Restricted-trace approximation for nuclear antiferromagnetism

Restricted Nonlinear Approximation 1

Restricted Nonlinear Approximation

We introduce a new form of nonlinear approximation called restricted approximation. It is a generalization of n-term wavelet approximation in which a weight function is used to control the terms in the wavelet expansion of the approximant. This form of approximation occurs in statistical estimation and in the characterization of interpolation spaces for certain pairs of L p and Besov spaces. We...

Truthful Approximation Mechanisms for Restricted Combinatorial Auctions

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for c...

Approximation algorithms for restricted Bayesian network structures

Bayesian Network structures with a maximum in-degree of k can be approximated with respect to a positive scoring metric up to an factor of 1/k.

Diophantine Exponents for Mildly Restricted Approximation

Abstract. We are studying the Diophantine exponent μn,l defined for integers 1 ≤ l < n and a vector α ∈ R by letting μn,l = sup{μ ≥ 0 : 0 < ‖x · α‖ < H(x) for infinitely many x ∈ Cn,l ∩ Zn}, where · is the scalar product and ‖ · ‖ denotes the distance to the nearest integer and Cn,l is the generalised cone consisting of all vectors with the height attained among the first l coordinates. We show...