Hicks, Illya V.2014-10-172014-10-172013-122013-12-04December 2Wood, Cynthia. "The Closure of the Minimal k-core Problem for Modeling k-assemblies." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/77595">https://hdl.handle.net/1911/77595</a>.https://hdl.handle.net/1911/77595In this thesis, I 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 minimal k-core problem has applications in the area of neuroscience. For example, 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. Recent studies have linked the concept of a particular type of cell assembly called k-assembly to the closure of a minimal k-core. Therefore, the proposed method puts us a step closer to test its mathematical definition.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.K-coresCell assemblyK-assemblyClique generalizationsThesis2014-10-17