Polytope Projects
How do you know what works and what doesn't? This book contains case studies highlighting the power of polytope projects for complex problem solving. Any sort of combinational problem characterized by a large variety of possibly complex constructions and deconstructions based on simple building...
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| Médium: | E-kniha |
| Jazyk: | English |
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Milton
CRC Press
2014
Taylor & Francis Group |
| Vydanie: | 1 |
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| ISBN: | 9781482204643, 1482204649 |
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| Abstract | How do you know what works and what doesn't? This book contains case studies highlighting the power of polytope projects for complex problem solving. Any sort of combinational problem characterized by a large variety of possibly complex constructions and deconstructions based on simple building blocks can be studied in a similar way. Although the majority of case studies are related to chemistry, the method is general and equally applicable to other fields for engineering or science. |
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| AbstractList | How do you know what works and what doesn't? This book contains case studies highlighting the power of polytope projects for complex problem solving. Any sort of combinational problem characterized by a large variety of possibly complex constructions and deconstructions based on simple building blocks can be studied in a similar way. Although the majority of case studies are related to chemistry, the method is general and equally applicable to other fields for engineering or science. |
| Author | Iordache, Octavian |
| Author_xml | – sequence: 1 givenname: Octavian surname: Iordache fullname: Iordache, Octavian organization: President, Polystochastic Montreal, Quebec, Canada |
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| ContentType | eBook |
| Copyright | 2014 by Taylor & Francis Group, LLC |
| Copyright_xml | – notice: 2014 by Taylor & Francis Group, LLC |
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| DOI | 10.1201/b15863 |
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| Keywords | Integer Partition Separation Schemas dot hasse Divided Wall Column dual Polytope Projects Ferrers Diagram Doe Graded Graphs Dual Graph Binary Matrix PSA Galois Lattice FCA Standard Young Tableaux Artifi Cial Life black tree Commutation Condition Binary Trees SMB graph M1 P1 commutation diagram Formal Concept Analysis condition binary Young Diagram Hasse Diagram ABCD ABCD Dynamic Combinatorial Chemistry Supramolecular Chemistry Catalan Trees |
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| PublicationDate | 2014 2013 2013-10-15T00:00:00 2013-10-15 |
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| Snippet | How do you know what works and what doesn't? This book contains case studies highlighting the power of polytope projects for complex problem solving. Any sort... |
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| SubjectTerms | Mathematical models Polytopes Self-organizing systems |
| TableOfContents | 5.1.2 Dual Graded Graphs for Compositions -- 5.1.3 Self-Evolvability and Polytopes -- 5.1.4 Entropy Calculus -- 5.1.5 Pascal Graphs for Compositions -- 5.2 Partitions -- 5.2.1 Integers Partition -- 5.2.2 Combinatorial Species -- 5.2.3 Dual Graded Graphs for Partitions -- 5.2.4 Entropy Calculus -- 5.2.5 Partitions as Dual Graded Graphs -- 5.2.6 Self-Evolvability and Polytopes -- References -- 6: Construction and Deconstruction -- 6.1 Crystal Growth -- 6.1.1 Dendrites and Crystals -- 6.1.2 Dual Graphs for 3-cores -- 6.1.3 Polytopes and Self-Evolvable 3-cores -- 6.2 Self-Configurable Modular Automata -- 6.2.1 Automata -- 6.2.2 Architecture -- 6.2.3 Assembly and Disassembly -- 6.2.4 Shifted Shapes -- 6.2.5 Entropy Calculus -- 6.3 Packing and