Inverse problem of persistent homology: A new method for structural analysis of proteins.

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610042
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tohoku University (2015-2016); Kyushu University (2014)
• Principal Investigator: Hiraoka Yasuaki 東北大学, 原子分子材料科学高等研究機構, 教授 (10432709)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: パーシステント写像 / 特異点

Outline of Final Research Achievements

In this research, we have formulated mathematical framework of inverse problems about persistent homology, and have developed a software which is applicable to real data. First, in direct problems, we studied the correspondence from point cloud data to persistence diagrams as differentiable maps. Then, we developed an algorithm to solve inverse solutions by using Newton method based on implicit function theorem. The developed software was applied to practical structural analysis of proteins and materials science.

Free Research Field

応用トポロジー