FRG: Collaborative Research: Mathematics of large scale urban crime

这个多学科项目旨在发展新的数学方法，在非线性偏微分方程理论、统计力学、图论和统计学的界面上，用于城市犯罪的可预测性和控制。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)社会网络空间嵌入模型，尤其是帮派活动模型；(3)探索新的地理分析方法，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。本项目的数学工作包括分析非线性PDE模型、分析统计物理模型，并进一步发展这些模型，以包括空间异质性、不同的罪犯运动模式和城市街头帮派网络。同时，它也为城市犯罪模式形成背后的机制提供了更深入的理解，并为地方执法机构提供了一些有用的算法和软件。犯罪数学是应用数学中的一个新兴课题，对全球范围的兴趣和与美国国土安全直接相关。这个专注的研究小组涉及研究人员之间的互动，他们的主要专业知识来自非常不同的领域——数学、物理学、人类学和犯罪学——因此，犯罪活动的模式形成从非常不同的观点和角度被剖析和理解。该项目涉及用于分析真实现场数据的算法开发和基于代理的城市犯罪模拟工具。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。该项目涉及各级学生和博士后学者的培训，包括一个重要的本科生组成部分。博士生和博士后学者也将获得宝贵的指导经验，这对他们的研究生涯发展是必要的。这项工作包括与当地执法机构和纯数学与应用数学研究所的直接互动。

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.