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Quantifying Intermembrane Distances with Serial Image Dilations
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Kernel method for corrections to scaling.

Kenji Harada1

  • 1Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 15, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a new kernel method using Gaussian process regression to accurately infer scaling laws, even with corrections to scaling. This approach improves the analysis of critical phenomena by overcoming limitations of conventional methods.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Scaling analysis is crucial for understanding universal properties in critical phenomena across various scientific fields.
  • Corrections to scaling often lead to ill-posed inference problems due to uncontrollable irrelevant scaling variables.

Purpose of the Study:

  • To address the ill-posed nature of scaling analysis caused by corrections to scaling.
  • To propose a novel kernel method for robust inference of scaling laws.

Main Methods:

  • Development of a new kernel method based on Gaussian process regression.
  • Testing the method's performance on example cases with varying data precision.

Main Results:

  • The proposed kernel method demonstrates accurate convergence of inference results as data precision increases.
  • The method effectively handles scaling functions even in the presence of corrections to scaling.

Conclusions:

  • The new Gaussian process regression-based kernel method offers a general solution for scaling analysis with corrections to scaling.
  • This method overcomes limitations of conventional approaches and is widely applicable to real-world critical phenomena data.