James Francis Peters

The paper explores mapping three-dimensional EEG data to a four-dimensional hypersphere using quaternion projections to analyze neural activity patterns.

The paper uses computational topology to analyze rs-fMRI data, identifying persistent BOLD signal structures called cortical lag threads and visualizing them as persistent barcodes.

The paper shows that variations in Renyi entropy correlate with changes in the scaling slope of brain scale-free dynamics, suggesting potential applications in mind reading and transcranial stimulation.

The paper proposes a topological framework showing that all brain activities are dual and interconnected across different spatiotemporal scales and cortical regions.

The paper proposes a model of cortical microcolumns as fullerene-like lattices where neural activity is represented as barcodes of neuron activation patterns, enabling artificial networks with robustness and plasticity.

The paper uses first-order predicate logic to evaluate whether mind is a function of brain activity, if mental faculties can be reduced, and if cognition and emotion are distinct.

This paper proposes a mathematical framework combining Borsuk's theory of shape and the Borsuk-Ulam theorem to model perception as a topological and ecological process.