Search Results (1,136)

The Hengduan Mountains region (HMR) is vulnerable to flash flood disasters, which account for the largest proportion of flood-related fatalities in China. Flash flood regionalization, which divides a region into homogeneous subdivisions based on flash flood-inducing factors, provides insights for the spatial distribution patterns of flash flood risk, especially in ungauged areas. However, existing methods for flash flood regionalization have not fully reflected the spatial topology structure of the inputted geographical data. To address this issue, this study proposed a novel framework combining a state-of-the-art unsupervised Graph Neural Network (GNN) method, Dink-Net, and Shapley Additive exPlanations (SHAP) for flash flood regionalization in the HMR. A comprehensive dataset of flash flood inducing factors was first established, covering geomorphology, climate, meteorology, hydrology, and surface conditions. The performances of two classic machine learning methods (K-means and Self-organizing feature map) and three GNN methods (Deep Graph Infomax (DGI), Deep Modularity Networks (DMoN), and Dilation shrink Network (Dink-Net)) were compared for flash-flood regionalization, and the Dink-Net model outperformed the others. The SHAP model was then applied to quantify the impact of all the inducing factors on the regionalization results by Dink-Net. The newly developed framework captured the spatial interactions of the inducing factors and characterized the spatial distribution patterns of the factors. The unsupervised Dink-Net model allowed the framework to be independent from historical flash flood data, which would facilitate its application in ungauged mountainous areas. The impact analysis highlights the significant positive influence of extreme rainfall on flash floods across the entire HMR. The pronounced positive impact of soil moisture and saturated hydraulic conductivity in the areas with a concentration of historical flash flood events, together with the positive impact of topography (elevation) in the transition zone from the Qinghai–Tibet Plateau to the Sichuan Basin, have also been revealed. The results of this study provide technical support and a scientific basis for flood control and disaster reduction measures in mountain areas according to local inducing conditions. Full article

Graphs are an effective data structure for characterizing ubiquitous connections as well as evolving behaviors that emerge in inter-wined systems. Limited by the stereotype of node-to-node connections, learning node representations is often confined in a graph diffusion process where local information has been excessively aggregated, as the random walk of graph neural networks (GNN) explores far-reaching neighborhoods layer-by-layer. In this regard, tremendous efforts have been made to alleviate feature over-smoothing issues such that current backbones can lend themselves to be used in a deep network architecture. However, compared to designing a new GNN, less attention has been paid to underlying topology by graph re-wiring, which mitigates not only flaws of the random walk but also the over-smoothing risk incurred by reducing unnecessary diffusion in deep layers. Inspired by the notion of non-local mean techniques in the area of image processing, we propose a non-local information exchange mechanism by establishing an express connection to the distant node, instead of propagating information along the (possibly very long) original pathway node-after-node. Since the process of seeking express connections throughout a graph can be computationally expensive in real-world applications, we propose a re-wiring framework (coined the express messenger wrapper) to progressively incorporate express links in a non-local manner, which allows us to capture multi-scale features without using a very deep model; our approach is thus free of the over-smoothing challenge. We integrate our express messenger wrapper with existing GNN backbones (either using graph convolution or tokenized transformer) and achieve a new record on the Roman-empire dataset as well as in terms of SOTA performance on both homophilous and heterophilous datasets. Full article

We extend Clarke’s local inversion theorem for Sobolev mappings. We use this result to find a general implicit function theorem for continuous locally Lipschitz mapping in the first variable and satisfying just a topological condition in the second variable. An application to control systems is given. Full article

To tackle the challenges arising from missing real-time measurement data and dynamic changes in network topology in optimizing and controlling distribution networks, this study proposes a data-driven collaborative optimization strategy tailored for multi-area clusters. Firstly, the distribution network is clustered based on electrical distance modularity and power balance indicators. Next, a collaborative optimization model for multiple area clusters is constructed with the objectives of minimizing node voltage deviations and active power losses. Then, a locally observable Markov decision model within the clusters is developed to characterize the relationship between the temporal operating states of the distribution network and the decision-making instructions. Using the Actor–Critic framework, the cluster agents are trained while considering the changes in cluster boundaries due to topology variations. A Critic network based on an attention encoder is designed to map the dynamically changing cluster observations to a fixed-dimensional space, enabling agents to learn control strategies under topology changes. Finally, case studies show the effectiveness and superiority of the proposed method. Full article

