Cyclicity in multivariate time series and applications to functional MRI data

One of the challenging problems in fMRI data analysis is the absence of natural time scale at which to consider the traces of the resting state, the aggregate name for the processes in the brain happening in the absence of task of strong external stimuli. This necessitates development of the tools that are able to extract from the time series information invariant with respect to reparametrization of the time coordinate. A recently developed notion of cyclicity, based on the hierarchy of iterated path integrals and corresponding algorithms were applied to several hundreds of the fMRI records, to reveal potential presence of an external auditory stimulus.