Abstract The Alzheimer's Disease Neuroimaging Initiative (ADNI) is an ongoing,
longitudinal, multicenter study designed to develop clinical, imaging, genetic, and …

Abstract The Alzheimer's Disease Neuroimaging Initiative (ADNI) is an ongoing,
longitudinal, multicenter study designed to develop clinical, imaging, genetic, and …

" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

Many data sets can be viewed as a noisy sampling of an underlying space, and tools from
topological data analysis can characterize this structure for the purpose of knowledge …

Topological data analysis offers a rich source of valuable information to study vision
problems. Yet, so far we lack a theoretically sound connection to popular kernel-based …

A suitable feature representation that can both preserve the data intrinsic information and
reduce data complexity and dimensionality is key to the performance of machine learning …

This work introduces a number of algebraic topology approaches, including multi-
component persistent homology, multi-level persistent homology, and electrostatic …

Proteins are the most important biomolecules for living organisms. The understanding of
protein structure, function, dynamics, and transport is one of the most challenging tasks in …

The brain network is usually constructed by estimating the connectivity matrix and
thresholding it at an arbitrary level. The problem with this standard method is that we do not …

Alzheimer's disease (AD) is an irreversible, progressive brain disorder that slowly destroys
memory and thinking skills. It is one of the leading types of dementia for persons aged above …