基于多层次灰色关联分析的创新合作网络节点评估研究

基于网络中心性指标的分析,有效融合网络度中心度、网络中介中心度、网络接近中心度、网络特征向量中心度四种中心性指标的优点,构建多层次灰色关联分析的节点综合评估模型,对网络中节点的重要性进行综合评估,对网络中核心节点予以判定.结合新一代信息技术领域专利合作网络的数据进行分析,结果表明模型在节点重要性排序结果上比以往的方法更科学,不同节点重要性区分度也更高.     

企业合作网络的度分布研究

本文根据企业合作网络的特点建立模型，并通过马氏链的方法推导出具有节点吸引力的企业合作网络的度分布。     

产学研合作创新网络规模、连接机制与创新绩效的关系研究——基于多主体仿真和动态系统论视角

为揭示产学研合作创新网络规模与连接机制对创新绩效的影响机理,运用Agent建模理论和Netlogo仿真平台构建产学研合作创新网络的仿真模型,对不同特性(小世界、无标度)偏好下的产学研合作创新网络进行仿真实验,并运用动态系统理论解释仿真的涌现现象。研究发现:①网络平均节点度(度数中心势)与网络平均创新绩效(节点加权平均收益的对数)之间存在鞍结分叉和跨临界分叉的组合现象;②网络平均距离(关系强度)与网络平均绩效之间呈指数增长分布轨道;③连接机制与网络平均绩效呈对数增长分布轨道;④实力择优连接机制提升网络平均节点度正向作用的效率较低;⑤随机组合择优连接机制更有利于提升小世界偏好网络平均距离的正向作用;⑥度择优连接机制更有利于提升无标度偏好网络平均创新绩效。     

基于结构元理论的模糊社会网络关系测量研究

模糊社会网络研究是社会网络研究中的一个热点。模糊数运算公式经常难以解析表达,制约了模糊社会网络理论探索与实践应用。模糊结构元理论在模糊运算中有着独特优势。运用结构元理论构建了广义模糊节点度、密度和接近中心度的测量方法;并结合算例验证了基于结构元理论的社会网络关系测量方法的有效性。     

基于结构元理论的广义模糊权值网络中心度分析

针对现有权值网络中心度测量要么只关注边数,要么只关注权值的问题,提出了一个基于结构元的模糊权值网络中心度的测量方法。运用模糊结构元理论解析表达了广义模糊权值网络程度中心度、广义模糊权值网络亲密中心度和广义模糊权值网络中间性中心度;并结合算例验证了基于结构元理论的广义模糊权值网络中心度测量方法的可行性,展示了结果的丰富性。     

两个离散网络间的广义同步

本文研究了两个离散网络之间的广义同步,其中每个网络的节点动力学是不同的,节点数目也没有要求是相等的.通过使用辅助系统方法,我们给出了基于李雅普诺夫稳定性理论的广义同步定理.最后,用数值例子来验证定理的有效性.     

基于改进节点重要度引力模型的航路网拥堵节点识别

航路网络存在一些关键航路点对系统整体具有重要控制作用,而有效辨识这些重要节点对缓解空中交通拥堵,提高航路运行效率具有极大意义.以复杂网络理论为基础,从网络视角结合中心度及节点服务能力通过改进传统引力模型进行节点重要度评估;然后基于改进节点重要度引力模型进行航路网络拥堵节点识别仿真,并将结果与传统介数法进行对比验证.研究表明:改进的引力模型识别的重要节点,不仅具有较大的中心度,且较多位于航路网络流量较大位置;基于引力模型识别航路网络节点重要度的准确率更高,在提高网络通行率基础上更及时地识别航路网络易拥堵节点,对预防节点失效、减少航路网络拥堵具有积极作用.     

广义伪分形网络上随机游走的平均首达时间的精确幂律

研究具有一个吸收点的广义伪分形网络上随机游走的平均首达时间.广义伪分形网络的显著特点是在每一次迭代中,每条现有的边会产生有限个节点.根据网络的演化算法,得到了平均首达时间的精确表达式.当网络的阶数足够大时,平均首达时间是按照网络节点数的幂律在增长.此外,可以通过改变网络参数来改善此类网络的随机游走的效率.这些研究结果是对伪分形网络相应结果的推广,将为深入研究各类分形网络的随机游走提供帮助.     

