Partial Order in Environmental Chemistry.

BACKGROUND: The theory of partial order is a branch of Discrete Mathematics and is often seen as pretty esoteric. However, depending on a suitable definition of an order relation, partial order theory has some statistical flavor. Here we introduce the application of partial order for environmental chemistry. OBJECTIVE: We showed that partial order is an instrument, which at the same time, has both data exploration - and evaluation potency. METHODS: The partial order theory was applied in this study. It depends on four indicators which describe the environmental hazards of chemicals. RESULTS: Nineteen organic chemicals were found within a monitoring study in the German river Main and were taken as an exemplary case. The results indicated that chemicals can have a high risk on the environment, however, the type of risk is different and should not conceptually merge into a single quantity. CONCLUSION: Partial order theory is of help to define different regulations and environmental management plans.

Assessing and Grouping Chemicals Applying Partial Ordering Alkyl Anilines as an Illustrative Example.

AIM AND OBJECTIVE: In chemistry, there is a long tradition in classification. Usually, methods are adopted from the wide field of cluster analysis. The present study focusses on the application of partial ordering methodology for the classification of 21 alkyl substituted anilines. MATERIALS AND METHODS: The analyses are based on the concepts from partial order methodology and cluster analyses. Here, with the example of 21 alkyl anilines, we show that concepts taken out from the mathematical discipline of partially ordered sets may be applied for classification. The chemical compounds are described by a multi-indicator system. For the present study four indicators, mainly taken from the field of environmental chemistry were applied and a graph of the ordering (Hasse diagram) was constructed. RESULTS: A Hasse diagram is an acyclic, transitively reduced, triangle-free graph that may have several graph-theoretical components. The Hasse diagram has been directed from a structural chemical point of view. Two cluster analysis methods are applied (K-means and a hierarchical cluster method) and compared with the results from the Hasse diagram. In both cases, the partitioning of the set of 21 compounds by the component structure of the Hasse diagram appears to be better interpretable. CONCLUSION: It is shown that the partial ordering approach indeed can be used for classification in the present case. However, it must be clearly stated that a guarantee for meaningful results, in general, cannot be given. For that, further theoretical work is needed.

Use of partial order in environmental pollution studies demonstrated by urban BTEX air pollution in 20 major cities worldwide.

Urban air pollution with benzene, toluene, ethyl benzene and xylenes (BTEX) is a common phenomenon in major cities where the pollution mainly originates from traffic as well as from residential heating. An attempt to rank cities according to their BTEX air pollution is not necessarily straight forward as we are faced with several individual pollutants simultaneously. A typical procedure is based on aggregation of data for the single compounds, a process that not only hides important information but is also subject to compensation effects. The present study applies a series of partial ordering tools to circumvent the aggregation. Based on partial ordering, most important indicators are disclosed, and an average ranking of the cities included in the study is derived. Since air pollution measurements are often subject to significant uncertainties, special attention has been given to the possible effect of uncertainty and/or data noise. Finally, the effect of introducing weight regimes is studied. In a concluding section the gross national income per person (GNI) is brought into play, demonstrating a positive correlation between BTEX air pollution and GNI. The results are discussed in terms of the ability/willingness to combat air pollution in the cities studied. The present study focuses on Almaty, the largest city in Kazakhstan and compares the data from Almaty to another 19 major cities around the world. It is found that the benzene for Almaty appears peculiar high. Overall Almaty appears ranked as the 8th most BTEX polluted city among the 20 cities included in the study.

Evaluation of analytical performance based on partial order methodology.

Classical measurements of performances are typically based on linear scales. However, in analytical chemistry a simple scale may be not sufficient to analyze the analytical performance appropriately. Here partial order methodology can be helpful. Within the context described here, partial order analysis can be seen as an ordinal analysis of data matrices, especially to simplify the relative comparisons of objects due to their data profile (the ordered set of values an object have). Hence, partial order methodology offers a unique possibility to evaluate analytical performance. In the present data as, e.g., provided by the laboratories through interlaboratory comparisons or proficiency testings is used as an illustrative example. However, the presented scheme is likewise applicable for comparison of analytical methods or simply as a tool for optimization of an analytical method. The methodology can be applied without presumptions or pretreatment of the analytical data provided in order to evaluate the analytical performance taking into account all indicators simultaneously and thus elucidating a "distance" from the true value. In the present illustrative example it is assumed that the laboratories analyze a given sample several times and subsequently report the mean value, the standard deviation and the skewness, which simultaneously are used for the evaluation of the analytical performance. The analyses lead to information concerning (1) a partial ordering of the laboratories, subsequently, (2) a "distance" to the Reference laboratory and (3) a classification due to the concept of "peculiar points".

