Adjacency Relations Research Articles

Fault diagnosis of rolling bearings under variable operating conditions based on improved graph neural networks

Abstract To address the issues of low diagnostic accuracy, insufficient generalization, and poor robustness in traditional fault diagnosis methods across different equipment and varying operating conditions, this paper proposes an improved graph neural network-based fault diagnosis method for rolling bearings to enhance model performance under complex conditions. First, the optimized wavelet transform coefficient features are used as nodes, and by exploring the correlations between features, node adjacency relationships are constructed. The associations between fault modes and feature node graphs under different conditions are studied, and a fault feature graph sample set based on subgraph structures is built, providing data for the subsequent graph neural network learning. Then, a multi-head attention mechanism (MHGAT) and multi-scale feature adaptive perception pooling (MSF-ASAP) are integrated to construct a multi-head graph attention mechanism model based on multi-scale feature adaptive perception pooling (MSM-GAT). MHGAT enhances the model's ability to perceive global information by learning different features from multiple perspectives and dimensions, thus improving the model's generalization. MSF-ASAP adaptively selects and aggregates information at multiple scales, enabling the model to effectively extract key features under various operating conditions, resist noise interference, and adapt to local information changes, thus improving the model's robustness under varying conditions and noisy environments. Experimental results under multiple and continuously varying conditions demonstrate that the proposed method outperforms traditional methods in terms of diagnostic accuracy and robustness. Notably, it exhibits excellent generalization when identifying unknown conditions, achieving over 95% accuracy in recognizing new conditions and maintaining over 92.5% accuracy in noisy environments.

Physics-informed line graph neural network for power flow calculation.

Power flow calculation plays a significant role in the operation and planning of modern power systems. Traditional numerical calculation methods have good interpretability but high time complexity. They are unable to cope with increasing amounts of data in power systems; therefore, many machine learning based methods have been proposed for more efficient power flow calculation. Despite the good performance of these methods in terms of computation speed, they often overlook the importance of transmission lines and do not fully consider the physical mechanisms in the power systems, thereby weakening the prediction accuracy of power flow. Given the importance of the transmission lines as well as to comprehensively consider their mutual influence, we shift our focus from bus adjacency relationships to transmission line adjacency relationships and propose a physics-informed line graph neural network framework. This framework propagates information between buses and transmission lines by introducing the concepts of the incidence matrix and the line graph matrix. Based on the mechanics of the power flow equations, we further design a loss function by integrating physical information to ensure that the output results of the model satisfy the laws of physics and have better interpretability. Experimental results on different power grid datasets and different scenarios demonstrate the accuracy of our proposed model.

Fuzzy Topological Spaces Generated by Fuzzy Digraphs

In this paper, we defined various fuzzy topological spaces on fuzzy digraph and study interrelation between them. Using adjacency relation on fuzzy vertices and fuzzy edges of fuzzy digraph we defined, namely two types of fuzzy topologies, left(right) fuzzy vertex topology and left(right) fuzzy edge topology on fuzzy digraph, respectively. We have obtained results related to fuzzy topology on fuzzy subdigraph [Formula: see text] of fuzzy digraph [Formula: see text]. Separation axioms [Formula: see text], [Formula: see text] and [Formula: see text] for these fuzzy topological spaces are studied. Some characterization results for fuzzy topological spaces related to isomorphic fuzzy digraphs are given. Further, we have shown that two fuzzy digraphs are isomorphic if and only if their corresponding fuzzy topologies are homeomorphic, this relation on set of fuzzy digraphs forms an equivalence relation. We have also defined and studied fuzzy bitopological spaces on fuzzy digraphs.

