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Structural and compositional complexities of hierarchical self-assembly: A hypergraph approach.

Alexei V Tkachenko1

  • 1Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA.

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Summary
This summary is machine-generated.

We introduce Blocks & Bonds (B&B), a hypergraph framework for describing self-assembled structures. A new compositional complexity measure strongly correlates with information content, simplifying complexity assessment for programmable matter.

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Area of Science:

  • Materials Science
  • Computational Chemistry
  • Information Theory

Background:

  • Programmable self-assembly is key for creating complex molecular and crystalline structures.
  • Classical chemical graph theory has limitations in representing intricate self-assembly features.

Purpose of the Study:

  • To introduce a generalized hypergraph formalism, Blocks & Bonds (B&B), for describing self-assembled architectures.
  • To define and validate new measures of structural and compositional complexity for these systems.

Main Methods:

  • Developed the Blocks & Bonds (B&B) hypergraph formalism.
  • Defined Structure Code (SC) for encoding self-assembled architectures.
  • Introduced Kolmogorov-style structural complexity and compositional complexity measures.
  • Empirically correlated complexity measures across diverse systems.

Main Results:

  • B&B generalizes chemical graph theory to include directed, multicolored interactions, symmetry, and hierarchy.
  • A strong correlation was found between token-based structural complexity and the simpler compositional complexity.
  • Compositional complexity is a practical, broadly applicable measure tracking information content.

Conclusions:

  • B&B hypergraphs offer a unified, scalable, and information-efficient representation for self-assembled structures.
  • Compositional complexity provides a computationally accessible yet accurate assessment of structural complexity.
  • The framework supports quantitative classification and inverse design of programmable matter.