Sergei Ovchinnikov
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Recent Publications

"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.

  1. Hyperplane arrangements in preference modelling, J. of Math. Psychology, 49 (2005) 481-488.
  2. Homogeneity properties of some $\ell-1$-spaces , Discrete & Computational Geometry, 35 (2006) 301-310.
  3. Decision making with ternary relations, in: B. Bouchon-Meunier, G. Coletti, and R.R. Yager (eds.) Modern Information Processing (Elsevier, 2006).
  4. Metric geometry of hypercubes, MATHWARE, XIV, no.1 (2007), 23-33.
  5. Primer on media theory, MATHWARE, XIV, no.2 (2007), 129-145.
  6. Fundamentals of media theory, Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 15 (2007), 649-680.
  7. Media theory - representations and examples, Discrete Applied Mathematics, 156 (2008), 1197-1219.
  8. Representations of T-similarity relations, Fuzzy Sets and Systems, 159 (2008), 2211-2220.
  9. Geometric representations of weak orders, to appear in: Uncertainty and Intelligent Information Systems, edited by R.R. Yager, B. Bouchon-Meunier, C. Marsala, and M. Rifqi, World Scientific Publishing Co Pte Ltd (Singapore).
  10. Partial cubes: structures and constructions, Discrete Mathematics , (to appear).
  11. Cubical token systems, Mathematical Social Sciences, (to appear).
Some of my papers in arXiv.org
  1. Universal metric spaces according to W. Holsztynski, http://xxx.lanl.gov/abs/math.GN/0004091.
  2. The lattice dimension of a tree, http://arxiv.org/abs/math/0402246.
  3. Weak order complexes, http://arxiv.org/abs/math/0403191.
  4. Boolean representation of manifolds and functions, http://arxiv.org/abs/math/0102007. Journal of Mathematical Analysis and Applications 263, 294-300 (2001)
Preprints
  1. Mediatic Graphs, (with J.-Cl. Falmagne, in review).

Complete list of publications