Media theory: interdisciplinary applied mathematics
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 311 - 320 |
| Physical Description: | X, 328 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783540716969 3540716963 9783540716976 |
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| 100 | 1 | |a Eppstein, David |d 1963- |e Verfasser |0 (DE-588)133890511 |4 aut | |
| 245 | 1 | 0 | |a Media theory |b interdisciplinary applied mathematics |c David Eppstein ; Jean-Claude Falmagne ; Sergei Ovchinnikov |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a X, 328 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Record in the Search Index
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| adam_text |
Contents
1 Examples and Preliminaries 1
1.1 A Jigsaw Puzzle 1
1.2 A Geometrical Example 4
1.3 The Set of Linear Orders 6
1.4 The Set of Partial Orders 7
1.5 An Isometric Subgraph of Z™ 8
1.6 Learning Spaces 10
1.7 A Genetic Mutations Scheme 11
1.8 Notation and Conventions 12
1.9 Historical Note and References 17
Problems 19
2 Basic Concepts 23
2.1 Token Systems 23
2.2 Axioms for a Medium 24
2.3 Preparatory Results 27
2.4 Content Families 29
2.5 The Effective Set and the Producing Set of a State 30
2.6 Orderly and Regulär Returns 31
2.7 Embeddings, Isomorphisms and Submedia 34
2.8 Oriented Media 36
2.9 The Root of an Oriented Medium 38
2.10 An Infinite Example 39
2.11 Projections 40
Problems 45
3 Media and Well-graded Families 49
3.1 Wellgradedness 49
3.2 The Grading Collection 52
3.3 Wellgradedness and Media 54
3.4 Cluster Partitions and Media 57
3.5 An Application to Clustered Linear Orders 62
3.6 A General Procedure 68 ,
Problems 68
4 Closed Media and U-Closed Families 73
4.1 Closed Media 73
4.2 Learning Spaces and Closed Media 78 •
4.3 Complete Media 80
4.4 Summarizing a Closed Medium 83
4.5 U-Closed Families and their Bases 86
4.6 Projection of a Closed Medium 94 i
Problems 98
5 Well-Graded Families of Relations 101
5.1 Preparatory Material 102 .
5.2 Wellgradedness and the Fringes 103
5.3 Partial Orders 106
5.4 Biorders and Interval Orders 107
5.5 Semiorders 110
5.6 Almost Connected Orders 114
Problems 119
6 Mediatic Graphs 123
6.1 The Graph of a Medium 123
6.2 Media Inducing Graphs 125
6.3 Paired Isomorphisms of Media and Graphs 130
6.4 From Mediatic Graphs to Media 132
Problems 136
7 Media and Partial Cubes 139
7.1 Partial Cubes and Mediatic Graphs 139
7.2 Characterizing Partial Cubes 142
7.3 Semicubes of Media 149
7.4 Projections of Partial Cubes 151
7.5 Uniqueness of Media Representations 154
7.6 The Isometric Dimension of a Partial Cube 158
Problems 159
8 Media and Integer Lattices 161
8.1 Integer Lattices 161
8.2 Defining Lattice Dimension 162
8.3 Lattice Dimension of Finite Partial Cubes 167
8.4 Lattice Dimension of Infinite Partial Cubes 171
8.5 Oriented Media 172
Problems 174
9 Hyperplane arrangements and their media 177
9.1 Hyperplane Arrangements and Their Media 177
9.2 The Lattice Dimension of an Arrangement 184
9.3 Labeled Interval Orders 186
9.4 Weak Orders and Cubical Complexes 188
Problems 196
10 Algorithms 199
10.1 Comparison of Size Parameters 199
10.2 Input Representation 202
10.3 Finding Concise Messages 211
10.4 Recognizing Media and Partial Cubes 217
10.5 Recognizing Closed Media 218
10.6 Black Box Media 222
Problems 227
11 Visualization of Media 229
11.1 Lattice Dimension 230
11.2 Drawing High-Dimensional Lattice Graphs 231
11.3 Region Graphs of Line Arrangements 234
11.4 Pseudoline Arrangements 238
11.5 Finding Zonotopal Tilings 246
11.6 Learning Spaces 252
Problems 260
12 Random Walks on Media 263
12.1 On Regulär Markov Chains 265
12.2 Discrete and Continuous Stochastic Processes 271