Building a 4D Cell Complex Topology Through the Extrusion Process

Abstract. This paper is a step forward towards a construction of 4D cell-complex models implemented using a topological data structure, dual half-edge. This allows for explicit representation of spatial relations among objects, such as adjacency relationship, coincidence or order of construction elements, e.g. vertices and edges. A method based on extrusion is proposed. An original 2D model is extruded to 3D, where adjacent cells sharing the same face are directly linked. Then extrusion to 4D is performed. In this case individual 4D cells sharing the same 3D cell are linked together. A model is kept valid at any stage of the construction process and links among cells are automatically provided by the construction operators. Implementation is based on the 4D data structure, which is used at each stage of construction, even in intermediate models of lower dimensionality.

Contradiction Hidden in Values of Urban Raster Data

Abstract. This paper discusses that raster data identified by the independent largest fraction method may include both manifest and hidden contradictions, and describes the underlying mechanisms of contradictions. Using the examples of zones of land use and floor-area ratio, we demonstrate that the cells including more than three different zone category combinations might be identified with a non-existing combination of the zone categories. For the zones in which the ratio of contradictory cells is comparatively large, this problem can be quite significant. We model, therefore, the probability of contradictory identification using the adjacency relationship of different categories, and demonstrate the good fitness of the model using actual urban raster data. The results reveal that there can be a significant proportion of hidden contradictions.

Self-Organizing and Routing Approach for Condition Monitoring of Railway Tunnels Based on Linear Wireless Sensor Network.

Real-time status monitoring is crucial in ensuring the safety of railway tunnel traffic. The primary monitoring method currently involves deploying sensors to form a Wireless Sensor Network (WSN). Due to the linear characteristics of railway tunnels, the resulting sensor networks usually have a linear topology known as a thick Linear Wireless Sensor Network (LWSN). In practice, sensors are deployed randomly within the area, and to balance the energy consumption among nodes and extend the network's lifespan, this paper proposes a self-organizing network and routing method based on thick LWSNs. This method can discover the topology, form the network from randomly deployed sensor nodes, establish adjacency relationships, and automatically form clusters using a timing mechanism. In the routing, considering the cluster heads' load, residual energy, and the distance to the sink node, the optimal next-hop cluster head is selected to minimize energy disparity among nodes. Simulation experiments demonstrate that this method has significant advantages in balancing network energy and extending network lifespan for LWSNs.

INCOMPLETE multi-view clustering based on low-rank adaptive graph learning

The challenge of acquiring complete data has led to substantial progress in incomplete multi-view clustering (IMVC) methods. Because graph structures can be excellent representations of data structure relationships, exceptional performance in handling incomplete data is demonstrated by graph-based methods at present. However, these methods still have their limitations. Most incomplete multi-view algorithms primarily focus on local information, neglecting global information. Therefore, these methods cannot dynamically recover the structural relationships in incomplete data by harnessing potential information from multiple perspectives and overall structural information. In response to the aforementioned concerns, we introduced an IMVC based on low-rank adaptive graph learning (IMVC-LAGL). This method initially constructs an affinity matrix based on the inter-view adjacency relationships. It also utilizes tensor low-rank constraints and consensus representation learning to explore higher-order correlations among different views. Subsequently, it adaptively reconstructs the incomplete graph structure to ultimately obtain a complete affinity relationship. It leads to excellent clustering results by integrating relevant information within views, overall structural information and potential information from multiple perspectives. We conducted experiments comparing our algorithm with eight incomplete multi-view algorithms using five different evaluation metrics. The results show that our algorithm achieves the best clustering results across eight datasets with varying missing rates. Particularly in the BBCSport dataset and YaleB dataset, the clustering accuracy of our algorithm is improved by 19.83 % and 16.41 %, respectively, compared with the second-best algorithm, under a 50 % missing rate.

