Wood, Cynthia I.Hicks, Illya V.2016-04-042016-04-042015Wood, Cynthia I. and Hicks, Illya V.. "The Minimalﾠk-Core Problem for Modelingﾠ k-Assemblies." <i>The Journal of Mathematical Neuroscience,</i> 5, (2015) Springer: http://dx.doi.org/10.1186/s13408-015-0027-4.https://hdl.handle.net/1911/88834The concept of cell assembly was introduced by Hebb and formalized mathematically by Palm in the framework of graph theory. In the study of associative memory, a cell assembly is a group of neurons that are strongly connected and represent a "concept" of our knowledge. This group is wired in a specific manner such that only a fraction of its neurons will excite the entire assembly. We link the concept of cell assembly to the closure of a minimal k-core and study a particular type of cell assembly called k-assembly. The goal of this paper is to find all substructures within a network that must be excited in order to activate a k-assembly. Through numerical experiments, we confirm that fractions of these important subgroups overlap. To explore the problem, we present a backtracking algorithm to find all minimal k-cores of a given undirected graph, which belongs to the class of NP-hard problems. The proposed method is a modification of the Bron and Kerbosch algorithm for finding all cliques of an undirected graph. The results in the tested graphs offer insight in analyzing graph structure and help better understand how concepts are stored.engThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.Journal articlecell assemblymemoryGraph theoryk-Assemblycomplexityk-Corehttp://dx.doi.org/10.1186/s13408-015-0027-4