CombiSimilarity, an innovative method to compare environmental and health data sets with different attribute sizes example: eighteen Organochlorine Pesticides in soil and human breast milk samples.

Human health and the health of the environment have entwined. In this paper we underpin this position by presenting a modeling approach named CombiSimilarity, which has been developed by the first author in the software tool PyHasse comprising a wide variety of partial ordering tools. A case study of 18 Organochlorine Pesticides (OCPs) detected in soil as well as in human breast milk samples in the Taurus Mountains in Turkey is carried out. Seven soil samples and 44 breast milk samples were measured. We seek to answer the question whether the contamination pattern in breast milk is associated with the contamination pattern in soil by studying the mutual quantitative relationships of the chemicals involved. We could demonstrate that there is a similarity with respect to the concentration profiles between the soil and breast milk pollution. Therefore the hypothesis may be formulated that the concentrations of chemicals in the milk samples are strongly related to the soil contamination. This supports the concept that soil could be a surrogate for human exposure at background locations.

Discrete mathematical data analysis approach: a valuable assessment method for sustainable chemistry.

Sustainable/Green Chemistry is a chemical philosophy encouraging the design of products and processes that reduce or eliminate the use and generation of hazardous substances. In this respect, metrical scientific disciplines like Chemometrics are important, because they indicate criteria for chemicals being hazardous or not. We demonstrated that sustainable principles in the disciplines Green Chemistry, Green Engineering, and Sustainability in Information Technology have main aspects in common. The use of non-hazardous chemicals or the more efficient use of chemical substances is one of these aspects. We take a closer look on the topic of the hazards of chemical substances. Our research focuses on data analyses concerning environmental chemicals named Persistent Organic Pollutants (POPs), which are found all over the world and pose a large risk to environment as well as to humans. The evaluation of the data is a major step in the elucidation of the danger of these chemicals. The data analysis method demonstrated here, is based on the theory of partially ordered sets and provides a generalized ranking. In our approach we investigate data sets of breast milk samples of women in Denmark, Finland, and Turkey which contained measurable levels of 20 POPs. The goal is twofold: On the one side the hazardous chemicals are to be identified and on the other side possible differences among the three nations should be detected, because in that case possible different uptake mechanisms may be supposed. The data analysis is performed by the free available software package PyHasse, written by the third author. We conclude that the data analysis method can well be applied for distinguishing between more or less dangerous existing chemicals. Furthermore, it should be used in sustainable chemistry in the same manner for detecting more and less sustainable chemicals.

Evaluation of organochlorine pesticides in breast milk samples in Turkey applying features of the partial order technique.

Exposure data to organochlorine pesticides (OCPs) of mothers' breast milk samples were measured in different locations in the Taurus Mountains/Turkey. Villages at five altitudes were looked upon. The data analysis method applied is the Hasse diagram technique, based on Discrete Mathematics. For each of the five regions, one Hasse diagram was calculated and showed the same maximal object, namely, p-p'-Dichlorodiphenyldichloroethane (DDE). In a further data investigation step, we performed the similarity analyses of the locations in order to quantify the similarities and incomparabilities. It was revealed that no correlation exists between most altitudes and the pattern of contamination of breast milk samples. The two lowest situated areas, Sahil at sea level and Ciftlikköy at 121 m above sea level were similar. We reduced the datasets by applying the interval analysis followed by similarity analyses. We observed that endrin (END1), mirex (MIRE), and pentachlorobenzene (PECB) reduce most severely the similarity.

Multi-criteria decision analyses. Viewing MCDA in terms of both process and aggregation methods: some thoughts, motivated by the paper of Huang, Keisler and Linkov.

The paper of Huang, Keisler and Linkov (HKL) (Huang et al., 2011) has motivated us to this note about the relation between ranking procedures and Multi-Criteria Decision Analysis (MCDA) tools. The key concept in the HKL-paper is in our eyes the 'trade-off'. A 'trade-off' seems necessary, when conflicting indicator values are present. HKL stress that the general application of MCDA is hampered by different terminology. We do not claim to have a solution for that problem. Nevertheless, we think that the discussion is worthwhile and this note presents some of our ideas, which basically imply the need of a broadening of the definition of MCDA.

Partially ordered sets: ranking and prediction of substances' properties.

