Dynamic Networks: Probabilistic Models and Inference Problems

网络在许多科学领域发挥着基础性作用，例如社会学中的友谊网络和生物学中的蛋白质-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基本结构，如几何结构和社区结构。许多网络随着时间的推移而演变和发展，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。本项目侧重于对许多应用程序常见的基本网络模型进行数学理解。发展这样的数学理论可以产生可应用于多个学科的基本见解，以及学科之间的联系，从而可能导致进一步的跨学科探索。这个项目研究了一系列涉及动态网络概率模型的问题。该项目旨在建立新的概率理论来分析和洞察这些模型，以及建立和分析揭示新现象的新模型。一个主要的关注点是增长网络的模型，这些模型在社会科学、经济学和生物学中非常丰富。特别是，该项目将调查种子图在增长随机图模型中的影响。在这样做时，该奖项将开发新的概率工具，以获得关于分支过程极限的量化结果，分支过程在概率理论和相关领域中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增长网络的概率模型来研究增长网络中的社区检测。这种观点引发了相关的新问题，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，从而加强对信息如何在网络上传播的了解。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.