Related papers: Statistical Topology and the Random Interstellar M…
Topological event detection allows for the distributed computation of homology by focusing on local changes occurring in a network over time. In this paper, a model for the monitoring of topological events in dynamically changing regions…
We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…
We investigate SU(2) gauge fields topology using new approach, which exploits the well known connection between SU(2) gauge theory and quaternionic projective sigma-models and allows to formulate the topological charge density entirely in…
(abridged) The large-scale distribution of galaxies is generally analyzed using the two-point correlation function. However, this statistic does not capture the topology of the distribution, and it is necessary to resort to higher order…
We test the isotropy of the local distribution of galaxies using the 2MASS extended source catalogue. By decomposing the full sky survey into distinct patches and using a combination of photometric and spectroscopic redshift data, we use…
Diffusion Models (DMs) are powerful generative models that add Gaussian noise to the data and learn to remove it. We wanted to determine which noise distribution (Gaussian or non-Gaussian) led to better generated data in DMs. Since DMs do…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
The uncertainties in material and other properties of structures are usually spatially correlated. We introduce an efficient technique for representing and processing spatially correlated random fields in robust topology optimisation of…
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…
In this letter we propose a physical explanation for recently reported correlations between pairs of close and antipodal gamma-ray bursts from publicly available BATSE catalogue. Our model is based on the cosmological scenario in which…
We propose a method to probe higher-order correlators of the primordial density field through the inhomogeneity of local non-Gaussian parameters, such as f_NL, measured within smaller patches of the sky. Correlators between n-point…
We present a method to constrain cosmic topology from the distribution of astronomical objects projected on the celestial sphere. This is an extension of the 3D method introduced in Fujii & Yoshii (2011) that is to search for a pair of…
(abridged) Spectroscopic observations of high-redshift galaxies slowly reveal the same complexity of the interstellar medium (ISM) as expected from resolved observations in nearby galaxies. While providing a wealth of diagnostics, such…
Tilted and non tilted homogeneous plane symmetric C-field cosmological models are investigated. Using the method of Narlikar and Padmanabhan [4], the solutions have been presented when the creation field C is function of time t only. To get…
The recently proposed non-Gaussian Mat\'{e}rn random field models, generated through Stochastic Partial differential equations (SPDEs), are extended by considering the class of Generalized Hyperbolic processes as noise forcings. The models…
We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the…
We present a novel population-based Bayesian inference approach to model the average and population variance of spatial distribution of a set of observables from ensemble analysis of low signal-to-noise ratio measurements. The method…
We obtain formulae for the expected number and height distribution of critical points of smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense…
We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an…
During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary (`spin') variables with observed means and covariances.…