🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.000931s)
  1. Decoding of Neural Data Using Cohomological Feature Extraction (2019)

    Erik Rybakken, Nils Baas, Benjamin Dunn
    Abstract We introduce a novel data-driven approach to discover and decode features in the neural code coming from large population neural recordings with minimal assumptions, using cohomological feature extraction. We apply our approach to neural recordings of mice moving freely in a box, where we find a circular feature. We then observe that the decoded value corresponds well to the head direction of the mouse. Thus, we capture head direction cells and decode the head direction from the neural population activity without having to process the mouse's behavior. Interestingly, the decoded values convey more information about the neural activity than the tracked head direction does, with differences that have some spatial organization. Finally, we note that the residual population activity, after the head direction has been accounted for, retains some low-dimensional structure that is correlated with the speed of the mouse.
  2. Using Persistent Homology to Reveal Hidden Information in Neural Data (2015)

    Gard Spreemann, Benjamin Dunn, Magnus Bakke Botnan, Nils A. Baas
    Abstract We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of the known stimuli that govern neuron activity, and the corresponding state of the animal throughout the experiment performed. Using a generalized linear model for neuron activity and simple assumptions on the effects of the external stimuli, we infer away any contribution to the observed spike trains by the candidate stimuli. Persistent homology then reveals useful information about any further, unknown, covariates.