Harmonic Analysis and Machine Learning for Emergency Response

本项目的研究主要集中在威胁检测和灾害管理方面。这一领域仍然需要重要的数学贡献，部分原因是正在进行的复杂数据问题革命，被称为大数据范式。该项目旨在弥合大数据鸿沟，为该领域提供附加值，同时扩大现代数学的影响。从这个角度来看，这个项目研究潜在的预测灾难场景，从放射性泄漏到现代战场问题，再到自然灾害。然而，在这个项目中，威胁的概念并不局限于地震、洪水或核爆炸，而是什么阻碍了受灾害影响的人们。本项目研究旨在提供有效的灾后管理方法。算法威胁检测（ATD）是一个预测概念，必须量化和有效地设计，以解决主要的防御问题。在分析了最近的灾难情景之后，我们制定了一套利用数学来帮助减轻灾害影响的技术。机器学习和深度学习是该套件的主要技术，涉及数据处理、谱图分析、具有定制非线性势的薛定谔特征图技术、传输模型，以及处理傅里叶散射变换、池化算子和卷积神经网络的最新创新、思想和结果。从本质上讲，这项工作开发了一个现代应用谐波分析和机器学习的工具包。这项工作中的数学严谨性将使我们能够构建快速有效的减灾实施方案。本文提出的思想和结果具有创新性，在威胁检测中的应用具有时效性和相关性。这些方法也可能影响其他科学领域。

The research presented in this project resides in threat detection and disaster management. Significant mathematical contributions to this field are still needed, due in part to the ongoing revolution with complex data problems, known as the Big Data paradigm. This project aims to bridge the big data gap, providing added value to the field while simultaneously expanding the impact of modern mathematics. With this point of view, this project studies potentially predictive disaster scenarios, from radioactive leaks, to modern battlefield issues, to natural disasters. However, the notion of threat in this project is not limited to an earthquake, flood, or nuclear explosion, but rather what impedes the people affected by disasters. The project research intends to provide efficient ways of disaster aftermath management.Algorithmic Threat Detection (ATD) is a predictive concept that must be quantified and effectively designed to address major defense problems. After analysis of recent disaster scenarios, a suite of technologies have been formulated that use mathematics to help mitigate disaster impacts. Machine learning and deep learning are major techniques in this suite, and involve data processing, spectral graph analysis, Schroedinger eigenmap technology with customized non-linear potentials, transport models, and recent innovations, ideas, and results dealing with Fourier scattering transforms, pooling operators, and convolutional neural networks. Essentially, this work develops a toolkit from modern applied harmonic analysis and machine learning. The mathematical rigor in this work will enable us to construct fast and efficient disaster mitigation implementations. The ideas and results proposed here are new and innovative, and the applications to threat detection are timely and relevant. These methods may also impact other areas of science.