FRG: Collaborative Research: Mathematics of large scale urban crime

FRG：合作研究：大规模城市犯罪的数学

• 批准号: 0968382
• 负责人: George Tita
• 金额: $ 8.35万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0968382&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Mathematics; large

This multidisciplinary project aims to develop new mathematical methods, at the interface of the theory of nonlinear partial differential equations, statistical mechanics, graph theory, and statistics, for predictability and control of urban crime. The project focuses on spatio-temporal crime patterns and includes (1) new mathematical analysis and comparisons to crime data for discrete and continuum models of crime hotspots; (2) models with spatially embedded social networks, especially with regard to gang activity; and (3) exploration of new methods of Geographic Profiling, incorporating detailed features of urban terrain and more accurate modes of criminal movement into existing models. Mathematical work on this project includes analysis of nonlinear PDE models, analysis of statistical physics models, and further development of these models to include spatial heterogeneity, different offender movement patterns, and urban street gang networks. At the same time it provides both a deeper understanding of the mechanisms behind pattern formation in urban crime and some useful algorithms and software for local law enforcement agencies.Mathematics of criminality is an emerging topic in applied mathematics with interest on a global scale and direct relevance to U.S. homeland security. This focused research group involves interactions between researchers whose primary expertise lies within very different fields -- mathematics, physics, anthropology, and criminology -- so that pattern formation of criminal activity is dissected and understood from very different viewpoints and perspectives. The project addresses algorithm development for analyzing real field data and agent-based simulation tools for urban crime. The research will also develop new models for urban crime and carry out mathematical analysis of these models. The project involves training of students and postdoctoral scholars at all levels, including a significant undergraduate component. Ph.D. students and postdoctoral scholars will also obtain valuable mentoring experience necessary for development of their research careers. The work includes direct interaction with local law enforcement agencies and the Institute for Pure and Applied Mathematics.

这个多学科项目的目的是开发新的数学方法，在非线性偏微分方程，统计力学，图论和统计学理论的接口，预测和控制城市犯罪。 该项目侧重于时空犯罪模式，包括：（1）对犯罪热点的离散和连续模型的犯罪数据进行新的数学分析和比较;（2）具有空间嵌入式社交网络的模型，特别是关于帮派活动的模型;（3）探索地理剖面绘制的新方法，将城市地形的详细特征和更准确的犯罪活动模式纳入现有模型。该项目的数学工作包括非线性偏微分方程模型的分析，统计物理模型的分析，以及这些模型的进一步发展，包括空间异质性，不同的罪犯运动模式，和城市街头帮派网络。 与此同时，它提供了更深层次的理解背后的机制，在城市犯罪模式的形成和一些有用的算法和软件，为当地的执法机构。犯罪数学是一个新兴的主题，在应用数学的兴趣在全球范围内，并直接关系到美国国土安全。这个重点研究小组涉及研究人员之间的互动，他们的主要专长在于非常不同的领域-数学，物理学，人类学和犯罪学-以便从非常不同的观点和角度剖析和理解犯罪活动的模式形成。该项目致力于开发用于分析真实的现场数据的算法和基于代理的城市犯罪模拟工具。这项研究还将开发新的城市犯罪模型，并对这些模型进行数学分析。 该项目涉及对各级学生和博士后学者的培训，包括一个重要的本科部分。 博士学生和博士后学者也将获得宝贵的指导经验，这对他们的研究事业发展是必要的。 这项工作包括与当地执法机构和理论与应用数学研究所直接互动。