By applying and generating concepts in order theory, a branch of discrete mathematics, we have addressed questions in different disciplines, ranging from chemistry and toxicology to biotechnology. Typical questions we solve include muticriteria decisions, where several attributes are used to come up with priorities for possible decisions. Others involve orderings (a particular case being a ranking) of different objects, e.g. bacteria, chemicals, geographical sites or radionuclides; or conditions required to attain a particular ordering. A recent application of order theory to chemistry showed that the periodic system corresponds to an ordered hypergraph.
So far this research has been conducted mainly by scientists at the Max Planck Institute for Mathematics in the Sciences and Leibniz-Institute of Freshwater Ecology and Inland Fisheries, but we are open to further collaboration with scientists and scholars of other institutions. There are also several research projects available for MSc and PhD students, as well as for postdocs.
Questions related to this research topic can be addressed to Guillermo Restrepo at restrepo@mis.mpg.de or guillermorestrepo@gmail.com.
References:
Leal, W.; Restrepo, G. Formal structure of periodic system of elements. Proc. R. Soc. A 2019, 475: 20180581.
Quintero, N.; Bruggemann, R.; Restrepo, G. Mapping posets into low dimensional spaces: The case of uranium trappers. MATCH Commun. Math. Comput. Chem. 2018, 80, 793-820.
Quintero, N.; Bruggemann, R.; Restrepo, G. Ranking of 38 prokaryotes according to their uranium uptake capacity in aqueous solutions: An approach from order theory through the Hasse Diagram Technique. Toxicol. Environ. Chem. 2017, 99, 1242-1269.
Restrepo, G.; Stadler, P. F. Assessing greenness of chemical reactions and synthesis plans through posetic landscapes. ACS Sustainable Chem. Eng., 2016, 4, 2191–2199.
Rincón-Villamizar, E.; Restrepo, G. Rules relating hepatotoxicity with structural attributes of drugs. Toxicol. Environ. Chem. 2014, 96, 594-613. 50 free eprints!
Restrepo, G.; Bernal, A. Ordering molecular energies by moving boxes. Chem. Phys. Lett. 2014, 612, 51-55.
Quintero, N.; Cohen, I. M.; Restrepo, G. Relating β+ radionuclides' properties by order theory. J. Radioanal. Nucl. Ch., 2013, 298, 1937-1946.
Restrepo, G.; Klein, D. J. Predicting densities of nitrocubanes using partial orders. J. Math. Chem. 2011, 49, 1311-1321.
Restrepo, G.; Basak, S. C.; Mills, D. Comparison of SAR and QSAR approaches to mutagenicity of aromatic and heteroaromatic amines. Curr. Comput-Aid Drug. 2011, 7, 109-121.
Brüggemann, R.; Voigt, K.; Restrepo, G.; Simon, U. The concept of stability fields and hot spots in ranking of environmental chemicals. Environ. Modell. Softw. 2008, 23, 1000-1012.
Restrepo, G.; Weckert, M.; Brüggemann, R.; Gerstmann, S.; Frank, H. Ranking of refrigerants, Environ. Sci. Technol. 2008, 42, 2925-2930.
Related sites:
PyHasse from Rainer Brüggemann.