Many problems can be solved by iteration multiple participants (processors, servers, routers etc.). Previous mathematical models for such asynchronous iterations assume a single function being iterated fixed set of participants. We will call static since the system's configuration does not change. However in several real-world examples, as inter-domain routing, both and change frequently while ...

We will consider four cardinal characteristics of the continuum, a, b, d, s and discuss how their study has prompted the development of some of the most powerful forcing techniques: creature forcing, coherent systems of iterations, Shelah’s method of template iterations and the method of boolean ultrapowers.

Continuing the work [Fuc08], I show that the translation functions developed previously map iterable λ-structures to iterable s-structures and vice versa. To this end, I analyze how the translation functions interact with the formation of extender ultrapowers and normal iterations. This analysis makes it possible to translate iterations, and, in a last step, iteration strategies, thus arriving ...

While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is a certain splitting of the total Hilbert space and its recursive iterations to further iterated subdivisions. This paper explores some implications for asso...

The orthogonal multi-matching pursuit (OMMP) is a natural extension of orthogonal matching pursuit (OMP). We denote the OMMP with the parameter M as OMMP(M) where M ≥ 1 is an integer. The main difference between OMP and OMMP(M) is that OMMP(M) selects M atoms per iteration, while OMP only adds one atom to the optimal atom set. In this paper, we study the performance of orthogonal multi-matching...