title: Compressive sensing reconstruction of feed-forward connectivity in pulse-coupled nonlinear networks.
abstract: Utilizing the sparsity ubiquitous in real-world network connectivity, we develop a theoretical framework for efficiently reconstructing sparse feed-forward connections in a pulse-coupled nonlinear network through its output activities. Using only a small ensemble of random inputs, we solve this inverse problem through the compressive sensing theory based on a hidden linear structure intrinsic to the nonlinear network dynamics. The accuracy of the reconstruction is further verified by the fact that complex inputs can be well recovered using the reconstructed connectivity. We expect this Rapid Communication provides a new perspective for understanding the structure-function relationship as well as compressive sensing principle in nonlinear network dynamics.
authors.affiliation: Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081, USA.
authors.forename: Victor J
authors.initials: VJ
authors.lastname: Barranca
authors.affiliation: Department of Mathematics, MOE-LSC, Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Douglas
authors.initials: D
authors.lastname: Zhou
authors.affiliation: Department of Mathematics, MOE-LSC, Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.|Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, New York 10012, USA.|NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates.
authors.forename: David
authors.initials: D
authors.lastname: Cai