二元de Bruijn网络的可靠性分析

证明了二元de Bruijn网络是极大限制边连通的,并且它们的最小限制边割只能分离一条孤立边或者一个三角形. 利用此结果分析了二元de Bruijn网络的可靠性,确定了它们的可靠多项式的前四项系数.     

具有随机脉冲的布尔控制网络的集合稳定性研究

在文章研究的具有随机脉冲的布尔控制网络的集合稳定性问题中,随机脉冲的引入使得模型对实际问题的研究更具真实性.首先,随机脉冲被描述为一组可供选择的具有相应概率的常规模型集合.同时,文章明确集合稳定性问题的目的是将系统中所有节点以概率1到达并稳定到给定节点集合.其次,提出一个判断给定系统的集合稳定性的充要条件.然后,对于可集合稳定系统,给出控制器和脉冲策略的设计方法.最后,通过一个数例说明获得成果的有效性.     

图与超图中的彩色匹配综述

超图H=(V,E)是一个二元组(V,E),其中超边集E中的元素是点集V的非空子集.因此图是一种特殊的超图,超图也可以看作是一般图的推广.特别地,如果超边集E中的元素均是点集V的k元子集,则称该超图为k-一致的.通常情况下,为叙述简便,我们也会将超边简称为边.图(超图)中的匹配是指图(超图)中互不相交的边的集合.对于图(超图)中的彩色匹配,有两种定义方式:一为染色图(超图)中互不相交且颜色不同的边的集合;二为顶点集均为[n]的多个染色图(超图)所构成的集族中互不相交且颜色均不同的边的集合,且每条边均来自集族中不同的图(超图).现主要介绍了图与超图中关于彩色匹配的相关结果.     

图上合作博弈和图的边密度

1977年, Myerson建立了以图作为合作结构的可转移效用博弈模型(也称图博弈), 并提出了一个分配规则, 也即"Myerson 值", 它推广了著名的Shapley值. 该模型假定每个连通集合(通过边直接或间接内部相连的参与者集合)才能形成可行的合作联盟而取得相应的收益, 而不考虑连通集合的具体结构. 引入图的局部边密度来度量每个连通集合中各成员之间联系的紧密程度, 即以该连通集合的导出子图的边密度来作为他们的收益系数, 并由此定义了具有边密度的Myerson值, 证明了具有边密度的Myerson值可以由"边密度分支有效性"和"公平性"来唯一确定.     

最短路的 Hu 算法的代数证明

设有一个有向图,顶点集合为 V={V_i|i=1,2…n},有向边集合记作 E.对于每一条有向边,对应一个实数,可正、可负、可为零,这个数叫做这条有向边的长度.这样的有向图叫做(一般)网络,记作 N(V,E).     

mC4的顶点被多重色集合可区别的一般边染色北大核心CSCD

简单图G的一个一般边染色是指若干种颜色关于图G的所有边的一个分配,不要求相邻的边被分配不同的颜色.设f是G的使用了k种颜色的一般边染色,若对(?)u,v∈V(G),u≠v,都有与u关联的边的颜色构成的多重集合异于与v关联的边的颜色构成的多重集合,那么称f是使用了k种颜色的顶点被多重色集合可区别的一般边染色.对G进行顶点被多重色集合可区别的一般边染色所需的最少颜色数记为c(G),并且称c(G)为图G的顶点被多重色集合可区别的一般边色数.本文确定了m个C_4的点不交的并mC_4的顶点被多重色集合可区别的一般边色数.     

已知拓扑下的最短网络

在平面上给定一个有n个固定点的集合S和一个含有m个可动点的集合M及连接这些点的边的集合T(T也称之为拓扑),确定M中点的位置,使点集V=SM的互联网络最短.本文证明了n是偶数m=-1及在满4度Steiner拓扑下最短网络的结构是4度Steiner树.     

一类具有非空核的拟均衡对策

自 Scarf 给出 n 人没有边支付对策的核存在的条件后,很多人致力于研究一般的没有边支付对策的核.但情况比较复杂,一般的没有边支付对策核非空要求的条件较强,即使是均衡对策,也不能保证核的非空性.因而,Weber 引进了拟均衡对策.本文研究了一类拟均衡对策,它们具有非空的核.本文中的定理1改进了文献[2]中的主要结论.     

