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

Phase-Coherent Transport through a Mesoscopic System: A New Probe of Non-Fermi-Liquid Behavior

A novel chiral interferometer is proposed that allows for a direct measurement of the phase of the transmission coefficient for transport through a variety of mesoscopic structures in a strong magnetic field. The effects of electron-electron interaction on this phase is investigated with the use of finite-size bosonization techniques combined with perturbation theory resummation. New non-Fermi-liquid phenomena are predicted in the FQHE regime that may be used to distinguish experimentally between Luttinger and Fermi liquids.Comment: 4 pages, 3 figures, Revte

Orbital mechanism of the circular photogalvanic effect in quantum wells

It is shown that the free-carrier (Drude) absorption of circularly polarized radiation in quantum well structures leads to an electric current flow. The photocurrent reverses its direction upon switching the light helicity. A pure orbital mechanism of such a circular photogalvanic effect is proposed that is based on interference of different pathways contributing to the light absorption. Calculation shows that the magnitude of the helicity dependent photocurrent in $n$-doped quantum well structures corresponds to recent experimental observations.Comment: 5 pages, 2 figures, to be published in JETP Letter

Tidally-Triggered Star Formation in Close Pairs of Galaxies

We analyze new optical spectra of a sample of 502 galaxies in close pairs and n-tuples, separated by <= 50/h kpc. We extracted the sample objectively from the CfA2 redshift survey, without regard to the surroundings of the tight systems. We probe the relationship between star formation and the dynamics of the systems of galaxies. The equivalent widths of H\alpha (EW(H\alpha) and other emission lines anti-correlate strongly with pair spatial separation (\Delta D) and velocity separation. We use the measured EW(H\alpha) and the starburst models of Leitherer et al. to estimate the time since the most recent burst of star for- mation began for each galaxy. In the absence of a large contribution from an old stellar population to the continuum around H\alpha, the observed \Delta D -- EW(H\alpha) correlation signifies that starbursts with larger separations on the sky are, on average, older. By matching the dynamical timescale to the burst timescale, we show that the data support a simple picture in which a close pass initiates a starburst; EW(H\alpha) decreases with time as the pair separation increases, accounting for the anti-correlation. This picture leads to a method for measuring the duration and the initial mass function of interaction-induced starbursts: our data are compatible with the starburst and orbit models in many respects, as long as the starburst lasts longer than \sim10^8 years and the delay between the close pass and the initiation of the starburst is less than a few \times 10^7 years. If there is no large contribution from an old stellar population to the continuum around H\alpha the Miller-Scalo and cutoff (M <= 30 M_\sun) Salpeter initial mass functions fit the data much better than a standard Salpeter IMF. (Abridged.)Comment: 43 pages, 22 figures, to appear in the ApJ; we correct an error which had minor effects on numerical values in the pape

Spin Needlets for Cosmic Microwave Background Polarization Data Analysis

Scalar wavelets have been used extensively in the analysis of Cosmic Microwave Background (CMB) temperature maps. Spin needlets are a new form of (spin) wavelets which were introduced in the mathematical literature by Geller and Marinucci (2008) as a tool for the analysis of spin random fields. Here we adopt the spin needlet approach for the analysis of CMB polarization measurements. The outcome of experiments measuring the polarization of the CMB are maps of the Stokes Q and U parameters which are spin 2 quantities. Here we discuss how to transform these spin 2 maps into spin 2 needlet coefficients and outline briefly how these coefficients can be used in the analysis of CMB polarization data. We review the most important properties of spin needlets, such as localization in pixel and harmonic space and asymptotic uncorrelation. We discuss several statistical applications, including the relation of angular power spectra to the needlet coefficients, testing for non-Gaussianity on polarization data, and reconstruction of the E and B scalar maps.Comment: Accepted for publication in Phys. Rev.