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.

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).

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.

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.

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.

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.

The Maximum and Minimum Value of Exponential RandićIndices of Quasi-Tree Graph

The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.

Weak External Bisection of Some Graphs

Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V1 ∪ V2 and V1 ∩ V2 = ∅. If a bipartition satisfies ∥V1∣ - ∣V2∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V1, V2) such that ∀v ∈ V1, at least half minuses one of the neighbors of v are in the V2;∀v ∈ V2, at least half minuses one of the neighbors of v are in the V1. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.

基于Graph Transformer的半监督异配图表示学习模型

现有的图卷积网络(GCN)模型基于同配性假设,无法直接应用于异配图的表示学习,且许多异配图表示学习的研究工作受消息传递机制的限制,导致节点特征混淆和特征过度挤压而出现过平滑问题。针对这些问题,提出一种基于Graph Transformer的半监督异配图表示学习模型HPGT(HeteroPhilic Graph Transformer)。首先,使用度连接概率矩阵采样节点的路径邻域,再通过自注意力机制自适应地聚合路径上的节点异配连接模式,编码得到节点的结构信息,用节点的原始属性信息和结构信息构建Transformer层的自注意力模块;其次,将每个节点自身的隐层表示与它的邻域节点的隐层表示分离更新以避免节点通过自注意力模块聚合过量的自身信息,再把每个节点表示与它的邻域表示连接,得到单个Transformer层的输出,另外,将所有的Transformer层的输出跳连到最终的节点隐层表示以防止中间层信息丢失;最后,使用线性层和Softmax层将节点的隐层表示映射到节点的预测标签。实验结果表明,与无结构编码(SE)的模型相比,基于度连接概率的SE能为Transformer层的自注意力模块提供有效的偏差信息,HPGT平均准确率提升0.99%~11.98%;与对比模型相比,在异配数据集(Texas、Cornell、Wisconsin和Actor)上,模型节点分类准确率提升0.21%~1.69%,在同配数据集(Cora、CiteSeer和PubMed)上,节点分类准确率分别达到了0.8379、0.7467和0.8862。以上结果验证了HPGT具有较强的异配图表示学习能力,尤其适用于强异配图节点分类任务。

Graph Transformers研究进展综述

随着图结构数据在各种实际场景中的广泛应用,对其进行有效建模和处理的需求日益增加。Graph Transformers(GTs)作为一类使用Transformers处理图数据的模型,能够有效缓解传统图神经网络(GNN)中存在的过平滑和过挤压等问题,因此可以学习到更好的特征表示。根据对近年来GTs相关文献的研究,将现有的模型架构分为两类:第一类通过绝对编码和相对编码向Transformers中加入图的位置和结构信息,以增强Transformers对图结构数据的理解和处理能力;第二类根据不同的方式(串行、交替、并行)将GNN与Transformers进行结合,以充分利用两者的优势。介绍了GTs在信息安全、药物发现和知识图谱等领域的应用,对比总结了不同用途的模型及其优缺点。最后,从可扩展性、复杂图、更好的结合方式等方面分析了GTs未来研究面临的挑战。

基于Graph-LSTMs的双重位置感知方面级情感分类

目前针对用户评论中方面词项情感分类任务的研究大多忽略了依存句法信息,或并未建立依存句法结构与单词之间的联系。为此,提出一种基于Graph-LSTMs的双重位置感知方面级情感分类方法。通过Graph-LSTMs学习词项的上下文语境特征;在双向GRU的输入中拼接具有双重位置信息的位置向量,优化句子情感编码;利用注意力机制捕获关键的情感特征,实现分类。在SemEval2014的两个数据集上的实验结果表明,该模型相比几种基线模型在准确率和Macro-F1这两个指标上提升明显。

基于路径存储表的Hashgraph共识算法优化与实现

Hashgraph是一种数据采用有向无环图(DAG)结构的区块链共识算法,Hashgraph引入了虚拟投票的概念,允许节点在无额外通信开销的情况下并发出块,实现异步场景下的拜占庭容错。然而,Hashgraph提出的虚拟投票算法存在算法时间复杂度较高、共识运行逻辑过于复杂等问题。为此,提出一种基于路径存储表的Hashgraph优化方案。首先,提出一种基于顶点可达表的见证人判定方法,通过存储路径的方式实时记录生成事件与历史事件的可达关系,在轮次划分阶段,通过查询顶点事件的可达信息取代回溯算法,降低见证人判断算法的时间复杂度;其次,针对顶点可达表无法跨轮次判断事件关系的问题,提出一种基于历史可达表的知名见证人判定方法,历史可达表将存储见证人与历史事件之间的可达关系,通过查询历史可达表解决知名见证人判定阶段需要反复回溯视图的问题;最后,根据顶点可达表和历史可达表改进Hashgraph中复杂的共识计算,提升算法效率,加快事件确认速度。实验结果表明,所提优化方案与Hashgraph原共识算法相比,算法运行效率提升65.76%,在吞吐量方面平均提升41.27%。

