Filtering techniques for the detection of Sunyaev-Zel'dovich clusters in multifrequency CMB maps

The problem of detecting Sunyaev-Zel'dovich (SZ) clusters in multifrequency CMB observations is investigated using a number of filtering techniques. A multifilter approach is introduced, which optimizes the detection of SZ clusters on microwave maps. An alternative method is also investigated, in which maps at different frequencies are combined in an optimal manner so that existing filtering techniques can be applied to the single combined map. The SZ profiles are approximated by the circularly-symmetric template $\tau (x) = [1 +(x/r_c)^2]^{-\lambda}$, with $\lambda \simeq \tfrac{1}{2}$ and $x\equiv |\vec{x}|$, where the core radius $r_c$ and the overall amplitude of the effect are not fixed a priori, but are determined from the data. The background emission is modelled by a homogeneous and isotropic random field, characterized by a cross-power spectrum $P_{\nu_1 \nu_2}(q)$ with $q\equiv |\vec{q}|$. The filtering methods are illustrated by application to simulated Planck observations of a $12.8^\circ \times 12.8^\circ$ patch of sky in 10 frequency channels. Our simulations suggest that the Planck instrument should detect $\approx 10000$ SZ clusters in 2/3 of the sky. Moreover, we find the catalogue to be complete for fluxes $S > 170$ mJy at 300 GHz.Comment: 12 pages, 7 figures; Corrected figures. Submitted to MNRA

Comparing filters for the detection of point sources

This paper considers filters (the Mexican hat wavelet, the matched and the scale-adaptive filters) that optimize the detection/separation of point sources on a background. We make a one-dimensional treatment, we assume that the sources have a Gaussian profile, i. e. $\tau (x) = e^{- x^2/2R^2}$, and a background modelled by an homogeneous and isotropic Gaussian random field, characterised by a power spectrum $P(q)\propto q^{-\gamma}, \gamma \geq 0$. Local peak detection is used after filtering. Then, the Neyman-Pearson criterion is used to define the confidence level for detections and a comparison of filters is done based on the number of spurious and true detections. We have performed numerical simulations to test theoretical ideas and conclude that the results of the simulations agree with the analytical results.Comment: 17 pages, 17 figures, accepted for publication in MNRA

The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature

The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these `curved' harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK) type approach, with two free parameters \ki, \kii which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere ${\bf S}^2$, hyperbolic plane ${\bf H}^2$, AntiDeSitter sphere {\bf AdS}^{\unomasuno} and DeSitter sphere {\bf dS}^{\unomasuno}) appear in this family, with the Euclidean and Minkowski spaces as flat limits. We solve the equations of motion for the `curved' harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: first by direct integration, second by obtaining the general CK version of the Binet's equation and third, as a consequence of its superintegrable character. The orbits are conics with centre at the potential origin in any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents those results of the theory of conics on spaces of constant curvature which are pertinent.Comment: 29 pages, 6 figure

Casimir invariants for the complete family of quasi-simple orthogonal algebras

A complete choice of generators of the center of the enveloping algebras of real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is obtained in a unified setting. The results simultaneously include the well known polynomial invariants of the pseudo-orthogonal algebras $so(p,q)$, as well as the Casimirs for many non-simple algebras such as the inhomogeneous $iso(p,q)$, the Newton-Hooke and Galilei type, etc., which are obtained by contraction(s) starting from the simple algebras $so(p,q)$. The dimension of the center of the enveloping algebra of a quasi-simple orthogonal algebra turns out to be the same as for the simple $so(p,q)$ algebras from which they come by contraction. The structure of the higher order invariants is given in a convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski" elements in the enveloping algebras. As an example showing this approach at work, the scheme is applied to recovering the Casimirs for the (3+1) kinematical algebras. Some prospects on the relevance of these results for the study of expansions are also given.Comment: 19 pages, LaTe

Towards two-dimensional metallic behavior at LaAlO3/SrTiO3 interfaces

Using a low-temperature conductive-tip atomic force microscope in cross-section geometry we have characterized the local transport properties of the metallic electron gas that forms at the interface between LaAlO3 and SrTiO3. At low temperature, we find that the carriers do not spread away from the interface but are confined within ~10 nm, just like at room temperature. Simulations taking into account both the large temperature and electric-field dependence of the permittivity of SrTiO3 predict a confinement over a few nm for sheet carrier densities larger than ~6 10^13 cm-2. We discuss the experimental and simulations results in terms of a multi-band carrier system. Remarkably, the Fermi wavelength estimated from Hall measurements is ~16 nm, indicating that the electron gas in on the verge of two-dimensionality.Comment: Accepted for publication in Physical Review Letter

Co-doped (La,Sr)TiO3-d: a high-Curie temperature diluted magnetic system with large spin-polarization

We report on tunneling magnetoresistance (TMR) experiments that demonstrate the existence of a significant spin polarization in Co-doped (La,Sr)TiO3-d (Co-LSTO), a ferromagnetic diluted magnetic oxide system (DMOS) with high Curie temperature. These TMR experiments have been performed on magnetic tunnel junctions associating Co-LSTO and Co electrodes. Extensive structural analysis of Co-LSTO combining high-resolution transmission electron microscopy and Auger electron spectroscopy excluded the presence of Co clusters in the Co-LSTO layer and thus, the measured ferromagnetism and high spin polarization are intrinsic properties of this DMOS. Our results argue for the DMOS approach with complex oxide materials in spintronics

Improved dead-time correction for PET scanners: Application to small-animal PET

Pile-up and dead-time are two main causes of nonlinearity in the response of a PET scanner as a function of activity in the field of view (FOV). For a given scanner and acquisition system, pile-up effects depend on the material and size of the object being imaged and on the distribution of activity inside and outside the FOV, because these factors change the singles-to-coincidences ratio (SCR). Thus, it is difficult to devise an accurate correction that would be valid for any acquisition. In this work, we demonstrate a linear relationship between SCR and effective dead-time, which measures the effects of both dead-time (losses) and pile-up (gains and losses). This relationship allows us to propose a simple method to accurately estimate dead-time and pile-up corrections using only two calibration acquisitions with, respectively, a high and low SCR. The method has been tested with simulations and experimental data for two different scanner geometries: a scanner with large area detectors and no pile-up rejection, and a scanner composed of two full rings of smaller detectors. Our results show that the SCR correction method is accurate within 7%, even for high activities in the FOV, and avoids the bias of the standard single-parameter method. © 2013 Institute of Physics and Engineering in Medicine.This work was partially funded by AMIT project (CEN-20101014) from the CDTICENIT program, CIBERsam (CB07/09/0031), projects TEC2010-21619-C04-01 and TEC2011-28972-C02-01 from Spanish Ministerio de Ciencia e Innovación, Spanish Government (ENTEPRASE Grant, PSE-300000-2009-5), PRECISION grant IPT-300000- 2010-3, CPAN (CSD-2007-00042@Ingenio2010), MEC (FPA2010-17142) and ARTEMIS program (S2009/DPI-1802) from Spanish Comunidad de Madrid and EU-ERDF program.Peer Reviewe