COLLABORATIVE RESEARCH: ATD: Algorithmic Aspects of Geometry for Using LIDAR and Wireless Sensor Networks for Combating Chemical Terror Attacks

合作研究：ATD：使用激光雷达和无线传感器网络对抗化学恐怖袭击的几何算法

• 批准号: 1222663
• 负责人: Feng Luo
• 金额: $ 35.11万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1222663&HistoricalAwards=false
• 关键词: COLLABORATIVE; RESEARCH; ATD; Algorithmic; Aspects

The project considers using a variety of sensors to monitor an unknown signal field over a spatial domain with unknown geometry, which may bear elevational variations. The main objective of this project is to develop mathematical algorithms that can integrate sensor readings from a large number of distributed devices and reconstruct both the signal field and the terrain. Specifically, the sensors involved in the project include the Light Detection And Ranging technology (LIDAR) and networked wireless sensors, for their complementary capabilities. LIDAR uses a constant number of powerful sensors, each takes an image from a distance. On the other hand, distributed wireless sensors use a large number of inexpensive sensors (possibly piggybacking on cellular phones), each takes a density reading at its position. The approach in this project is to use conformal and hyperbolic geometry, discrete curvature flows, topology and numerical analysis to develop novel algorithms to generate accurate density map. From the networking perspective, this project addresses the problems of LIDAR image fusion, network localization, sensor deployment, and integration of LIDAR and sensor data. The project is motivated by the potentially devastating chemical terror attacks. Biological and chemical agents, used by adversaries, could potentially spread to a large region in a short time. This project focuses on development of algorithmic tools and techniques for gathering timely, accurate and useful information about the chemical or biological spread in case of such an attack. By exploiting the geometric properties of LIDAR data and sensor network data, the project provides critical observations on fundamental questions of how to organize such a large scale network; how to manage sensor data; and how to use the network for acting on the environment and the users.

该项目考虑使用各种传感器来监测具有未知几何结构的空间域上的未知信号场，该空间域可能具有海拔变化。这个项目的主要目标是开发数学算法，可以整合来自大量分布式设备的传感器读数，并重建信号场和地形。具体地说，该项目涉及的传感器包括光探测和测距技术(LIDAR)和联网无线传感器，它们的功能互补。激光雷达使用固定数量的强大传感器，每个传感器从远处拍摄一张图像。另一方面，分布式无线传感器使用大量廉价的传感器(可能搭载在移动电话上)，每个传感器在其位置上都有一个密度读数。该项目的方法是利用共形和双曲几何、离散曲率流、拓扑学和数值分析来开发新的算法来生成准确的密度图。该项目从组网的角度解决了激光雷达图像融合、网络定位、传感器部署以及激光雷达和传感器数据的集成等问题。该项目的动机是潜在的破坏性化学恐怖袭击。敌方使用的生物和化学制剂可能会在短时间内扩散到大片地区。该项目的重点是开发算法工具和技术，以便在发生此类攻击时及时、准确和有用地收集有关化学或生物扩散的信息。通过利用激光雷达数据和传感器网络数据的几何特性，该项目就如何组织如此大规模的网络、如何管理传感器数据以及如何利用网络对环境和用户采取行动等基本问题提供关键观察。

项目成果

Volume and rigidity of hyperbolic polyhedral 3-manifolds: VOLUME AND RIGIDITY OF HYPERBOLIC POLYHEDRAL 3-MANIFOLDS

双曲多面体 3-流形的体积和刚度：双曲多面体 3-流形的体积和刚度

• DOI: 10.1112/topo.12046
• 发表时间: 2018
• 期刊: Journal of Topology
• 影响因子: 1.1
• 作者: Luo, Feng;Yang, Tian
• 通讯作者: Yang, Tian

A new combinatorial class of $3$-manifold triangulations

一个新的 $3$ 流形三角剖分组合类

• DOI: 10.4310/ajm.2017.v21.n3.a7
• 发表时间: 2017
• 期刊: Asian Journal of Mathematics
• 影响因子: 0.6
• 作者: Luo, Feng;Tillmann, Stephan
• 通讯作者: Tillmann, Stephan