网络故障概率多项式系数及其特性

让二元组(G,ρ)表示一个网络,其中G为反映网络拓扑结构的图,ρ为该网络各边出故障的概率.当网络的节点故障概率可以忽略不计时,网络的故障概率,即该网络因为边的故障而使得某两点不能通讯的概率P(G,ρ),可表为P(G,ρ)=sum from i=0 to 6 m_iρ~i(1-ρ)~(e-i),其中e为图G的边的条数,m_i为图G中具有i条边的截集(或断集)的个数,称为故障概率多项式系数。本文将讨论m_i的作用及其特性。     

边着色路到完全图的嵌入

一、一个猜想设 P_n 为具有 n 个顶点的一条路,它的 n-1条边着上了不同的颜色,若这个着色能扩充为 n 个顶点的完全图 K_n 的一个正常的 x′(K_n)一边着色,则称边着色路 P_n 能嵌入于完全图.一般说来,设 G 是具有边色数 x′(G)的一个简单图,令 M(G)为 G 中所有满足以下性质的子图 H(?)G 的集合:存在 G 的一种正常的 x′(G)-边着色使得 H 的各条边具有不同的颜色.设 K_n 是 n 个顶点的完全图,把集合 M(K_n)简记为 M_n 于是我们一开始提出的问题“P_n 能否嵌入于完全图”等价于“P_n 是否属于 M_n”.     

On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia

This paper presents the first topological analysis of the economic structure of an entire country based on payments data obtained from Swedbank. This data set is exclusive in its kind because around 80% of Estonia's bank transactions are done through Swedbank; hence, the economic structure of the country can be reconstructed. Scale-free networks are commonly observed in a wide array of different contexts such as nature and society. In this paper, the nodes are comprised by customers of the bank (legal entities) and the links are established by payments between these nodes. We study the scaling-free and structural properties of this network. We also describe its topology, components and behaviors. We show that this network shares typical structural characteristics known in other complex networks: degree distributions follow a power law, low clustering coefficient and low average shortest path length. We identify the key nodes of the network and perform simulations of resiliency against random and targeted attacks of the nodes with two different approaches. With this, we find that by identifying and studying the links between the nodes is possible to perform vulnerability analysis of the Estonian economy with respect to economic shocks.     

Pairwise-stability and Nash equilibria in network formation

Suppose that individual payoffs depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and sufficient conditions on the network link marginal payoffs such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks. We thank William Thomson, an associate editor and two anonymous referees for their suggestions that led to substantial improvements. We also thank Sjaak Hurkens, Bettina Klaus, Jordi Massó and Giovanni Neglia for helpful conversations. The first author gratefully acknowledges the financial support from the Spanish Ministry of Education and FEDER through grant SEJ2005-01481/ECON, the Fundación BBVA and the Barcelona Economics Program of XREA. The second author is grateful to the Netherlands Organization for Scientific Research (NWO) for its support under grant VIDI-452-06-013.     

Communication network formation with link specificity and value transferability

We model strategic communication network formation with (i) link specificity: link maintenance lowers specific attention and thus value (negative externality previously ignored for communication) and (ii) value transferability via indirect links for informational but not for social value (positive externality modeled uniformly before). Assuming only social value, the pairwise stable set includes many nonstandard networks under high and particular combinations of complete components under low link specificity. Allowing for social and informational value reduces this set to certain fragmented networks under high and the complete network under low link specificity. These extremes are efficient, whereas intermediate link specificity generates inefficiency.     

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.     

Farsighted free trade networks

The paper examines whether bilateral free trade agreements can lead to global free trade. We reconsider the endogenous tariff model introduced by Goyal and Joshi (2006) who study pairwise stability of free trade networks. We depart from their analysis by adopting the concept of pairwise farsightedly stable networks (Herings et al. 2009, GEB). We show that the complete network (i.e., global free trade) constitutes a pairwise farsightedly stable set. In particular, there is a farsightedly improving path from the empty network (i.e., no free trade agreement in place) to the complete network, which involves link additions only, while farsightedly improving paths from preexisting free trade networks may involve link deletion (i.e., dissolution of some bilateral FTAs). Moreover, we show that pairwise farsightedly stable set of networks is not unique. One implication of our results is that bilateral trade negotiations, if properly channeled, can lead to global free trade, although some bilateral agreements may have to be dissolved first to pave the way towards global free trade.     

