Brain tumor segmentation requires precise delineation of hierarchical structures from multi-sequence MRI. However, existing deep learning methods primarily rely on visual features, showing insufficient discriminative power in ambiguous boundary regions. Moreover, they lack explicit integration of medical domain knowledge such as anatomical semantics and geometric topology. We propose a knowledge-guided framework, Synchronized Tri-modal Prior Fusion (STPF), that explicitly integrates three heterogeneous knowledge priors: pathology-driven differential features (T1ce-T1, T2-FLAIR, T1/T2) encoding contrast patterns, unsupervised semantic descriptions transformed into voxel-level guidance via spatialization operators, and geometric constraints extracted through persistent homology analysis. A dual-level fusion architecture dynamically allocates prior weights at the voxel level based on confidence and at the sample level through hypernetwork-generated conditional vectors. Furthermore, nested output heads structurally ensure the hierarchical constraint ETsubseteqTCsubseteqWT. STPF achieves a mean Dice coefficient of 0.868 on the BraTS 2020 dataset, surpassing the best baseline by 2.6% points (3.09% relative improvement). Notably, five-fold cross-validation yields coefficients of variation between 0.23% and 0.33%, demonstrating stable performance. Additionally, ablation experiments show that removing topological and semantic priors leads to performance degradation of 2.8% and 3.5%, respectively. By explicitly integrating medical knowledge priors—anatomical semantics and geometric constraints—STPF improves segmentation accuracy in ambiguous boundary regions while demonstrating generalization capability and clinical deployment potential.Supplementary informationThe online version contains supplementary material available at 10.1186/s12880-026-02189-3.

HighlightsWhat are the main findings?A training-free geometric method is proposed for LiDAR point cloud registration on resource-constrained edge platforms.The modular pipeline synergistically combines asymmetric candidate expansion with uncertainty-aware refinement to effectively handle sensor noise and sparse correspondences.What are the implications of the main findings?The framework provides a plug-and-play solution for real-time robotics perception, bridging the gap between theoretical accuracy and practical deployment on low-power hardware.The results validate that optimized geometric methods remain superior in interpretability and generalization for industrial LiDAR sensing under challenging low-overlap conditions.Accurate LiDAR point cloud registration on resource-constrained edge platforms is a prerequisite for intelligent robotics and industrial automation, yet it remains challenging because low-overlap matching, false correspondences, and fine alignment must be handled under limited computing budgets without GPU acceleration. While learning-based methods have advanced the field, their heavy hardware dependency and training requirements often hinder their practical deployment on mobile edge devices. To bridge this gap, this paper proposes GeoRescue, a training-free geometric registration framework designed for high-precision perception under stringent hardware limits. The method consists of three modular stages: Asymmetric Correspondence Expansion (ACE), which enlarges the candidate correspondence set to reduce the loss of true matches; Dynamic Geometric Topology Gating (DGTG), which suppresses false matches through distance-consistency-based hypothesis filtering; and Uncertainty-Aware Manifold Refinement (UAMR), which improves fine alignment by explicitly modeling local anisotropic noise via covariance-guided optimization. Experiments on 3DMatch, 3DLoMatch, and KITTI show that GeoRescue achieves registration recall rates of 84.84% and 41.27%, respectively, and a 94.95% success rate on KITTI. Remarkably, the framework matches the accuracy of high-capacity learning models while running on a GPU-free, 15 W edge CPU platform (Intel Core i5-8265U). These results indicate that GeoRescue provides a deployment-ready solution with an optimal efficiency–accuracy trade-off for LiDAR sensing and robotics perception in complex, real-world scenarios.

