AF: Small: Explorations of Theoretical Models of Self-Assembly

在本提案中，pi计划调查自组装理论模型中的一些基本问题，并计划直接吸引大量学生参与研究活动。自组装是简单的部件通过局部相互作用自主地聚集在一起形成复杂结构的过程。自组装系统在自然界中大量存在，是生物有机体形成的关键机制。此外，自组装技术正在成为在纳米尺度上操纵物质的强大工具。对自组装理论成熟的数学和计算理解的发展是朝着利用自组装的力量大规模制造复杂的纳米级设备（如电路，分子马达，纳米级计算机和纳米生物医学设备）迈出的重要一步。这个项目的重点是理论研究，包括数学分析和仿真软件的开发。这样的理论工作很好地补充了正在进行的实验研究，这个项目的一个关键部分包括定期访问顶级实验研究实验室，如Erik Winfree？在加州理工学院的DNA和自然算法小组和拉塞尔·迪顿？他在阿肯色大学的DNA和生物分子计算小组参与了有关自组装模型和系统发展的互利讨论。这种参与可以帮助指导他们的长期实验路径，并为pi提供对实验室现实的宝贵见解。在这个提案中，pi提出了一系列不同的项目，他们将在学生的大量参与下进行。以下是其中几个项目的简要描述：pi将研究自组装系统自我复制和进化的能力。这些能力是生命系统的基本基石，这些研究将为了解生命系统的起源和功能提供洞见。pi将沿着几个方向扩展他们最近引入的一个强大的容错模型，即模糊温度容错。如果要从人工自组装系统中实现实质性的产品，新的容错技术是极其重要的。pi将继续研究随机化技术的力量，以减少瓷砖的复杂性，同时生成自组装形状的近似值。pi将极大地扩展教师和研究人员可用的自组装软件。PIs模拟器目前被几个教师和研究小组使用，并有很大的希望帮助吸引更多的学生进入这个领域，以及一般的研究。该项目对本科生研究的强调具有更广泛的影响，这是NSF特别感兴趣的。德克萨斯泛美大学（UTPA）位于德克萨斯州南部的格兰德山谷地区，拥有18,000多名学生，其中西班牙裔学生占89%，女性学生占59%。该提案的主要目标是通过在以学生为中心的研究研讨会的环境中开展大部分研究来增加UTPA计算机科学学生的研究活动。pi计划将目前的研究研讨会进一步发展为完整的课程，使更多的学生参与原创研究。由于UTPA学生群体的性质，该计划将有助于扩大未被充分代表的少数群体对计算机科学研究生的参与。pi还建议通过提供急需的教育和研究软件来支持更广泛的研究社区。

Project AbstractIn this proposal the PIs present plans to investigate a number of fundamental problems within theoretical models of self-assembly, as well as plans to directly engage a large number of students in research activities. Self-assembly is the process by which simple components autonomously come together by way of local interactions to form complex structures. Self-assembling systems are abundant in nature and are the key mechanisms for the formation of biological organisms. Further, self-assembly technology is emerging as a powerful tool for manipulating matter at the nanoscale. The development of a mature mathematical and computational understanding of self-assembly theory is an important step towards harnessing the power of self-assembly for the large scale fabrication of complex nanoscale devices such as circuits, molecular motors, nanoscale computers, and nano-biomedical devices.The focus of this project is theoretical studies which involve mathematical analyses and also the development of simulation software. Such theoretical work well complements ongoing experimental research and a key portion of this project involves regular visits to top experimental research labs such as Erik Winfree?s DNA and Natural Algorithms Group at Caltech and Russell Deaton?s DNA and Biomolecular Computing group at the University of Arkansas to engage in mutually beneficial discussions regarding the development of self-assembling models and systems. Such involvement can help to guide their long range experimental paths as well as provide the PIs with invaluable insight into the laboratory realities.In this proposal the PIs present a diverse array of projects which they will pursue with heavy student involvement. The following are brief descriptions of a few: the PIs will study the ability of self-assembling systems to self-replicate and evolve. These abilities are the fundamental cornerstones of living systems, and such studies will provide insights into how living systems originated and function. The PIs will extend, along several directions, a powerful model of fault tolerance which they recently introduced, fuzzy temperature fault tolerance. New fault tolerance techniques are of extreme importance if substantial products are to be realized from artificial self-assembling systems. The PIs will pursue studies in the power of randomization techniques for reducing tile complexity while generating close approximations of self-assembled shapes. The PIs will greatly extend the self-assembly software available for both teachers and researchers. The PIs simulator is currently used by several instructors and research groups and has great promise to help draw more students into the field, and research in general.The emphasis on undergraduate research of this project has broader impacts that are of particular interest to the NSF. The University of Texas-Pan American (UTPA), located in the South Texas Rio Grande Valley area, has more than 18,000 students, with an 89% Hispanic and 59% female student population. A primary goal of this proposal is to increase the research activity of UTPA Computer Science students by developing a large portion of the research within the environment of student-centered research seminars. The PIs plan to further develop current research seminars into full courses to involve a larger number of students in original research. Because of the nature of the UTPA student body, this plan will help broaden participation in post graduate Computer Science among under-represented minority groups. The PIs also propose to support the broader research community by providing much needed educational and research software.