Partitioning Signed Two-Mode Networks

Structural balance theory forms the foundation for a generalized blockmodel method useful for delineating the structure of signed social one-mode networks for social actors (for example, people or nations). Heider's unit formation relation was dropped. We re-examine structural balance by formulating Heider's unit formation relations as signed two-mode data. Just as generalized blockmodeling has been extended to analyze two-mode unsigned data, we extend it to analyze signed two-mode network data and provide a formalization of the extension. The blockmodel structure for signed two-mode networks has positive and negative blocks, defined in terms of different partitions of rows and columns. These signed blocks can be located anywhere in the block model. We provide a motivating example and then use the new blockmodel type to delineate the voting patterns of the Supreme Court justices for all of their nonunanimous decisions for the 2006–07 term. Interpretations are presented together with a statement of further problems meriting attention for partitioning signed two-mode data.     

基于混沌理论的创新网络中组织间信任演化研究

以往关于信任的研究是在稳定均衡的假设下进行的,然而信任演化过程中会表现出非线性的混沌状态,具有复杂系统的特征。基于演化博弈理论和混沌理论,建立了创新网络中组织间信任演化模型,分析了创新网络中组织间信任的复杂性、初值敏感性、分岔行为及内随机性等混沌特性,推导出信任演化方程与Logistic映射之间的关系,采用Lyapunov稳定性理论进行混沌性判定,证明创新网络中组织间信任通过倍周期分岔通往混沌,得到了信任从有序进入混沌的一般条件,运用算例进行仿真展示信任演化通往混沌的过程,分析创新网络中信任演化进入混沌区的实际意义,并选择硅谷和筑波科技城两个实例做对比分析,验证了该研究的实用性和有效性。创新网络中组织间信任的混沌演化反映出信任发展的非线性特点,为创新网络中组织间信任的混沌利用和控制提供理论指导。     

Diversity and Popularity in Organizations and Communities

This paper examines social groupings whose structure depends only on the distribution of ability to attract attention. When people‘s attention is a scarce resource, those individuals who are rated highest by a large number of other individuals will have to ration their attention, resulting in constraints on the social structure of the group. The incidence of popular individuals by that definition reflects the extent to which individuals agree on who their highest-rated colleague is. We propose three basic distributions or ways to generate the matrix of perceived ability so as to yield popularity profiles that can be parametrically adjusted to match observations. We demonstrate that each of these assumption sets leads to a slightly different correlation between the value of the assumption‘s parameter and the set of observable popularity patterns. Since popularity, in real life, often determines such things as power, centrality, over-utilization and perhaps reduced accessibility, having more realistic ways of representing it is important for modeling and understanding virtual organizations and communities.     

Gossip in Organizations

Three hypotheses about the effects of different informal social network structures on gossip behavior are developed and tested. Gossip is defined as a conversation about a third person who is not participating in the conversation. Having analyzed the costs and benefits of gossip, we prefer the coalition hypothesis.~It states that gossip will flourish in social networks that have a relatively large number of coalition triads, that is ego and alter having a good relationship amongst themselves and both having a bad relationship with tertius, the object of gossip. Two rivalling hypotheses are developed. The constraint hypothesis predicts that the inclination towards gossip is greater, the larger the number of structural holes in the personal network of the gossipmonger.~The closure hypothesis predicts that more gossip will be found in networks with a large number of closed triads, that is where both gossipmonger and listener have a good relationship with the absent third person. The hypotheses are tested using a newly developed instrument to measure gossip behavior and network data from six work organizations and six school classes. The data support the coalition hypothesis and do not support the two rivalling hypotheses.     

Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings

Social action is situated in fields that are simultaneously composed of interpersonal ties and relations among organizations, which are both usefully characterized as social networks. We introduce a novel approach to distinguishing different network macro-structures in terms of cohesive subsets and their overlaps. We develop a vocabulary that relates different forms of network cohesion to field properties as opposed to organizational constraints on ties and structures. We illustrate differences in probabilistic attachment processes in network evolution that link on the one hand to organizational constraints versus field properties and to cohesive network topologies on the other. This allows us to identify a set of important new micro-macro linkages between local behavior in networks and global network properties. The analytic strategy thus puts in place a methodology for Predictive Social Cohesion theory to be developed and tested in the context of informal and formal organizations and organizational fields. We also show how organizations and fields combine at different scales of cohesive depth and cohesive breadth. Operational measures and results are illustrated for three organizational examples, and analysis of these cases suggests that different structures of cohesive subsets and overlaps may be predictive in organizational contexts and similarly for the larger fields in which they are embedded. Useful predictions may also be based on feedback from level of cohesion in the larger field back to organizations, conditioned on the level of multiconnectivity to the field.     

计算网络最小割的问题的注记

对网络最小割的计算进行了研究,给出了简化求最小割的理论依据.     

网络最短的最优解集结构

The shortest path problem in a network G is to find shortest paths between some specified source vertices and terminal vertices when the lengths of edges are given. The structure of the optimal solutions set on the shortest paths is studied in this paper. First,the conditions of having unique shortest path between two distinguished vertices s and t in a network G are discussed;Second,the structural properties of 2-transformation graph (?) on the shortest-paths for G are presented heavily.     

Operating Points in Infinite Nonlinear Networks Approximated by Finite Networks

Given a nonlinear infinite resistive network, an operating point can be determined by approximating the network by finite networks obtained by shorting together various infinite sets of nodes, and then taking a limit of the nodal potential functions of the finite networks. Initially, by taking a completion of the node set of the infinite network under a metric given by the resistances, limit points are obtained that represent generalized ends, which we call ``terminals,' of the infinite network. These terminals can be shorted together to obtain a generalized kind of node, a special case of a 1-node. An operating point will involve Kirchhoff's current law holding at 1-nodes, and so the flow of current into these terminals is studied. We give existence and bounds for an operating point that also has a nodal potential function, which is continuous at the 1-nodes. The existence is derived from the said approximations.

     

Methodological Issues in Studying Effects of Networks in Organizations

Three methodological issues are discussed that are important for the analysis of data on networks in organizations. The first is the two-level nature of the data: individuals are nested in organizations. This can be dealt with by using multilevel statistical methods. The second is the complicated nature of statistical methods for network analysis. The third issue is the potential of mathematical modeling for the study of network effects and network evolution in organizations. Two examples are given of mathematical models for gossip in organizations. The first example is a model for cross-sectional data, the second is a model for longitudinal data that reflect the joint development of network structure and individual behavior tendencies.     

网络最小割计算的一点注记

给出了具有单一源和单一汇网络割的数目,完善了一些文献中的不完整之处.     

On Cost Allocation in Hub-Like Networks

We consider telecommunication network design in which each pair of nodes can communicate via a direct link and the communication flow can be delivered through any path in the network. The cost of flow through each link is discounted if and only if the amount of flow exceeds a certain threshold. This exploitation of economies of scale encourages the concentration of flows and use of relatively small number of links. We will call such networks hub-like networks. The cost of services delivered through a hub-like network is distributed among its users who may be individuals or organizations with possibly conflicting interests. The cooperation of these users is essential for the exploitation of economies of scale. Consequently, there is a need to find a fair distribution of the cost of providing the service among users of such network. In order to describe this cost allocation problem we formulate the associated cooperative game, to be referred to as the hub-like game. Special attention is paid to users' contribution to economies of scale. We then demonstrate that certain cost allocation solutions (the core and the nucleolus of the hub-like game), which provide users with the incentive to cooperate, can be efficiently characterized.     

