Logic, Topology and Genomics

逻辑、拓扑和基因组学

基本信息

  • 批准号:
    1620271
  • 负责人:
  • 金额:
    $ 20万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2016
  • 资助国家:
    美国
  • 起止时间:
    2016-09-01 至 2020-08-31
  • 项目状态:
    已结题

项目摘要

The goal of the project is to apply methods of logic and topology to several important problems in genomics and medicine. The first application is mining large scale clinical databases for information that would be usable for clinicians and/or biological researchers. The PI plans to design and implement a method applying ideas from persistent homology theory in a logic-based framework. The starting point of this approach is the notion of "redescriptions" introduced by Parida (senior consultant for the project) and Ramakrishnan in the context of knowledge discovery. A mathematical reformulation leads to certain filtered complexes arising from set systems, which are then amenable to analysis using tools from topology. A second application will be in the area of phylogenetics. Studying population admixtures is a very active area of research in population genomics. The PI will use topological methods to not only detect but also discriminate ancient from recent admixture, and validate the approach by testing it on large simulated populations where the admixtures are known in advance. Generating such populations pose unique challenges that have been tackled by Parida and her group recently.A common practical difficulty encountered in many applications of topological data analysis is computing persistent homology groups of filtrations of very large simplicial complexes. The sizes of these complexes makes the computations of their persistent homology bar-codes using current generation publicly available software impossible. The second part of the project will address this shortcoming. The PI will investigate a new approach towards improving efficiency of computing persistent homology groups over existing algorithms. This approach will be useful in a wide variety of applications where topological data analysis is currently being used. The PI plans to implement this algorithm and develop it into a general purpose software-package for computing approximations of persistent homology invariants of filtrations of large complexes. The project will bring together tools from two different areas of mathematics -- logic and topology -- in a novel way, as a method towards analyzing large data-sets. In addition, the PI will also study the underlying mathematical problems that come up -- on the interface of logic and topology which are fundamentally interesting in their own rights, and should have other applications as well. The PI also intends to work with a graduate student and involve them in all aspects of the proposed research.
该项目的目标是将逻辑和拓扑学方法应用于基因组学和医学中的几个重要问题。第一个应用是挖掘大规模的临床数据库,以获得临床医生和/或生物研究人员可用的信息。PI计划在基于逻辑的框架中设计和实现一种应用持久同源理论思想的方法。 这种方法的出发点是Parida(该项目的高级顾问)和Ramakrishnan在知识发现的背景下引入的“重新描述”概念。一个数学的重新表述导致某些过滤复合物从集合系统中产生,然后可以使用拓扑学的工具进行分析。 第二个应用将在遗传学领域。研究群体混合物是一个非常活跃的研究领域 在人口基因组学中。PI将使用拓扑方法不仅检测,而且还区分古代和现代的混合物,并通过在预先已知混合物的大型模拟种群上进行测试来验证该方法。Parida等人最近致力于解决这一问题,在拓扑数据分析的许多应用中遇到的一个常见的实际困难是计算极大单纯复形的滤子的持久同调群.这些复合物的大小使得使用当前一代公开可用的软件来计算它们的持久同源性条形码是不可能的。该项目的第二部分将解决这一缺陷。 PI将研究一种新的方法来提高现有算法计算持久同源群的效率。这种方法将是有用的,在各种各样的应用程序中,拓扑数据分析目前正在使用。PI计划实施该算法,并将其开发成一个通用软件包,用于计算大型复合物过滤的持久同源不变量的近似值。该项目将以一种新颖的方式将来自两个不同数学领域-逻辑和拓扑学-的工具结合在一起,作为分析大型数据集的方法。此外,PI还将研究出现的基本数学问题-在逻辑和拓扑学的接口上,这些问题本身就很有趣,而且还应该有其他应用。PI还打算与研究生合作,并让他们参与拟议研究的各个方面。

项目成果

期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Zeroes of polynomials on definable hypersurfaces: pathologies exist, but they are rare
可定义超曲面上多项式的零点:病理现象存在,但很少见
  • DOI:
    10.1093/qmath/haz022
  • 发表时间:
    2019
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Basu, Saugata;Lerario, Antonio;Natarajan, Abhiram
  • 通讯作者:
    Natarajan, Abhiram
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Saugata Basu其他文献

