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Media Theory: Interdisciplinary Applied Mathematics / Edition 1

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Overview

This book presents 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 features. The book considers the evolution of such a system over time and analyzes such a structure from algebraic and probabilistic (shastic) standpoints.

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Editorial Reviews

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"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)

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Product Details

  • ISBN-13: 9783642090837
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 11/19/2010
  • Edition description: Softcover reprint of hardcover 1st ed. 2008
  • Edition number: 1
  • Pages: 328
  • Product dimensions: 0.71 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Examples and Preliminaries.- Basic Concepts.- Media and Well-graded Families.- Closed Media and—-Closed Families.- Well-Graded Families of Relations.- Mediatic Graphs.- Media and Partial Cubes.- Media and Integer Lattices.- Hyperplane arrangements and their media.- Algorithms.- Visualization of Media.- Random Walks on Media.- Applications.

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