Ultrafast femtosecond lasers, with their unique "cold ablation" characteristics, exhibit broad application prospects in the machining of complex hard surfaces of high-end aerospace equipment (e.g., face gears). However, existing femtosecond ablation prediction models are mostly based on the assumption of normal plane irradiation, severely ignoring the drastic variations in the dynamic angle of incidence (θ) caused by complex three-dimensional geometric topologies. Addressing this theoretical gap, this paper innovatively proposes a 3D nonlinear ablation prediction model coupling the dynamic evolution of local incident angles and the multi-pulse incubation effect. First, the spatial incident angles at the micro-nodes of the face gear tooth surface are extracted via a discrete meshing method. Subsequently, by integrating the dynamic polarization reflectivity of the 18Cr2Ni4WA alloy with the spatial projection distortion of the Gaussian beam, closed-form analytical solutions for the elliptical spot area, the effective material removal area, and the central pit depth-incorporating the effective penetration depth-are derived. Simultaneous five-axis laser machining experiments and computer vision-based morphological feature extraction (eccentricity quantification) confirm that: within the range of small to medium incident angles ([Formula: see text]), the experimentally measured morphological evolution is highly consistent with the theoretical model ([Formula: see text]). However, approaching the extreme large angle ([Formula: see text]), the ablation spot severely degrades into an asymmetrical "spindle" shape, and the machining depth experiences an anomalous nonlinear plunge. Combined with ultrafast dynamic analysis, it is revealed that this extreme morphological distortion is primarily attributed to the asymmetrical plasma inverse Bremsstrahlung shielding induced by the large angle, as well as the hindered recast layer expulsion dynamics under high-frequency thermal accumulation. This study profoundly reveals the microscopic evolution laws of laser-material spatiotemporal coupling on complex continuous surfaces, providing a solid theoretical foundation for adaptive trajectory and energy compensation strategies in future multi-axis femtosecond laser precision modifications.

Satellite images provide a wealth of information that is used in various applications such as urban planning, environmental monitoring and terrain analysis. However, converting raw satellite data into a grid image suitable for these applications remains a challenge. this study proposes a three-stage methodology that integrates advanced image processing techniques to transform satellite image surfaces into a mesh image to enhance the utility in e geometric topology. The first phase involves applying intelligent detectors technology to identifying the edges of objects within the satellite image. By detecting high-density change points which are characteristic points at edge intersections especially at corners or angular features formed by objects. In the second stage, these features are processed using SIFT which ensures that scale-invariant features are extracted across different images. The final stage utilizes Delaunay triangulation to create the mesh, effectively converting the satellite image surfaces into a mesh representation. This mesh representation is a type of graph consisting of nodes (representing extracted features) and edges (connecting these nodes). Such a representation opens up new possibilities for analysis and study and providing an organized and detailed depiction of the Earth's surface. The mesh image produced through this methodology can be applied to numerous scientific and practical applications, bridging the gap between raw satellite data and its practical utilization in various fields. The satellite images used in this study are high-resolution raster optical images, commonly employed in applications such as urban mapping, environmental monitoring, and geographic analysis. These types of images are typically captured by satellites like Landsat. Such raster optical imagery provides detailed visual information that is essential for analyzing surface features and patterns. The results demonstrate the effectiveness of the proposed system, achieving a Ki metric value of (104.46) compared to (78.51) in previous approaches, indicating superior mesh quality

The rapid transition from backyard to industrial livestock production has profoundly altered the geochemical characteristics of agricultural wastes, yet conventional risk assessment frameworks remain predominantly concentration-oriented and lack the capacity to resolve structural imbalances within the heavy metal suite. This study proposes a novel two-dimensional geometric fingerprinting framework to quantify the decoupling between pollution magnitude and structural distortion in livestock manure. A total of 204 manure samples were collected from a representative intensive farming region in the Sichuan Basin, Southwest China. Eight heavy metals and pH were analyzed, and concentrations were dynamically normalized using the pH-dependent thresholds defined in the Ministry of Ecology and Environment of the People's Republic of China standard GB 15618-2018. Two geometric descriptors were derived from radar projections of risk quotients: the comprehensive risk area (Sarea), representing cumulative pollution magnitude, and the coefficient of variation (CV), quantifying fingerprint distortion. Results revealed a significant expansion of pollution magnitude under industrial farming, accompanied by intensified structural imbalance, primarily driven by excessive Cu and Zn inputs. Principal component analysis further confirmed a clear structural divergence between backyard and industrial systems. Critically, no significant linear correlation was observed between Sarea and CV, demonstrating a stochastic decoupling between total load and geochemical structure. This dual-indicator framework reveals that pollution magnitude does not inherently predict structural distortion, highlighting the inadequacy of single-metric assessments. By integrating dynamic regulatory normalization with geometric topology, the study establishes a structural early warning paradigm for manure management.

Abstract End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology. Our main result is that every end-space can be topologically represented by a special order tree. Our main proof ingredient is a structure theorem that we introduce, which carves out the order-tree-like structure of any graph in such a way that there is a natural bijection between the ends of the graph and the limit-type down-closed chains of the order-tree.

