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Exploring a general and effective method of isomorphism identification is an arduous task. For this aim, some new concepts such as binary link path and link-assortment adjacency matrix are introduced in this paper. On this basis, a new method is proposed to improve the operability of isomorphism identification and relieve the computational pressure. By generating new elements from structural features and connection relations among links or vertices in the graph, it transforms traditional high-ranking adjacency matrix into new low-ranking adjacency matrix. Some typical graphs including kinematic chains, topological graphs, and planetary gear trains are used to verify the effectiveness of the proposed method. As shown by a comparison with results in the cited references, the proposed method is available in isomorphism identification. [ABSTRACT FROM AUTHOR]

A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines. [ABSTRACT FROM AUTHOR]

Forecasting traffic flow is crucial for Intelligent Traffic Systems (ITS), traffic control, and traffic management systems. Complex spatial and temporal interactions of traffic networks make traffic forecasting tasks challenging. Recently, Graph Convolutional Network (GCN) has attracted researchers' attention as it can better represent graph-shaped road networks and extract spatial features of traffic. However, traditional GCN has some drawbacks since it uses a static adjacency matrix which is unable to capture the time-varying features of traffic propagation. To overcome this, we represent the traffic road network as a dynamic graph and use a probabilistic spatiotemporal adjacency matrix to identify the time-varying impacts of adjacent roads on target roads in GCN. In addition, to find the similarity among the nonadjacent nodes, we have employed node-specific learning in GCN rather than sharing parameters in traditional GCN. This node-specific learning helps our model to learn detailed characteristics of road networks. For temporal feature extractions, we used a Gated Recurrent Unit (GRU) that captures the local trend of traffic flow and an attention mechanism to capture the global trend of traffic flow. We compared the performance of our model with baseline models using two real-world datasets. Experimental results show that our model is effective in forecasting both short and long-term traffic flow. Source code of our model is available at https://github.com/atkia/PSTGCN [ABSTRACT FROM AUTHOR]

How to mine many interesting subgraphs in uncertain graph has become an important research field in data mining. In this paper, a novel algorithm Uncertain Maximal Frequent Subgraph Mining Algorithm Based on Adjacency Matrix and Weight (UMFGAMW) is proposed. The definition of the adjacency matrix and the standard matrix coding for uncertain graph are presented. The correspondence between the adjacency matrix and uncertain graph is established. A new vertex ordering policy for computing the standard coding of uncertain graph adjacency matrix is designed. The complexity of uncertain graph standard coding is reduced, and the matching speed of uncertain subgraph standard coding is improved. The definition of the weight of uncertain graph and the mean weight of uncertain edge is proposed. The importance of the uncertain subgraphs that meet the minimum support threshold in the graph dataset is fully considered. Finally, a depth-first search weighted uncertain maximal frequent subgraph mining algorithm is discussed. According to the limiting condition of the uncertain maximum frequent subgraph and weighed uncertain edge, the number of mining results is reduced effectively. Experimental results demonstrate that the UMFGAMW algorithm has higher efficiency and better scalability. [ABSTRACT FROM AUTHOR]

Predicting olfactory perceptions from odorant molecules is challenging due to the complex and potentially discontinuous nature of the perceptual space for smells. In this study, we introduce a deep learning model, Mol-PECO (Molecular Representation by Positional Encoding of Coulomb Matrix), designed to predict olfactory perceptions based on molecular structures and electrostatics. Mol-PECO learns the efficient embedding of molecules by utilizing the Coulomb matrix, which encodes atomic coordinates and charges, as an alternative of the adjacency matrix and its Laplacian eigenfunctions as positional encoding of atoms. With a comprehensive dataset of odor molecules and descriptors, Mol-PECO outperforms traditional machine learning methods using molecular fingerprints and graph neural networks based on adjacency matrices. The learned embeddings by Mol-PECO effectively capture the odor space, enabling global clustering of descriptors and local retrieval of similar odorants. This work contributes to a deeper understanding of the olfactory sense and its mechanisms. [ABSTRACT FROM AUTHOR]

Identifying the rank of species in a complex ecosystem is a difficult task, since the rank of each species invariably depends on the interactions stipulated with other species through the adjacency matrix of the network. A common ranking method in economic and ecological networks is to sort the nodes such that the layout of the reordered adjacency matrix looks maximally nested with all nonzero entries packed in the upper left corner, called Nestedness Maximization Problem (NMP). Here we solve this problem by defining a suitable cost-energy function for the NMP which reveals the equivalence between the NMP and the Quadratic Assignment Problem, one of the most important combinatorial optimization problems, and use statistical physics techniques to derive a set of self-consistent equations whose fixed point represents the optimal nodes' rankings in an arbitrary bipartite mutualistic network. Concurrently, we present an efficient algorithm to solve the NMP that outperforms state-of-the-art network-based metrics and genetic algorithms. Eventually, our theoretical framework may be easily generalized to study the relationship between ranking and network structure beyond pairwise interactions, e.g. in higher-order networks. Species forming complex ecological or economic ecosystems are organized in hierarchies and the ranks of such species are determined by the adjacency matrix of their interaction network. We introduce a framework to calculate the ranks of species by finding the optimal permutation of rows and columns that makes the adjacency matrix maximally nested. [ABSTRACT FROM AUTHOR]

Pose estimation in crowded scenes is key to understanding human behavior in real-life applications. Most existing CNN-based pose estimation methods often depend on the appearance of visible parts as cues to localize human joints. However, occlusion is typical in crowded scenes, and invisible body parts have no valid features for joint localization. Introducing prior information about the human pose structure to infer the locations of occluded parts is a natural solution to this problem. In this paper, we argue that learning structural information based on human joints alone is not enough to address human body variations and could be prone to overfitting. From a perspective on the human pose as a dual representation of joints and limbs, we propose a pose refinement network, coined as dual graph network (DGN), to jointly learn its structural information of body joints and limbs by incorporating the cooperative constraints between two branches. Specifically, our DGN has two coupled graph convolutional network (GCN) branches to model the structure information of joints and limbs. Each stage in the branch is composed of a feature aggregator and a GCN module for inter-branch information fusion and intra-branch context extraction, respectively. In addition, to enhance the modeling capacity of GCN, we design an adaptive GCN layer (AGL) embedded in the GCN module to handle each pose instance based on its graph structure. We also propose a heatmap-guided sampling to leverage the features of the body parts to provide rich visual features for the inference of occluded parts. We perform extensive experiments on five challenging datasets to demonstrate the effectiveness of our DGN on pose estimation. Our DGN obtains significant performance improvement from 67.9 to 72.4 mAP in the CrowdPose dataset with the same CNN-based pose estimator and training strategy as the OPEC-Net. It shows that, compared to the OPEC-Net only considering joints, our DGN has a clear advantage due to the joint consideration of both joints and limbs. Meanwhile, our DGN is also helpful for pose estimation in general datasets (i.e., COCO and Pose track) with less occlusion and mutual interference, demonstrating the generalization power of DGN on refining human poses. [ABSTRACT FROM AUTHOR]

