Publications - Published papers
Please find below publications of our group. Currently, we list 565 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 (
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webmaster@bioinf.uni-leipzig.de
) is restricted to our local network and chosen collaborators.
If you have problems accessing electronic information, please let us know:webmaster@bioinf.uni-leipzig.de
©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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PREPRINT 13-045: [ PDF ]
Status: Published
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.