Properties of a planar cubic graph

It is shown that a planar cubic graph can always be reduced to another planar cubic graph with fewer vertices. It is also shown that if a planar cubic graph is edge-3- colorable then the reduction of the number of its vertices is possible without changing colors of its edges.     

特殊图的最优标号

标号图(G,L)由图G和它的标号L∶V(G)→{1,2,…,n｝组成.其中n=|V(G)|.在标号图(G,L)中,如果一条路P=u1,u2,…,uk(k≥1)的长度为0(k=1)或者对任意的i(i=1,2,…,k-1;k＞1),满足L(ui)+2≥L(ui+1),则称P为不连续增长路.标号(G,L)图中所有的不连续增长路的数目记为d(G,L).如果图G的一种标号L使得d(G,L)达到最大,则称之为图G的最优标号.在这里,给出了毛毛虫图的一种最优标号.     

关于群方程f(n)=6解的结论

设f(n)是n阶群的同构类数目,对于给定的正整数k,满足方程f(n)=k的正整数n叫做群方程f(n)=k的解。本文利用群论及数论知识对群方程f(n)=6的解进行讨论,得到了一些结论.     

Controllability and extensions

Control problems in Hilbert spaces are treated in a measure-theoretical framework; instead of dealing with a set of admissible trajectory-control pairs, a set of measures defined by the boundary conditions and the differential equations of the problem are considered. The concept of weak controllability is introduced; a system has this property if every pair of initial and final points, (t_a,x_a) and (t_b,x_b) can be weakly joined; this is possible if a set of linear equalities involving measures has a solution. In turn, this is shown to be equivalent to the possibility of extending a linear functional in a positive manner. Necessary and sufficient conditions for controllability are derived, and applied to the study of a finite-dimensional system with the control appearing linearly.     

小波域红外能量图人脸识别中小波基的选取

小波域红外能量图人脸识别技术不但可实现全天候人脸识别,而且能够减少人脸识别中的数据复杂度,但是其识别率和时间花费与小波基的选取有关。为此对几种常用的小波基分别进行了实验,并对实验结果进行了分析和总结。实验结果表明,具有正交性和对称性的小波具有较高的红外人脸识别率。     

Welfare improvement windows for innovation policy

The question this article addresses is, how far from its optimal level can an innovation policy be implemented at, yet still improve social welfare relative to the laissez-faire outcome? The concern for policymakers is that even an intervention which enhances welfare if set at its optimal magnitude might actually make matters worse if implemented to the wrong degree. Understanding the performance of suboptimal policy levels is practically important, since the complexity and uncertainty of innovation make optimal policy magnitudes elusive in the real world. The model developed herein to investigate this issue is an R&D rivalry game where firms invest in R&D, then engage in Cournot competition. A policymaker seeks to improve welfare by choosing the levels of an R&D subsidy and consumer price subsidy. Results show that the welfare improvement window, defined as the set of all policy levels that improve social welfare, can be worryingly narrow. However, certain features of an innovation process and market lead to wider welfare improvement windows, such as stronger spillovers and moderately costly R&D. Policymakers stand a better chance of improving social welfare by intervening where these features are present.     

隐性知识外显案例之多案例诱导型适配研究

[目的/意义]知识经济时代知识成为核心资源,隐性知识是组织创造价值的源泉。文章设计了一套隐性知识外显案例的多案例诱导型适配方法,对知识用户提供过程辅助,以此提高组织隐性知识的应用效益。[方法/过程]采用熵权法确定案例条件方面权重,利用向量相似度算法计算待解问题与案例库中既有历史案例之间的视图相似度,从而确定待解问题的多案例适配集;针对适配案例集中存在的冗余方面不利于挖掘出案例条件空间对决策空间的决定关系问题,采用遗传算法简化待解问题的适配案例集,并基于简化的适配案例集,利用C4. 5决策树算法求解待解问题诱导型适配的解轨迹。[结果/结论]算例表明,与业内既有适配方法相比,文章提出的多案例诱导型适配方法合理、有效,具有相对优势。     