Identifying sets of key players in a social network

A procedure is described for finding sets of key players in a social network. A key assumption is that the optimal selection of key players depends on what they are needed for. Accordingly, two generic goals are articulated, called KPP-POS and KPP-NEG. KPP-POS is defined as the identification of key players for the purpose of optimally diffusing something through the network by using the key players as seeds. KPP-NEG is defined as the identification of key players for the purpose of disrupting or fragmenting the network by removing the key nodes. It is found that off-the-shelf centrality measures are not optimal for solving either generic problem, and therefore new measures are presented. Stephen P. Borgatti is Professor of Organization Studies at the Carroll School of Management, Boston College. His research is focused on social networks, social cognition and knowledge management. He is also interested in the application of social network analysis to the solution of managerial problems.     

Graphical Explanation in Belief Networks

Abstract

Belief networks provide an important bridge between statistical modeling and expert systems. This article presents methods for visualizing probabilistic “evidence flows” in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in expert systems, we present a hierarchy of explanations, ranging from simple colorings to detailed displays. Our approach complements parallel work on textual explanations in belief networks. Graphical-Belief, Mathsoft Inc.'s belief network software, implements the methods.     

Failure in Complex Social Networks

A class of inhomogenously wired networks called “scale-free” networks have been shown to be more robust against failure than more homogenously connected exponential networks. The robustness of scale-free networks consists in their ability to remain connected even when failure occurs. The diffusion of information and disease across a network only requires a single contact between nodes, making network connectivity the crucial determinant of whether or not these “simple contagions” will spread. However, for “complex contagions,” such as social movements, collective behaviors, and cultural and social norms, multiple reinforcing ties are needed to support the spread of a behavior diffusion. I show that scale-free networks are much less robust than exponential networks for the spread of complex contagions, which highlights the value of more homogenously distributed social networks for the robust transmission of collective behavior.     

Insensitive Bandwidth Sharing in Data Networks

We represent a data network as a set of links shared by a dynamic number of competing flows. These flows are generated within sessions and correspond to the transfer of a random volume of data on a pre-defined network route. The evolution of the stochastic process describing the number of flows on all routes, which determines the performance of the data transfers, depends on how link capacity is allocated between competing flows. We use some key properties of Whittle queueing networks to characterize the class of allocations which are insensitive in the sense that the stationary distribution of this stochastic process does not depend on any traffic characteristics (session structure, data volume distribution) except the traffic intensity on each route. We show in particular that this insensitivity property does not hold in general for well-known allocations such as max-min fairness or proportional fairness. These results are ilustrated by several examples on a number of network topologies.     

B_a空间中神经网络和平移网络的逼近

讨论了具一个隐层单元的神经网络在B_a空间中逼近的特征性定理并给出了逼近估计.对于平移网络,建立了Favard型估计.Orlicz空间中的相应结果均作为应用而给出.     

Lines of curvature near umbilical points on surfaces immersed in R4

LetM be a compact orientable surface,I:M R⁴ an immersion of classC ^r and a normal unitary smooth vector field. We prove that in the space of pairs (I, ) the family of pairs all whose umbilical points are Darbouxian is generic.     

复杂网络研究领域演进中的复杂性

复杂网络的研究作为新兴的交叉学科,已经成为当前的一个研究热点.运用文献计量学中的共词分析方法结合知识可视化技术,考察和分析了复杂网络研究领域的演进过程.通过研究发现,在学科演进的过程中,往往伴随着涌现性、非线形、自组织等复杂性现象的发生.     

衡量网络可靠性的新模型

本文分析了传统的网络可靠性优化设计方法所存在的问题 ,给出了网络的通信通路数的定义 ,并基于网络的通信通路数给出了更能反映网络运行的实际情况的网络可靠性的定量模型 ,从而解决了传统网络可靠性优化设计方法所存在的问题 .     

B_a空间中神经网络和平移网络的逼近

讨论了具一个隐层单元的神经网络在Ba空间中逼近的特征性定理并给出了逼近估计.对于平移网络,建立了Favard型估计.Orlicz空间中的相应结果均作为应用而给出.