Unpacking -- 6.3.1 VLSI Design -- 6.3.2 Dual Graded Graphs for Packing -- 6.3.3 Self-Evolvability and Polytopes -- References -- 7: Strong and Weak Molecular Interactions -- 7.1 Molecular and Supramolecular -- 7.2 Dynamic Combinatorial Libraries and Templating -- 7.3 Polytopes for Supramolecular Chemistry -- 7.4 G-quadruplexes -- 7.5 Supramolecular Tiling -- 7.6 Stereochemistry for Cyclic Compounds -- References -- 8: Synthesis and Decomposition Reactions -- 8.1 Evolutionary Biotechnology -- 8.1.1 DNA and RNA -- 8.1.2 Rooted Trees for Secondary RNA Structure -- 8.1.3 Polytope for RNA Structure -- 8.1.4 Reflected Graphs -- 8.1.5 Autocatalytic Network for Ribozyme Self-Construction -- 8.2 Chemical Reaction Networks -- 8.2.1 Alkanes -- 8.2.2 Deuterated Thiophenes -- 8.2.3 Chlorobenzenes -- 8.2.4 Self-Evolvability and Polytopes -- 8.2.5 Hemoglobin Oxygenation -- 8.3 Chemical Organization -- References -- 9: Data and Concepts Analysis -- 9.1 Formal Concept Analysis -- 9.1.1 Contexts and Concepts -- 9.1.2 FCA for Separation Schemas -- 9.1.4 Polytope for FCA Lattices -- 9.2 Nesting Line Diagrams 9.2.1 Two-levels Formal Context -- 9.2.2 Graphs Spanning for Comparison -- 9.2.3 Self-Evolvability and Polytopes -- 9.2.4 Entropy Calculus -- References -- 10: Design of Experiments and Analysis -- 10.1 Design of Experiment and Hasse Diagrams -- 10.1.1 Hasse Diagrams -- 10.1.2 Entropy Calculus -- 10.2 Permutation Trees for Designs of Experiments -- 10.3 Self-Evolvability and Polytopes -- References -- 11: Premises and Perspectives -- 11.1 Premises -- 11.1.1 n-Levels Systems -- 11.1.2 Complementarity and Duality -- 11.1.3 Closure and "Self" -- 11.1.4 Polytope Framework -- 11.1.5 Generic Models -- 11.1.6 Informational Criteria -- 11.1.7 Foundations -- 11.2 Perspectives -- 11.2.1 Technologies and Materials -- 11.2.2 Biosystems and Bio-inspired Systems -- 11.2.3 Information and Knowledge Systems -- 11.2.4 Economy, Society and Ecology -- 11.2.5 Ethics and Law -- References -- Appendix 1: Informational Entropy Cover -- Half Title -- Title Page -- Copyright Page -- Preface -- Table of Contents -- List of Tables -- Abbreviations -- 1: Introduction -- 1.1 Diversifying and Unifying Ways -- 1.2 Categorification and Decategorification -- 1.3 Polytope Projects -- References -- 2: Methods and Models -- 2.1 Differential Posets -- 2.2 Dual Graded Graphs -- 2.3 Updown Categories -- 2.4 Combinatorial Species -- 2.5 Polytopes and n-Levels Systems -- 2.6 Differential Models -- 2.6.1 Modeling Differential Posets -- 2.6.2 Derivative Complexes -- 2.6.3 Differential Ring of Polytopes -- 2.6.4 Combinatorial Differential Calculus -- 2.6.5 Generic Models -- References -- 3: Separation and Integration -- 3.1 Binary Rooted Trees for Separation -- 3.1.1 Separation Sequences -- 3.1.2 Binary Rooted Trees as Combinatorial Species -- 3.1.3 Configurations as Dual Graded Graphs -- 3.1.4 Distributed Separation Configurations -- 3.1.5 Self-Evolvability and Polytopes -- 3.1.6 Entropy Calculus -- 3.2 Lifted Binary Trees -- 3.2.1 Configurations as Dual Graded Graphs -- 3.2.2 Integration Schemas -- 3.2.3 Self-Evolvability and Polytopes -- 3.2.4 Entropy Calculus -- 3.3 Rooted Trees -- 3.3.1 Dual Graded Graphs for Rooted Trees -- 3.3.2 Self-Evolvability and Polytopes -- 3.3.3 Entropy Calculus -- References -- 4: Cyclic and Linear -- 4.1 Cyclic Separations -- 4.1.1 Presentations -- 4.1.2 Dual Graded Graphs for Necklaces -- 4.1.3 Non-crossing Partitions -- 4.1.4 Self-Evolvability and Polytopes -- 4.1.5 Entropy Calculus -- 4.2 Evolvability for Linear vs. Cyclical Schemas -- 4.2.1 Evolvability Request -- 4.2.2 Dual Graded Graphs for Catalan Trees -- 4.2.3 Fibonacci Graphs -- 4.2.4 Cyclical Schemas -- 4.2.5 Self-Evolvability and Polytopes -- 4.2.6 Entropy Calculus -- References -- 5: Compositions and Decompositions -- 5.1 Compositions -- 5.1.1 Integers Composition |
| Title | Polytope Projects |
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