Ideal-based Zero-divisor Graphs of Non-commutative Rings

这份报纸介绍非可交换的戒指的一张理想男孩的零除数的图，表示我(R) 。我(R) 是一张指导的图。性质和图的可能的结构被学习。

The Zero-divisor Graphs of Abelian Regular Rings

We introduce the zero-divisor graph for an abelian regular ring and show that if R, S are abelian regular, then (K0(R),[R])≌(K0(S),[S])if and only if they have isomorphic reduced zero-divisor graphs. It is shown that the maximal right quotient ring of a potent semiprimitive normal ring is abelian regular,moreover,the zero-divisor graph of such a ring is studied.

On the Cozero-Divisor Graphs of Commutative Rings

Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs and such as connectivity, diameter, girth, clique numbers and planarity. We also study the cozero-divisor graphs of the direct products of two arbitrary commutative rings.

Analysis of Distance-Based Topological Polynomials Associated with Zero-Divisor Graphs

Chemical compounds are modeled as graphs.The atoms of molecules represent the graph vertices while chemical bonds between the atoms express the edges.The topological indices representing the molecular graph corresponds to the different chemical properties of compounds.Let a,b be are two positive integers,andΓ(Z_(a)×Z_(b))be the zero-divisor graph of the commutative ring Z_(a)×Z_(b).In this article some direct questions have been answered that can be utilized latterly in different applications.This study starts with simple computations,leading to a quite complex ring theoretic problems to prove certain properties.The theory of finite commutative rings is useful due to its different applications in the fields of advanced mechanics,communication theory,cryptography,combinatorics,algorithms analysis,and engineering.In this paper we determine the distance-based topological polynomials and indices of the zero-divisor graph of the commutative ring Z_(p^(2))×Z_(q)(for p,q as prime numbers)with the help of graphical structure analysis.The study outcomes help in understanding the fundamental relation between ring-theoretic and graph-theoretic properties of a zero-divisor graphΓ(G).

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.

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).

A Sharding Scheme Based on Graph Partitioning Algorithm for Public Blockchain

Blockchain technology,with its attributes of decentralization,immutability,and traceability,has emerged as a powerful catalyst for enhancing traditional industries in terms of optimizing business processes.However,transaction performance and scalability has become the main challenges hindering the widespread adoption of blockchain.Due to its inability to meet the demands of high-frequency trading,blockchain cannot be adopted in many scenarios.To improve the transaction capacity,researchers have proposed some on-chain scaling technologies,including lightning networks,directed acyclic graph technology,state channels,and shardingmechanisms,inwhich sharding emerges as a potential scaling technology.Nevertheless,excessive cross-shard transactions and uneven shard workloads prevent the sharding mechanism from achieving the expected aim.This paper proposes a graphbased sharding scheme for public blockchain to efficiently balance the transaction distribution.Bymitigating crossshard transactions and evening-out workloads among shards,the scheme reduces transaction confirmation latency and enhances the transaction capacity of the blockchain.Therefore,the scheme can achieve a high-frequency transaction as well as a better blockchain scalability.Experiments results show that the scheme effectively reduces the cross-shard transaction ratio to a range of 35%-56%and significantly decreases the transaction confirmation latency to 6 s in a blockchain with no more than 25 shards.

Anomaly Detection Algorithm of Power System Based on Graph Structure and Anomaly Attention

In this paper, we propose a novel anomaly detection method for data centers based on a combination of graphstructure and abnormal attention mechanism. The method leverages the sensor monitoring data from targetpower substations to construct multidimensional time series. These time series are subsequently transformed intograph structures, and corresponding adjacency matrices are obtained. By incorporating the adjacency matricesand additional weights associated with the graph structure, an aggregation matrix is derived. The aggregationmatrix is then fed into a pre-trained graph convolutional neural network (GCN) to extract graph structure features.Moreover, both themultidimensional time series segments and the graph structure features are inputted into a pretrainedanomaly detectionmodel, resulting in corresponding anomaly detection results that help identify abnormaldata. The anomaly detection model consists of a multi-level encoder-decoder module, wherein each level includesa transformer encoder and decoder based on correlation differences. The attention module in the encoding layeradopts an abnormal attention module with a dual-branch structure. Experimental results demonstrate that ourproposed method significantly improves the accuracy and stability of anomaly detection.

