Related papers: Robust Morphological Measures for Large-Scale Stru…
We investigate to what extent the cosmic crystallographic methods aimed to detect the topology of the universe using catalogues of cosmic objects would be damaged by various observational uncertainties. We find that the topological…
The morphological classification of galaxies provides vital physical information about the orbital motions of stars in galaxies, and correlates in interesting ways with star formation history, and other physical properties. Galaxy…
We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…
Weak gravitational lensing provides a unique method to directly measure the distribution of mass in the universe. Because the distortions induced by lensing in the shape of background galaxies are small, the measurement of weak lensing…
We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determine the set of Betti numbers ($\beta_{\rm k},k=1,...,D$), which…
Sophisticated analysis of modern large-scale structure surveys requires mock catalogs. Mock catalogs are used to optimize survey design, test reduction and analysis pipelines, make theoretical predictions for basic observables and propagate…
The K-means algorithm is among the most commonly used data clustering methods. However, the regular K-means can only be applied in the input space and it is applicable when clusters are linearly separable. The kernel K-means, which extends…
This is a short review of a series of papers which, in collaboration with Yue Ma, establish several novel existence results for systems of coupled wave-Klein-Gordon equation. Our method, the Hyperbolic Hyperboloidal Method, has allowed us…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…
Smooth deformations of a Minkowski type metric in a four-dimensional space-time manifold are considered. Deformations of the basic spin-tensorial fields associated with this metric are calculated and their application to calculating the…
The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is…
We present a Bayesian inference approach to estimating the cumulative mass profile and mean squared velocity profile of a globular cluster given the spatial and kinematic information of its stars. Mock globular clusters with a range of…
Context. The main feature of the spatial large-scale galaxy distribution is an intricate network of galaxy filaments. Although many attempts have been made to quantify this network, there is no unique and satisfactory recipe for that yet.…
Beyond the linear regime, the power spectrum and higher order moments of the matter field no longer capture all cosmological information encoded in density fluctuations. While non-linear transforms have been proposed to extract this…
Evidence of excess filamentarity is considered for two spatial point process applications: local minima in whole earth precipitation modelling and locations of cold clumps in the Milky Way. A diagnostic test using the number of aligned…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…
We establish pointwise and distributional fractal tube formulas for a large class of compact subsets of Euclidean spaces of arbitrary dimensions. These formulas are expressed as sums of residues of suitable meromorphic functions over the…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
A new method for analyzing the morphological features of point patterns is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of anisotropic distributions.…