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Maria-Veronica Ciocanel1, Punit Gandhi2, Karl Niklas3

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We developed a new method to measure approximate and maximal symmetries using transformation information (TI). This framework helps track symmetry evolution and understand biological development and evolutionary history.

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Area of Science:

  • * Mathematical Biology
  • * Evolutionary Biology
  • * Developmental Biology

Background:

  • * Accurate quantification of symmetry is crucial for understanding biological performance, development, and evolutionary history.
  • * Existing methods may not fully capture the nuances of approximate or evolving symmetries.
  • * Transformation Information (TI) offers an entropy-based measure of symmetry deviations.

Purpose of the Study:

  • * To further develop the Transformation Information (TI) measure for quantifying approximate and maximal symmetries.
  • * To establish a framework for characterizing the evolution of symmetry by analyzing critical points in TI.
  • * To explore the connections between symmetry transitions, morphology, and underlying biological dynamics.

Main Methods:

  • * Extended the Transformation Information (TI) framework to identify maximal symmetries at critical points.
  • * Applied the enhanced TI measure to probability distributions and differential equation models.
  • * Analyzed qualitative changes in symmetry properties across static and growing domains.

Main Results:

  • * Demonstrated the ability of TI to quantify approximate and maximal symmetries.
  • * Identified critical points in TI that correspond to significant symmetry transitions.
  • * Revealed connections between symmetry changes, morphological shifts, and system dynamics.

Conclusions:

  • * The developed TI framework provides a pathway toward a general mathematical theory for symmetry transitions.
  • * This approach offers insights into the evolution of biological forms and functions.
  • * The study links mathematical symmetry analysis to observable biological phenomena.