12.3 Continuous Random Walks on a Medium 273
12.4 Asymptotic Probabilities 279
12.5 Random Walks and Hyperplane Arrangements 280
Problems 282
13 Applications 285
13.1 Building a Learning Space 285
13.2 The Entailment Relation 291
13.3 Assessing Knowledge in a Learning Space 293
13.4 The Stochastic Analysis of Opinion Polls 297
13.5 Concluding Remarks 302
Problems 303
Appendix: A Catalog of Small Mediatic Graphs 305
Glossary 309
Bibliography 311
Index 321 |
| adam_txt |
Contents
1 Examples and Preliminaries 1
1.1 A Jigsaw Puzzle 1
1.2 A Geometrical Example 4
1.3 The Set of Linear Orders 6
1.4 The Set of Partial Orders 7
1.5 An Isometric Subgraph of Z™ 8
1.6 Learning Spaces 10
1.7 A Genetic Mutations Scheme 11
1.8 Notation and Conventions 12
1.9 Historical Note and References 17
Problems 19
2 Basic Concepts 23
2.1 Token Systems 23
2.2 Axioms for a Medium 24
2.3 Preparatory Results 27
2.4 Content Families 29
2.5 The Effective Set and the Producing Set of a State 30
2.6 Orderly and Regulär Returns 31
2.7 Embeddings, Isomorphisms and Submedia 34
2.8 Oriented Media 36
2.9 The Root of an Oriented Medium 38
2.10 An Infinite Example 39
2.11 Projections 40
Problems 45
3 Media and Well-graded Families 49
3.1 Wellgradedness 49
3.2 The Grading Collection 52
3.3 Wellgradedness and Media 54
3.4 Cluster Partitions and Media 57
3.5 An Application to Clustered Linear Orders 62
3.6 A General Procedure 68 ,
Problems 68
4 Closed Media and U-Closed Families 73
4.1 Closed Media 73
4.2 Learning Spaces and Closed Media 78 •
4.3 Complete Media 80
4.4 Summarizing a Closed Medium 83
4.5 U-Closed Families and their Bases 86
4.6 Projection of a Closed Medium 94 i
Problems 98
5 Well-Graded Families of Relations 101
5.1 Preparatory Material 102 .
5.2 Wellgradedness and the Fringes 103
5.3 Partial Orders 106
5.4 Biorders and Interval Orders 107
5.5 Semiorders 110
5.6 Almost Connected Orders 114
Problems 119
6 Mediatic Graphs 123
6.1 The Graph of a Medium 123
6.2 Media Inducing Graphs 125
6.3 Paired Isomorphisms of Media and Graphs 130
6.4 From Mediatic Graphs to Media 132
Problems 136
7 Media and Partial Cubes 139
7.1 Partial Cubes and Mediatic Graphs 139
7.2 Characterizing Partial Cubes 142
7.3 Semicubes of Media 149
7.4 Projections of Partial Cubes 151
7.5 Uniqueness of Media Representations 154
7.6 The Isometric Dimension of a Partial Cube 158
Problems 159
8 Media and Integer Lattices 161
8.1 Integer Lattices 161
8.2 Defining Lattice Dimension 162
8.3 Lattice Dimension of Finite Partial Cubes 167
8.4 Lattice Dimension of Infinite Partial Cubes 171
8.5 Oriented Media 172
Problems 174
9 Hyperplane arrangements and their media 177
9.1 Hyperplane Arrangements and Their Media 177
9.2 The Lattice Dimension of an Arrangement 184
9.3 Labeled Interval Orders 186
9.4 Weak Orders and Cubical Complexes 188
Problems 196
10 Algorithms 199
10.1 Comparison of Size Parameters 199
10.2 Input Representation 202
10.3 Finding Concise Messages 211
10.4 Recognizing Media and Partial Cubes 217
10.5 Recognizing Closed Media 218
10.6 Black Box Media 222
Problems 227
11 Visualization of Media 229
11.1 Lattice Dimension 230
11.2 Drawing High-Dimensional Lattice Graphs 231
11.3 Region Graphs of Line Arrangements 234
11.4 Pseudoline Arrangements 238
11.5 Finding Zonotopal Tilings 246
11.6 Learning Spaces 252
Problems 260
12 Random Walks on Media 263
12.1 On Regulär Markov Chains 265
12.2 Discrete and Continuous Stochastic Processes 271
12.3 Continuous Random Walks on a Medium 273
12.4 Asymptotic Probabilities 279
12.5 Random Walks and Hyperplane Arrangements 280
Problems 282
13 Applications 285
13.1 Building a Learning Space 285
