General Pattern Theory A Mathematical Study of Regular Structures

The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyse the mathematical properties of the resulting regular structures, and to apply them to practically occuring patterns in nature and the man-made world. Starting from an algebraic formulation of such representations they are studied in terms of their topological, dynamical and probabilistic aspects. Patterns are expressed through their typical behaviour as well as through their variability around their typical form. Employing the representations (regular structures) algorithms are derived for the understanding, recognition, and restoration of observed patterns. The algorithms are investigated through computer experiments.

1 - Generators and configurations
2 - Images and patterns
3 - Some topologies on regular structures
4 - Abstract biological patterns
5 - Patterns of collective behaviour
6 - Patterns generated from extremum principles
7 - General principles of MPT
8 - Pattern synthesis
9 - First limit problem in MPT
10 - Second limit problem in MPT
11 - Mixed limit problem in MPT
12 - Chapter 12: Deformation mechanisms
13 - Ends and means in pattern analysis
14 - Bayesian pattern inference
15 - Lattice-based models
16 - Continuum-based models
17 - Non-Bayesian pattern inference
18 - Pattern recognition
19 - Creating generators
20 - Creating acceptor functions and connectors