Utilisation de tests basés sur des statistiques d'ordre supérieur dans l'analyse de séries temporelles mesurées dans l'espace

Tests of hypotheses based on Higher Order Statistics (HOS) are reviewed in the particular context of the identification of nonlinear processes in space plasma. The time series under study are associated with the measurements of electric or/and magnetic field components, or/and counting rates of particles. The basic principles of HOS techniques are reviewed. A general and unified procedure is suggested in order to construct statistical tests: (1) for detecting a non-gaussian or transient signal in a gaussian (or non-gaussian) noise, (2) testing a stochastic time series for non-gaussianity (including non-linearity), (3) studying non-linear wave interactions by using the kth-order coherency function. Asymptotic theory of estimates of the kthorder spectra is implemented in a digital signal processing framework. The effectiveness of the signal detection algorithms is demonstrated through computer simulations. Examples of application on the analysis of satellite data are given.Des tests d'hypothèses basés sur des statistiques d'ordre supérieur sont revus dans le contexte particulier de l'identification de processus non-linéaires dans les plasmas spatiaux. Les séries temporelles étudiées sont associées à la mesure de composantes du champ électrique et/ou magnétique d'ondes ou de turbulences, et/ou de données particules. Les principes de base des statistiques d'ordre supérieur sont brièvement rappelés. Une procédure générale et unifiée est suggérée afin de construire des tests statistiques permettant: (1) de détecter des signaux non-gaussiens ou transitoires au sein d'un bruit gaussien (ou non-gaussien), (2) de tester si une série temporelle est associée ou non à un processus stochastique issu d'un processus non-linéaire, (3) d'étudier des interactions non-linéaires à plusieurs ondes par l'utilisation de la fonction de cohérence d'ordre k. La théorie asymptotique des estimés des spectres d'ordre k est mise en oeuvre dans le cas discret. L'efficacité des algorithmes de détection est démontrée par le biais de simulations numériques. Des exemples d'applications à des données satellites sont présentés

Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data

We measure cosmic weak lensing shear power spectra with the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalog covering 137deg$^2$ of the sky. Thanks to the high effective galaxy number density of $\sim$17 arcmin$^{-2}$ even after conservative cuts such as magnitude cut of $i<24.5$ and photometric redshift cut of $0.3\leq z \leq 1.5$, we obtain a high significance measurement of the cosmic shear power spectra in 4 tomographic redshift bins, achieving a total signal-to-noise ratio of 16 in the multipole range $300 \leq \ell \leq 1900$. We carefully account for various uncertainties in our analysis including the intrinsic alignment of galaxies, scatters and biases in photometric redshifts, residual uncertainties in the shear measurement, and modeling of the matter power spectrum. The accuracy of our power spectrum measurement method as well as our analytic model of the covariance matrix are tested against realistic mock shear catalogs. For a flat $\Lambda$ cold dark matter ($\Lambda$CDM) model, we find $S_8\equiv \sigma_8(\Omega_{\rm m}/0.3)^\alpha=0.800^{+0.029}_{-0.028}$ for $\alpha=0.45$ ($S_8=0.780^{+0.030}_{-0.033}$ for $\alpha=0.5$) from our HSC tomographic cosmic shear analysis alone. In comparison with Planck cosmic microwave background constraints, our results prefer slightly lower values of $S_8$, although metrics such as the Bayesian evidence ratio test do not show significant evidence for discordance between these results. We study the effect of possible additional systematic errors that are unaccounted in our fiducial cosmic shear analysis, and find that they can shift the best-fit values of $S_8$ by up to $\sim 0.6\sigma$ in both directions. The full HSC survey data will contain several times more area, and will lead to significantly improved cosmological constraints.Comment: 43 pages, 21 figures, accepted for publication in PAS

Reconstruction of the cosmic microwave background lensing for Planck

Aims. We prepare real-life cosmic microwave background (CMB) lensing extraction with the forthcoming Planck satellite data by studying two systematic effects related to the foreground contamination: the impact of foreground residuals after a component separation on the lensed CMB map, and the impact of removing a large contaminated region of the sky. Methods. We first use the generalized morphological component analysis (GMCA) method to perform a component separation within a simplified framework, which allows a high statistics Monte-Carlo study. For the second systematic, we apply a realistic mask on the temperature maps and then restore them with a recently developed inpainting technique on the sphere. We investigate the reconstruction of the CMB lensing from the resultant maps using a quadratic estimator in the flat sky limit and on the full sphere. Results. We find that the foreground residuals from the GMCA method does not significantly alter the lensed signal, which is also true for the mask corrected with the inpainting method, even in the presence of point source residuals

