Generalized topologies: Hypergraphs, chemical reactions and biological evolution

Christoph Flamm, Bärbel M. R. Stadler, Peter Stadler

Veröffentlichungen: Beitrag in BuchBeitrag in Buch/SammelbandPeer Reviewed


In the analysis of complex networks, the description of evolutionary pro-cesses, or investigations into dynamics on fitness or energylandscapes notions such assimilarity, neighborhood, connectedness, or continuity of change appear in a natural way.These concepts are of an inherently topological nature. Nevertheless, the connection tothe mathematical discipline of point set topology is rarelymade in the literature, presum-ably because in most applications there is no natural objectcorresponding to an open orclosed set. The link to textbook topology thus cannot made ina straightforward manner.Many of the deep results of point set topology still remain valid, however, when opensets are abandoned an generalizations of the closure operator are used a the foundation of the mathematical theory. Here we survey some applications of such generalized point settopologies to chemistry and biology, providing an overview of the underlying mathematical structures.
TitelAdvances in Mathematical Chemistry and Applications
Redakteure*innenSubash C. Basak, Guillermo Restrepo, Jose L. Villaveces
Herausgeber (Verlag)Bentham Science Publishers
ISBN (elektronisch)978-1-68108-053-6, 978-1-68108-052-9
PublikationsstatusVeröffentlicht - 2015

ÖFOS 2012

  • 104022 Theoretische Chemie
  • 106005 Bioinformatik