For a simple graph G, let A(G) be the adjacency matrix and D(G) be the diagonal matrix of the vertex degrees of graph G. For a real number α ∈ [ 0 , 1 ] , the generalized adjacency matrix A α (G) is defined as A α (G) = α D (G) + (1 - α) A (G) . The largest eigenvalue of the matrix A α (G) is the generalized adjacency spectral radius or the A α -spectral radius of the graph G. In this paper, we obtain some new sharp lower and upper bounds for the generalized adjacency spectral radius of G, in terms of different parameters like vertex degrees, the maximum and the second maximum degrees, the number of vertices and the number of edges, etc, associated with the structure of graph G. The extremal graphs attaining these bounds are characterized. We show that our bounds improve some recent given bounds in the literature in some cases. Further, our results extend some known results for the adjacency and/or the signless Laplacian spectral radius of a graph G to a general setting. [ABSTRACT FROM AUTHOR]

Under elimination of two arcs, spectrum of digraph having ring structure and two Hamiltonian cycles is shown real, if and only if the number of vertices is even and “interval between arcs,” eliminated from the same cycle, is maximal. Possibility to apply the obtained results to evaluate failure-resistance of networks with ring topology is considered. [ABSTRACT FROM AUTHOR]

Flowcharts have broad applications in the fields of software development, engineering design, and scientific experimentation. Current flowchart data structure is mainly based on the adjacency list, cross-linked list, and adjacency matrix of the graph structure. Such design originated from the fact that any two nodes could have a connection relationship. But flowcharts have clear regularities, and their nodes have a certain inflow or outflow relationship. When graph structures such as an adjacency table or an adjacency matrix are used to store a flowchart, there is a large room for optimization in terms of traversal time and storage complexities, as well as usage convenience. In this paper we propose two hierarchical data structures for flowchart design. In the proposed structures, a flowchart is composed of levels, layers, and numbered nodes. The nodes between layers are connected according to a certain set of systematic design rules. Compared with the traditional graph data structures, the proposed schemes significantly reduce the storage space, improve the traversal efficiency, and resolve the problem of nesting between sub-charts. Experimental data based on flowchart examples used in this paper show that, compared with adjacency list, the hierarchical table data structure reduces the traversal time by 50% while their storage spaces are similar; compared with adjacency matrix, the hierarchical matrix data structure reduces the traversal time by nearly 70% and saves the storage space by about 50%. The proposed structures could have broad applications in flowchart-based software development, such as low-code engineering for smart industrial manufacturing. [ABSTRACT FROM AUTHOR]

A smooth traffic flow is very crucial for an intelligent traffic system. Consequently, traffic forecasting is critical in achieving unwrinkled traffic flow. However, due to its spatial and temporal interdependence, traffic forecasting might be more difficult. Graph neural networks (GNN) are widely used to obtain traffic forecasting due to their capability to operate in non-Euclidean data. The topological connection of the traffic network plays a crucial role in graph structure learning. Therefore, the importance of the adjacency matrix in graph construction might be significant for effective traffic forecasting. As a result, for efficient graph construction, a Deep Spatial-Temporal Graph Neural Network (DSTGNN) is proposed for the construction of the weighted adjacency matrix and traffic speed prediction accurately by recording topological and temporal information. Three different weighted adjacency matrices are suggested depending on three different proposed algorithms for different variations of traffic's spatial condition. The new adjacency matrix is used in a novel DSTGNN for predicting the traffic state. The novel model comprised multiple layers with skip connections to adequately extract the variation of temporal and spatial information. DSTGNN outperforms the standard and other graph neural network models on four traffic speed datasets, SZ-taxi, Los-loop, PeMSD7, and METR-LA. [ABSTRACT FROM AUTHOR]

As an essential part of traffic management, traffic flow prediction attracts worldwide attention to intelligent traffic systems (ITSs). Complicated spatial dependencies due to the well-connected road networks and time-varying traffic dynamics make this problem extremely challenging. Recent works have focused on modeling this complicated spatial-temporal dependence through graph neural networks with a fixed weighted graph or an adaptive adjacency matrix. However, fixed graph methods cannot address data drift due to changes in the road network structure, and adaptive methods are time consuming and prone to be overfitting because the learning algorithm thoroughly optimizes the adaptive matrix. To address this issue, we propose a principal graph embedding convolutional recurrent network (PGECRN) for accurate traffic flow prediction. First, we propose the adjacency matrix graph embedding (AMGE) generation algorithm to solve the data drift problem. AMGE can model the distribution of spatiotemporal series after data drift by extracting the principal components of the original adjacency matrix and performing an adaptive transformation. At the same time, it has fewer parameters, alleviating overfitting. Then, except for the essential spatial correlations, traffic flow data are also temporally dynamic. We utilize temporal variation by integrating gated recurrent units (GRU) and AMGE to comprise the proposed model. Finally, PGECRN is evaluated on two real-world highway datasets, PeMSD4 and PeMSD8. Compared with the existing baselines, the better prediction accuracy of our model shows that it can accurately and efficiently model traffic flow. [ABSTRACT FROM AUTHOR]

Action recognition methods based on spatial-temporal skeleton graphs have been applied extensively. The spatial and temporal graphs are generally modeled individually in previous approaches. Recently, many researchers capture the correlation information of temporal and spatial dimensions in spatial-temporal graphs. However, the existing methods have several issues such as 1. The existing modal graphs are defined based on the human body structure which is not flexible enough; 2. The approach to extracting non-local neighborhood features is insufficiently powerful; 3. Attention modules are limited to a single scale; 4. The fusion of multiple data streams is not sufficiently effective. This work proposes a novel multi-stream adaptive 3D attention graph convolution network for skeleton-based action recognition that improves the aforementioned issues. The method utilizes an adaptive topology graph with an adaptive connection coefficient to adaptively optimize the topology of the graph during the training process according to the input data. An optimal high-order adjacency matrix is constructed in our work to balance the weight bias, which captures non-local neighborhood features precisely. Moreover, we design a multi-scale attention mechanism to aggregate information from multiple ranges, which makes the graph convolution focus on more efficient nodes, frames, and channels. To further improve the performance of the model, a novel multi-stream framework is proposed to aggregate the high-order information of the skeleton. The experiment results on the NTU-RGBD and Kinetics-Skeleton prove that our proposed method reveals better results than existing methods. [ABSTRACT FROM AUTHOR]