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.

A Bitcoin Address Multi-Classification Mechanism Based on Bipartite Graph-Based Maximization Consensus

Bitcoin is widely used as the most classic electronic currency for various electronic services such as exchanges,gambling,marketplaces,and also scams such as high-yield investment projects.Identifying the services operated by a Bitcoin address can help determine the risk level of that address and build an alert model accordingly.Feature engineering can also be used to flesh out labeled addresses and to analyze the current state of Bitcoin in a small way.In this paper,we address the problem of identifying multiple classes of Bitcoin services,and for the poor classification of individual addresses that do not have significant features,we propose a Bitcoin address identification scheme based on joint multi-model prediction using the mapping relationship between addresses and entities.The innovation of the method is to(1)Extract as many valuable features as possible when an address is given to facilitate the multi-class service identification task.(2)Unlike the general supervised model approach,this paper proposes a joint prediction scheme for multiple learners based on address-entity mapping relationships.Specifically,after obtaining the overall features,the address classification and entity clustering tasks are performed separately,and the results are subjected to graph-basedmaximization consensus.The final result ismade to baseline the individual address classification results while satisfying the constraint of having similarly behaving entities as far as possible.By testing and evaluating over 26,000 Bitcoin addresses,our feature extraction method captures more useful features.In addition,the combined multi-learner model obtained results that exceeded the baseline classifier reaching an accuracy of 77.4%.

Smart Contract Vulnerability Detection Method Based on Feature Graph and Multiple Attention Mechanisms

The fast-paced development of blockchain technology is evident.Yet,the security concerns of smart contracts represent a significant challenge to the stability and dependability of the entire blockchain ecosystem.Conventional smart contract vulnerability detection primarily relies on static analysis tools,which are less efficient and accurate.Although deep learning methods have improved detection efficiency,they are unable to fully utilize the static relationships within contracts.Therefore,we have adopted the advantages of the above two methods,combining feature extraction mode of tools with deep learning techniques.Firstly,we have constructed corresponding feature extraction mode for different vulnerabilities,which are used to extract feature graphs from the source code of smart contracts.Then,the node features in feature graphs are fed into a graph convolutional neural network for training,and the edge features are processed using a method that combines attentionmechanismwith gated units.Ultimately,the revised node features and edge features are concatenated through amulti-head attentionmechanism.The result of the splicing is a global representation of the entire feature graph.Our method was tested on three types of data:Timestamp vulnerabilities,reentrancy vulnerabilities,and access control vulnerabilities,where the F1 score of our method reaches 84.63%,92.55%,and 61.36%.The results indicate that our method surpasses most others in detecting smart contract vulnerabilities.

Privacy-Preserving Multi-Keyword Fuzzy Adjacency Search Strategy for Encrypted Graph in Cloud Environment

In a cloud environment,outsourced graph data is widely used in companies,enterprises,medical institutions,and so on.Data owners and users can save costs and improve efficiency by storing large amounts of graph data on cloud servers.Servers on cloud platforms usually have some subjective or objective attacks,which make the outsourced graph data in an insecure state.The issue of privacy data protection has become an important obstacle to data sharing and usage.How to query outsourcing graph data safely and effectively has become the focus of research.Adjacency query is a basic and frequently used operation in graph,and it will effectively promote the query range and query ability if multi-keyword fuzzy search can be supported at the same time.This work proposes to protect the privacy information of outsourcing graph data by encryption,mainly studies the problem of multi-keyword fuzzy adjacency query,and puts forward a solution.In our scheme,we use the Bloom filter and encryption mechanism to build a secure index and query token,and adjacency queries are implemented through indexes and query tokens on the cloud server.Our proposed scheme is proved by formal analysis,and the performance and effectiveness of the scheme are illustrated by experimental analysis.The research results of this work will provide solid theoretical and technical support for the further popularization and application of encrypted graph data processing technology.