Mineral dissolution in fractured-pore rocks is a critical process in subsurface applications, including petroleum extraction, geothermal energy development, and carbon dioxide sequestration. Understanding the evolution of geometric topology and permeability is essential for scaling up research and guiding engineering design. In this study, we integrated a linear Boolean model with a self-affine rough surface approach to generate synthetic fracture-pore rock structures with varying degrees of matrix geometrical heterogeneity. The dual-distribution function lattice Boltzmann method was employed to simulate the mineral dissolution and quantify permeability evolution across a broad spectrum of Péclet (Pe) and Damköhler (Da) numbers. Our results indicate that changes in mechanical aperture and reactive surface area are primarily governed by the Da number. Furthermore, under high Pe and Da conditions, increased matrix heterogeneity leads to nonlinear alterations in permeability. Finally, we proposed a predictive diagram for permeability evolution during mineral dissolution under diverse matrix heterogeneity scenarios.

The spontaneous internalization of electrostatic interactions by large atomic models in molten salts

Abstract To explore the independent influence of topological perforation on electromechanical performance, this study introduces a novel iso-volumetric perforation strategy for honeycomb and origami-based piezoelectric cellular structures. By strictly maintaining a 30% volume fraction, we decouple geometric topology from relative density. Finite element analysis reveals that transversely perforated honeycombs surprisingly exhibit superior stiffness compared to intact configurations, a phenomenon driven by the dominant wall thickening effect. Conversely, axial perforations significantly enhance longitudinal piezoelectric coupling, achieving a coefficient of 8.31 C/m 2 . These findings demonstrate that strategic perforation effectively optimizes the trade-off between mechanical stiffness and sensitivity for next-generation sensors.

The internal flow of nozzles governs the performance and stability of aerospace and high-speed systems, making accurate and efficient flow prediction essential. However, traditional computational fluid dynamics (CFD) approaches are still limited by prohibitive computational costs and inflexibility under variable geometric configurations. To address these challenges, this study proposes a dual-end convolutional squeeze-and-excitation (DE-ConvSE) adapter U-Net for rapid nozzle flow prediction, in which a U-Net backbone is augmented with DE-ConvSE adapters. The network integrates geometric topology encoding and boundary condition mapping to accurately reconstruct velocity, pressure, and temperature distributions. To enable efficient adaptation to previously unseen nozzle geometries, an adapter-based incremental learning strategy is introduced, where the pretrained backbone is frozen and only a small set of adapter parameters is updated. This strategy substantially improves the generalization capability of the model while maintaining high computational efficiency and mitigating catastrophic forgetting. Validation on a convergent–divergent nozzle benchmark demonstrates that the proposed approach achieves high reconstruction accuracy, with maximum symmetric relative errors below 9.14% and mean absolute errors below 5.21%. Compared with CFD solvers, the proposed method is mesh-free and provides orders-of-magnitude acceleration, highlighting its potential for real-time flow prediction and design optimization in advanced fluid dynamic systems.

Flat bands, electronic states with nearly dispersionless energy-momentum structure, provide fertile ground for unconventional quantum phases. Recent observations of flat bands at the Fermi level in kagome metals open the possibility of unifying topology and correlation-driven heavy-fermion physics. Here we show that topology and heavy-fermion correlations coexist in the layered kagome metal YbCr6Ge6. At high temperatures, an intrinsic kagome flat band-arising from frustrated hopping on the kagome lattice-dominates the Fermi level. Upon cooling, localized Yb 4f-states hybridize with the topological kagome flat bands, transforming this state into momentum-independent Kondo resonance states across the entire Brillouin zone. Topological analysis of the hybridization gaps reveals filling-tunable weak and strong topological Kondo-insulating regimes, and identifies a topological Dirac-Kondo semimetal. Taken together, these results identify YbCr6Ge6 as a prototype of a topological heavy-fermion system and a platform where geometric frustration, strong correlations, and topology converge, with broad implications for correlated quantum matter.

High-Resolution Range Profile (HRRP)-based space object classification is severely limited by aspect sensitivity. Inspired by the intrinsic complementarity between HRRP and LiDAR point clouds, this work investigates the feasibility and effectiveness of fusing these two modalities to address this limitation. We propose the Point-HRRP-Net framework. This framework employs dual-stream extractors to independently encode HRRP electromagnetic signatures and 3D point cloud geometric topologies. Subsequently, a Bi-Directional Cross-Attention (Bi-CA) mechanism is designed to fuse the two modalities. To enable information interaction, this mechanism utilizes point-to-point attention to correlate radar scattering features with 3D geometric points, thereby constructing a comprehensive target representation. Due to data scarcity, we constructed a paired simulation dataset for evaluation. Experimental results demonstrate that the proposed framework consistently outperforms its constituent single-modality baselines. The model achieves 57.67% accuracy on the 180 split and demonstrates generalization capability to unseen viewpoints. Ablation studies further validate the efficacy of the Bi-CA mechanism and the selected feature extractors. Finally, we assess the potential sim-to-real discrepancies and evaluate deployment feasibility across various hardware platforms.