Efficient and Robust Signal Detection Algorithms for the Communication Applications

Signal detection and estimation has been prevalent in signal processing and communications for many years. The relevant studies deal with the processing of information-bearing signals for the purpose of information extraction. Nevertheless, new robust and efficient signal detection and estimation techniques are still in demand since there emerge more and more practical applications which rely on them. In this dissertation work, we proposed several novel signal detection schemes for wireless communications applications, such as source localization algorithm, spectrum sensing method, and normality test. The associated theories and practice in robustness, computational complexity, and overall system performance evaluation are also provided

Search for non-Gaussianity in Large Scale Structure surveys

In this work we put constraints on the primordial non-Gaussianities by using recent Large Scale Structure (LSS) surveys. The importance of measuring the amplitude of the primordial non-Gaussianity lies in the fact that it is the most prominent observational probe of the very early Universe. The plethora of the inflationary scenarios describing the early Universe makes it urgent to decide between them and create a solid physical theory for this era. The different inflation models predict different amount of non-Gaussianity in the primordial density perturbations, which will seed the LSS we observe. Therefore here we use the clustering results of prominent LSS surveys in order to test if they have the statistical power to constrain the primordial non-Gaussianity. We review the clustering of the radio sources from the NRAO VLA Sky Survey at z ∼ 1. The non-Gaussianity measured is one of the best determinations coming from LSS in the literature, f_{NL}= 62 ± 27 (68% CL). We also use the full scale range clustering of the LRG's from the CMASS of SDSS BOSS DR8 at z = 0.55. By using the scale dependence of the bias, originating from the existence of primordial non-Gaussianity, we fit non-Gaussian models to the large scales of our sample in order to measure the f_{NL}. The resulting fits show that there is room in this sample for non-Gaussianity. Although due to the large scale uncertainty errors the standard ΛCDM model cannot be excluded. Recently the measured non-Gaussianity from the SDSS BOSS CMASS sample, −92 < f_{NL} < 398 at 95% CL, shows that the constraints are not tight. This was expected because of the large scale statistical uncertainties in the clustering of this sample. Our best-fit measured f_{NL} = 71 ± 11 (1σ) is consistent with their measurements. The H-a emitters from HiZELS at a narrow redshift selection z = 2.23 are a promising survey for non-Gaussianity, but in order to gain any interesting constraints we have to wait for a larger sample. Finally we analyze the clustering of the ∼ 30, 000 quasar sample of SDSS BOSS DR9 at an effective redshift of z_{eff}= 2.4. The results show an amplitude excess in the clustering of the sample at the large scales. By fitting non-Gaussian models to the correlation function we measure, f_{NL} = 135 ± 9 at 1σ CL. ΛCDM fits the clustering results until 40 h-1 Mpc. However we cannot exclude the standard cosmological model since at the large scales that constrain f_{NL}, our results remain sensitive to the effects of systematic errors. We check the quasar sample for any potential systematics and particularly for the systematic effects of galactic extinction, seeing, sky brightness and foreground stars. Similar to previous studies the largest systematic comes from the presence of foreground stars. When we correct for such systematics we find, f_{NL}= 63 ± 16 (1σ). The measured amount of non-Gaussianity after correcting for the systematic effects is consistent with the results coming from the NVSS radio sources sample. Since the large scale amplitude of the clustering results is directly affected by systematics, we need to apply a more sophisticated method for correcting such effects. In any case, our original results show that the quasar sample shows excellent potential for determining the amplitude of primordial non-Gaussianity

Reconstruction of the CMB lensing for Planck

We prepare real-life Cosmic Microwave Background (CMB) lensing extraction with the forthcoming Planck satellite data, by studying two systematic effects related to the foregrounds contamination: the impact of foreground residuals after a component separation on the lensed CMB map, and of removing a large contaminated region of the sky. We first use the Generalized Morphological Component Analysis (GMCA) method to perform a component separation within a simplified framework which allows a high statistics Monte-Carlo study. For the second systematic, we apply a realistic mask on the temperature maps and then, restore them using a recent inpainting technique on the sphere. We investigate the reconstruction of the CMB lensing from the resultant maps using a quadratic estimator in the flat sky limit and on the full sphere. We find that the foreground residuals from the GMCA method does not alter significantly the lensed signal, nor does the mask corrected with the inpainting method, even in the presence of point sources residuals.Comment: 14 pages, 7 figures, major update to account for the impact of the point sources emissio

Different aspects of the interplay between light and the large-scale structure of the Universe

