matrix formalism and optimize four quasi-independent phase profiles using an extended Gerchberg–Saxton algorithm with a three-parameter (α,ψ,h) design library, where the pillar height h serves as a third degree of freedom to overcome the linear phase constraint inherent to the two-angle parameterization. Numerical simulations at 0.8 THz demonstrate simultaneous projection of four independent holographic images with mean diffraction efficiency 60.4% and inter-channel crosstalk below 3.2%, doubling the information capacity of conventional dual-channel PB holograms. An intrinsic ~24× common-mode noise suppression arising from electromagnetic duality symmetry is also demonstrated. This work establishes a direct link between fundamental electromagnetic symmetry and high-capacity wavefront engineering. Full article

We develop an operator-theoretic framework for extreme events in reflexive financial systems, identifying inverse evolution—the deterministic contraction of the manifold of admissible futures—as the structural mechanism underlying crashes and melt-ups. The interpolation constraint, which forces all analytical continuations to match the terminal empirical price, resolves the apparent continuum of stochastic paths into a discrete, countable spectrum of metastable futures. This countable manifold is stabilized by a spectral regularizer that preserves dimensionality through a “wait-and-adjust” re-categorization logic. Within this unified structure, we distinguish three pathways to collapse: (i) the Black Swan, a crisis of spectral weight; (ii) the projection operator, a rank-reducing projection that restores symmetry by exclusion; and (iii) the reactivation operator, a breakdown of spectral truncation that reactivates suppressed behaviour with large emergent return (Heavy) modes and forces the system into a regime of manifold resumption. Central to all modalities is the emergent return, an effective mass parameter whose sign determines whether collapse manifests as reflexive contraction (crash) or reflexive amplification (melt-up). The resulting dynamics exhibit cross-domain universality. The same operator grammar governs geopolitical choke-points, institutional purges, technological monopolies, retail-driven short squeezes, and other macrosystems in which dimensionality is either forcibly reduced or abruptly restored. Full article

Symbolic execution of embedded systems faces path explosion, Satisfiability Modulo Theories (SMT) solver bottlenecks, interrupt nondeterminism, and environment modeling complexity. Recent artificial intelligence (AI)-guided approaches using reinforcement learning, graph neural networks, and large language models improve exploration efficiency, yet all reason over raw symbolic states and ignore structural equivalences that arise from symmetry in embedded software. This paper presents S³E, a formal framework that organizes symbolic execution around equivalence classes of states under symmetry transformations. Symmetry groups partition the state space into orbits, and exploration proceeds over canonical representatives within quotient transition systems. Symmetry-aware AI components operate on orbit representatives rather than raw states. Four theoretical results support the framework: orbit preservation, quotient soundness, canonicalization correctness, and constraint reuse correctness. An illustrative case study based on a FreeRTOS-like scheduling environment shows how symmetry reduction collapses equivalent states into orbits, with the potential for reductions that scale factorially with symmetric components. S³E is a theoretical framework; a toy-model prototype validates the core quotient-exploration and constraint-caching mechanis, while empirical evaluation on production firmware remains future work. Full article

PT symmetry-based wireless power transfer (WPT) systems can achieve nearly constant output power and transfer efficiency within a coupling region, but their practical implementation is limited by strict parameter matching and poor adaptability to unequal load losses. To overcome these limitations, this paper proposes a global quasi-PT symmetric modeling method for a single-transmitter, dual-constant-power receiver WPT system. Unlike classical PT-symmetric models that impose strict symmetry on individual receiver branches, the proposed model treats the entire secondary side as an equivalent subsystem. Therefore, quasi-PT symmetry is established by approximately balancing the total secondary loss with the primary gain, rather than by enforcing identical branch losses. Based on this global model, the frequency-splitting behavior is analyzed, the strong-coupling condition is derived, and the permissible ranges of the quality factor and inductance are obtained. Theoretical calculations show that the allowable ranges of both $Q$ and $L$ under quasi-PT symmetry are approximately three times wider than those under classical PT symmetry, significantly reducing the requirement for parameter precision. Further analysis demonstrates that, under global quasi-PT symmetric strong coupling, the system can maintain near constant efficiency even when the two receiver branches have unequal losses. This relaxes the conventional constraint of precisely matched receiver losses and improves the flexibility of multi-load WPT operation. In addition, for the secondary coplanar coils, the transition from far-field coupling to near-field coupling is investigated, and a boundary-distance formula is derived. When the distance between the secondary coils is smaller than this boundary distance, the influence of cross-coupling on power distribution is further analyzed, providing guidance for receiver coil layout optimization. Experimental results verify the proposed theoretical model and analysis. The proposed global quasi-PT-symmetric method improves parameter tolerance, supports unequal receiver losses, and offers a practical design framework for robust multi-load WPT systems under variable operating conditions. Full article