Sparse road networks in high-risk geological disaster areas, characterized by long segments, few nodes, and limited alternative routes, face significant vulnerabilities to geological hazards such as landslides, rockfalls, and collapses. These disruptions hinder emergency response and resource delivery, highlighting the need for enhanced resilience strategies. This study develops a dynamic resilience assessment framework using a two-layer topological model to analyze and optimize the resilience of such networks. The model incorporates trunk and local layers to capture dynamic changes during disasters, and it is validated using the road network in Tibet. The findings demonstrate that critical nodes, including tunnels, bridges, and interchanges, play a decisive role in maintaining network performance. Resilience is influenced by disaster type, duration, and traffic capacity, with collapse events showing moderate resilience and debris flows exhibiting rapid recovery but low survivability. Notably, half-width traffic interruptions achieve the highest overall resilience (0.7294), emphasizing the importance of partial traffic restoration. This study concludes that protecting critical nodes, optimizing resource allocation, and implementing adaptive management strategies are essential for mitigating disaster impacts and enhancing recovery. The proposed framework offers a practical tool for decision-makers to improve transportation resilience in high-risk geological disaster areas. Full article

Resorting to microcanonical ensemble Monte Carlo simulations, we study the geometric and topological properties of the state space of a model of a network glass-former. This model, a Lennard-Jones binary mixture, does not crystallize due to frustration. We have found two peaks in specific heat at equilibrium and at low energy, corresponding to important changes in local ordering. These singularities were accompanied by inflection points in geometrical markers of the potential energy level sets—namely, the mean curvature, the dispersion of the principal curvatures, and the variance of the scalar curvature. Pinkall’s and Overholt’s theorems closely relate these quantities to the topological properties of the accessible state-space manifold. Thus, our analysis provides strong indications that the glass transition is associated with major changes in the topology of the energy level sets. This important result suggests that this phase transition can be understood through the topological theory of phase transitions. Full article

In the laser powder bed fusion (LPBF) process, the surface quality of intermediate layers impacts interlayer bonding and part forming quality. Due to the complex dynamic process inherent in LPBF, current monitoring methods struggle to achieve high-quality in situ online monitoring, which limits the in-depth understanding of the evolution mechanisms of the surface morphology of LPBF intermediate layers. This paper employs an optimized coaxial optical imaging method to monitor key LPBF processes and analyzes the intermediate layer surface morphology evolution mechanism considering heat, force, and mass transfer. Results indicate that LPBF intermediate layer surfaces are influenced by energy density, melt pool behavior, and previous layer morphology, forming complex topological structures. At a low energy density, insufficient powder melting causes balling, extended by subsequent melt pools to form a reticulated structure and local large-scale protrusions. Heat accumulation at a high energy density promotes melt pool expansion, reduces melt track overlap, and effectively eliminates defects from previous layers via remelting, with spatter becoming the main defect. Additionally, the melt pool wettability on the part contours captures external powder, forming unique, overhanging contour protrusions. This paper enhances understanding of LPBF intermediate layer surface morphology formation mechanisms and provides a theoretical basis for optimizing surface quality. Full article

Temporal lobe epilepsy (TLE) is considered a network disorder rather than a localized lesion, making it essential to study the network mechanisms underlying TLE. In this study, we constructed directed brain networks based on clinical MEG data using the Granger Causality Analysis (GCA) method, aiming to provide new insights into the network mechanisms of TLE. MEG data from 13 lTLE and 21 rTLE patients and 14 healthy controls (HCs) were analyzed. The preprocessed MEG data were used to construct directed brain networks using the GCA method and undirected brain networks using the Pearson Correlation Coefficient (PCC) method. Graph theoretical analysis extracted global and local topologies from the binary matrix, and SVM classified topologies with significant differences (p < 0.05). Comparative studies were performed on connectivity strengths, graph theory metrics, and SVM classifications between GCA and PCC, with an additional analysis of GCA-weighted network connectivity. The results show that TLE patients showed significantly increased functional connectivity based on GCA compared to the control group; similarities of the hub brain regions between lTLE and rTLE patients and the cortical–limbic–thalamic–cortical loop were identified; TLE patients exhibited a significant increase in GCA-based Global Clustering Coefficient (GCC) and Global Local Efficiency (GLE); most brain regions with abnormal local topological properties in TLE patients overlapped with their hub regions. The directionality of brain connectivity has played a significantly more pivotal role in research on TLE. GCA may be a potential tool in MEG analysis to distinguish TLE patients and HC effectively. Full article

