Related papers: Analyzing Galaxy Catalogues with Minkowski Functio…
We propose an anisotropic generalisation of the line correlation function (ALCF) to separate and quantify phase information in the large-scale structure of galaxies. The line correlation function probes the strictly non-linear regime of…
Ma-Minda class (of starlike functions) consists of all normalized analytic functions $f$ on the unit disk for which the image of $zf'(z)/f(z)$ is contained in the some starlike region in the right-half plane. We obtain the best possible…
We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic…
Since the recent dissertation by Steffen Winter, for certain self-similar sets $F$ the growth behaviour of the Minkowski functionals of the parallel sets $F_\varepsilon := \{x\in \mathbb R^d : d(x,F)\leq \varepsilon\}$ as $\varepsilon…
We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
An alternative characterization of Minkowski--Lyapunov functions is derived. The derived characterization enables a computationally efficient utilization of Minkowski--Lyapunov functions in arbitrary finite dimensions. Due to intrinsic…
We review cosmological inference from galaxy surveys at low and high redshifts, with emphasis on new Southern sky surveys. We focus on several issues: (i) The importance of understanding selection effects in catalogues and matching Northern…
Morphological classification is a key piece of information to define samples of galaxies aiming to study the large-scale structure of the universe. In essence, the challenge is to build up a robust methodology to perform a reliable…
In this manuscript I review the mathematics and physics that underpins recent work using the clustering of galaxies to derive cosmological model constraints. I start by describing the basic concepts, and gradually move on to some of the…
In this short note we show that functions in the modulation space $\mathscr{F}W=\{ f: \sum_{j\in\mathbb{Z}^n}\| \hat{f}(\cdot+2\pi j)\|_{L_\infty([-\pi,\pi]^n)}<\infty \}$ enjoy similar recovery properties as band-limited functions. If…
In these lectures I cover a number of topics in cosmological data analysis. I concentrate on general techniques which are common in cosmology, or techniques which have been developed in a cosmological context. In fact they have very general…
We present here a brief summary of the currenly on-going IFU surveys of galaxies in the Local Universe, describing their main characteristics, including their sample selections, instrumental setups, wavelength ranges, and area of the…
We present a study on the variations of the luminosity function of galaxies around clusters in a numerical simulation with semi-analytic galaxies, attempting to detect these variations in the 2dF Galaxy Redshift Survey. We subdivide the…
1 : We use properties of the Stern Sequence for numerical computations of moments $\int^1_0 t^n d?(t)$ associated to Minkowski's Question Mark function.
In recent years, deep learning approaches have achieved state-of-the-art results in the analysis of point cloud data. In cosmology, galaxy redshift surveys resemble such a permutation invariant collection of positions in space. These…
CMB polarization data is usually analyzed using $E$ and $B$ modes because they are scalars quantities under rotations along the lines of sight and have distinct physical origins. We explore the possibility of using the Stokes parameters $Q$…
The angular power spectrum of the Cosmic Microwave Background (CMB) anisotropies is a key tool to study the Universe. However, it is blind to the presence of non--Gaussianities and deviations from statistical isotropy, which instead can be…
We explore the new technique developed recently in \cite{Rosenhaus:2014woa} and suggest a correspondence between the $N$-point correlation functions on spacetime with conical defects and the $(N+1)$-point correlation functions in regular…
Conformal Field Theory in a Minkowski setting is discussed in an embedding space approach, paying special attention to causality constraints for four-point amplitudes. The physics of dilatation and Lorentz boost is emphasized in specifying…