There are at least two significant applications of partial order theory in chemistry: Ranking methods and substances' properties prediction. In both cases, a set of objects is endowed with a partial order relation e.g. "more polluting than", "can be obtained from", "more reactive than" etc. The couple of set and partial order relation is known in mathematics as a partially ordered set (poset). Ranking methods, such as the Hasse diagram technique, lead to a partial order where several incomparabilities (lack of order) appear between pairs of objects. This phenomenon is quite common in ranking studies, and it often is circumvented by a combination of object features leading to a total order. However, such a combination introduces subjectivities and bias in the ranking process. Here a step-by-step procedure is shown to turn incomparabilities into comparabilities taking into account all the possible bias by a linear combination of features. In such a manner, it is possible to predict how probable it is to obtain a particular total order from a given poset. Similarly, it is possible to calculate the needed bias over certain attributes to obtain a particular total order. An example application is shown where substances are ranked according to their bioconcentration factor and biodegradation potential. Another application of partial order theory to chemistry has to do with the prediction of properties for a set of substances related in a (preferably systematic) chemical fashion. A customary relation is "can be obtained from"; if such a relation is set up for a given molecular structure e.g. benzene, and all its substituted derivatives (say chlorinated ones) are considered, then the set of benzene and its chlorinated derivatives are partially ordered. Taking advantage of the poset generated, different methods can be applied to predict properties of the substances considered in the poset. Such methods include the poset-average, cluster expansion, and splinoid methods. In this paper we discuss each one of these methods, its advantages and disadvantages and we outline its applicability to estimate cooperative free energies of hemoglobins with different degree of oxygenation.

Influence of altitude concerning the contamination of humus soils in the German Alps: a data evaluation approach using PyHasse.

BACKGROUND, AIM AND SCOPE: In an international project named MONARPOP (Monitoring Network in the Alpine Region for Persistent and other Organic Pollutants), selected chemicals in different environmental media were analysed in the years 2004 and 2005. Seventeen pesticides were chosen and analysed in humus and mineral soil in the German Alps. The samples were taken at different altitudes. MATERIALS AND METHODS: In such a rather complex environmental datasets, it is often necessary to compare different sets of criteria and their influence on rankings. In the similarity analysis which is part of the theory of the Hasse diagram technique, we intend to calculate the similarity of different rankings. Furthermore, we perform a so-called dominance-dominance/dominance-separability method, followed by a sensitivity analysis, both subroutines in the newly developed PyHasse programme in order to find out if the concentration of the chemicals can be related to the altitudes at which the samples were taken. RESULTS AND DISCUSSION: It can be demonstrated that the altitude has a considerable influence on the concentration of some organic chemicals in humus: The concentrations of some chemicals increase with the altitude. This increase shows certain irregularities for which several explication attempts including possible effects of atmospheric stratification phenomena in valleys have been made. CONCLUSION: These results should be complemented in further studies with MONARPOP monitoring data from other Alpine countries, e.g. Austria, Switzerland, Italy and Slovenia.

Ranking of pharmaceuticals detected in the environment: aggregation and weighting procedures.

Pharmaceuticals are omnipresent in waste-water world-wide. Research has shown that many pharmaceuticals are not completely removed during wastewater treatment, and as a result, this has led to their occurrence being reported in waste water treatment plant effluents, rivers and lakes, and more rarely in groundwater and in drinking water. Hence, it is only logical that pharmaceutical residues in the environment and their potential toxic effects have been recognized as one of the emerging research areas in environmental chemistry. A lack of data, especially ecotoxicological and fate data on pharmaceuticals, is evident. The extent to which data are missing should therefore be looked upon in more detail in order to trigger further political steps in performing studies concerning the risk assessment of pharmaceuticals in the environment. In this investigation, we evaluate the data-availability of 16 pharmaceuticals in 17 Internet databases which means we examine a 16 (objects) x 17 (attributes) data-matrix. The consideration of the chosen pharmaceutical in databases is coded 0 = not available, or 1 = available. For the evaluation of the data-matrix, we apply the multi-criteria decision method named METEOR (Method of Evaluation by Order Theory). In contrast to conventional multi-criteria decision aids, like the well-known PROMETHEE, AHP, SMART, ORESTE as well as different versions of ELECTRE, we support the basic consideration of environmetrics: let first the data speak and let us then include subjective preferences in order to get a unique decision. The basis of METEOR is a data-matrix in which the objects are characterized by a set of attributes (indicators). By means of the attributes, a partial order is derived. In the subsequent steps, attributes are aggregated by a weighting procedure, allowing a high degree of involvement of experts, stakeholders and other participants. All conducted approaches show that the data-situation on the chosen test-set of 16 well-known and highly produced pharmaceuticals is far from being satisfactory. For the two well-known pharmaceuticals roxithomycin (antibiotic) and diatrizoate (contrast media), the data-situation is extremely bad, independent of how the weighting is performed. The data-availability for diatrizoate is a little better. The best data coverage is detected for the chemicals carbamazepine, diazepam, ethinyl estradiol, 5-fluorouracil, and phenazone. The issue of pharmaceuticals in the environment and the unavailability of data necessitate much closer communication between science and medical healthcare and politicians in the future.

