AF: Small: Self-Organizing Particle Systems

本项目的目标是为自组织粒子系统的算法研究奠定基础。粒子系统是简单计算粒子的物理系统，它可以与其他粒子结合，并可以利用这些键与邻近粒子进行通信，并从一个点移动到另一个(未占用的)点。这些粒子系统应该能够自组织，以便在没有任何中央控制的情况下适应所需的形状。自组织粒子系统有许多有趣的应用，如用于监测和修复目的的涂层对象，用于外科手术的纳米设备的形成和分子尺度的电子结构。虽然在这一领域已经有了相当多的系统工作，特别是在模块化自重构机器人系统的背景下，但到目前为止在这一领域的理论工作还很少，本项目将通过提出基本模型和解决这一领域的一些基本算法问题，为严格的自组织粒子系统算法研究奠定基础。更具体地说，这个为期三年的项目的主要目标是(I)提炼受变形虫启发的2D粒子系统模型，并为3D粒子系统开发合适的模型；以及(Ii)开发智能油漆问题、覆盖和桥接问题、形状形成问题以及2D和3D中的巨噬细胞问题的自组织算法。如果人们真的想要抓住这些系统的本质，在某种程度上模仿自然界中已经存在的系统，那么就需要一种变革性的、新颖的思维方法。拟议的研究将在几个方面产生影响，例如：(I)弥合自组织粒子系统领域的理论和实践之间的差距，对许多应用领域，如微制造和细胞工程产生影响；(Ii)国际合作；(Iii)多学科活动，因为本提案中的主题将促进与研究人员在多个领域的合作，如纳米级微制造、细胞工程、纳米级医学应用、生物化学和计算机科学；以及(Iv)加强亚利桑那州立大学和整个计算机科学理论和算法社区的多样性。

The goal of this project is to lay the foundations for algorithmic research on self-organizing particle systems. Particle systems are physical systems of simple computational particles that can bond to other particles and that can use these bonds in order to communicate with neighboring particles and to move from one spot to another (non-occupied) spot. These particle systems are supposed to be able to self-organize in order to adapt to a desired shape without any central control. Self-organizing particle systems have many interesting applications like coating objects for monitoring and repair purposes and the formation of nano-scale devices for surgery and molecular-scale electronic structures. While there has been quite a lot of systems work in this area, especially in the context of modular self-reconfigurable robotic systems, only very little theoretical work has been done in this area so far.This project will prepare the ground for rigorous algorithmic research on self-organizing particle systems by proposing basic models and solving some basic algorithmic problems in this area. More specifically, the main objectives of this three-year project are (i) to refine an amoeba-inspired model  for particle systems in 2D, and to develop appropriate models for particle systems in 3D; and (ii) to develop self-organizing algorithms for the smart paint problem, covering and bridging problems, shape formation problems, and the macrophage problem in 2D and 3D. A transformative, novel thinking approach will be needed if one indeed wants to capture the essential nature of these systems, in some ways mimicking those that already exist in nature.The proposed research will have an impact in several respects, such as: (i) bridging the gap between theory and practice in the area of self-organizing particle systems, with impact on many application areas such as micro-fabrication and cellular engineering; (ii) international collaboration; (iii) multidisciplinary activities, since the topics in this proposal will foster collaboration with researchers in multiple areas such as nano-scale micro-fabrication, cellular engineering, nano-scale medical applications, biochemistry, and computer science; and (iv) enhancing diversity at Arizona State University and at the Computer Science Theory\Algorithms community at large.