Reconstructing 3D building models from point clouds acquired by UAV sensors remains challenging due to irregular building geometries and sensor noise. This paper proposes an unsupervised, geometry-oriented reconstruction method based on the line-symmetric bilateral point distribution features. The method constructs baselines from farthest point pairs within local bounding spheres, then applies dual-parameter constraints (point–line distance and point statistics on both sides of a line of symmetry) combined with density peak ranking to detect building corners without training data. Evaluations show that the method reduces Cloud-to-Mesh error by 15–20% over Polyfit, DIF method, and PolyGNN, while retaining fine details in complex L-shaped and U-shaped buildings. Reconstruction quality remains stable under 0.05 m Gaussian noise. The training-free, lightweight design enables scalable, automated 3D building reconstruction for digital-twin applications. Full article

The electromagnetic coupling phase at the complex resonance pole is a fundamental property of nucleon excitations. However, its extraction from pion photoproduction data remains model-dependent, particularly for the $\Delta \left(1232\right)$ resonance, where modern multichannel analyses report helicity amplitude phases ranging from $+3°$ to $-18°$. In this Letter, we present a largely model-independent geometric S-matrix formalism that provides a physical constraint for this ambiguity. By imposing Watson’s final-state interaction theorem, a direct consequence of S-matrix unitarity and time-reversal symmetry, on the real energy axis and performing an analytic continuation, we isolate the kinematic threshold barriers of the photoproduction ($k·q$) and elastic ($q^3$) amplitudes. For the dominant $M_{1+}$ multipole transition of the $\Delta \left(1232\right)$, our method yields a kinematically constrained prediction of ${\varphi }_{EM}={-8.5°}_{-1.0°}^{+0.6°}$ for the electromagnetic residue phase. This geometric constraint explains the numerical results of coupled-channel phenomenological fits, validating the extractions by the SAID and Bonn–Gatchina groups, and establishes a theoretical benchmark for evaluating resonance properties. Full article

In industrial trajectory planning and real-time motion control, quintic B-splines are widely used for corner smoothing owing to their local support and high-order continuity. However, existing evaluation methods mainly rely on basis-function recursion or the de Boor algorithm, with limited attention paid to the analytical properties of fixed-topology continuity-constrained structures. This study reveals that, under geometric symmetry and C³ continuity constraints at the junction points, higher-order derivative control-point structures undergo progressive geometric degeneration, whereby second- and third-order derivatives reduce to one-dimensional forms governed by a single direction. Based on this degeneration property, a closed-form reconstruction method for fixed-topology quintic B-spline corner smoothing is developed, yielding unified closed-form expressions for curve position and first- to third-order derivatives. Mathematical analysis proves equivalence between the proposed reconstruction and the original quintic B-spline representation. Numerical validation and efficiency evaluation demonstrate machine-precision consistency with conventional B-spline evaluation while achieving an approximately 3–7-fold speedup in curve and derivative evaluation. System-level trajectory-planning simulations further confirm reduced geometric computation load. The proposed method provides an efficient analytical evaluation framework for real-time trajectory planning and demonstrates how continuity constraints can be exploited to derive efficient analytical spline representations. Full article

The KdV–Burgers equation $u_t+u{u}_x-v{u}_{xx}+\beta u_{xxx}=0$ models the interplay of nonlinearity, dispersion and dissipation. Through the potential $u=v_x$, a Lagrangian density is constructed for the resulting potential system. Application of Noether’s theorem yields an infinite-dimensional symmetry $V=f(x,t)\partial v$, where f satisfies the linearized equation $f_t-v{f}_{xx}+\beta f_{xxx}=0$. This symmetry generates an infinite family of continuity equations of the form $D_{t}T+D_{x}X=0$ with $T=f(x,t)$ and $X=-f_{x}u+v{f}_x-\beta f_{xx}$. For ν > 0, these relations constitute linear potential balance laws rather than classical conservation laws, as the density T depends explicitly on the auxiliary field f and on time. In the inviscid limit ν = 0, the family reduces to the classical KdV conservation hierarchy. High-accuracy spectral simulations confirm the validity of these identities up to discretization error. Full article

