Affine Iterations and Wrapping Effect

Estimates on the Spectrum of Fractals Arising from Affine Iterations

In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are most often not groups. We show that nonetheless those fractals that come from iteration of affine mappings in R have a spectral duality which is instead based...

Euclidian Shape and Motion from Multiple Perspective Views by Affine Iterations

Euclidean Shape and Motion from Multiple Perspective Views by Affine Iterations

In this paper, we describe a method for solving the Euclidean reconstruction problem with a perspective camera model by incrementally performing Euclidean reconstruction with either a weak or a paraperspective camera model. With respect to other methods that compute shape and motion from a sequence of images with a calibrated camera, this method converges in a few iterations, is computationally...

The wrapping effect, ellipsoid arithmetic, stability and confidence regions

The wrapping effect is one of the main reasons that the application of interval arithmetic to the enclosure of dynamical systems is difficult. In this paper the source of wrapping is analyzed algebraically and geometrically. A new method for reducing the wrapping effect is proposed, based on an interval ellipsoid arithmetic. Applications are given to the verification of stability regions for no...

Affine Monads and Side-Effect-Freeness

The notions of side-effect-freeness and commutativity are typical for probabilistic models, as subclass of quantum models. This paper connects these notions to properties in the theory of monads. A new property of a monad (‘strongly affine’) is introduced. It is shown that for such strongly affine monads predicates are in bijective correspondence with side-effect-free instruments. Also it is sh...