相关论文: Real-space computation of $E$/$B$-mode maps I: For…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
Foreground masking and incomplete sky coverage complicate CMB polarization analyses by inducing mode coupling and imperfect E/B separation, with particularly strong impact on searches for primordial $B$-modes. We present SkyReconNet-P, a…
One of the main obstacles for extracting the Cosmic Microwave Background (CMB) from mm/submm observations is the pollution from the main Galactic components: synchrotron, free-free and thermal dust emission. The feasibility of using simple…
In this paper, we characterize all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral bi-Carleman operator in $L_2(R)$ with bounded and arbitrarily smooth kernel on $R^2$. In addition, we give…
The characterization of the dust polarization foreground to the Cosmic Microwave Background (CMB) is a necessary step towards the detection of the B-mode signal associated with primordial gravitational waves. We present a method to simulate…
We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…
We present a real-space spectral method for computing the orbital magnetization of crystals. Starting from the commutator form of the orbital magnetization operator, we formulate an energy-resolved spectral function that is amenable to…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
Polarization is the next frontier of CMB analysis, but its signal is dominated over much of the sky by foregrounds which must be carefully removed. To determine the efficacy of this cleaning it is necessary to have sensitive tests for…
In the framework of studies of the CMB polarization and its Galactic foregrounds, the angular power spectra of thermal dust polarization maps have revealed an intriguing E/B asymmetry and a positive TE correlation. In interpretation studies…
We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.
The Cosmic Microwave Background is characterized by temperature and linear polarization fields. Dipole modulation in the temperature field has been extensively studied in the context of hemispherical power asymmetry. In this article, we…
The B-mode polarisation power spectrum in the Cosmic Microwave Background (CMB) is about four orders of magnitude fainter than the CMB temperature power spectrum. Any instrumental imperfections that couple temperature fluctuations to B-mode…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and kernel sets of finite rank operators leads to showing that…
Given a Banach space $E$, we ask which closed subspaces may be realised as the kernel of a bounded operator $E \rightarrow E$. We prove some positive results which imply in particular that when $E$ is separable every closed subspace is a…
Simulated maps of the microwave background (CMB) radiation are generally created using one of two methods: all-sky simulations use the spherical harmonic transform, while maps covering small areas approximate the sky as flat, allowing the…
A majority of shape correspondence frameworks are based on devising pointwise and pairwise constraints on the correspondence map. The functional maps framework allows for formulating these constraints in the spectral domain. In this paper,…
The polarization of cosmic microwave background (CMB) can be used to constrain cosmological birefringence, the rotation of the linear polarization of CMB photons potentially induced by parity violating physics beyond the standard model.…
We study the effects of astrophysical foregrounds on the ability of CMB B-mode polarization experiments to constrain the primordial tensor-to-scalar ratio, r. To clean the foreground contributions we use parametric, maximum likelihood…