This paper presents a novel adaptive crack-tip extended isogeometric analysis (adaptive CT XIGA) framework based on locally refined B-splines (LR B-splines) for efficient and accurate fracture modeling in two-dimensional solids. The XIGA method facilitates crack modeling without requiring the specific locations of crack faces and enables crack propagation simulation without remeshing by employing localized enrichment functions. LR B-splines, as an advanced extension of B-splines and NURBS, offer high-order continuity, precise geometric representation, and local refinement capabilities, thereby enhancing computational accuracy and efficiency. Various local mesh refinement strategies, designed based on crack and crack-tip locations, are investigated. Among these strategies, the crack-tip topological refinement strategy is adopted for local refinement in the adaptive CT XIGA framework. Stress intensity factors (SIFs) are evaluated using the contour interaction integral technique, while the maximum circumferential stress criterion is adopted to predict the crack growth direction. Numerical examples demonstrate the accuracy, efficiency, and robustness of adaptive CT XIGA. The results confirm that the proposed framework achieves superior error convergence rates and significantly reduces computational costs compared to a-posteriori-error-based adaptive XIGA methods, particularly in crack propagation simulations. These advantages establish adaptive CT XIGA as a powerful and efficient tool for addressing complex fracture problems in solid mechanics. Full article

This paper considers a decentralized and autonomous wireless network of low SWaP (size, weight, and power) fixed-wing UAVs (unmanned aerial vehicles) used for remote exploration and monitoring of targets in an inaccessible area lacking communication infrastructure. Here, the UAVs collaborate to find target(s) and use routing protocols to forward the sensed data of target(s) to an aerial base station (BS) in real-time through multihop communication, which can then transmit the data to a control center. However, the unpredictability of target locations and the highly dynamic nature of autonomous, decentralized UAV networks result in frequent route breaks or traffic disruptions. Traditional routing schemes cannot quickly adapt to dynamic UAV networks and can incur large control overhead and delays. In addition, their performance suffers from poor network connectivity in sparse networks with multiple objectives (exploration and monitoring of targets), which results in frequent route unavailability. To address these challenges, we propose two routing schemes: Pipe routing and TC-Pipe routing. Pipe routing is a mobility-, congestion-, and energy-aware scheme that discovers routes to the BS on-demand and proactively switches to alternate high-quality routes within a limited region around the routes (referred to as the “pipe”) when needed. TC-Pipe routing extends this approach by incorporating a decentralized topology control mechanism to help maintain robust connectivity in the pipe region around the routes, resulting in improved route stability and availability. The proposed schemes adopt a novel approach by integrating the topology control with routing protocol and mobility model, and rely only on local information in a distributed manner. Comprehensive evaluations under diverse network and traffic conditions—including UAV density and speed, number of targets, and fault tolerance—show that the proposed schemes improve throughput by reducing flow interruptions and packet drops caused by mobility, congestion, and node failures. At the same time, the impact on coverage performance (measured in terms of coverage and coverage fairness) is minimal, even with multiple targets. Additionally, the performance of both schemes degrades gracefully as the percentage of UAV failures in the network increases. Compared to schemes that use dedicated UAVs as relay nodes to establish a route to the BS when the UAV density is low, Pipe and TC-Pipe routing offer better coverage and connectivity trade-offs, with the TC-Pipe providing the best trade-off. Full article

