Brüggemann / Carlsen Partial Order in Environmental Sciences and Chemistry

1. Auflage 2006
ISBN: 978-3-540-33970-0
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 406 Seiten

This book explains the theory and practice of order relations in such a way that no specific mathematical skill is needed to understand the advantages of this algebraization. It acts as a primer in a mathematical technique which is useful in many expanding disciplines, like genomics, techniques of decision support, and sustainability. This book is recommended to those who are interested in the interface between sciences and management.

Rainer Brüggemann studied chemistry at the Ludwig-Maximilians University, Munich. He received his PhD in 1977. He joined a research group in 1980 at the Technical University of Berlin. 1984 saw him move to the GSF - National Research Center for Environment and Health in Neuherberg near Munich. Since 1996 he is senior scientist at the Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Berlin.

Lars Carlsen studied chemistry at the University in Copenhagen. He received his PhD in 1977 and his DSc in 1989. In 1991 he joined the National Environmental Research Institute in Denmark as Director of the Department of Environmental Chemistry. Since 1999 he has been an assigned professor in environmental chemistry at the Roskilde University, Denmark, and in 2000 he founded his own consultancy, 'Awareness Center'.

Autoren/Hrsg.

Brüggemann, Rainer

Carlsen, Lars

Inhaltsverzeichnis

1;Preface;5
2;Contents;8
3;List of Contributors;10
4;1 Chemistry and Partial Order;14
4.1;Partial Ordering of Properties: The Young Diagram Lattice and Related Chemical Systems;15
4.1.1;Abstract;15
4.1.2;The Basic Terms: Examples of Posets, The Hasse Diagram;15
4.1.3;Some Posets of Chemical Interest;19
4.1.4;The Young-Diagram Lattice, Ordering of Muirhead and generalization of Karamata;25
4.1.5;Ordering of Tree graphs;27
4.1.6;Grid Graphs Based on Molecular Path Codes of Lengths 2 and 3: Relation to Ordering of Young Diagrams;35
4.1.7;References;36
4.2;Hasse Diagrams and their Relation to Molecular Periodicity;39
4.2.1;Abstract;39
4.2.2;Individual molecules;39
4.2.3;Inorganic molecules;40
4.2.4;Organic molecules;42
4.2.5;References;44
4.3;Directed Reaction Graphs as Posets;46
4.3.1;Abstract;46
4.3.2;Introduction;46
4.3.3;Posetic Substitution Reaction Networks & Chemical Structure;48
4.3.4;Molecular Properties & the Reaction Poset;52
4.3.5;Molecular Property Interpolation;58
4.3.6;General Discussion;61
4.3.7;Prognosis;65
4.3.8;References;66
5;2 Environmental Chemistry and Systems;69
5.1;Introduction to partial order theory exemplified by the Evaluation of Sampling Sites;70
5.1.1;Abstract;70
5.1.2;Introduction;71
5.1.3;Overview;71
5.1.4;Partial order;72
5.1.5;Introductory remarks;72
5.1.6;The rationale of using Hasse diagrams;74
5.1.7;Prerequisites;76
5.1.8;Graphs and Hasse diagrams;77
5.1.9;Simple elements of interpreting a Hasse diagram;87
5.1.10;Characterizing a Hasse diagram as a whole;90
5.1.11;Sensitivity study;100
5.1.12;Evaluation of Sampling Sites;103
5.1.13;Discussion and Conclusion;114
5.1.14;References;116
5.2;Comparative Evaluation and Analysis of Water Sediment Data;120
5.2.1;Abstract;120
5.2.2;Results;123
5.2.3;Summary and Conclusions;156
5.2.4;Appendix;158
5.2.5;References;160
5.3;Prioritizing PBT Substances;161
5.3.1;Abstract;161
5.3.2;Introduction;161
5.3.3;Materials and Methods;162
5.3.4;Substances studied;162
5.3.5;QSARs;165
5.3.6;Partial Order Ranking;165
5.3.7;Results;166
5.3.8;Discussion;166
5.3.9;Conclusions;167
5.3.10;References;167
6;3 Quantitative Structure Activity Relationships;169
6.1;Interpolation Schemes in QSAR;170
6.1.1;Abstract;170
