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Principal Investigator  
Principal Investigator's Name: Kun Meng
Institution: Brown University
Department: Division of Applied Mathematics
Country:
Proposed Analysis: I plan to use the ADNI data in the following projects: 1. Applications of topological data analysis (TDA) to fMRI functional connectivity analysis. This project transforms the functional data form of fMRI into topological form and applies TDA to analyze the functional connectivity structures. This project is potentially relevant to the following papers: 'Population-level Task-evoked Functional Connectivity via Fourier Analysis' and 'Discriminative persistent homology of brain networks.' 2. Applications of TDA to grayscale images. Grayscale images essentially contain geometric (topological) information. This project transforms the topological structures in the images into functional data and applies functional data analysis to the transformed data. This project is a generalization of the following two papers: 'Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis' and 'Randomness and Statistical Inference of Shapes via the Smooth Euler Characteristic Transform.'
Additional Investigators  
Investigator's Name: Jinyu Wang
Proposed Analysis: I plan to use the ADNI data in the following projects: 1. Applications of topological data analysis (TDA) to fMRI functional connectivity analysis. This project transforms the functional data form of fMRI into topological form and applies TDA to analyze the functional connectivity structures. This project is potentially relevant to the following papers: 'Population-level Task-evoked Functional Connectivity via Fourier Analysis' and 'Discriminative persistent homology of brain networks.' 2. Applications of TDA to grayscale images. Grayscale images essentially contain geometric (topological) information. This project transforms the topological structures in the images into functional data and applies functional data analysis to the transformed data. This project is a generalization of the following two papers: 'Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis' and 'Randomness and Statistical Inference of Shapes via the Smooth Euler Characteristic Transform.'