Partial Order Concepts in Applied Sciences

Marco Fattore, Degree in Theoretical Physics, Ph. D in Statistics, Assistant Professor in Applied Statistics, Department of Statistics and Quantitative Methods, University of Milano-Bicocca. His main research interests pertain to mathematical structures in data analysis, with a particular focus on Partial Order Theory and the measurement of multidimensional poverty and inequality. He also works on Big Data analysis and applied multivariate statistics in socio-economics.Rainer Brüggemann has studied chemistry in the Ludwig-Maximilians University Munich (LMU) and received his PhD at LMU, in quantum chemistry.After a time as post doc working about spectroscopical issues he joined a group, performing risk assessment studies with respect to nuclear waste disposal sites (Technical University in Berlin). Position in the Helmholtz-Center Munich (former: GSF - National Research Center for Environment and Health). There he was one of the authors of the evaluation software code for chemicals "E4CHEM". Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Berlin. Together with Prof. Steinberg an award concerning their work in limnologyNow, retired, he is working mainly about partial order and its applications.

• Part I.Theoretical and methodological advances.- 1.Endowing posets with flesh: if, why and how?.- 2.Incomparability/inequality measures and clustering.- 3.Incomparable – what now, IV. Incomparabilities - a modeling challenge.- 4.Partial Ordering and Metrology Analyzing Analytical Performance.- 5.Functionals and synthetic indicators over finite posets.-6.Evaluation, considered as problem orientable mathematics over lattices.- 7.A combined lexicographic-average rank approach for evaluating uncertain multi-indicator matrices with risk metrics.- Part II.Partial Order Theory in socio-economic sciences.- 8.Peculiarities in multidimensional regional poverty.- 9.Application of Partial Order Theory to Multidimensional Poverty Analysis in Switzerland.- 10.Analysis of social participation: a multidimensional approach based on the theory of partial ordering.- 11.POSET analysis of panel data with POSAC.- 12.Partially Ordered SetTheory and Sen’s capability approach: a fruitful relationship.- Part III.Partial Order Theory in environmental sciences.- 13.Ranking Chemicals with Respect to Accidents Frequency.- 14.Formal Concept Analysis applications in chemistry: from radionuclides and molecular structure to toxicity and diagnosis.- 15.Partial Order Analysis of the government dependence of  the  Sustainable  Development  Performance  in Germany´s Federal States.- Part IV.New applications of Partial Order Theory.- 16.A matching problem, partial order and an analysis applying the Copeland index.- 17.Application of the Mixing Partial Order to Genes.- 18.Analysing ethnopharmacological data matrices on traditional uses of medicinal plants with the contribution of Partial Order Techniques.- Part V.Software developments.- 19.PARSEC: An R package for partial orders in socio-economics.- 20.PyHasse and cloud computing.div>