Cosmic Sculpture: A new way to visualise the Cosmic Microwave Background

3D printing presents an attractive alternative to visual representation of physical datasets such as astronomical images that can be used for research, outreach or teaching purposes, and is especially relevant to people with a visual disability. We here report the use of 3D printing technology to produce a representation of the all-sky Cosmic Microwave Background (CMB) intensity anisotropy maps produced by the Planck mission. The success of this work in representing key features of the CMB is discussed as is the potential of this approach for representing other astrophysical data sets. 3D printing such datasets represents a highly complementary approach to the usual 2D projections used in teaching and outreach work, and can also form the basis of undergraduate projects. The CAD files used to produce the models discussed in this paper are made available.Comment: Accepted for publication in the European Journal of Physic

Determination of transition frequencies in a single 138^{138}Ba+^{+} ion

Transition frequencies between low-lying energy levels in a single trapped $^{138}$Ba$^{+}$ ion have been measured with laser spectroscopy referenced to an optical frequency comb. By extracting the frequencies of one-photon and two-photon components of the line shape using an eight-level optical Bloch model, we achieved 0.1 MHz accuracy for the 5d $^{2}$D$_{3/2}$ - 6p $^{2}$P$_{1/2}$ and 6s $^{2}$S$_{1/2}$ - 5d $^{2}$D$_{3/2}$ transition frequencies, and 0.2 MHz for the 6s $^{2}$S$_{1/2}$ - 6p $^{2}$P$_{1/2}$ transition frequency.Comment: 5 pages, 7 figures, submitted to Phys. Rev.

Performance assessment of portuguese secondary schools: the society and educational authorities perspectives

This paper describes a performance assessment of Portuguese secondary schools using data envelopment analysis (DEA). The assessment adopts two perspectives: a society perspective where schools are viewed as promoting students achievement given student characteristics in terms of academic abilities and socio-economic background; and an educational authorities perspective where schools are viewed as transforming a set of resources (including student academic abilities, socio-economic background, and also school resources, such as teachers) into students' achievement. Two types of DEA analysis are performed for each perspective: one using an output oriented model allowing factor weights to vary freely from school to school and another using a model that restricts factor weights to be equal for all schools. The first model is well suited for identifying inefficient schools, whereas the latter is best suited for improving discrimination between efficient schools when pursuing the identification of benchmarks. Our sample comprised a small number of schools and therefore the results obtained are mainly illustrative of the potential of the method. Future research will explore the use of this method for the assessment of schools at a national leve

Golden tilings

A. Pinto and D. Sullivan [3] proved a one-to-one correspondence between: (i) Cl+ conjugacy classes of expanding circle maps; (ii) solenoid functions and (iii) Pinto-Sullivan's dyadic tilings on the real line. Here, we prove a one-to-one correspondence between: (i) golden tilings; (ii) smooth conjugacy classes of golden diffeomorphism of the circle that are fixed points of renormalization; (iii) smooth conjugacy classes of Anosov difeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugated to the Anosov automorphism G(x, y) = (x + y, x) and (iv) solenoid functions