Search Results (1,229)

This study develops a stochastic degradation-based reliability framework for mechanical systems subject to interacting operational stresses and imperfect maintenance. The degradation dynamics are formulated in cumulative damage space and modeled using a geometric Itô diffusion process, in which the drift term incorporates a multiplicative degradation kernel representing the combined influence of load, speed, misalignment, and environmental exposure. Imperfect maintenance is represented through a continuous attenuation functional embedded within the drift structure, allowing maintenance actions to reduce degradation growth without restoring the system to an as-good-as-new condition. Using a logarithmic transformation, the multiplicative stochastic differential equation is converted into an additive diffusion process, enabling analytical treatment via Itô’s lemma. A closed-form reliability expression is then obtained through first-passage analysis, yielding a lognormal survival function governed directly by the degradation dynamics. Numerical evaluation demonstrates physically consistent wear-out behavior and confirms the stability of the derived reliability formulation. The model further enables reliability-based maintenance optimization through preventive replacement analysis. Sensitivity results indicate that system reliability is strongly influenced by the degradation growth parameter governing the stochastic drift. The proposed framework provides a mathematically tractable connection between stochastic degradation modeling, reliability theory, and maintenance optimization. Beyond its application to conveyor belt systems, the formulation offers a general analytical structure for reliability assessment of degrading engineering systems governed by multiplicative stochastic dynamics. Full article

We construct a connection-theoretic framework for parallel transport of spectral components along parameter families of signals on the similarity group $\tilde{G}=\mathbb{R}\times \mathrm{SO}\left(2\right)$. Let ${\left\{f_t\right\}}_{t\in I}$ be a signal family that evolves under a $C^1$ group trajectory. The frequency support of the associated scale-rotation transforms produces three Hilbert subbundles over the parameter interval, and the trajectory velocity induces a covariant derivative on each subbundle. The standard spectral viewpoint treats transformation behavior at individual parameter values. Our formulation instead organizes the propagation of spectral components along the entire parameter path and provides closed-form transport operators together with error bounds on each subbundle. We derive three explicit parallel transport formulas. On the equivariant subbundle the transport is an exact isometric translation. On the coupled subbundle, the transport combines log-scale translation with a phase factor $e^{i{n}_0\Delta \theta }$. On the invariant subbundle, the transport is approximate, with the quantitative bound $\parallel {\Pi }^{\mathrm{inv}}F-F\parallel \le \epsilon \left|\Delta \tau \right|\parallel F\parallel$, where ${\Pi }^{\mathrm{inv}}$ denotes the parallel transport operator on that subbundle. We introduce the notion of non-parallelism rate as a pointwise measure of deviation from parallel evolution, and we prove that cumulative deviation along the path is bounded by the path integral of this quantity. The bound separates into two parts. One part is controlled by trajectory estimation error and reflects geometric mismatch. The other part is controlled by intrinsic appearance variation and reflects non-geometric drift. We also show that regularity transfers from the signal family to the spectral sections, and we establish a discrete transport theorem whose finite-sum error bounds recover the continuous estimates in the small-step limit. The framework provides a quantitative geometric tool for multi-scale feature evolution under continuous scale-rotation transformations. Full article

Dominant flow channels formed during the late stages of waterflooding can severely reduce sweep efficiency and intensify ineffective interwell circulation. Conventional identification approaches, including tracer testing, well testing, and numerical simulation, often suffer from high operational cost, long execution time, or limited adaptability to heterogeneous interwell connectivity. Although ant colony optimization (ACO) is suitable for path-search problems in reservoir networks, its performance depends strongly on hyperparameter settings, and sample-by-sample parameter tuning introduces substantial online computational overhead. This study proposes a structure-informed GIN–ACO framework for adaptive dominant flow channel identification in connection-element reservoir graphs. A physics-constrained benchmark model is first established using Darcy’s law and the connection element method to provide reference flow paths. A geometry-based surrogate model is then developed to approximate flow splitting coefficients efficiently while preserving the main physical trends. Based on graph topology and geometric descriptors, a graph isomorphism network is trained to predict task-specific ACO parameters, replacing iterative online search with direct parameter inference. Experiments on 1000 synthetic reservoir graphs show that the proposed method achieves a 100% success rate with an average online computation time of 143.5 ms, outperforming fixed-parameter ACO, PSO-ACO, and BO-ACO. On 20 semi-realistic SPE10 reservoir models, GIN–ACO achieves a success rate of 92 ± 1% with an average runtime of 160.3 ± 5 ms. Ablation studies further confirm that graph-structure learning, combined topology–geometry features, and GIN-based parameter prediction are essential for robust performance. The proposed framework provides a promising and computationally efficient route for structure-aware dominant channel identification in connection-element reservoir models. Full article

