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    Network reconstruction using time-delayed spike-train cross-correlation with limited information and classification according to spectral properties

    Author
    Volosov, Paulina
    View/Open
    180407_Volosov_rpi_0185E_11712.pdf (8.208Mb)
    Other Contributors
    Kovacic, Gregor; Holmes, Mark H.; Kramer, Peter Roland, 1971-; Zhou, Douglas;
    Date Issued
    2020-08
    Subject
    Mathematics
    Degree
    PhD;
    Terms of Use
    This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.;
    Metadata
    Show full item record
    URI
    https://hdl.handle.net/20.500.13015/2637
    Abstract
    We begin by reconstructing the entire network using time-delayed spike-train correlation, and we determine the time required before an adequate reconstruction becomes possible and compare this to time spans employed by experimentalists. We then sample the reconstruction matrix randomly and use the tool of matrix completion to fill in the rest of the network. To more closely mimic experimental settings, we next examine a small subnetwork of the network and determine how much information we can deduce about the whole network from this small piece. An examination of the spectral properties of connectivity matrices forms a major part of this analysis, and we formulate a metric which classifies the complex architectural network structure. Our results have practical implications for network science and computational neuroscience.; The extent of the relation between architectural and functional connectivity in the cerebral cortex is a question which has attracted much attention in recent years. Neuroscientists frequently use the functional connectivity of neurons, i.e. the measures of causality or correlations between the neuronal activities of certain parts of a network, to infer the architectural connectivity of the network, which indicates the locations of underlying synaptic connections between neurons. Architectural connectivity can be used in the modeling of neuronal processing and in the forming of conjectures about the nature of the neural code. These two types of connectivity are by no means identical, and typically no one-to-one correspondence or mapping exists from one to the other. In particular, certain standard measures of functional connectivity, such as simple correlations, give rise to an undirected network, while synaptic architectural connectivity is always directed. Nevertheless, architectural connectivity can often be inferred from functional connectivity, and this work is one attempt to determine how to do so. Our work focuses on mimicking experimental constraints and thus addresses the question of how to infer information about a complex architecture given only limited information about neuronal dynamics.;
    Description
    August 2020; School of Science
    Department
    Dept. of Mathematical Sciences;
    Publisher
    Rensselaer Polytechnic Institute, Troy, NY
    Relationships
    Rensselaer Theses and Dissertations Online Collection;
    Access
    Restricted to current Rensselaer faculty, staff and students. Access inquiries may be directed to the Rensselaer Libraries.;
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