The rapid advancement of microservice architecture in the cloud has led to the necessity of effectively detecting, classifying, and diagnosing run failures in microservice applications. Due to the high dynamics of cloud environments and the complex dependencies between microservices, it is challenging to achieve robust real-time system fault identification. This paper proposes an interpretable fault diagnosis framework tailored for microservice architecture, namely Multi-scale Learnable Transformation Graph for Fault Classification and Diagnosis(MTG_CD). Firstly, we employ multi-scale neural transformation and graph structure adjacency matrix learning to enhance data diversity while extracting temporal-structural features from system monitoring metrics Secondly, a graph convolutional network (GCN) is utilized to fuse the extracted temporal-structural features in a multi-feature modeling approach, which helps to improve the accuracy of anomaly detection. To identify the root cause of system faults, we finally conduct a coarse-grained level diagnosis and exploration after obtaining the results of classifying the fault data. We evaluate the performance of MTG_CD on the microservice benchmark SockShop, demonstrating its superiority over several baseline methods in detecting CPU usage overhead, memory leak, and network delay faults. The average macro F1 score improves by 14.05%. [ABSTRACT FROM AUTHOR]

The thermal error reduces the machining accuracy of machine tools, and should be effectively controlled. But the accurate prediction of the thermal error is challenging because of the complex and dynamic running conditions. In previous studies, the temporal feature of the thermal error is considered, and the spatial feature of the thermal error is not considered. However, the thermal error has temporal-spatial (TS) behaviors, and then it is not sufficient to consider the temporal feature only, leading to a low prediction accuracy and poor robustness. Furthermore, most studies on the TS modeling ignore the complexity of the spatial feature, resulting in the spatial feature of the thermal error not being comprehensively captured. When building a TS model, many studies simply connect the spatial model with the temporal model in series. However, the spatial feature changes with the running time, and the series model cannot truly reflect the TS features. To address these challenges, a new dynamic TS memory graph convolutional network (DTSMGCN) model is proposed to learn the dynamic TS features of the thermal error in this study. The generation mechanism of the thermal error is demonstrated by solving the heat conduction equation, and the dynamic TS behaviors are revealed by the Laplace transform. The designed DTSMGCN cell consists of the marginal unit, joint unit, and hybrid adjacency matrix, and can capture the temporal feature of each variable and the TS features among variables. Moreover, to expedite the training process and improve the executing efficiency, an industrial-oriented machine learning big data framework (IOMLBDF) is designed. The proposed DTSMGCN model is embedded into the designed IOMLBDF. The results show that the DTSMGCN model outperforms other machine learning models, and the designed IOMLBDF can improve the training efficiency when increasing the number of virtual machine nodes and achieve the real-time control of the thermal error. [ABSTRACT FROM AUTHOR]

The Brain Tumor presents a highly critical situation concerning the brain, characterized by the uncontrolled growth of an abnormal cell cluster. Early brain tumor detection is essential for accurate diagnosis and effective treatment planning. In this paper, a novel Convolutional Neural Network (CNN) based Graph Neural Network (GNN) model is proposed using the publicly available Brain Tumor dataset from Kaggle to predict whether a person has brain tumor or not and if yes then which type (Meningioma, Pituitary or Glioma). The objective of this research and the proposed models is to provide a solution to the non-consideration of non-Euclidean distances in image data and the inability of conventional models to learn on pixel similarity based upon the pixel proximity. To solve this problem, we have proposed a Graph based Convolutional Neural Network (GCNN) model and it is found that the proposed model solves the problem of considering non-Euclidean distances in images. We aimed at improving brain tumor detection and classification using a novel technique which combines GNN and a 26 layered CNN that takes in a Graph input pre-convolved using Graph Convolution operation. The objective of Graph Convolution is to modify the node features (data linked to each node) by combining information from nearby nodes. A standard pre-computed Adjacency matrix is used, and the input graphs were updated as the averaged sum of local neighbor nodes, which carry the regional information about the tumor. These modified graphs are given as the input matrices to a standard 26 layered CNN with Batch Normalization and Dropout layers intact. Five different networks namely Net-0, Net-1, Net-2, Net-3 and Net-4 are proposed, and it is found that Net-2 outperformed the other networks namely Net-0, Net-1, Net-3 and Net-4. The highest accuracy achieved was 95.01% by Net-2. With its current effectiveness, the model we propose represents a critical alternative for the statistical detection of brain tumors in patients who are suspected of having one. [ABSTRACT FROM AUTHOR]

Multivariate time series forecasting is an important issue in industries, agriculture, finance, and other applications. There are many challenging problems in it such as non-linear and complicated relationships among the series. The entanglement of latent multiple different sequence patterns maybe one of the most reasons for the time series complex behavior, and decomposition can help reveal the hidden evolution law. Graph is a good modelling tool for multiple entities and graph neural network has showed better learning ability for spatial dependence, but its high memory consumption requires valid solutions. Inspired by the above two points, we propose a Temporal Decomposition enhanced Graph neural network for Multivariate time Series Forecasting, namely TDG4MSF, which mainly consists of four components: temporal decomposition enhanced representation learning, graph structure learning, gated GNNML-based representation learning and MLP-based forecasting. A progressive quadratic decomposition architecture is designed in the temporal decomposition enhanced representation learning that extracts the different periodic patterns of time series. Graph structure learning is used to construct adjacency matrix to represent the spatial topological structure. The temporal decomposition enhanced representation and adjacency matrix are fed into gated GNNML to integrating temporal and spatial information between variables. A MLP-based forecasting is utilized to make multivariate time series prediction. Experimental results show the effectiveness of our model in short- and medium-term prediction scenarios are superior to the state-of-the-art methods, which help make exact decisions timely. Code is available at: https://github.com/TYUT-Theta/MHZN.git. [ABSTRACT FROM AUTHOR]

The traffic flow prediction task is essential to the urban intelligent transportation system. Due to the complex correlation of traffic flow data, insufficient use of spatiotemporal features will often lead to significant deviations in prediction results. This paper proposes an adaptive traffic flow prediction model AD-GNN based on spatiotemporal graph neural network. The gated temporal convolutional network captures the temporal dependence between layers. Moreover, the diffusion graph convolutional network simulates the spatial relationship between nodes. Then, the parameterized adjacency matrix is used to construct an adaptive convolutional network to adaptively mine the implicit global deep spatial dependence. The experimental results show that the model has good prediction performance on three real public datasets and can sufficiently meet real needs. [ABSTRACT FROM AUTHOR]

A novel approach (TOMOCOMD-CARDD) to computer-aided “rational” drug design is illustrated. This approach is based on the calculation of the non-stochastic and stochastic linear indices of the molecular pseudograph’s atom-adjacency matrix representing molecular structures. These TOMOCOMD-CARDD descriptors are introduced for the computational (virtual) screening and “rational” selection of new lead antibacterial agents using linear discrimination analysis. The two structure-based antibacterial-activity classification models, including non-stochastic and stochastic indices, classify correctly 91.61% and 90.75%, respectively, of 1525 chemicals in training sets. These models show high Matthews correlation coefficients (MCC=0.84 and 0.82). An external validation process was carried out to assess the robustness and predictive power of the model obtained. These QSAR models permit the correct classification of 91.49% and 89.31% of 505 compounds in an external test set, yielding MCCs of 0.84 and 0.79, respectively. The TOMOCOMD-CARDD approach compares satisfactorily with respect to nine of the most useful models for antimicrobial selection reported to date. Finally, an in silico screening of 87 new chemicals reported in the anti-infective field with antibacterial activities is developed showing the ability of the TOMOCOMD-CARDD models to identify new lead antibacterial compounds. [ABSTRACT FROM AUTHOR]

