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Area of Science:

  • Computational Biology
  • Data Science
  • Statistical Physics

Background:

  • Understanding memory in symbolic sequences is crucial for various fields.
  • Existing methods may not fully capture complex correlation structures.

Purpose of the Study:

  • Introduce a general method for analyzing memory in symbolic sequences.
  • Define and quantify the memory profile of a sequence.
  • Demonstrate the method's utility on synthetic and real-world data.

Main Methods:

  • Higher-order Markov analysis of symbolic sequences.
  • Representing sequences as mixtures of minimal-order Markov matrices.
  • Defining the memory profile based on these matrices.

Main Results:

  • The memory profile accurately reflects the true order of correlations.
  • Successful validation using tunable synthetic sequences.
  • Demonstrated application in extracting stochastic properties from real data.

Conclusions:

  • The proposed method provides a robust framework for memory analysis in symbolic sequences.
  • The memory profile is a powerful tool for characterizing sequence complexity.
  • This protocol facilitates the discovery of underlying stochastic properties in diverse datasets.