Entity alignment in knowledge graphs plays a crucial role in ensuring the consistency and integration of data across different domains. For example, in power topology, accurate entity matching is essential for optimizing system design and control. However, traditional approaches to entity alignment often rely heavily on language models to extract general features, which can overlook important logical aspects such as temporal and event-centric relationships that are crucial for precise alignment.To address this issue, we propose EAL (Entity Alignment with Logical Capturing), a novel and lightweight RNN-based framework designed to enhance logical feature learning in entity alignment tasks. EAL introduces a logical paradigm learning module that effectively models complex-event relationships, capturing structured and context-aware logical patterns that are essential for alignment. This module encodes logical dependencies between entities to dynamically capture both local and global temporal-event interactions. Additionally, we integrate an adaptive logical attention mechanism that prioritizes influential logical features based on task-specific contexts, ensuring the extracted features are both relevant and discriminative. EAL also incorporates a key feature alignment framework that emphasizes critical event-centric logical structures. This framework employs a hierarchical feature aggregation strategy combining low-level information on temporal events with high-level semantic patterns, enabling robust entity matching while maintaining computational efficiency. By leveraging a multi-stage alignment process, EAL iteratively refines alignment predictions, optimizing both precision and recall. Experimental results on benchmark datasets demonstrate the effectiveness and robustness of EAL, which not only achieves superior performance in entity alignment tasks but also provides a lightweight yet powerful solution that reduces reliance on large language models. Full article

The increasing reliance on 3D scanning and meshless methods highlights the need for algorithms optimized for point-cloud geometry representations in CAE simulations. While voxel-based binning methods are simple, they often compromise geometry and topology, particularly with coarse voxelizations. We propose an algorithm based on a Series of Local Triangulations (SOLT) as an intermediate representation for point clouds, enabling efficient upsampling and downsampling. This robust and straightforward approach preserves the integrity of point clouds, ensuring resampling without feature loss or topological distortions. The proposed techniques integrate seamlessly into existing engineering workflows, avoiding complex optimization or machine learning methods while delivering reliable, high-quality results for a large number of examples. Resampled point clouds produced by our method can be directly used for solving PDEs or as input for surface reconstruction algorithms. We demonstrate the effectiveness of this approach with examples from mechanically sampled point clouds and real-world 3D scans. Full article

Spatial cognition, a critical component of human cognitive function, can be enhanced through targeted training, such as virtual reality (VR)-based interventions. Recent advances in electroencephalography (EEG)-based functional connectivity analysis have highlighted the importance of network topology features for understanding cognitive processes. In this paper, a framework based on a cross fuzzy entropy network graph (CFENG) is proposed to extract spatial cognitive EEG network topological features. This framework involves calculating the similarity and symmetry between EEG channels using cross fuzzy entropy, constructing weighted directed network graphs, transforming one-dimensional EEG signals into two-dimensional brain functional connectivity networks, and extracting both local and global topological features. The model’s performance is evaluated and interpreted using an XGBoost classifier. Experiments on an EEG dataset from group spatial cognitive training validated the CFENG model. In the Gamma band, the CFENG achieved 97.82% classification accuracy, outperforming existing methods. Notably, the asymmetrically distributed EEG channels Fp1, P8, and Cz contributed most to spatial cognitive signal classification. An analysis after 28 days of training revealed that specific VR games enhanced functional centrality in spatial cognition-related brain regions, reduced information flow path length, and altered information flow symmetry. These findings support the feasibility of VR-based spatial cognitive training from a brain functional connectivity perspective. Full article

In this paper, we introduce the notions of finite coarse shape path and finite coarse shape path connectedness of a topological space. We prove that the solenoid ${\Sigma }_{\left(p_n\right)}$, which is known to be coarse shape path connected but not shape path connected, is not finite coarse shape path connected either. Furthermore, we show that every finite coarse shape path induces an isomorphism between finite coarse shape groups of the topological space at different base points, with some interesting and useful properties. We also show that finite coarse shape groups of the same space, in general, depend on the choice of a base point. Hence, the pointed finite coarse shape type of $\left(X,x\right)$, in general, depends on the choice of the point x. Finally, we prove that if X is a finite coarse shape path connected paracompact locally compact space, then the pointed finite coarse shape type of $\left(X,x\right)$ does not depend on the choice of the point x. Full article

This article investigates the continuity of derivatives of real-valued functions from a topological perspective. This is achieved by the characterization of their sets of discontinuity. The same principle is applied to Gateaux derivatives and gradients in Euclidean spaces. This article also introduces a generalization of the derivatives from the perspective of the modulus of continuity and characterizes their sets of discontinuities. There is a need for such generalizations when dealing with physical phenomena, such as fractures, shock waves, turbulence, Brownian motion, etc. Full article