An Embedded Network Approach for Scale-Up of Fluctuation-driven Systems

To address computational \scale-up" issues in modeling of large regions of the cortex, many coarse-graining procedures have been invoked to obtain e ective descriptions of neuronal network dynamics. However, because of local averaging in space and time, these methods do not contain detailed spike information, and, thus, cannot be used to investigate, e.g., cortical mechanisms which are encoded through detailed spike-timing patterns. To retain spike information, we develop a hybrid theoretical framework which embeds a subnetwork of point neurons within, and fully interacting with, a coarse-grained network of dynamical background. We employ our newly developed kinetic theory for the description of the coarse-grained background, in combination of a Poisson spike reconstruction procedure to ensure that our method works for the uctuation-driven regime as well as the meandriven regime. This embedded network approach is veri ed to be dynamically accurate and numerically eÆcient. As an example, we use this embedded representation to construct \reverse-time correlations" as spiked-triggered averages in a ring model of orientation tuning dynamics. Corresponding author: David Cai, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012. Phone: 212-998-3310, Fax: 212-995-4121, email: [email protected].