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Polarization-Sensitive Two-Photon Microscopy for a Label-Free Amyloid Structural Characterization
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Microstructural degeneracy associated with a two-point correlation function and its information content.

C J Gommes1, Y Jiao, S Torquato

  • 1Department of Chemical Engineering, University of Liège, Liège 4000, Belgium. cedric.gommes@ulg.ac.be

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Microstructure characterization using two-point correlation functions can be ambiguous. This study quanties microstructural degeneracy and introduces an information-theoretic approach to assess reconstruction accuracy.

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Area of Science:

  • Materials Science
  • Statistical Physics
  • Image Analysis

Background:

  • Two-point correlation functions incompletely characterize microstructures, leading to degeneracy.
  • Microstructural degeneracy quantifies the number of distinct structures sharing a correlation function.

Purpose of the Study:

  • To provide a comprehensive analysis of microstructural degeneracy.
  • To develop a method for assessing the accuracy of microstructure reconstruction from correlation functions.

Main Methods:

  • Mapping microstructural degeneracy to ground-state degeneracies in reconstruction problems.
  • Calculating the energy profile and landscape roughness of reconstruction problems.
  • Calibrating roughness as a proxy for degeneracy using Monte Carlo simulations.
  • Relating results to the information content of correlation functions.

Main Results:

  • The energy profile's steepness serves as a proxy for ground-state degeneracy.
  • A Monte Carlo algorithm was used to calibrate this roughness metric.
  • Results are expressible in terms of the information content of correlation functions.
  • A formula for calculating the information content of correlation functions is provided.

Conclusions:

  • Reconstruction accuracy requires information content comparable to the microstructure's pixel count.
  • The developed framework and information content formula offer broad applicability.
  • This work advances the understanding of microstructure characterization and reconstruction.