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ISIPTA
1999
IEEE
13 years 12 months ago
Nonlinear Filtering of Convex Sets of Probability Distributions
A solution is provided to the problem of computing a convex set of conditional probability distributions that characterize the state of a nonlinear dynamic system as it evolves in...
John Kenney, Wynn C. Stirling
COMBINATORICA
2008
129views more  COMBINATORICA 2008»
13 years 7 months ago
The combinatorial encoding of disjoint convex sets in the plane
We introduce a new combinatorial object, the double-permutation sequence, and use it to encode a family of mutually disjoint compact convex sets in the plane in a way that capture...
Jacob E. Goodman, Richard Pollack
COMBINATORICS
2004
108views more  COMBINATORICS 2004»
13 years 7 months ago
On the Chromatic Number of Intersection Graphs of Convex Sets in the Plane
Let G be the intersection graph of a finite family of convex sets obtained by translations of a fixed convex set in the plane. We show that every such graph with clique number k i...
Seog-Jin Kim, Alexandr V. Kostochka, Kittikorn Nak...
CORR
2010
Springer
113views Education» more  CORR 2010»
13 years 7 months ago
Opaque sets
The problem of finding "small" sets that meet every straight-line which intersects a given convex region was initiated by Mazurkiewicz in 1916. We call such a set an opa...
Adrian Dumitrescu, János Pach
CCCG
2009
13 years 5 months ago
On symmetric realizations of the simplicial complex of 3-crossing-free sets of diagonals of the octagon
Motivated by the question of the polytopal realizability of the simplicial complex n,k of (k + 1)-crossing-free sets of diagonals of the convex n-gon, we study the first open case...
Jürgen Bokowski, Vincent Pilaud