Realizations of Symmetric Maps by Symmetric Polyhedra

Commuting pairs of patterns and symmetric realizations

Computation of Signature Symmetric Balanced Realizations

A new numerical scheme for computing balancing coordinate transformations for signature symmetric realizations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and hyperbolic Jacobi-type rotations is considered. Local quadratic convergence of th...

Beam Splitter Realizations of Totally Symmetric Mode Couplers

We discuss the symmetric multiport and show in a constructive way how it can be decomposed into a set of beam splitters. Based on the decomposition we estimate the number of beam splitters needed. It is shown, that for more than three input ports the number of beam splitters needed is less than the number indicated by the standard decomposition scheme. y Also with the Academy of Finland.

Stability of Spherically Symmetric Wave Maps

We study Wave Maps from R2+1 to the hyperbolic plane H2 with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some H1+μ, μ > 0. We show that such Wave Maps don’t develop singularities in finite time and stay close to the Wave Map extending the spherically symmetric data(whose existence is ensured by a theorem of Christodoulou-T...

Irreducible Complexity of Iterated Symmetric Bimodal Maps

The concept of irreducible complexity of a biological system was introduced by Behe [1] in 1996. His point of view is that an organism consisting of a finite, possibly very large, number of independent components, coupled together in some way, exhibits irreducible complexity if, by removing any of its components, the reduced system no longer functions meaningfully. Using the language of nonline...