Hierarchical and ultrametric mathematical methods were applied for the
investigation of complex systems. This talk gives a revew of several
applications of ultrametric methods. We will discuss the following
examples -- trees, buildings, wavelets, applications to spin glasses,
proteins and genetic code.
- Wavelets can be used for hierarchical function representations.
- Clustering is a method of classification with a help of trees.
Multiclustering is a generalisation of clustering related to buildings.
- Application to spin glasses: we will discuss $p$-adic parameters for
the Parisi matrix.
- Another application of hierarchical methods is to description of
protein dynamics by $p$-adic diffusion. Hierarchy in protein structure and
DNA packing can be also discussed.
- Genetic code can be described by 2-adic plane -- 2-dimensional
Further applications include hierarchical models in machine learning,
in particular, in deep learning.