最小生成树问题的Kruscal算法的一种实现方法

本文讨论了针对带权连通图的一种可行性存储结构———单链表结构的构造问题 ,并研究了在该结构上构造最小生成树的算法 .算法已在机器上得到了实现     

含有一个一度顶点的满足A(H)=3的图

关于图方程A(H)=n的讨论，重点是研究A(H)=2及A(H)=3的图H及其母图的性质，这就需要研究不同类型的A(H)=3的图。本文给出了含有一个一度顶点的满足A(H)=3的图。     

基于Visual Graph的电气控制仿真

主要介绍软件VisualGraph在电气控制电路仿真方面的应用。以“电动机正反转控制”为例,说明如何利用VisualGraph实现对电气控制电路的仿真。     

浅谈图表信息在中学数学解题中的应用

图表信息这一考试热点问题的兴起改变了人们对传统的图表题的认识与思维方式。从图表信息的意义及其相关概念入手,探讨了图表信息在各类解题中的新思路,提出了图表信息在解题中的具体应用。     

Bi-directional h-index: A new measure of node centrality in weighted and directed networks

This paper builds an index family, named bi-directional h-index, to measure node centrality in weighted directed networks. Bi-directional h-index takes the directed degree centrality as the initial value and iteratively uses more network information to update the node’s importance. We prove the convergence of the iterative process after finite iterations and introduce an asynchronous updating process that provides a decentralized, local method to calculate the bi-directional h-index in large-scale networks and dynamic networks. The theoretical analysis manifests that the bi-directional h-index is feasible and significant for establishing a greater conceptual framework that includes some existing index concepts, such as lobby index, node’s h-index, c-index and iterative c-index. An example using journal citation networks indicates that the bi-directional h-index is different from directed degree centrality, directed node strength, directed h-degree and the HITS algorithm in ranking node importance. It is irreplaceable and can reflect these measures of node’s importance.     

智慧教育的三重境界：从环境、模式到体制

智慧教育作为教育信息化的高端形态,目前在全球范围内已受到越来越多的关注。虽然世界各国提出了不同的智慧教育方略,但智慧教育的愿景目标却都体现出打造智慧国家和城市、变革教学模式和培养卓越人才的主旨,因此需要从国家层面和文化境界来把握智慧教育。通过对现代教育系统的构成要素进行逻辑演绎,可以得出智慧教育系统包括智慧学习环境、新型教学模式和现代教育制度三重境界。智慧教育具有感知、适配、关爱、公平、和谐五大本质特征,通过智慧学习环境传递教育智慧,通过新型教学模式启迪学生智慧,通过现代教育制度孕育人类智慧。智慧教育的三重境界在＂智慧＂显现度、过程稳定性、涉及范围等方面呈现出明显的层级关系：从环境、模式到制度,＂智慧＂显现度呈现出从显性到隐性的特征,过程稳定性呈现出从动态到稳定的特征,涉及范围呈现出从微观到宏观的特征。     

Rank-based self-training for graph convolutional networks

Graph Convolutional Networks (GCNs) have been established as a fundamental approach for representation learning on graphs, based on convolution operations on non-Euclidean domain, defined by graph-structured data. GCNs and variants have achieved state-of-the-art results on classification tasks, especially in semi-supervised learning scenarios. A central challenge in semi-supervised classification consists in how to exploit the maximum of useful information encoded in the unlabeled data. In this paper, we address this issue through a novel self-training approach for improving the accuracy of GCNs on semi-supervised classification tasks. A margin score is used through a rank-based model to identify the most confident sample predictions. Such predictions are exploited as an expanded labeled set in a second-stage training step. Our model is suitable for different GCN models. Moreover, we also propose a rank aggregation of labeled sets obtained by different GCN models. The experimental evaluation considers four GCN variations and traditional benchmarks extensively used in the literature. Significant accuracy gains were achieved for all evaluated models, reaching results comparable or superior to the state-of-the-art. The best results were achieved for rank aggregation self-training on combinations of the four GCN models.     

对称图法化简逻辑函数之对称方形图法

使用一种新的逻辑函数化简的图形法,使得化简5变量及以上的逻辑函数变得简单、直观、容易操作。这种对称方形图法化简方法采用方形图的对称性并在格雷码中找到一种既能满足最小项逻辑相邻,又能保证最小项对称相邻并符合方形图的对称性质的编码。化简过程则是根据方形图的对称性找出所有相邻的最小项,从而消掉n个变化的量,保留(m-n)个不变的量,最后将输出结果表示为与或式得到最终结果。这种化简方法对于任意变量的逻辑函数都适用并且可以将复杂度减少到最小,清晰度提升到一定的高度。     

Robust graph learning with graph convolutional network

Graph convolutional network (GCN) is a powerful tool to process the graph data and has achieved satisfactory performance in the task of node classification. In general, GCN uses a fixed graph to guide the graph convolutional operation. However, the fixed graph from the original feature space may contain noises or outliers, which may degrade the effectiveness of GCN. To address this issue, in this paper, we propose a robust graph learning convolutional network (RGLCN). Specifically, we design a robust graph learning model based on the sparse constraint and strong connectivity constraint to achieve the smoothness of the graph learning. In addition, we introduce graph learning model into GCN to explore the representative information, aiming to learning a high-quality graph for the downstream task. Experiments on citation network datasets show that the proposed RGLCN outperforms the existing comparison methods with respect to the task of node classification.     

HGNN: Hyperedge-based graph neural network for MOOC Course Recommendation

Previous studies on Course Recommendation (CR) mainly focus on investigating the sequential relationships among courses (RNN is applied) and fail to learn the similarity relationships among learners. Moreover, existing RNN-based methods can only model courses’ short-term sequential patterns due to the inherent shortcomings of RNNs. In light of the above issues, we develop a hyperedge-based graph neural network, namely HGNN, for CR. Specifically, (1) to model the relationships among learners, we treat learners (i.e., hyperedges) as the sets of courses in a hypergraph, and convert the task of learning learners’ representations to induce the embeddings for hyperedges, where a hyperedge-based graph attention network is further proposed. (2) To simultaneously consider courses’ long-term and short-term sequential relationships, we first construct a course sequential graph across learners, and learn courses’ representations via a modified graph attention network. Then, we feed the learned representations into a GRU-based sequence encoder to infer their short-term patterns, and deem the last hidden state as the learned sequence-level learner embedding. After that, we obtain the learners’ final representations by a product pooling operation to retain features from different latent spaces, and optimize a cross-entropy loss to make recommendations. To evaluate our proposed solution HGNN, we conduct extensive experiments on two real-world datasets, XuetangX and MovieLens. We conduct experiments on MovieLens to prove the extensibility of our solution on other collections. From the experimental results, we can find that HGNN evidently outperforms other recent CR methods on both datasets, achieving 11.96% on P@20, 16.01% on NDCG@20, and 27.62% on MRR@20 on XuetangX, demonstrating the effectiveness of studying CR in a hypergraph, and the importance of considering both long-term and short-term sequential patterns of courses.