| Preface | 7 |
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| Contents | 10 |
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| Abbreviations | 13 |
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| List of Figures | 14 |
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| List of Tables | 18 |
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| 1 Introduction | 19 |
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| 1.1 Polytope Projects | 19 |
| 1.1.1 Levels and Emergence | 19 |
| 1.1.2 Integrative Closure | 21 |
| 1.1.3 Self-integrative Closure | 22 |
| 1.1.4 Polystochastic Models | 24 |
| 1.1.5 Hyperstructures | 26 |
| 1.1.6 Meta-Meta-Modeling Architectures | 28 |
| 1.1.7 Polytopes and n-Levels Systems | 29 |
| 1.2 Smart Systems | 31 |
| 1.2.1 Smart Materials and Structures | 31 |
| 1.2.2 Cyber-Physical Systems | 34 |
| 1.2.3 Intelligent Technical Systems | 37 |
| References | 39 |
| 2 Processes Synthesis | 42 |
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| 2.1 Flow-Sheets Generation | 42 |
| 2.1.1 Separation Sequences | 42 |
| 2.1.2 Configurations as Dual Graded Graphs | 43 |
| 2.1.3 Integration Schemes | 46 |
| 2.1.4 Lattices for Process Synthesis | 50 |
| 2.1.5 Integration of Lattices | 51 |
| 2.2 Cyclic Separations | 53 |
| 2.2.1 Cyclic Operations | 53 |
| 2.2.2 Non-Crossing Partitions | 54 |
| 2.2.3 Dual Graded Graphs for Evolving Schemes | 57 |
| 2.2.4 Polytope for Cyclic Operations | 59 |
| References | 61 |
| 3 Molecules and Networks | 64 |
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| 3.1 Periodic Features | 64 |
| 3.1.1 Smart Drug Delivery Systems | 64 |
| 3.1.2 Drug Delivery and Dual Graded Graphs | 66 |
| 3.1.3 Chronoterapy Case Studies | 69 |
| 3.1.4 Periodic Table of Elements | 74 |
| 3.2 Reaction Networks | 75 |
| 3.2.1 Chemical Reaction Networks | 75 |
| 3.2.2 Azines | 76 |
| 3.2.3 Hemoglobin Oxygenation | 78 |
| 3.2.4 Adsorption of Polar Species | 79 |
| References | 80 |
| 4 Conditioned Walks | 82 |
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| 4.1 Restricted Permutations | 82 |
| 4.1.1 Placements and Packing | 82 |
| 4.1.2 Templating and Twin Trees | 86 |
| 4.2 Self-Avoiding Walks | 89 |
| 4.2.1 Folding and Meanders | 89 |
| 4.2.2 Self-Avoiding Polygons | 91 |
| References | 96 |
| 5 Assembling and Configuring | 98 |
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| 5.1 Self-assembling | 98 |
| 5.1.1 Self-assembly of Tiles | 98 |
| 5.1.2 Computation in Cells | 101 |
| 5.1.3 Permutation Trees | 102 |
| 5.2 Self-reconfiguring | 104 |
| 5.2.1 Metamorphic Robots | 104 |
| 5.2.2 Construction and Deconstruction | 106 |
| 5.2.3 Shifted Shapes | 108 |
| 5.2.4 Skew Strip Shapes | 111 |
| References | 112 |
| 6 Devices and Technologies | 115 |
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| 6.1 Microreactors | 115 |
| 6.1.1 Microtechnology and Chemical Plants | 115 |
| 6.1.2 Dual Graded Graphs for Microreactors | 118 |
| 6.1.3 Set Partitions | 121 |
| 6.1.4 Numbering-up and Chains | 124 |
| 6.2 Timed Automata | 130 |
| 6.2.1 Heaps of Pieces and Timed Automata | 130 |
| 6.2.2 Paint Factory | 131 |
| References | 134 |
| 7 Concepts and Knowledge | 136 |
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| 7.1 Engineering Design | 136 |
| 7.1.1 Inferential Design Theory | 136 |
| 7.1.2 Dual Graded Graphs for Design | 138 |
| 7.1.3 Algebra of Design | 142 |
| 7.2 Concept Analysis | 145 |
| 7.2.1 Contexts and Concepts | 145 |
| 7.2.2 Multiple Separation Schemes | 145 |
| 7.2.3 Polytope for Lattices | 146 |
| 7.2.4 Meta-Meta-Modeling Approach | 149 |
| References | 151 |
| 8 Industrial Systems | 153 |
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| 8.1 Smart Manufacturing | 153 |
| 8.1.1 Industry 4.0 | 153 |
| 8.1.2 Smart Manufacturing Leadership Coalition | 155 |
| 8.1.3 Reference Architectures | 157 |
| 8.1.4 Generic Smart Grid Architecture Model | 159 |
| 8.2 Systems Development | 163 |
| 8.2.1 V-Model | 163 |
| 8.2.2 Polytope Projects for Continuous Engineering | 166 |
| 8.2.3 Logic and Hopf Algebras | 169 |
| References | 170 |
| 9 Polytope Perspectives | 172 |
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| 9.1 Synopsis | 172 |
| 9.1.1 Methodology | 172 |
| 9.1.2 General Theories | 178 |
| 9.2 Perspectives | 181 |
| 9.2.1 Leading Projects | 181 |
| 9.2.2 Society 4.0 | 182 |
| References | 186 |
| Appendix A: Dual Graded Graphs | 189 |
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| Appendix B: Hopf Algebras | 191 |
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| Index | 195 |