Tambe, Mary2019-02-122019-02-122018-09https://hdl.handle.net/11299/201734University of Minnesota M.S. thesis. September 2018. Major: Mathematics. Advisor: Duane Nykamp. 1 computer file (PDF); iii, 28 pages.Our perception of the world is influenced by the way our brains process information received from millions of neurons. Our senses are based on information sent to the brain in the form of sequences of stereotyped electrical impulses, or spikes. We attempt to answer a central question: how do we understand and analyze neural responses when their relationship to external variables such as stimuli, location or behavior is unclear? Our main innovation is that we first ignore these external variables and instead look for structure solely within data representing neural activity such as spike trains. Our preliminary results on synthetic data show how the diffusion maps algorithm applied to data preprocessed in a novel way, captures the one-dimensional manifold corresponding to a simulated rat's movement around a track. Diffusion maps reveals the structure of a one-dimensional manifold within the neural activity, as would be expected from the fact that the neural activity is strongly correlated with the rat's position.enDiffusion mapsDimensionality reductionManifoldNeural activityPrevious time measureSpike train dataThesis or Dissertation