In recent years, there has been a growing prevalence of deep learning in various domains, owing to advancements in information technology and computing power. Graph neural network methods within deep learning have shown remarkable capabilities in processing graph-structured data, such as social networks and traffic networks. As a result, they have garnered significant attention from researchers.However, real-world data often face challenges like data sparsity and missing labels, which can hinder the performance and generalization ability of graph convolutional neural networks. To overcome these challenges, our research aims to effectively extract the hidden features and topological information of graph convolutional neural networks. We propose an innovative model called Adaptive Feature and Topology Graph Convolutional Neural Network (AAGCN). By incorporating an adaptive layer, our model preprocesses the data and integrates the hidden features and topological information with the original data’s features and structure. These fused features are then utilized in the convolutional layer for training, significantly enhancing the expressive power of graph convolutional neural networks.To evaluate the effectiveness of the adaptive layer in the AAGCN model, we conducted node classification experiments on real datasets. The results validate its ability to address data sparsity and improve the classification performance of graph convolutional neural networks.In conclusion, our research primarily focuses on addressing data sparsity and missing labels in graph convolutional neural networks. The proposed AAGCN model, which incorporates an adaptive layer, effectively extracts hidden features and topological information, thereby enhancing the expressive power and classification performance of these networks. [ABSTRACT FROM AUTHOR]

Phase-encoded oscillating neural networks offer compelling advantages over metal-oxide-semiconductor-based technology for tackling complex optimization problems, with promising potential for ultralow power consumption and exceptionally rapid computational performance. In this work, we investigate the ability of these networks to solve optimization problems belonging to the nondeterministic polynomial time complexity class using nanoscale vanadium-dioxide-based oscillators integrated onto a Silicon platform. Specifically, we demonstrate how the dynamic behavior of coupled vanadium dioxide devices can effectively solve combinatorial optimization problems, including Graph Coloring, Max-cut, and Max-3SAT problems. The electrical mappings of these problems are derived from the equivalent Ising Hamiltonian formulation to design circuits with up to nine crossbar vanadium dioxide oscillators. Using sub-harmonic injection locking techniques, we binarize the solution space provided by the oscillators and demonstrate that graphs with high connection density (η > 0.4) converge more easily towards the optimal solution due to the small spectral radius of the problem's equivalent adjacency matrix. Our findings indicate that these systems achieve stability within 25 oscillation cycles and exhibit power efficiency and potential for scaling that surpasses available commercial options and other technologies under study. These results pave the way for accelerated parallel computing enabled by large-scale networks of interconnected oscillators. Oscillating neural networks promise ultralow power consumption and rapid computation for tackling complex optimization problems. Here, the authors demonstrate VO2 oscillators to solve NP-complete problems with projected power consumption of 13 µW/oscillator. [ABSTRACT FROM AUTHOR]

In the field of skeleton-based action recognition, accurately recognizing human actions is crucial for applications such as virtual reality and motion analysis. However, this task faces challenges such intraindividual action differences and long-term temporal dependencies. To address these challenges, we propose an innovative model called spatial-temporal graph neural ordinary differential equations (STG-NODE). First, in the data preprocessing stage, the dynamic time warping (DTW) algorithm is used to normalize and calculate 3D skeleton data to facilitate the derivation of customized adjacency matrices for improving the influence of intraindividual action differences. Secondly, a custom ordinary differential equation (ODE) integrator is applied based on the initial conditions of the temporal features, producing a solution function that simulates the dynamic evolution trend of the events of interest. Finally, the outstanding ODE solver is used to numerically solve the time features based on the solution function to increase the influence of long-term dependencies on the recognition accuracy of the model and provide it with a more powerful temporal modeling ability. Through extensive experiments conducted on the NTU RGB+D 60 and Kinetics Skeleton 400 benchmark datasets, we demonstrate the superior performance of STG-NODE in the action recognition domain. The success of the STG-NODE model also provides new ideas and methods for the future development of the action recognition field. [ABSTRACT FROM AUTHOR]

In practical scenarios, many graphs dynamically evolve over time. The new node classification without labels and historical information is challenging. To address this challenge, we design a double-layer attentive graph convolutional network (DLA-GCN) based on the transfer learning, which mainly includes three deep learning components: the double-layer graph convolutional network (DLGCN), node multi-parameter learning (NMPL) algorithm, and domain-adversarial transfer learning (DATL) method. In terms of dynamic spatial correlation, DLGCN jointly exploits the pre-defined and adaptive adjacency matrix to capture local and global feature aggregation. An inter-graph attention mechanism is further used to produce a unified representation for each node in graphs by automatically merging different spatial correlations. To reduce the complexity and improve accuracy, the matrix decomposition method is designed to learn the node-specific patterns of nodes in the NMPL component. In terms of dynamic time correlation, DATL is proposed to learns and transfers similar features as historical information of new nodes by optimizing three different loss functions, namely source classifier loss, domain classifier loss, and target classifier loss as a whole. The experimental results on two real-world graph classification datasets show that the proposed approach can improve the accuracy by 18% and 10%, respectively, compared with the state-of-art baselines. [ABSTRACT FROM AUTHOR]

Graph theory can be used to address problems with complex network structures. Congenital heart diseases (CHDs) involve complex abnormal connections between chambers, vessels, and organs. We proposed a new method to represent CHDs based on graph theory, wherein vertices were defined as the spaces through which blood flows and edges were defined by the blood flow between the spaces and direction of the blood flow. The CHDs of tetralogy of Fallot (TOF) and transposition of the great arteries (TGA) were selected as examples for constructing directed graphs and binary adjacency matrices. Patients with totally repaired TOF, surgically corrected d-TGA, and Fontan circulation undergoing four-dimensional (4D) flow magnetic resonance imaging (MRI) were included as examples for constructing the weighted adjacency matrices. The directed graphs and binary adjacency matrices of the normal heart, extreme TOF undergoing a right modified Blalock–Taussig shunt, and d-TGA with a ventricular septal defect were constructed. The weighted adjacency matrix of totally repaired TOF was constructed using the peak velocities obtained from 4D flow MRI. The developed method is promising for representing CHDs and may be helpful in developing artificial intelligence and conducting future research on CHD. [ABSTRACT FROM AUTHOR]

