In this talk Manish discusses how the application of TDA-based Mapper technique can facilitate examination of the organization of intrinsic brain activity in individuals with fragile X syndrome (FXS) at the single participant level. FXS is known to be the leading known single gene cause of Autism Spectrum Disorders. The resting state fMRI data were gathered from individuals with FXS and healthy controls. The severity of autism symptoms was assessed using Social Communication Questionnaire. Without collapsing data in space or time, we extracted a representation of overall brain dynamics for each participant using Mapper. The brain’s dynamical representation was later quantified using discrete-time finite-state Markov Chains and community detection tools from network science. Preliminary results suggest a relation between the average degree of a Markov Chain graph and severity of autism symptoms observed in individuals with FXS. Altogether, he presents one of the first applications of TDA-based methodologies to examine brain activity dynamics in clinical populations.