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Finding the principal points of a random variable

Emilio CarrizosaE. CondeA. CastañoD. Romero-Morales — 2001

RAIRO - Operations Research - Recherche Opérationnelle

The p -principal points of a random variable X with finite second moment are those p points in minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.

Finding the principal points of a random variable

Emilio CarrizosaE. CondeA. CastañoD. Romero–Morales — 2010

RAIRO - Operations Research

The -principal points of a random variable with finite second moment are those points in minimizing the expected squared distance from to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.

Maximal rationally connected fibrations and movable curves

Luis E. Solá CondeMatei Toma — 2009

Annales de l’institut Fourier

A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered...

A classification theorem on Fano bundles

Roberto MuñozLuis E. Solá CondeGianluca Occhetta — 2014

Annales de l’institut Fourier

In this paper we classify rank two Fano bundles on Fano manifolds satisfying H 2 ( X , ) H 4 ( X , ) . The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ( ) , that allows us to obtain the cohomological invariants of X and . As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

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