Harmonic Analysis and Machine Learning for Emergency Response

该项目中提出的研究驻留在威胁检测和灾难管理。这一领域仍然需要重大的数学贡献，部分原因是复杂数据问题的持续革命，称为大数据范式。该项目旨在弥合大数据差距，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性灾难场景，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，威胁的概念不仅限于地震，洪水或核爆炸，而是阻碍受灾害影响的人。 该项目的研究目的是提供有效的灾害善后管理方法。军事威胁检测（ATD）是一个预测性的概念，必须量化和有效地设计，以解决主要的防御问题。 在分析最近的灾难情景后，制定了一套利用数学来帮助减轻灾难影响的技术。机器学习和深度学习是该套件中的主要技术，涉及数据处理，谱图分析，具有自定义非线性势的Schroedinger特征映射技术，传输模型以及最近的创新，想法和结果处理傅立叶散射变换，池化算子和卷积神经网络。从本质上讲，这项工作开发了一个工具包，从现代应用谐波分析和机器学习。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。 这里提出的想法和结果是新的和创新的，和威胁检测的应用程序是及时的和相关的。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.