Related papers: Robust Morphological Measures for Large-Scale Stru…
Aleksandrov, and then Zeeman, showed that the causal relations among the set of points in a Minkowski space of dimension greater than 2 determine the Minkowski space structure of the set up to a global conformal factor. We show that in any…
We extend a recently developed galaxy morphology classification method, Quantitative Multiwavelength Morphology (QMM), to connect galaxy morphologies to their underlying physical properties. The traditional classification of galaxies…
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes.…
The most difficult aspect of the realistic modeling of granular materials is how to capture the real shape of the particles. Here we present a method to simulate granular materials with complex-shaped particles. The particle shape is…
In this report we present experimental results using \emph{Haussdorf-Besicovich} fractal dimension for performing morphological galaxy classification. The fractal dimension is a topological, structural and spatial property that give us…
The Hyperboloidal Foliation Method presented in this monograph is based on a (3+1)-foliation of Minkowski spacetime by hyperboloidal hypersurfaces. It allows us to establish global-in-time existence results for systems of nonlinear wave…
The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of…
We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to…
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 paper, we show that Minkowski Functionals (MFs) of weak gravitational lensing (WL) convergence maps contain significant non-Gaussian, cosmology-dependent information. To do this, we use a large suite of cosmological ray-tracing…
The traditional method of morphological classification, by visual inspection of images of uniform quality and by reference to standards for each type, is critically examined. The rate of agreement among traditional morphologists on the…
Classification of galaxy morphology is a challenging but meaningful task for the enormous amount of data produced by the next-generation telescope. By introducing the adaptive polar coordinate transformation, we develop a rotationally…
The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our…
The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial…
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action S[f] which gives the statistical weight…
We investigate the inclusion of clustering maps in a weak lensing Minkowski functional (MF) analysis of DES-like and LSST-like simulations to constrain cosmological parameters. The standard 3x2pt approach to lensing and clustering data uses…
Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for…
We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of…
Gravitational flexion has recently been introduced as a technique by which one can map out and study substructure in clusters of galaxies. Previous analyses involving flexion have measured the individual galaxy-galaxy flexion signal, or…
Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks. We introduce a fast, learnt, unsupervised vectorization…