نتایج جستجو برای: convex hull
تعداد نتایج: 60150 فیلتر نتایج به سال:
Let g be a Gaussian random vector in R. Let N = N(n) be a positive integer and let KN be the convex hull of N independent copies of g. Fix R > 0 and consider the ratio of volumes VN := E vol(KN ∩RB 2 )/ vol(RB 2 ). For a large range of R = R(n), we establish a sharp threshold for N , above which VN → 1 as n → ∞, and below which VN → 0 as n → ∞. We also consider the case when KN is generated by ...
Choose n random, independent points in R according to the standard normal distribution. Their convex hull Kn is the Gaussian random polytope. We prove that the volume and the number of faces of Kn satisfy the central limit theorem, settling a well known conjecture in the field.
Let us assume we are given a co-bounded, convex hull I′′. It is well known that every set is stochastically symmetric. We show that S̄ (1|l|) < −1 1 Θ
We consider geometric functionals of the convex hull of normally distributed random points in Euclidean space R. In particular, we determine the asymptotic behaviour of the expected value of such functionals and of related geometric probabilities, as the number of points increases.
for every path a. The corresponding one-shot or stage game is denoted by G = ( {Ai}i=1, { fi}i=1 ) . The usual interpretation is that Ai is a set of pure actions.1 The set of feasible payoff vectors of the stage game G is given by the set F ≡ {p ∈ Rn| f (a) = p for some a ∈ A}. Let F∗ be the convex hull of the set of feasible payoffs. It should be clear that any normalized payoff in the repeate...
We present two statistical depth functions given in terms of the random variable defined as the minimum number of observations of a random vector that are needed to include a fixed given point in their convex hull. This random variable measures the degree of outlyingness of a point with respect to a probability distribution. We take advantage of this in order to define the new depth functions. ...
For a set P of n points in the unit ball b ⊆ Rd, consider the problem of finding a small subset T ⊆ P such that its convex-hull ε-approximates the convex-hull of the original set. Specifically, the Hausdorff distance between the convex hull of T and the convex hull of P should be at most ε. We present an efficient algorithm to compute such an ε′-approximation of size kalg, where ε′ is a functio...
Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex position, if none of its members is contained in the convex hull of the union of the others. For any xed k 5, we give a linear upper bound on P k (n), the maximum size of a family F with the property that any k members of F are in convex position, but no n are.
We consider the conjecture by Aichholzer, Aurenhammer, Hurtado, and Krasser that any two points sets with the same cardinality and the same size convex hull can be triangulated in the “same” way, more precisely via compatible triangulations. We show counterexamples to various strengthened versions of this conjecture.
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