Autonomous vehicles operating at signalized intersections face fundamental challenges arising from queue dynamics, signal-phase transitions, and tightly coupled multi-vehicle interactions. Conventional motion-planning methods, which rely primarily on instantaneous perception, are inherently reactive and struggle to reason about short-term traffic evolution. This paper presents a Transformer-based predictive motion-planning framework that embeds short-term traffic state prediction directly into the structure of the planning problem. A lightweight spatial–temporal Transformer model is designed to forecast traffic occupancy, queue evolution, and interaction patterns using historical trajectories, signal-phase information, and road topology. By converting predicted traffic dynamics into explicit spatial–temporal constraints, a hierarchical motion planner jointly optimizes path geometry and speed profiles through dynamically constructed feasible corridors. The proposed framework is evaluated using a joint SUMO–CARLA simulation platform under realistic traffic conditions derived from real-world datasets, including pNEUMA and CitySim. The experimental results across straight-through, queueing, and turning scenarios show that prediction-aware planning significantly reduces high-risk driving time and intersection travel time while maintaining stable real-time computational performance. Beyond scenario-level improvements, the results indicate that transforming traffic prediction into planning constraints provides a generalizable paradigm for proactive, feasibility-aware autonomous driving at signalized intersections. From a methodological perspective, the proposed framework can be interpreted through the lens of symmetry and asymmetry in intelligent transportation systems: the conventional symmetric decoupling between prediction and planning modules is deliberately broken by embedding predicted traffic states as time-varying, directionally asymmetric constraints, while the permutation symmetry of the multi-head attention mechanism is preserved over lane-segment tokens to provide a structured inductive bias for traffic state forecasting. This symmetry-aware design highlights how controlled symmetry breaking in modeling and optimization can yield safer, more efficient, and more adaptive autonomous driving behaviors in signalized urban environments. Full article

In oil and gas field development, accurate prediction of the near-wellbore stress distribution is important for ensuring wellbore integrity, particularly in tight shale reservoirs where the medium can be approximated as nearly homogeneous. The large stress gradient and multi-physics coupling of the near-wellbore stress field are key factors limiting high-precision prediction. Physics-informed neural networks (PINNs) allow integration of governing physical laws into network training processes. However, conventional PINNs cannot accurately capture local stress concentration features and lack the ability to generalize across different parameter settings. This study uses the near-wellbore stress concentration problem as an example to improve the prediction accuracy of PINNs through the incorporation of additional physical constraints and modifications to the network architecture. Furthermore, the method is extended to a physics-informed Deep Operator Network (PI-DeepONet) framework with enhanced generalization capability. The results show that, after introducing the proposed constraints, the stress field exhibits strict biaxial symmetry. The angle-adaptive residual module decreases the near-wellbore stress error from about 40–45% to less than 5%. Based on this method, the near-wellbore stress field under different in situ stress combinations can be predicted instantaneously without retraining. Full article

In recent years, deep convolutional neural networks (DCNNs) have made strong progress on single-image super-resolution (SISR). Most of them work in a fully supervised way: they learn a non-linear mapping from a low-resolution (LR) image to its high-resolution (HR) version. The main problem is that this needs ground-truth HR images for supervision, which makes these methods hard to use widely. To ease this problem, we propose a weakly supervised framework named AASPNet (Adaptive Attention-Based Symmetric Progressive Network). It has two parts: an upsampling process and a downsampling process. Each part is built from several training units, but only the first unit needs supervision. In other words, with only $\times 2$ supervision, AASPNet can produce HR results at $\times 4$ and $\times 8$. The symmetry between the two parts is used in two ways. First, it gives consistency constraints that help recover more accurate HR images. Second, a cross self-supervision recovers HR images in a weakly supervised way, using both image and feature consistency between the upsampling and downsampling parts. We also add an adaptive attention strategy to pick out useful features, so the HR images get better. Experiments on several benchmark datasets show that our weakly supervised AASPNet reaches results that are close to state-of-the-art fully supervised DCNN methods. Full article

To address the lack of comprehensive quality evaluation indicators for heat treatment after bilateral induction hardening of high-speed linear guide rails, this study draws on the concept of geometric tolerance to innovatively propose a quantitative evaluation indicator for the “symmetry” of the hardening layer depth profile, and conducts non-destructive evaluation research based on ultrasonic transverse wave backscattering technology. Aiming at the complex cross-sectional profile of the guide rail and the problem of anisotropic acoustic scattering, a multi-dimensional symmetry characterization framework driven jointly by “local pair-wise tolerance zone constraints” and a “global equivalent case depth metric” was established. This dual-driven evaluation framework effectively eliminates the evaluation loophole of “false symmetry” caused by the mutual cancellation of opposite positive and negative local deviations. By constructing an equivalent hardened layer model based on discrete feature point mapping, the interference of non-parallel complex curved surfaces on traditional continuous B-scan imaging is successfully circumvented, achieving stable characterization of the overall hardening layer coverage under specific process parameters. A 15 MHz water-immersed point-focusing ultrasonic transverse wave oblique incidence detection system was developed, paired with a self-designed spring-loaded passive conformal tracking clamping mechanism for continuous automated scanning. Experimental results demonstrate that the overall equivalent symmetry of the tested guide rail specimens remains above 98%. Verified by the metallographic Vickers hardness gradient method, the equivalent relative error between the ultrasonically measured case depth and the physical case depth is only 1.0% and 1.6%. This proves that this non-destructive evaluation method possesses excellent measurement accuracy and holds significant industrial value for online non-destructive monitoring. Full article