We develop an information-geometric framework for describing quantum state-update processes associated with measurement and statistical distinguishability. The approach is based on the quantum relative entropy and the quantum Fisher information metric, which together induce a natural Riemannian geometry on the manifold of quantum states. Using the second-order expansion of relative entropy, we show how the Fisher metric governs the local structure of distinguishability between nearby states and defines a corresponding thermodynamic length. This geometric structure provides an effective description of finite quantum state transitions in terms of fluctuation geometry and information-space distance. The formalism is applied to thermal two-level systems and harmonic oscillator states, illustrating how the Fisher metric encodes susceptibilities, fluctuations, and geometric transition costs. We also discuss the relation between thermodynamic length, dissipation bounds, and optimal paths in state space. Within this framework, wave function collapse is interpreted not as a microscopic dynamical mechanism, but as an effective state-update process that admits a geometric characterization in the manifold of density operators. The resulting perspective unifies concepts from quantum information theory, thermodynamics, and differential geometry within a common operational framework based on statistical distinguishability. Possible connections with quantum speed limits, entanglement geometry, and holographic relations between relative entropy and gravitational dynamics are briefly discussed. Full article

Road drainage infrastructure in ENSO-vulnerable Andean regions faces compounding threats from climatic variability, geometric inadequacy, and systemic maintenance neglect. This study presents a STEM-integrated Project-Based Learning (PjBL) diagnostic framework applied to 42 road segments along corridors connecting Loja, Ecuador, selected through a purposive-stratified spatial-coverage protocol. Using ArcGIS Survey123, standardised field data were collected on structure presence, geometry, failure modes, and condition across four structure types: crown gutters, road gutters, hydraulic chutes, and culverts. The Composite Drainage Deficiency Index (DDI, 0–100) was derived from five equally weighted binary indicators and validated through Monte Carlo Dirichlet weight-perturbation analysis and jackknife leave-one-out resampling, confirming rank-order invariance to admissible alternative weightings. The results reveal severe systemic deficiencies, including crown gutters absent at 88.1% (95% CI: 75.0–94.8) and road gutters at 81.0% (95% CI: 66.7–90.0) of sites. Every segment exhibited at least one drainage failure (100%; 95% CI: 91.6–100). The DDI identified 73.8% of segments in the High or Critical band (DDI ≥ 60; mean = 60.2 ± 20.4). Hierarchical clustering isolated one geometric outlier whose exclusion altered the aggregate metrics by <1.2%. These findings establish a georeferenced baseline for maintenance prioritisation and validate the methodological reproducibility of academically integrated field protocols for infrastructure diagnostics. Full article

The 15-minute neighborhood paradigm has reshaped the evaluation system of urban pedestrian mobility, shifting pedestrian network assessment from single facility supply to holistic topological structural analysis. Structural fracture of pedestrian systems has thus become a prominent challenge restricting high-quality sustainable urban travel and neighborhood renewal. Existing studies mainly focus on macroscopic accessibility and geometric connectivity, lacking systematic multi-dimensional quantitative measurement and refined typological identification of network topological fractures. Taking 52 typical 15-min neighborhoods in Baohe District, Hefei as research samples, this paper constructs a four-dimensional topological fracture evaluation system, and conducts empirical analysis through correlation analysis, K-means++ clustering and micro topological feature mining. The results show that functional fracture and hierarchical fracture are weakly correlated and relatively independent (ρ = 0.068). Four distinct topological fracture types are classified, among which the Cognitive Disorientation type accounts for the largest proportion of 37.3%. Microscopic topological verification further reveals the formation mechanisms and spatial differentiation laws of various fracture patterns. This study provides a scientific typological basis and targeted topological intervention strategies for sustainable governance, classified regulation and optimized upgrading of urban pedestrian travel networks. Full article

