title: Observability of Neuronal Network Motifs.
abstract: We quantify observability in small (3 node) neuronal networks as a function of 1) the connection topology and symmetry, 2) the measured nodes, and 3) the nodal dynamics (linear and nonlinear). We find that typical observability metrics for 3 neuron motifs range over several orders of magnitude, depending upon topology, and for motifs containing symmetry the network observability decreases when observing from particularly confounded nodes. Nonlinearities in the nodal equations generally decrease the average network observability and full network information becomes available only in limited regions of the system phase space. Our findings demonstrate that such networks are partially observable, and suggest their potential efficacy in reconstructing network dynamics from limited measurement data. How well such strategies can be used to reconstruct and control network dynamics in experimental settings is a subject for future experimental work.
authors.affiliation: Center for Neural Engineering, Penn State University, University Park, PA 16802.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Whalen
authors.affiliation: Department of Mechanical Engineering, Penn State University, University Park, PA 16802.
authors.forename: Sean N
authors.initials: SN
authors.lastname: Brennan
authors.affiliation: Department of Engineering Science and Mechanics, Neurosurgery, and Physics, Penn State University, University Park, PA 16802.
authors.forename: Timothy D
authors.initials: TD
authors.lastname: Sauer
authors.affiliation: Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030.
authors.forename: Steven J
authors.initials: SJ
authors.lastname: Schiff