Partial Order in Environmental Sciences and Chemistry

Preface

Contents

List of Contributors

1 Chemistry and Partial Order

Partial Ordering of Properties: The Young Diagram Lattice and Related Chemical Systems

Abstract

The Basic Terms: Examples of Posets, The Hasse Diagram

Some Posets of Chemical Interest

The Young-Diagram Lattice, Ordering of Muirhead and generalization of Karamata

Ordering of Tree graphs

Grid Graphs Based on Molecular Path Codes of Lengths 2 and 3: Relation to Ordering of Young Diagrams

References

Hasse Diagrams and their Relation to Molecular Periodicity

Abstract

Individual molecules

Inorganic molecules

Organic molecules

References

Directed Reaction Graphs as Posets

Abstract

Introduction

Posetic Substitution Reaction Networks & Chemical Structure

Molecular Properties & the Reaction Poset

Molecular Property Interpolation

General Discussion

Prognosis

References

2 Environmental Chemistry and Systems

Introduction to partial order theory exemplified by the Evaluation of Sampling Sites

Abstract

Introduction

Overview

Partial order

Introductory remarks

The rationale of using Hasse diagrams

Prerequisites

Graphs and Hasse diagrams

Simple elements of interpreting a Hasse diagram

Characterizing a Hasse diagram as a whole

Sensitivity study

Evaluation of Sampling Sites

Discussion and Conclusion

References

Comparative Evaluation and Analysis of Water Sediment Data

Abstract

Results

Summary and Conclusions

Appendix

References

Prioritizing PBT Substances

Abstract

Introduction

Materials and Methods

Substances studied

QSARs

Partial Order Ranking

Results

Discussion

Conclusions

References

3 Quantitative Structure Activity Relationships

Interpolation Schemes in QSAR

Abstract

Introduction

Methods

Partial Order based QSARs

Giving molecules an identity

Conclusions and Outlook

References

New QSAR Modelling Approach Based on Ranking Models by Genetic Algorithms - Variable Subset Selection ( GA- VSS)

Abstract

Introduction

Theory

Partial order ranking QSAR model for similarly acting phenylurea herbicides

Conclusions

References

4 Decision support

Aspects of Decision Support in Water Management: Data based evaluation compared with expectations

Abstract

Introduction

Methods

Evaluation Results

Discussion

Conclusions and Prospect

Acknowledgements

References

A Comparison of Partial Order Technique with Three Methods of Multi- Criteria Analysis for Ranking of Chemical Substance

Abstract

Introduction

Survey of the Ranking Methods

Data

The Hasse Diagram

Results of Multi-Criteria Analysis

Discussion

Conclusion

References

5 Field, Monitoring and Information

Developing decision support based on field data and partial order theory

Abstract

Introduction

Data background for illustration

Correlation analysis

References

Evaluation of Biomonitoring Data

Abstract

Introduction

The German Environmental Specimen Bank

Evaluation Methods

The Data Set

Hasse Diagrams or POSETs

Conclusions and Outlook

References

Exploring Patterns of Habitat Diversity Across Landscapes Using Partial Ordering

Abstract

Introduction

Pennsylvania Biodiversity Context

Progression of partial and incomplete orderings

Rank range runs

Rank range end-member elimination effect

Second order analysis

References

Information Systems and Databases

Abstract

Environmental Data, Databases and Information Systems

Selection of Databases (Objects) and Parameters and Chemicals ( Attributes)

Environmetrical and Chemometrical Methods Used

Application of Evaluation Methods to Data-Matrix

Discussion and Conclusion

References

6 Rules and Complexity

Contexts, Concepts, Implications and Hypotheses

Abstract

Contexts and their concepts

Implications

References

Partial Orders and Complexity: The Young Diagram Lattice

Abstract

Introduction

Mixing

Complexity

Entropy

Complexity

Complexity and the Young Diagram Lattice

YDL Examples

Complexity Metaphor – Other Posets and Beyond

Conclusion

References

7 Historical remarks

Hasse Diagrams and Software Development

Abstract

Historical notes concerning the development of WHASSE

Helmut Hasse

Rationale on the use of partial order

Model order estimation

Quantification of fate and impact of contaminants

Development of software

References

Introductory References

Posets (books)

Posets as tools for data exploration

Posets as tools to chemical investigations

Posets and Multicriteria Decision Analysis

Posets and Linear extensions

Posac

Formal Concept Analysis

Index