CAREER: Identifying emergent dynamics in stochastic systems

字母O和D可以相互转换，而不需要交叉、切割或连接线条。K和X，或者字母B和数字8也是一样。这些例子反映了在数学中被称为拓扑不变量的性质。近年来，拓扑不变量的研究领域已经成为表征材料整体特性的一种强有力的方法，而不考虑杂质和缺陷等细节。目前，这个框架主要描述的是处于平衡状态的系统，其中相同的原子以有序的方式排列。相比之下，生物系统往往远离平衡，由许多不同的组成部分组成，这些组成部分表现出无序和噪音。该职业奖支持建立生物系统和模拟生物系统的合成材料的拓扑不变量理论的研究。PI将采用跨学科的方法，采用数学、物理和生物学的理论方法，确定使生物功能强大的一般原理，即使外部条件发生变化，也能在很长一段时间内保持相同类型的行为。该奖项还支持教育和推广活动，旨在通过培养物理与舞蹈和运动之间的相互作用，提高代表性不足群体对科学的兴趣。具体的努力包括开设一门关于舞蹈和物理的跨学科课程，在高中使用舞蹈和动作的教学模块，以及关于舞蹈物理的示范。技术总结：了解蛋白质、rna、代谢物和其他生物学相关分子的基本成分如何产生生物学功能，将能够精确定位干预措施，以增强健康。然而，对于这些复杂的噪声系统，目前还没有一个很好的理论。仅举一个例子，尽管人类基因组测序成功，但由于可能的反应和构型的大相空间，预测所得蛋白质和大分子的行为仍然具有挑战性。这个项目的目标是发展一个基于物理原理的可推广的理论，可以预测生命系统中稳定和进化的功能。具体来说，PI将采用跨学科的方法，利用拓扑学、分子生物学和非平衡物理学的最新理论发展来实现这一目标。拓扑不变量已被证明对分析紧急函数很有用，因为它们表征了整个系统的特性，并且对局部细节、无序和噪声不敏感。它们支持边缘状态，这减少了系统对低维空间的响应，并为在大的反应空间内出现全局循环提供了一种机制。这项研究工作将为一个教育平台提供有关动力学和物理运动的基本原理的信息，使物理对传统上在科学领域代表性不足的学生更切实可行。在人类互动的规模上，这项跨学科的工作将通过物理学与舞蹈和运动之间的相互作用来促进包容性和多样性，目的是增加代表性不足群体对科学的兴趣。这项工作将包括以下三项工作。首先，PI将在莱斯大学开设一个新的舞蹈和物理跨学科课程，以吸引最初可能对科学不感兴趣的学生。其次，PI将与Rice Office of STEM Engagement合作，与休斯顿的教师一起开发高中舞蹈和动作教学模块，将现有的学生群体整合到科学讨论中。第三，PI将与一个非营利性的黑人、土著和有色人种组织合作，在课后活动和服务欠缺的社区的公共活动中设计舞蹈物理学的演示，以培养公众的科学素养。这些教育工作将把不同的世界聚集在一起，激发现有社区的新知识，并增加STEM教育中代表性不足的学生的管道。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThe letters O and D can be transformed into each other without having to cross, cut, or connect lines. Similarly for K and X, or for the letter B and number 8. These examples reflect properties that are known in mathematics as topological invariants. Recently, the research field of topological invariants has emerged as a powerful method to characterize global properties of materials, irrespective of details such as impurities and defects. Currently, this framework largely describes systems at equilibrium, with identical atoms that are arranged in an orderly manner. In contrast, biological systems are often far away from equilibrium and consist of many different components that exhibit disorder and noise. This CAREER award supports research to establish a theory of topological invariants for biological systems and for synthetic materials that mimic biological systems. The PI will use an interdisciplinary approach, employing theoretical methods from mathematics, physics, and biology, to identify general principles that render biological functions robust, maintaining the same type of behavior over long periods of time even if external conditions change. The award also supports educational and outreach activities that aim at increasing interest in science among under-represented groups through nurturing the interplay between physics with dance and movement. Specific efforts include the development of an interdisciplinary class on dance and physics, teaching modules on dance and movement for use in high schools, and demonstrations on the physics of dance.TECHNICAL SUMMARYUnderstanding how the underlying components of proteins, RNAs, metabolites and other biologically relevant molecules give rise to biological function would enable precise targeting of interventions to enhance health. However, there still does not exist a good theory for these complex and noisy systems. As just one example, despite successful sequencing of the human genome, it remains challenging to predict the behavior of resulting proteins and macromolecules due to the large phase space of possible reactions and configurations. The goal of this project is to develop a generalizable theory based on physical principles that can predict stable and evolving function in living systems. Specifically, the PI will use an interdisciplinary approach that draws on recent theoretical developments in topology, molecular biology, and non-equilibrium physics to achieve this goal. Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support edge states, which reduce the system response to a lower dimensional space and offer a mechanism for the emergence of global cycles within a large space of reactions. This research effort will inform an educational platform about the underlying principles of dynamics and physical movement, towards making physics more tangible to students traditionally under-represented in science. At the scale of human interactions, this interdisciplinary work will foster inclusion and diversity through the interplay between physics with dance and movement with the objective of increasing interest in science among under-represented groups. This effort will comprise the following three efforts. First, the PI will create a new interdisciplinary class on dance and physics at Rice to draw students who may not be initially interested in science. Second, in collaboration with the Rice Office of STEM Engagement, the PI will work with Houston teachers to develop teaching modules on dance and movement for use in high schools, towards integrating existing student groups into discussions on science. Third, the PI will work with a non-profit black, indigenous and people of color organization to design demonstrations on the physics of dance in afterschool activities and public events for underserved communities, in order to foster public scientific literacy. These educational efforts will bring different worlds together to inspire new knowledge in existing communities and increase the pipeline of under-represented students in STEM education.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.