The main subject of this thesis is the influence of intrinsic alignments on weak lensing measurements. One possible source of intrinsic alignments are correlations in the angular momenta of neighbouring galaxies. Employing an improved ansatz for the angular momentum correlation function I show that the typical correlation length of Milky Way-sized haloes is about 1 Mpc/h which is slightly smaller than earlier work in this field suggested. Establishing the constitutive formalism to describe intrinsic alignments consistently in the framework of 3d cosmic shear I compute the resulting covariance matrices of different alignment types. For a Eucild-like survey it turns out that intrinsic alignments are more than one order of magnitude smaller than the lensing signal. In addition the parameter estimation bias in a two-dimensional non-tomographic weak lensing measurement is computed. The matter density Omega_m and the normalization of the linear matter power spectrum sigma_8 are most severely biased if intrinsic alignments are described by an angular momentum based alignment model. In the second part of my thesis I address secondary anisotropies of the cosmic microwave background: weak gravitational lensing and the nonlinear integrated Sachs-Wolfe (iSW) effect. The characteristic imprint of lensing can be used to reconstruct the lensing potential power spectrum. I show how this reconstruction is biased in the presence of primordial non-Gaussianities. For current values of f_NL, however, the bias is completely negligible on all but the largest angular scales. Finally, a novel analytical approach for the computation of the nonlinear iSW effect valid in the translinear regime is presented. It allows to identify two distinct contributions: the change of the gravitational self-energy density of the large-scale structure with (conformal) time and the Birkinshaw-Gull effect

Advanced statistical methods for detecting the Epoch of Reionisation

This thesis investigates the widefield foreground contamination on the expected 21cm power spectrum, by modelling these sources with multi-component 2D Gaussians. Additionally, we calculate the skew spectrum for a set of seven cosmological 21cm simulations, characterising how the higher order statistic changes with respect to the X-ray heating and ionisation topologies. We then develop an analytical framework for estimating the interferometric skew spectrum, applying this to realistic foreground models, and to a fiducial 21cm simulation

The Cosmic 21-cm Revolution Charting the first billion years of our universe

The redshifted 21-cm signal is set to transform astrophysical cosmology, bringing a historically data-starved field into the era of Big Data. Corresponding to the spin-flip transition of neutral hydrogen, the 21-cm line is sensitive to the temperature and ionization state of the cosmic gas, as well as to cosmological parameters. Crucially, with the development of new interferometers it will allow us to map out the first billion years of our universe, enabling us to learn about the properties of the unseen first generations of galaxies. Rapid progress is being made on both the observational and theoretical fronts, and important decisions on techniques and future direction are being made. The Cosmic 21-cm Revolution gathers contributions from current leaders in this fast-moving field, providing both an overview for graduate students and a reference point for current researchers

Non Gaussianity of primordial gravitational waves and cosmic density and velocity fields

We study non-Gaussianity of primordial gravitational waves (GWs) generated during inflation, and of present day matter and galaxy density and velocity fields in the Universe. We show that non-Gaussianity of primordial GWs is a crucial test of their origin and can be used to constrain the energy density fraction of spectator gauge fields in the early Universe if the primordial GWs are sourced by a spectator sector. We consider a particular inflation model containing a scalar inflaton, and spectator axion and SU(2) gauge fields. The axion and the gauge fields are coupled to each other via a Chern-Simons like interaction. Because of this coupling, the gauge fields experience a tachyonic instability during inflation and get amplified. The SU(2) gauge fields have a tensor degree of freedom which linearly sources GWs that are helical, and can be strongly scale-dependent. Moreover, their amplitude can be much larger than vacuum fluctuations of the metric. In this thesis however, we focus on scale-independent GWs produced in this model. We study the bispectrum of these scale- independent GWs, and find that its production is dominated by the self-interaction of the gauge fields. The shape of the tensor bispectrum is approximately an equilateral shape for 3<=mQ<=4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/Ph^2 , is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas we show that the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions. The present-day cosmic density and velocity fields in the Universe are also highly non- Gaussian due to non-linear gravitational evolution. By assuming the matter and galaxy density distributions to be log-normal, and the velocity field to be linearly generated from the matter density field, we show that the pairwise line-of-sight velocity distribution of log-normal fields is non-Gaussian and looks qualitatively similar to that measured from N-body simulations. The moments of the pairwise velocity PDF can in principle be ana- lytically calculated for this simple setting, giving us a handle on modelling of the full PDF. We compare the redshift space monopole and quadrupole power spectrum for our mock catalogs, finding a good match with the Kaiser prediction on large scales. We present a public code to generate log-normal mock catalogs of galaxies in redshift space which can be used to study the cross-correlation between galaxy positions and weak lensing fields. Our code is also being used to study power spectrum and bispectrum covariance matrices in real and redshift space, which will be useful for upcoming galaxy surveys such as PFS and Euclid