SpaGRA: Graph augmentation facilitates domain identification for spatially resolved transcriptomics

Recent advances in spatially resolved transcriptomics (SRT) have provided new opportunities for characterizing spatial structures of various tissues. Graph-based geometric deep learning have gained widespread adoption for spatial domain identification tasks. Currently, most methods define adjacency relation between cells or spots by their spatial distance in SRT data, which overlooks key biological interactions like gene expression similarities, and leads to inaccuracies in spatial domain identification. To tackle this challenge, we propose a novel method, SpaGRA (https://github.com/sunxue-yy/SpaGRA), for automatic multi-relationship construction based on graph augmentation. SpaGRA uses spatial distance as prior knowledge and dynamically adjusts edge weights with multi-head graph attention networks (GATs). This helps SpaGRA to uncover diverse node relationships and enhance message passing in geometric contrastive learning. Additionally, SpaGRA uses these multi-view relationships to construct negative samples, addressing sampling bias posed by random selection. Experimental results show that SpaGRA demonstrates superior domain identification performance on multiple datasets generated from different protocols. Using SpaGRA, we analyzed the functional regions in the mouse hypothalamus, identified key genes related to heart development in mouse embryos, and observed cancer-associated fibroblasts enveloping cancer cells in the latest Visium HD data. Overall, SpaGRA can effectively characterize spatial structures across diverse SRT datasets.

Spatio-temporal Dual Graph Neural Networks for Travel Time Estimation

Travel time estimation is one of the core tasks for the development of intelligent transportation systems. Most previous works model the road segments or intersections separately by learning their spatio-temporal characteristics to estimate travel time. However, due to the continuous alternations of the road segments and intersections in a path, the dynamic features are supposed to be coupled and interactive. Therefore, modeling one of them limits further improvement in accuracy of estimating travel time. To address the above problems, a novel graph-based deep learning framework for travel time estimation is proposed in this article, namely, Spatio-temporal Dual Graph Neural Networks (STDGNN). Specifically, we first establish the node-wise and edge-wise graphs to, respectively, characterize the adjacency relations of intersections and that of road segments. To extract the joint spatio-temporal correlations of the intersections and road segments, we adopt the spatio-temporal dual graph learning approach that incorporates multiple spatial-temporal dual graph learning modules with multi-scale network architectures for capturing multi-level spatial-temporal information from the dual graph. Finally, we employ the multi-task learning approach to estimate the travel time of a given whole route, each road segment and intersection simultaneously. We conduct extensive experiments to evaluate our proposed model on three real-world trajectory datasets, and the experimental results show that STDGNN significantly outperforms several state-of-art baselines.

Homotopy properties of the complex of frames of a unitary space

AbstractLet be a finite‐dimensional vector space equipped with a nondegenerate Hermitian form over a field . Let be the graph with vertex set the one‐dimensional nondegenerate subspaces of and adjacency relation given by orthogonality. We give a complete description of when is connected in terms of the dimension of and the size of the ground field . Furthermore, we prove that if , then the clique complex of is simply connected. For finite fields , we also compute the eigenvalues of the adjacency matrix of . Then, by Garland's method, we conclude that for all , where is a field of characteristic 0, provided that . Under these assumptions, we deduce that the barycentric subdivision of deformation retracts to the order complex of the certain rank selection of that is Cohen–Macaulay over . Finally, we apply our results to the Quillen poset of elementary abelian ‐subgroups of a finite group and to the study of geometric properties of the poset of nondegenerate subspaces of and the poset of orthogonal decompositions of .

Path planning in additive manufacturing with multi-robot collaboration based on structural primitive partitioning

Directed Energy Deposition (DED) technology is increasingly favored for swiftly fabricating large structural components due to its high printing efficiency. Despite its advantages, challenges persist in achieving satisfactory surface finish and forming precision, hindering its widespread adoption across industries. To address these issues, this paper presents a novel multi-robot collaborative path planning method based on structural primitive partitioning. This method simplifies path planning complexities and seamlessly integrates into process planning software, thereby enhancing overall functionality. This method decomposes complex polygons into tiny primitives (TP), organizing them into TP sets based on bridge and adjacency relations. These sets are then structured into first-level structural TP (F-TP) and second-level structural TP (S-TP), followed by the establishment of monotonic structural TP (M-TP). A minimum rectangular box recalculates the filling path for each M-TP, while the external contour path and internal zigzag path form a complete printing path. Additionally, an optimal printing sequence planning algorithm for multi-robot using a KD-tree-based search algorithm is presented, ensuring the shortest non-productive path and collision avoidance during printing. Experimental verification with four structures of varying geometric features demonstrates a partitioning accuracy of 99.5 % and absence of surface defects in the printed parts. The proposed method presents a viable and effective solution for enhancing the quality of parts produced via DED.

