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There is demand in diverse fields for a reliable method of estimating the entropy associated with correlations. The estimation of a unique entropy directly from the Pearson correlation matrix has remained an open problem for more than half a century. All existing approaches lack generality insofar as they require thresholding choices that arbitrarily remove possibly important information. Here we propose an objective procedure for directly estimating a unique entropy of a general Pearson matrix. We show that upon rescaling the Pearson matrix satisfies all necessary conditions for an analog of the von Neumann entropy to be well defined. No thresholding is required. We demonstrate the method by estimating the entropy from neuroimaging time series of the human brain under the influence of a psychedelic., Comment: 12 pages, 6 figures

In this paper we present the design and measured performance of a novel cryogenic motor based on a superconducting magnetic bearing (SMB). The motor is tailored for use in millimeter-wave half-wave plate (HWP) polarimeters, where a HWP is rapidly rotated in front of a polarization analyzer or polarization-sensitive detector. This polarimetry technique is commonly used in cosmic microwave background (CMB) polarization studies. The SMB we use is composed of fourteen yttrium barium copper oxide (YBCO) disks and a contiguous neodymium iron boron (NdFeB) ring magnet. The motor is a hollow-shaft motor because the HWP is ultimately installed in the rotor. The motor presented here has a 100 mm diameter rotor aperture. However, the design can be scaled up to rotor aperture diameters of approximately 500 mm. Our motor system is composed of four primary subsystems: (i) the rotor assembly, which includes the NdFeB ring magnet, (ii) the stator assembly, which includes the YBCO disks, (iii) an incremental encoder, and (iv) the drive electronics. While the YBCO is cooling through its superconducting transition, the rotor is held above the stator by a novel hold and release mechanism (HRM). The encoder subsystem consists of a custom-built encoder disk read out by two fiber optic readout sensors. For the demonstration described in this paper, we ran the motor at 50 K and tested rotation frequencies up to approximately 10 Hz. The feedback system was able to stabilize the the rotation speed to approximately 0.4%, and the measured rotor orientation angle uncertainty is less than 0.15 deg. Lower temperature operation will require additional development activities, which we will discuss.

Instabilities and turbulence extending to the smallest dynamical scales play important roles in the deposition of energy and momentum by gravity waves throughout the atmosphere. However, these dynamics and their effects have been impossible to quantify to date due to lack of observational guidance. Serendipitous optical images of polar mesospheric clouds at ~82 km obtained by star cameras aboard a cosmology experiment deployed on a stratospheric balloon provide a new observational tool, revealing instability and turbulence structures extending to spatial scales < 20 m. At 82 km, this resolution provides sensitivity extending to the smallest turbulence scale not strongly influenced by viscosity: the "inner scale" of turbulence, $l_0\sim$10($\nu^3$/$\epsilon$)$^{1/4}$. Such images represent a new window into small-scale dynamics that occur throughout the atmosphere but are impossible to observe in such detail at any other altitude. We present a sample of images revealing a range of dynamics features, and employ numerical simulations that resolve these dynamics to guide our interpretation of several observed events., Comment: 10 pages, 5 figures. Figures available online: http://cosmology.phys.columbia.edu/pmc/

We present polarization observations of two Galactic plane fields centered on Galactic coordinates (l,b)=(0 deg,0 deg) and (329 deg, 0 deg) at Q- (43 GHz) and W-band (95 GHz), covering between 301 and 539 square degrees depending on frequency and field. These measurements were made with the QUIET instrument between 2008 October and 2010 December, and include a total of 1263 hours of observations. The resulting maps represent the deepest large-area Galactic polarization observations published to date at the relevant frequencies with instrumental rms noise varying between 1.8 and 2.8 uK deg, 2.3-6 times deeper than corresponding WMAP and Planck maps. The angular resolution is 27.3' and 12.8' FWHM at Q- and W-band, respectively. We find excellent agreement between the QUIET and WMAP maps over the entire fields, and no compelling evidence for significant residual instrumental systematic errors in either experiment, whereas the Planck 44 GHz map deviates from these in a manner consistent with reported systematic uncertainties for this channel. We combine QUIET and WMAP data to compute inverse-variance-weighted average maps, effectively retaining small angular scales from QUIET and large angular scales from WMAP. From these combined maps, we derive constraints on several important astrophysical quantities, including a robust detection of polarized synchrotron spectral index steepening of ~0.2 off the plane, as well as the Faraday rotation measure toward the Galactic center (RM=-4000 +/- 200 rad m^-2), all of which are consistent with previously published results. Both the raw QUIET and the co-added QUIET+WMAP maps are made publicly available together with all necessary ancillary information., Comment: 22 pages, 18 figures; accepted for publication in ApJ; data are available on Lambda (http://lambda.gsfc.nasa.gov)

