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A Practical Guide to Phylogenetics for Nonexperts

A Practical Guide to Phylogenetics for Nonexperts

Published on: February 5, 2014

p-Adic mathematics and theoretical biology.

Branko Dragovich¹, Andrei Yu Khrennikov², Sergei V Kozyrev³

¹Institute of Physics, University of Belgrade, Belgrade, Serbia; Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia.

|November 14, 2020

Summary

This article introduces p-adic mathematics, including ultrametrics and p-adic analysis, and explores their applications in theoretical and mathematical biology for modeling complex biological systems.

Keywords:

Biological complexity Biological information Cognition Genetic code Hierarchical systems Mathematical biology Protein dynamics Theoretical biology Ultrametrics p-adic modeling p-adic numbers

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Area of Science:

Mathematics
Theoretical Biology
Mathematical Biology

Background:

P-adic mathematics offers novel frameworks for complex systems.
Ultrametrics and p-adic analysis are key components with growing applications.
Biological systems often exhibit hierarchical structures amenable to advanced mathematical modeling.

Purpose of the Study:

To provide an overview of fundamental p-adic mathematics concepts.
To highlight current and potential applications in theoretical and mathematical biology.
To propose p-adic mathematics as a natural tool for describing hierarchical biological phenomena.

Main Methods:

Introduction to ultrametrics.
Explanation of p-adic numbers and p-adic analysis.
Discussion of applications in modeling cognitive processes, genetic code, and protein dynamics.

Main Results:

P-adic mathematics provides a robust framework for understanding biological complexity.
Applications demonstrated in modeling cognitive processes, genetic code, and protein dynamics.
Ultrametric concepts are well-suited for systems with hierarchical organization.

Conclusions:

P-adic mathematics and ultrametric concepts are valuable tools for mathematical biology.
These mathematical frameworks have significant potential for future biological research.
The hierarchical nature of biological systems aligns well with p-adic mathematical structures.