Partial order in chemistry.

In chemistry, there is broad use of graphs and graph-theoretical invariants derived from them. Less known are directed graphs, as e.g., motivated in reaction networks. Here, the focus is on directed graphs derived from order theory. General approaches based on the structure of molecules as well as those derived from multivariate aspects in evaluation are discussed.

A hitchhiker's guide to poset ranking.

When ranking objects (like chemicals, geographical sites, river sections, etc.) by multicriteria analysis, it is in most cases controversial and difficult to find a common scale among the criteria of concern. Therefore, ideally, one should not resort to such artificial additional constraints. The theory of partially ordered sets (or posets for short) provides a solid formal framework for the ranking of objects without assigning a common scale and/or weights to the criteria, and therefore constitutes a valuable alternative to traditional approaches. In this paper, we aim to give a comprehensive literature review on the topic. First we formalize the problem of ranking objects according to some predefined criteria. In this theoretical framework, we focus on several algorithms and illustrate them on a toy example. To conclude, a more realistic real-world application shows the power of some of the algorithms considered in this paper.

Basic principles of Hasse diagram technique in chemistry.

Principles of partial order applied to ranking are explained. The Hasse diagram technique (HDT) is the application of partial order theory based on a data matrix. In this paper, HDT is introduced in a stepwise procedure, and some elementary theorems are exemplified. The focus is to show how the multivariate character of a data matrix is realized by HDT and in which cases one should apply other mathematical or statistical methods. Many simple examples illustrate the basic theoretical ideas. Finally, it is shown that HDT is a useful alternative for the evaluation of antifouling agents, which was originally performed by amoeba diagrams.

Ranking of refrigerants.

Environmental ranking of refrigerants is of need in many instances. The aim is to assess the relative environmental hazard posed by 40 refrigerants, including those used in the past, those presently used, and some proposed substitutes. Ranking is based upon ozone depletion potential, global warming potential, and atmospheric lifetime and is achieved by applying the Hasse diagram technique, a mathematical method that allows us to assess order relationships of chemicals. The refrigerants are divided into 13 classes, of which the chlorofluorocarbons, hydrofluorocarbons, hydrochlorofluorocarbons, hydrofluoroethers, and hydrocarbons contain the largest number of single substances. The dominance degree, a method for measuring order relationships among classes, is discussed and applied to the 13 refrigerant classes. The results show that some hydrofluoroethers are as problematic as the hydrofluorocarbons. Hydrocarbons and ammonia are the least problematic refrigerants with respect to the three environmental properties.

Ecological scenarios analyzed and evaluated by a shallow lake model.

We applied the complex ecosystem model EMMO, which was adopted to the shallow lake Müggelsee (Germany), in order to evaluate a large set of ecological scenarios. By means of EMMO, 33 scenarios and 17 indicators were defined to characterize their effects on the lake ecosystem. The indicators were based on model outputs of EMMO and can be separated into biological indicators, such as chlorophyll-a and cyanobacteria, and hydro-chemical indicators, such as phosphorus. The question to be solved was, what is the ranking of the scenarios based on their characterization by these 17 indicators? And how can we handle high quantities of complex data within evaluation procedures? The scenario evaluation was performed by partial order theory which, however, did not provide a clear result. By subsequently applying the hierarchical cluster analysis (complete linkage) it was possible to reduce the data matrix to indicator and scenario representatives. Even though this step implies losses of information, it simplifies the application of partial order theory and the post processing by METEOR. METEOR is derived from partial order theory and allows the stepwise aggregation of indicators, which subsequently leads to a distinct and clear decision. In the final evaluation result the best scenario was the one which defines a minimum nutrient input and no phosphorus release from the sediment while the worst scenario is characterized by a maximum nutrient input and extensive phosphorus release from the sediment. The reasonable and comprehensive results show that the combination of partial order, cluster analysis and METEOR can handle big amounts of data in a very clear and transparent way, and therefore is ideal in the context of complex ecosystem models, like that we applied.

