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Generalized topological spaces in evolutionary theory and combinatorial chemistry
Bärbel M R Stadler1, Peter F Stadler
1Institut für Theoretische Chemie und Molekulare Strukturbiologie Universität, Wien, Vienna, Austria. baer@tbi.univie.ac.at
Journal of Chemical Information and Computer Sciences
|June 28, 2002
Summary
Combinatorial search spaces and molecular evolution are more complex than graphs. Recombination reveals non-graphical structures, impacting search processes, which are explored using point set topology.
Area of Science:
- Computational chemistry
- Evolutionary biology
- Theoretical computer science
Background:
- Combinatorial chemistry and molecular evolution search spaces are typically modeled as graphs.
- Recombination introduces non-graphical structures into these search spaces.
- The implications of these non-graphical structures for search processes are not well understood.
Purpose of the Study:
- To introduce a general formalism from point set topology.
- To apply this formalism to understand non-graphical structures in combinatorial search spaces.
- To explore the implications for fitness landscapes, evolutionary trajectories, and artificial chemistries.
Main Methods:
- Review of a general formalism from point set topology.
- Application of topological concepts to combinatorial search spaces.
- Analysis of fitness landscapes and evolutionary dynamics.
Main Results:
- Demonstration that recombination implies non-graphical search space structures.
- Formal topological framework for analyzing complex search spaces.
- Insights into the dynamics of evolutionary search and artificial chemistries.
Conclusions:
- Point set topology provides a powerful framework for understanding non-graphical search spaces.
- This approach offers new perspectives on molecular evolution and combinatorial optimization.
- The study highlights the limitations of graph-based models for certain complex systems.