Related papers: Statistical Topology and the Random Interstellar M…
A central question in multimodal neuroimaging analysis is to understand the association between two imaging modalities and to identify brain regions where such an association is statistically significant. In this article, we propose a…
This paper studies network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are investigated. It is shown…
We study the energy landscape near the ground state of a model of a single particle in a random potential with trivial topology. More precisely, we find the large dimensional limit of the Hessian spectrum at the global minimum of the…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
We study the asymptotic laws for the number, Betti numbers, and isotopy classes of connected components of zero sets of real Gaussian random fields, where the random zero sets almost surely consist of submanifolds of codimension greater…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
We study statistical properties of galaxy structures in several samples extracted from the 2dF Galaxy Redshift Survey. In particular, we measured conditional fluctuations by means of the scale-length method and determined their probability…
Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem…
Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations…
We study the evolution of non-linear structure as a function of scale in samples from the 2dF Galaxy Redshift Survey, constituting over 221 000 galaxies at a median redshift of z=0.11. The two flux-limited galaxy samples, located near the…
We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this…
We study a multipole vector-based decomposition of cosmic microwave background (CMB) data in order to search for signatures of a multiconnected topology of the universe. Using 10^6 simulated maps, we analyse the multipole vector…
In order to investigate whether galaxy structures are compatible with the predictions of the standard LCDM cosmology, we focus here on the analysis of several simple and basic statistical properties of the galaxy density field. Namely, we…
Asymptotic normality is frequently observed in large combinatorial structures, rigorously established for many quantities such as cycles or inversions in random permutations, the number of prime factors of random integers, and various…
This paper reviews selected aspects of the growth of cosmological structure, covering the following general areas: (1) expected characteristics of linear density perturbations according to various candidate theories for the origin of…
In this paper, we introduce the topological persistence diagram as a statistic for Cosmic Microwave Background (CMB) temperature anisotropy maps. A central concept in `Topological Data Analysis' (TDA), the idea of persistence is to…
Isotropic covariance structures can be unreasonable for phenomena in three-dimensional spaces such as the ocean. In the ocean, the variability of the response may vary with depth, and ocean currents may lead to spatially varying anisotropy.…
In this work, we study the evolution of Betti curves obtained by persistent-homological analysis of point clouds formed by halos in different cosmological $N$-body simulations. We show that they can be approximated with a scaled log-normal…
The Local Interstellar Medium (LISM) is a unique environment that presents an opportunity to study general interstellar phenomena in great detail and in three dimensions. In particular, high resolution optical and ultraviolet spectroscopy…
We use simulated maps of the cosmic microwave background anisotropy to quantify the ability of different statistical tests to discriminate between Gaussian and non-Gaussian models. Despite the central limit theorem on large angular scales,…