The dualistic approach of FCA: a further insight into Ontario Lake sediments.

The investigation of object-by-attribute matrices is very common in statistics and data analysis with the aim of uncovering every possible relationship among objects and/or attributes. Formal Concept Analysis (FCA) is a method, which stems directly from partial order and lattice theory, which provides an efficient tool to symmetrically uncover linkages among objects and attributes whenever a relation stands among the two sets. It provides efficacious graphical representation and computes association rules between attributes, thus helping in the detection of possible synergism or antagonism of attributes. In this paper, FCA potentialities are discussed and described by means of a case study already investigated by other partial order techniques: the case of Lake Ontario sediment samples. Data derive from a 'test battery' for a simultaneous analysis of degradation of Lake Ontario samples, which are basically of two typologies: hygienic and toxicity tests. A multi-valued approach is adopted to cope with the ordinal feature of data. Results highlight interesting interaction among hygienic compounds and a synergism between the two toxicity tests.

Climate change affects timing and size of populations of an invasive cyanobacterium in temperate regions.

Cylindrospermopsis raciborskii, an invasive freshwater cyanobacterium, originated from the tropics but has spread to temperate zones over the last few decades. Its northernmost populations in Europe occur in North German lakes. How such dramatic changes in its biogeography are possible and how its population dynamics in the newly invaded habitats are regulated are still unexplained. We therefore conducted a long-term (1993-2005) study of two German lakes to elucidate the mechanisms behind C. raciborskii population dynamics and to identify the abiotic constraints on its development. Our data revealed that pelagic populations of C. raciborskii thrived for three months during the summer, contributing up to 23% of the total cyanobacteria biovolume. Population sizes varied greatly between years without exhibiting any distinct long-term trends. In the annual lifecycle, C. raciborskii filaments emerged in the pelagic habitat when the temperature rose above 15-17 degrees C. At that time, mean photosynthetically active radiation in the mixed water column (I (mix)) overstepped its maximum. Rates of population net increase were highest at the beginning of the season (0.15-0.28 day(-1)), declined continuously over time, and were significantly positively correlated with I (mix). This indicates that the onset of the pelagic population is temperature-mediated and that I (mix) controls its growth. Since I (mix) peaks before the population onset, the time of germination is of crucial importance for successful development. To test this hypothesis, we designed a model to simulate pelagic population size, starting at different dates in the annual cycle. Moving the population onset forward by 30 days resulted in a doubling of the population size. We therefore conclude that an earlier rise in water temperature associated with climate change has promoted the spread of C. raciborskii to the temperate zone. Earlier warming permits earlier germination, thereby shifting the pelagic populations to a phase with higher I (mix), which advances growth and the population establishment.

Structure-fate relationships of organic chemicals derived from the software packages E4CHEM and WHASSE.

A risk assessment of chemicals is to be performed on the basis of the model EUSES, developed by the Commission of the European Union. The model package E4CHEM (Exposure Estimation for Potentially Ecotoxic Environmental Chemicals), developed in 1984-1992, is presented and applied in this paper as a model which allows a model-supported evaluation of chemicals. E4CHEM consequently does not have the wide applicability and technical comfort of the more recently developed model EUSES. The simulation models of E4CHEM characterize the chemical behavior in the environment by many aspects. Hence, there is a need to condense all of these aspects to get a clear impression of what will be the fate of the chemicals. Starting with the already published concept of exposure maps, we will discuss how partial orders may be helpful in establishing generalized structure-fate relationships. The software WHASSE is applied.

Aspects of decision support in water management--example Berlin and Potsdam (Germany) II--improvement of management strategies.

Methods related to partial order theory such as the Hasse diagram technique (HDT) are increasingly used in the field of multi-criteria decision support. The HDT has the advantage of being a transparent evaluation tool, supported by several data analysis tools such as the concept of antagonistic indicators. However, the evaluation usually does not lead to a clear decision, because more than one possible solution is offered. In the example presented here, three of the nine water management strategies (scenarios) evaluated by HDT were identified as winners. However, these strategies were not comparable with each other because of the conflicting evaluation of at least two different indicators. Such antagonisms describe the advantage and disadvantage of each scenario. Based on this background information, a new innovative approach is demonstrated, enabling the stakeholders to design new, modified management strategies, with reduced negative effects. After improvement of the three potential solutions, one clear winner scenario could be identified.