David Eppstein, Jean-Claude Falmagne, Sergei Ovchinnikov (auth.)3540716963, 978-3-540-71696-9
The focus of this book is a mathematical structure modeling a physical or biological system that can be in any of a number of `states.’ Each state is characterized by a set of binary features, and differs from some other neighbor state or states by just one of those feature. A simple example of a `state’ is a partial solution of a jigsaw puzzle, which can be transformed into another partial solution or into the final solution just by adding or removing a single adjoining piece. The evolution of such a system over time is considered. Such a structure is analyzed from algebraic and probabilistic (stochastic) standpoints.
Table of contents :
Front Matter….Pages I-X
Examples and Preliminaries….Pages 1-21
Basic Concepts….Pages 23-47
Media and Well-graded Families….Pages 49-71
Closed Media and ∪-Closed Families….Pages 73-99
Well-Graded Families of Relations….Pages 101-121
Mediatic Graphs….Pages 123-137
Media and Partial Cubes….Pages 139-160
Media and Integer Lattices….Pages 161-175
Hyperplane arrangements and their media….Pages 177-198
Algorithms….Pages 199-228
Visualization of Media….Pages 229-262
Random Walks on Media….Pages 263-284
Applications….Pages 285-303
Back Matter….Pages 305-328
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