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Quantification of Protein Interaction Network Dynamics using Multiplexed Co-Immunoprecipitation
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Higher-order percolation processes on multiplex hypergraphs.

Hanlin Sun1, Ginestra Bianconi1,2

  • 1School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.

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|October 16, 2021
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Summary
This summary is machine-generated.

This study introduces a framework to assess hypergraph robustness and higher-order percolation. It reveals how structural correlations impact these processes, offering insights into complex systems and epidemic spreading.

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Area of Science:

  • Network Science
  • Complex Systems Theory
  • Statistical Physics

Background:

  • Higher-order interactions are crucial in complex systems like brains and social networks.
  • Hypergraphs and simplicial complexes model these interactions, enabling study of structure-function relationships.

Purpose of the Study:

  • Establish a general framework for assessing hypergraph robustness.
  • Characterize critical properties of higher-order percolation processes.
  • Investigate the relationship between hypergraph structure and function.

Main Methods:

  • Formulation of the random multiplex hypergraph ensemble with layer-specific hyperedge cardinalities.
  • Mapping multiplex hypergraphs to multiplex bipartite networks under a structural cutoff.
  • Analysis of higher-order percolation, interdependent percolation, and K-core percolation.

Main Results:

  • Structural correlations significantly affect hypergraph percolation properties.
  • A wide range of critical behaviors are observed in higher-order percolation.
  • Mechanisms for discontinuous transitions in complex systems are elucidated.

Conclusions:

  • The framework provides insights into epidemic spreading and contagion on higher-order networks.
  • Understanding higher-order percolation is key to comprehending complex system resilience.
  • Structural correlations play a vital role in the functional dynamics of complex systems.