BIGDATA: F: DKM: Spectral Analysis and Control of Evolving Large Scale Networks

在过去的十年中，复杂网络的研究已经扩散到许多科学分支。我们如何描述互联网、电网或人脑的连接结构？在这些不同的制度的结构之下是否有普遍的原则？大量数据库和可靠的数据分析工具的可用性为探索这些结构性问题提供了一个强大的框架。此外，由于大多数现实世界中的网络结构都在不断演化，因此需要了解网络的动态复杂性，以提供对此类网络的真实描述。本项目将开发有效的算法来分析大规模网络的结构特性。PI还将探索局部结构属性和全局谱图相关属性之间的联系，例如邻接矩阵的谱半径或拉普拉斯算子的谱间隙。分析将扩展到时间演变的网络和网络演变的动态模型将开发。该提案的三个科学目标是：（1）设计算法以有效地估计大规模网络的局部和全局结构特性，（2）使用来自谱图理论和凸优化的工具将图的局部结构特性与其全局谱特性相关联，以及（3）开发网络演化的预测模型，以及控制策略，以驱动网络结构向期望的频谱特性演进。网络无处不在（互联网、web、生物网络和社交网络等），并且在不断发展。因此，开发有效的工具来理解网络的结构和光谱性质的演变是非常相关的许多科学学科。该项目将支持和培训一名博士生，并让本科生参与宾夕法尼亚大学的研究。欲了解更多信息，请访问该项目网站：http://sites.google.com/site/victormpreciado/research-projects/nsf_bigdata_2014

During the last decade, the study of complex networks has diffused through many branches of science. How do we characterize the connectivity structure of the Internet, the power grid, or the human brain? Are there universal principles underlying the structure of these diverse systems? The availability of massive databases and reliable tools for data analysis provide a powerful framework to explore these structural questions. Furthermore, as the structure of most real-world networks is inherently evolving, an understanding of the dynamical complexity of networks is needed to provide a realistic description of such networks.This project will develop efficient algorithms to analyze structural properties of large-scale networks. The PIs will also explore the connection between local structural properties and global spectral graph properties of relevance, such as the spectral radius of the adjacency matrix or the spectral gap of the Laplacian. The analysis will be extended to time-evolving networks and dynamic models of network evolution will be developed. Three scientific objectives of this proposal are: (1) designing algorithms to efficiently estimate local and global structural properties of large-scale networks, (2) relating local structural properties of a graph with its global spectral properties, using tools from spectral graph theory and convex optimization, and (3) developing predictive models of network evolution, as well as control strategies to drive the evolution of the network structure towards desirable spectral properties. Networks are ubiquitous (the Internet, the web, biological, and social networks to name a few), and are continually evolving. Thus, developing efficient tools for understanding the evolution of structural and spectral properties of networks is of great relevance to many scientific disciplines. The project will support and train one PhD student, as well as involve undergraduate students in research at the University of Pennsylvania.For further information see the project web site at: http://sites.google.com/site/victormpreciado/research-projects/nsf_bigdata_2014