Media Theory Interdisciplinary Applied Mathematics

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  • Edition: 1st
  • Pages: 330
  • Book Code: 244
  • ISBN-10: 3642422772
  • ISBN-13: 978-3642422775
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  • Book Name: Media theory interdisciplinary applied mathematics
  • Book Author: ( i ) David Eppstein, ( ii ) Jean-Claude Falmagne, ( iii ) Sergei Ovchinnikov
  • Book Publishers: Springer-Verlag Berlin Heidelberg,
  • Publish Date: (November 27, 2014)
  • Format: Hand Book
  • Language: English
  • Category: Mathematics, Engineering
  • Edition: 1st
  • Pages: 330
  • Book Code: 244
  • ISBN-10: 3642422772
  • ISBN-13: 978-3642422775
  • Book Quality: Backpaper

Additional information

Weight 1 kg
Dimensions 12 × 8 × 4 in
Book Binding

Paperback

Book Quality

Printing

Language

English

Edition

1st

Pages

330

Book Code

244

ISBN-10

3642422772

ISBN-13:

978-3642422775

About Book

he 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 astate’ 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.

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,
reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication
or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,
1965, in its current version, and permission for use must always be obtained from Springer. Violations
are liable to prosecution under the German Copyright Law.
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,
even in the absence of a specific statement, that such names are exempt from the relevant protective laws
and regulations and therefore free for general use.
Cover Design: KünkelLopka, Heidelberg

Preface

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 neigh-
bor state or states by just one of those features. In some situations, what
distinguishes a state S from a neighbor state T is that S has a particular fea-
ture that T does not have. A familiar example is a partial solution of a jigsaw
puzzle, with adjoining pieces. Such a state can be transformed into another
state, that is, another partial solution or the final solution, just by adding
a single adjoining piece. This is the first example discussed in Chapter 1. In
other situations, the difference between a state S and a neighbor state T may
reside in their location in a space, as in our second example, in which in which
S and T are regions located on different sides of some common border.
We formalize the mathematical structure as a semigroup of ‘messages’
transforming states into other states. Each of these messages is produced by
the concatenation of elementary transformations called ‘tokens (of informa-
tion).’ The structure is specified by two constraining axioms. One states that
any state can be produced from any other state by an appropriate kind of
message. The other axiom guarantees that such a production of states from
other states satisfies a consistency requirement.
What motivates our interest in this semigroup is, first, that it provides
an algebraic formulation for mathematical systems researched elsewhere and
earlier by other means. A prominent example is the ‘isometric subgraph of
a hypercube’ (see Djokovi´c, 1973, for an early reference), that is, a subraph
in which the distance between vertices is identical to that in the parent hy-
percube. But there are many other cases. We shall outline some of them in
our first chapter, reserving in depth treatment for later parts of this book.
Until recently, however, no common algebraic axiomatization of these out-
wardly different concepts had been proposed. Our purpose is to give here
the first comprehensive treatment of such a structure,

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Media theory interdisciplinary applied mathematics

Media Theory Interdisciplinary Applied Mathematics

1,800.00

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