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This paper continues the series of publications about applications of partial ordering. The focus of this publication is the derivation of approximate analytical expressions for the averaged rank and the ranking probabilities. To derive such combinatorial formulas a local partial order is suggested as an approximation. The performance of the approximation is rather high; we therefore conclude that three very simple descriptors of the local partial order seem to be sufficient to get a rough impression of the linear order, induced by the averaged ranks and the ranking probabilities of empirical partially ordered sets. Linear order derived from the partial order, ranking probabilities, and other characteristics are considered as parts of a so-called "General Ranking Model" (GRM). Following the local partial order, the averaged rank of an object x can be estimated applying the following simple formula: Rk(av) = (S+1)*(N+1)/(N+1-U). S is the number of successors of the object x, N is the total number of objects (of the quotient set), and U is the number of objects incomparable with x. More complex formulas for the ranking probabilities are given in the text. A list of abbreviations and symbols can be found in Tables 3 and 4.

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This paper is dedicated to Prof. Paola Gramatica on the occasion of her retirement.Abstract: In March 2018 the term Novichok (HoSYhok) became publically known following an attempted murder of a former Russian spy in Salisbury, UK. Novichok is the name of a group of nerve agents secretly produced by Russia in the later stages of the Cold War. These compounds were never declared under the Chemical Weapons Convention and very little is known about the actual identity and characteristics of these compounds. Structures of some of the Novichoks have been reported by a former Russian chemist, Vil Mirzayanov, previously working at the Russian State Scientific Research Institute of Organic Chemistry and Technology (GOSNIIOKhT). It was in this context claimed that at least two compounds of the Novichok family, known as Novichok-5 and Novichok-7 were 5-8 times more potent than the hitherto most toxic nerve agent, VX. The present study elucidates, applying a series of QSAR models toxicity, skin permeation, pharmacokinetic aspects as well as the environmental fate of a series of Novichoks. Virtually the results from the different studies related to human health point in the same direction, i. e., the Novichoks are significantly less toxic than VX and the skin permeation much lower and less efficient than observed for VX. Hence, the claim by Mirzayanov could not be substantiated. Methods The Novichok FamilyNovichok (in Russian HoSYhok = newbie or newcomer) is the name for a group of compounds that are closely related [a] Prof.

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An alternative to the often cumbersome and time-consuming risk assessments of chemical substances could be more reliable and advanced priority setting methods. An elaboration of the simple scoring methods is provided by Hasse Diagram Technique (HDT) and/or Multi-Criteria Analysis (MCA). The present study provides an in depth evaluation of HDT relative to three MCA techniques. The new and main methodological step in the comparison is the use of probability concepts based on mathematical tools such as linear extensions of partially ordered sets and Monte Carlo simulations. A data set consisting of 12 High Production Volume Chemicals (HPVCs) is used for illustration. It is a paradigm in this investigation to claim that the need of external input (often subjective weightings of criteria) should be minimized and that the transparency should be maximized in any multicriteria prioritisation. The study illustrates that the Hasse diagram technique (HDT) needs least external input, is most transparent and is least subjective. However, HDT has some weaknesses if there are criteria which exclude each other. Then weighting is needed. Multi-Criteria Analysis (i.e. Utility Function approach, PROMETHEE and concordance analysis) can deal with such mutual exclusions because their formalisms to quantify preferences allow participation e.g. weighting of criteria. Consequently MCA include more subjectivity and loose transparency. The recommendation which arises from this study is that the first step in decision making is to run HDT and as the second step possibly is to run one of the MCA algorithms.