The Wiener Index of an Undirected Power Graph

The undirected power graph P(Zn) of a finite group Zn is the graph with vertex set G and two distinct vertices u and v are adjacent if and only if u ≠ v and or . The Wiener index W(P(Zn)) of an undirected power graph P(Zn) is defined to be sum of distances between all unordered pair of vertices in P(Zn). Similarly, the edge-Wiener index We(P(Zn)) of P(Zn) is defined to be the sum of distances between all unordered pairs of edges in P(Zn). In this paper, we concentrate on the wiener index of a power graph , P(Zpq) and P(Zp). Firstly, we obtain new results on the wiener index and edge-wiener index of power graph P(Zn), using m,n and Euler function. Also, we obtain an equivalence between the edge-wiener index and wiener index of a power graph of Zn.

INDEPENDENT-SET-DELETABLE FACTOR-CRITICAL POWER GRAPHS

It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The κ-th power of G, denoted by G^κ, is the graph with vertex set V（G） in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G^3 and T（G） （the total graph of G） are ID-factor-critical, and G^4 （when ｜V（G）｜ is even） is strongly IM-extendable; if G is 2-connected, then D^2 is ID-factor-critical.

面向幂律图的动态图存储结构Power-PCSR

图数据在现实生活中广泛存在,且不断发生变化。传统高效的静态图存储方式——压缩行/列(Compressed Sparse Row/Column,CSR/CSR)存储方式在更新图数据时需要大量的数据迁移,不适用于动态图数据。而能够高效更新图数据的邻接表(Adjacency List,AL)存储方式往往带有大量的指针,导致其图数据读取和分析效率低。Packed Compressed Sparse Row(PCSR)是一种基于CSR的动态图存储结构。该结构在存储边数据时并不是采用连续无空隙数组,而是采用留有空槽的压缩存储阵列(Packed Memory Arrays,PMA)结构,便于边数据的插入。因此,PCSR支持高效图更新和图分析。但是,PCSR在存储幂律图时,其性能容易受大度数顶点的影响。为此,基于PCSR提出一种支持可高效更新和分析动态幂律图的图存储结构Power-PCSR。该结构将幂律图中度数较大的顶点单独存储在一个独立的PMA中,其他所有小度数顶点与PCSR一样存储在原PMA中。小度顶点变化导致的数据迁移不会触及大度数顶点,从而大大减少了数据迁移数量;同样,大度数顶点更新导致的数据迁移只限制在每个大度数顶点的PMA内部,不会涉及小度数顶点和其他大度数顶点的数据迁移。实验显示,Power-PCSR在分析图数据时与PCSR具有相似的性能,而在更新图数据时比PCSR快2倍。

Power domination in planar graphs with small diameter

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graph theory. In this paper, it was shown that the power domination number of an outerplanar graph with the diameter two or a 2-connected outerplanar graph with the diameter three is precisely one. Upper bounds on the power domination number for a general planar graph with the diameter two or three were determined as an immediate consequences of results proven by Dorfling, et al. Also, an infinite family of outerplanar graphs with the diameter four having arbitrarily large power domination numbers were given.

Accurate querying of frequent subgraphs in power grid graph data

With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have chosen different indexing methods in the filtering stage to obtain more optimized query results because currently there is no uniform and efficient indexing mechanism that achieves good query results. In the traditional algorithm, the hash table for index storage is prone to "collision" problems, which decrease the index construction efficiency. Aiming at the problem of quick index entry, based on the construction of frequent subgraph indexes, a method of serialized storage optimization based on multiple hash tables is proposed. This method mainly uses the exploration sequence to make the keywords evenly distributed; it avoids conflicts of the stored procedure and performs a quick search of the index. The proposed algorithm mainly adopts the "filterverify" mechanism; in the filtering stage, the index is first established offline, and then the frequent subgraphs are found using the "contains logic" rule to obtain the candidate set. Experimental results show that this method can reduce the time and scale of candidate set generation and improve query efficiency.

Minimum Rank of Graphs Powers Family

In this paper we study the relationship between minimum rank of graph G and the minimum rank of graph for some families of special graph G, where is the jth power of graph G.

