Convolutional neural networks on the HEALPix sphere: a pixel-based algorithm and its application to CMB data analysis

We describe a novel method for the application of convolutional neural networks (CNNs) to fields defined on the sphere, using the Hierarchical Equal Area Latitude Pixelization scheme (HEALPix). Specifically, we have developed a pixel-based approach to implement convolutional and pooling layers on the spherical surface, similarly to what is commonly done for CNNs applied to Euclidean space. The main advantage of our algorithm is to be fully integrable with existing, highly optimized libraries for NNs (e.g., PyTorch, TensorFlow, etc.). We present two applications of our method: (i) recognition of handwritten digits projected on the sphere; (ii) estimation of cosmological parameter from simulated maps of the cosmic microwave background (CMB). The latter represents the main target of this exploratory work, whose goal is to show the applicability of our CNN to CMB parameter estimation. We have built a simple NN architecture, consisting of four convolutional and pooling layers, and we have used it for all the applications explored herein. Concerning the recognition of handwritten digits, our CNN reaches an accuracy of 95%, comparable with other existing spherical CNNs, and this is true regardless of the position and orientation of the image on the sphere. For CMB-related applications, we tested the CNN on the estimation of a mock cosmological parameter, defining the angular scale at which the power spectrum of a Gaussian field projected on the sphere peaks. We estimated the value of this parameter directly from simulated maps, in several cases: temperature and polarization maps, presence of white noise, and partially covered maps. For temperature maps, the NN performances are comparable with those from standard spectrum-based Bayesian methods. For polarization, CNNs perform about a factor four worse than standard algorithms. Nonetheless, our results demonstrate, for the first time, that CNNs are able to extract information from polarization fields, both in full-sky and masked maps, and to distinguish between E and B-modes in pixel space. Lastly, we have applied our CNN to the estimation of the Thomson scattering optical depth at reionization (\u3c4) from simulated CMB maps. Even without any specific optimization of the NN architecture, we reach an accuracy comparable with standard Bayesian methods. This work represents a first step towards the exploitation of NNs in CMB parameter estimation and demonstrates the feasibility of our approach

CHALLENGES FOR PRESENT AND FUTURE COSMIC MICROWAVE BACKGROUND OBSERVATIONS: SYSTEMATIC EFFECTS AND FOREGROUND EMISSION IN POLARIZATION

The study and characterization of the Cosmic Microwave Background (CMB) polarized signal represent, nowadays, one of the most im- portant branches of observational cosmology. In the curl component of the CMB polarization (also known as \u201cB-modes\u201d) it is thought to be hiding the imprint of primordial gravitational waves generated during the inflationary epoch. The observation of this signal would therefore open the door to the study of the physics of the very early universe. The CMB B-modes signal is extremely faint, at the level of fraction of \ub5K, and sophisticated experiments with high sensitivity are needed to detect it. Moreover, the control of instrumental systematic effects and the characterization of foreground emission represent important challenges for this kind of measurements. In this thesis we investigated these two issues focusing on two specific and explicatory experimental cases. By analyzing the multi-frequency polarized observations of the Planck satellite, we studied the contamination arising from the Galactic foreground emission in the CMB observation carried out by the BICEP2 experiment. We showed how the polarized thermal dust emission dominates over the CMB B-modes signal at frequencies as low as 150 GHz and even at high Galactic latitudes. For what concern the instrumental systematic effects we developed a simulation pipeline for the LSPE (Large Scale Polarization Explorer) low frequency instrument. LSPE is a future balloon-borne experiment, aimed at observing the CMB polarized signal on the very large angular scales. Our pipeline simulates the sky observation of the STRIP instrument allowing to understand the expected scientific performance. The presence of possible sources of instrumental systematic effects is also considered and their expected impact on final scientific results is determined

An XMM-Newton view of Planetary Nebulae in the Small Magellanic Cloud. The X-ray luminous central star of SMP SMC 22

During an X-ray survey of the Small Magellanic Cloud, carried out with the XMM-Newton satellite, we detected significant soft X-ray emission from the central star of the high-excitation planetary nebula SMP SMC 22. Its very soft spectrum is well fit with a non local thermodynamical equilibrium model atmosphere composed of H, He, C, N, and O, with abundances equal to those inferred from studies of its nebular lines. The derived effective temperature of 1.5x10^5 K is in good agreement with that found from the optical/UV data. The unabsorbed flux in the 0.1-0.5 keV range is about 3x10^{-11} erg cm^-2 s^-1, corresponding to a luminosity of 1.2x10^37 erg/s at the distance of 60 kpc. We also searched for X-ray emission from a large number of SMC planetary nebulae, confirming the previous detection of SMP SMC 25 with a luminosity of (0.2-6)x10^35 erg/s (0.1-1 keV). For the remaining objects that were not detected, we derived flux upper limits corresponding to luminosity values from several tens to hundreds times smaller than that of SMP SMC 22. The exceptionally high X-ray luminosity of SMP SMC 22 is probably due to the high mass of its central star, quickly evolving toward the white dwarf's cooling branch, and to a small intrinsic absorption in the nebula itself.Comment: Accepted for publication on Astronomy and Astrophysic