Sparse subspace clustering (SSC) focuses on revealing the structure and distribution of high dimensional data from an algebraic perspective. It is a two-phase clustering technique, performing sparse representation of the high dimensional data and subsequently cutting the induced affinity graph, which cannot achieve an optimal or expected clustering result. To address this challenge, this paper proposes an approach to subspace representation collaborative clustering (SRCC) for incomplete high dimensional data. In the proposed model, both phases of sparse subspace representation and clustering are integrated into a unified optimization, in which a fuzzy partition matrix is introduced as a bridge to cluster the extracted sparse representation features of the data. At the same time, the missing entries are adaptively imputed along with the two phases. To generalize SRCC to a semi-supervised case, an adjacency matrix of incomplete data is constructed with the ideas of 'Must-link' and 'Cannot-link'. Meanwhile, a semi-supervised indicator matrix is introduced to promote discriminative capacity of revealing global and local structures of incomplete data and enhance the performance of clustering. The semi-supervised sparse representation collaborative clustering (S3RCC) is modeled. Extensive experiments on lots of real-world benchmark datasets demonstrate the superior performance of the proposed two models on imputation and clustering of incomplete data compared to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper seeks to design the least-cost delivery routes relating to the distribution of geotowns through the shortest distance matrix estimated by the multiple traveling salesman problems. We construct the initial distance matrix based on road distance considering all the nodes. Based on the adjacency matrix, we use the R package "sna" to calculate the different measures of centrality in the network. Next, we apply the traveling salesman problem to connect all the nodes at once for planning the trip in the proposed circuit. Finally, we use the Louvain community detection algorithm to cluster geotowns for better tourism planning and ease of travel. Based on the proposed geoheritage sites in Northeast India, the tourist spots may be organized and interconnected. This paper promotes and develops an approach to incorporating national geosites with national geoheritages and moves towards geoparks, keeping in view conservation measures of appropriate international impartial organizations. [ABSTRACT FROM AUTHOR]

This paper presents four centrality measurements applied to an alternating current (AC) microgrid (MG) modeled as a multiplex network. The MG secondary control is separated into a frequency and a power-sharing layers, each one with a different adjacency matrix. A physical layer is also considered with an admittance matrix representing the impedances among the inverters. Centrality measures are used to determine the importance of nodes in separate layers, thereafter adjacency and Laplacian matrices are redefined to calculate the role of nodes in the multiplex system. First, a global adjacency matrix is calculated by the matrix sum of each adjacency matrix. Second, the adjacency matrix is calculated by a supra-Laplacian matrix. The first eigenvalue of the perturbed matrix is used to determine the diffusivity in the network using as leaders the sets obtained by the centrality measures. The role of the nodes in the system is verified in a simulated MG model of 37 nodes. Degree centrality and energy Laplacian measures present similar sets of nodes; however, the fastest set of nodes is found using the Eigenvector measurements for uniform and supra Laplacian approach. [ABSTRACT FROM AUTHOR]

In complex traffic scenes, accurate identification of pedestrian orientations can help drivers determine pedestrian trajectories and help reduce traffic accidents. However, there are still many challenges in pedestrian orientation recognition. First, due to the irregular appearance of pedestrians, it is difficult for general Convolutional Neural Networks (CNNs) to extract discriminative features. In addition, more features of body parts help to judge the orientation of pedestrians. For example, head, arms and legs. However, they are usually small and not conducive to feature extraction. Therefore, in this work, we use several discrete values to define the orientation of pedestrians, and propose a Gated Graph Neural Network (GGNN)-based Graph Recurrent Attention Network (GRAN) to classify the orientation of pedestrians. The contributions are as follows: (1) We construct a body parts graph consisting of head, arms and legs on the feature maps output by the CNN backbone. (2) Mining the dependencies between body parts on the graph via the proposed GRAN, and utilizing the encoder–decoder to propagate features among graph nodes. (3) In this process, we propose an adjacency matrix with attention edge weights to dynamically represent graph node relationships, and the edge weights are learned during network training. To evaluate the proposed method, we conduct experiments on three different benchmarks (PDC, PDRD, and Cityscapes) with 8, 3, and 4 orientations, respectively. Note that the orientation labels for PDRD and Cityscapes are annotated by our hand. The proposed method achieves 97%, 91% and 90% classification accuracy on the three data sets, respectively. The results are all higher than current state-of-the-art methods, which demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Temporal satellite networks can accurately describe the dynamic process of satellite networks by considering the interaction relationship and interaction sequence between satellite nodes. In addition, the measurement of node importance in satellite networks plays a crucial role in understanding the structure and function of the network. The classical supra-adjacency matrix (SAM) temporal model identifies the key nodes in the temporal network to some extent, which ignores the differences of inter-layer connectivity relationships leading to the inability to reflect the dynamic variations of satellite nodes. Therefore, the evaluation method based on time slot correlation is proposed to measure the importance of satellite nodes in this paper. Firstly, the correlation coefficient of time slot nodes is defined to measure the coupling relationship of adjacent time slots. Secondly, the dynamic supra-adjacency matrix (DSAM) temporal network model is proposed considering the correlation between adjacent time slots and the characteristics of link time. Finally, the node importance ranking results in each time slot and a global perspective are obtained by utilizing the eigenvector centrality. Experimental simulations of the Iridium and Orbcomm constellations demonstrate that the DSAM method has a relatively accurate recognition rate and high stability. [ABSTRACT FROM AUTHOR]

The visualization of dynamic graphs is a challenging task owing to the various properties of the underlying relational data and the additional time-varying property. For sparse and small graphs, the most efficient approach to such visualization is node-link diagrams, whereas for dense graphs with attached data, adjacency matrices might be the better choice. Because graphs can contain both properties, being globally sparse and locally dense, a combination of several visual metaphors as well as static and dynamic visualizations is beneficial. In this paper, a visually and algorithmically scalable approach that provides views and perspectives on graphs as interactively linked node-link and adjacency matrix visualizations is described. As the novelty of this technique, insights such as clusters or anomalies from one or several combined views can be used to influence the layout or reordering of the other views. Moreover, the importance of nodes and node groups can be detected, computed, and visualized by considering several layout and reordering properties in combination as well as different edge properties for the same set of nodes. As an additional feature set, an automatic identification of groups, clusters, and outliers is provided over time, and based on the visual outcome of the node-link and matrix visualizations, the repertoire of the supported layout and matrix reordering techniques is extended, and more interaction techniques are provided when considering the dynamics of the graph data. Finally, a small user experiment was conducted to investigate the usability of the proposed approach. The usefulness of the proposed tool is illustrated by applying it to a graph dataset, such as e co-authorships, co-citations, and a Comprehensible Perl Archive Network distribution. [ABSTRACT FROM AUTHOR]

