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Directed Reaction Graphs as Posets

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Partial Order in Environmental Sciences and Chemistry

Abstract

Reaction diagrams are considered especially for the circumstance of progressive substitution (or addition) on a fixed molecular skeleton, and it is noted that these naturally form Hasse diagrams for a partially ordered set (or poset) of the substituted structures. The possibility that different properties are similarly ordered is a further natural consideration, and is here illustrated for several different properties for (methyl & chloro) substituted benzenes.

This posetic approach thence provides a novel approach to structure/ property and structure/bioactivity correlations, with focus in some sense beyond simple molecular structure, in that this approach attends to how a structure fits into a systematic (reaction) network of structures. Different manners for fitting and prediction of properties are noted, with illustration of an especially simple “poset-average” scheme. Some numerical evidence indicates that such approaches are quite reasonable. It is emphasized that such directed reaction graphs admitting posetic treatment are widespread.

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Authors and Affiliations

  1. Texas A&M University @ Galveston, Galveston, Texas, 77553-1675

    D. J. Klein & T. Ivanciuc

Authors
  1. D. J. Klein
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  2. T. Ivanciuc
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Editors and Affiliations

  1. Dept. Ecohydrology, Leibniz Institute of Freshwater Ecology and Inland Fisheries, Müggelseedamm 310, 12587, Berlin-Friedrichshagen, Germany

    Rainer Brüggemann

  2. Awareness-Center, Hyldeholm 4, 4000, Roskilde-Veddelev, Denmark

    Lars Carlsen

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Klein, D.J., Ivanciuc, T. (2006). Directed Reaction Graphs as Posets. In: Brüggemann, R., Carlsen, L. (eds) Partial Order in Environmental Sciences and Chemistry. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-33970-1_3

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