Medium-resolution cryo-electron microscopy (cryo-EM) density maps preserve substantial information about protein secondary-structure organization; however, accurately recovering the topology and connectivity of α-helices and β-strands remains challenging due to noise, structural heterogeneity, and the intrinsic resolution limitations that obscure residue-level detail. Topology determination is a key intermediate step toward building atomic protein models from medium-resolution cryo-EM density maps. It requires identifying the correct correspondence and orientation between secondary-structure elements (SSEs), i.e., α-helices and β-strands, predicted from the amino-acid sequence and those detected in the three dimensional (3D) density map. Despite significant advances in cryo-EM reconstruction and molecular modelling, this correspondence problem remains a challenging task, particularly in the presence of noisy density maps and in large, topologically complex α/β proteins. To address this issue, we propose a fully automated, classification-based framework that infers protein secondary-structure topology directly from medium-resolution cryo-EM density maps. Specifically, we cast topology determination as a supervised classification problem in three-dimensional space, leveraging geometric learning on model-derived Cα coordinate representations to establish SSE correspondences, and a Dynamic Time Warping (DTW)-based procedure to resolve density-stick directionality. Validation on a benchmark of 38 proteins spanning both simulated and experimental cryo-EM maps and covering diverse fold classes (α, β, and α/β) demonstrates strong and consistent performance. Among the evaluated predictors, the Voronoi (1-NN) classifier achieves the highest average correspondence quality, with a mean F1-score of 96.82% across the full benchmark. The framework also scales to large, topologically dense targets containing up to 65 secondary-structure elements while preserving very fast correspondence inference (<3 ms), offering a substantial improvement over prior baselines in both accuracy and computational cost. Overall, the classification-driven strategy provides reliable SSE-to-density matching and, when coupled with DTW-based direction selection, yields stronger topology constraints that directly support model building and refinement from medium-resolution cryo-EM reconstructions, while remaining easy to integrate into existing structural interpretation pipelines. Full article

The transition to mixed traffic flows comprising Connected and Automated Vehicles (CAVs) and Human-Driven Vehicles (HVs) induces a fundamental spatial reconfiguration of risk in freeway merging areas. This study proposes a novel spatiotemporal safety assessment framework to characterize the dynamic evolution of risk hotspots. Unlike traditional models, the framework integrates a conflict prediction model based on Negative Binomial regression with a high-resolution, grid-based risk mapping technique. By applying this framework to data from a microscopically simulated and carefully calibrated environment, we successfully identify a distinct migration pattern of risk hotspots: as CAV penetration increases, high-risk zones shift from the static geometric bottleneck at the ramp merge point to a dynamic interaction interface on the mainline. This paradigm shift is further quantified using a multi-dimensional indicator system. A case study demonstrates that increasing the CAV penetration rate from 10% to 50% can improve the safety grade of a merging area from D (Poor) to A (Excellent). The proposed framework provides a practical tool for refined safety diagnostics and offers insights for spatiotemporal risk analysis, informing the development of future cooperative control strategies in mixed traffic environments. Full article

