Constructive spherical codes on layers of flat tori

A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere S^{2L-1} of R^{2L} and designing a structured codebook on each torus layer. The resulting spherical code can be the image of a lattice restricted to a specific hyperbox in R^L in each layer. Group structure and homogeneity, useful for efficient storage and decoding, are inherited from the underlying lattice codebook. A systematic method for constructing such codes are presented and, as an example, the Leech lattice is used to construct a spherical code in R^{48}. Upper and lower bounds on the performance, the asymptotic packing density and a method for decoding are derived.Comment: 9 pages, 5 figures, submitted to IEEE Transactions on Information Theor

Knowledge and attitude towards the gradual reduction of salt in bread – an online survey

Aim: Assess knowledge and attitude towards the gradual reduction of salt in bread and the potential impact on eating habits of children (6-18 years) and their families, as part as a Health Impact Assessment pilot study.N/

Entropy, non-ergodicity and non-Gaussian behaviour in ballistic transport

Ballistic transportation introduces new challenges in the thermodynamic properties of a gas of particles. For example, violation of mixing, ergodicity and of the fluctuation-dissipation theorem may occur, since all these processes are connected. In this work, we obtain results for all ranges of diffusion, i.e., both for subdiffusion and superdiffusion, where the bath is such that it gives origin to a colored noise. In this way we obtain the skewness and the non-Gaussian factor for the probability distribution function of the dynamical variable. We put particular emphasis on ballistic diffusion, and we demonstrate that in this case, although the second law of thermodynamics is preserved, the entropy does not reach a maximum and a non-Gaussian behavior occurs. This implies the non-applicability of the central limit theorem.Comment: 9 pages, 2 figure

Radiative decay Z_H-> \gamma A_H in the little Higgs model with T-parity

In the little Higgs model with T-parity (LHTM), the only tree-level kinematically allowed two-body decay of the Z_H boson is Z_H-> A_H H and thus one-loop induced two-body decays may have a significant rate. We study the Z_H-> \gamma A_H decay, which is induced at the one-loop level by a fermion triangle and is interesting as it depends on the mechanism of anomaly cancellation of the model. All the relevant two- and three-body decays of the Z_H gauge boson arising at the tree-level are also calculated. We consider a small region of the parameter space where the scale of the symmetry breaking f is still allowed to be as low as 500 GeV by electroweak precision data. We first analyze the scenario of a Higgs boson with a mass of 120 GeV. We found that the Z_H->\gamma A_H branching ratio can be of the order of a tree-level three-body decay and may be at the reach of detection at the LHC for f close to 500 GeV, but it may be difficult to detect for f=1 TeV. There is also an scenario where the Higgs boson has an intermediate mass such that the Z_H-> A_H H decay is closed, the Z_H-> \gamma A_H gets considerably enhanced and the chances of detection get a large boost.Comment: 19 pages, 9 figures, 2 table