Survey and Prospect for Applying Knowledge Graph in Enterprise Risk Management

Enterprise risk management holds significant importance in fostering sustainable growth of businesses and in serving as a critical element for regulatory bodies to uphold market order.Amidst the challenges posed by intricate and unpredictable risk factors,knowledge graph technology is effectively driving risk management,leveraging its ability to associate and infer knowledge from diverse sources.This review aims to comprehensively summarize the construction techniques of enterprise risk knowledge graphs and their prominent applications across various business scenarios.Firstly,employing bibliometric methods,the aim is to uncover the developmental trends and current research hotspots within the domain of enterprise risk knowledge graphs.In the succeeding section,systematically delineate the technical methods for knowledge extraction and fusion in the standardized construction process of enterprise risk knowledge graphs.Objectively comparing and summarizing the strengths and weaknesses of each method,we provide recommendations for addressing the existing challenges in the construction process.Subsequently,categorizing the applied research of enterprise risk knowledge graphs based on research hotspots and risk category standards,and furnishing a detailed exposition on the applicability of technical routes and methods.Finally,the future research directions that still need to be explored in enterprise risk knowledge graphs were discussed,and relevant improvement suggestions were proposed.Practitioners and researchers can gain insights into the construction of technical theories and practical guidance of enterprise risk knowledge graphs based on this foundation.

Multi-modal knowledge graph inference via media convergence and logic rule

Media convergence works by processing information from different modalities and applying them to different domains.It is difficult for the conventional knowledge graph to utilise multi-media features because the introduction of a large amount of information from other modalities reduces the effectiveness of representation learning and makes knowledge graph inference less effective.To address the issue,an inference method based on Media Convergence and Rule-guided Joint Inference model(MCRJI)has been pro-posed.The authors not only converge multi-media features of entities but also introduce logic rules to improve the accuracy and interpretability of link prediction.First,a multi-headed self-attention approach is used to obtain the attention of different media features of entities during semantic synthesis.Second,logic rules of different lengths are mined from knowledge graph to learn new entity representations.Finally,knowledge graph inference is performed based on representing entities that converge multi-media features.Numerous experimental results show that MCRJI outperforms other advanced baselines in using multi-media features and knowledge graph inference,demonstrating that MCRJI provides an excellent approach for knowledge graph inference with converged multi-media features.

Analysis on the Changes of Research Hotspots in the Prevention and Treatment of COVID-19 by Traditional Chinese Medicine Based on Knowledge Graph

Objective: To grasp the changing trend of research hotspots of traditional Chinese medicine in the prevention and treatment of COVID-19, and to better play the role of traditional Chinese medicine in the prevention and treatment of COVID-19 and other diseases. Methods: The research literature from 2020 to 2022 was searched in the CNKI database, and CiteSpace software was used for visual analysis. Results: The papers on the prevention and treatment of COVID-19 by traditional Chinese medicine changed from cases, overviews, reports, and efficacy studies to more in-depth mechanism research, theoretical exploration, and social impact analysis, and finally formed a theory-clinical-society Influence-institutional change and other multi-dimensional achievement systems. Conclusion: Analyzing the changing trends of TCM hotspots in the prevention and treatment of COVID-19 can fully understand the important value of TCM, take the coordination of TCM and Western medicine as an important means to deal with public health security incidents, and promote the exploration of the potential efficacy of TCM, so as to enhance the role of TCM in Applications in social stability, emergency security, clinical practice, etc.

Predicting Traffic Flow Using Dynamic Spatial-Temporal Graph Convolution Networks

Traffic flow prediction plays a key role in the construction of intelligent transportation system.However,due to its complex spatio-temporal dependence and its uncertainty,the research becomes very challenging.Most of the existing studies are based on graph neural networks that model traffic flow graphs and try to use fixed graph structure to deal with the relationship between nodes.However,due to the time-varying spatial correlation of the traffic network,there is no fixed node relationship,and these methods cannot effectively integrate the temporal and spatial features.This paper proposes a novel temporal-spatial dynamic graph convolutional network(TSADGCN).The dynamic time warping algorithm(DTW)is introduced to calculate the similarity of traffic flow sequence among network nodes in the time dimension,and the spatiotemporal graph of traffic flow is constructed to capture the spatiotemporal characteristics and dependencies of traffic flow.By combining graph attention network and time attention network,a spatiotemporal convolution block is constructed to capture spatiotemporal characteristics of traffic data.Experiments on open data sets PEMSD4 and PEMSD8 show that TSADGCN has higher prediction accuracy than well-known traffic flow prediction algorithms.