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"Media Theory",
by D.Eppstein, J.-Cl.Falmagne and S.Ovchinnikov,
Springer, 2008. Sample chapter.
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. The evolution of such a system over time is considered. Such a structure is
analyzed from algebraic and probabilistic (stochastic) standpoints.
- Hyperplane arrangements in preference modelling,
J. of Math. Psychology, 49 (2005) 481-488.
- Homogeneity properties of some $\ell-1$-spaces
, Discrete & Computational Geometry, 35 (2006) 301-310.
- Decision making with ternary relations, in: B. Bouchon-Meunier, G. Coletti, and R.R. Yager (eds.)
Modern Information Processing (Elsevier, 2006).
- Metric geometry of hypercubes,
MATHWARE, XIV, no.1 (2007), 23-33.
- Primer on media theory, MATHWARE,
XIV, no.2 (2007), 129-145.
- Fundamentals of media theory, Int. J. of Uncertainty, Fuzziness and
Knowledge-Based Systems 15 (2007), 649-680.
- Media theory - representations and examples,
Discrete Applied Mathematics, 156 (2008), 1197-1219.
- Representations of T-similarity relations,
Fuzzy Sets and Systems, 159 (2008), 2211-2220.
- Cubical token systems, Mathematical Social Sciences,
56 (2008) 149-165.
- Partial cubes: structures and constructions, Discrete Mathematics,
308 (2008) 5597-5621.
- Geometric representations of weak orders, in:
Uncertainty and Intelligent Information Systems, B. Bouchon-Meunier, R.R. Yager, C. Marsala, and M.
Rifqi eds, World Scientific Publishing Co Pte Ltd (Singapore) (2008), 447-456.
- Mediatic Graphs, (with J.-Cl. Falmagne), in:
The Mathematics of Preference, Choice and Order, S.J Brams, W.V. Gehrlein, F. Roberts eds,
Springer (2009), 325-343.
- Discrete picewise linear functions, to appear in the
European Journal of Combinatorics.
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