In this paper, ABCD matrix is introduced to study the paraxial transmission of light on a constant gaussian curvature surface (CGCS), which first time our knowledge. It also proved that curved can be used as implementation fractional Fourier transform, we further generalize obtain transfer an arbitrary with gently varying by optics. As beam propagation example, based Collins integral, analytica...

In this paper we introduce the correlation matrix of a Boolean mapping, a useful concept in demonstrating and proving properties of Boolean functions and mappings. It is argued that correlation matrices are the “natural” representation for the proper understanding and description of the mechanisms of linear cryptanalysis [4]. It is also shown that the difference propagation probabilities and th...

Detailed performance assessment of space–time coding algorithms in realistic channels is critically dependent upon accurate knowledge of the wireless channel spatial characteristics. This paper presents an experimental measurement platform capable of providing the narrowband channel transfer matrix for wireless communications scenarios. The system is used to directly measure key multiple-input–...

We consider the model of random surfaces with extrinsic curvature term embedded into 3d Euclidean lattice Z 3. On a 3d Euclidean lattice it has equivalent representation in terms of transfer matrix K(Q i , Q f), which describes the propagation of loops Q. We study the spectrum of the transfer matrix K(Q i , Q f) on finite dimensional lattices. The renormalisation group technique is used to inve...

We illustrate the relationship between message passing algorithms in GMRFs and matrix factorization algorithms. Specifically, we show that message passing on trees is equivalent to Gaussian elimination, while Loopy Belief Propagation is equivalent to Gauss-Seidel relaxation. Similarly, recently introduced message passing algorithms such as the Extended Message Passing, and the Embedded Subgraph...