Publications - Published papers

Please find below publications of our group. Currently, we list 508 papers. Some of the publications are in collaboration with the group of Sonja Prohaska and are also listed in the publication list for her individual group. Access to published papers (access) is restricted to our local network and chosen collaborators. If you have problems accessing electronic information, please let us know:

©NOTICE: All papers are copyrighted by the authors; If you would like to use all or a portion of any paper, please contact the author.

Generalized topologies: hypergraphs, chemical reactions, and biological evolution

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

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In Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces, editors, Advances in Mathematical Chemistry: With applications to chemoinformatics, bioinformatics, drug d iscovery, and Predictive toxicology. Bentham (2013)

Abstract


In the analysis of complex networks, the description of evolutionary processes, or investigations into dynamics on fitness or energy landscapes notions such as similarity, neighborhood, connectedness, or continuity of change appear in a natural way. These concepts are of an inherently topological nature. Nevertheless, the connection to the mathematical discipline of point set topology is rarely made in the literature, presumably because in most applications there is no natural object corresponding to an open or closed set. The link to textbook topology thus cannot made in a straightforward manner. Many of the deep results of point set topology still remain valid, however, when open sets 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 set topologies to chemistry and biology, providing an overview of the underlying mathematical structures.