We develop a topological-combinatorial framework applying classical Ramsey theory to systems of arcs connecting points on Jordan curves and their higher-dimensional analogues. A Jordan curve Λ partitions the plane into interior and exterior regions, enabling a canonical two-coloring of every arc connecting points on Λ according to whether its interior lies in Int(Λ) or Ext(Λ). Using this intrinsic coloring, we prove that any configuration of six points on Λ necessarily contains a monochromatic triangle, and that this property is invariant under all homeomorphisms of the plane. Extending the construction by including arcs lying on Λ itself yields a natural three-coloring, from which the classical value R3,3.3=17 guarantees the appearance of monochromatic triangles for sufficiently large point sets. For infinite point sets on Λ, the infinite Ramsey theorem ensures the existence of infinite monochromatic cliques, which we likewise show to be preserved under arbitrary topological deformations. The framework extends to Jordan surfaces and Jordan–Brouwer hypersurfaces in higher dimensions, where interior, exterior, and boundary regions again generate canonical colorings and Ramsey-type constraints. These results reveal a general principle: the separation properties of codimension-one topological boundaries induce universal combinatorial structures—such as monochromatic triangles and infinite monochromatic subsets—that are stable under continuous deformations. The approach offers new links between geometric topology, extremal combinatorics, and the analysis of constrained networks and interfaces.

The dynamic behavior of relaxed steel wire ropes under slowly varying pulse loads is dominated by the geometric wave impedance effect caused by the helical geometric topology. This study proposes a numerical analysis framework based on high-fidelity parametric solid modeling and implicit dynamics to investigate a Seale-type 6×19S-WSC steel wire rope. Under baseline conditions without pretension and friction, the helical structure forces significant modal conversion and geometric scattering of the axially incident waves, producing an energy attenuation effect akin to “geometric filtering”. Parametric analysis varying the core wire diameter reveals that the helical structure causes the axial wave speed to decrease by orders of magnitude compared to the material’s inherent wave speed. Furthermore, changes in core wire size induce a non-monotonic variation in the dynamic response, revealing a competitive mechanism between overall stiffness increase and a “dynamic decoupling” effect caused by interlayer gaps. This study confirms the dominant role of geometric wave impedance in the dynamic performance of relaxed steel wire ropes.

Fragment-based molecular generation has emerged as a promising paradigm in structure-based drug design (SBDD), deriving effective compounds with advanced properties, including chemical validity, synthetic feasibility, pharmacological relevance, etc. However, existing approaches often struggle with generating molecules which can both conform to 3D structural constraints and retain chemical plausibility. This is largely due to the fact that prior works often treat scaffolds and R-groups of molecules indiscriminately, overlooking the distinct semantic roles played by scaffolds and R-groups. Specifically, the scaffold serves as the rigid structural backbone that determines the global geometric topology and binding pose, whereas R-groups act as functional substituents responsible for fine-tuning local physicochemical interactions. Therefore, in this work, we propose fragment-based dual conditional diffusion (FDC-Diff), a novel dual conditional diffusion framework that integrates chemical priors and structural cues for fragment-based molecular generation. Unlike traditional de novo methods that generate atoms sequentially, FDC-Diff decomposes the molecule generation process into two semantically complementary stages. Given the protein pocket and an initial fragment, in the first stage, a spatially constrained scaffold is constructed to capture the global molecular topology. In the second stage, R-groups onto the obtained scaffold are elaborated to capture local semantics to further refine molecular properties. To ensure synthetic accessibility, initial fragments and scaffold-modification hierarchy are derived from curated reaction rules, and a physical-chemistry-inspired refinement step is applied to optimize final conformations. Experimental results on multiple SBDD benchmarks demonstrate that FDC-Diff achieves state-of-the-art performance in terms of comprehensive evaluations. Furthermore, our model excels at producing chemically valid, spatially compatible, and pharmacologically relevant molecules, suggesting its potential as a feasible tool for fragment-based drug design.