Graph-based spatial co-location pattern mining: integrate geospatial analysis and logical reasoning

ABSTRACT Spatial co-location patterns reflect the inherent correlations among geographical elements. Mining co-location patterns of POIs can provide valuable insights for urban planning and resource management. Generally, co-location mining comprises two steps: proximity relationship determination (geospatial analysis) and frequent pattern recursion (logical reasoning). Previous methods often separate these two steps: serializing proximity relationships to enumerate frequent sequences. However, this approach suffers from limited flexibility and intuitiveness: as continuous spatial contexts are segmented into numerous small parts, it fails to adequately represent geographic correlations and hinders the effective visualization of logical reasoning. Facing these challenges, this study proposes a novel graph-based spatial co-location mining method (GSCM), which leverages graphs to integrate geospatial analysis and logical reasoning. Initially, to establish adjacency relationships, GSCM constructs the adaptive neighborhood graph, which dynamically adjusts proximity thresholds to accommodate geographic heterogeneity. Subsequently, the Apriori logical recursive process is realized on the graph structure. By leveraging graph searching, pruning, and growing, the potential growth directions of co-location patterns are identified, enhancing both the efficiency and intuition of frequent pattern recursion. Through experiments conducted on large-scale POI datasets from Wuhan, GSCM is compared with existing baseline methods, verifying its potential to uncover co-location patterns in complex spatial contexts.

Graph constrained empirical wavelet transform and its application in bearing fault diagnosis

The signal decomposition based on frequency domain distribution is a fundamental methodology for mechanical component fault diagnosis. However, existing methods face challenges such as susceptibility to noise interference and limited adaptability. Therefore, this paper proposes the graph constrained empirical wavelet transform (GCEWT) method. This method introduces structured information, such as the interrelationships among different parts of the frequency domain distribution of vibration signals, into the boundary detection process of empirical wavelet transform. The high-dimensional connectivity among different parts of the time-frequency distribution is utilized to construct an adjacency matrix. By constructing an adjacent graph, the proposed method encodes the adjacency relationships among frequency bands to constrain the low-dimensional spatial relationships between them. In conjunction with spectral clustering algorithms, the GCEWT method determines the boundaries for empirical wavelet transformation in the frequency domain. This approach achieves structured and adaptive decomposition of vibration signals from components of critical equipment, facilitating the structured and adaptive extraction of fault features. The effectiveness of the proposed method is validated using vibration data from both wind turbine drivetrain systems and aircraft engines. The experimental results demonstrate that the proposed method yields more reasonable signal decomposition results compared to traditional algorithms. Additionally, the proposed method proves to be more effective in extracting weak fault features of bearings in the presence of noise.

