Colloquium
Topological data analysis and its applications to vascular flows and gravitational waves
작성자Author
수학과
작성일Date
20190902 13:43
조회Views
505
분야Field  Math Colloquium  

날짜Date  20191122  시간Time  17;00 ~ 18:00 
장소Place  Math. Bldg. 404  초청자Host  조성문 
연사Speaker  정재훈  소속Affiliation  아주대 (Ajou Univ.)/SUNY Buffalo 
TOPIC  Topological data analysis and its applications to vascular flows and gravitational waves  
소개 및 안내사항Content  Abstract: Topological data analysis (TDA) has been proven a useful tool for finding hidden patterns in the given data set. In this talk, we will consider two problems and explain how TDA can be applied to solve these problems. First, we will consider vascular disease and its diagnosis. Cardiovascular disease is the leading cause of death worldwide. The methodologies used today for diagnosis are based on the geometric approach using the angiography and/or direct measurement of the fractional flow reserve with catheter or computational fluid dynamics. Numerical indices obtained by these methods, however, do not necessarily provide clear interpretation of the vasculature unless the case is extreme and the intervention is inevitable. In this talk, we present a new approach using TDA for stenotic vascular flows. The key element of TDA for vascular disease presented in this talk is to project the vascular data unto the ndimensional unit sphere and then find the number of generators of the homology group at each dimension. The proposed method is promising in that the method can reveal fine details of disease status. Similar technique will be applied to our second problem — the gradational wave detection problem. Black hole mergers perturb the background spacetime. The perturbation propagates in the form of the gravitational wave. But the signature is highly weak to detect and the detection problem becomes highly challenging. Convolutional neural network (CNN) has been proven to a possible tool for extracting wave signatures and thus detecting the gravitational wave out of noisy signals. However, CNN approach also fails if the signaltonoise ratio is highly low. We show that the signatures extracted by TDA, if added to the original signal, can be a remedy for the gravitational wave detection problem. 
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