CAREER: Fundamental Research in Geometric Folding

摘要：0347776发明：MITPRINCIPAL调查员：德缅因，Erik D.TITLE：CAREER：几何成形基础研究CAREER：几何成形基础研究折叠和展开是计算几何的一个新兴领域，研究连杆、纸张和多面体等几何对象的连续运动和重新配置及其物理表现，如蛋白质、包装和金属板材。折叠问题出现在许多令人惊讶的背景下，从纯计算几何到自组织无线网络，再到蛋白质折叠。这项研究旨在建立几何折叠的基本理论，并随着这一理论的发展，探索在整个科学和工程中的潜在应用。潜在的应用包括安全气囊设计、空间展开和药物设计。这项研究解决了几何折叠中几个基本未解决的问题。如何有效地计算重新配置任意两个所需构型之间的平面链连杆的运动？对于边长都相等的3D链条连杆，是否总是存在这样的运动？核糖体可以生物合成哪些构型的蛋白质(被视为3D链连接)？在疏水-亲水模型中，单一设计的蛋白质能够稳定地折叠成所需的形状，效率如何？无线信标在全局几何结构中定位自己的效率如何？仅提供有关其邻居的本地信息？如何有效地将纸张的最佳折叠设计成所需的形状？一个多面体必须被切割成多少块才能展开而不重叠？除了解决这样的问题外，研究人员还在合著一本关于折叠的书，并将折叠作为一个有趣的领域本身和作为展示其他领域材料的工具来进行教育。

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.