STTraj2Vec: A spatio-temporal trajectory representation learning approach

Computing trajectory similarity plays a critical role in various spatio-temporal applications that involve trajectory analysis. In recent years, trajectory representation learning has been extensively studied and applied for trajectory similarity calculation. However the majority of existing algorithms for trajectory representation generally have two problems. The first problem is the emphasis of spatial similarity over temporal similarity, and even to discard the temporal dimension of spatio-temporal trajectories. As a result, the outputs of these approaches cannot fully represent the similarity of spatio-temporal trajectories. The second problem is the introduction of additional information, such as the topology of the road network, which increases the uncertainty of capturing the spatio-temporal correlation of trajectories and prevents their application in scenarios where it is difficult to obtain such information. This poses a significant challenge when dealing with complex and time-varying traffic networks. This paper proposes a novel method, named STTraj2Vec (Spatio-temporal Trajectory 2 Vector), which relies only on spatio-temporal trajectories to capture their similarity without spatio-temporal separation. This takes into account the whole spatio-temporal trajectory information. In this method, an extended clustering algorithm is introduced, which maps the trajectory into a point-region quadtree, and constructs a time-varying virtual network structure based on the point-region quadtree. In this method, an extended clustering algorithm is introduced, which maps each trajectory into a point-region quadtree, and then completes density clustering through the adjacency relation of leaf nodes to construct a time-varying virtual network structure. This virtual network structure not only considers the spatial proximity, but also the time, so as to reflect the spatio-temporal characteristics of the trajectory more accurately. Then, a novel spatially and temporally integrated random walk algorithm is designed, which carries out spatiotemporal random walk on the virtual network structure, to capture the spatiotemporal characteristics of the trajectory, and thus obtains the representation of all nodes in the virtual network. Furthermore, each trajectory is converted into a sequence of vectors on the virtual road network according to the latitude, longitude, and time of the trajectory points. Finally, based on these node representations and trajectories, a transformer model with ranking loss is employed to capture the distinct contributions of the various locations and times to the similarity computation and encode each sequence of vectors into target vectors. Experiments on two public datasets show that STTraj2Vec is superior to the state-of-the-art methods in terms of effectiveness for top-k trajectory similarity search and trajectory clustering, while exhibiting low parameter sensitivity and high model robustness.

The continuous-time magnetic quantum walk and its probability invariance on a class of graphs

Let [Formula: see text] be a nonnegative integer and [Formula: see text] the power set of the set [Formula: see text]. Then there is an adjacency relation in [Formula: see text] such that [Formula: see text] together with the relation forms a regular graph. In this paper, we propose a model of continuous-time magnetic quantum walk (MQW) on the graph [Formula: see text], and investigate its properties from a viewpoint of probability and quantum information. We first introduce a magnetic Laplacian [Formula: see text] on the graph [Formula: see text] and examine its spectrum. And then, with [Formula: see text] as the Hamiltonian, we construct our model of continuous-time MQW on the graph [Formula: see text]. We find that the model has probability distributions that are completely independent of the magnetic potential at all times. And we show that it has perfect state transfer at time [Formula: see text] when the magnetic potential satisfies some mild conditions. Some other interesting results are also obtained.

Time‐varying Extremum Graphs

AbstractWe introduce time‐varying extremum graph (tveg), a topological structure to support visualization and analysis of a time‐varying scalar field. The extremum graph is a sub‐structure of the Morse–Smale complex. It captures the adjacency relationship between cells in the Morse decomposition of a scalar field. We define the tveg as a time‐varying extension of the extremum graph and demonstrate how it captures salient feature tracks within a dynamic scalar field. We formulate the construction of the tveg as an optimization problem and describe an algorithm for computing the graph. We also demonstrate the capabilities of tveg towards identification and exploration of topological events such as deletion, generation, split and merge within a dynamic scalar field via comprehensive case studies including a viscous fingers and a 3D von Kármán vortex street dataset.

Long-term prediction method for PM2.5 concentration using edge channel graph attention network and gating closed-form continuous-time neural networks

Fine particulate matter such as PM2.5 threatens significantly to the environment and human health, so it is essential to design a reliable long-term prediction method for PM2.5 concentrations. Existing long-term PM2.5 prediction models inadequately utilize urban spatial features, fail to consider the role of meteorological factors in PM2.5 levels, and overlook the interaction between PM2.5 concentrations in different cities. To tackle this issue, we propose two new models and integrate them. Firstly, we develop a spatial feature model (ECGAT) for extracting PM2.5 concentration among regions based on Graph Neural Networks (GNN), edge-channel mechanisms, and Graph Attention Convolution (GATConv). This model utilizes GNN to extract urban adjacency relationships and meteorological features, employs edge-channel mechanisms to recalculate weights for interactions between cities, and outputs spatial correlations through GATConv. Secondly, we propose Gating Closed-form Continuous-time Neural Networks (GCFC) as a temporal model to extract the PM2.5 concentration's temporal features. The fusion of these two models, named ECGAT-GCFC (EGCFC), enhances the model's capability to capture spatiotemporal features and improves performance in PM2.5 long-term predictions. Results from real-world data analysis show that the proposed algorithm outperforms state-of-the-art existing prediction models in predicting PM2.5 levels over long durations. Compared to baseline models, EGCFC reduces RMSE by an average of 3.39 %, decreases MAE by 4.83 %, increases R2 by 4.89 %, CSI by 3.13 %, and lowers FAR by 11.39 %. These indicate that EGCFC is an effective method for predicting trends in urban PM2.5 concentrations.

