We give algorithms with polynomially bounded complexities (for fixed degrees) for computing the generalized Euler-Poincaré characteristic of semi-algebraic sets defined by symmetric polynomials. This is in contrast to the best complexity of the known algorithms for the same problem in the non-symmetric situation, which is singly exponential. This singly exponential complexity for the latter pro...

Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper and monic (or regular) triangular set is given. An improved zero decomposition algorithm which can be used to reduce the zero set of an equation system in ge...

In this paper, we introduce a concept of a farsighted stable set for a partition function game and interpret the union of all farsighted stable sets as the core of the game, to be called the strongcore, which reduces to the traditional core if the worth of every coalition is independent of the partition to which it belongs and the game is adequately represented by a characteristic function. We ...

Distributional estimates for the Carleson operator acting on characteristic functions of measurable sets of finite measure were obtained by Hunt [12]. In this article we describe a simple method that yields such estimates for general operators acting on one or more functions. As an application we discuss how distributional estimates are obtained for the linear and bilinear Hilbert transform. Th...

We show the following new lowness results for the probabilistic class ZPP NP. The class AM \ coAM is low for ZPP NP. As a consequence it follows that Graph Iso-morphism and several group-theoretic problems known to be in AM \ coAM are low for ZPP NP. The class IPPP/poly], consisting of sets that have interactive proof systems with honest provers in P/poly are also low for ZPP NP. We consider lo...

We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which includes the topological Euler characteristic and geometric descriptors to specify the content, shape and connectivity of spatial sets.

A class of self-similar sets of entangled quantum states is introduced, for which a recursive definition is provided. These sets, the “Bell gems,” are defined by the subsystem exchange symmetry characteristic of the Bell states. Each Bell gem is shown to be an orthonormal basis of maximally entangled elements.

In this paper we consider an isotropic variant of the BMO-type norm recently introduced in [6]. We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.