We have developed some mathematical methods for data analysis, of application in classification, estimation of substances' properties, assessment of algorithms' performance and characteriation of (hyper)networks. Some of them are based on discrete structures such as partially ordered sets, others derived from other data analysis techniques such as hierarchical cluster analysis or formal concept analysis or more geometrical ones as curvatures for discrete structures such as graphs and hypergraphs.
So far this research has been conducted mainly by scientists at the Max Planck Institute for Mathematics in the Sciences, 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:
Restrepo, G. Chemical space: limits, evolution and modelling of an object bigger than our universal library. Digital Discovery 2022, DOI: 10.1039/D2DD00030J
Restrepo, G. Semiotic thoughts on biological sequence representations. Comb. Chem. High T. Scr. 2022, 25, 349-353.
Leal, W.; Restrepo, G.; Stadler, P. F.; Jost, J. Forman-Ricci curvature for hypergraphs. arXiv, 2019.
Leal, W.; Llanos, E. J.; Restrepo, G.; Suárez, C. F.; Patarroyo, M. E. How frequently do clusters occur in hierarchical cluster analysis?: A graph theoretical approach to studying ties in proximity. J. Cheminform., 2016, 8, 4.
Quintero, N. Y.; Restrepo, G. Formal Concept Analysis applications in chemistry: from radionuclides and molecular structure to toxicity and diagnosis. In Partial Order Concepts in Applied Sciences, Fattore, M.; Brüggemann, R., Eds.; Springer: Berlin, Germany, 2016; Chapter 14.
Advances in mathematical chemistry and applications, Volume 2, Basak, S. C.; Restrepo, G.; Villaveces, J. L., Eds.; Elsevier-Bentham: Sharjah, UAE, 2015.
Bernal, A.; Llanos, E.; Leal, W.; Restrepo, G. Similarity in Chemical Reaction Networks: Categories, Concepts and Closures. In Advances in mathematical chemistry and applications, Basak, S. C.; Restrepo, G.; Villaveces, J. L., Eds.; Bentham: Sharjah, UAE, 2015; Chapter 2, 24-54.
Advances in mathematical chemistry and applications, Volume 1, Basak, S. C.; Restrepo, G.; Villaveces, J. L., Eds.; Elsevier-Bentham: Sharjah, UAE, 2014.
Restrepo, G.; Klein, D. J. Predicting densities of nitrocubanes using partial orders. J. Math. Chem. 2011, 49, 1311-1321.
Restrepo, G.; Brüggemann, R.; Klein, D. Partially ordered sets: ranking and prediction of substances' properties. Curr. Comput-Aid Drug. 2011, 7, 133-145.
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.
Restrepo, G.; Mesa, H. Chemotopology: beyond neighbourhoods. Curr. Comput-Aid Drug. 2011, 7, 90-97.
Nava, J.; Kreinovich, V.; Restrepo, G.; Klein, D. Discrete Taylor series as a simple way to predict properties of chemical substances like benzenes and cubanes. J. Uncert. Syst. 2010, 4, 270-290.
Mesa, H.; Restrepo, G. On dendrograms and topologies. MATCH Commun. Math. Comput. 2008, 60, 371-384.
Restrepo, G.; Mesa, H.; Llanos, E. J. Three dissimilarity measures to contrast dendrograms. J. Chem. Inf. Model. 2007, 47, 761-770.
Brüggemann, R.; Restrepo, G.; Voigt, K. Structure-fate relationships of organic chemicals derived from the software packages E4CHEM and WHASSE. J. Chem. Inf. Model. 2006, 46, 894-902.
Daza, M. C.; Restrepo, G.; Uribe, E. A.; Villaveces, J. L. Quantum chemical and chemotopological study of fourth row monohydrides. Chem. Phys. Lett. 2006, 428, 55-61.