CAREER: Network Centrality and Its Applications in Detection, Dynamics, and Load Balancing

职业：网络中心性及其在检测、动态和负载平衡中的应用

• 批准号: 2141621
• 负责人: Sayan Banerjee
• 金额: $ 45万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2027-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2141621&HistoricalAwards=false
• 关键词: CAREER; Network; Centrality; Its; Applications

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). This project aims to develop a mathematical understanding of networks that evolve over time and the processes that take place on them. The key idea is to identify network attributes that carry a footprint of a network's past and to exploit them in reconstructing the early stages of a network from its current configuration. This can be used to detect, for example, the origin of a rumor spread, popular individuals and their influence in a social network, or a source of a disease outbreak. The results are expected to have significant applications in national security and public health. Another key research direction is to develop a systematic understanding of how local interactions in a large network influence its global geometry. This knowledge can be used to increase the overall efficiency of a network of servers through cooperative local interactions, with potential applications in improving routing schemes for airport security, supermarket distribution systems, and distribution of vaccines and other medicines. The project aims to develop a robust toolbox across many disciplines in science and engineering. The project involves significant educational activities and integration of research and education. The activities aim to prepare a diverse STEM workforce through long-term research and career mentoring for undergraduate and graduate students. Course material and review papers emerging from this research will be freely available online to students and researchers. Centrality driven networks connect the fields of dynamic random networks and reinforced processes. The first part of the project investigates centrality driven networks, in which incoming vertices attach to one or more existing vertices with probability proportional to their centrality scores. Centrality measures like PageRank, which interpolate the global and local network geometries, will be used to study network archaeology questions. Novel dynamic networks driven by PageRank and opinion dynamics will also be analyzed. The second part of the project explores centrality-driven routing policies for networks where each vertex has a server with a unit service rate. Jobs arriving at a subset of vertices designated arrival nodes myopically explore the network in search of less busy servers to minimize their waiting time. Optimal placement of the arrival nodes will be analyzed using a new notion of load centrality. Diffusion limits and load balancing based on Dirichlet energy functionals will be used to study systems in heavy traffic. The techniques used in the research will rely on a delicate interplay between discrete time and continuous time dynamics to move beyond model specific computations. As a byproduct, the project aims to provide new characterizations of branching process limits and rates of convergence.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.

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。该项目旨在对随着时间的推移而演变的网络及其上发生的过程进行数学理解。其关键思想是识别携带网络过去足迹的网络属性，并利用它们从当前配置重建网络的早期阶段。例如，这可以用于检测谣言传播的起源、社交网络中受欢迎的个人及其影响力，或者疾病爆发的来源。预计这些结果将在国家安全和公共卫生方面有重要的应用。另一个关键的研究方向是系统地了解大型网络中的局部相互作用如何影响其全局几何形状。这种知识可以用来提高整体效率的服务器网络，通过合作的本地互动，在改善机场安全，超市配送系统，以及疫苗和其他药品的分配路由方案的潜在应用。该项目旨在为科学和工程领域的许多学科开发一个强大的工具箱。该项目涉及重大的教育活动和研究与教育的结合。这些活动旨在通过对本科生和研究生的长期研究和职业指导，为多元化的STEM劳动力做好准备。从这项研究中产生的课程材料和评论论文将在网上免费提供给学生和研究人员。中心性驱动网络连接了动态随机网络和强化过程的领域。该项目的第一部分研究中心性驱动的网络，其中传入顶点连接到一个或多个现有顶点的概率与其中心性得分成正比。中心性的措施，如PageRank，插入全球和本地网络的几何形状，将被用来研究网络考古学问题。还将分析由PageRank和意见动态驱动的新型动态网络。该项目的第二部分探讨了网络的中心驱动的路由策略，其中每个顶点都有一个服务器的单位服务率。到达指定到达节点的顶点子集的作业短视地探索网络，以寻找不那么繁忙的忙碌，以最小化它们的等待时间。到达节点的最佳位置将使用一个新的概念负载中心性进行分析。基于Dirichlet能量泛函的扩散极限和负载平衡将用于研究大流量系统。研究中使用的技术将依赖于离散时间和连续时间动态之间的微妙相互作用，以超越模型特定的计算。作为一个副产品，该项目旨在提供分支过程限制和收敛率的新特征。该奖项反映了NSF的法定使命，并被认为值得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。

项目成果

Dimension-free local convergence and perturbations for reflected Brownian motions

• DOI: 10.1214/22-aap1818
• 发表时间: 2020-09
• 期刊: The Annals of Applied Probability
• 作者: Sayantan Banerjee;Brendan Brown

The Inert Drift Atlas Model

惰性漂移图集模型

• DOI: 10.1007/s00220-022-04589-2
• 发表时间: 2022
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Banerjee, Sayan;Budhiraja, Amarjit;Estevez, Benjamin
• 通讯作者: Estevez, Benjamin

Domains of attraction of invariant distributions of the infinite Atlas model

• DOI: 10.1214/22-aop1570
• 发表时间: 2021-03
• 期刊: The Annals of Probability
• 作者: Sayantan Banerjee;A. Budhiraja

Degree centrality and root finding in growing random networks

增长随机网络中的度中心性和寻根

• DOI: 10.1214/23-ejp930
• 发表时间: 2023
• 期刊: Electronic Journal of Probability
• 影响因子: 1.4
• 作者: Banerjee, Sayan;Huang, Xiangying
• 通讯作者: Huang, Xiangying