A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

Heterophilic Graph Neural Network Based on Spatial and Frequency Domain Adaptive Embedding Mechanism

Graph Neural Networks(GNNs)play a significant role in tasks related to homophilic graphs.Traditional GNNs,based on the assumption of homophily,employ low-pass filters for neighboring nodes to achieve information aggregation and embedding.However,in heterophilic graphs,nodes from different categories often establish connections,while nodes of the same category are located further apart in the graph topology.This characteristic poses challenges to traditional GNNs,leading to issues of“distant node modeling deficiency”and“failure of the homophily assumption”.In response,this paper introduces the Spatial-Frequency domain Adaptive Heterophilic Graph Neural Networks(SFA-HGNN),which integrates adaptive embedding mechanisms for both spatial and frequency domains to address the aforementioned issues.Specifically,for the first problem,we propose the“Distant Spatial Embedding Module”,aiming to select and aggregate distant nodes through high-order randomwalk transition probabilities to enhance modeling capabilities.For the second issue,we design the“Proximal Frequency Domain Embedding Module”,constructing adaptive filters to separate high and low-frequency signals of nodes,and introduce frequency-domain guided attention mechanisms to fuse the relevant information,thereby reducing the noise introduced by the failure of the homophily assumption.We deploy the SFA-HGNN on six publicly available heterophilic networks,achieving state-of-the-art results in four of them.Furthermore,we elaborate on the hyperparameter selection mechanism and validate the performance of each module through experimentation,demonstrating a positive correlation between“node structural similarity”,“node attribute vector similarity”,and“node homophily”in heterophilic networks.

Weighted Forwarding in Graph Convolution Networks for Recommendation Information Systems

Recommendation Information Systems(RIS)are pivotal in helping users in swiftly locating desired content from the vast amount of information available on the Internet.Graph Convolution Network(GCN)algorithms have been employed to implement the RIS efficiently.However,the GCN algorithm faces limitations in terms of performance enhancement owing to the due to the embedding value-vanishing problem that occurs during the learning process.To address this issue,we propose a Weighted Forwarding method using the GCN(WF-GCN)algorithm.The proposed method involves multiplying the embedding results with different weights for each hop layer during graph learning.By applying the WF-GCN algorithm,which adjusts weights for each hop layer before forwarding to the next,nodes with many neighbors achieve higher embedding values.This approach facilitates the learning of more hop layers within the GCN framework.The efficacy of the WF-GCN was demonstrated through its application to various datasets.In the MovieLens dataset,the implementation of WF-GCN in LightGCN resulted in significant performance improvements,with recall and NDCG increasing by up to+163.64%and+132.04%,respectively.Similarly,in the Last.FM dataset,LightGCN using WF-GCN enhanced with WF-GCN showed substantial improvements,with the recall and NDCG metrics rising by up to+174.40%and+169.95%,respectively.Furthermore,the application of WF-GCN to Self-supervised Graph Learning(SGL)and Simple Graph Contrastive Learning(SimGCL)also demonstrated notable enhancements in both recall and NDCG across these datasets.

An End-To-End Hyperbolic Deep Graph Convolutional Neural Network Framework

Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.

A Temporal Knowledge Graph Embedding Model Based on Variable Translation

Knowledge representation learning(KRL)aims to encode entities and relationships in various knowledge graphs into low-dimensional continuous vectors.It is popularly used in knowledge graph completion(or link prediction)tasks.Translation-based knowledge representation learning methods perform well in knowledge graph completion(KGC).However,the translation principles adopted by these methods are too strict and cannot model complex entities and relationships(i.e.,N-1,1-N,and N-N)well.Besides,these traditional translation principles are primarily used in static knowledge graphs and overlook the temporal properties of triplet facts.Therefore,we propose a temporal knowledge graph embedding model based on variable translation(TKGE-VT).The model proposes a new variable translation principle,which enables flexible transformation between entities and relationship embedding.Meanwhile,this paper considers the temporal properties of both entities and relationships and applies the proposed principle of variable translation to temporal knowledge graphs.We conduct link prediction and triplet classification experiments on four benchmark datasets:WN11,WN18,FB13,and FB15K.Our model outperforms baseline models on multiple evaluation metrics according to the experimental results.

RSscore:Reaction superiority learned from reaction mapping hypergraph

The selection of chemical reactions is directly related to the quality of synthesis pathways,so a reasonable reaction evaluation metric plays a crucial role in the design and planning of synthesis pathways.Since reaction conditions also need to be considered in synthesis pathway design,a reaction metric that combines reaction time,temperature,and yield is required for chemical reactions of different reaction agents.In this study,a chemical reaction graph descriptor which includes the atom-atom mapping relationship is proposed to effectively describe reactions.Then,through pre-training using graph contrastive learning and fine-tuning through supervised learning,we establish a model for generating the probability of reaction superiority(RSscore).Finally,to validate the effectiveness of the current evaluation index,RSscore is applied in two applications,namely reaction evaluation and synthesis routes analysis,which proves that the RSscore provides an important agents-considered evaluation criterion for computer-aided synthesis planning(CASP).