Multi-Source Information Fusion Graph Convolution Network for traffic flow prediction

As a fundamental technology in the field of intelligent transportation systems, traffic flow prediction has a wide range of applications. The utilization of Graph Convolutional Network (GCN) models is notable for capturing the complex spatial–temporal dependencies in traffic data, leading to a significant improvement in prediction accuracy. However, most existing graph construction methods overlook joint impact of auxiliary information such as weather and traffic speed on the road topology. Moreover, the research on interactions within time series at coarse temporal resolutions remains insufficiently explored, giving rise to unsatisfactory long-term prediction performance. In this study, we present a novel framework, namely Multi-Source Information Fusion Graph Convolution Network (MIFGCN), for spatial–temporal traffic flow prediction. Our key innovation lies in creating a dynamic graph that integrates weather, traffic speed, and global spatial information, effectively simulating significant traffic fluctuations caused by subtle ancillary information in the road network. Simultaneously, it captures the evolving hidden adjacency relationships between nodes over time. Furthermore, by combining with an attention-based temporal interaction module, MIFGCN learns multiscale temporal correlations at course temporal resolutions, enhancing the ability for long-term prediction. Experiments conducted on four real-world traffic datasets demonstrate that MIFGCN outperforms various state-of-the-art baselines, especially achieving a 10.50% average improvement on the PeMS08 dataset.

On the mil graph of module over ring

Let $M$ be an unital left module over a ring $R$ with unity. We define an undirected (\textit{nil graphs}) for the module $M$ as a graph whose vertex set is $M^*=M-{0}$ and any two distinct vertices $x$ and $y$, in these graphs, are adjacent if and only if there exist $r \in R$ such that $r^{2} (x+y) = 0$ and $r(x+y)\neq 0$. In this paper, we study the graph's adjacency, diameter, radius, and eulerian and hamiltonian properties. We also defined another nil graph $\Gamma^{*}_{N} (M)$, in which we reduced the vertex set to $N(M^*)$, set of all non-zero nil elements of the module, and keep the adjacency relation same as that of $\Gamma_{N} (M)$. We investigate the adjacency, diameter, radius, eulerian and hamiltonian properties of the graph $\Gamma^{*}_{N} (\mathbb{Z}_{p^n})$ and compare these properties among both the graphs.

A hierarchical model with hexagon grids for multi-objective route planning in large-scale off-road environments

Off-road route planning plays a vital role across various domains, including civil transportation, earthquake relief and civil production. Off-road route planning requires the consideration of a diverse range of environmental constraints, which is a considerable challenge compared with conventional route planning along existing networks. We aimed to present a multi-objective route planning method for off-road environments. Specifically, we designed a heuristic function incorporating multiple characteristics to generate reliable route planning solutions based on Pareto optimality. We also constructed a hierarchical hexagonal grid model by merging similar grid cells and reconstructing adjacency relationships with other grid cells to achieve high efficiency. The proposed method was compared with conventional route planning methods using single- and multi-objective approaches in traditional and hierarchical hexagonal grid models. The proposed method can effectively plan off-road routes, improve optimal route distance and trafficability, and provide more efficient route solutions. It reduced the planning time by 97.1% compared with multi-objective route planning based on a traditional hexagonal grid model.