Related papers: Statistical Topology and the Random Interstellar M…
We prove the convergence of the solutions of the parabolic wave equation to that of the Gaussian white-noise model widely used in the physical literature. The random medium is isotropic and is assumed to have integrable correlation…
Star formation is a multi-scale problem, and only global simulations that account for the connection from the molecular cloud scale gas flow to the accreting protostar can reflect the observed complexity of protostellar systems.…
We present a new method of modelling numerical systems where there are two distinct output solution classes, for example tipping points or bifurcations. Gaussian process emulation is a useful tool in understanding these complex systems and…
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological…
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology…
The statistical translation invariance of cosmological random fields is broken by a finite survey boundary, correlating the observable Fourier modes. Standard methods for generating Gaussian fields either neglect these correlations, or are…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
I review recent results derived from numerical simulations of the turbulent interstellar medium (ISM), in particular concerning the nature and formation of turbulent clouds, methods for comparing the structure in simulations and…
Modern surveys have provided the astronomical community with a flood of high-dimensional data, but analyses of these data often occur after their projection to lower-dimensional spaces. In this work, we introduce a local two-sample…
Extreme values geostatistics make it possible to model the asymptotic behaviors of random phenomena which depends on space or time parameters. In this paper, we propose new models of the extremal coefficient within a spatial stationary…
This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we…
MHD Turbulence is a critical component of the current paradigms of star formation, particle transport, magnetic reconnection and evolution of the ISM. Progress on this difficult subject is made via numerical simulations and observational…
With the explosive deployment of non-terrestrial networks (NTNs), the computational complexity of network performance analysis is rapidly escalating. As one of the most suitable mathematical tools for analyzing large-scale network…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…
The chaotical dynamics is studied in different Friedmann-Robertson- Walker cosmological models with scalar (inflaton) field and hydrodynamical matter. The topological entropy is calculated for some particular cases. Suggested scheme can be…
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…