Related papers: Statistical Topology and the Random Interstellar M…
Spatial documentation is exponentially increasing given the availability of Big IoT Data, enabled by the devices miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence…
This article studies the problem of reconstructing the topology of a network of interacting agents via observations of the state-evolution of the agents. We focus on the large-scale network setting with the additional constraint of…
Spatial statistics is traditionally based on stationary models on $\mathbb{R^d}$ like Mat\'ern fields. The adaptation of traditional spatial statistical methods, originally designed for stationary models in Euclidean spaces, to effectively…
In this work we study the properties of the mass density field in the non-Gaussian world models simulated by Grossi et al. 2007. In particular we focus on the one-point density probability distribution function of the mass density field in…
The statistical properties of cosmic structures are well known to be strong probes for cosmology. In particular, several studies tried to use the cosmic void counting number to obtain tight constrains on Dark Energy. In this paper we…
In almost all structure formation models, primordial perturbations are created within a homogeneous and isotropic universe, like the one we observe. Because their ensemble averages inherit the symmetries of the spacetime in which they are…
We review and study some of the properties of smooth Gaussian random fields defined on a homogeneous space, under the assumption that the probability distribution is invariant under the isometry group of the space. We first give an…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
Classical field forecast evaluation relies mainly on local scores such as RMSE or MAE. These metrics severely over-penalize small spatial or temporal displacements of coherent structures, a limitation known as the double-penalty issue and…
We present a study of the small-scale structure of the interstellar medium in the Milky Way. We used HST STIS data to measure N(HI) in a pencil-beam toward 59 AGNs and compared the results with the values seen at 9 arcmin - 36 arcmin…
The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying…
We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We…
Subtle alterations in brain network topology often evade detection by traditional statistical methods. To address this limitation, we introduce a Bayesian inference framework for topological comparison of brain networks that…
The space-time disclination is studied by making use of the decomposition theory of gauge potential in terms of antisymmetric tensor field and $\phi$-mapping method. It is shown that the self-dual and anti-self-dual parts of the curvature…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
Random fields are mathematical structures used to model the spatial interaction of random variables along time, with applications ranging from statistical physics and thermodynamics to system's biology and the simulation of complex systems.…
Local-type primordial non-Gaussianity couples statistics of the curvature perturbation \zeta on vastly different physical scales. Because of this coupling, statistics (i.e. the polyspectra) of \zeta in our Hubble volume may not be…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
We introduce a new 2-D hexagon technique to probe the topological structure of the universe, in which we map regions of the sky with high and low galaxy densities onto a 2-D lattice of hexagon unit cells, We define filled cells as…