CAREER: Identifying emergent dynamics in stochastic systems

非技术总结字母O和D可以相互转换，而无需交叉，切割或连接线条。K和X也是如此，字母B和数字8也是如此。这些例子反映了数学中称为拓扑不变量的性质。最近，拓扑不变量的研究领域已经成为一个强大的方法来表征材料的整体性能，而不考虑细节，如杂质和缺陷。目前，这个框架主要描述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，由许多表现出无序和噪声的不同组成部分组成。这个职业奖支持研究，建立一个拓扑不变的生物系统和模拟生物系统的合成材料的理论。PI将使用跨学科的方法，采用数学，物理学和生物学的理论方法，以确定使生物功能稳健的一般原则，即使外部条件发生变化，也能在长时间内保持相同类型的行为。该奖项还支持旨在通过培养物理与舞蹈和运动之间的相互作用来提高代表性不足的群体对科学的兴趣的教育和宣传活动。具体工作包括开发舞蹈和物理学的跨学科课程，高中使用的舞蹈和运动教学模块，以及舞蹈物理学演示。技术总结了解蛋白质、RNA、代谢物和其他生物相关分子的基本成分如何产生生物功能，将使干预措施能够精确定位，以增强健康。然而，对于这些复杂的、有噪声的系统，至今还没有一个好的理论。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。该项目的目标是开发一种基于物理原理的可推广理论，可以预测生命系统中稳定和不断发展的功能。具体来说，PI将使用跨学科的方法，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。拓扑不变量被证明对分析突现函数是有用的，因为它们表征了整个系统的属性，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，并提供了一种机制，在一个大的反应空间内出现全局循环。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，使物理学对传统上在科学领域代表性不足的学生来说更加有形。在人类互动的范围内，这项跨学科工作将通过物理与舞蹈和运动之间的相互作用促进包容性和多样性，目的是提高代表性不足的群体对科学的兴趣。这一努力将包括以下三项努力。首先，PI将在赖斯创建一个新的舞蹈和物理跨学科课程，以吸引那些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，与休斯顿教师合作开发高中舞蹈和运动教学模块，将现有的学生团体融入科学讨论。第三，PI将与一个非营利的黑人、土著和有色人种组织合作，为服务不足的社区设计课后活动和公共活动中的舞蹈物理演示，以培养公众的科学素养。这些教育工作将把不同的世界结合在一起，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NSF的法定使命，并通过使用基金会的智力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.