Brüggemann / Carlsen Partial Order in Environmental Sciences and Chemistry

1. Auflage 2006
ISBN: 978-3-540-33970-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 406 Seiten

When you edit a book, the editors should ask themselves, why are we - ing this and whom are we doing this for? To whom could this book be valuable as a source of information and possibly inspiration and of course are there other books with similar topics on the market? Indeed the mat- matical structure 'partial order' is explained in many mathematical te- books, which require different degrees of mathematical skills to comp- hend. Thus, as far as we can tell, all these books are dedicated directly towards mathematician working in the area of Discrete Mathematics and Theoretical Informatics. Although partial order is very well known in quantum mechanics, especially within the context of Young-diagrams, l- erature stressing the application aspect of partial order seems to be not available. However, an increasing number of publications in scientific journals have in recent years appeared, applying partial order to various fields of chemistry and environmental sciences. A recent summary can be found in a special issue of the journal Match - Commun. Math. Comput. Chem. 2000, edited by Klein and Brickmann. However, we believe that this journal possibly is too specific and as such it may not reach scientists actually applying partial order in various fields of research. Hence, we dared to initiate the editing of this book in order to address a broader au- ence and we were happy to convincing distinguished scientists working with different aspects of partial order theory to contribute to this book.

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