Adaptive Density Estimation on the Circle by Nearly-Tight Frames

This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the so-called Mexican needlets, which describe a nearly-tight frame on the circle. We study the asymptotic behaviour of the $L^{2}$-risk function for these estimates, in particular its adaptivity, proving that its rate of convergence is nearly optimal.Comment: 30 pages, 3 figure

Energetic electrons in the midlatitude nighttime E region

Nike Apache 14.439 was launched from Wallops Island at 0003 EST on 1 November 1972, a very disturbed night (K sub P = 8). A Geiger counter in the payload detected electrons ( keV) with a maximum flux of 1086 + or -261/sq cm/sec/ster. The height-averaged ionization rate in the upper E region is calculated from the measured electron density profile and has a value of 35 1/cu/cm/sec. The ionization rate can be reconciled with the observed flux of electrons ( 70 2 keV) if the spectrum ( keV) is of the form J ( E) = J sub O exp(-E/E sub O) with E sub O equal to 8.3 keV. The ionization rate on this and other nights is found to be strongly dependent on geomagnetic activity. It is suggested that energetic electrons are the principal source of ionization at midlatitudes in the upper E region near midnight, even under rather quiet geomagnetic conditions

Clustering of Galaxies in a Hierarchical Universe: I. Methods and Results at z=0

We introduce a new technique for following the formation and evolution of galaxies in cosmological N-body simulations. Dissipationless simulations are used to track the formation and merging of dark matter halos as a function of redshift. Simple prescriptions, taken directly from semi-analytic models of galaxy formation, are adopted for cooling, star formation, supernova feedback and the merging of galaxies within the halos. This scheme enables us to study the clustering properties of galaxies and to investigate how selection by type, colour or luminosity influences the results. In this paper, we study properties of the galaxy distribution at z=0. These include luminosity functions, colours, correlation functions, pairwise peculiar velocities, cluster M/L ratios and star formation rates. We focus on two variants of a CDM cosmology: a high- density model with Gamma=0.21 (TCDM) and a low-density model with Omega=0.3 and Lambda=0.7 (LCDM). Both are normalized to reproduce the I-band Tully-Fisher relation near a circular velocity of 220 km/s. Our results depend strongly both on this normalization and on the prescriptions for star formation and feedback. Very different assumptions are required to obtain an acceptable model in the two cases. For TCDM, efficient feedback is required to suppress the growth of galaxies low-mass field halos. Without it, there are too many galaxies and the correlation function turns over below 1 Mpc. For LCDM, feedback must be weak, otherwise too few L* galaxies are produced and the correlation function is too steep. Given the uncertainties in modelling some of the key physical processes, we conclude that it is not yet possible to draw conclusions about the values of cosmological parameters from studies of this kind. Further work on global star formation and feedback effects is required to narrow the range of possibilitiesComment: 43 pages, Latex, 16 figures included, 2 additional GIF format figures, submitted to MNRA

Introducing Mexican needlets for CMB analysis: Issues for practical applications and comparison with standard needlets

Over the last few years, needlets have a emerged as a useful tool for the analysis of Cosmic Microwave Background (CMB) data. Our aim in this paper is first to introduce in the CMB literature a different form of needlets, known as Mexican needlets, first discussed in the mathematical literature by Geller and Mayeli (2009a,b). We then proceed with an extensive study of the properties of both standard and Mexican needlets; these properties depend on some parameters which can be tuned in order to optimize the performance for a given application. Our second aim in this paper is then to give practical advice on how to adjust these parameters in order to achieve the best properties for a given problem in CMB data analysis. In particular we investigate localization properties in real and harmonic spaces and propose a recipe on how to quantify the influence of galactic and point source masks on the needlet coefficients. We also show that for certain parameter values, the Mexican needlets provide a close approximation to the Spherical Mexican Hat Wavelets (whence their name), with some advantages concerning their numerical implementation and the derivation of their statistical properties.Comment: 40 pages, 11 figures, published version, main modification: added section on more realistic galactic and point source mask

Spectroscopic membership for the populous 300 Myr-old open cluster NGC 3532

NGC 3532 is an extremely rich open cluster embedded in the Galactic disc, hitherto lacking a comprehensive, documented membership list. We provide membership probabilities from new radial velocity observations of solar-type and low-mass stars in NGC 3532, in part as a prelude to a subsequent study of stellar rotation in the cluster. Using extant optical and infra-red photometry we constructed a preliminary photometric membership catalogue, consisting of 2230 dwarf and turn-off stars. We selected 1060 of these for observation with the AAOmega spectrograph at the Anglo-Australian Telescope and 391 stars for observations with the Hydra-South spectrograph at the Victor Blanco Telescope, obtaining spectroscopic observations over a decade for 145 stars. We measured radial velocities for our targets through cross-correlation with model spectra and standard stars, and supplemented them with radial velocities for 433 additional stars from the literature. We also measured log g, Teff, and [Fe/H] from the AAOmega spectra. Together with proper motions from Gaia DR2 we find 660 exclusive members. The members are distributed across the whole cluster sequence, from giant stars to M dwarfs, making NGC 3532 one of the richest Galactic open clusters known to date, on par with the Pleiades. From further spectroscopic analysis of 153 dwarf members we find the metallicity to be marginally sub-solar, with [Fe/H]=-0.07. Exploiting trigonometric parallax measurements from Gaia DR2 we find a distance of $484^{+35}_{-30}$ pc. Based on the membership we provide an empirical cluster sequence in multiple photometric passbands. A comparison of the photometry of the measured cluster members with several recent model isochrones enables us to confirm the 300 Myr cluster age. However, all of the models evince departures from the cluster sequence in particular regions, especially in the lower mass range. (abridged)Comment: Accepted for publication in A&A. 19 pages, 18 Figures, and 6 Table

Current-Carrying Ground States in Mesoscopic and Macroscopic Systems

We extend a theorem of Bloch, which concerns the net orbital current carried by an interacting electron system in equilibrium, to include mesoscopic effects. We obtain a rigorous upper bound to the allowed ground-state current in a ring or disc, for an interacting electron system in the presence of static but otherwise arbitrary electric and magnetic fields. We also investigate the effects of spin-orbit and current-current interactions on the upper bound. Current-current interactions, caused by the magnetic field produced at a point r by a moving electron at r, are found to reduce the upper bound by an amount that is determined by the self-inductance of the system. A solvable model of an electron system that includes current-current interactions is shown to realize our upper bound, and the upper bound is compared with measurements of the persistent current in a single ring.Comment: 7 pager, Revtex, 1 figure available from [email protected]