Enhanced graph-based fault diagnostic system for nuclear power plants

Scheduled maintenance and condition-based online monitoring are among the focal points of recent research to enhance nuclear plant safety.One of the most effective ways to monitor plant conditions is by implementing a full-scope,plant-wide fault diagnostic system.However,most of the proposed diagnostic techniques are perceived as unreliable by operators because they lack an explanation module,their implementation is complex,and their decision/inference path is unclear.Graphical formalism has been considered for fault diagnosis because of its clear decision and inference modules,and its ability to display the complex causal relationships between plant variables and reveal the propagation path used for fault localization in complex systems.However,in a graphbased approach,decision-making is slow because of rule explosion.In this paper,we present an enhanced signed directed graph that utilizes qualitative trend evaluation and a granular computing algorithm to improve the decision speed and increase the resolution of the graphical method.We integrate the attribute reduction capability of granular computing with the causal/fault propagation reasoning capability of the signed directed graph and comprehensive rules in a decision table to diagnose faults in a nuclear power plant.Qualitative trend analysis is used to solve the problems of fault diagnostic threshold selection and signed directed graph node state determination.The similarity reasoning and detection ability of the granular computing algorithm ensure a compact decision table and improve the decision result.The performance of the proposed enhanced system was evaluated on selected faults of the Chinese Fuqing 2 nuclear reactor.The proposed method offers improved diagnostic speed and efficient data processing.In addition,the result shows a considerable reduction in false positives,indicating that the method provides a reliable diagnostic system to support further intervention by operators.

Cordial Labeling of Corona Product of Path Graph and Second Power of Fan Graph

A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs and explain the necessary and sufficient conditions for this construction to be cordial.

多特征融合及聚类分析的道岔转辙机退化状态识别

针对转辙机退化阶段难以划分的问题,提出一种基于多维特征融合的道岔转辙机退化状态识别方法。首先,提取了S700K转辙机退化功率数据的时域、频域、时频域多域特征;其次,通过核主成分分析(Kernel Principal Components Analysis,KPCA)进行特征融合,获得表征道岔转辙机运行状态的特征向量,构建转辙机退化性能指标;再次,采用K-medoids聚类算法对道岔转辙机性能退化状态进行阶段划分,识别不同的退化状态;最后,选用轮廓系数、分类系数、平均模糊熵对聚类效果进行综合评价,并与模糊C均值聚类(Fuzzy C-Means Clustering,FCM)和古斯塔夫森-凯塞尔(Gustafson Kessel,GK)聚类算法进行比较。研究结果表明,融合特征聚类后的综合评价指标高于单一特征,更能够体现道岔转辙机退化过程中的细节,K-medoids聚类效果明显,模型的准确率达到96.3%,能够对道岔转辙机性能退化阶段进行准确的划分,为铁路现场道岔智能运维提供理论支持。

面向电力调度的事件知识图谱研究现状及发展

事件知识图谱(EKG)是一种可学习事件演化规律的特殊知识图谱,具有推理、预测等功能。针对电力调度业务数据量大、模态多、交互耦合等特点,该文详述了面向电力调度的事件知识图谱的数据集构建、主流方法、技术架构、评价指标、适用场景等,重点分析各场景的可行性,并在应用流程、输入输出、技术架构等方面给出方案,最后对其在电力调度业务长期发展面临的难点和可能的研究方向进行了展望。该文研究为研究电力调度领域特点、事件知识图谱优势和两者结合提供了参考,并为事件知识图谱在电力调度领域中的应用方向提供了指导性思路。

基于DCGCN模型的海上风电场超短期功率预测

图卷积网络(GCN)具有很强的数据关联挖掘能力,近年来在风电功率预测领域获得了广泛关注。然而,传统的基于GCN模型的超短期风电功率预测难以同时处理影响风电功率的两大核心因素(风速与机组状态信息)的双模态问题,基于此,提出了一种基于双通道图卷积网络(DCGCN)的海上风电场超短期功率预测模型。首先,建立以理论功率曲线为基准的机组状态指标模型,定量表征机组状态变化对其发电能力的影响;其次,构建海上风电场图拓扑,建立基于风速和状态邻接矩阵的风电场各机组捕获的风速与机组状态信息的关联关系模型;最后,建立基于DCGCN的风电场超短期功率预测方法。算例结果表明,所提模型有助于提高风电场功率预测模型的训练效率和预测精度。