KGTLIR:An Air Target Intention Recognition Model Based on Knowledge Graph and Deep Learning

As a core part of battlefield situational awareness,air target intention recognition plays an important role in modern air operations.Aiming at the problems of insufficient feature extraction and misclassification in intention recognition,this paper designs an air target intention recognition method(KGTLIR)based on Knowledge Graph and Deep Learning.Firstly,the intention recognition model based on Deep Learning is constructed to mine the temporal relationship of intention features using dilated causal convolution and the spatial relationship of intention features using a graph attention mechanism.Meanwhile,the accuracy,recall,and F1-score after iteration are introduced to dynamically adjust the sample weights to reduce the probability of misclassification.After that,an intention recognition model based on Knowledge Graph is constructed to predict the probability of the occurrence of different intentions of the target.Finally,the results of the two models are fused by evidence theory to obtain the target’s operational intention.Experiments show that the intention recognition accuracy of the KGTLIRmodel can reach 98.48%,which is not only better than most of the air target intention recognition methods,but also demonstrates better interpretability and trustworthiness.

AFSTGCN:Prediction for multivariate time series using an adaptive fused spatial-temporal graph convolutional network

The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.

Position-Aware and Subgraph Enhanced Dynamic Graph Contrastive Learning on Discrete-Time Dynamic Graph

Unsupervised learning methods such as graph contrastive learning have been used for dynamic graph represen-tation learning to eliminate the dependence of labels.However,existing studies neglect positional information when learning discrete snapshots,resulting in insufficient network topology learning.At the same time,due to the lack of appropriate data augmentation methods,it is difficult to capture the evolving patterns of the network effectively.To address the above problems,a position-aware and subgraph enhanced dynamic graph contrastive learning method is proposed for discrete-time dynamic graphs.Firstly,the global snapshot is built based on the historical snapshots to express the stable pattern of the dynamic graph,and the random walk is used to obtain the position representation by learning the positional information of the nodes.Secondly,a new data augmentation method is carried out from the perspectives of short-term changes and long-term stable structures of dynamic graphs.Specifically,subgraph sampling based on snapshots and global snapshots is used to obtain two structural augmentation views,and node structures and evolving patterns are learned by combining graph neural network,gated recurrent unit,and attention mechanism.Finally,the quality of node representation is improved by combining the contrastive learning between different structural augmentation views and between the two representations of structure and position.Experimental results on four real datasets show that the performance of the proposed method is better than the existing unsupervised methods,and it is more competitive than the supervised learning method under a semi-supervised setting.

GATiT:An Intelligent Diagnosis Model Based on Graph Attention Network Incorporating Text Representation in Knowledge Reasoning

The growing prevalence of knowledge reasoning using knowledge graphs(KGs)has substantially improved the accuracy and efficiency of intelligent medical diagnosis.However,current models primarily integrate electronic medical records(EMRs)and KGs into the knowledge reasoning process,ignoring the differing significance of various types of knowledge in EMRs and the diverse data types present in the text.To better integrate EMR text information,we propose a novel intelligent diagnostic model named the Graph ATtention network incorporating Text representation in knowledge reasoning(GATiT),which comprises text representation,subgraph construction,knowledge reasoning,and diagnostic classification.In the text representation process,GATiT uses a pre-trained model to obtain text representations of the EMRs and additionally enhances embeddings by including chief complaint information and numerical information in the input.In the subgraph construction process,GATiT constructs text subgraphs and disease subgraphs from the KG,utilizing EMR text and the disease to be diagnosed.To differentiate the varying importance of nodes within the subgraphs features such as node categories,relevance scores,and other relevant factors are introduced into the text subgraph.Themessage-passing strategy and attention weight calculation of the graph attention network are adjusted to learn these features in the knowledge reasoning process.Finally,in the diagnostic classification process,the interactive attention-based fusion method integrates the results of knowledge reasoning with text representations to produce the final diagnosis results.Experimental results on multi-label and single-label EMR datasets demonstrate the model’s superiority over several state-of-theart methods.

BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).

Inductive Relation Prediction by Disentangled Subgraph Structure

Currently,most existing inductive relation prediction approaches are based on subgraph structures,with subgraph features extracted using graph neural networks to predict relations.However,subgraphs may contain disconnected regions,which usually represent different semantic ranges.Because not all semantic information about the regions is helpful in relation prediction,we propose a relation prediction model based on a disentangled subgraph structure and implement a feature updating approach based on relevant semantic aggregation.To indirectly achieve the disentangled subgraph structure from a semantic perspective,the mapping of entity features into different semantic spaces and the aggregation of related semantics on each semantic space are updated.The disentangled model can focus on features having higher semantic relevance in the prediction,thus addressing a problem with existing approaches,which ignore the semantic differences in different subgraph structures.Furthermore,using a gated recurrent neural network,this model enhances the features of entities by sorting them by distance and extracting the path information in the subgraphs.Experimentally,it is shown that when there are numerous disconnected regions in the subgraph,our model outperforms existing mainstream models in terms of both Area Under the Curve-Precision-Recall(AUC-PR)and Hits@10.Experiments prove that semantic differences in the knowledge graph can be effectively distinguished and verify the effectiveness of this method.

