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In this talk, I review some recent work on cosmic microwave background (CMB) anisotropies in an open universe. I emphasize that the observed CMB anisotropies are still consistent with a low value of $\Omega$, and I address the question of…
The Rayleigh scattering of cosmic microwave background (CMB) photons off the neutral hydrogen produced during recombination effectively creates an additional scattering surface after recombination that encodes new cosmological information,…
Large data-sets defined on the sphere arise in many fields. In particular, recent and forthcoming observations of the anisotropies of the cosmic microwave background (CMB) made on the celestial sphere contain approximately three and fifty…
The COBE satellite has discovered anisotropies in the cosmic microwave background (CMB) consistent with a scale invariant spectrum of density perturbations. As reviewed in this lecture, topological defect models of structure formation…
Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a…
Gravitational waves (GWs) passing through the Earth cause a correlated pattern of time-dependent deflections of the apparent position of astronomical sources. We build upon standard lensing reconstruction techniques to develop a new…
A recent paper by Hsu & Zee (physics/0510102) suggests that if a Creator wanted to leave a message for us, and she wanted it to be decipherable to all sentient beings, then she would place it on the most cosmic of all billboards, the Cosmic…
Cosmic microwave background lensing has become a new cosmological probe, carrying rich information on the matter power spectrum and distances over the redshift range $z\approx1$-4. We investigate the role of scale dependent new physics,…
Spiral waves in active media react to small perturbations as particle-like objects. Here we apply the asymptotic theory to the interaction of spiral waves with a localized inhomogeneity, which leads to a novel prediction: drift of the…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
This article investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented.…
Peculiar velocities encode rich cosmological information, but their transverse components are hard to measure. Here, we present the first observations of a novel effect of transverse velocities: the dipole signatures that they imprint on…
We present a new proof of a theorem of Mallat which describes a construction of wavelets starting from a quadrature mirror filter. Our main innovation is to show how the scaling function associated to the filter can be used to identify a…
We provide a new derivation of the anisotropies of the cosmic microwave background (CMB), and find an exact expression that can be readily expanded perturbatively. Close attention is paid to gauge issues, with the motivation to examine the…
Wavelets are known to be closely related to atomic orbital. A new approach of 2D, 3D and multidimensional wavelet system is proposed from a paralell with anti-symmetric systems of several isolated particles. The theory of fermionic states…
Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the…
The Cosmological Principle, which states that the Universe is homogeneous and isotropic (when averaged on large scales), is the foundational assumption of Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies such as the current standard…
We summarise the construction of exact axisymmetric scale-discretised wavelets on the sphere and on the ball. The wavelet transform on the ball relies on a novel 3D harmonic transform called the Fourier-Laguerre transform which combines the…
Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or a single…