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DMS-EPSRC: The Dynamics and Structure of Multiway Networks

DMS-EPSRC：多路网络的动力学和结构

基本信息

批准号：
2146079
负责人：
Anil Damle
金额：
$ 20万
依托单位：
Cornell University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-15 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2146079&HistoricalAwards=false
关键词：
DMS EPSRC Dynamics Structure Multiway

项目摘要

Network science is a widespread mathematical framework for interacting systems and connected data. Much of the power of network science comes from breaking down complex connectivity into basic structure: nodes that model entities and edges that connect two nodes at a time. For example, social relationships can be modeled as networks where individuals are nodes and edges correspond to friendship, family, or work relationships. Transportation systems, the Internet, and gene regulation can similarly be modeled by networks. This awarded project centers on the mathematical development of multiway networks, which model interactions between more than two entities at a time. The research will involve the development and theoretical analysis of new types of dynamical systems on multiway networks, including diffusions, random walks, and consensus formation to understand processes involving the spread of information or disease. The dynamics will be studied on empirical data and new mathematical models developed in the project, which will in turn lead to new algorithms for data science and machine learning. Much of the funding of this award goes to support a graduate student working on the topics of the award.Graphs or networks are a broadly used mathematical model for complex systems and relational data. The research in this award will advance the understanding of dynamics and structure of multiway networks, which go beyond graphs by directly modeling multiway interactions. The methodology is based on hypergraph and simplicial complex models of multiway networks, and studying random walks, diffusions, and consensus in the context of these models. The research is organized around four directions. The first is the development of random network models and the collection of empirical data for motivating and evaluating new dynamical systems. The second involves the theory and analysis of dynamics on hypergraphs. The third is based on new types of dynamics for simplicial complexes and how these differ from similar dynamics on hypergraphs. The fourth is the development of new data science and machine learning algorithms for multiway networks based on these dynamics, such as clustering and semi-supervised learning.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.

网络科学是一个广泛的数学框架，用于交互系统和连接数据。网络科学的大部分力量来自于将复杂的连通性分解为基本结构：模拟实体的节点和一次连接两个节点的边。例如，社会关系可以被建模为网络，其中个人是节点，而边对应于友谊、家庭或工作关系。交通系统、互联网和基因调控也可以用网络来模拟。这个获奖项目的重点是多路网络的数学发展，它一次模拟两个以上实体之间的交互。该研究将涉及多路网络上新型动力系统的开发和理论分析，包括扩散、随机游走和共识形成，以了解涉及信息或疾病传播的过程。将根据该项目中开发的经验数据和新的数学模型来研究动态，这反过来又会导致数据科学和机器学习的新算法。该奖项的大部分资金用于支持研究该奖项主题的研究生。图或网络是复杂系统和关系数据的广泛使用的数学模型。该奖项的研究将促进对多路网络的动力学和结构的理解，通过直接建模多路交互，超越了图形。该方法是基于超图和单纯复杂的多路网络模型，并在这些模型的背景下研究随机游走，扩散和共识。研究围绕四个方向展开。第一个是随机网络模型的开发和经验数据的收集，以激励和评估新的动力系统。第二部分是超图动力学的理论与分析。第三个是基于单纯复形的新类型的动力学，以及这些动力学与超图上的类似动力学有何不同。第四个奖项是基于这些动力学为多路网络开发新的数据科学和机器学习算法，如聚类和半监督学习。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。