CAREER: Statistical and Geometric Analysis for Tree-Shaped Data

职业:树形数据的统计和几何分析

基本信息

项目摘要

This project will build a geometric, mathematical framework for analyzing tree-shaped data, which occurs in disease, cancer, and medical imaging. The evolutionary histories of viruses, relationships of tumor mutations over time, and images of lung airways and arteries are all tree-shaped. The geometry of trees must be considered during analysis to avoid errors and bias, but traditional statistical methods are of limited use. Furthermore, technological improvements such as genetic sequencing are producing increasingly large and complex datasets of such trees. This project will develop new mathematical tools to understand and derive insights from tree-shaped data. An educational component will create training programs and extra-curricular opportunities for undergraduates to participate in research and learn valuable statistical and technical skills. Many of the students are expected to be from low-income and underrepresented groups, thus broadening the participation of these groups in STEM industry and research.This research will develop methods for analyzing tree data that use both the tree shape and the length of its edges in a mathematically integrated way. The majority of existing tree analysis methods only focus on the tree shape, but the proposed methods will be based on the underlying non-Euclidean geometric space in which the data lie. This research will contribute to the growing field of geometric statistics with a mathematical formulation and method of computation for bias in tree-shaped data, and two-sample tests validated on biologically realistic data. In scaling these statistical methods to meet the Big Data challenge, this research will continue to expand the field of computational geometry to piece-wise Euclidean, non-positively curved spaces. Finally, this research will lead to characterizing the first continuous geometric spaces for phylogenetic networks.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.
该项目将建立一个几何数学框架,用于分析疾病,癌症和医学成像中发生的树形数据。 病毒的进化历史、肿瘤突变随时间的关系以及肺气道和动脉的图像都是树状的。在分析过程中必须考虑树木的几何形状,以避免错误和偏差,但传统的统计方法是有限的使用。 此外,基因测序等技术进步正在产生越来越大和复杂的此类树木数据集。 该项目将开发新的数学工具来理解树形数据并从中获得见解。 教育部分将为本科生创造培训计划和课外机会,让他们参与研究并学习有价值的统计和技术技能。 预计学生中有许多来自低收入和代表性不足的群体,从而扩大这些群体在STEM产业和研究中的参与。本研究将开发以数学综合方式使用树形和边长的树形数据分析方法。现有的大多数树分析方法只关注树的形状,但所提出的方法将基于数据所在的底层非欧几何空间。这项研究将有助于几何统计的数学公式和方法的计算偏差在树形数据,和两个样本的测试验证生物现实的数据不断增长的领域。在扩展这些统计方法以应对大数据挑战的过程中,这项研究将继续将计算几何领域扩展到分段欧几里德非正弯曲空间。最后,这项研究将导致表征第一个连续的几何空间的系统发育networks.This奖项反映了NSF的法定使命,并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

项目成果

期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
ON THE MAXIMUM AGREEMENT SUBTREE CONJECTURE FOR BALANCED TREES
  • DOI:
    10.1137/20m1379678
  • 发表时间:
    2022-01-01
  • 期刊:
  • 影响因子:
    0.8
  • 作者:
    Bordewich,Magnus;Linz,Simone;Wicke,Kristina
  • 通讯作者:
    Wicke,Kristina
Maximum Covering Subtrees for Phylogenetic Networks
系统发育网络的最大覆盖子树
  • DOI:
    10.1109/tcbb.2020.3040910
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Davidov, Nathan;Hernandez, Amanda;Mckenna, Patrick;Medlin, Karen;Jian, Justin;Mojumder, Roadra;Owen, Megan;Quijano, Andrew;Rodriguez, Amanda;St.John, Katherine
  • 通讯作者:
    St.John, Katherine
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Megan Owen其他文献

Shortest Paths and Convex Hulls in 2D Complexes with Non-Positive Curvature
具有非正曲率的二维复合体中的最短路径和凸包
  • DOI:
  • 发表时间:
    2016
  • 期刊:
  • 影响因子:
    0
  • 作者:
    A. Lubiw;Daniela Maftuleac;Megan Owen
  • 通讯作者:
    Megan Owen
Don’t Stop the Game: The Importance of the Preparticipation Sports Evaluation
  • DOI:
    10.1016/j.yfpn.2024.01.001
  • 发表时间:
    2024-05-01
  • 期刊:
  • 影响因子:
  • 作者:
    Teresa Whited;Megan Owen
  • 通讯作者:
    Megan Owen
Properties for the Fréchet mean in Billera-Holmes-Vogtmann treespace
Billera-Holmes-Vogtmann 树空间中 Fréchet 均值的属性
  • DOI:
    10.1016/j.aam.2020.102072
  • 发表时间:
    2019
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Maria Anaya;Olga Anipchenko;Aisha Ashfaq;Joyce Chiu;Mahedi Kaiser;Max Shoji Ohsawa;Megan Owen;E. Pavlechko;K. S. John;Shivam Suleria;Keith Thompson;Corrine Yap
  • 通讯作者:
    Corrine Yap
Statistics in BHV Tree Space
BHV 树空间中的统计
  • DOI:
  • 发表时间:
    2017
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Megan Owen
  • 通讯作者:
    Megan Owen
Computing Geodesic Distances in Tree Space
  • DOI:
    10.1137/090751396
  • 发表时间:
    2009-03
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Megan Owen
  • 通讯作者:
    Megan Owen

Megan Owen的其他文献

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