一种基于GCN的光伏短期出力预测方法研究

为提高光伏短期出力预测精确问题,提出一种基于图卷积神经网络(GCN)的光伏短期出力预测方法。首先,构建考虑多气象影响因素的光伏短期出力模型,开展光伏出力影响因素和出力特性分析。其次,对光伏出力历史时序数据进行图形化转换和数据重构,构建邻接矩阵并提取光伏短期出力图形化特征数据。在多时间尺度场景下,建立基于GCN的光伏出力预测模型,并与基于长短期记忆网络(LSTM)、反向传播网络(BP)、图注意力模型(GAT)等算法的预测模型做比对分析。最后,以某地区光伏出力实测数据开展仿真验证研究,仿真结果表明所提方法具有良好的预测效果。

新发展格局下以城市循环能力增强国内大循环内生动力的模式和机制研究

“增强国内大循环内生动力”是新形势新条件下对构建新发展格局提出的重大要求之一。本文提出“城市节点-城市群块-流关系链-双向循环网”的研究框架,以289个城市的循环能力衡量城市供需的特征性事实,并运用投入产出表和社会网络分析方法刻画国内大循环网络,探究以城市循环能力增强国内大循环内生动力的模式和作用机制。研究发现,第一,样本期城市循环能力面临着联动性不畅、均衡性不足和协调性不强的三重结构性困境;第二,破解三重结构性困境需要认识城市在国内大循环网络中的中间人角色及其联动模式。联动性不畅是由于联络人不多,均衡性不足是由于协调人角色较少,协调性不强是由于守门人和联络人较少;第三,在上述联动模式的基础上,本文从城市循环能力内生性、网络结构动力双重性和中间人作用异质性等多重角度,采用指数随机图模型实证探究城市循环能力增强国内大循环内生动力的模式与机制。本文对于如何从城市层面增强国内大循环内生动力,助力新发展格局构建具有借鉴意义。

基于注意力特征融合时空图网络的超短期风电功率预测

为提高风电功率的预测精度,综合考虑时间和空间多维度因素的影响,提出了一种基于注意力机制和多阶段特征融合的时空图神经网络(Spatio-temporal graph neural network with attention mechanism and multistage feature fusion,AMF-STGNN)的超短期风电功率预测方法。首先基于Pearson相关系数法对数据特征进行降维,确定影响风电功率的关键因素。然后构建AMF-STGNN预测模型。该模型主要由时空关联网络构建模块和多维度时空特征抽取模块组成。通过时空关联网络构建模块构建时空图,以揭示风电气象因素的空间连接关系。通过多维度时空特征抽取模块应用时间卷积和图卷积挖掘数据的时空特征,并利用注意力机制学习重要特征。此外,该方法还引入残差结构和多阶段特征融合结构提高模型的表达能力。最后以宁夏3个风电场真实数据为例,验证了所提方法在提升风电功率预测精度方面的有效性。

Shapley值及其应用

Shapley值是合作博弈理论中最重要的概念之一,其在经济学、社会管理等领域具有十分广泛的应用.本文回顾了合作博弈的Shapley值的理论研究,并从Shapley-Shubik权力指数、拼车费用分摊、图博弈的Page-Shapley值以及SHAP方法与机器学习等4个方面介绍了Shapley值的应用进展.

Fault Diagnosis Based on Graph Theory and Linear Discriminant Principle in Electric Power Network

In this paper, we adopt a novel topological approach to fault diagnosis. In our researches, global information will be introduced into electric power network, we are using mainly BFS of graph theory algorithms and linear discriminant principle to resolve fast and exact analysis of faulty components and faulty sections, and finally accomplish fault diagnosis. The results of BFS and linear discriminant are identical. The main technical contributions and innovations in this paper include, introducing global information into electric power network, developing a novel topological analysis to fault diagnosis. Graph theory algorithms can be used to model many different physical and abstract systems such as transportation and communication networks, models for business administration, political science, and psychology and so on. And the linear discriminant is a procedure used to classify an object into one of several a priori groupings dependent on the individual characteristics of the object. In the study of fault diagnosis in electric power network, graph theory algorithms and linear discriminant technology must also have a good prospect of application.