Model Change Active Learning in Graph-Based Semi-supervised Learning

Active learning in semi-supervised classification involves introducing additional labels for unlabelled data to improve the accuracy of the underlying classifier.A challenge is to identify which points to label to best improve performance while limiting the number of new labels."Model Change"active learning quantifies the resulting change incurred in the classifier by introducing the additional label(s).We pair this idea with graph-based semi-supervised learning(SSL)methods,that use the spectrum of the graph Laplacian matrix,which can be truncated to avoid prohibitively large computational and storage costs.We consider a family of convex loss functions for which the acquisition function can be efficiently approximated using the Laplace approximation of the posterior distribution.We show a variety of multiclass examples that illustrate improved performance over prior state-of-art.

A Value for Games Defined on Graphs

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

Social Robot Detection Method with Improved Graph Neural Networks

Social robot accounts controlled by artificial intelligence or humans are active in social networks,bringing negative impacts to network security and social life.Existing social robot detection methods based on graph neural networks suffer from the problem of many social network nodes and complex relationships,which makes it difficult to accurately describe the difference between the topological relations of nodes,resulting in low detection accuracy of social robots.This paper proposes a social robot detection method with the use of an improved neural network.First,social relationship subgraphs are constructed by leveraging the user’s social network to disentangle intricate social relationships effectively.Then,a linear modulated graph attention residual network model is devised to extract the node and network topology features of the social relation subgraph,thereby generating comprehensive social relation subgraph features,and the feature-wise linear modulation module of the model can better learn the differences between the nodes.Next,user text content and behavioral gene sequences are extracted to construct social behavioral features combined with the social relationship subgraph features.Finally,social robots can be more accurately identified by combining user behavioral and relationship features.By carrying out experimental studies based on the publicly available datasets TwiBot-20 and Cresci-15,the suggested method’s detection accuracies can achieve 86.73%and 97.86%,respectively.Compared with the existing mainstream approaches,the accuracy of the proposed method is 2.2%and 1.35%higher on the two datasets.The results show that the method proposed in this paper can effectively detect social robots and maintain a healthy ecological environment of social networks.

Hyperbolic hierarchical graph attention network for knowledge graph completion

Utilizing graph neural networks for knowledge embedding to accomplish the task of knowledge graph completion(KGC)has become an important research area in knowledge graph completion.However,the number of nodes in the knowledge graph increases exponentially with the depth of the tree,whereas the distances of nodes in Euclidean space are second-order polynomial distances,whereby knowledge embedding using graph neural networks in Euclidean space will not represent the distances between nodes well.This paper introduces a novel approach called hyperbolic hierarchical graph attention network(H2GAT)to rectify this limitation.Firstly,the paper conducts knowledge representation in the hyperbolic space,effectively mitigating the issue of exponential growth of nodes with tree depth and consequent information loss.Secondly,it introduces a hierarchical graph atten-tion mechanism specifically designed for the hyperbolic space,allowing for enhanced capture of the network structure inherent in the knowledge graph.Finally,the efficacy of the proposed H2GAT model is evaluated on benchmark datasets,namely WN18RR and FB15K-237,thereby validating its effectiveness.The H2GAT model achieved 0.445,0.515,and 0.586 in the Hits@1,Hits@3 and Hits@10 metrics respectively on the WN18RR dataset and 0.243,0.367 and 0.518 on the FB15K-237 dataset.By incorporating hyperbolic space embedding and hierarchical graph attention,the H2GAT model successfully addresses the limitations of existing hyperbolic knowledge embedding models,exhibiting its competence in knowledge graph completion tasks.

Insider threat detection approach for tobacco industry based on heterogeneous graph embedding

In the tobacco industry,insider employee attack is a thorny problem that is difficult to detect.To solve this issue,this paper proposes an insider threat detection method based on heterogeneous graph embedding.First,the interrelationships between logs are fully considered,and log entries are converted into heterogeneous graphs based on these relationships.Second,the heterogeneous graph embedding is adopted and each log entry is represented as a low-dimensional feature vector.Then,normal logs and malicious logs are classified into different clusters by clustering algorithm to identify malicious logs.Finally,the effectiveness and superiority of the method is verified through experiments on the CERT dataset.The experimental results show that this method has better performance compared to some baseline methods.

Algorithm for Visualization of Zero Divisor Graphs of the Ring ℤn Using MAPLE Coding

This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤn modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.

Perfect 1-k Matchings of Bipartite Graphs

Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is incident with exactly k edges in M. A perfect 1-k matching is an optimal semi-matching related to the load-balancing problem, where a semi-matching is an edge subset M such that each vertex in Y is incident with exactly one edge in M, and a vertex in X can be incident with an arbitrary number of edges in M. In this paper, we give three sufficient and necessary conditions for the existence of perfect 1-k matchings and for the existence of 1-k matchings covering | X |−dvertices in X, respectively, and characterize k-elementary bipartite graph which is a graph such that the subgraph induced by all k-allowed edges is connected, where an edge is k-allowed if it is contained in a perfect 1-k matching.

On an Invariant of Tournament Digraphs

To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.