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Stochastic Systems for Interacting Populations

相互作用群体的随机系统

基本信息

批准号：
1804492
负责人：
Wai Fan
金额：
$ 15.43万
依托单位：
University of Wisconsin-Madison
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-06-01 至 2018-11-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1804492&HistoricalAwards=false
关键词：
Stochastic Systems Interacting Populations

项目摘要

This research project investigates probability questions arising in the study of population dynamics and genealogies with multi-species interactions. The latter study is a key to understanding biodiversity in ecosystems, epidemiological spread, heterogeneity of cancer tumors, and the mechanisms underlying many complex systems in nature. This project is the first step towards the development of more refined models that not only address standing questions in virology and ecology, but also catalyze the generation of new mathematical methods. The involvement of undergraduate students in stochastic analysis and simulations will enhance their ability to work at the interface between probability and applied sciences. The principal investigator aims to design various spatial stochastic models, including nonstandard interacting particle systems, interacting superprocesses, and coupled stochastic partial differential equations on general metric graphs, to contribute to a deeper understanding of the effect of spatial structures and randomness on various population dynamics and their genealogies in different scales of observation. New challenges arise in the study of well-posedness and time asymptotic properties of these models. The project will focus on two research directions.(i) Explore new connections among these models. Outcomes of this research are expected to include scaling limit theorems and duality formulas that rigorously justify the new connections.(ii) Study the long-time behavior of these spatial stochastic models. New probabilistic methods will be developed to compute quantities of interest, such as the asymptotic shape of competition outcome and the propagation speeds of travelling waves 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.

本研究项目探讨在种群动态和多物种相互作用的谱系研究中出现的概率问题。后一项研究是理解生态系统生物多样性、流行病学传播、癌症肿瘤异质性以及自然界许多复杂系统背后机制的关键。这个项目是朝着发展更精细的模型迈出的第一步，这些模型不仅解决了病毒学和生态学中存在的问题，而且还促进了新的数学方法的产生。参与随机分析和模拟的本科生将提高他们在概率论和应用科学之间的界面工作的能力。在不同的观测尺度下，设计不同的空间随机模型，包括非标准相互作用粒子系统、相互作用超过程和一般度量图上的耦合随机偏微分方程，以深入了解空间结构和随机性对各种种群动态及其谱系的影响。这些模型的适定性和时间渐近性质的研究提出了新的挑战。该项目将重点研究两个方向。探索这些模式之间的新联系。这项研究的结果预计将包括尺度极限定理和对偶公式，严格证明新的联系。（ii）研究这些空间随机模型的长期行为。将开发新的概率方法来计算感兴趣的数量，例如竞争结果的渐近形状和网络上行波的传播速度。该奖项反映了美国国家科学基金会的法定使命，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。