Fitting functions for dark matter density profiles

We present a unified parameterization of the fitting functions suitable for density profiles of dark matter haloes or elliptical galaxies. A notable feature is that the classical Einasto profile appears naturally as the continuous limiting case of the cored subfamily amongst the double power-law profiles of Zhao (1996). Based on this, we also argue that there is basically no qualitative difference between halo models well-fitted by the Einasto profile and the standard NFW model. This may even be the case quantitatively unless the resolutions of simulations and the precisions of fittings are sufficiently high to make meaningful distinction possible.Comment: 13 pages (6 pages main text + 5 pages appendices + 2 pages full tables) including 5 figures and 7 tables. submitted to MNRA

PCA and K-Means decipher genome

In this paper, we aim to give a tutorial for undergraduate students studying statistical methods and/or bioinformatics. The students will learn how data visualization can help in genomic sequence analysis. Students start with a fragment of genetic text of a bacterial genome and analyze its structure. By means of principal component analysis they ``discover'' that the information in the genome is encoded by non-overlapping triplets. Next, they learn how to find gene positions. This exercise on PCA and K-Means clustering enables active study of the basic bioinformatics notions. Appendix 1 contains program listings that go along with this exercise. Appendix 2 includes 2D PCA plots of triplet usage in moving frame for a series of bacterial genomes from GC-poor to GC-rich ones. Animated 3D PCA plots are attached as separate gif files. Topology (cluster structure) and geometry (mutual positions of clusters) of these plots depends clearly on GC-content.Comment: 18 pages, with program listings for MatLab, PCA analysis of genomes and additional animated 3D PCA plot

Electronic structure and magnetic properties of Gd-doped and Eu-rich EuO

The effects of Gd doping and O vacancies on the magnetic interaction and Curie temperature of EuO are studied using first-principles calculations. Linear response calculations in the virtual crystal approximation show a broad maximum in the Curie temperature as a function of doping, which results from the combination of the saturating contribution from indirect exchange and a decreasing contribution from the f-d hopping mechanism. Non-Heisenberg interaction at low doping levels and its effect on the Curie temperature are examined. The electronic structure of a substitutional Gd and of an O vacancy in EuO are evaluated. When the 4f spins are disordered, the impurity state goes from single to double occupation, but correlated bound magnetic polarons are not ruled out. At higher vacancy concentrations typical for Eu-rich EuO films, the impurity states broaden into bands and remain partially filled. To go beyond the homogeneous doping picture, magnetostructural cluster expansions are constructed, which describe the modified exchange parameters near Gd dopants or O vacancies. Thermodynamic properties are studied using Monte Carlo simulations. The Curie temperature for Gd-doped EuO agrees with the results of the virtual crystal approximation and shows a maximum of about 150 K. At 3.125% vacancy concentration the Curie temperature increases to 120 K, consistent with experimental data for Eu-rich film samples.Comment: 15 pages, 13 figures, under review in Physical Review