Clustering dense graphs: A web site graph paradigm

Typically graph-clustering approaches assume that a cluster is a vertex subset such that for all of its vertices, the number of links connecting a vertex to its cluster is higher than the number of links connecting the vertex to the remaining graph. We consider a cluster such that for all of its vertices, the number of links connecting a vertex to its cluster is higher than the number of links connecting the vertex to any other cluster. Based on this fundamental view, we propose a graph-clustering algorithm that identifies clusters even if they contain vertices more strongly connected outside than inside their cluster; hence, the proposed algorithm is proved exceptionally efficient in clustering densely interconnected graphs. Extensive experimentation with artificial and real datasets shows that our approach outperforms earlier alternate clustering techniques.     

基于资源分配图的死锁检测算法的改进

本文提出一种基于资源分配图的死锁检测算法,由于以进程间通信的方式进行死锁检测,使得该算法既适用于集中式系统又适用于分布式系统,该算法的时间复杂度是o(e)。     

Generation of trees of a graph with the use of decomposition

The method of tree generation of a graph decomposed into any number of parts is described in this paper. The decomposition of a graph is defined. The formula for the generation of trees of a decomposed graph is given in Theorem I. The necessary and sufficient conditions which a graph decomposition must satisfy to avoid duplications in the generated set of trees are discussed and results are summarized in Theorems II and III. A criterion for existence of such a decomposition is formulated in Theorem IV and also an appropriate algorithm for the graph decomposition is suggested.     

基于司法判决书的知识图谱构建与知识服务应用分析

【目的/意义】构建基于司法判决书的案件知识图谱是对司法数字资源的有效利用,有助于提升司法智能化 水平,积极响应国家“智慧法院”建设发展战略。【方法/过程】以“网络诈骗”领域为例,用“自顶向下”的方式构建知 识图谱。首先,结合文书内容与专家意见构建案件领域本体;接着,通过知识抽取、知识表示、知识融合等环节获取 实体、属性及关系;再利用Neo4j生成案件知识图谱。最后,提出了基于知识图谱的智慧司法知识服务框架。【结果/ 结论】基于 2015年-2020年的“网络诈骗”领域司法判决书,构建了含有约 3万个实体和 18万条关系的案件知识图 谱,并详细阐述了具备基础资源层、知识图谱层、服务应用层的智慧司法知识服务框架设计。【创新/局限】实现了案 件知识图谱的实体类型扩充,以丰富图谱应用场景,并将知识图谱技术与智慧司法知识服务框架进行融合;局限在 于仅使用网络诈骗领域判决书数据进行实证研究。     

边传递图上的最快混合马氏过程

考虑加权连通图上的简单连续时间马氏过程,每条边上赋权为马氏过程的转移速率,使得马氏过程混合时间最短的赋权问题称之为最快混合马氏过程问题(FMMP).我们证明FMMP在图自同构群的不变点集合中取到最优,并且在边传递图中解析地得到了最优解.     

A procedure for comparing passive,active, and semi-active approaches to vibration isolation

A procedure is developed which uses bond graph modeling and a digital computer to determine if semi-active control can provide a suitable performance in an application where totally active control is considered. The application areas principally addressed are those in which the disturbance inputs to the system are of zero mean, i.e. shock and vibration control.The procedure is developed through examples and then generalized to systems of high order and large complexity. The procedure consists basically of designing a control strategy suitable for totally active control and then enforcing a passivity constraint on the actuating device. Experience has shown that semi-active control approaches that of totally active control in most vibration isolation applications.     

