The 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.

中文翻译：

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建模k组件的最小k核问题。

细胞组装的概念是由赫布（Hebb）提出的，并由棕榈（Palm）在图论的框架内进行数学形式化。在联想记忆的研究中，细胞组装是一组紧密相连的神经元，代表我们知识的“概念”。该组以特定方式连接，因此只有一部分神经元会激发整个程序集。我们将电池组装的概念与最小k核的闭合联系起来，并研究一种称为k组装的特殊类型的电池组装。本文的目的是找到网络中所有必须被激发才能激活k组件的子结构。通过数值实验，我们确认这些重要子组的各个部分重叠。为了探讨这个问题，我们提出了一种回溯算法，可以找到给定无向图的所有最小k核，这些核属于NP难题的一类。所提出的方法是对Bron和Kerbosch算法的修改，用于查找无向图的所有派系。经过测试的图形中的结果为分析图形结构提供了见识，并有助于更好地理解概念的存储方式。