S-PASS view of polarized Galactic synchrotron at 2.3 GHz as a contaminant to CMB observations

We have analyzed the southern sky emission in linear polarization at 2.3 GHz as observed by the S-band Polarization All Sky Survey (S-PASS). Our purpose is to study the properties of the diffuse Galactic polarized synchrotron as a contaminant to B-mode observations of the cosmic microwave background (CMB) polarization. We studied the angular distribution of the S-PASS signal at intermediate and high Galactic latitudes by means of the polarization angular power spectra. The power spectra, computed in the multipole interval 20 64 ` 641000, show a decay of the spectral amplitude as a function of multipole for ` . 200, typical of the diffuse emission. At smaller angular scales, power spectra are dominated by the radio point source radiation. We find that, at low multipoles, spectra can be approximated by a power law CEE;BB ` /, with ' 3, and characterized by a B-To-E ratio of about 0.5. We measured the polarized synchrotron spectral energy distribution (SED) in harmonic space, by combining S-PASS power spectra with low frequency WMAP and Planck ones, and by fitting their frequency dependence in six multipole bins, in the range 20 64 \u2113 64 140. Results show that the recovered SED, in the frequency range 2.333 GHz, is compatible with a power law with \u3b2 s =-3:22 \ub1 0:08, which appears to be constant over the considered multipole range and in the different Galactic cuts. Combining the S-PASS total polarized intensity maps with those coming from WMAP and Planck we derived a map of the synchrotron spectral index \u3b2 s at angular resolution of 2\ub0 on about 30% of the sky. The recovered \u3b2s distribution peaks at the value around-3.2. It exibits an angular power spectrum which can be approximated with a power law C`\u2113 ` with \u3b3-2:6. We also measured a significant spatial correlation between synchrotron and thermal dust signals, as traced by the Planck 353 GHz channel. This correlation reaches about 40% on the larger angular scales, decaying considerably at the degree scales. Finally, we used the S-PASS maps to assess the polarized synchrotron contamination to CMB observations of the B-modes at higher frequencies. We divided the sky in small patches (with fsky ' 1%) and find that, at 90 GHz, the minimal contamination, in the cleanest regions of the sky, is at the level of an equivalent tensor-To-scalar ratio rsynch 4810--3-. Moreover, by combining S-PASS data with Planck 353 GHz observations, we recover a map of the minimum level of total polarized foreground contamination to B-modes, finding that there is no region of the sky, at any frequency, where this contamination lies below equivalent tenor-To-scalar ratio rFG ' 10-3. This result confirms the importance of observing both high and low frequency foregrounds in CMB B-mode measurements

The Large-Scale Polarization Explorer (LSPE)

The LSPE is a balloon-borne mission aimed at measuring the polarization of the Cosmic Microwave Background (CMB) at large angular scales, and in particular to constrain the curl component of CMB polarization (B-modes) produced by tensor perturbations generated during cosmic inflation, in the very early universe. Its primary target is to improve the limit on the ratio of tensor to scalar perturbations amplitudes down to r = 0.03, at 99.7% confidence. A second target is to produce wide maps of foreground polarization generated in our Galaxy by synchrotron emission and interstellar dust emission. These will be important to map Galactic magnetic fields and to study the properties of ionized gas and of diffuse interstellar dust in our Galaxy. The mission is optimized for large angular scales, with coarse angular resolution (around 1.5 degrees FWHM), and wide sky coverage (25% of the sky). The payload will fly in a circumpolar long duration balloon mission during the polar night. Using the Earth as a giant solar shield, the instrument will spin in azimuth, observing a large fraction of the northern sky. The payload will host two instruments. An array of coherent polarimeters using cryogenic HEMT amplifiers will survey the sky at 43 and 90 GHz. An array of bolometric polarimeters, using large throughput multi-mode bolometers and rotating Half Wave Plates (HWP), will survey the same sky region in three bands at 95, 145 and 245 GHz. The wide frequency coverage will allow optimal control of the polarized foregrounds, with comparable angular resolution at all frequencies.Comment: In press. Copyright 2012 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibite

Quantum dynamics in ultra-cold atomic physics

We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially large. These phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum EPR entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorp- tion, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator

Characterization of foreground emission on degree angular scales for CMB B-mode observations: Thermal dust and synchrotron signal from Planck and WMAP data

We quantify the contamination from polarized diffuse Galactic synchrotron and thermal dust emissions to the B modes of the cosmic microwave background (CMB) anisotropies on the degree angular scale, using data from the Planck and Wilkinson Microwave Anisotropy Probe (WMAP) satellites. We compute power spectra of foreground polarized emissions in 352 circular sky patches located at Galactic latitude | b | > 20\ub0, each of which covers about 1.5% of the sky. We make use of the spectral properties derived from Planck and WMAP data to extrapolate, in frequency, the amplitude of synchrotron and thermal dust B-mode spectra in the multipole bin centered at \u2113 43 80. In this way we estimate the amplitude and frequency of the foreground minimum for each analyzed region. We detect both dust and synchrotron signal on degree angular scales and at a 3\u3c3 confidence level in 28 regions. Here the minimum of the foreground emission is found at frequencies between 60 and 100 GHz with an amplitude expressed in terms of the equivalent tensor-to-scalar ratio, rFG,min, between 3c0.06 and 3c1. Some of these regions are located at high Galactic latitudes in areas close to the ones that are being observed by suborbital experiments. In all the other sky patches where synchrotron or dust B modes are not detectable with the required confidence, we put upper limits on the minimum foreground contamination and find values of rFG,min between 3c0.05 and 3c1.5 in the frequency range 60-90 GHz. Our results indicate that, with the current sensitivity at low frequency, it is not possible to exclude the presence of synchrotron contamination to CMB cosmological B modes at the level requested to measure a gravitational waves signal with r 43 0.01 at frequency 72 100 GHz anywhere. Therefore, more accurate data are essential in order to better characterize the synchrotron polarized component and, eventually, to remove its contamination to CMB signal through foreground cleaning. \ua9 2016 ESO

Mean field effects on the scattered atoms in condensate collisions

We consider the collision of two Bose Einstein condensates at supersonic velocities and focus on the halo of scattered atoms. This halo is the most important feature for experiments and is also an excellent testing ground for various theoretical approaches. In particular we find that the typical reduced Bogoliubov description, commonly used, is often not accurate in the region of parameters where experiments are performed. Surprisingly, besides the halo pair creation terms, one should take into account the evolving mean field of the remaining condensate and on-condensate pair creation. We present examples where the difference is clearly seen, and where the reduced description still holds.Comment: 6 pages, 4 figure

A coherent polarimeter array for the Large Scale Polarization Explorer balloon experiment

We discuss the design and expected performance of STRIP (STRatospheric Italian Polarimeter), an array of coherent receivers designed to fly on board the LSPE (Large Scale Polarization Explorer) balloon experiment. The STRIP focal plane array comprises 49 elements in Q band and 7 elements in W-band using cryogenic HEMT low noise amplifiers and high performance waveguide components. In operation, the array will be cooled to 20 K and placed in the focal plane of a $\sim 0.6$ meter telescope providing an angular resolution of $\sim1.5$ degrees. The LSPE experiment aims at large scale, high sensitivity measurements of CMB polarization, with multi-frequency deep measurements to optimize component separation. The STRIP Q-band channel is crucial to accurately measure and remove the synchrotron polarized component, while the W-band channel, together with a bolometric channel at the same frequency, provides a crucial cross-check for systematic effects.Comment: In press on the Proceedings of the SPIE Conference Astronomical Telescopes + instrumentation 2012, Amsterdam, paper 8446-27

Measurements of tropospheric ice clouds with a ground-based CMB polarization experiment, POLARBEAR

The polarization of the atmosphere has been a long-standing concern for ground-based experiments targeting cosmic microwave background (CMB) polarization. Ice crystals in upper tropospheric clouds scatter thermal radiation from the ground and produce a horizontally polarized signal. We report a detailed analysis of the cloud signal using a ground-based CMB experiment, Polarbear, located at the Atacama desert in Chile and observing at 150 GHz. We observe horizontally polarized temporal increases of low-frequency fluctuations ("polarized bursts," hereafter) of 720.1 K when clouds appear in a webcam monitoring the telescope and the sky. The hypothesis of no correlation between polarized bursts and clouds is rejected with >24\u3c3 statistical significance using three years of data. We consider many other possibilities including instrumental and environmental effects, and find no reasons other than clouds that can explain the data better. We also discuss the impact of the cloud polarization on future ground-based CMB polarization experiments