M-G-P型复杂网络中有寿命节点的进入退出机制

现实中复杂网络结构复杂,形式多样,处在高度动态变化的过程.为了更好地理解真实网络的演化,基于复杂网络的特性进行分析,建立了Poissotn连续时间增长节点具有寿命的M-G-P型复杂网络模型,模型中包括:新节点加入、节点老化和老节点退出等,基于齐次马尔可夫链对模型的度分布进行计算,得出M-G-P型网络的度分布符合幂律分布,模型和BA模型一样能产生指数γ=3的无标度网络,验证了导致无标度网络度分布特征起关键性作用的是链接的偏好特性.     

超网络中心性度量的υ-Position值方法

利用合作博弈理论的分配规则如Shapley值、Banzhaf值等来度量政治、经济和社会网络中节点的中心性或者重要性是识别网络中关键节点的一类重要方法。考虑到在超网络中代表各类组织的超边在网络中发挥的作用不同,本文研究了超网络博弈上一类广义Position值的分配规则,被称为υ-position值。它可以作为网络中度值测度的一类推广,以此来度量网络中参与者的中心性和相对重要性。其次,证明了超网络结构上类Shapley-position值可由分支超边指数和局部平衡超边贡献两个性质所唯一刻画。最后, 举例分析了υ-position值在超网络中心性测度中的应用。     

Oriented matroid systems

The domination invariant has played an important part in reliability theory. While most of the work in this field has been restricted to various types of network system models, many of the results can be generalized to much wider families of systems associated with matroids. Previous papers have explored the relation between undirected network systems and matroids. In this paper the main focus is on directed network systems and their relation to oriented matroids. An oriented matroid is a special type of matroid where the circuits are signed sets. Using these signed sets one can e.g., obtain a set theoretic representation of the direction of the edges of a directed network system. Classical results for directed network systems include the fact that the signed domination is either +1 or −1 if the network is acyclic, and zero otherwise. It turns out that these results can be generalized to systems derived from oriented matroids. Several classes of systems for which the generalized results hold will be discussed. These include oriented versions of k-out-of-n systems and a certain class of systems associated with matrices.     

Basis properties and algorithmic specializations for gub transformed networks

Applying standard transformations of generalized upper bounding (GUB) theory to a pure or generalized network basis is shown to yield a reduced working basis that is itself a basis for a reduced network. As a result, the working basis can be represented via specialized data structures for networks. The resultant GUB based specializations to the network simplex algorithm are described.     

有容量限制的广义网络均衡比较

近些年来,Wardrop原理在有容量限制的交通网络中沿着两个方向被学者推广,形成了几种不同的广义网络均衡定义.在路径、路段上两种类型的容量限制下,通过对四种广义网络均衡进行比较,得到这些均衡解之间的相互关系;用反例说明广义均衡解集包含关系不成立的情况;得到这些广义均衡解的效率损失.     

A unified network performance measure with importance identification and the ranking of network components

In this paper, we propose the first network performance measure that can be used to assess the efficiency of a network in the case of either fixed or elastic demands. Such a measure is needed for many different applications since only when the performance of a network can be quantifiably measured can the network be appropriately managed. Moreover, as we demonstrate, the proposed performance measure, which captures flow information and behavior, allows one to determine the criticality of various nodes (as well as links) through the identification of their importance and ranking. We present specific networks for which the performance/efficiency is computed along with the importance rankings of the nodes and links. The new measure can be applied to transportation networks, supply chains, financial networks, electric power generation and distribution networks as well as to the Internet and can be used to assess the vulnerability of a network to disruptions.     

Global optimization of multilevel electricity market models including network design and graph partitioning

We consider the combination of a network design and graph partitioning model in a multilevel framework for determining the optimal network expansion and the optimal zonal configuration of zonal pricing electricity markets, which is an extension of the model discussed in Grimm et al. (2019) that does not include a network design problem. The two classical discrete optimization problems of network design and graph partitioning together with nonlinearities due to economic modeling yield extremely challenging mixed-integer nonlinear multilevel models for which we develop two problem-tailored solution techniques. The first approach relies on an equivalent bilevel formulation and a standard KKT transformation thereof including novel primal-dual bound tightening techniques, whereas the second is a tailored generalized Benders decomposition. For the latter, we strengthen the Benders cuts of Grimm et al. (2019) by using the structure of the newly introduced network design subproblem. We prove for both methods that they yield global optimal solutions. Afterward, we compare the approaches in a numerical study and show that the tailored Benders approach clearly outperforms the standard KKT transformation. Finally, we present a case study that illustrates the economic effects that are captured in our model.     

