A Path Algorithm for Constrained Estimation

Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new path following algorithm for quadratic programming based on exact penalization. Similar penalties arise in $l_1$ regularization in model selection. Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. The exact path following method starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. Path following in lasso penalized regression, in contrast, starts with a large value of the penalty constant and works its way downward. In both settings, inspection of the entire solution path is revealing. Just as with the lasso and generalized lasso, it is possible to plot the effective degrees of freedom along the solution path. For a strictly convex quadratic program, the exact penalty algorithm can be framed entirely in terms of the sweep operator of regression analysis. A few well chosen examples illustrate the mechanics and potential of path following.Comment: 26 pages, 5 figure

Sinusoidal magnetic structure in a three-dimensional antiferromagnetic Co2(OH)AsO4: Incommensurate-commensurate magnetic phase transition

Co2 OH AsO4 has been prepared by hydrothermal synthesis and characterized from x-ray and neutron powder diffraction. The structure consists of a three-dimensional framework in which Co 1 O5-trigonal bipyramid dimers and Co 2 O6-octahedra chains are simultaneously present. The magnetic structure has been determined by neutron D2B and D1B powder-diffraction data. Below 22 K, the Co2 OH AsO4 phase shows an incommensurate antiferromagnetic structure along the b direction. The propagation vector 0, ,0 is temperature dependent with a value of =0.430 at the lowest temperature 1.8 K . Magnetization measurements of Co2 OH AsO4 show a complex magnetic behavior with the presence of three different signals. Between 6 and 21 K, a strong dependence of the magnetic field is observed with a shift of the inflexion point associated to the three-dimensional antiferromagnetic ordered from 18 K at 1 kOe to 20.1 K at 90 kOe. The small splitting observed in the zero-field-cooled-field-cooled curves at low temperatures is characteristic of ferromagnetic interactions but saturation is not reached even up to 90 kOe. Heat-capacity measurements show an unusual dependence on the magnetic field for antiferromagnetic transitions with a jump at the Neél temperature quite small 2 J/Kmol . The magnetic contribution exhibits a -type anomaly associated to the three-dimensional antiferromagnetic ordering. Surprisingly, the anomaly grows with the magnetic field and becomes better defined. Neutron powder diffraction in different fields shows a magnetic phase transition. The incommensurate magnetic structure evolves at low temperatures toward a collinear AF phase for fields higher than 35 kOe

First Detection of Polarization of the Submillimetre Diffuse Galactic Dust Emission by Archeops

We present the first determination of the Galactic polarized emission at 353 GHz by Archeops. The data were taken during the Arctic night of February 7, 2002 after the balloon--borne instrument was launched by CNES from the Swedish Esrange base near Kiruna. In addition to the 143 GHz and 217 GHz frequency bands dedicated to CMB studies, Archeops had one 545 GHz and six 353 GHz bolometers mounted in three polarization sensitive pairs that were used for Galactic foreground studies. We present maps of the I, Q, U Stokes parameters over 17% of the sky and with a 13 arcmin resolution at 353 GHz (850 microns). They show a significant Galactic large scale polarized emission coherent on the longitude ranges [100, 120] and [180, 200] deg. with a degree of polarization at the level of 4-5%, in agreement with expectations from starlight polarization measurements. Some regions in the Galactic plane (Gem OB1, Cassiopeia) show an even stronger degree of polarization in the range 10-20%. Those findings provide strong evidence for a powerful grain alignment mechanism throughout the interstellar medium and a coherent magnetic field coplanar to the Galactic plane. This magnetic field pervades even some dense clouds. Extrapolated to high Galactic latitude, these results indicate that interstellar dust polarized emission is the major foreground for PLANCK-HFI CMB polarization measurement.Comment: Submitted to Astron. & Astrophys., 14 pages, 12 Fig., 2 Table

QUBIC: The QU Bolometric Interferometer for Cosmology

One of the major challenges of modern cosmology is the detection of B-mode polarization anisotropies in the CMB. These originate from tensor fluctuations of the metric produced during the inflationary phase. Their detection would therefore constitute a major step towards understanding the primordial Universe. The expected level of these anisotropies is however so small that it requires a new generation of instruments with high sensitivity and extremely good control of systematic effects. We propose the QUBIC instrument based on the novel concept of bolometric interferometry, bringing together the sensitivity advantages of bolometric detectors with the systematics effects advantages of interferometry. Methods: The instrument will directly observe the sky through an array of entry horns whose signals will be combined together using an optical combiner. The whole set-up is located inside a cryostat. Polarization modulation will be achieved using a rotating half-wave plate and interference fringes will be imaged on two focal planes (separated by a polarizing grid) tiled with bolometers. We show that QUBIC can be considered as a synthetic imager, exactly similar to a usual imager but with a synthesized beam formed by the array of entry horns. Scanning the sky provides an additional modulation of the signal and improve the sky coverage shape. The usual techniques of map-making and power spectrum estimation can then be applied. We show that the sensitivity of such an instrument is comparable with that of an imager with the same number of horns. We anticipate a low level of beam-related systematics thanks to the fact that the synthesized beam is determined by the location of the primary horns. Other systematics should be under good control thanks to an autocalibration technique, specific to our concept, that will permit the accurate determination of most of the systematics parameters.Comment: 12 pages, 10 figures, submitted to Astronomy and Astrophysic

