The effect of the linear term on the wavelet estimator of primordial non-Gaussianity

In this work we present constraints on different shapes of primordial non-Gaussianity using the Wilkinson Microwave Anisotropy Probe (WMAP) 7-year data and the spherical Mexican hat wavelet fnl estimator including the linear term correction. In particular we focus on the local, equilateral and orthogonal shapes. We first analyse the main statistical properties of the wavelet estimator and show the conditions to reach optimality. We include the linear term correction in our estimators and compare the estimates with the values already published using only the cubic term. The estimators are tested with realistic WMAP simulations with anisotropic noise and the WMAP KQ75 sky cut. The inclusion of the linear term correction shows a negligible improvement (< 1 per cent) in the error-bar for any of the shapes considered. The results of this analysis show that, in the particular case of the wavelet estimator, the optimality for WMAP anisotropy levels is basically achieved with the mean subtraction and in practical terms there is no need of including a linear term once the mean has been subtracted. Our best estimates are now: local fnl = 39.0 +/ 21.4, equilateral fnl = -62.8 +/- 154.0 and orthogonal fnl = -159.8 +/- 115.1 (all cases 68 per cent CL). We have also computed the expected linear term correction for simulated Planck maps with anisotropic noise at 143 GHz following the Planck Sky Model and including a mask. The improvement achieved in this case for the local fnl error-bar is also negligible (0.4 per cent).Comment: 8 pages, 5 figures, 4 tables. Minor revision, one figure added, accepted for publication in MNRA

The realizability problem as a special case of the infinite-dimensional truncated moment problem

The realizability problem is a well-known problem in the analysis of complex systems, which can be modeled as an infinite-dimensional moment problem. More precisely, as a truncated K-moment problem where K is the space of all possible configurations of the components of the considered system. The power of this reformulation has been already exploited by Kuna, Lebowitz, and Speer [Ann. Appl. Probab. 21 (2011), pp. 1253-1281], where necessary and sufficient conditions of Haviland type have been obtained for several instances of the realizability problem. In this article we exploit this same reformulation to apply to the realizability problem the recent advances obtained by Curto, Ghasemi, Infusino, and Kuhlmann [J. Operator Theory 90 (2023), pp. 223-261] for the truncated moment problem for linear functionals on general unital commutative algebras. This provides alternative proofs and sometimes extensions of several results of Kuna, Lebowitz, and Speer [Ann. Appl. Probab. 21 (2011), pp. 1253-1281], allowing to finally embed them in the above-mentioned unified framework for the infinite-dimensional truncated moment problem

Wilkinson Microwave Anisotropy Probe 7-yr constraints on fNL with a fast wavelet estimator

A new method to constrain the local non-linear coupling parameter fNL based on a fast wavelet decomposition is presented. Using a multiresolution wavelet adapted to the HEALPix pixelization, we have developed a method that is 10^2 times faster than previous estimators based on isotropic wavelets and 10^3 faster than the KSW bispectrum estimator, at the resolution of the Wilkinson Microwave Anisotropy Probe (WMAP) data. The method has been applied to the WMAP 7-yr V+W combined map, imposing constraints on fNL of -69 < fNL < 65 at the 95 per cent CL. This result has been obtained after correcting for the contribution of the residual point sources which has been estimated to be fNL = 7 +/- 6. In addition, a Gaussianity analysis of the data has been carried out using the third order moments of the wavelet coefficients, finding consistency with Gaussianity. Although the constrainsts imposed on fNL are less stringent than those found with optimal estimators, we believe that a very fast method, as the one proposed in this work, can be very useful, especially bearing in mind the large amount of data that will be provided by future experiments, such as the Planck satellite. Moreover, the localisation of wavelets allows one to carry out analyses on different regions of the sky. As an application, we have separately analysed the two hemispheres defined by the dipolar modulation proposed by Hoftuft et al. (2009). We do not find any significant asymmetry regarding the estimated value of fNL in those hemispheres.Comment: 8 pages, 5 figures. Submitted and Accepted for publication in MNRA

A Recursive approach to the matrix moment problem

In this paper, we study the truncated matrix moment problem in one variable through recursive matrix extensions. \ We give necessary and sufficient conditions for a recursive matrix extension of finite data to be a matrix moment sequence in the classical cases of Hamburger, Stieltjes, and Hausdorff moment problems. \ We also discuss matricial subnormal completion and matricial $k$--hyponormal completion problems and provide an analog of Stampfli's Theorem on flat propagation for $2$--hyponormal matricial weighted shifts.Comment: 27 page

Longitudinal and radial variation of the wood density in an unmanaged stand of Araucaria angustifolia.

Edição dos abstracts do 24º IUFRO World Congress, 2014, Salt Lake City. Sustaining forests, sustaining people: the role of research

Improved constraints on primordial non-Gaussianity for the Wilkinson Microwave Anisotropy Probe 5-yr data

We present new constraints on the non-linear coupling parameter fnl with the Wilkinson Microwave Anisotropy Probe (WMAP) data. We use an updated method based on the spherical Mexican hat wavelet (SMHW) which provides improved constraints on the fnl parameter. This paper is a continuation of a previous work by Curto et al. where several third order statistics based on the SMHW were considered. In this paper, we use all the possible third order statistics computed from the wavelet coefficient maps evaluated at 12 angular scales. The scales are logarithmically distributed from 6.9 arcmin to 500 arcmin. Our analysis indicates that fnl is constrained to -18 < fnl < +80 at 95% confidence level (CL) for the combined V+W WMAP map. This value has been corrected by the presence of undetected point sources, which adds a positive contribution of Delta_fnl = 6 +- 5. Our result excludes at ~99% CL the best-fitting value fnl=87 reported by Yadav & Wandelt. We have also constrained fnl for the Q, V and W frequency bands separately, finding compatibility with zero at 95 % CL for the Q and V bands but not for the W band. We have performed some further tests to understand the cause of this deviation which indicate that systematics associated to the W radiometers could be responsible for this result. Finally we have performed a Galactic North-South analysis for fnl. We have not found any asymmetry, i.e. the best-fitting fnl for the northern pixels is compatible with the best-fitting fnl for the southern pixels.Comment: 6 pages, 4 figures, 4 tables. Accepted for publication in Ap