The problem of predicting links in large networks is an important task in a variety of practical applications, including social sciences, biology and computer security. In this paper, statistical techniques for link prediction based on the popular random dot product graph model are carefully presented, analysed and extended to dynamic settings. Motivated by a practical application in cyber-security, this paper demonstrates that random dot product graphs not only represent a powerful tool for inferring differences between multiple networks, but are also efficient for prediction purposes and for understanding the temporal evolution of the network. The probabilities of links are obtained by fusing information at two stages: spectral methods provide estimates of latent positions for each node, and time series models are used to capture temporal dynamics. In this way, traditional link prediction methods, usually based on decompositions of the entire network adjacency matrix, are extended using temporal information. The methods presented in this article are applied to a number of simulated and real-world graphs, showing promising results. [ABSTRACT FROM AUTHOR]

Improving the human reliability of the human–machine interface (HMI) of deep-sea manned submersible is of great importance for the development of the deep-sea field. Based on the SHEL (Software S, Hardware H, Environment E, Liveware L) model, this study classifies the performance shaping factors (PSF) that affect the human reliability of submersible HMIs and builds a PSF system. The interpretative structural model (ISM) is used to matrix the interactions between the elements that make up the system of PSF. A multi-level recursive structure is obtained by building the corresponding adjacency matrix. The Noisy-OR model is introduced to construct a Bayesian network in order to build a new HMI evaluation method. A real case of Bayesian network causal inference verifies the validity of the built method. This study proposes a set of HMI human reliability evaluation methods applicable to deep-sea manned submersible, which provides a new idea for human reliability assessment. [ABSTRACT FROM AUTHOR]

The characteristics of common prosperity include harmonious relationships between humans and the environment, as well as sustainable economic and social growth. The process of achieving common prosperity will necessarily have an impact on carbon emissions. In this article, panel statistics collected from 30 Chinese provinces and cities between the years 2006 and 2020 are utilized to assess the level of common prosperity and the intensity of carbon emissions in China. Then the SDM model is applied to explore the effects of the common prosperity level on the intensity of carbon emissions. The findings reveal that: (i) The common prosperity level in China has shown an increasing tendency. Between 2006 and 2020, the mean level of common prosperity increased from 0.254 to 0.486. From the regional perspective, eastern China has seen greater levels of common prosperity than central China, while central China has experienced greater levels of common prosperity than western China; regional disparities in the degree of common prosperity are substantial among Chinese provinces from 2006 to 2020; the common prosperity level is relatively high in economically developed provinces and relatively low in economically backward provinces. (ii) China's carbon emission intensity shows a continuous downward tendency. The annual average intensity of China's carbon emissions decreased from 4.458 in 2006 to 2.234 in 2020. From the regional perspective, the three main regions' carbon emission intensity likewise exhibits a decline in tendency between 2006 and 2020; still, western China continues to have the greatest carbon emission intensity, following central China, while eastern China has the smallest; however, certain provinces, notably Inner Mongolia and Shanxi, continue to have high carbon emission intensity. (iii) China's common prosperity level and carbon emission intensity both exhibit positive spatial autocorrelation at a 1% significant level under the adjacency matrix. The spatial agglomeration effect is significant, and adjacent provinces can affect each other. (iv) The SDM (Spatial Durbin Model) model test with fixed effects finds that the increase in the level of common prosperity suppresses the intensity of carbon emissions in the local area and neighboring regions. (v) The mediating effects model indicates that the process of common prosperity suppresses carbon emission intensity through high-quality economic development, narrowing the income disparity, and the development of a sharing economy. [ABSTRACT FROM AUTHOR]

Link prediction aims to predict missing links or eliminate spurious links by employing known complex network information. As an unsupervised linear feature representation method, matrix factorization (MF)-based autoencoder (AE) can project the high-dimensional data matrix into the low-dimensional latent space. However, most of the traditional link prediction methods based on MF or AE adopt shallow models and single adjacency matrices, which cannot adequately learn and represent network features and are susceptible to noise. In addition, because some methods require the input of symmetric data matrix, they can only be used in undirected networks. Therefore, we propose a deep manifold matrix factorization autoencoder model using global connectivity matrix, called DM-MFAE-G. The model utilizes PageRank algorithm to get the global connectivity matrix between nodes for the complex network. DM-MFAE-G performs deep matrix factorization on the local adjacency matrix and global connectivity matrix, respectively, to obtain global and local multi-layer feature representations, which contains the rich structural information. In this paper, the model is solved by alternating iterative optimization method, and the convergence of the algorithm is proved. Comprehensive experiments on different real networks demonstrate that the global connectivity matrix and manifold constraints introduced by DM-MFAE-G significantly improve the link prediction performance on directed and undirected networks. [ABSTRACT FROM AUTHOR]

The manuscript proposes a fault diagnosis method based on graph neural network (GNN) with one-shot learning to effectively diagnose rolling bearings under variable operating conditions. In this proposed method, the convolutional neural network is utilized for feature extraction, reducing loss in the process. Subsequently, GNN applies an adjacency matrix to generate codes for one-shot learning. Experimental verification is conducted using open data from Case Western Reserve University Rolling Bearing Data Center, where four different working conditions with six types of typical faults are selected as input signals. The classification accuracy of the proposed method reaches 98.02%. To further validate its effectiveness, traditional single-learning neural networks such as Siamese, Matching Net, Prototypical Net and (Stacked Auto Encoder) SAE are introduced as comparisons. Simulation results that the proposed method outperforms all chosen methods. [ABSTRACT FROM AUTHOR]

Session-based recommender systems (SBR) aim to predict the next action of an anonymous user session. Recently Graph Neural Networks (GNN) models have gained a lot of attention in this task. Existing models learn sequential complex transition patterns using the Gated Graph Neural Networks (GGNN) architecture. We argue that learning non-sequential complex transition patterns may be sufficient in SBR due to the short time interval and length of the sessions. To fully exploit the advantages of non-sequential GNN such as scalability, we design Simplified Graph Neural Network for Session-based Recommendation SimGNN, a non-sequential, linear GNN model for interaction representation. SimGNN uses the k-th power of the normalized adjacency matrix and the current session interactions to learn the k-th layer interaction representation. To improve the representation, SimGNN uses a highway gating mechanism. From the interaction representation learned by the proposed non-sequential and linear model, SimGNN models local preference and global preference and uses a proposed gating mechanism to aggregate these preferences. Experimental results showed that SimGNN outperforms state-of-the-art sequential GGNN models for SBR in terms of accuracy metrics - precision and mean reciprocal ranking. [ABSTRACT FROM AUTHOR]

