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Partial Order in Environmental Sciences and Chemistry

von: Rainer Brüggemann, Lars Carlsen

Springer-Verlag, 2006

ISBN: 9783540339700 , 406 Seiten

Format: PDF, OL

Kopierschutz: Wasserzeichen

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Partial Order in Environmental Sciences and Chemistry


 

Preface

5

Contents

8

List of Contributors

10

1 Chemistry and Partial Order

14

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

15

Abstract

15

The Basic Terms: Examples of Posets, The Hasse Diagram

15

Some Posets of Chemical Interest

19

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

25

Ordering of Tree graphs

27

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

35

References

36

Hasse Diagrams and their Relation to Molecular Periodicity

39

Abstract

39

Individual molecules

39

Inorganic molecules

40

Organic molecules

42

References

44

Directed Reaction Graphs as Posets

46

Abstract

46

Introduction

46

Posetic Substitution Reaction Networks & Chemical Structure

48

Molecular Properties & the Reaction Poset

52

Molecular Property Interpolation

58

General Discussion

61

Prognosis

65

References

66

2 Environmental Chemistry and Systems

69

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

70

Abstract

70

Introduction

71

Overview

71

Partial order

72

Introductory remarks

72

The rationale of using Hasse diagrams

74

Prerequisites

76

Graphs and Hasse diagrams

77

Simple elements of interpreting a Hasse diagram

87

Characterizing a Hasse diagram as a whole

90

Sensitivity study

100

Evaluation of Sampling Sites

103

Discussion and Conclusion

114

References

116

Comparative Evaluation and Analysis of Water Sediment Data

120

Abstract

120

Results

123

Summary and Conclusions

156

Appendix

158

References

160

Prioritizing PBT Substances

161

Abstract

161

Introduction

161

Materials and Methods

162

Substances studied

162

QSARs

165

Partial Order Ranking

165

Results

166

Discussion

166

Conclusions

167

References

167

3 Quantitative Structure Activity Relationships

169

Interpolation Schemes in QSAR

170

Abstract

170

Introduction

170

Methods

171

Partial Order based QSARs

176

Giving molecules an identity

179

Conclusions and Outlook

184

References

185

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

187

Abstract

187

Introduction

188

Theory

189

Partial order ranking QSAR model for similarly acting phenylurea herbicides

208

Conclusions

218

References

219

4 Decision support

224

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

225

Abstract

225

Introduction

226

Methods

227

Evaluation Results

233

Discussion

235

Conclusions and Prospect

238

Acknowledgements

239

References

239

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

241

Abstract

241

Introduction

242

Survey of the Ranking Methods

243

Data

247

The Hasse Diagram

248

Results of Multi-Criteria Analysis

251

Discussion

254

Conclusion

258

References

259

5 Field, Monitoring and Information

261

Developing decision support based on field data and partial order theory

263

Abstract

263

Introduction

264

Data background for illustration

265

Correlation analysis

266

References

286

Evaluation of Biomonitoring Data

288

Abstract

288

Introduction

288

The German Environmental Specimen Bank

289

Evaluation Methods

291

The Data Set

297

Hasse Diagrams or POSETs

299

Conclusions and Outlook

307

References

309

Exploring Patterns of Habitat Diversity Across Landscapes Using Partial Ordering

311

Abstract

311

Introduction

312

Pennsylvania Biodiversity Context

313

Progression of partial and incomplete orderings

315

Rank range runs

317

Rank range end-member elimination effect

325

Second order analysis

326

References

327

Information Systems and Databases

328

Abstract

328

Environmental Data, Databases and Information Systems

329

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

330

Environmetrical and Chemometrical Methods Used

333

Application of Evaluation Methods to Data-Matrix

338

Discussion and Conclusion

349

References

350

6 Rules and Complexity

353

Contexts, Concepts, Implications and Hypotheses

355

Abstract

355

Contexts and their concepts

355

Implications

358

References

365

Partial Orders and Complexity: The Young Diagram Lattice

366

Abstract

366

Introduction

366

Mixing

367

Complexity

369

Entropy

371

Complexity

371

Complexity and the Young Diagram Lattice

372

YDL Examples

376

Complexity Metaphor – Other Posets and Beyond

378

Conclusion

380

References

381

7 Historical remarks

382

Hasse Diagrams and Software Development

383

Abstract

383

Historical notes concerning the development of WHASSE

383

Helmut Hasse

384

Rationale on the use of partial order

384

Model order estimation

385

Quantification of fate and impact of contaminants

385

Development of software

386

References

389

Introductory References

391

Posets (books)

391

Posets as tools for data exploration

391

Posets as tools to chemical investigations

393

Posets and Multicriteria Decision Analysis

394

Posets and Linear extensions

394

Posac

395

Formal Concept Analysis

395

Index

397