Increasing Physical Layer Security through Scrambled Codes and ARQ

We develop the proposal of non-systematic channel codes on the AWGN wire-tap channel. Such coding technique, based on scrambling, achieves high transmission security with a small degradation of the eavesdropper's channel with respect to the legitimate receiver's channel. In this paper, we show that, by implementing scrambling and descrambling on blocks of concatenated frames, rather than on single frames, the channel degradation needed is further reduced. The usage of concatenated scrambling allows to achieve security also when both receivers experience the same channel quality. However, in this case, the introduction of an ARQ protocol with authentication is needed.Comment: 5 pages, 4 figures; Proc. IEEE ICC 2011, Kyoto, Japan, 5-9 June 201

Measuring the eccentricity of the Earth orbit with a nail and a piece of plywood

I describe how to obtain a rather good experimental determination of the eccentricity of the Earth orbit, as well as the obliquity of the Earth rotation axis, by measuring, over the course of a year, the elevation of the Sun as a function of time during a day. With a very simple "instrument" consisting of an elementary sundial, first-year students can carry out an appealing measurement programme, learn important concepts in experimental physics, see concrete applications of kinematics and changes of reference frames, and benefit from a hands-on introduction to astronomy.Comment: 12 pages, 6 figure

Shearlets and Optimally Sparse Approximations

Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field.Comment: in "Shearlets: Multiscale Analysis for Multivariate Data", Birkh\"auser-Springe

All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.Comment: 19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be publishe