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Motivation and Introduction Simplices are the building blocks of TDA that combine to give a simplicial complex approximation of the underlying space $X$. One of the most commonly observed ideas in mathematics is to generalize mathematical objects of interest. In other words, we wish to “peel off” a subset of the object’s properties to understand...

Introduction and Motivation The contents of this post are predominantly based on the review paper by Otter et al. 1 which discusses the computational aspects of Persistent Homology (PH). To begin with, the first four sections of the paper give a very good introduction to TDA without getting lost in unnecessary mathematical details. I believe tha...

Our brain activity is constantly fluctuating as we engage in different activities on a daily basis. In fact, the brain is quite active even while we are resting with our eyes closed. fMRI is a safe and non-invasive neuroimaging tool that plays quite an essential role in understanding brain activity and brain function. The discovery that a change...

The purpose of this post is to quickly introduce some brain anatomy basics before proceeding to understand functional Magnetic Resonance Imaging, or fMRI for short. My main reference to understanding these basics is the first chapter of The Statistical Analysis of Functional MRI Data by Nicole A. Lazar. Two introductory Neuroscience resources, w...