Very recently tracking was approached using classification techniques such as support vector machines. The object to be tracked is discriminated by a classifier from the background. In a similar spirit we propose a novel on-line AdaBoost feature selection algorithm for tracking. The distinct advantage of our method is its capability of on-line training. This allows to adapt the classifier while...

The two most commonly used topologies on R are the ordinary topology and the density topology. The ordinary topology is, of course, more widely known, and has the open intervals as its basic sets. The density topology, on the other hand, appears naturally in deeper studies of the structure of measurable sets. Its open sets are all measurable sets S ⊂ R which have the property that if x ∈ S, the...

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in P. Such pair of arrangements has an additional property: they admit conjugated equations on the ring of polynomials over Q( √ 5).

If A C R then A is homogeneous provided that A + Q = A. As an application we give an elementary proof of Menu’s theorem that the real line can be decomposed in two homogeneous homeomorphic subsets. We also show that such a decomposition is not topologically unique. There are homogeneous A, B C R with A RBA, B ~ RBB but A B.

Let be a real number > 1. Addition and multiplication by a xed positive integer of real numbers represented in base are shown to be computable by an on-line algorithm, and thus are continuous functions. When is a Pisot number, these functions are computable by an on-line nite automaton.

We give a very brief survey on ZFC theory (Zermelo-Fraenkel Set Theory) and we present an intuitive introduction to the method of forcing and some applications to the real line. Our exposition will be very informal, without any claim of completeness and rigour. The idea is just to give a very intuitive idea of what Set Theory and forcing-method are, and why they are interesting and useful from ...

We prove a certain type of inequalities concerning the integral of the Fourier transform of a function integrable on the real line.

This thesis explores an approach to Hilbert's twelfth problem for real quadratic number elds, concerning the determination of an explicit class eld theory for such elds. The basis for our approach is a paper by Manin proposing a theory of Real Multiplication realising such an explicit theory, analogous to the theory of Complex Multiplication associated to imaginary quadratic elds. Whereas ellip...