This work presents a novel approach to estimate brain functional connectivity networks via generative learning. Due to the complexity and variability of rs-fMRI signal, we consider it as a random variable, and utilize variational autoencoder networks to encode it as a confidence distribution in the latent space rather than as a fixed vector, so as to establish the relationship between them. First, the mean time series of each brain region of interest is mapped into a multivariate Gaussian distribution. The correlation between two brain regions is measured by the Jensen-Shannon divergence that describes the statistical similarity between two probability distributions, and then the adjacency matrix is created to indicate the functional connectivity strength of pairwise brain regions. Meanwhile, our findings show that the adjacency matrices obtained at VAE latent spaces of different dimensionalities have good complementarity for MCI identification in precision and recall, and the classification performance can be further boosted by an efficient cascade of classifiers. This proposal constructs brain functional networks from a statistical modeling standpoint, improving the statistical ability of population data and the generalization ability of observation data variability. We evaluate the proposed framework over the task of identifying subjects with MCI from normal controls, and the experimental results on the public dataset show that our method significantly outperforms both the baseline and current state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The analysis of node order structure in dynamic temporal networks is significant for network propagation control. To further accurately characterize the inter-layer coupling relationship of dynamic temporal networks, this paper firstly defines the node neighborhood structure homogeneity rate and node neighborhood location heterogeneity rate based on the node neighborhood structure evolution feature information and node neighborhood location evolution feature information, and integrates the influence of the change in both neighborhood structure and neighborhood location on the node importance in the process of node temporal evolution. Secondly, a Supra-Adjacency Matrix based on Neighborhood Structure (NSAM) temporal network node importance order structure modeling method is proposed by combining the local structure and overall structure evolution information of nodes during the temporal evolution process. Finally, the node importance order structure of the dynamic temporal network is obtained by combining the eigenvector centrality to represent the node importance attribute value. Simulations show that compared with the classical hierarchical temporal network model, the NSAM model can improve the identification accuracy by 38.2% and 7.8%, respectively, and can identify the important nodes in the dynamic temporal network more effectively. [ABSTRACT FROM AUTHOR]

Predicting soil heavy metal (HM) content is crucial for monitoring soil quality and ensuring ecological health. However, existing methods often neglect the spatial dependency of data. To address this gap, our study introduces a novel graph neural network (GNN) model, Multi-Scale Attention-based Graph Neural Network for Heavy Metal Prediction (MSA-GNN-HMP). The model integrates multi-scale graph convolutional network (MS-GCN) and attention-based GNN (AGNN) to capture spatial relationships. Using surface soil samples from the Pearl River Basin, we evaluate the MSA-GNN-HMP model against four other models. The experimental results show that the MSA-GNN-HMP model has the best predictive performance for Cd and Pb, with a coefficient of determination (R2) of 0.841 for Cd and 0.886 for Pb, and the lowest mean absolute error (MAE) of 0.403 mg kg−1 for Cd and 0.670 mg kg−1 for Pb, as well as the lowest root mean square error (RMSE) of 0.563 mg kg−1for Cd and 0.898 mg kg−1 for Pb. In feature importance analysis, latitude and longitude emerged as key factors influencing the heavy metal content. The spatial distribution prediction trend of heavy metal elements by different prediction methods is basically consistent, with the high-value areas of Cd and Pb respectively distributed in the northwest and northeast of the basin center. However, the MSA-GNN-HMP model demonstrates superior detail representation in spatial prediction. MSA-GNN-HMP model has excellent spatial information representation capabilities and can more accurately predict heavy metal content and spatial distribution, providing a new theoretical basis for monitoring, assessing, and managing soil pollution. [ABSTRACT FROM AUTHOR]

Spatio-temporal feature extraction and fusion are crucial to traffic prediction accuracy. However, the complicated spatio-temporal correlations and dependencies between traffic nodes make the problem quite challenging. In this paper, a multi-scale spatio-temporal network (MSSTN) is proposed to exploit complicated local and nonlocal correlations in traffic flow for traffic prediction. In the proposed method, a convolutional neural network, a self-attention module, and a graph convolution network (GCN) are integrated to extract and fuse multi-scale temporal and spatial features to make predictions. Specifically, a self-adaption temporal convolutional neural network (SATCN) is first employed to extract local temporal correlations between adjacent time slices. Furthermore, a self-attention module is applied to capture the long-range nonlocal traffic dependence in the temporal dimension and fuse it with the local features. Then, a graph convolutional network module is utilized to learn spatio-temporal features of the traffic flow to exploit the mutual dependencies between traffic nodes. Experimental results on public traffic datasets demonstrate the superiority of our method over compared state-of-the-art methods. The ablation experiments confirm the effectiveness of each component of the proposed model. Our implementation on Pytorch is publicly available at https://github.com/csust-sonie/MSSTN. [ABSTRACT FROM AUTHOR]

A general method for the enumeration of various classes of chord diagrams with even and odd numbers of chord intersections is considered. The method is based on the calculation of the Pfaffian and Hafnian of the constraint matrix characterizing a class of diagrams. [ABSTRACT FROM AUTHOR]

Fix a positive integer N and a real number 0 < β < 1 / (N + 1) . Let Γ be the homogeneous symmetric Cantor set generated by the IFS { ϕ i (x) = β x + i 1 - β N : i = 0 , 1 , … , N }. For m ∈ Z + we show that there exist infinitely many translation vectors t = (t 0 , t 1 , … , t m) with 0 = t 0 < t 1 < ⋯ < t m such that the union ⋃ j = 0 m (Γ + t j) is a self-similar set. Furthermore, for 0 < β < 1 / (2 N + 1) , we give a finite algorithm to determine whether the union ⋃ j = 0 m (Γ + t j) is a self-similar set for any given vector t . Our characterization relies on determining whether some related directed graph has no cycles, or whether some related adjacency matrix is nilpotent. [ABSTRACT FROM AUTHOR]

Graph neural networks (GNNs) leverage graph convolutions or their approximations to cope with graph-structured data. According to whether convolution is applied to the spectral domain or spatial domain, advances in this direction are generally divided into spectral approaches and spatial approaches. However, current study generally utilizes one of the approaches, while ignoring the combination of the two approaches. In this paper, we propose hybrid deep graph convolutional networks (HDGCNs), novel neural network architectures that combine the spectral approach and the spatial approach to calculate the adjacency matrix, leveraging the deep graph convolutional networks (GCNs) to release the advantages of this combination. In this way, the gap between spectral approaches and spatial approaches is eliminated, and the characteristics of the two approaches are merged together. Extensive experiments on citation networks and web networks offer evidence that the proposed models outperform state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Graph entropy is an important measure of the evolution and complexity of networks. Bipartite graph is a special network and an important mathematical model for system resource allocation and management. In reality, a network system usually has obvious directionality. The direction of the network, or the movement trend of the network, can be described with spectrum index. However, little research has been done on the eigenvalue-based entropy of directed bipartite network. In this study, based on the adjacency matrix, the in-degree Laplacian matrix and the in-degree signless Laplacian matrix of directed bipartite graph, we defined the eigenvalue-based entropy for the directed bipartite network. Using the eigenvalue-based entropy, we described the evolution law of the directed bipartite network structure. Aiming at the direction and bipartite feature of the directed bipartite network, we improved the generation algorithm of the undirected network. We then constructed the directed bipartite nearest-neighbor coupling network, directed bipartite small-world network, directed bipartite scale-free network, and directed bipartite random network. In the proposed model, spectrum of those directed bipartite network is used to describe the directionality and bipartite property. Moreover, eigenvalue-based entropy is empirically studied on a real-world directed movie recommendation network, in which the law of eigenvalue-base entropy is observed. That is, if eigenvalue-based entropy value of the recommendation system is large, the evolution of movie recommendation network becomes orderless. While if eigenvalue-based entropy value is small, the structural evolution of the movie recommendation network tends to be regular. The simulation experiment shows that eigenvalue-based entropy value in the real directed bipartite network is between the values of a directed bipartite small world and a scale-free network. It shows that the real directed bipartite network has the structural property of the two typical directed bipartite networks. The coexistence of the small-world phenomena and the scale-free phenomena in the real network is consistent with the evolution law of typical network models. The experimental results show that the validity and rationality of the definition of eigenvalue-based entropy, which serves as a tool in the analysis of directed bipartite networks. [ABSTRACT FROM AUTHOR]