13.2 The Entailment Relation 291
13.3 Assessing Knowledge in a Learning Space 293
13.4 The Stochastic Analysis of Opinion Polls 297
13.5 Concluding Remarks 302
Problems 303
Appendix: A Catalog of Small Mediatic Graphs 305
Glossary 309
Bibliography 311
Index 321 |
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| author | Eppstein, David 1963- Falmagne, Jean-Claude 1934- Ovchinnikov, Sergei 1950- |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T21:02:08Z |
| indexdate | 2024-07-20T09:41:57Z |
| institution | BVB |
| isbn | 9783540716969 3540716963 9783540716976 |
| language | English |
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| physical | X, 328 S. Ill., graph. Darst. 24 cm |
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| publisher | Springer |
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| spelling | Eppstein, David 1963- Verfasser (DE-588)133890511 aut Media theory interdisciplinary applied mathematics David Eppstein ; Jean-Claude Falmagne ; Sergei Ovchinnikov 1. ed. Berlin [u.a.] Springer 2008 X, 328 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 311 - 320 Modellen (theorie) gtt Numerieke wiskunde gtt Systeemtheorie gtt Combinatorial group theory Model theory Set theory Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Diskretes System (DE-588)4401225-1 gnd rswk-swf Diskretes System (DE-588)4401225-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Falmagne, Jean-Claude 1934- Verfasser (DE-588)120260980 aut Ovchinnikov, Sergei 1950- Verfasser (DE-588)1029590540 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2930586&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016526306&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eppstein, David 1963- Falmagne, Jean-Claude 1934- Ovchinnikov, Sergei 1950- Media theory interdisciplinary applied mathematics Modellen (theorie) gtt Numerieke wiskunde gtt Systeemtheorie gtt Combinatorial group theory Model theory Set theory Mathematisches Modell (DE-588)4114528-8 gnd Diskretes System (DE-588)4401225-1 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4401225-1 |
| title | Media theory interdisciplinary applied mathematics |
| title_auth | Media theory interdisciplinary applied mathematics |
| title_exact_search | Media theory interdisciplinary applied mathematics |
| title_exact_search_txtP | Media theory interdisciplinary applied mathematics |
| title_full | Media theory interdisciplinary applied mathematics David Eppstein ; Jean-Claude Falmagne ; Sergei Ovchinnikov |
| title_fullStr | Media theory interdisciplinary applied mathematics David Eppstein ; Jean-Claude Falmagne ; Sergei Ovchinnikov |
| title_full_unstemmed | Media theory interdisciplinary applied mathematics David Eppstein ; Jean-Claude Falmagne ; Sergei Ovchinnikov |
| title_short | Media theory |
| title_sort | media theory interdisciplinary applied mathematics |
| title_sub | interdisciplinary applied mathematics |
| topic | Modellen (theorie) gtt Numerieke wiskunde gtt Systeemtheorie gtt Combinatorial group theory Model theory Set theory Mathematisches Modell (DE-588)4114528-8 gnd Diskretes System (DE-588)4401225-1 gnd |
| topic_facet | Modellen (theorie) Numerieke wiskunde Systeemtheorie Combinatorial group theory Model theory Set theory Mathematisches Modell Diskretes System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2930586&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016526306&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT eppsteindavid mediatheoryinterdisciplinaryappliedmathematics AT falmagnejeanclaude mediatheoryinterdisciplinaryappliedmathematics AT ovchinnikovsergei mediatheoryinterdisciplinaryappliedmathematics |