We present polarization measurements of extragalactic radio sources observed during the Cosmic Microwave Background polarization survey of the Q/U Imaging Experiment (QUIET), operating at 43 GHz (Q-band) and 95 GHz (W-band). We examine sources selected at 20 GHz from the public, $>$40 mJy catalog of the Australia Telescope (AT20G) survey. There are $\sim$480 such sources within QUIET's four low-foreground survey patches, including the nearby radio galaxies Centaurus A and Pictor A. The median error on our polarized flux density measurements is 30--40 mJy per Stokes parameter. At S/N $> 3$ significance, we detect linear polarization for seven sources in Q-band and six in W-band; only $1.3 \pm 1.1$ detections per frequency band are expected by chance. For sources without a detection of polarized emission, we find that half of the sources have polarization amplitudes below 90 mJy (Q-band) and 106 mJy (W-band), at 95% confidence. Finally, we compare our polarization measurements to intensity and polarization measurements of the same sources from the literature. For the four sources with WMAP and Planck intensity measurements $>1$ Jy, the polarization fraction are above 1% in both QUIET bands. At high significance, we compute polarization fractions as much as 10--20% for some sources, but the effects of source variability may cut that level in half for contemporaneous comparisons. Our results indicate that simple models---ones that scale a fixed polarization fraction with frequency---are inadequate to model the behavior of these sources and their contributions to polarization maps., Comment: 16 pages, 10 figures. Submitted to ApJ

We discuss the design, fabrication, and testing of prototype horn-coupled, lumped-element kinetic inductance detectors (LEKIDs) designed for cosmic microwave background (CMB) studies. The LEKIDs are made from a thin aluminum film deposited on a silicon wafer and patterned using standard photolithographic techniques at STAR Cryoelectronics, a commercial device foundry. We fabricated twenty-element arrays, optimized for a spectral band centered on 150 GHz, to test the sensitivity and yield of the devices as well as the multiplexing scheme. We characterized the detectors in two configurations. First, the detectors were tested in a dark environment with the horn apertures covered, and second, the horn apertures were pointed towards a beam-filling cryogenic blackbody load. These tests show that the multiplexing scheme is robust and scalable, the yield across multiple LEKID arrays is 91%, and the noise-equivalent temperatures (NET) for a 4 K optical load are in the range 26$\thinspace\pm6 \thinspace \mu \mbox{K} \sqrt{\mbox{s}}$.

We present the results of a feasibility study, which examined deployment of a ground-based millimeter-wave polarimeter, tailored for observing the cosmic microwave background (CMB), to Isi Station in Greenland. The instrument for this study is based on lumped-element kinetic inductance detectors (LEKIDs) and an F/2.4 catoptric, crossed-Dragone telescope with a 500 mm aperture. The telescope is mounted inside the receiver and cooled to $<\,4$ K by a closed-cycle $^4$He refrigerator to reduce background loading on the detectors. Linearly polarized signals from the sky are modulated with a metal-mesh half-wave plate that is rotated at the aperture stop of the telescope with a hollow-shaft motor based on a superconducting magnetic bearing. The modular detector array design includes at least 2300 LEKIDs, and it can be configured for spectral bands centered on 150~GHz or greater. Our study considered configurations for observing in spectral bands centered on 150, 210 and 267~GHz. The entire polarimeter is mounted on a commercial precision rotary air bearing, which allows fast azimuth scan speeds with negligible vibration and mechanical wear over time. A slip ring provides power to the instrument, enabling circular scans (360 degrees of continuous rotation). This mount, when combined with sky rotation and the latitude of the observation site, produces a hypotrochoid scan pattern, which yields excellent cross-linking and enables 34\% of the sky to be observed using a range of constant elevation scans. This scan pattern and sky coverage combined with the beam size (15~arcmin at 150~GHz) makes the instrument sensitive to $5 < \ell < 1000$ in the angular power spectra.