In maritime search and rescue and underwater surveillance missions employing forward-looking sonar, strong reverberation and complex underwater environments often substantially degrade the target signal-to-clutter ratio (SCR), presenting significant challenges for target detection. Existing algorithms typically simplify the point spread function (PSF) into an ideal isotropic model, thereby overlooking the inherent anisotropy induced by its sidelobe structures. This physical model mismatch leads to target energy leakage and severely limits detection performance in complex backgrounds. To overcome the limitations of current target models and detection algorithms, this paper introduces a Gaussian 5 Superposition (G5S) model to accurately characterize the physical features of the PSF and proposes a Laplacian-of-G5S-based Local Adaptive Detection (LoG5S-LAD) method through the construction of a LoG5S filtering operator. Initially, a high-SCR target likelihood map is generated using Hessian-matrix-based geometric gating and LoG5S matched filtering techniques. Subsequently, robust background suppression and the effective preservation of faint targets are achieved through morphological artifact suppression, connected component screening, and a high-energy exemption mechanism. The effectiveness of the proposed framework is validated through model fitting experiments, as well as comprehensive simulations and detection tests across various sonar configurations. Experimental results indicate that the G5S model demonstrates precise fitting capabilities and strong physical adaptability. Furthermore, the proposed LoG5S-LAD algorithm significantly enhances the SCR while maintaining robust detection performance for faint and small-scale targets. Full article

This paper studies a realization-theoretic problem inside the standard Lorentz-covariant Fourier-dual framework on $L^2\left({\mathbb{R}}^{3,1}\right)$: whether position-space and momentum-space geometric translations can be placed on equal structural footing without leaving the ordinary X- and K-polarized realizations. Working on the common Schwartz core $\mathcal{S}\left({\mathbb{R}}^{3,1}\right)$, we first isolate a Fourier-compatibility obstruction: Fourier transform exchanges geometric translations with character actions, while the Poincaré algebra contains at most one Lorentz-covariant abelian translation ideal. The main result is that, within the resulting Fourier-compatible realization class, the minimal operator-generated Lie algebra is the Lorentz–Heisenberg algebra. We then determine the full center of its universal enveloping algebra, derive the normalized Lorentz-bivector invariants, orbit data, and connected stabilizers in nondegenerate sectors, and show that the orbit variable is a normalized Lorentz bivector rather than a momentum vector. Finally, for fixed spectral elements in the dual translation sectors, we derive the associated scalar, Dirac, and vector equations in position and momentum space and show that, in the regular polarized realizations, the represented Heisenberg sector induces dual local abelian phase groups, compatible covariant derivatives, curvatures, and primary Dirac–Maxwell systems. Full article

The prediction accuracy of RNA’s tertiary structure remains a core challenge in the field of computational biology. Existing models frequently encounter significant challenges due to the complexities of diverse topologies and the intricate nature of long-range interactions. We introduce RNAFoldDiff, a generative framework that integrates a sequence-aware graph transformer with a geometric diffusion process for end-to-end RNA 3D structure prediction. RNA sequences and secondary structures are converted into graph representations that capture backbone connectivity and base pair topology. The transformer models local motifs and global dependencies, while the diffusion module iteratively denoises coordinates into physically consistent conformations. The model was pretrained on more than 15,000 structural motifs from the RNA 3D Hub and fine-tuned on complete RNAs from the RNA-Puzzles dataset. In benchmarking tests, RNAFold-Diff achieved an average root mean square deviation (RMSD) of 2.64 Å, a Global Distance Test (GDT) score of 68.7%, and a base pair accuracy of 89.5%, reducing RMSD by nearly 30% and improving GDT by 9 points compared to RoseTTAFoldNA. The framework also outperformed FARFAR2, SimRNA, and RNAformer. Ablation experiments confirmed the contributions of diffusion refinement, edge-aware graph encoding, and motif-level pretraining, while qualitative analyses showed biologically plausible folds including helices, junctions, and multiloops. By combining topology-aware graph learning with generative diffusion, RNAFoldDiff advances RNA tertiary structure modeling and provides a practical tool for RNA design, ribozyme analysis, and structure-guided drug discovery. Full article

