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Abstract

The Local Field Potential (LFP) summarizes synaptic and somato-dendritic
currents in a bounded ball around the electrode and is dependent on the spatial
distribution of neurons. Both fine-grained properties and the temporal distribution
of typical waveforms in spontaneous LFP have been used to identify global brain states
(see e.g. [1] for P-waves in stages of sleep). While some LFP signatures have been
studied in detail (in addition to Pons, see e.g. sleep spindles in the Thalamus and
areas of the cortex [2], sharp-wave-ripples [3] in the Hippocampus and k-complexes
[4]), it stands to understand the relationship between simultaneous signaling in
cortical and subcortical areas. To characterize the mesoscale spontaneous activity,
we quantify data-driven properties of LFP and use them to describe different brain
states. Inspired by [5], we treat frequency-localized temporary increases in LFP power
simultaneously recorded from Cortex, Hippocampus, Pons and LGN as neural events that
carry information about the brain state. Here, we give a characterization of neural
events in the 0-60Hz frequency range using tools from topological data analysis. In
detail, we look at collections of barcodes computed using persistence homology [6]
in two different ways. First, we look at the sublevel set filtration of a neural event
to describe its critical points. Second, we use Vietoris-Rips filtration of the
point-cloud of the delay embedding [7,8] of a neural event to describe periodicity.
Both collections of barcodes are mapped to their persistence landscape spaces [9,10]
for statistical description of the neural events. Both neural events representations
are stable with respect to noise. They can be used for comparison of sustained
low-frequency activity between different brain sites, as well as local spatial
variability of the electrode position.