Collaborative Research: Computational Topology and Categorification of Cancer Genomic Data: Theory and Algorithms

社会正在以前所未有的速度产生数据，目前估计每天有2.5万亿字节。其中许多数据集非常复杂，特别是因为它们往往涉及难以确定的相互依存关系。在癌症基因组学领域，可以获得数千个测量结果，目的是发现表征生物过程的分子特征。然而，由于识别健康细胞和癌细胞中存在的结构所涉及的主要计算挑战，该领域的进展受到限制。该项目旨在开发新的拓扑方法，以检测从乳腺癌患者获得的不同类型数据中隐藏的依赖关系。该项目将集中培训三名研究生，每年在这些新的方法，并扩大本科生和研究生课程的数据分析和应用拓扑。结果和材料将通过开放获取和标准期刊上的出版物、会议演示和开源软件广泛传播给科学界。研究结果还将通过培训课程和艺术展览与公众分享，包括10至12年级的教师和学生。在过去的十年中，基因组技术已经彻底改变了遗传学领域，为识别与特定表型相关的数千种遗传/分子信号提供了新方法。在这些方法中，全基因组关联研究通过同时测试数千个遗传位点来加速特定遗传元件的鉴定。然而，这些方法对于识别遗传元素的共同出现和遗传元素之间的相互作用不太有用，这些条件似乎在生物体中普遍存在。为了解决这一差距，PI将开发新的数学方法，以识别癌症中遗传因素之间的相互作用，从而验证许多癌症表型受共同发生的遗传事件调控的假设。使用现代拓扑和数据分析的组合工具，包括机器学习技术，研究小组将通过以下方式识别这种共现：分析同源群的生成器，实施计算数据驱动的纤维束理论，以及使用Khovanov类型分类方法开发癌症演变的新模型。该项目的最终目标是开发新的时间序列分析计算工具，帮助识别隐藏的相互依赖的数据。该奖项反映了NSF的法定使命，并已被认为是值得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的支持。

Society is generating data at an unprecedented rate, currently estimated at 2.5 quintillion bytes daily. Many of these data sets are notably complex, particularly because they often involve interdependencies which are difficult to identify. In the field of cancer genomics, thousands of measurements can be obtained with the objective of discovering molecular signatures that characterize biological processes. However, advances in this area have been limited due to major computational challenges involved in identifying the structures that are present in both healthy and cancerous cells. This project aims to develop new topological methods to detect hidden dependencies within and across different types of data obtained from breast cancer patients. The project will intensively train three graduate students each year in these novel methods and expand the undergraduate and graduate curricula in data analysis and applied topology. Results and materials will be broadly disseminated to the scientific community through publications in open access and standard journals, conference presentations, and open source software. Results will be also shared with the public, including teachers and students in grades 10th to 12th, through training courses and art exhibits. Genomic technologies have revolutionized the field of genetics over the past decade, providing new methods for identifying thousands of genetic/molecular signals associated to specific phenotypes. Among these methods, Genome Wide Association Studies have accelerated the identification of specific genetic elements by testing thousands of genetic loci simultaneously. These approaches, however, are less useful for identifying co-occurrences of and interactions among genetic elements, conditions that appear to be ubiquitous in living organisms. To address this gap, the PIs will develop new mathematical methods to enable the identification of interactions among genetic elements in cancer, thereby testing the hypothesis that many cancer phenotypes are regulated by co-occurring genetic events. Using the combined tools of modern topological and data analyses, including machine learning techniques, the research team will identify such co-occurrences by: analyzing generators of homology groups, implementing a computational data-driven theory of fiber bundles, and developing new models of cancer evolution using Khovanov-type categorification methods. The ultimate goal of this project is to develop new computational tools in time series analysis that help identify hidden interdependencies of data.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.