Link prediction is a fundamental research issue in complex network, which can reveal the potential relationships between users. Most of link prediction algorithms are heuristic and based on topology structure. Weisfeiler–Lehman Neural Machine (WLNM), regarded as a new-generation method, has shown promising performance and thus got attention in link prediction. WLNM extracts an enclosing subgraph of each target link and encodes the subgraph as an adjacency matrix. But it does not consider the relationship between other links of the enclosing subgraph and target links. Therefore, WLNM does not make full use of the topology information around the link, and the extracted enclosing subgraph can only partially represent the topological features around the target link. In this work, a novel approach is proposed, named weighted enclosing subgraph-based link prediction (WESLP). It incorporates the link weights in the enclosing subgraph to reflect their relationship with the target link, and the Katz index between nodes is used to measure the relationship between two links. The prediction models are trained by different classifiers based on these weighted enclosing subgraphs. Experiments show that our proposed method consistently performs well on different real-world datasets. [ABSTRACT FROM AUTHOR]

Link prediction is a fundamental task that predicts whether a link exists between two nodes based on the currently observed network. Existing approaches such as heuristic-based algorithms assume that two nodes are likely to have a link in a network. In fact, they limit algorithm effectiveness when the assumptions are not correct. Moreover, these link prediction algorithms lack generalization ability, which indicates that they have different effects on different types of networks. For example, the common neighbours algorithm works well on social networks, but it shows poor performance on electric power networks. Inspired by the image inpainting technology of generative adversarial networks and the adjacency matrix representation of networks, we propose a new framework for link prediction based on the image inpainting method, named the Generative Image Inpainting for Link Prediction algorithm (GIILP), to address these problems. The key idea of the GIILP is that the network can be converted into an image (the image is a form of the adjacency matrix (two dimensions)). Pixel values represent the likelihood of two nodes. Thus, the problem of predicting a possible link between nodes is converted into filling missing pixels in an image. The link information of the network can be expressed by the image information, which means that our algorithm does not need assumptions such as heuristics, and works regardless of the dataset type. The experimental results on multiple link prediction public datasets demonstrate that our algorithm has an advantage over other algorithms, including heuristic-based and deep learning methods. [ABSTRACT FROM AUTHOR]

The quinary reciprocal system Li+,K+||F–,Cl–,Br–, has been divided into simplexes using graph theory: by making up an adjacency matrix and solving a logical expression. The results have been used to construct the phase tree of the system, which has a linear structure and consists of four stable secant tetrahedra, four stable pentatopes, and one stable hexatope. The number and composition of phases crystallizing in the system have been predicted. The LiF–KCl–KBr–Li2CrO4 stable tetrahedron has been studied using differential thermal analysis and X-ray diffraction. The tetrahedron has no invariant equilibrium points. The continuous series of solid solutions between potassium chloride and potassium bromide has been shown to be stable, without decomposition. Three solid phases have been shown to crystallize in the tetrahedron: LiF, Li2CrO4, and KClxBr1–x. [ABSTRACT FROM AUTHOR]

In recent years, great achievements have been made in graph convolutional network (GCN) for non-Euclidean spatial data feature extraction, especially the skeleton-based feature extraction. However, the fixed graph structure determined by the fixed adjacency matrix usually causes the problems such as the weak spatial modeling ability, the unsatisfactory generalization performance, the excessively large number of model parameters, and so on. In this paper, a spatially adaptive residual graph convolutional network (SARGCN) is proposed for action recognition based on skeleton feature extraction. Firstly, the uniform and fixed topology is not required in our graph. Secondly, a learnable parameter matrix is added to the GCN operation, which can enhance the model's capabilities of feature extraction and generalization, while reducing the number of parameters. Therefore, compared with the several existing models mentioned in this paper, the least number of parameters are used in our model while ensuring the comparable recognition accuracy. Finally, inspired by the ResNet architecture, a residual connection is introduced in GCN to obtain higher accuracy at lower computational costs and learning difficulties. Extensive experimental on two large-scale datasets results validate the effectiveness of our proposed approach, namely NTU RGB+D 60 and NTU RGB+D 120. [ABSTRACT FROM AUTHOR]

Topological quantum field theories (TQFT) encode properties of quantum states in the topological features of abstract manifolds. One can use the topological avatars of quantum states to develop intuition about different concepts and phenomena of quantum mechanics. In this paper we focus on the class of simplest topologies provided by a specific TQFT and investigate what the corresponding states teach us about entanglement. These "planar connectome" states are defined by graphs of simplest topology for a given adjacency matrix. In the case of bipartite systems the connectomes classify different types of entanglement matching the classification of stochastic local operations and classical communication (SLOCC). The topological realization makes explicit the nature of entanglement as a resource and makes apparent a number of its properties, including monogamy and characteristic inequalities for the entanglement entropy. It also provides tools and hints to engineer new measures of entanglement and other applications. Here the approach is used to construct purely topological versions of the dense coding and quantum teleportation protocols, giving diagrammatic interpretation of the role of entanglement in quantum computation and communication. Finally, the topological concepts of entanglement and quantum teleportation are employed in a simple model of information retrieval from a causally disconnected region, similar to the interior of an evaporating black hole. [ABSTRACT FROM AUTHOR]

As an effective method for mining latent information between labels, label correlation is widely adopted by many scholars to model multi-label learning algorithms. Most existing multi-label algorithms usually ignore that the correlation between labels may be asymmetric while asymmetry correlation commonly exists in the real-world scenario. To tackle this problem, a multi-label learning algorithm with asymmetry label correlation (ACML, Asymmetry Label Correlation for Multi-Label Learning) is proposed in this paper. First, measure the adjacency between labels to construct the label adjacency matrix. Then, cosine similarity is utilized to construct the label correlation matrix. Finally, we constrain the label correlation matrix with the label adjacency matrix. Thus, asymmetry label correlation is modeled for multi-label learning. Experiments on multiple multi-label benchmark datasets show that the ACML algorithm has certain advantages over other comparison algorithms. The results of statistical hypothesis testing further illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]