Related papers: Computing the luminosity distance via optimal homo…
The first objective of this thesis is to fill the lack in cosmology of a description on the past light cone: the null hypersurface on which observed signals propagate. Its second goal is to evaluate the importance of inhomogeneities in the…
We present the first determination of the Hubble constant $H_0$ from strong lensing time delay data and type Ia supernova luminosity distances that is independent of the cosmological model. We also determine the spatial curvature…
A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…
This paper presents the algorithm for determining the Lemaitre-Tolman (LT) model that best fits given datasets for maximum stellar ages, and SNIa luminosities, both as functions of redshift. It then applies it to current cosmological data.…
The systemic velocity or redshift of galaxies is a convenient tool to calculate their distances in the absence of primary methods, but the uncertainties on these flow distances may be substantial due to galaxy peculiar motions. Here, we…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a…
In the lattice approach to Loop Quantum Gravity on a fixed graph computations tend to be involved and are rarely analytically manageable. But, when interested in the expectation values of coherent states on the lattice which are sharply…
In the last few years, there has been significant progress in the development of machine learning methods tailored to astrophysics and cosmology. We have recently applied one of these, namely, the neural network bundle method, to the…
We provide an analytical estimate of the effect of a spherical inhomogeneity on light beams that travel through it. We model the interior of the inhomogeneity in terms of the Lemaitre-Tolman-Bondi metric. We assume that the beam source is…
The cosmic distance ladder is the succession of techniques by which it is possible to determine distances to astronomical objects. Here, we present a new method to build the cosmic distance ladder, going from local astrophysical…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
We propose a self-improving algorithm for computing Voronoi diagrams under a given convex distance function with constant description complexity. The $n$ input points are drawn from a hidden mixture of product distributions; we are only…
We introduce a geometric and operator-theoretic formalism viewing optimization algorithms as discrete connections on a space of update operators. Each iterative method is encoded by two coupled channels-drift and diffusion-whose algebraic…
In order to measure distances with minimal systematics using the correlation between galaxy luminosities and rotation rates it is necessary to adhere to a strict and tested recipe. We now derive a measure of rotation from a new…
Although the formulas for the light deflection due to quadrupole gravitational field of deflecting bodies are well known, the formulas are rather complicated, so that massive computations of quadrupole light deflection (e.g., in the…
The distance transform algorithm is popular in computer vision and machine learning domains. It is used to minimize quadratic functions over a grid of points. Felzenszwalb and Huttenlocher (2004) describe an O(N) algorithm for computing the…
We use a Bayesian approach to derive the distance probability distribution for one object from its parallax with measurement uncertainty for two spatial distribution priors, viz. a homogeneous spherical distribution and a galactocentric…
Gromov-Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov-Hausdorff distance is equivalent to solving an NP-Hard…