NetSE: Medium: Modeling and Analysis of Network Dynamics

在过去的20年里，数字网络的数量和类型都有了快速的增长，这当然是从因特网及其组成网络和万维网开始的。我们现在有广泛的在线社交网络（osn），如Facebook， Twitter，移动自组织网络（manet）和延迟容忍网络（dtn）。这些网络遍布我们生活的方方面面，并在商业、商务、通信和连接方面提供越来越多的服务。其中许多网络持续处于动态变化和/或极其庞大的状态。例如，MANET或DTN的拓扑结构是不断变化的，而Facebook等OSN的拓扑结构是快速增长和演变的。由于这种网络的动态性和规模，其建模、分析和测量具有挑战性。因此，传统的数学技术是不合适的，根本需要新的技术。本研究将集中于三个相互关联的问题。首先是开发有用而准确的模型，以捕捉当今的动态。社会和技术网络。第二是开发和研究一类描述和搜索此类网络的技术。这些技术基于一个非常简单的机制，即让代理通过随机选择去哪里来探索网络。这在数学文献中被称为随机漫步，并且在静态网络中显示出理想的搜索和表征特性，在动态网络中显示出前景。最后，许多静态网络表现出所谓的幂定律，即节点的邻居数量分布大致衰减为k&amp；#8722；在A中，k是邻居的数目A是一个大于1的正常数。第三个问题是了解动态网络中的幂律是由什么构成的，幂律是如何形成的，以及对网络的健康可能有什么影响。更广泛的影响。这项工作将通过提供对manet和osn等数字网络的更深入理解和一套管理和监测工具，对社会产生积极影响。该项目包括一个全面的传播计划，包括公开发布网络表征工具。教育计划包括跨专业研讨会，通过REU网站参与研究的本科生，以及到南美洲的国际推广。

There has been a rapid increase in the number and types of digital networks over the last 2 decades beginning, of course with the Internet, its constituent networks, and the World Wide Web. We now have a wide range of on-line social networks (OSNs) such as Facebook, Twitter, mobile ad hoc networks (MANETs) and delay tolerant networks (DTNs). These networks pervade all aspects of our lives and provide a growing range of services in commerce, business, communications, and connectivity. Many of these networks are continually in a dynamic state of flux and/or extremely large. For example, the topology of a MANET or a DTN is constantly changing, and that of an OSN such as Facebook is rapidly growing and evolving. The modeling, analysis, and measurement of such networks are challenging, due to their dynamism and sizes. As a consequence, traditional mathematical techniques are not suitable and fundamentally new techniques are needed.This research will focus on three interrelated problems. The first is to develop useful and accurate models that capture the dynamics of today?s social and technological networks. The second is to develop and study a class of techniques for characterizing and searching such networks. These techniques are based on a very simple mechanism, namely to let an agent explore the network by randomly choosing where to go. This is known as a random walk in the mathematics literature and has been shown to exhibit desirable search and characterization properties in static networks that shows promise in dynamic networks. Last, many static networks exhibit what is known as a power law, namely that the distribution for the number of neighbors of a node roughly decays as k−a where k is the number of neighbors and a is a positive constant greater than one. The third problem is to understand what constitutes a power law in a dynamic network, how this power law comes to be, and what implications there might be regarding the health of the network.Broader Impact. The work will positively impact society by providing a deeper understanding of and a set of tools for managing and monitoring digital networks such as MANETs and OSNs. The project includes a comprehensive dissemination plan including public release of tools for network characterization. The education plan includes cross-specialty seminars, undergraduate involvement in research through a REU site, and international outreach to South America.