Diagnostic precision of image-guided multisampling core needle biopsy of suspected lymphomas in a primary care hospital

We evaluated the diagnostic quality of image-guided multisampling core needle biopsy (CNB) in patients investigated for suspected lymphoma in a primary care hospital. A total of 112 patients were consecutively assessed during a 3-year period. There were 80 lymphoid site biopsies and 32 non-lymphoid site biopsies. Eight to nine cores were obtained from different parts of the biopsy site. Two cores were systematically frozen, allowing for further morphological, immunochemistry and molecular studies. The diagnostic yield of CNB for malignancy was 100%. Only 47% (41/87) of patients with initial suspicion of lymphoma were finally diagnosed with Lymphoma. The diagnostic yield of CNB for lymphoma typing was 98% (62/63), according to the WHO classification. The diagnostic yield of CNB for complete lymphoma subtyping/grading was 86% (54/63). The diagnostic yield of CNB for a definite diagnosis of benignity was only 47% (8/17). In a primary care setting, multisampling CNB is a minimally invasive, and very accurate procedure for confirming malignancy in patients with suspected lymphoma, presenting with superficial/deep-seated, lymphoid/non-lymphoid site targets. With a very high diagnostic yield for lymphoma typing and a high diagnostic yield for complete lymphoma subtyping/grading a therapeutic decision can be taken in most patients

Planck Intermediate Results. IX. Detection of the Galactic haze with Planck

Using precise full-sky observations from Planck, and applying several methods of component separation, we identify and characterize the emission from the Galactic "haze" at microwave wavelengths. The haze is a distinct component of diffuse Galactic emission, roughly centered on the Galactic centre, and extends to |b| ~35 deg in Galactic latitude and |l| ~15 deg in longitude. By combining the Planck data with observations from the WMAP we are able to determine the spectrum of this emission to high accuracy, unhindered by the large systematic biases present in previous analyses. The derived spectrum is consistent with power-law emission with a spectral index of -2.55 +/- 0.05, thus excluding free-free emission as the source and instead favouring hard-spectrum synchrotron radiation from an electron population with a spectrum (number density per energy) dN/dE ~ E^-2.1. At Galactic latitudes |b|<30 deg, the microwave haze morphology is consistent with that of the Fermi gamma-ray "haze" or "bubbles," indicating that we have a multi-wavelength view of a distinct component of our Galaxy. Given both the very hard spectrum and the extended nature of the emission, it is highly unlikely that the haze electrons result from supernova shocks in the Galactic disk. Instead, a new mechanism for cosmic-ray acceleration in the centre of our Galaxy is implied.Comment: 15 pages, 9 figures, submitted to Astronomy and Astrophysic

Planck 2015 results. XXIII. The thermal Sunyaev-Zeldovich effect--cosmic infrared background correlation

We use Planck data to detect the cross-correlation between the thermal Sunyaev-Zeldovich (tSZ) effect and the infrared emission from the galaxies that make up the the cosmic infrared background (CIB). We first perform a stacking analysis towards Planck-confirmed galaxy clusters. We detect infrared emission produced by dusty galaxies inside these clusters and demonstrate that the infrared emission is about 50% more extended than the tSZ effect. Modelling the emission with a Navarro--Frenk--White profile, we find that the radial profile concentration parameter is $c_{500} = 1.00^{+0.18}_{-0.15}$. This indicates that infrared galaxies in the outskirts of clusters have higher infrared flux than cluster-core galaxies. We also study the cross-correlation between tSZ and CIB anisotropies, following three alternative approaches based on power spectrum analyses: (i) using a catalogue of confirmed clusters detected in Planck data; (ii) using an all-sky tSZ map built from Planck frequency maps; and (iii) using cross-spectra between Planck frequency maps. With the three different methods, we detect the tSZ-CIB cross-power spectrum at significance levels of (i) 6 $\sigma$, (ii) 3 $\sigma$, and (iii) 4 $\sigma$. We model the tSZ-CIB cross-correlation signature and compare predictions with the measurements. The amplitude of the cross-correlation relative to the fiducial model is $A_{\rm tSZ-CIB}= 1.2\pm0.3$. This result is consistent with predictions for the tSZ-CIB cross-correlation assuming the best-fit cosmological model from Planck 2015 results along with the tSZ and CIB scaling relations.Comment: 18 pages, 16 figure

