Distributions of distances in information strings

Area of Science:

• Information theory
• Computational biology
• Linguistics
• Computer science

Background:

• Understanding patterns in information strings is crucial across diverse fields.
• Symbol repetition and spacing provide fundamental insights into data structure.
• Previous analyses have not comprehensively compared multiple distributions for symbol distance metrics.

Purpose of the Study:

• To investigate and compare the precision of four statistical distributions (exponential, Weibull, log-normal, negative binomial) in describing distances between identical symbols.
• To identify significant correlations in symbol spacing patterns within biological, language, and computer-generated information strings.

Main Methods:

• Analysis of symbol distances in biological sequences, natural language text, and executable program files (*.exe).
• Application and comparison of four distinct probability distributions: exponential, Weibull, log-normal, and negative binomial.
• Statistical correlation analysis to assess the significance of observed patterns.

Main Results:

• The four distributions model symbol distances with varying degrees of precision.
• Highly significant correlations were detected between symbol distances in the analyzed information strings.
• The choice of distribution impacts the accuracy of pattern description.

Conclusions:

• Symbol distance patterns exhibit significant correlations across biological, linguistic, and computational domains.
• Statistical distributions provide a framework for quantifying these patterns, with varying effectiveness.
• Further research can leverage these findings for improved data compression, pattern recognition, and anomaly detection.