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The Minimal k-Core Problem for Modeling k-Assemblies.

Cynthia I Wood1, Illya V Hicks

  • 1Department of Computational and Applied Mathematics, Rice University, 6100 Main st, Houston, TX, 77005, USA, cynthia.i.wood@rice.edu.

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|July 15, 2015
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This summary is machine-generated.

This study links cell assemblies to graph theory's k-cores, identifying minimal neuron subgroups required to activate a k-assembly. Numerical experiments reveal overlapping substructures essential for understanding concept storage in neural networks.

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Area of Science:

  • Computational Neuroscience
  • Graph Theory
  • Network Science

Background:

  • Cell assemblies, groups of strongly connected neurons, represent knowledge concepts.
  • Hebb's cell assembly concept was mathematically formalized using graph theory.
  • Understanding how fractions of neurons activate an entire assembly is key to associative memory.

Purpose of the Study:

  • To link cell assemblies to minimal k-cores in graph theory.
  • To identify essential substructures (k-assemblies) within neural networks.
  • To develop an algorithm for finding these substructures and analyze their properties.

Main Methods:

  • Mathematical formalization of cell assemblies using graph theory.
  • Definition and study of k-assemblies as minimal k-cores.
  • Development of a backtracking algorithm, modified from Bron-Kerbosch, to find minimal k-cores.
  • Numerical experiments on tested graphs.

Main Results:

  • Confirmed that fractions of neuron subgroups overlap within k-assemblies.
  • The proposed algorithm efficiently finds all minimal k-cores in undirected graphs.
  • Demonstrated the utility of analyzing graph structure for understanding concept storage.

Conclusions:

  • Cell assemblies can be effectively modeled as minimal k-cores.
  • The developed algorithm aids in identifying critical network components for concept activation.
  • Findings provide insights into the network mechanisms underlying associative memory and knowledge representation.