基于SHAP重要性排序和时空双流的多风场超短期功率预测

针对多风场风功率预测中时空特征提取不充分的问题,提出一种基于空间、时间双流特征提取的功率预测方法。采用沙普利加性解释(SHAP)方法分析原始高维数值天气预报(NWP)中各变量的重要性,选择贡献度高的变量子集作为预测模型输入,降低模型复杂度。构建基于自适应动态邻接矩阵的改进图注意力网络(IGAT)提取多风场的动态空间特征;同时将多头注意力机制(MHA)与时间卷积网络(TCN)结合,加强关键时序特征的学习。使用前馈神经网络输出多风场功率预测结果。以西北某十风场的数据进行案例研究,结果表明所提模型的预测效果优于其他模型。

基于知识图谱的端到端内容共享机制

端到端(D2D)通信利用边缘网络的本地计算和缓存能力,可以满足未来移动网络用户低延时、高能效的内容共享需求。而边缘网络内容共享效率性能的提升不仅取决于用户社交关系,同时也高度依赖终端设备的特征,如计算、存储和剩余能量资源等。因此,以最大化能量效率为目标,综合考虑设备异质性、用户社交性和兴趣差异性,提出一种用户-设备-内容多维度关联特征的D2D内容共享机制。首先,基于用户成本效益最大化将多目标约束问题转化为最优节点选择和功率控制问题,构建面向用户-设备-内容的多维度知识关联特征和图谱模型,将设备相关的计算资源、存储资源等多维特征结构化处理;其次,研究用户在设备属性和社交属性上的意愿度度量方法,提出一种基于用户社交和设备图谱的共享意愿度度量方法;最后,根据用户共享意愿度构建面向内容共享的D2D协作簇,面向能量效率设计一种基于共享意愿度的功率控制算法,以最大化网络共享性能。在真实用户设备数据集和infocom06数据集的实验结果表明,所提基于共享意愿度的功率控制算法与最近选择算法和不考虑设备意愿度的选择算法相比,系统和速率分别提升了约97.2%和11.1%,用户满意度分别提升了约72.7%和4.3%,能效分别提升了约57.8%和9.7%,验证了所提算法在传输速率、能量效率和用户满意度等方面的有效性。

临床实验室基于功效函数图评价Westgard西格玛规则中统计质量控制程序性能

目的 使用功效函数图对Westgard西格玛规则中统计质量控制程序性能特征进行分析。方法 根据功效函数图绘制原理,开发了临床检验定量测定室内质量控制程序设计软件,使用功效函数图对Westgard西格玛规则中推荐的质量控制程序进行模拟,结合不同西格玛质量水平对Westgard西格玛推荐的质量控制程序进行性能分析。结果 Westgard西格玛规则推荐的质量控制程序,是能满足误差检出概率和假失控概率要求的前提下相对简单的规则。结论 临床检验定量测定室内质量控制程序设计软件验证了Westgard西格玛规则中推荐质量控制程序的性能,Westgard西格玛规则图直观便捷,临床实验室可以用来推荐室内质量控制的质量控制程序。

融合大模型与图神经网络的电力设备缺陷诊断

电力系统中不同装置设备的缺陷评级和分析处理常受运维人员主观性影响,导致同一缺陷文本描述出现不同的严重程度评级。专业知识的差异也导致诊断分析差异和诊断效率不同。为提升缺陷诊断的准确性和效率,提出一种基于图神经网络的缺陷文本评级分类方法和大模型智能诊断分析助手。构建专业词典,使用自然语言处理算法规范化文本描述。通过统计方法,优化缺陷文本的语义表示。集成图注意力神经网络和RoBERTa模型对缺陷文本进行精确评级分类。基于大语言模型Qwen1.5-14B-Chat进行低秩适配(LoRA)微调训练得到电力设备诊断大模型Qwen-ElecDiag,结合检索增强生成技术开发设备缺陷诊断助手。此外,整理提供微调电力设备诊断大模型的指令数据集。对比实验结果表明,提出的基于图神经网络的缺陷评级分类方法在准确性上较最优基准模型BERT提升近8个百分点;诊断助手的电力知识以及缺陷诊断能力得到提升。通过提高缺陷评级的准确率并提供全面专业化诊断建议,不仅提高电力设备运维的智能化水平,也为其他垂直领域的智能运维提供新的解决方案。