BeschreibungThe 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.
InhaltsverzeichnisExamples and Preliminaries.
Media and Well-graded Families.
Closed Media and ?-Closed Families.
Well-Graded Families of Relations.
Media and Partial Cubes.
Media and Integer Lattices.
Hyperplane arrangements and their media.
Visualization of Media.
Random Walks on Media.
From the reviews:
"The book takes its readers a long way from motivational examples at the beginning to the formal definition, algebraic, combinatorial, and geometric representations, to algorithmic problems, to several intuitive ways of visualizing media, and finally to serious applications. ' The mathematician will find a nicely expounded theory with many ramifications. The theorems and proofs are clear and exhaustive, well balanced between rigor and intuition." (Reinhard Suck, Journal of Mathematical Psychology, Vol. 52, 2008)
"The book introduces a new mathematical structure called `medium', 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(s) by just one of those features. ' The book does not require much background knowledge and therefore is easily readable. Graduate students, researchers and university media may take advantage of the ideas therein." (George Stoica, Zentralblatt MATH, Vol. 1149, 2008)