The 'Butterfly effect' in Cayley graphs with applications to genomics

Area of Science:

• Computational Biology
• Group Theory
• Discrete Mathematics

Background:

• Systems involving sequential transformations, such as genome rearrangements or Rubik's cube permutations, are common in science and mathematics.
• Understanding the stability of these transformations under minor sequence alterations is crucial for applications.

Purpose of the Study:

• To investigate the sensitivity of sequential permutation transformations to small changes in the applied sequence.
• To analyze how deleting or replacing a single permutation impacts the final state.

Main Methods:

• Analysis of walks in Cayley graphs of groups with specified generators.
• Examination of permutation groups and generators relevant to computational genomics.
• Statistical analysis of perturbation effects.

Main Results:

• Demonstrated that minor perturbations in permutation sequences can lead to significant differences in final states.
• Quantified the 'difference' between states using metrics like minimum permutation distance.
• Identified implications for computational genomics and theoretical group studies.

Conclusions:

• Sequential permutation systems exhibit sensitivity to perturbations.
• Findings have relevance for understanding genome rearrangement processes and theoretical group structures.
• The study provides a framework for analyzing the robustness of such transformations.