Planck Intermediate Results. IV. The XMM-Newton validation programme for new Planck galaxy clusters

We present the final results from the XMM-Newton validation follow-up of new Planck galaxy cluster candidates. We observed 15 new candidates, detected with signal-to-noise ratios between 4.0 and 6.1 in the 15.5-month nominal Planck survey. The candidates were selected using ancillary data flags derived from the ROSAT All Sky Survey (RASS) and Digitized Sky Survey all-sky maps, with the aim of pushing into the low SZ flux, high-z regime and testing RASS flags as indicators of candidate reliability. 14 new clusters were detected by XMM, including 2 double systems. Redshifts lie in the range 0.2 to 0.9, with 6 clusters at z>0.5. Estimated M500 range from 2.5 10^14 to 8 10^14 Msun. We discuss our results in the context of the full XMM validation programme, in which 51 new clusters have been detected. This includes 4 double and 2 triple systems, some of which are chance projections on the sky of clusters at different z. We find that association with a RASS-BSC source is a robust indicator of the reliability of a candidate, whereas association with a FSC source does not guarantee that the SZ candidate is a bona fide cluster. Nevertheless, most Planck clusters appear in RASS maps, with a significance greater than 2 sigma being a good indication that the candidate is a real cluster. The full sample gives a Planck sensitivity threshold of Y500 ~ 4 10^-4 arcmin^2, with indication for Malmquist bias in the YX-Y500 relation below this level. The corresponding mass threshold depends on z. Systems with M500 > 5 10^14 Msun at z > 0.5 are easily detectable with Planck. The newly-detected clusters follow the YX-Y500 relation derived from X-ray selected samples. Compared to X-ray selected clusters, the new SZ clusters have a lower X-ray luminosity on average for their mass. There is no indication of departure from standard self-similar evolution in the X-ray versus SZ scaling properties. (abridged)Comment: accepted by A&

Planck Intermediate Results II: Comparison of Sunyaev-Zeldovich measurements from Planck and from the Arcminute Microkelvin Imager for 11 galaxy clusters

A comparison is presented of Sunyaev-Zeldovich measurements for 11 galaxy clusters as obtained by Planck and by the ground-based interferometer, the Arcminute Microkelvin Imager. Assuming a universal spherically-symmetric Generalised Navarro, Frenk & White (GNFW) model for the cluster gas pressure profile, we jointly constrain the integrated Compton-Y parameter (Y_500) and the scale radius (theta_500) of each cluster. Our resulting constraints in the Y_500-theta_500 2D parameter space derived from the two instruments overlap significantly for eight of the clusters, although, overall, there is a tendency for AMI to find the Sunyaev-Zeldovich signal to be smaller in angular size and fainter than Planck. Significant discrepancies exist for the three remaining clusters in the sample, namely A1413, A1914, and the newly-discovered Planck cluster PLCKESZ G139.59+24.18. The robustness of the analysis of both the Planck and AMI data is demonstrated through the use of detailed simulations, which also discount confusion from residual point (radio) sources and from diffuse astrophysical foregrounds as possible explanations for the discrepancies found. For a subset of our cluster sample, we have investigated the dependence of our results on the assumed pressure profile by repeating the analysis adopting the best-fitting GNFW profile shape which best matches X-ray observations. Adopting the best-fitting profile shape from the X-ray data does not, in general, resolve the discrepancies found in this subset of five clusters. Though based on a small sample, our results suggest that the adopted GNFW model may not be sufficiently flexible to describe clusters universally.Comment: update to metadata author list onl

Planck intermediate results. III. The relation between galaxy cluster mass and Sunyaev-Zeldovich signal

We examine the relation between the galaxy cluster mass M and Sunyaev-Zeldovich (SZ) effect signal D_A^2 Y for a sample of 19 objects for which weak lensing (WL) mass measurements obtained from Subaru Telescope data are available in the literature. Hydrostatic X-ray masses are derived from XMM-Newton archive data and the SZ effect signal is measured from Planck all-sky survey data. We find an M_WL-D_A^2 Y relation that is consistent in slope and normalisation with previous determinations using weak lensing masses; however, there is a normalisation offset with respect to previous measures based on hydrostatic X-ray mass-proxy relations. We verify that our SZ effect measurements are in excellent agreement with previous determinations from Planck data. For the present sample, the hydrostatic X-ray masses at R_500 are on average ~ 20 per cent larger than the corresponding weak lensing masses, at odds with expectations. We show that the mass discrepancy is driven by a difference in mass concentration as measured by the two methods, and, for the present sample, the mass discrepancy and difference in mass concentration is especially large for disturbed systems. The mass discrepancy is also linked to the offset in centres used by the X-ray and weak lensing analyses, which again is most important in disturbed systems. We outline several approaches that are needed to help achieve convergence in cluster mass measurement with X-ray and weak lensing observations.Comment: 19 pages, 9 figures, matches accepted versio