Dynamic Networks: Probabilistic Models and Inference Problems

网络在许多科学领域中发挥着重要作用，例如社会学中的友谊网络和生物学中的蛋白质相互作用网络。这些领域问题的核心是需要了解相关网络中的底层结构，例如几何结构和社区结构。许多网络随着时间的推移而发展和壮大，这在其底层结构上留下了印记。该项目的主要目标是了解网络的增长如何与其他底层结构（如社区结构）相互作用。该项目侧重于对许多应用程序常见的基本网络模型的数学理解。发展这样的数学理论可以导致可以应用于多个学科的基本见解，以及学科之间的联系，可以导致进一步的跨学科探索。该项目研究涉及动态网络概率模型的广泛问题。该项目旨在建立新的概率理论来分析和提供对这些模型的洞察力，以及建立和分析揭示新现象的新模型。一个主要的重点是增长网络的模型，这是丰富的社会科学，经济学和生物学。特别是，该项目将研究种子图在增长随机图模型中的影响。在此过程中，该奖项将开发新的概率工具，以获得分支过程极限的定量结果，这些结果在概率论和相关领域具有更广泛的独立兴趣。该项目的第二个主题将是通过引入具有社区结构的不断增长的网络的概率模型来研究不断增长的网络中的社区检测。这一观点有助于提出相关的新问题，例如从多个时间点观察到的网络中检测社区。最后，该奖项还将研究网络上的随机过程，从而加深对信息如何在网络上传播的理解。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Networks play a fundamental role in many areas of science, such as the network of friendships in sociology and protein-protein interaction networks in biology. At the heart of problems in these areas is a need to understand underlying structures in the relevant network, such as geometric structure and community structure. Many networks evolve and grow over time and this leaves a mark on their underlying structure. The broad goal of this project is to understand how the growth of a network interacts with other underlying structures such as community structure. The project focuses on a mathematical understanding of fundamental network models that are common to many applications. Developing such a mathematical theory can lead to fundamental insights that can be applied across multiple disciplines, as well as to connections between disciplines that can lead to further cross-disciplinary explorations. This project studies a wide range of problems involving probabilistic models of dynamic networks. The project aims to build novel probabilistic theory to analyze and provide insight into such models, as well as to build and analyze novel models that shed light on new phenomena. A main focus is on models of growing networks, which are abundant in the social sciences, economics, and biology. In particular, the project will investigate the influence of the seed graph in growing random graph models. In doing so, the award will develop novel probabilistic tools to obtain quantitative results on the limits of branching processes, which are of independent interest more widely in probability theory and related fields. A second theme of the project will be the study of community detection in growing networks by introducing probabilistic models of growing networks with community structure. This perspective lends itself to relevant new questions, such as detecting communities from networks observed at multiple time points. Finally, the award will also study stochastic processes on networks, resulting in enhanced understanding of how information spreads on networks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.