Programmable electromagnetic environments, including reconfigurable intelligent surface (RIS)-assisted systems, are often described in terms of physical or controllable degrees of freedom. Such counts, however, do not determine which channel or operator directions can actually be distinguished by a finite measurement architecture. This paper develops an operator-space formulation of observable degrees of freedom for programmable propagation systems. We distinguish three nested layers: the physical operator space generated by the family of physically admissible propagation operators, the effective operator space selected by architectural constraints, and the observable subspace induced by a finite probing architecture. Once the effective space is fixed, observability is characterized by the spectrum of the associated measurement Gram operator. To remove arbitrary amplitude scaling, we introduce a common probe-energy normalization and define the resolution-dependent observable dimension $N_{\mathrm{obs}}\left(\eta \right)$ from the normalized Gram spectrum. The same spectrum also yields an observability condition number, which quantifies the stability of the visible subspace. We then extend the construction to symmetry-resolved operator spaces, showing how invariant probing can create sectorial blind subspaces and how controlled symmetry breaking produces second-order restricted visibility inside the original blind subspace. The mathematical ingredients are standard finite-dimensional tools from operator theory, frame theory, representation theory, and matrix concentration; the contribution is their integration into a measurement-oriented degrees-of-freedom framework for programmable electromagnetic environments. Numerical experiments with normalized probing families, sectorial decompositions, controlled symmetry breaking, and a canonical narrowband RIS-inspired model illustrate that architectures with the same effective dimension and probing budget can exhibit substantially different observable dimensions and conditioning. The results support the view that practical electromagnetic design should optimize not only the number of accessible modes or control states, but also the Gram geometry through which those directions are measured. Full article

This study develops an interval-valued q-spherical fuzzy rough set TOPSIS framework (IVq-SFRS-TOPSIS) for multi-criteria group decision-making when expert judgments contain interval uncertainty, neutrality, and granular indiscernibility. The revised framework clarifies the relationship between interval-valued q-spherical and interval-valued T-spherical fuzzy models, defines admissible approximation operators over compatible domains, and introduces a radial projection step that guarantees closure under the IVq-SFN constraint whenever component-wise extrema would otherwise violate it. The proposed framework provides a mathematically balanced representation of interval-valued q-spherical fuzzy information, reflecting the concept of symmetry and supporting reliable group decision-making under uncertainty. The TOPSIS procedure is then formulated through expert aggregation, benefit–cost normalization, entropy-based criteria weighting, ideal-solution distance calculation, and closeness-coefficient ranking. The method is illustrated through a sustainable smart city development case using four AI-based alternatives and six criteria. Rather than claiming unconditional superiority, the revised comparative and sensitivity analyses examine how the ranking changes under alternative fuzzy decision models, different q values, perturbations to criteria weights, and perturbations to the decision matrix. The results indicate that the proposed framework provides an interpretable rough-boundary representation and a reproducible ranking mechanism for complex MCDM problems under interval-valued q-spherical uncertainty. Full article

The density dependence of nuclear symmetry energy remains one of the key uncertainties in contemporary nuclear physics, with significant implications for the structure of exotic nuclei, the dynamics of heavy-ion collisions, and the properties of astrophysical objects such as neutron stars and core-collapse supernovae. However, extracting robust constraints requires observables that are minimally affected by final-state interactions and are reliably predicted by transport models. This review synthesizes recent theoretical and experimental advancements in constraining the symmetry energy by leveraging isospin diffusion in heavy-ion reactions within the Fermi energy domain. Recent results from the INDRA-FAZIA collaboration, including isospin transport ratio data and Boltzmann–Uehling–Uhlenbeck (BUU) transport model calculations, are highlighted. Confidence regions for the symmetry energy are extracted from isospin transport ratios and isospin diffusion currents by utilizing state-of-the-art nuclear functionals, including both ab initio and phenomenological approaches, with a particular focus on the density regions probed by these experiments. The resulting constraints will aid future Bayesian studies of the nuclear equation of state and contribute to a more unified understanding of dense matter in both terrestrial experiments and astrophysical environments. Full article