Multi-Phase Quadrature Domains and a Related Minimization Problem

In this paper we introduce the multi-phase version of the so-called Quadrature Domains (QD), which refers to a generalized type of mean value property for harmonic functions. The well-established and developed theory of one-phase QD was recently generalized to a two-phase version, by one of the current authors (in collaboration). Here we introduce the concept of the multi-phase version of the problem, and prove existence as well as several properties of such solutions. In particular, we discuss possibilities of multi-junction points.     

A generalized linear production model: A unifying model

We introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producersS is not restricted to be the vector sum of the resources held by the members ofS. We provide sufficient conditions for the non-emptiness of the core of the associated generalized linear production game, and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem. Our generalized linear production model is a proper generalization of the linear production model introduced by Owen, and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework. We use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non-empty core. We further employ our model to prove the non-emptiness of the core of two other classes of cooperative games, which were not previously studied in the literature, and we also use our generalized model to provide an alternative proof for the non-emptiness of the core of the class of minimum cost spanning tree games. Thus, it appears that the generalized linear production model is a unifying model which can be used to explain the non-emptiness of the core of cooperative games generated by various, seemingly different, optimization models.This research was partially done while the author was visiting the Graduate School of Business Administration at Tel-Aviv University. The research was partially supported by Natural Sciences and Engineering Research Council Canada Grant A4181 and by SSHRC leave fellowship 451-83-0030.Dedicated to George B. Dantzig.     

Measuring agility of networked organizational structures via network entropy and mutual information

While the agility of networked organizational structures is important for organizational performance, studies on how to evaluate it remain scant, probably because the difficulty in measuring network evolution. In this conceptual paper, we propose two measures - network entropy and mutual information - to characterize the agility of networked organizational structure. Rooted in graph theory and information theory, these two measures capture network evolution in a comprehensive and parsimonious way. They indicate the uncertainty (or disorder) at the network level as well as the degree distribution at the individual level. We also propose an algorithm for applying them in the scenario of adding links to a network while holding the number of nodes fixed. Both simulated and real networks are used for demonstration. Implications and areas for future research are discussed in the end.     

Jamming communication networks under complete uncertainty

This paper describes a problem of interdicting/jamming wireless communication networks in uncertain environments. Jamming communication networks is an important problem with many applications, but has received relatively little attention in the literature. Most of the work on network interdiction is focused on preventing jamming and analyzing network vulnerabilities. Here, we consider the case where there is no information about the network to be jammed. Thus, the problem is reduced to jamming all points in the area of interest. The optimal solution will determine the locations of the minimum number of jamming devices required to suppress the network. We consider a subproblem which places jamming devices on the nodes of a uniform grid over the area of interest. The objective here is to determine the maximum grid step size. We derive upper and lower bounds for this problem and provide a convergence result. Further, we prove that due to the cumulative effect of the jamming devices, the proposed method produces better solutions than the classical technique of covering the region with uniform circles.     

On-line algorithms for networks of temporal constraints

We consider a semi-dynamic setting for the Temporal Constraint Satisfaction Problem (TCSP), where we are requested to maintain the path-consistency of a network under a sequence of insertions of new (further) constraints between pairs of variables. We show how to maintain the path-consistency in O(nR³) amortized time on a sequence of Θ(n²) insertions, where n is the number of vertices of the network and R is its range, defined as the maximum size of the minimum interval containing all the intervals of a single constraint.Furthermore we extend our algorithms to deal with more general temporal networks where variables can be points and/or intervals and constraints can also be defined on pairs of different kinds of variables. For such cases our algorithms maintain their performance. Finally, we adapt our algorithms to also maintain the arc-consistency of such generalized networks in O(R) amortized time for Θ(n²) insertions.