Heuristic Expanding Disconnected Graph:A Rapid Path Planning Method for Mobile Robots

Existing mobile robots mostly use graph search algorithms for path planning,which suffer from relatively low planning efficiency owing to high redundancy and large computational complexity.Due to the limitations of the neighborhood search strategy,the robots could hardly obtain the most optimal global path.A global path planning algorithm,denoted as EDG*,is proposed by expanding nodes using a well-designed expanding disconnected graph operator(EDG)in this paper.Firstly,all obstacles are marked and their corners are located through the map pre-processing.Then,the EDG operator is designed to find points in non-obstruction areas to complete the rapid expansion of disconnected nodes.Finally,the EDG*heuristic iterative algorithm is proposed.It selects the candidate node through a specific valuation function and realizes the node expansion while avoiding collision with a minimum offset.Path planning experiments were conducted in a typical indoor environment and on the public dataset CSM.The result shows that the proposed EDG*reduced the planning time by more than 90%and total length of paths reduced by more than 4.6%.Compared to A*,Dijkstra and JPS,EDG*does not show an exponential explosion effect in map size.The EDG*showed better performance in terms of path smoothness,and collision avoidance.This shows that the EDG*algorithm proposed in this paper can improve the efficiency of path planning and enhance path quality.

A graph neural network approach to the inverse design for thermal transparency with periodic interparticle system

Recent years have witnessed significant advances in utilizing machine learning-based techniques for thermal metamaterial-based structures and devices to attain favorable thermal transport behaviors.Among the various thermal transport behaviors,achieving thermal transparency stands out as particularly desirable and intriguing.Our earlier work demonstrated the use of a thermal metamaterial-based periodic interparticle system as the underlying structure for manipulating thermal transport behavior and achieving thermal transparency.In this paper,we introduce an approach based on graph neural network to address the complex inverse design problem of determining the design parameters for a thermal metamaterial-based periodic interparticle system with the desired thermal transport behavior.Our work demonstrates that combining graph neural network modeling and inference is an effective approach for solving inverse design problems associated with attaining desirable thermal transport behaviors using thermal metamaterials.

Feature Matching via Topology-Aware Graph Interaction Model

Feature matching plays a key role in computer vision. However, due to the limitations of the descriptors, the putative matches are inevitably contaminated by massive outliers.This paper attempts to tackle the outlier filtering problem from two aspects. First, a robust and efficient graph interaction model,is proposed, with the assumption that matches are correlated with each other rather than independently distributed. To this end, we construct a graph based on the local relationships of matches and formulate the outlier filtering task as a binary labeling energy minimization problem, where the pairwise term encodes the interaction between matches. We further show that this formulation can be solved globally by graph cut algorithm. Our new formulation always improves the performance of previous localitybased method without noticeable deterioration in processing time,adding a few milliseconds. Second, to construct a better graph structure, a robust and geometrically meaningful topology-aware relationship is developed to capture the topology relationship between matches. The two components in sum lead to topology interaction matching(TIM), an effective and efficient method for outlier filtering. Extensive experiments on several large and diverse datasets for multiple vision tasks including general feature matching, as well as relative pose estimation, homography and fundamental matrix estimation, loop-closure detection, and multi-modal image matching, demonstrate that our TIM is more competitive than current state-of-the-art methods, in terms of generality, efficiency, and effectiveness. The source code is publicly available at http://github.com/YifanLu2000/TIM.

Dynamic interwell connectivity analysis of multi-layer waterflooding reservoirs based on an improved graph neural network

The analysis of interwell connectivity plays an important role in the formulation of oilfield development plans and the description of residual oil distribution. In fact, sandstone reservoirs in China's onshore oilfields generally have the characteristics of thin and many layers, so multi-layer joint production is usually adopted. It remains a challenge to ensure the accuracy of splitting and dynamic connectivity in each layer of the injection-production wells with limited field data. The three-dimensional well pattern of multi-layer reservoir and the relationship between injection-production wells can be equivalent to a directional heterogeneous graph. In this paper, an improved graph neural network is proposed to construct an interacting process mimics the real interwell flow regularity. In detail, this method is used to split injection and production rates by combining permeability, porosity and effective thickness, and to invert the dynamic connectivity in each layer of the injection-production wells by attention mechanism.Based on the material balance and physical information, the overall connectivity from the injection wells,through the water injection layers to the production layers and the output of final production wells is established. Meanwhile, the change of well pattern caused by perforation, plugging and switching of wells at different times is achieved by updated graph structure in spatial and temporal ways. The effectiveness of the method is verified by a combination of reservoir numerical simulation examples and field example. The method corresponds to the actual situation of the reservoir, has wide adaptability and low cost, has good practical value, and provides a reference for adjusting the injection-production relationship of the reservoir and the development of the remaining oil.