CAREER: Fundamental Research in Geometric Folding

摘要：提案：0347776机构：麻省理工学院主要研究者：Demaine， Erik d .标题：职业：几何折叠基础研究职业：几何折叠基础研究折叠和展开是计算几何的一个新兴领域，研究几何物体（如连杆、纸张和多面体）及其物理表现（如蛋白质、包装和金属板）的连续运动和重新配置。从纯计算几何到自组织无线网络再到蛋白质折叠，折叠问题出现在令人惊讶的许多环境中。本研究旨在建立几何折叠的基本理论，并随着该理论的发展，探索在科学和工程中的潜在应用。潜在的应用包括安全气囊设计、空间部署和药物设计。本研究解决了几何折叠中几个尚未解决的基本问题。如何有效地计算在任意两个期望构型之间重新配置平面链连杆的运动？对于边长相等的三维链环，是否总是存在这样的运动？核糖体可以生物合成哪些结构的蛋白质（视为3D链连接）？在亲水-疏水模型中，如何有效地设计出稳定折叠成所需形状的蛋白质？无线信标在给定其邻居的局部信息的情况下，如何有效地在全局几何结构中定位自己？如何有效地设计纸张的最佳折叠成所需的形状？一个多面体必须切成多少块才能展开而不重叠？除了解决这些问题外，研究者还与人合作撰写了一本关于折叠的书，并将折叠教育作为一个有趣的领域，同时作为展示其他领域材料的工具。

ABSTRACTPROPOSAL: 0347776INSTITUTION: MITPRINCIPAL INVESTIGATOR: Demaine, Erik D.TITLE: CAREER: Fundamental Research in Geometric FoldingCAREER: Fundamental Research in Geometric FoldingFolding and unfolding is an emerging field of computational geometry studying the continuous motion and reconfiguration of geometric objects such as linkages, paper, and polyhedra and their physical manifestations such as proteins, packaging, and sheet metal. Folding problems arise in surprisingly many contexts, ranging from pure computational geometry to ad-hoc wireless networks to protein folding. This research aims to build a basic theory of geometric folding and, as this theory develops, to explore potential applications throughout science and engineering. Potential applications include air-bag design, space deployment, and drug design.This research addresses several fundamental unsolved problems in geometric folding. How can one efficiently compute motions that reconfigure a planar chain linkage between any two desired configurations? Do such motions always exist for 3D chain linkages whose edge lengths are all equal? Which configurations of proteins (viewed as a 3D chain linkage) can be biosynthesized by a ribosome? How efficiently can one-design proteins in the hydrophobic-hydrophilic model that fold stably into a desired shape? How efficiently can wireless beacons locate themselves in a global geometry given just local information about their neighbors? How efficiently can be design optimal foldings of paper into desired shapes? How many pieces must a polyhedron be cut into to unfold without overlap? In addition to solving problems such as these, the investigator is coauthoring a book about folding and is pursuing education of folding both as an interesting area in its own right and as a vehicle for presenting material in other areas.