团队中枢节点的效率模型

集团性是社会网络的显著特征.团队作为一个小规模的社会网络,也存在网络结构的非均匀性以及中枢节点.在阐述团队网络的集团性和中枢节点导致网络的两面性等结构特征的基础上,运用小世界模型的局部效率和集聚系数等指标,建立了团队中枢节点的效率模型,并通过网络结构的调整(如加键和断键重连)研究了网络结构对中枢节点的效率的影响.     

A biased random-key genetic algorithm for road congestion minimization

One of the main goals in transportation planning is to achieve solutions for two classical problems, the traffic assignment and toll pricing problems. The traffic assignment problem aims to minimize total travel delay among all travelers. Based on data derived from the first problem, the toll pricing problem determines the set of tolls and corresponding tariffs that would collectively benefit all travelers and would lead to a user equilibrium solution. Obtaining high-quality solutions for this framework is a challenge for large networks. In this paper, we propose an approach to solve the two problems jointly, making use of a biased random-key genetic algorithm for the optimization of transportation network performance by strategically allocating tolls on some of the links of the road network. Since a transportation network may have thousands of intersections and hundreds of road segments, our algorithm takes advantage of mechanisms for speeding up shortest-path algorithms.     

Contractually stable networks

We consider situations where players are part of a network and belong to coalitions in a given coalition structure. We propose the concept of contractual stability to predict the networks that are going to emerge at equilibrium when the consent of coalition partners is needed for adding or deleting links. Two different decision rules for consent are analyzed: simple majority and unanimity. We characterize the coalition structures that make the strongly efficient network contractually stable under the unanimity decision rule and the coalition structures that sustain some critical network as contractually stable under the simple majority decision rule and under any decision rule requiring the consent of any proportion of coalition partners. Requiring the consent of coalition members may help to reconcile stability and efficiency in some classical models of network formation.     

Development of the tree-based link labeling algorithm for optimal path-finding in urban transportation networks

The optimal path-finding algorithm which is an important module in developing route guidance systems and traffic control systems has to provide correct paths to consider U-turns, P-turns, and no-left-turns in urban transportation networks.Traditional methods which have been used to consider those regulations on urban transportation networks can be categorized into network representation and algorithmic methods like the vine-building algorithm. First, network representation methods use traditional optimal path-finding algorithms with modifications to the network structure: for example, just adding dummy nodes and links to the existing network allows constraint-search in the network. This method which creates large networks is hard to implement and introduces considerable difficulties in network coding. With the increased number of nodes and links, the memory requirement tremendously increases, which causes the processing speed to slow down. For these reasons, the method has not been widely accepted for incorporating turning regulations in optimal path-finding problems in transportation networks. Second, algorithmic methods, as they are mainly based on the vine-building algorithm, have been suggested for determining optimal path for networks with turn penalties and prohibitions. However, the algorithms, although they nicely reflect the characteristics of urban transportation networks, frequently provide infeasible or suboptimal solutions.The algorithm to be suggested in this research is a method which is basically based on Dijkstra's algorithm [1] and the tree-building algorithm used to construct optimal paths. Unlike the traditional node labeling algorithms which label each node with minimum estimated cost, this algorithm labels each link with minimum estimated cost.Comparison with the vine-building algorithm shows that the solution of the link-labeling algorithm is better than that of the vine-building algorithm which very frequently provides suboptimal solutions. As a result, the algorithm allows turning regulations, while providing an optimal solution within a reasonable time limit.     

On the existence and uniqueness of pairwise stable networks

In this paper we show how externalities between links affect the existence and uniqueness of pairwise stable (PS) networks. For this we introduce the properties ordinal convexity (concavity) and ordinal strategic complements (substitutes) of utility functions on networks. It is shown that there exists at least one PS network if the profile of utility functions is ordinal convex and satisfies the ordinal strategic complements property. On the other hand, ordinal concavity and ordinal strategic substitutes are sufficient for some uniqueness properties of PS networks. Additionally, we elaborate on the relation of the link externality properties to definitions in the literature.