On Projections of Semi-Algebraic Sets Defined by Few Quadratic Inequalities
  • DOI:
    10.1007/s00454-007-9014-1
  • 发表时间:
    2007-09-15
  • 期刊:
  • 影响因子:
    0.600
  • 作者:
    Saugata Basu;Thierry Zell
  • 通讯作者:
    Thierry Zell
Prevalence of Myxozoan Parasites of Riverine Fishes of Jalpaiguri District, West Bengal, India
印度西孟加拉邦贾尔派古里地区河流鱼类粘虫寄生虫的流行情况
On the Number of Topological Types Occurring in a Parameterized Family of Arrangements
  • DOI:
    10.1007/s00454-008-9079-5
  • 发表时间:
    2008-05-17
  • 期刊:
  • 影响因子:
    0.600
  • 作者:
    Saugata Basu
  • 通讯作者:
    Saugata Basu
An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions
  • DOI:
    10.1007/s00493-009-2357-x
  • 发表时间:
    2009-09-01
  • 期刊:
  • 影响因子:
    1.000
  • 作者:
    Saugata Basu;Richard Pollack;Marie-Françoise Roy
  • 通讯作者:
    Marie-Françoise Roy
Efficient algorithm for computing the Euler–Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities
  • DOI:
    10.1007/s00037-006-0214-5
  • 发表时间:
    2006-10-01
  • 期刊:
  • 影响因子:
    1.000
  • 作者:
    Saugata Basu
  • 通讯作者:
    Saugata Basu

Saugata Basu的其他文献

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{{ truncateString('Saugata Basu', 18)}}的其他基金

Collaborative Research: AF: Small: On the Complexity of Semidefinite and Polynomial Optimization through the Lens of Real Algebraic Geometry
合作研究:AF:小:通过实代数几何的视角探讨半定和多项式优化的复杂性
  • 批准号:
    2128702
  • 财政年份:
    2021
  • 资助金额:
    $ 20万
  • 项目类别:
    Standard Grant
AF: Small: Symmetry, Randomness and Computations in Real Algebraic Geometry
AF:小:实代数几何中的对称性、随机性和计算
  • 批准号:
    1910441
  • 财政年份:
    2019
  • 资助金额:
    $ 20万
  • 项目类别:
    Standard Grant
AF: Small: Quantitative and Algorithmic Aspects of Semi-algebraic Sets and Partitions
AF:小:半代数集和分区的定量和算法方面
  • 批准号:
    1618981
  • 财政年份:
    2016
  • 资助金额:
    $ 20万
  • 项目类别:
    Standard Grant
AF: Small: Algorithmic and Quantitative Semi-Algebraic Geometry and Applications
AF:小:算法和定量半代数几何及其应用
  • 批准号:
    1319080
  • 财政年份:
    2013
  • 资助金额:
    $ 20万
  • 项目类别:
    Standard Grant
Algorithmic Problems in Semi-algebraic Geometry and Topology
半代数几何和拓扑中的算法问题
  • 批准号:
    1036361
  • 财政年份:
    2010
  • 资助金额:
    $ 20万
  • 项目类别:
    Standard Grant
AF: Small: Algorithmic and Quantitative Problems in Semi-algebraic and O-minimal Geometry
AF:小:半代数和 O 最小几何中的算法和定量问题
  • 批准号:
    0915954
  • 财政年份:
    2009
  • 资助金额:
    $ 20万
  • 项目类别:
    Standard Grant
Algorithmic Problems in Semi-algebraic Geometry and Topology
半代数几何和拓扑中的算法问题
  • 批准号:
    0634907
  • 财政年份:
    2006
  • 资助金额:
    $ 20万
  • 项目类别:
    Standard Grant
CAREER: Algorithmic Semi-Algebraic Geometry and Its Applications
职业:算法半代数几何及其应用
  • 批准号:
    0133597
  • 财政年份:
    2002
  • 资助金额:
    $ 20万
  • 项目类别:
    Continuing Grant
Design and Implementation of Algorithms in Semi-Algebraic Geometry
半代数几何算法的设计与实现
  • 批准号:
    0049070
  • 财政年份:
    2000
  • 资助金额:
    $ 20万
  • 项目类别:
    Standard Grant
Design and Implementation of Algorithms in Semi-Algebraic Geometry
半代数几何算法的设计与实现
  • 批准号:
    9901947
  • 财政年份:
    1999
  • 资助金额:
    $ 20万
  • 项目类别:
    Standard Grant

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