The Stratospheric Kinetic Inductance Polarimeter (SKIP) is a proposed balloon-borne experiment designed to study the cosmic microwave background, the cosmic infrared background and Galactic dust emission by observing 1133 square degrees of sky in the Northern Hemisphere with launches from Kiruna, Sweden. The instrument contains 2317 single-polarization, horn-coupled, aluminum lumped-element kinetic inductance detectors (LEKID). The LEKIDs will be maintained at 100 mK with an adiabatic demagnetization refrigerator. The polarimeter operates in two configurations, one sensitive to a spectral band centered on 150 GHz and the other sensitive to 260 and 350 GHz bands. The detector readout system is based on the ROACH-1 board, and the detectors will be biased below 300 MHz. The detector array is fed by an F/2.4 crossed-Dragone telescope with a 500 mm aperture yielding a 15 arcmin FWHM beam at 150 GHz. To minimize detector loading and maximize sensitivity, the entire optical system will be cooled to 1 K. Linearly polarized sky signals will be modulated with a metal-mesh half-wave plate that is mounted at the telescope aperture and rotated by a superconducting magnetic bearing. The observation program consists of at least two, five-day flights beginning with the 150 GHz observations., Comment: J Low Temp Phys DOI 10.1007/s10909-013-1014-3 The final publication is available at link.springer.com

The Q/U Imaging ExperimenT (QUIET) has observed the cosmic microwave background (CMB) at 43 and 95GHz. The 43-GHz results have been published in QUIET Collaboration et al. (2011), and here we report the measurement of CMB polarization power spectra using the 95-GHz data. This data set comprises 5337 hours of observations recorded by an array of 84 polarized coherent receivers with a total array sensitivity of 87 uK sqrt(s). Four low-foreground fields were observed, covering a total of ~1000 square degrees with an effective angular resolution of 12.8', allowing for constraints on primordial gravitational waves and high-signal-to-noise measurements of the E-modes across three acoustic peaks. The data reduction was performed using two independent analysis pipelines, one based on a pseudo-Cl (PCL) cross-correlation approach, and the other on a maximum-likelihood (ML) approach. All data selection criteria and filters were modified until a predefined set of null tests had been satisfied before inspecting any non-null power spectrum. The results derived by the two pipelines are in good agreement. We characterize the EE, EB and BB power spectra between l=25 and 975 and find that the EE spectrum is consistent with LCDM, while the BB power spectrum is consistent with zero. Based on these measurements, we constrain the tensor-to-scalar ratio to r=1.1+0.9-0.8 (r<2.8 at 95% C.L.) as derived by the ML pipeline, and r=1.2+0.9-0.8 (r<2.7 at 95% C.L.) as derived by the PCL pipeline. In one of the fields, we find a correlation with the dust component of the Planck Sky Model, though the corresponding excess power is small compared to statistical errors. Finally, we derive limits on all known systematic errors, and demonstrate that these correspond to a tensor-to-scalar ratio smaller than r=0.01, the lowest level yet reported in the literature., Comment: 10 pages, 6 figures, 3 tables, submitted to ApJ, This paper should be cited as "QUIET Collaboration (2012)." v2: updated to reflect published version

Scanning tunneling spectroscopies are performed below 100~mK on nano-crystalline boron-doped diamond films characterized by Transmission Electron Microscopy and transport measurements. We demonstrate a strong correlation between the local superconductivity strength and the granular structure of the films. The study of the spectral shape, amplitude and temperature dependence of the superconductivity gap enables us to differentiate intrinsically superconducting grains that follow the BCS model, from grains showing a different behavior involving the superconducting proximity effect.