6.1.2;Introduction;170
6.1.3;Methods;171
6.1.4;Partial Order based QSARs;176
6.1.5;Giving molecules an identity;179
6.1.6;Conclusions and Outlook;184
6.1.7;References;185
6.2;New QSAR Modelling Approach Based on Ranking Models by Genetic Algorithms - Variable Subset Selection ( GA- VSS);187
6.2.1;Abstract;187
6.2.2;Introduction;188
6.2.3;Theory;189
6.2.4;Partial order ranking QSAR model for similarly acting phenylurea herbicides;208
6.2.5;Conclusions;218
6.2.6;References;219
7;4 Decision support;224
7.1;Aspects of Decision Support in Water Management: Data based evaluation compared with expectations;225
7.1.1;Abstract;225
7.1.2;Introduction;226
7.1.3;Methods;227
7.1.4;Evaluation Results;233
7.1.5;Discussion;235
7.1.6;Conclusions and Prospect;238
7.1.7;Acknowledgements;239
7.1.8;References;239
7.2;A Comparison of Partial Order Technique with Three Methods of Multi- Criteria Analysis for Ranking of Chemical Substance;241
7.2.1;Abstract;241
7.2.2;Introduction;242
7.2.3;Survey of the Ranking Methods;243
7.2.4;Data;247
7.2.5;The Hasse Diagram;248
7.2.6;Results of Multi-Criteria Analysis;251
7.2.7;Discussion;254
7.2.8;Conclusion;258
7.2.9;References;259
8;5 Field, Monitoring and Information;261
8.1;Developing decision support based on field data and partial order theory;263
8.1.1;Abstract;263
8.1.2;Introduction;264
8.1.3;Data background for illustration;265
8.1.4;Correlation analysis;266
8.1.5;References;286
8.2;Evaluation of Biomonitoring Data;288
8.2.1;Abstract;288
8.2.2;Introduction;288
8.2.3;The German Environmental Specimen Bank;289
8.2.4;Evaluation Methods;291
8.2.5;The Data Set;297
8.2.6;Hasse Diagrams or POSETs;299
8.2.7;Conclusions and Outlook;307
8.2.8;References;309
8.3;Exploring Patterns of Habitat Diversity Across Landscapes Using Partial Ordering;311
8.3.1;Abstract;311
8.3.2;Introduction;312
8.3.3;Pennsylvania Biodiversity Context;313
8.3.4;Progression of partial and incomplete orderings;315
8.3.5;Rank range runs;317
8.3.6;Rank range end-member elimination effect;325
8.3.7;Second order analysis;326
8.3.8;References;327
8.4;Information Systems and Databases;328
8.4.1;Abstract;328
8.4.2;Environmental Data, Databases and Information Systems;329
8.4.3;Selection of Databases (Objects) and Parameters and Chemicals ( Attributes);330
8.4.4;Environmetrical and Chemometrical Methods Used;333
8.4.5;Application of Evaluation Methods to Data-Matrix;338
8.4.6;Discussion and Conclusion;349
8.4.7;References;350
9;6 Rules and Complexity;353
9.1;Contexts, Concepts, Implications and Hypotheses;355
9.1.1;Abstract;355
9.1.2;Contexts and their concepts;355
9.1.3;Implications;358
9.1.4;References;365
9.2;Partial Orders and Complexity: The Young Diagram Lattice;366
9.2.1;Abstract;366
9.2.2;Introduction;366
9.2.3;Mixing;367
9.2.4;Complexity;369
9.2.5;Entropy;371
9.2.6;Complexity;371
9.2.7;Complexity and the Young Diagram Lattice;372
9.2.8;YDL Examples;376
9.2.9;Complexity Metaphor – Other Posets and Beyond;378
9.2.10;Conclusion;380
9.2.11;References;381
10;7 Historical remarks;382
10.1;Hasse Diagrams and Software Development;383
10.1.1;Abstract;383
10.1.2;Historical notes concerning the development of WHASSE;383
10.1.3;Helmut Hasse;384
10.1.4;Rationale on the use of partial order;384
10.1.5;Model order estimation;385
10.1.6;Quantification of fate and impact of contaminants;385
10.1.7;Development of software;386
10.1.8;References;389
10.2;Introductory References;391
10.2.1;Posets (books);391
10.2.2;Posets as tools for data exploration;391
10.2.3;Posets as tools to chemical investigations;393
10.2.4;Posets and Multicriteria Decision Analysis;394
10.2.5;Posets and Linear extensions;394
10.2.6;Posac;395
10.2.7;Formal Concept Analysis;395
11;Index;397