The Shortest Vector Problem (SVP) is a fundamental challenge in computational number theory and lattice-based cryptography, with critical implications for cryptanalysis, coding theory, and computational geometry. Classical algorithms such as enumeration, sieving, and basis reduction techniques either suffer from exponential time complexity or prohibitive memory demands. This work presents a novel SVP-solving framework rooted in sheaf theory and the geometry of Etalé spaces, providing a categorical and topological interpretation of vector localization, difference computation, and sieving procedures. By embedding the lattice problem into a manifold structure and defining fractional coordinate spaces via exact sequences, we develop a generalized coboundary map formulation that subsumes classical vector-difference methods used in sieving. Orthogonalization through algorithms such as LLL reduces search complexity, while the Etalé-space-based sieving allows for localized, memory-aware updates. Complexity analysis shows that while the algorithm retains exponential dependence on lattice dimension in the worst case, careful selection of subset coverings and coarse-graining strategies can reduce memory requirements from exponential to polynomial scaling. The proposed approach bridges the gap between geometric group theory, algebraic topology, and algorithmic lattice reduction, offering a mathematically rigorous and computationally viable method for SVP in moderate dimensions.

Abstract We undertake to determine the homotopy type of gyrations of sphere products and of connected sums, thereby generalising results known in earlier literature as ‘Fico's Lemmata’ which underpin gyrations in their original formulation from geometric topology. We provide applications arising from recasting these results into the modern homotopy theoretic setting.

Extracting high-fidelity mesh surfaces from Signed Distance Fields (SDFs) has become a fundamental operation in geometry processing. Despite significant progress over the past decades, key challenges remain-namely, how to automatically capture the intricate geometric and topological structures en coded in the zero level set of SDFs. In this paper, we present a novel isosurface extraction algorithm that introduces two key innovations: 1) An incrementally constructed power diagram through the addition of sample points, which enables repeated updates to the extracted surface via its dual-regular Delaunay tetrahedralization; and 2) An adaptive point insertion strategy that identifies regions exhibiting the greatest discrepancy between the current mesh and the underlying continuous surface. As the teaser figure shows, our framework progressively refines the extracted mesh with minimal computational cost until it sufficiently approximates the underlying surface. Experimental results demonstrate that our approach outperforms state-of-the art methods, particularly for models with intricate geometric variations and complex topologies.

For the engineering application of electrodynamic levitation (EDS) maglev trains, it is crucial to address the fatigue durability challenges of onboard superconducting magnets under dynamic loads. This study systematically investigates the equivalent testing methods for fatigue durability of high temperature superconducting (HTS) magnets subjected to traveling magnetic fields during high-speed operation. To address the issues of electromagnetic rigidity and high-power loss inherent in electromagnetic vibration test platform, a novel excitation coil topology for simulating the AC component of the traveling magnetic field is proposed. The testing method first employs an equivalent circuit algorithm to establish an effective computational approach for the traveling magnetic field, achieving over 95% consistency in spatial field distribution accuracy. Based on this, a new geometric topology for ground based electromagnetic excitation coils is proposed. Comparative analysis shows that the magnetic field distribution experienced by the superconducting magnet is consistent between operational and equivalent testing modes, with magnetic field reproduction accuracy exceeding 95%. Furthermore, a fatigue durability experimental platform for superconducting magnets is developed. This platform can reproduce the equivalent traction and levitation traveling magnetic fields during maglev train operation. Additionally, the heat generated by the AC current reproduction method supports the continuous operation of the test platform, providing essential support for generating fatigue testing scenarios and offering a theoretical foundation for the engineering application of EDS Maglev trains.

In order to realize the internet of everything in sixth generation (6G), the emerging 6G applications have brought increasing demands for the high-speed communication and high-accuracy positioning concurrently. Relying on the potentials of high transmission power, large quantity and excellent geometric topology, low earth orbit (LEO) satellites have become strong candidates for providing integrated communication and positioning (ICAP) services. However, the resource competition between services and high dynamics of space-ground environment make it intractable to strike a balance between communication and positioning performance, which is one of the key design issue in LEO-ICAP networks. Against this backdrop, we consider an ICAP system with multiple LEO satellites, and adopt communication rate and squared position error bound (SPEB) as performance evaluation metrics. Based on that, we further formulate a weighted utility maximization problem, where the balance between communication and positioning performance can be achieved by jointly optimizing the subcarrier and power allocation, while simultaneously satisfying users’ quality of service (QoS) requirements. To solve this mixed-integer nonlinear programming problem, we propose a compressed sensing-based resource allocation algorithm, where the sparsity property of optimization variables is exploited to reformulate the problem into a continuous form, and the sequential convex programming method is then applied to solve the problem iteratively until convergence. Extensive simulations verify the superiority of our proposed algorithm compared to various benchmark schemes, where the proposed algorithm achieves a sum-rate improvement of at least 22% and a SPEB reduction of at least 28%, showing its effectiveness in realizing the balanced optimization of communication and positioning performance.