CAREER: Mathematical Frameworks and Theory for Conceptual Models in Economics, Ecology and Criminology

职业：经济学、生态学和犯罪学概念模型的数学框架和理论

• 批准号: 2042413
• 负责人: Nancy Rodriguez
• 金额: $ 42.88万
• 依托单位: University of Colorado at Boulder
• 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: 2021-06-01 至 2026-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2042413&HistoricalAwards=false
• 关键词: CAREER; Mathematical; Frameworks; Theory; Conceptual

Recent advances in criminology, economics, and ecology have led to the realization that to derive qualitative and quantitative understanding of very complex systems and phenomena involved one needs to mathematize many conceptual models developed in these sciences. The overarching objective of this project is to develop mathematical frameworks for such conceptual models and contribute to the qualitative and quantitative understanding of these complex systems. One project will focus on the role that movement has in ecological systems or that redistribution has in economic systems. The objectives are to understand what movement strategies are optimal and why clustering of competing populations work. With rapid shifts in the environment and in the economy, it is crucial to investigate the relative success of different movement strategies to be able to predict which populations will survive under competition. Another project will develop and study models for rioting activity. This will enable us to tease out the most important factors behind the dynamics of different riots. A final project will draw from work in mathematical epidemiology to develop a multi-scale model for crime from a public health perspective, which can help us to test the effect of different policies on the dynamics of violent crimes. This research will provide a quantitative framework and tools that non-technical scientists can use to make significant advances in their work. The models developed here will provide ways to test intervention and policy strategies helping to quantify their effects.These projects will be integrated with an educational plan focused on empowering the Latinx community through a series of activities in collaboration with CU Boulder’s Science Discovery. First, the PI will meet with teenagers to discuss her research through the Teen Science Cafe program. Second, the PI will provide research experience opportunities for high school students who are underrepresented minorities, with the aim of encouraging them to attend college and major in a STEM field. Finally, the PI will develop hands-on activities to help the Latinx community understand the models used to inform the social distancing and stay-at-home policies implemented during the COVID-19 pandemic in Colorado. This research consists of three projects. The first project aims to use a local and non-local reaction-advection-diffusion framework to understand the optimality of different movement strategies, particularly, in the presence of an Allee effect. The second project will focus on development and study of models for rioting activity. In particular, the PI will study traveling wave solutions, which have been observed in many real-life riots. The final project will draw from work in mathematical epidemiology to develop a multi-scale model for crime from a public health perspective using a kinetic equations framework. The successful completion of these projects will also advance the qualitative understanding of traveling wave solutions and generalized fronts for local and non-local reaction-advection-diffusion equations in spatially heterogeneous environments.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.

犯罪学，经济学和生态学方面的最新进展已导致人们意识到，对于涉及的非常复杂的系统和现象，人们需要对这些科学发展中开发的数学模型需要进行定性和定量的理解。该项目的总体目标是为这种概念模型开发数学框架，并有助于对这些复杂系统的定性和定量理解。一个项目将侧重于运动在生态系统中或重新分布在经济体系中的作用。这些目标是了解哪些运动策略是最佳的，以及为什么竞争人群的聚集起作用。随着环境和经济的快速变化，至关重要的是要研究不同运动策略的相对成功，以预测哪些人口将在竞争中生存。另一个项目将开发和研究用于骚乱活动的模型。这将使我们能够教授不同骚乱动态背后的最重要因素。最终项目将从数学流行病学的工作中汲取灵感，从公共卫生的角度开发犯罪的多尺度模型，这可以帮助我们测试不同政策对暴力犯罪动态的影响。这项研究将提供一个定量框架和工具，非技术科学家可以用来在其工作中取得重大进步。这里开发的模型将提供测试干预和政策策略有助于量化其效果的方法。这些项目将与一项旨在通过与Cu Boulder的科学发现合作通过一系列活动来赋予拉丁裔社区能力的教育计划。首先，PI将与青少年会面，通过Teen Science Cafe计划讨论她的研究。其次，PI将为少数群体不足的高中学生提供研究经验机会，以鼓励他们上大学并在STEM领域上学。最后，PI将开展动手活动，以帮助拉丁裔社区了解用于告知科罗拉多州Covid-19大流行期间实施的社会疏远和居住政策的模型。这项研究由三个项目组成。第一个项目旨在使用局部和非本地反应 - 侵蚀 - 扩散框架来了解不同运动策略的最佳性，尤其是在存在效果的情况下。第二个项目将着重于开发和研究骚乱活动的模型。特别是，PI将研究行驶波解决方案，这些途径已在许多现实生活中观察到。最终项目将从数学流行病学的工作中汲取灵感，以使用动力学方程框架从公共卫生的角度从公共卫生的角度开发多尺度模型。这些项目的成功完成还将推进对波动波解决方案的定性理解，并在空间异质性环境中对本地和非本地反应反转扩散方程进行了广义的阵线。该奖项反映了NSF的法定任务，并通过使用该基金会的智力功能和广泛的影响来评估NSF的法定任务，并被认为是珍贵的支持。

项目成果

What Can Partial Differential Equations Tell Us about Life?

偏微分方程可以告诉我们关于生活的什么信息？

• 发表时间: 2023
• 期刊: the journal of undergraduate mathematics and its applications
• 作者: Rodriguez, Nancy