To address the accuracy limitations in identifying micro-scale and low-distinguishability defects, we proposes an improved EfficientNet model for wafer defect classification in semiconductor fabrication. In particular, we construct the model using EfficientNetV2 architectures as the backbone and introduce a multi-scale self-attention enhancement module to strengthen the capture capability for critical defect characteristics. This module consists of four parallel self-attention enhancement modules, aiming to obtain spatial context information at different levels and enhance relevant features through a self-attention mechanism. Meanwhile, we merge the manually extracted features of defects with the CNN’s fully connected layer, effectively compensating for the deficiency of automatic features in the differentiated representation of defects. The manual feature extraction module leverages image processing techniques to capture diverse morphological characteristics of defects including geometric features, moment features and texture features. We simulate and generate a lithography SEM image dataset with various types of defects based on the typical line-space structure and the ICCAD2019 mask pattern dataset. The total sample size of the wafer defect dataset is 1500, covering 15 typical defects with an average distribution. The classification performance of models is evaluated on the simulated defect dataset. The results indicate that the overall classification accuracy of the improved model reaches 96.60%, representing an improvement of 8.14% compared to the original EfficientNetV2. This demonstrates the superiority of the proposed model in addressing classification tasks involving micro-scale and low-distinguishability defects. Full article

Road networks are fundamental components of transportation infrastructure and play a crucial role in various geospatial applications. Although deep learning-based semantic segmentation models have achieved promising results in extracting roads from high-resolution remote sensing imagery, the resulting networks often suffer from topological fragmentation due to occlusions and shadows. To address this issue, we propose a topology-aware road extraction method that integrates deep learning-based segmentation with a graph-based connectivity refinement strategy. Specifically, a Pyramid Scene Parsing Network (PSPNet) is first employed to generate initial road probability maps. Subsequently, a connectivity-oriented post-processing pipeline is introduced, which incorporates a multi-source cost function strategy and a direction-aware Dijkstra search algorithm. By utilizing endpoint tangent vectors as inertial weights, the algorithm effectively reconstructs fragmented segments while ensuring geometric smoothness and topological consistency. Furthermore, a dynamic road width restoration strategy is applied to transform refined skeletons into physically consistent road entities. Experiments conducted on two publicly available datasets, CHN6-CUG and DeepGlobe, demonstrate the effectiveness of the proposed method. Quantitative results show that the refinement process significantly enhances road connectivity with a minimal trade-off in pixel-level accuracy. Specifically, the Conn metric increases by 0.1989 on the CHN6-CUG dataset and 0.3055 on the DeepGlobe dataset, while MIoU remains high with only marginal decreases of 1.07% and 0.45%, respectively. These findings indicate that the method effectively restores structural continuity, helping with reliable road network generation and subsequent integration into Geographic Information System (GIS)-based applications such as urban planning and autonomous navigation. Full article

Mobi spaces were introduced by the authors as a possible algebraic axiomatization of spaces in which any two points are connected by a geodesic path. Previous work has focused primarily on the algebraic properties of these structures; here, we return to the original geometric motivation. We present new characterizations of mobi spaces inspired by the important class of smooth manifolds that arise as open subsets of Euclidean (n)-space endowed with a Riemannian metric. We show that such manifolds satisfy the axioms of a mobi space, thereby providing a broad family of natural geometric examples. Full article

In geometric communication networks, a backbone is useful only if it is inexpensive to build and, at the same time, close enough to the demand points it must serve. This paper studies a backbone design problem in geometric communication networks that explicitly captures this trade-off between connectivity and user coverage. Two classical combinatorial optimization paradigms—the minimum spanning tree (MST), which promotes low-cost connectivity, and the dominating tree (DT), which additionally enforces that every node either belongs to the backbone or is adjacent to an active backbone node—are considered. To compare both paradigms within a common framework, this paper proposes a unified mixed-integer optimization model that balances backbone-construction and user-assignment costs. Three classes of exact formulations, namely MTZ, single-flow, and cut-set formulations, are developed. In particular, the single-flow model with valid inequalities and root-aware connectivity cuts is strengthened. For larger instances, the exact approach is complemented with a local branching matheuristic. Finally, theoretical results on computational complexity, formulation structure, and dominance relations between the MST and DT models are provided. Computational experiments show that the single-flow formulation achieves the best scalability. Furthermore, a sensitivity analysis with respect to the communication radius and the weighting parameter $\alpha$ reveals a structural transition: as the network becomes denser or the objective becomes more coverage-oriented, MST and DT solutions tend to converge. The results give a concrete way to identify when domination constraints are worth imposing and when a simpler spanning tree design already captures the relevant structure. Full article