异质性影响共享资源集体供给的机理研究

从共享资源自发合作治理(集体供给)中异质性影响机理两种截然"相反"的观点出发,引出对异质性"U型曲线"关系的讨论。依个体决策知识结构的不同,将个体间交往的知识状态划分为形成与未形成新的共同知识两类;并分别构建理论模型分析。结论表明:一般情况下,单维异质性与共享资源产出水平之间(基本)满足单调关系,"U型曲线"只是一种特例;两种"相反"观点的表象背后,是其各自分析目的以及研究对象所处决策场景或状态的差异。     

Reproducing knowledge: Xerox and the story of knowledge management

This paper is a commentary on discursive transformations that occur in stories told about Xerox's photocopier technicians, comparing particularly Orr's brilliant ethnographic study and a later management case study. It argues that significant shifts take place in how knowledge is understood between these accounts so that what begins as elusive, oral, improvised and social becomes increasingly presented as encodable in a structured database, countable, auditable, individualistic. These ideological transformations seem much to do with Xerox's own historic need to rebrand itself, and simply to sell a commercial product. Thus, how knowledge is represented and what knowledge management might mean seems to be heavily influenced by corporate vested interests. The paper stresses the need to capture complexity in case studies if they are to promote a realistic or critical understanding of the organisation.     

关于合作向量场的不变函数

在本文中,我们证明了R_ ~n上的合作和不可约向量场拥有一个处处非常数的不变函数的充要条件是奇点构成一条含原点的无界有序曲线;如果这样的不变函数存在,则每条有界轨线收敛于奇点。     

Bipartite output consensus for heterogeneous linear multi-agent systems with fully distributed protocol

This paper addresses the problem of bipartite output consensus of heterogeneous multi-agent systems over signed graphs. First, under the assumption that the sub-graph describing the communication topology among the agents is connected, a fully distributed protocol is provided to make the heterogeneous agents achieve bipartite output consensus. Then for the case that the topology graph has a directed spanning tree, a novel adaptive consensus protocol is designed, which also avoids using any global information. Each of these two protocols consists of a solution pair of the regulation equation and a homogeneous compensator. Numerical simulations show the effectiveness of the proposed approach.     

Jointly modeling intra- and inter-session dependencies with graph neural networks for session-based recommendations

Recently, graph neural networks (GNNs) have achieved promising results in session-based recommendation. Existing methods typically construct a local session graph and a global session graph to explore complex item transition patterns. However, studies have seldom investigated the repeat consumption phenomenon in a local graph. In addition, it is challenging to retrieve relevant adjacent nodes from the whole training set owing to computational complexity and space constraints. In this study, we use a GNN to jointly model intra- and inter-session item dependencies for session-based recommendations. We construct a repeat-aware local session graph to encode the intra-item dependencies and generate the session representation with positional awareness. Then, we use sessions from the current mini-batch instead of the whole training set to construct a global graph, which we refer to as the session-level global graph. Next, we aggregate the K-nearest neighbors to generate the final session representation, which enables easy and efficient neighbor searching. Extensive experiments on three real-world recommendation datasets demonstrate that RN-GNN outperforms state-of-the-art methods.     

一种新的椭球算法

基于更动约束的思想[1 ] 与方法 ,提出了求解线性规划问题的新椭球算法 .它与L .G .Khachian的椭球算法[2 ] 不同 ,在新算法的椭球迭代过程中 ,不仅用约束不等式割掉不含约束集的半个椭球 (椭球中心不在约束集内时 ) ,称之为约束割 ;而且在椭球中心落在约束集内时 ,它用目标不等式割掉含约束集的半个椭球 ,称之为目标割 .新算法的不等式系统是由原规划 (或对偶规划 )的约束不等式与目标不等式组成的 (规模小 ) ,而不是由原椭球算法的K K T条件[5] 组成的不等式系统 (规模大 ) .这种新椭球算法即有多项式计算复杂性的特性 ,又在迭代过程中得到一系列单调趋向最优解的可行解 (在解存在时 ) .如果认为已得满意解 ,可随时停机 .对于实际问题 ,大多数是变量有界的 ,初始椭球不大 ,因此新算法更为实际 ,有效 .