RTG: Mathematics of Information and Data with Applications to Science

大数据革命已经改变了工程、工业、数学和科学的许多领域。例如，通过全基因组关联研究、望远镜观测和petaflop计算机上的计算模拟生成的数据为更好地了解我们周围的世界提供了巨大的机会。这些庞大的数据集也带来了许多挑战，近年来，关于如何从越来越多的数据中操作、存储和提取有意义的信息的研究出现了爆炸式增长。数学分析、算法和见解一直是并将继续是这项研究工作的重要组成部分。该RTG项目将专注于数据科学的数学基础和应用，并将促进联合收割机结合不同数学视角的研究合作，以应对新出现的挑战和机遇。数据科学的数学挑战也提供了一个独特的变革性机会，为下一代开发更系统和综合的培训。该项目将扩大和提高向研究生和博士后研究员提供的教育和研究培训的范围和质量，并将使更多的本科生，特别是来自历来代表性不足群体的学生，在应用数学的课程和研究经验，增加在数据科学培训的劳动力。该项目的重点是研究和培训数据科学及其应用的数学基础。研究项目具有很强的跨学科的味道，结合基本的随机，统计，组合，动力学和计算方面的具体应用。项目将涉及与来自其他学科的领域科学家的合作，包括天体物理学，生物学，工程学和神经科学。主题将包括应用机器学习和贝叶斯统计工具来推导，分析和模拟偏微分方程;使用统计推断设计最佳闭环实验;推进离散优化技术;开发神经科学中的组合模型;理解高维度量的随机投影;构建保留大型数据集相关结构的降维技术。教育活动的重点是本科生，研究生和博士后研究员的垂直整合培训。培训活动包括第一年的研讨会，重点是数据和社会正义的接口，增强本科生和研究生课程，本科生，研究生和博士后研究员的夏季研究经验，以及高级研究生和博士后研究员的工作组。更广泛的影响包括招聘、留住和培训一批受过数据科学培训的应用数学家。此外，该研究计划在全基因组关联研究、闭环神经科学实验设计、单细胞数据比对、图像恢复、哈勃数据模拟、自组装、动态脑数据推断、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进行评估，被认为值得支持和更广泛的影响审查标准。

The big-data revolution has transformed many areas of engineering, industry, mathematics, and science. For instance, data generated through genome-wide association studies, observations from telescopes, and computational simulations on petaflop computers provide tremendous opportunities to better understand the world around us. These massive datasets also pose many challenges, and there has been an explosion of research in recent years about how to manipulate, store, and extract meaningful information from ever-larger amounts of data. Mathematical analysis, algorithms, and insights have been and will continue to be a crucial component of this research effort. This RTG project will focus on the mathematical foundations and applications of data science and will catalyze research collaborations that combine different mathematical perspectives to address emerging challenges and opportunities. The mathematical challenges of data science also present a unique and transformative opportunity to develop more systematic and integrated training for the next generation; the project will broaden and enhance the scope and quality of the educational and research training provided to graduate students and postdoctoral fellows and will involve more undergraduate students, particularly students from historically underrepresented groups, in courses and research experiences in applied mathematics, increasing the workforce trained in data science.The project focuses on research and training in the mathematical foundations of data science and its applications. The research projects have strong interdisciplinary flavor, combining fundamental stochastic, statistical, combinatorial, dynamical, and computational aspects with concrete applications. Projects will involve collaborations with domain scientists from other disciplines, including astrophysics, biology, engineering, and neuroscience. Topics will include applying machine learning and Bayesian statistics tools to deriving, analyzing, and simulating partial differential equations; designing optimal closed-loop experiments using statistical inference; advancing techniques in discrete optimization; developing combinatorial models in neuroscience; understanding random projections of high-dimensional measures; and constructing dimension reduction techniques that preserve relevant structure of large data sets. The educational activities focus on vertically integrated training of undergraduates, graduate students, and postdoctoral fellows. Training activities include a first-year seminar focused on the interface of data and social justice, enhanced undergraduate and graduate curricula, summer research experiences for undergraduates, graduate students, and postdoctoral fellows, and working groups for advanced graduate students and postdoctoral fellows. The broader impacts include the recruitment, retention, and training of a diverse cohort of applied mathematicians trained in data science. In addition, the research planned in genome-wide association studies, design of closed-loop neuroscience experiments, single-cell data alignment, image restoration, simulation of Hubble data, self-assembly, inference of dynamical brain data, and data compression and reduction aims to have impact in applications.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.